Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Curved nonlinear waveguides","authors":"Laura Baldelli ,&nbsp;David Krejčiřík","doi":"10.1016/j.na.2025.113814","DOIUrl":"10.1016/j.na.2025.113814","url":null,"abstract":"<div><div>The Dirichlet <span><math><mi>p</mi></math></span>-Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap between the lowest point of the generalised spectrum and the essential spectrum is positive whenever the cross-section is centrally symmetric and the tube is asymptotically straight, untwisted and non-trivially bent. Second, a Hardy-type inequality is derived for unbent and non-trivially twisted tubes.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113814"},"PeriodicalIF":1.3,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143820290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"H1 regularity of the minimizers for the inviscid total variation and Bingham fluid problems for H1 data","authors":"François Bouchut ,&nbsp;Carsten Carstensen ,&nbsp;Alexandre Ern","doi":"10.1016/j.na.2025.113809","DOIUrl":"10.1016/j.na.2025.113809","url":null,"abstract":"<div><div>The Bingham fluid model for viscoplastic materials involves the minimization of a nondifferentiable functional. The regularity of the associated solution is investigated here. The simplified scalar case is considered first: the total variation minimization problem. Our main result proves for a convex domain <span><math><mi>Ω</mi></math></span> that a right-hand side <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> gives a solution <span><math><mrow><mi>u</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>. Homogeneous Dirichlet conditions involve an additional trace term, then <span><math><mrow><mi>f</mi><mo>∈</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> implies <span><math><mrow><mi>u</mi><mo>∈</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>. In the case of the inviscid vector Bingham fluid model, boundary conditions are difficult to handle, but we prove the local <span><math><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mtext>loc</mtext></mrow><mrow><mn>1</mn></mrow></msubsup><msup><mrow><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> regularity of the solution for <span><math><mrow><mi>f</mi><mo>∈</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mtext>loc</mtext></mrow><mrow><mn>1</mn></mrow></msubsup><msup><mrow><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span>. The proofs rely on several generalizations of a lemma due to Brézis and on the viscous approximation. We obtain Euler–Lagrange characterizations of the solution. Homogeneous Dirichlet conditions on the viscous problem lead in the vanishing viscosity limit to relaxed boundary conditions of frictional type.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113809"},"PeriodicalIF":1.3,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Aharonov-Bohm operators with multiple colliding poles of any circulation","authors":"Veronica Felli ,&nbsp;Benedetta Noris ,&nbsp;Giovanni Siclari","doi":"10.1016/j.na.2025.113813","DOIUrl":"10.1016/j.na.2025.113813","url":null,"abstract":"<div><div>This paper deals with quantitative spectral stability for Aharonov-Bohm operators with many colliding poles of whichever circulation. An equivalent formulation of the eigenvalue problem is derived as a system of two equations with real coefficients, coupled through prescribed jumps of the unknowns and their normal derivatives across the segments joining the poles with the collision point. Under the assumption that the sum of all circulations is not integer, the dominant term in the asymptotic expansion for eigenvalues is characterized in terms of the minimum of an energy functional associated with the configuration of poles. Estimates of the order of vanishing of the eigenvalue variation are then deduced from a blow-up analysis, yielding sharp asymptotics in some particular examples.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113813"},"PeriodicalIF":1.3,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On well-posedness results for the cubic–quintic NLS on T3","authors":"Yongming Luo ,&nbsp;Xueying Yu ,&nbsp;Haitian Yue ,&nbsp;Zehua Zhao","doi":"10.1016/j.na.2025.113806","DOIUrl":"10.1016/j.na.2025.113806","url":null,"abstract":"<div><div>We consider the periodic cubic–quintic nonlinear Schrödinger equation <span><span><span>(CQNLS)</span><span><math><mrow><mrow><mo>(</mo><mi>i</mi><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>Δ</mi><mo>)</mo></mrow><mi>u</mi><mo>=</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>4</mn></mrow></msup><mi>u</mi></mrow></math></span></span></span>on the three-dimensional torus <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> with <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>R</mi><mo>∖</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span>. As a first result, we establish the small data well-posedness of for arbitrarily given <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. By adapting the crucial perturbation arguments in Zhang (2006) to the periodic setting, we also prove that is always globally well-posed in <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> in the case <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"257 ","pages":"Article 113806"},"PeriodicalIF":1.3,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differentiability of monotone maps related to non quadratic costs","authors":"Cristian E. Gutiérrez ,&nbsp;Annamaria Montanari","doi":"10.1016/j.na.2025.113804","DOIUrl":"10.1016/j.na.2025.113804","url":null,"abstract":"<div><div>The cost functions considered are <span><math><mrow><mi>c</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span>, with <span><math><mrow><mi>h</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mfenced><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfenced></mrow></math></span>, homogeneous of degree <span><math><mrow><mi>p</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, with positive definite Hessian in the unit sphere. We consider monotone maps <span><math><mi>T</mi></math></span> with respect to that cost and establish local scale invariant <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-estimates of <span><math><mi>T</mi></math></span> minus affine functions, which are applied to obtain differentiability properties of <span><math><mi>T</mi></math></span> a.e. It is also shown that these maps are related to maps of bounded deformation, and further differentiability and Hölder continuity properties are derived.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"257 ","pages":"Article 113804"},"PeriodicalIF":1.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143783218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Normalizing flows as approximations of optimal transport maps via linear-control neural ODEs","authors":"A. Scagliotti ,&nbsp;S. Farinelli","doi":"10.1016/j.na.2025.113811","DOIUrl":"10.1016/j.na.2025.113811","url":null,"abstract":"<div><div>In this paper, we consider the problem of recovering the <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-optimal transport map T between absolutely continuous measures <span><math><mrow><mi>μ</mi><mo>,</mo><mi>ν</mi><mo>∈</mo><mi>P</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> as the flow of a linear-control neural ODE, where the control depends only on the time variable and takes values in a finite-dimensional space. We first show that, under suitable assumptions on <span><math><mrow><mi>μ</mi><mo>,</mo><mi>ν</mi></mrow></math></span> and on the controlled vector fields governing the neural ODE, the optimal transport map is contained in the <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-closure of the flows generated by the system. Then, we tackle the problem under the assumption that only discrete approximations of <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math></span> of the original measures <span><math><mrow><mi>μ</mi><mo>,</mo><mi>ν</mi></mrow></math></span> are available: we formulate approximated optimal control problems, and we show that their solutions give flows that approximate the original optimal transport map <span><math><mi>T</mi></math></span>. In the framework of generative models, the approximating flow constructed here can be seen as a ‘Normalizing Flow’, which usually refers to the task of providing invertible transport maps between probability measures by means of deep neural networks. We propose an iterative numerical scheme based on the Pontryagin Maximum Principle for the resolution of the optimal control problem, resulting in a method for the practical computation of the approximated optimal transport map, and we test it on a two-dimensional example.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"257 ","pages":"Article 113811"},"PeriodicalIF":1.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hypergraph p-Laplacian regularization on point clouds for data interpolation","authors":"Kehan Shi ,&nbsp;Martin Burger","doi":"10.1016/j.na.2025.113807","DOIUrl":"10.1016/j.na.2025.113807","url":null,"abstract":"<div><div>As a generalization of graphs, hypergraphs are widely used to model higher-order relations in data. This paper explores the benefit of the hypergraph structure for the interpolation of point cloud data that contain no explicit structural information. We define the <span><math><msub><mrow><mi>ɛ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-ball hypergraph and the <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-nearest neighbor hypergraph on a point cloud and study the <span><math><mi>p</mi></math></span>-Laplacian regularization on the hypergraphs. We prove the variational consistency between the hypergraph <span><math><mi>p</mi></math></span>-Laplacian regularization and the continuum <span><math><mi>p</mi></math></span>-Laplacian regularization in a semisupervised setting when the number of points <span><math><mi>n</mi></math></span> goes to infinity while the number of labeled points remains fixed. A key improvement compared to the graph case is that the results rely on weaker assumptions on the upper bound of <span><math><msub><mrow><mi>ɛ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. To solve the convex but non-differentiable large-scale optimization problem, we utilize the stochastic primal–dual hybrid gradient algorithm. Numerical experiments on data interpolation verify that the hypergraph <span><math><mi>p</mi></math></span>-Laplacian regularization outperforms the graph <span><math><mi>p</mi></math></span>-Laplacian regularization in preventing the development of spikes at the labeled points.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"257 ","pages":"Article 113807"},"PeriodicalIF":1.3,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Beurling–Deny formula for Sobolev–Bregman forms","authors":"Michał Gutowski,&nbsp;Mateusz Kwaśnicki","doi":"10.1016/j.na.2025.113808","DOIUrl":"10.1016/j.na.2025.113808","url":null,"abstract":"<div><div>For an arbitrary regular Dirichlet form <span><math><mi>E</mi></math></span> and the associated symmetric Markovian semigroup <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span>, we consider the corresponding Sobolev–Bregman form <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><msub><mrow><mo>|</mo></mrow><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></msub><msubsup><mrow><mo>‖</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>‖</mo></mrow><mrow><mi>p</mi></mrow><mrow><mi>p</mi></mrow></msubsup></mrow></math></span>, where <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span>. We prove a variant of the Beurling–Deny formula for <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>. As an application, we prove the corresponding Hardy–Stein identity. Our results extend previous works in this area, which either required that <span><math><mi>E</mi></math></span> is translation-invariant, or that <span><math><mi>u</mi></math></span> is sufficiently regular.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"257 ","pages":"Article 113808"},"PeriodicalIF":1.3,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The horospherical p-Christoffel–Minkowski problem in hyperbolic space","authors":"Tianci Luo,&nbsp;Yong Wei","doi":"10.1016/j.na.2025.113799","DOIUrl":"10.1016/j.na.2025.113799","url":null,"abstract":"<div><div>The horospherical <span><math><mi>p</mi></math></span>-Christoffel–Minkowski problem, introduced by Li and Xu (2022), involves prescribing the <span><math><mi>k</mi></math></span>-th horospherical <span><math><mi>p</mi></math></span>-surface area measure for <span><math><mi>h</mi></math></span>-convex domains in hyperbolic space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>. This problem generalizes the classical <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> Christoffel–Minkowski problem in Euclidean space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>. In this paper, we study a fully nonlinear equation associated with this problem and establish the existence of a uniformly <span><math><mi>h</mi></math></span>-convex solution under suitable assumptions on the prescribed function. The proof relies on a full rank theorem, which we demonstrate using a viscosity approach inspired by the work of Bryan et al. (2023).</div><div>When <span><math><mrow><mi>p</mi><mo>=</mo><mn>0</mn></mrow></math></span>, the horospherical <span><math><mi>p</mi></math></span>-Christoffel–Minkowski problem in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> reduces to a Nirenberg-type problem on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> in conformal geometry. As a consequence, our result also provides the existence of solutions to this Nirenberg-type problem.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"257 ","pages":"Article 113799"},"PeriodicalIF":1.3,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Long time asymptotic behavior of a self-similar fragmentation equation","authors":"Gaetano Agazzotti ,&nbsp;Madalina Deaconu ,&nbsp;Antoine Lejay","doi":"10.1016/j.na.2025.113805","DOIUrl":"10.1016/j.na.2025.113805","url":null,"abstract":"<div><div>Using the Mellin transform, we study self-similar fragmentation equations whose breakage rate follows the power law distribution, and a particle is split into a fixed number of smaller particles. First, we show how to extend the solution of such equations to measure-valued initial conditions, by a closure argument on the Mellin space. Second, we use appropriate series representations to give a rigorous proof to the asymptotic behavior of the moments, completing some results known through heuristic derivations.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"257 ","pages":"Article 113805"},"PeriodicalIF":1.3,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143724891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}