数学最新文献

{"title":"Min-min minimization for the fractional ℓ0-regularized problem","authors":"Jun Wang ,&nbsp;Qiang Ma ,&nbsp;Cheng Zhou","doi":"10.1016/j.amc.2025.129499","DOIUrl":"10.1016/j.amc.2025.129499","url":null,"abstract":"<div><div>In this paper, we present a novel unconstrained fractional <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> regularization (<span>FL0R</span>) model to solve cardinality minimization. Firstly, we construct an interesting <span><math><mi>min</mi><mo>⁡</mo><mo>−</mo><mi>min</mi></math></span> minimization from <span>FL0R</span> by introducing a middle variable of sparsity. Then, we prove that the solution to <span><math><mi>min</mi><mo>⁡</mo><mo>−</mo><mi>min</mi></math></span> minimization with a given sparsity is one of <span>FL0R</span>. Finally, some numerical examples are presented to illustrate the effectiveness and validity of the new model.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"503 ","pages":"Article 129499"},"PeriodicalIF":3.5,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899777","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":"Dirichlet problem on perturbed conical domains via converging generalized power series","authors":"Martin Costabel ,&nbsp;Matteo Dalla Riva ,&nbsp;Monique Dauge ,&nbsp;Paolo Musolino","doi":"10.1016/j.jde.2025.113379","DOIUrl":"10.1016/j.jde.2025.113379","url":null,"abstract":"<div><div>We consider the Poisson equation with homogeneous Dirichlet conditions in a family of domains in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> indexed by a small parameter <em>ε</em>. The domains depend on <em>ε</em> only within a ball of radius proportional to <em>ε</em> and, as <em>ε</em> tends to zero, they converge in a self-similar way to a domain with a conical boundary singularity. We construct an expansion of the solution as a series of real positive powers of <em>ε</em>, and prove that it is not just an asymptotic expansion as <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>, but that, for small values of <em>ε</em>, it converges normally in the Sobolev space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. The phenomenon that solutions to boundary value problems on singularly perturbed domains may have <em>convergent</em> expansions is the subject of the Functional Analytic Approach by Lanza de Cristoforis and his collaborators. This approach was originally adopted to study small holes shrinking to interior points of a smooth domain and heavily relies on integral representations obtained through layer potentials. We choose a different technique that allows us to relax all regularity assumptions. We forgo boundary layer potentials and instead exploit expansions in terms of eigenfunctions of the Laplace-Beltrami operator on the intersection of the cone with the unit sphere. The basis for our analysis is a two-scale cross-cutoff ansatz for the solution that has similarities with the Maz'ya-Nazarov-Plamenevskij construction of a multiscale system for the asymptotic expansion of solutions of boundary value problems on domains singularly perturbed near singular points of the boundary. Specifically, we write the solution as a sum of a function in the slow variable multiplied by a cutoff function depending on the fast variable, plus a function in the fast variable multiplied by a cutoff function depending on the slow variable. While the cutoffs are considered fixed, the two unknown functions are solutions to a <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> system of partial differential equations that depend on <em>ε</em> in a way that can be analyzed in the framework of generalized power series when the right-hand side of the Poisson equation vanishes in a neighborhood of the perturbation. In this paper, we concentrate on this case. The treatment of more general right-hand sides requires a supplementary layer in the analysis and is postponed to a forthcoming paper.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"439 ","pages":"Article 113379"},"PeriodicalIF":2.4,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899800","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":"Optimal coloring of (P2 + P3, gem)-free graphs","authors":"Arnab Char,&nbsp;T. Karthick","doi":"10.1016/j.disc.2025.114554","DOIUrl":"10.1016/j.disc.2025.114554","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Given a graph &lt;em&gt;G&lt;/em&gt;, the parameters &lt;span&gt;&lt;math&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; respectively denote the chromatic number and the clique number of &lt;em&gt;G&lt;/em&gt;. A function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, for all &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is called a &lt;em&gt;χ-binding function&lt;/em&gt; for the given class of graphs &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; if every &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; satisfies &lt;span&gt;&lt;math&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, and the &lt;em&gt;smallest χ-binding function&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is defined as &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;max&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mtext&gt; and &lt;/mtext&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. In general, the problem of obtaining the smallest &lt;em&gt;χ&lt;/em&gt;-binding function for the given class of graphs seems to be extremely hard, and only a few classes of graphs are studied in this direction. In this paper, we study the class of (&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, gem)-free graphs, and prove that the function &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; defined by &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;⌈&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⌉&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, for &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; is the smallest &lt;em&gt;χ&lt;/em&gt;-binding function for the class of (&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, gem)-free graphs. Also we completely characterize the class of (&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, gem)-free","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 10","pages":"Article 114554"},"PeriodicalIF":0.7,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and nonexistence of minimizer for Thomas-Fermi-Dirac-von Weizsäcker model on lattice graph","authors":"Yong Liu ,&nbsp;Jun Wang ,&nbsp;Kun Wang ,&nbsp;Wen Yang ,&nbsp;Yanni Zhu","doi":"10.1016/j.jde.2025.113360","DOIUrl":"10.1016/j.jde.2025.113360","url":null,"abstract":"<div><div>The focus of our paper is to investigate the possibility of a minimizer for the Thomas-Fermi-Dirac-von Weizsäcker model on the lattice graph <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. The model is described by the following functional:<span><span><span><math><mi>E</mi><mo>(</mo><mi>φ</mi><mo>)</mo><mo>=</mo><munder><mo>∑</mo><mrow><mi>y</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></munder><mrow><mo>(</mo><mo>|</mo><mi>∇</mi><mi>φ</mi><mo>(</mo><mi>y</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mo>(</mo><mi>φ</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>)</mo></mrow><mrow><mfrac><mrow><mn>10</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mo>−</mo><msup><mrow><mo>(</mo><mi>φ</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>)</mo></mrow><mrow><mfrac><mrow><mn>8</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mo>+</mo><munder><mo>∑</mo><mrow><mfrac><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow><mrow><mspace></mspace><mspace></mspace><mi>y</mi><mo>≠</mo><mi>x</mi></mrow></mfrac></mrow></munder><mfrac><mrow><msup><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><msup><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>|</mo></mrow></mfrac><mo>,</mo></math></span></span></span> with the additional constraint that <span><math><munder><mo>∑</mo><mrow><mi>y</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></munder><msup><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>y</mi><mo>)</mo><mo>=</mo><mi>m</mi></math></span>. We begin by establishing the existence of a minimizer for this model when <em>m</em> is sufficiently small. Conversely, we demonstrate that no minimizer exists when <em>m</em> exceeds a certain threshold. Additionally, we extend our analysis to a subset <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> and prove the nonexistence of a minimizer for the following functional:<span><span><span><math><mi>E</mi><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>=</mo><mo>|</mo><mo>∂</mo><mi>Ω</mi><mo>|</mo><mo>+</mo><munder><mo>∑</mo><mrow><mfrac><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>Ω</mi></mrow><mrow><mspace></mspace><mi>y</mi><mo>≠</mo><mi>x</mi></mrow></mfrac></mrow></munder><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>|</mo></mrow></mfrac><mo>,</mo></math></span></span></span> under the constraint that <span><math><mo>|</mo><mi>Ω</mi><mo>|</mo><mo>=</mo><mi>V</mi></math></span> is sufficiently large.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113360"},"PeriodicalIF":2.4,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899124","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":"Inverse coefficient problems for the heat equation with fractional Laplacian","authors":"Azizbek Mamanazarov, Durvudkhan Suragan","doi":"10.1007/s13540-025-00414-4","DOIUrl":"https://doi.org/10.1007/s13540-025-00414-4","url":null,"abstract":"<p>In the present paper, we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point ensures the existence of a weak solution for the inverse problem. Furthermore, if there is an additional datum at the observation point, it leads to a specific formula for the time-dependent source coefficient. Moreover, we investigate inverse problems involving non-local data of the fractional heat equation.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"14 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898233","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":"Corrigendum to “A note on the hit problem for the polynomial algebra of six variables and the sixth algebraic transfer” [J. Algebra 613 (2023) 1–31]","authors":"Đặng Võ Phúc","doi":"10.1016/j.jalgebra.2025.04.010","DOIUrl":"10.1016/j.jalgebra.2025.04.010","url":null,"abstract":"<div><div>In this corrigendum, we are making a slight correction to Remark 3.15 on pages 14–15 of <span><span>[1]</span></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 463-464"},"PeriodicalIF":0.8,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895761","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":"A spatio-temporal radial basis function collocation method based on Hausdorff fractal distance for Hausdorff derivative heat conduction equations in three-dimensional anisotropic materials","authors":"Jiayu Wang ,&nbsp;Lin Qiu ,&nbsp;Yingjie Liang ,&nbsp;Fajie Wang","doi":"10.1016/j.amc.2025.129501","DOIUrl":"10.1016/j.amc.2025.129501","url":null,"abstract":"<div><div>In this paper, the spatio-temporal radial basis function (RBF) collocation method based on Hausdorff fractal distance is developed and used to simulate the transient heat transfer problems in anisotropic materials governed by Hausdorff derivative heat conduction equations. We introduce Hausdorff fractal distance into the conventional RBFs, and based on this incorporation, establish a meshless method to address Hausdorff derivative heat conduction problems, in which the anisotropy of the thermal conductivity of the material and spatio-temporal fractal characteristics are taken into account. We set the source points of the collocation method outside the spatial computational domain instead of distributing them within the original domain to further improve the accuracy of the method. Numerical experiments carried out in this study demonstrate the superior performance of the proposed approach compared to the finite element method and traditional RBF collocation method, showing that the developed method can be considered as a competitive tool for simulating Hausdorff derivative transient heat conduction problems in complex geometries.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"502 ","pages":"Article 129501"},"PeriodicalIF":3.5,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143894403","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":"Avoiding trusted setup in isogeny-based commitments","authors":"Gustave Tchoffo Saah, Tako Boris Fouotsa, Emmanuel Fouotsa, Célestin Nkuimi-Jugnia","doi":"10.1007/s10623-025-01633-9","DOIUrl":"https://doi.org/10.1007/s10623-025-01633-9","url":null,"abstract":"<p>In 2021, Sterner proposed a commitment scheme based on supersingular isogenies. For this scheme to be binding, one relies on a trusted party to generate a starting supersingular elliptic curve of unknown endomorphism ring. In fact, the knowledge of the endomorphism ring allows one to compute an endomorphism of degree a power of a given small prime. Such an endomorphism can then be split into two to obtain two different messages with the same commitment. This is the reason why one needs a curve of unknown endomorphism ring, and the only known way to generate such supersingular curves is to rely on a trusted party or on some expensive multiparty computation. We observe that if the degree of the endomorphism in play is well chosen, then the knowledge of the endomorphism ring is not sufficient to efficiently compute such an endomorphism and in some particular cases, one can even prove that endomorphism of a certain degree do not exist. Leveraging these observations, we adapt Sterner’s commitment scheme in such a way that the endomorphism ring of the starting curve can be known and public. This allows us to obtain isogeny-based commitment schemes which can be instantiated without trusted setup requirements.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"51 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898087","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":"Gauge Transformations and Long-Time Asymptotics for the New Coupled Integrable Dispersionless Equations","authors":"Xumeng Zhou,&nbsp;Xianguo Geng,&nbsp;Minxin Jia,&nbsp;Yunyun Zhai","doi":"10.1007/s11040-025-09507-1","DOIUrl":"10.1007/s11040-025-09507-1","url":null,"abstract":"<div><p>This work aims to investigate the asymptotic behavior analysis of solutions to the Cauchy problem of new coupled integrable dispersionless equations. Utilizing the gauge transformations, spectral analysis and inverse scattering method, we show that the solutions of new coupled integrable dispersionless equations can be expressed in terms of the solutions of two matrix Riemann–Hilbert problems formulated in the complex <span>(lambda )</span>-plane. Applying the nonlinear steepest descent method to the two associated matrix-valued Riemann–Hilbert problems, we obtain precise leading-order asymptotic formulas and uniform error estimates for the solutions of new coupled integrable dispersionless equations.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"k-path-connectivity of the complete balanced tripartite graph Kn,n,n for n+1≤k≤2n−4","authors":"Shasha Li,&nbsp;Xiaoxue Gao,&nbsp;Qihui Jin","doi":"10.1016/j.dam.2025.04.043","DOIUrl":"10.1016/j.dam.2025.04.043","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Given a graph &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and a set &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; of size at least 2, an &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;em&gt;-path&lt;/em&gt; in &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is a path that connects all vertices of &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. Two &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-paths &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; are said to be &lt;em&gt;internally disjoint&lt;/em&gt; if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;0̸&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Let &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; denote the maximum number of internally disjoint &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-paths in &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;em&gt;-path-connectivity&lt;/em&gt; of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, denoted by &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, is then defined as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;min&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Therefore, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is exactly the classical connectivity &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is exactly the maximum number of edge-disjoint Hamilton paths in &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. It is established that for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 279-294"},"PeriodicalIF":1.0,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}