数学最新文献

{"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}

{"title":"Lower bounds on Loewy lengths of modules of finite projective dimension","authors":"Nawaj KC ,&nbsp;Josh Pollitz","doi":"10.1016/j.aim.2025.110309","DOIUrl":"10.1016/j.aim.2025.110309","url":null,"abstract":"<div><div>This article is concerned with nonzero modules of finite length and finite projective dimension over a local ring. We show the Loewy length of such a module is larger than the regularity of the ring whenever the ring is strict Cohen-Macaulay, establishing a conjecture of Corso–Huneke–Polini–Ulrich for such rings. In fact, we show the stronger result that the Loewy length of a nonzero module of finite flat dimension is at least the regularity for strict Cohen-Macaulay rings, which significantly strengthens a theorem of Avramov–Buchweitz–Iyengar–Miller. As an application we simultaneously verify a Lech-like conjecture, comparing generalized Loewy length along flat local extensions, and a conjecture of Hanes for strict Cohen-Macaulay rings. Finally, we also give notable improvements to known lower bounds for Loewy lengths without the strict Cohen-Macaulay assumption. The strongest general bounds we achieve are over complete intersection rings.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"473 ","pages":"Article 110309"},"PeriodicalIF":1.5,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143896107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Logarithmic tautological rings of the moduli spaces of curves","authors":"Rahul Pandharipande,&nbsp;Dhruv Ranganathan,&nbsp;Johannes Schmitt,&nbsp;Pim Spelier","doi":"10.1016/j.aim.2025.110291","DOIUrl":"10.1016/j.aim.2025.110291","url":null,"abstract":"<div><div>We define the logarithmic tautological rings of the moduli spaces of Deligne–Mumford stable curves (together with a set of additive generators lifting the decorated strata classes of the standard tautological rings). While these algebras are infinite dimensional, a connection to polyhedral combinatorics via a new theory of homological piecewise polynomials allows an effective study. A complete calculation is given in genus 0 via the algebra of piecewise polynomials on the cone stack of the associated Artin fan (lifting Keel's presentation of the Chow ring of <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span>). Counterexamples to the simplest generalizations in genus 1 are presented. We show, however, that the structure of the log tautological rings is determined by the complete knowledge of all relations in the standard tautological rings of the moduli spaces of curves. In particular, Pixton's conjecture concerning relations in the standard tautological rings lifts to a complete conjecture for relations in the log tautological rings of the moduli spaces of curves. Several open questions are discussed.</div><div>We develop the entire theory of logarithmic tautological classes in the context of arbitrary smooth normal crossings pairs <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> with explicit formulas for intersection products. As a special case, we give an explicit set of additive generators of the full logarithmic Chow ring of <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> in terms of Chow classes on the strata of <em>X</em> and piecewise polynomials on the cone stack.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"474 ","pages":"Article 110291"},"PeriodicalIF":1.5,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Heat kernel estimates and their stabilities for symmetric jump processes with general mixed polynomial growths on metric measure spaces","authors":"Joohak Bae ,&nbsp;Jaehoon Kang ,&nbsp;Panki Kim ,&nbsp;Jaehun Lee","doi":"10.1016/j.jde.2025.113377","DOIUrl":"10.1016/j.jde.2025.113377","url":null,"abstract":"<div><div>In this paper, we consider a symmetric pure jump Markov process <em>X</em> on a metric measure space with volume doubling conditions. Our focus is on estimating the transition density <span><math><mi>p</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> of <em>X</em> and studying its stability when the jumping kernel exhibits general mixed polynomial growth.</div><div>Unlike previous work, in our setting, the rate function governing the jump growth may not be comparable to the scale function that determines whether <span><math><mi>p</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> has near-diagonal or off-diagonal estimates. Under the assumption that lower scaling index of scale function is greater than 1, we establish stabilities of heat kernel estimates. Additionally, if the metric measure space admits a conservative diffusion process with a transition density satisfying sub-Gaussian bounds, we generalize heat kernel estimates from <span><span>[3, Theorems 1.2 and 1.4]</span></span> using the rate function and the function <em>F</em> related to walk dimension of underlying space. As an application, we prove the equivalence between a finite moment condition based on <em>F</em> and a generalized Khintchine-type law of iterated logarithm at infinity for symmetric Markov processes.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113377"},"PeriodicalIF":2.4,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899122","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":"Affine groups as flag-transitive and point-primitive automorphism groups of symmetric designs","authors":"Seyed Hassan Alavi ,&nbsp;Mohsen Bayat ,&nbsp;Ashraf Daneshkhah ,&nbsp;Alessandro Montinaro","doi":"10.1016/j.disc.2025.114555","DOIUrl":"10.1016/j.disc.2025.114555","url":null,"abstract":"<div><div>In this article, we investigate symmetric designs admitting flag-transitive and point-primitive affine automorphism groups. We prove that if a flag-transitive automorphism group <em>G</em> of a symmetric <span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>λ</mi><mo>)</mo></math></span> design with <em>λ</em> prime is point-primitive of affine type, then <span><math><mi>G</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>6</mn></mrow></msup><mo>:</mo><msub><mrow><mi>S</mi></mrow><mrow><mn>6</mn></mrow></msub></math></span> and <span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>λ</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>16</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, or <em>G</em> is a subgroup of <span><math><mi>A</mi><mi>Γ</mi><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span> for some odd prime power <em>q</em>. In conclusion, we present a classification of flag-transitive and point-primitive symmetric designs with <em>λ</em> prime, which says that such an incidence structure is a projective space <span><math><mrow><mi>PG</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>, it has parameter set <span><math><mo>(</mo><mn>15</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></span>, <span><math><mo>(</mo><mn>7</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, <span><math><mo>(</mo><mn>11</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, <span><math><mo>(</mo><mn>11</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, <span><math><mo>(</mo><mn>16</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> or <span><math><mo>(</mo><mn>45</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></span>, or <span><math><mi>v</mi><mo>=</mo><msup><mrow><mi>p</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> where <em>p</em> is an odd prime and the automorphism group is a subgroup of <span><math><mi>A</mi><mi>Γ</mi><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 10","pages":"Article 114555"},"PeriodicalIF":0.7,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900019","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":"Prescribed-time distributed resource allocation algorithm for heterogeneous linear multi-agent networks with unbalanced directed communication","authors":"Yuxiao Lian ,&nbsp;Baoyong Zhang ,&nbsp;Deming Yuan ,&nbsp;Yao Yao ,&nbsp;Bo Song","doi":"10.1016/j.amc.2025.129498","DOIUrl":"10.1016/j.amc.2025.129498","url":null,"abstract":"<div><div>In this paper, a prescribed-time distributed algorithm is proposed to solve the resource allocation problem among the heterogeneous linear multi-agent systems over unbalanced directed networks. First, an estimator with prescribed-time convergence performance is designed to cope with the asymmetry of the unbalanced network topology. Then, a novel prescribed-time convergence result that features an adjustable convergence rate is developed. Based on this result, it is shown that the algorithm developed in this paper ensures the agents' outputs accurately reach the optimal solution within a prescribed-time and they are maintained at the optimum thereafter. Furthermore, a parameter selection rule is formulated to reflect the low conservatism of the algorithm. This indicates that the parameters affecting the convergence speed of the algorithm are not necessary to rely on the global information. Finally, the performance of the proposed algorithm is illustrated through simulations.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"503 ","pages":"Article 129498"},"PeriodicalIF":3.5,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895684","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}