数学最新文献

{"title":"On Some Number Theoretic Sum","authors":"V. V. Iudelevich","doi":"10.1134/S1064562424601586","DOIUrl":"10.1134/S1064562424601586","url":null,"abstract":"<p>We obtain an asymptotic formula for the sum \u0000      <span>(Q(x) = sumlimits_{substack{ n leqslant x r(n + 1) ne 0 } } frac{{r(n)}}{{r(n + 1)}};;(x to + infty ),)</span> \u0000where <span>(r(n))</span> denotes the number of representations of <i>n</i> as a sum of two squares.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"25 - 28"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equitable coloring of graphs beyond planarity","authors":"Weichan Liu","doi":"10.1016/j.dam.2025.10.020","DOIUrl":"10.1016/j.dam.2025.10.020","url":null,"abstract":"<div><div>An equitable coloring of a graph is a proper coloring where the sizes of any two different color classes do not differ by more than one. A graph is IC-planar if it can be drawn in the plane so that no two crossed edges have a common endpoint, and is NIC-planar graph if it can be embedded in the plane in such a way that no two pairs of crossed edges share two endpoints. Zhang, Wang, and Xu proved that every IC-planar graph with maximum degree <span><math><mrow><mi>Δ</mi><mo>≥</mo><mn>12</mn></mrow></math></span> and every NIC-planar graph with maximum degree <span><math><mrow><mi>Δ</mi><mo>≥</mo><mn>13</mn></mrow></math></span> have equitable <span><math><mi>Δ</mi></math></span>-colorings. In this paper, we reduce the threshold from 12 to 10 for IC-planar graphs and from 13 to 11 for NIC-planar graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 685-693"},"PeriodicalIF":1.0,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320100","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":"High-order asymptotic expansion for the nonlinear Klein-Gordon equation in the non-relativistic limit regime","authors":"Jia Shen ,&nbsp;Yanni Wang ,&nbsp;Haohao Zheng","doi":"10.1016/j.jde.2025.113832","DOIUrl":"10.1016/j.jde.2025.113832","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper presents an investigation into the high-order asymptotic expansion for 2D and 3D cubic nonlinear Klein-Gordon equations in the non-relativistic limit regime. There are extensive numerical and analytical results concerning that the solution of NLKG can be approximated by first-order modulated Schrödinger profiles in terms of &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;em&gt;v&lt;/em&gt; is the solution of related NLS and “&lt;span&gt;&lt;math&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;” denotes the complex conjugate. Particularly, the best analytical result up to now is given in &lt;span&gt;&lt;span&gt;[20]&lt;/span&gt;&lt;/span&gt;, which proves that the &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; norm of the error can be controlled by &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;-data, &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. As for the high-order expansion, to our best knowledge, there are only numerical results, while the theoretical one is lacking.&lt;/div&gt;&lt;div&gt;In this paper, we extend this study further and give the first high-order analytical result. We introduce the high-order expansion inspired by the numerical experiments in &lt;span&gt;&lt;span&gt;[24]&lt;/span&gt;&lt;/span&gt;, &lt;span&gt;&lt;span&gt;[15]&lt;/span&gt;&lt;/span&gt;:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&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;8&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;em&gt;w&lt;/em&gt; is the solution to some specific Schrödinger-type equation. We show that the &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; estimate of th","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113832"},"PeriodicalIF":2.3,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325331","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":"Free interface problem of Navier-Stokes-Darcy equations without surface tension","authors":"Ningning Gao ,&nbsp;Jinjing Liu ,&nbsp;Lei Yao","doi":"10.1016/j.jde.2025.113850","DOIUrl":"10.1016/j.jde.2025.113850","url":null,"abstract":"<div><div>This paper investigates the free interface problem of incompressible Navier-Stokes-Darcy equations without surface tension in a finite-depth domain. We establish the global-in-time solution for the free interface problem of Navier-Stokes-Darcy equations in a horizontally infinite domain, without any low frequency assumptions of the initial data, in both two and three dimensions. Moreover, we present the decay of the solution. The key point lies in estimating <span><math><mn>4</mn><mi>N</mi><mo>−</mo><mn>1</mn></math></span> order horizontal spatial derivatives of the “Eulerian horizontal spatial derivative” <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>A</mi></mrow></msub></math></span> of the solution. This allows us to handle the 4<em>N</em> order horizontal spatial derivatives of the solution and facilitates the nonlinear cancellation of the highest order spatial regularity of the free boundary.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113850"},"PeriodicalIF":2.3,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325339","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":"Adaptive fault tolerant optimal control for high-order fully actuated system and its application in spacecraft attitude tracking using reinforcement learning","authors":"Xueqi Wu,&nbsp;Wei Sun","doi":"10.1016/j.amc.2025.129774","DOIUrl":"10.1016/j.amc.2025.129774","url":null,"abstract":"<div><div>This study addresses the adaptive optimal tracking problem for high-order fully actuated system (FAS). First, an optimal control strategy based on FAS theory and reinforcement learning (RL) is proposed, effectively solving the tracking problem within the actor-critic framework. Next, within the identifier-actor-critic framework, a sliding mode optimized control scheme for high-order FAS with actuator fault is introduced. Specifically, unlike existing fault-tolerant control results for high-order FAS, this method ensures trajectory tracking and performance optimization even in the presence of actuator faults, while avoiding the need for persistent excitation condition. Considering the strong robustness and rapid response advantages of sliding mode control (SMC), synchronous rapid tracking and optimal control of multiple variables are achieved by establishing a (<em>n-1</em>)-order sliding mode surface. Furthermore, rigorous theoretical analysis proves the boundedness of all signals within the closed-loop system. Finally, the effectiveness of the proposed control approaches are verified by a numerical simulation and a practical example of the spacecraft attitude system.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"512 ","pages":"Article 129774"},"PeriodicalIF":3.4,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145326086","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":"Unbounded Integral Hankel Operators","authors":"Alexander Pushnitski,&nbsp;Sergei R. Treil","doi":"10.1134/S1234567825030073","DOIUrl":"10.1134/S1234567825030073","url":null,"abstract":"<p> For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"297 - 320"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Eigenvalue Estimates for the Coulombic One-Particle Density Matrix and the Kinetic Energy Density Matrix","authors":"Alexander Sobolev","doi":"10.1134/S1234567825030103","DOIUrl":"10.1134/S1234567825030103","url":null,"abstract":"<p> Consider a bound state (an eigenfunction) <span>(psi)</span> of an atom with <span>(N)</span> electrons. We study the spectra of the one-particle density matrix <span>(gamma)</span> and the one-particle kinetic energy density matrix <span>(tau)</span> associated with <span>(psi)</span>. The paper contains two results. First, we obtain the bounds <span>(lambda_k(gamma)le C k^{-8/3})</span> and <span>(lambda_k(tau)le C k^{-2})</span> with some positive constants <span>(C)</span> that depend explicitly on the eigenfunction <span>(psi)</span>. The sharpness of these bounds is confirmed by the asymptotic results obtained by the author in earlier papers. The advantage of these bounds over the ones derived by the author previously is their explicit dependence on the eigenfunction. Moreover, their new proofs are more elementary and direct. The second result is new, and it pertains to the case where the eigenfunction <span>(psi)</span> vanishes at the particle coalescence points. In particular, this is true for totally antisymmetric <span>(psi)</span>. In this case, the eigenfunction <span>(psi)</span> exhibits enhanced regularity at the coalescence points, which leads to the faster decay of the eigenvalues: <span>(lambda_k(gamma)le C k^{-10/3})</span> and <span>(lambda_k(tau)le C k^{-8/3})</span>. </p><p> The proofs rely on estimates for the derivatives of the eigenfunction <span>(psi)</span> that depend explicitly on the distance to the coalescence points. Some of these estimates are borrowed directly from, and some are derived using the methods of, a recent paper by S. Fournais and T. Ø. Sørensen. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"347 - 365"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Notes on discrepancy and anti-discrepancy in oriented graphs","authors":"András London","doi":"10.1016/j.dam.2025.10.019","DOIUrl":"10.1016/j.dam.2025.10.019","url":null,"abstract":"<div><div>A new piece of the combinatorial discrepancy puzzle, the problem of <em>oriented anti-discrepancy</em> is addressed. That is, roughly speaking, given a graph <span><math><mi>G</mi></math></span> and a family <span><math><mi>F</mi></math></span>, for any orientation of <span><math><mi>G</mi></math></span> we ask that how large the difference between the “forward” and “backward” edges of a copy <span><math><mrow><mi>F</mi><mo>∈</mo><mi>F</mi></mrow></math></span> can be in <span><math><mi>G</mi></math></span> with respect to the orientation, assuming that the notion of direction is natural in <span><math><mi>F</mi></math></span>. In contrast to the standard discrepancy problem, we search for a copy <span><math><mi>F</mi></math></span> such that the difference is minimized. We give proper definitions for some graph classes where the forward and backward orientations of the edges are determined in a natural way. Some results are presented for both the oriented anti-discrepancy and the oriented discrepancy problems.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 283-289"},"PeriodicalIF":1.0,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321311","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":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(25)00445-8","DOIUrl":"10.1016/S0378-4754(25)00445-8","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Page 1100"},"PeriodicalIF":4.4,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324227","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":"Two-disjoint-cycle-cover vertex bipancyclicity of bubble-sort star graphs","authors":"Hanle Dai ,&nbsp;Yan-Quan Feng ,&nbsp;Young Soo Kwon ,&nbsp;Da-Wei Yang","doi":"10.1016/j.amc.2025.129787","DOIUrl":"10.1016/j.amc.2025.129787","url":null,"abstract":"<div><div>Let <span><math><msub><mi>r</mi><mn>1</mn></msub></math></span> and <span><math><msub><mi>r</mi><mn>2</mn></msub></math></span> denote two positive integers satisfying <span><math><mrow><msub><mi>r</mi><mn>1</mn></msub><mo>≤</mo><msub><mi>r</mi><mn>2</mn></msub></mrow></math></span>. A bipartite graph <span><math><mi>G</mi></math></span> is defined as two-disjoint-cycle-cover (abbreviated as 2-DCC) vertex <span><math><mrow><mo>[</mo><msub><mi>r</mi><mn>1</mn></msub><mo>,</mo><msub><mi>r</mi><mn>2</mn></msub><mo>]</mo></mrow></math></span>-bipancyclic if, for its any pair of distinct vertices <span><math><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></math></span> and any even integer <span><math><mi>ℓ</mi></math></span> within the range <span><math><mrow><msub><mi>r</mi><mn>1</mn></msub><mo>≤</mo><mi>ℓ</mi><mo>≤</mo><msub><mi>r</mi><mn>2</mn></msub></mrow></math></span>, there exist two cycles <span><math><msub><mi>C</mi><mn>1</mn></msub></math></span> of length <span><math><mi>ℓ</mi></math></span> and <span><math><msub><mi>C</mi><mn>2</mn></msub></math></span> of length <span><math><mrow><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>−</mo><mi>ℓ</mi></mrow></math></span> in <span><math><mi>G</mi></math></span>, such that <span><math><mrow><mi>V</mi><mrow><mo>(</mo><msub><mi>C</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>∩</mo><mi>V</mi><mrow><mo>(</mo><msub><mi>C</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>=</mo><mi>∅</mi></mrow></math></span>, <span><math><mrow><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><msub><mi>C</mi><mn>1</mn></msub><mo>)</mo></mrow></math></span> and <span><math><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><msub><mi>C</mi><mn>2</mn></msub><mo>)</mo></mrow></math></span>. In this work, we establish that an <span><math><mi>n</mi></math></span>-dimensional bubble-sort star graph <span><math><mrow><mi>B</mi><msub><mi>S</mi><mi>n</mi></msub></mrow></math></span> is 2-DCC <span><math><mrow><mo>[</mo><mn>4</mn><mo>,</mo><mfrac><mrow><mi>n</mi><mo>!</mo></mrow><mn>2</mn></mfrac><mo>]</mo></mrow></math></span>-bipancyclic for <span><math><mrow><mi>n</mi><mo>≥</mo><mn>4</mn></mrow></math></span>. This finding generalizes a result given by Zhang et al. (2023) and is optimal, given that <span><math><mrow><mi>B</mi><msub><mi>S</mi><mi>n</mi></msub></mrow></math></span> is bipartite and contains <span><math><mrow><mi>n</mi><mo>!</mo></mrow></math></span> vertices.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"512 ","pages":"Article 129787"},"PeriodicalIF":3.4,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145326087","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}