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Modelling and nonclassical symmetry analysis of a complex porous media flow in a dilating channel 膨胀通道中复杂多孔介质流动的建模与非经典对称性分析
IF 2.9 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2025-08-04 DOI: 10.1016/j.physd.2025.134834
Sougata Mandal, Sukhendu Ghosh
{"title":"Modelling and nonclassical symmetry analysis of a complex porous media flow in a dilating channel","authors":"Sougata Mandal,&nbsp;Sukhendu Ghosh","doi":"10.1016/j.physd.2025.134834","DOIUrl":"10.1016/j.physd.2025.134834","url":null,"abstract":"<div><div>This investigation focuses on the symmetry analysis and explicit solution of a fluid flow inside a channel filled with a porous material. The walls of the channel are weakly permeable and dilating vertically. There is an inflow through the pores of the walls that develops flow within the channel. The configuration pertains to the fluid flow, exhibiting either injection or suction across the porous walls at an absolute velocity while experiencing uniform expansion or contraction. The entire flow dynamics is modelled by the Darcy–Brinkman equations. The classical and nonclassical symmetry analysis based on the invariance principle, brings a fourth-order nonlinear ordinary differential equation. The analytical solution is obtained by a double perturbation method, and the comparison is carried out with the numerical solution calculated using the shooting method. A stronger wall expansion pushes the mean-flow through the channel and strengthens the flow rate. The velocity profiles are much fuller for relatively larger Darcy numbers, and behave like a Hartmann flow for the smaller Darcy numbers. Notably, a flow reversal phenomenon is noticed for a suction flow with strong wall dilation rates. Moreover, this study explores a set of conservation laws for the governing model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134834"},"PeriodicalIF":2.9,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767073","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}
引用次数: 0
Sign-equivalence in cluster algebras: Classification and applications to Markov-type equations 簇代数中的符号等价:分类及其在马尔可夫型方程中的应用
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-08-04 DOI: 10.1016/j.jpaa.2025.108058
Zhichao Chen , Zixu Li
{"title":"Sign-equivalence in cluster algebras: Classification and applications to Markov-type equations","authors":"Zhichao Chen ,&nbsp;Zixu Li","doi":"10.1016/j.jpaa.2025.108058","DOIUrl":"10.1016/j.jpaa.2025.108058","url":null,"abstract":"<div><div>In this paper, we define the sign-equivalent exchange matrices by whose mutation-equivalent class only contains two elements and give them a classification. We give a Diophantine explanation for the differences between rank 2 cluster algebras of finite type and infinite type based on <span><span>[7]</span></span>. We classify the positive integer points of the Markov mutation invariant and its variant, which correspond to the famous Markov equation and another Markov-type equation. As an application, several classes of Diophantine equations with cluster algebraic structures are exhibited.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 10","pages":"Article 108058"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144771671","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}
引用次数: 0
K-stable Fano threefolds of rank 2 and degree 28 2阶28度的k -稳定Fano三倍
IF 1.2 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-08-04 DOI: 10.1112/jlms.70259
Joseph Malbon
{"title":"K-stable Fano threefolds of rank 2 and degree 28","authors":"Joseph Malbon","doi":"10.1112/jlms.70259","DOIUrl":"https://doi.org/10.1112/jlms.70259","url":null,"abstract":"<p>Moduli spaces of Fano varieties have historically been difficult to construct. However, recent work has shown that smooth K-polystable Fano varieties of fixed dimension and volume can be parametrised by a quasi-projective moduli space. In this paper, we prove that all smooth Fano threefolds with Picard rank 2 and degree 28 are K-polystable, except for some explicit cases which we describe.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70259","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144773685","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}
引用次数: 0
Discrete incremental voting on expanders 扩展器的离散增量投票
IF 0.7 3区 数学
Discrete Mathematics Pub Date : 2025-08-04 DOI: 10.1016/j.disc.2025.114708
Colin Cooper , Tomasz Radzik , Takeharu Shiraga
{"title":"Discrete incremental voting on expanders","authors":"Colin Cooper ,&nbsp;Tomasz Radzik ,&nbsp;Takeharu Shiraga","doi":"10.1016/j.disc.2025.114708","DOIUrl":"10.1016/j.disc.2025.114708","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Pull voting is a random process in which vertices of a connected graph have initial opinions chosen from a set of &lt;em&gt;k&lt;/em&gt; distinct opinions, and at each step a random vertex alters its opinion to that of a randomly chosen neighbour until the system reaches a state where each vertex holds the same opinion.&lt;/div&gt;&lt;div&gt;In general the opinions of the vertices in pull voting are regarded as incommensurate, whereas we consider a type of pull voting, which we call &lt;em&gt;discrete incremental voting&lt;/em&gt;, suitable for moving towards consensus on integer opinions such as &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&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;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. On observing the opinion of a random neighbour, the vertex updates its opinion by a discrete change in the direction of the neighbour's opinion, if different. In the simplest case, the vertex increases its opinion by +1 if the opinion of the chosen neighbour is larger, or decreases its opinion by −1, if the opinion of the neighbour is smaller. If initially there are only two adjacent integer opinions, incremental voting coincides with pull voting, whereas if there are more than two opinions this is not the case.&lt;/div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&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;/math&gt;&lt;/span&gt; be a connected non-bipartite &lt;em&gt;n&lt;/em&gt;-vertex graph, and let &lt;em&gt;λ&lt;/em&gt; be the absolute second eigenvalue of the transition matrix &lt;em&gt;P&lt;/em&gt; of a simple random walk on &lt;em&gt;G&lt;/em&gt; with stationary distribution &lt;span&gt;&lt;math&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&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;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. Let the initial opinions of the vertices be chosen from &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&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;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; be the initial opinion of vertex &lt;em&gt;v&lt;/em&gt;, and let &lt;span&gt;&lt;math&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; be the initial weighted average opinion. We show that provided &lt;span&gt;&lt;math&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;o&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;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; the following holds with high probability. If &lt;em&gt;c&lt;/em&gt; is integer then the final opinion is &lt;em&gt;c&lt;/em&gt;. Otherwise the final opinion is &lt;span&gt;&lt;math&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; with probability &lt;span&gt;&lt;math&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;mi&gt;c&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&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; with probability &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⌈&lt;","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 1","pages":"Article 114708"},"PeriodicalIF":0.7,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767053","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}
引用次数: 0
fastkqr: A Fast Algorithm for Kernel Quantile Regression fastkqr:核分位数回归的快速算法
IF 2.4 2区 数学
Journal of Computational and Graphical Statistics Pub Date : 2025-08-04 DOI: 10.1080/10618600.2025.2541004
Qian Tang, Yuwen Gu, Boxiang Wang
{"title":"fastkqr: A Fast Algorithm for Kernel Quantile Regression","authors":"Qian Tang, Yuwen Gu, Boxiang Wang","doi":"10.1080/10618600.2025.2541004","DOIUrl":"https://doi.org/10.1080/10618600.2025.2541004","url":null,"abstract":"","PeriodicalId":15422,"journal":{"name":"Journal of Computational and Graphical Statistics","volume":"29 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144770050","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}
引用次数: 0
Liouville theorems of semilinear elliptic inequalities in a half-space 半空间中半线性椭圆不等式的Liouville定理
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-08-04 DOI: 10.1016/j.jde.2025.113664
Lorenzo D'Ambrosio , Enzo Mitidieri
{"title":"Liouville theorems of semilinear elliptic inequalities in a half-space","authors":"Lorenzo D'Ambrosio ,&nbsp;Enzo Mitidieri","doi":"10.1016/j.jde.2025.113664","DOIUrl":"10.1016/j.jde.2025.113664","url":null,"abstract":"<div><div>In this paper, we discuss several applications derived from the first part <span><span>[20]</span></span>, with a particular emphasis on the qualitative properties of solutions of integral and differential inequalities on a half-space, as well as the corresponding Liouville theorems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"447 ","pages":"Article 113664"},"PeriodicalIF":2.3,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766557","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}
引用次数: 0
Rationality for arbitrary closure operations and the test ideal of full extended plus closure 任意闭包操作的合理性及全扩展正闭包的检验理想
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-08-04 DOI: 10.1016/j.jpaa.2025.108059
Zhan Jiang , Rebecca R.G.
{"title":"Rationality for arbitrary closure operations and the test ideal of full extended plus closure","authors":"Zhan Jiang ,&nbsp;Rebecca R.G.","doi":"10.1016/j.jpaa.2025.108059","DOIUrl":"10.1016/j.jpaa.2025.108059","url":null,"abstract":"<div><div>We extend the notion of F-rationality to other closure operations, inspired by the work of Smith, Epstein and Schwede, and Ma and Schwede, which describe F-rationality in terms of the canonical module and top local cohomology module. We give conditions for a closure operation cl on a Cohen-Macaulay complete local ring under which cl-rationality is equivalent to parameter ideals being cl-closed. We also demonstrate that full extended plus closure as defined by Heitmann and weak full extended plus closure as defined by the first named author have no big test elements.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 10","pages":"Article 108059"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767035","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}
引用次数: 0
Generator polynomial matrices of the Galois hulls of multi-twisted codes 多扭曲码伽罗瓦壳的生成多项式矩阵
IF 1.2 3区 数学
Finite Fields and Their Applications Pub Date : 2025-08-04 DOI: 10.1016/j.ffa.2025.102712
Ramy Taki Eldin , Patrick Solé
{"title":"Generator polynomial matrices of the Galois hulls of multi-twisted codes","authors":"Ramy Taki Eldin ,&nbsp;Patrick Solé","doi":"10.1016/j.ffa.2025.102712","DOIUrl":"10.1016/j.ffa.2025.102712","url":null,"abstract":"<div><div>In this study, we consider the Euclidean and Galois hulls of multi-twisted (MT) codes over a finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msup></mrow></msub></math></span> of characteristic <em>p</em>. Let <strong>G</strong> be a generator polynomial matrix (GPM) of an MT code <span><math><mi>C</mi></math></span>. For any <span><math><mn>0</mn><mo>≤</mo><mi>κ</mi><mo>&lt;</mo><mi>e</mi></math></span>, the <em>κ</em>-Galois hull of <span><math><mi>C</mi></math></span>, denoted by <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span>, is the intersection of <span><math><mi>C</mi></math></span> with its <em>κ</em>-Galois dual. The main result in this paper is that a GPM for <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span> has been obtained from <strong>G</strong>. We start by associating a linear code <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> with <strong>G</strong>. We show that <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> is quasi-cyclic. In addition, we prove that the dimension of <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span> is the difference between the dimension of <span><math><mi>C</mi></math></span> and that of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span>. Thus the determinantal divisors are used to derive a formula for the dimension of <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span>. Finally, we deduce a GPM formula for <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span>. In particular, we handle the cases of <em>κ</em>-Galois self-orthogonal and linear complementary dual MT codes; we establish equivalent conditions that characterize these cases. Equivalent results can be deduced immediately for the classes of cyclic, constacyclic, quasi-cyclic, generalized quasi-cyclic, and quasi-twisted codes, because they are all special cases of MT codes. Some numerical examples, containing codes with the best-known parameters, are used to illustrate the theoretical results.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"109 ","pages":"Article 102712"},"PeriodicalIF":1.2,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772334","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}
引用次数: 0
Stability in Bondy's theorem on paths and cycles 路径和循环上邦迪定理的稳定性
IF 1.2 1区 数学
Journal of Combinatorial Theory Series B Pub Date : 2025-08-04 DOI: 10.1016/j.jctb.2025.07.004
Bo Ning , Long-Tu Yuan
{"title":"Stability in Bondy's theorem on paths and cycles","authors":"Bo Ning ,&nbsp;Long-Tu Yuan","doi":"10.1016/j.jctb.2025.07.004","DOIUrl":"10.1016/j.jctb.2025.07.004","url":null,"abstract":"<div><div>In this paper, we study the stability result of a well-known theorem of Bondy. We prove that for any 2-connected non-hamiltonian graph, if every vertex except for at most one vertex has degree at least <em>k</em>, then it contains a cycle of length at least <span><math><mn>2</mn><mi>k</mi><mo>+</mo><mn>2</mn></math></span> except for some special families of graphs. Our results imply several previous classical theorems including a deep and old result by Voss. We point out our result on stability in Bondy's theorem can directly imply a positive solution (in a slight stronger form) to the following problem: Is there a polynomial time algorithm to decide whether a 2-connected graph <em>G</em> on <em>n</em> vertices has a cycle of length at least <span><math><mi>min</mi><mo>⁡</mo><mo>{</mo><mn>2</mn><mi>δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>}</mo></math></span>? This problem originally motivates the recent study on algorithmic aspects of Dirac's theorem by Fomin, Golovach, Sagunov, and Simonov, although a stronger problem was solved by them by completely different methods. Our theorem can also help us to determine all extremal graphs for wheels on odd number of vertices. We also discuss the relationship between our results and some previous problems and theorems in spectral graph theory and generalized Turán problems.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"175 ","pages":"Pages 213-239"},"PeriodicalIF":1.2,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772391","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}
引用次数: 0
Regularity and convergence of critical points of an Ambrosio-Tortorelli functional with linear growth and of its Γ-limit 线性增长的Ambrosio-Tortorelli泛函及其Γ-limit临界点的正则性和收敛性
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-08-04 DOI: 10.1016/j.jde.2025.113654
Rebecca Continolo, Virginia Lorenzini, Riccardo Scala, Giuseppe Scianna
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