数学最新文献

{"title":"Typicality of operators on Fréchet algebras admitting a hypercyclic algebra","authors":"William Alexandre ,&nbsp;Clifford Gilmore ,&nbsp;Sophie Grivaux","doi":"10.1016/j.aim.2025.110406","DOIUrl":"10.1016/j.aim.2025.110406","url":null,"abstract":"<div><div>This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fréchet algebras, endowed with the topology of pointwise convergence. Our main results show that within natural Polish spaces of continuous operators acting on the algebra <span><math><mi>H</mi><mo>(</mo><mi>C</mi><mo>)</mo></math></span> of entire functions on <span><math><mi>C</mi></math></span>, a typical operator supports a hypercyclic algebra. We also investigate the case of the complex Fréchet algebras <span><math><mi>X</mi><mo>=</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math></span>, <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>&lt;</mo><mo>+</mo><mo>∞</mo></math></span>, or <span><math><mi>X</mi><mo>=</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math></span> endowed with the coordinatewise product, and show that whenever <span><math><mi>M</mi><mo>&gt;</mo><mn>1</mn></math></span>, a typical operator on <em>X</em> of norm less than or equal to <em>M</em> admits a hypercyclic algebra.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"478 ","pages":"Article 110406"},"PeriodicalIF":1.5,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306863","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":"Symmetry breaking bifurcation and the stability of stationary solutions of a phase-field model","authors":"Yasuhito Miyamoto ,&nbsp;Tatsuki Mori ,&nbsp;Sohei Tasaki ,&nbsp;Tohru Tsujikawa ,&nbsp;Shoji Yotsutani","doi":"10.1016/j.jde.2025.113500","DOIUrl":"10.1016/j.jde.2025.113500","url":null,"abstract":"<div><div>We have been investigating the global bifurcation diagrams of stationary solutions for a phase field model proposed by Fix and Caginalp in a one-dimensional case. It has recently been shown that there exists a secondary bifurcation with a symmetry-breaking phenomenon from a branch consisting of symmetric solutions in the case where the total enthalpy equals zero. In this paper, we determine the stability/instability of all symmetric solutions and asymmetric solutions near the secondary bifurcation point. Moreover, we show representation formulas for all eigenvalues and eigenfunctions for the linearized eigenvalue problem around the symmetric solutions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113500"},"PeriodicalIF":2.4,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306837","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":"Decoding driving states based on normalized mutual information features and hyperparameter self-optimized Gaussian kernel-based radial basis function extreme learning machine","authors":"Jichi Chen ,&nbsp;Fuchang Fan ,&nbsp;Chunfeng Wei ,&nbsp;Kemal Polat ,&nbsp;Fayadh Alenezi","doi":"10.1016/j.chaos.2025.116751","DOIUrl":"10.1016/j.chaos.2025.116751","url":null,"abstract":"<div><div>This study presents an analysis of driver's unfavorable driving states (UDS) using normalized mutual information (NMI) features and a hyperparameter self-optimized radial basis function extreme learning machine (RBF-ELM). By computing the mutual information across different frequency bands (including delta, theta, alpha, beta, and gamma frequency bands) in EEG signals, brain functional connectivity matrices are constructed to reveal the nonlinear coupling relationships between brain regions. The introduction of NMI reduces the effects of signal dimensionality differences, which ensures the comparability of features across subjects. After preprocessing and band-pass filtering of EEG signals, NMI features from five frequency bands are extracted, and RBF-ELM is then employed for distinguishing UDS. In the RBF-ELM model, an automatic hyperparameter optimization approach is implemented, combining grid search and five-fold cross-validation to select the optimal number of hidden layer neurons and regularization parameters. The experimental results show that the NMI features from the beta band provide excellent classification performance, achieving an accuracy of 94.06 % in detecting UDS. Moreover, the hyperparameter self-optimized RBF-ELM model exhibits outstanding performance on the test set, with an area under the receiver operating characteristic (ROC) curve (AUC) value of 0.9915. Compared to classic machine learning algorithms, the proposed method outperforms support vector machine, ensemble learning, linear discriminant analysis, logistic regression, neural networks, and k-nearest neighbors in terms of accuracy, sensitivity, precision, and specificity. The method presented in this paper provides a promising solution for real-time monitoring of drivers' psychological states and fatigue warning.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116751"},"PeriodicalIF":5.3,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144308144","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":"Dynamic evolution of cooperation based on adaptive reputation threshold and game transition","authors":"Hongyu Yue ,&nbsp;Xiaojin Xiong ,&nbsp;Minyu Feng ,&nbsp;Attila Szolnoki","doi":"10.1016/j.chaos.2025.116693","DOIUrl":"10.1016/j.chaos.2025.116693","url":null,"abstract":"<div><div>In real-world social systems, individual interactions are frequently shaped by reputation, which not only influences partner selection but also affects the nature and benefits of the interactions themselves. We propose a heterogeneous game transition model that incorporates a reputation-based dynamic threshold mechanism to investigate how reputation regulates game evolution. In our framework, individuals determine the type of game they engage in according to their own and their neighbors’ reputation levels. In turn, the outcomes of these interactions modify their reputations, thereby driving the adaptation and evolution of future strategies in a feedback-informed manner. Through simulations on two representative topological structures, square lattice and small-world networks, we find that network topology exerts a profound influence on the evolutionary dynamics. Due to its localized connection characteristics, the square lattice network fosters the long-term coexistence of competing strategies. In contrast, the small-world network is more susceptible to changes in system parameters due to the efficiency of information dissemination and the sensitivity of strategy evolution. Additionally, the reputation mechanism is significant in promoting the formation of a dominant state of cooperation, especially in contexts of high sensitivity to reputation. Although the initial distribution of reputation influences the early stage of the evolutionary path, it has little effect on the final steady state of the system. Hence, we can conclude that the ultimate steady state of evolution is primarily determined by the reputation mechanism and the network structure.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116693"},"PeriodicalIF":5.3,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144308170","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":"Convergence Analysis of the Monte Carlo Method for the Random Navier–Stokes–Fourier System","authors":"Mária Lukáčová-Medviďová, Bangwei She, Yuhuan Yuan","doi":"10.1137/23m1563232","DOIUrl":"https://doi.org/10.1137/23m1563232","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1254-1280, June 2025. <br/> Abstract. In the present paper, we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier–Stokes–Fourier system. The Monte Carlo method, frequently used for approximating statistical moments, is combined with a suitable deterministic discretization method in physical space and time. Under the assumption that numerical densities and temperatures are bounded in probability, we prove the convergence of random finite volume solutions to the statistical strong solution by applying genuine stochastic compactness arguments. Further, we show the convergence and error estimates for Monte Carlo estimators of the expectation and deviation. We present several numerical results to illustrate the theoretical results.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"38 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144311938","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":"Blow-up and boundedness in a chemotaxis system with flux-limited diffusion and logistic source","authors":"Monica Marras ,&nbsp;Stella Vernier-Piro ,&nbsp;Tomomi Yokota","doi":"10.1016/j.na.2025.113868","DOIUrl":"10.1016/j.na.2025.113868","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper we consider radially symmetric solutions of the parabolic–elliptic cross-diffusion system with flux limitation term, &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&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;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&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;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;under no-flux boundary conditions, where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;) is a ball, &lt;span&gt;&lt;math&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; are positive constants and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; . Under suitable conditions on the data, we prove that the solution is global in time. If &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, under conditions on the data, we prove that the solution &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; blows up in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;-norm at finite time &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113868"},"PeriodicalIF":1.3,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306506","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":"Enumeration of sets of equiangular lines with common angle arccos⁡(1/3)","authors":"Kiyoto Yoshino","doi":"10.1016/j.disc.2025.114647","DOIUrl":"10.1016/j.disc.2025.114647","url":null,"abstract":"<div><div>In 2018, Szöllősi and Östergård used a computer to enumerate sets of equiangular lines with common angle <span><math><mi>arccos</mi><mo>⁡</mo><mo>(</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>)</mo></math></span> in dimension 7. They observed that the numbers <span><math><mi>ω</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> of sets of <em>n</em> equiangular lines with common angle <span><math><mi>arccos</mi><mo>⁡</mo><mo>(</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>)</mo></math></span> in dimension 7 are almost symmetric around <span><math><mi>n</mi><mo>=</mo><mn>14</mn></math></span>. In this paper, we prove without a computer that the numbers <span><math><mi>ω</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> are indeed almost symmetric by considering isometries from root lattices of rank at most 8 to the root lattice <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>8</mn></mrow></msub></math></span> of rank 8 and type <em>E</em>. Also, they determined the number <span><math><mi>s</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> of sets of <em>n</em> equiangular lines with common angle <span><math><mi>arccos</mi><mo>⁡</mo><mo>(</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>)</mo></math></span> for <span><math><mi>n</mi><mo>≤</mo><mn>13</mn></math></span>. We construct all the sets of equiangular lines with common angle <span><math><mi>arccos</mi><mo>⁡</mo><mo>(</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>)</mo></math></span> in dimension greater than 7 from root lattices of type <em>A</em> or <em>D</em> with the aid of switching roots. As an application, we determine the number <span><math><mi>s</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> for every positive integer <em>n</em>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 12","pages":"Article 114647"},"PeriodicalIF":0.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307727","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":"Riemann boundary value problems for the Chaplygin gas outside a convex cornered wedge","authors":"Bingsong Long","doi":"10.1016/j.nonrwa.2025.104433","DOIUrl":"10.1016/j.nonrwa.2025.104433","url":null,"abstract":"<div><div>We consider two-dimensional Riemann boundary value problems of Euler equations for the Chaplygin gas with two piecewise constant initial data outside a convex cornered wedge. In self-similar coordinates, when the flow at the wedge corner is subsonic, this problem can be reformulated as a boundary value problem for nonlinear degenerate elliptic equations in concave domains containing a corner larger than <span><math><mi>π</mi></math></span>. It is shown that there does not exist a global Lipschitz solution for this case. We analyze the sign of the flow velocity along a certain direction, and then obtain this result by deriving a contradiction. Besides, the unique existence of the solution to the problem is established when the flow at the wedge corner is supersonic. The results obtained here are also valid for the problem of shock diffraction by a convex cornered wedge.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104433"},"PeriodicalIF":1.8,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307731","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":"Finite Element Approximation of Stationary Fokker–Planck–Kolmogorov Equations with Application to Periodic Numerical Homogenization","authors":"Timo Sprekeler, Endre Süli, Zhiwen Zhang","doi":"10.1137/24m1692848","DOIUrl":"https://doi.org/10.1137/24m1692848","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1315-1343, June 2025. <br/> Abstract. We propose and rigorously analyze a finite element method for the approximation of stationary Fokker–Planck–Kolmogorov (FPK) equations subject to periodic boundary conditions in two settings: one with weakly differentiable coefficients, and one with merely essentially bounded measurable coefficients under a Cordes-type condition. These problems arise as governing equations for the invariant measure in the homogenization of nondivergence-form equations with large drifts. In particular, the Cordes setting guarantees the existence and uniqueness of a square-integrable invariant measure. We then suggest and rigorously analyze an approximation scheme for the effective diffusion matrix in both settings based on the finite element scheme for stationary FPK problems developed in the first part. Finally, we demonstrate the performance of the methods through numerical experiments.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"100 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144311937","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":"Proof of Lew's conjecture on the spectral gaps of simplicial complexes","authors":"Xiongfeng Zhan,&nbsp;Xueyi Huang,&nbsp;Huiqiu Lin","doi":"10.1016/j.jcta.2025.106091","DOIUrl":"10.1016/j.jcta.2025.106091","url":null,"abstract":"<div><div>As a generalization of graph Laplacians to higher dimensions, the combinatorial Laplacians of simplicial complexes have garnered increasing attention. Let <em>X</em> be a simplicial complex on <em>n</em> vertices, and let <span><math><mi>X</mi><mo>(</mo><mi>k</mi><mo>)</mo></math></span> denote the set of all <em>k</em>-dimensional simplices of <em>X</em>. The <em>k</em>-th spectral gap <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is the smallest eigenvalue of the reduced <em>k</em>-dimensional Laplacian of <em>X</em>. For any <span><math><mi>k</mi><mo>≥</mo><mo>−</mo><mn>1</mn></math></span>, Lew (2020) <span><span>[24]</span></span> established a lower bound for <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span>:<span><span><span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>≥</mo><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo><mrow><mo>(</mo><munder><mi>min</mi><mrow><mi>σ</mi><mo>∈</mo><mi>X</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></munder><mo>⁡</mo><msub><mrow><mi>deg</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>⁡</mo><mo>(</mo><mi>σ</mi><mo>)</mo><mo>+</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>−</mo><mi>d</mi><mi>n</mi><mo>≥</mo><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>−</mo><mi>d</mi><mi>n</mi><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>deg</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>⁡</mo><mo>(</mo><mi>σ</mi><mo>)</mo></math></span> and <em>d</em> denote the degree of <em>σ</em> in <em>X</em> and the maximal dimension of a missing face of <em>X</em>, respectively. In this paper, we identify the unique simplicial complex that achieves the lower bound of the <em>k</em>-th spectral gap, <span><math><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>−</mo><mi>d</mi><mi>n</mi></math></span>, for some <em>k</em>, thereby confirming a conjecture proposed by Lew.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"217 ","pages":"Article 106091"},"PeriodicalIF":0.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306865","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}