数学最新文献

{"title":"Sequence entropy and IT-tuples for minimal group actions","authors":"Chunlin Liu ,&nbsp;Xiangtong Wang ,&nbsp;Leiye Xu","doi":"10.1016/j.aim.2025.110183","DOIUrl":"10.1016/j.aim.2025.110183","url":null,"abstract":"<div><div>Let <em>G</em> be an infinite discrete countable group and <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> a minimal <em>G</em>-system. First, we prove that<span><span><span><math><msubsup><mrow><mi>h</mi></mrow><mrow><mi>t</mi><mi>o</mi><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mi>log</mi><mo>⁡</mo><munder><mo>∑</mo><mrow><mi>μ</mi><mo>∈</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>e</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></mrow></munder><msup><mrow><mi>e</mi></mrow><mrow><msubsup><mrow><mi>h</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><msubsup><mrow><mi>h</mi></mrow><mrow><mi>t</mi><mi>o</mi><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><msubsup><mrow><mi>h</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> are the supremum of the topological and metric sequence entropy, respectively. Additionally, if <em>G</em> is abelian, there exists <span><math><mi>K</mi><mo>∈</mo><mi>N</mi><mo>∪</mo><mo>{</mo><mo>∞</mo><mo>}</mo></math></span> with <span><math><mi>log</mi><mo>⁡</mo><mi>K</mi><mo>≤</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mi>t</mi><mi>o</mi><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> such that it is a regular <em>K</em>-to-one extension of its maximal equicontinuous factor.</div><div>Furthermore, for any infinite countable discrete group <em>G</em>, we show that if the factor map from a minimal <em>G</em>-system to its maximal equicontinuous factor is regular <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-to-one and almost <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-to-one, then the system admits <span><math><mo>⌈</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>/</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⌉</mo></math></span>-IT-tuples, where <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∈</mo><mi>N</mi><mo>∪</mo><mo>{</mo><mo>∞</mo><mo>}</mo></math></span> and <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>N</mi></math></span>. As a corollary, we refine the upper bound on the number of ergodic measures for systems that are almost <em>N</em>-to-one extensions of their maximal equicontinuous factors and lack <em>K</em>-IT-tuples, thereby improving the result of Huang et al. (2021) <span><span>[17]</span></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110183"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521276","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":"Some results and problems on tournament structure","authors":"Tung Nguyen ,&nbsp;Alex Scott ,&nbsp;Paul Seymour","doi":"10.1016/j.jctb.2025.02.002","DOIUrl":"10.1016/j.jctb.2025.02.002","url":null,"abstract":"<div><div>This paper is a survey of results and problems related to the following question: is it true that if <em>G</em> is a tournament with sufficiently large chromatic number, then <em>G</em> has two vertex-disjoint subtournaments <span><math><mi>A</mi><mo>,</mo><mi>B</mi></math></span>, both with large chromatic number, such that all edges between them are directed from <em>A</em> to <em>B</em>? We describe what we know about this question, and report some progress on several other related questions, on tournament colouring and domination.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"173 ","pages":"Pages 146-183"},"PeriodicalIF":1.2,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511292","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":"Canonical extensions via fitted sublocales","authors":"Tomáš Jakl,&nbsp;Anna Laura Suarez","doi":"10.1007/s10485-025-09802-6","DOIUrl":"10.1007/s10485-025-09802-6","url":null,"abstract":"<div><p>We study restrictions of the correspondence between the lattice <span>(textsf{SE}(L))</span> of strongly exact filters, of a frame <i>L</i>, and the coframe <span>(mathcal {S}_o(L))</span> of fitted sublocales. In particular, we consider the classes of exact filters <span>(textsf{E}(L))</span>, regular filters <span>(textsf{R}(L))</span>, and the intersections <span>(mathcal {J}(textsf{CP}(L)))</span> and <span>(mathcal {J}(textsf{SO}(L)))</span> of completely prime and Scott-open filters, respectively. We show that all these classes of filters are sublocales of <span>(textsf{SE}(L))</span> and as such correspond to subcolocales of <span>(mathcal {S}_o(L))</span> with a concise description. The theory of polarities of Birkhoff is central to our investigations. We automatically derive universal properties for the said classes of filters by giving their descriptions in terms of polarities. The obtained universal properties strongly resemble that of the canonical extensions of lattices. We also give new equivalent definitions of subfitness in terms of the lattice of filters.\u0000</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"33 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-025-09802-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterizing traces of processes defined by precedence and response constraints: An order theory approach","authors":"Mark Dukes,&nbsp;Anton Sohn","doi":"10.1016/j.dam.2025.02.028","DOIUrl":"10.1016/j.dam.2025.02.028","url":null,"abstract":"<div><div>In this paper we consider a general system of activities that can, but do not have to, occur. This system is governed by a set containing two types of constraints: precedence and response. A precedence constraint dictates that an activity can only occur if it has been preceded by some other specified activity. Response constraints are similarly defined. An execution of the system is a listing of activities in the order they occur and which satisfies all constraints. These listings are known as <em>traces</em>. Such systems naturally arise in areas of theoretical computer science and decision science. An outcome of the freedom with which activities can occur is that there are many different possible executions, and gaining a combinatorial insight into these is a non-trivial problem.</div><div>We characterize all of the ways in which such a system can be executed. Our approach uses order theory to provide a classification in terms of the linear extensions of posets constructed from the constraint sets. This characterization is essential in calculating the stakeholder utility metrics that have been developed by the first author that allow for quantitative comparisons of such systems/processes. It also allows for a better understanding of the theoretical backbone to these processes.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"368 ","pages":"Pages 112-125"},"PeriodicalIF":1.0,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143512582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On intersecting families of subgraphs of perfect matchings","authors":"Melissa Fuentes,&nbsp;Vikram Kamat","doi":"10.1016/j.disc.2025.114460","DOIUrl":"10.1016/j.disc.2025.114460","url":null,"abstract":"<div><div>The seminal Erdős–Ko–Rado (EKR) theorem states that if <span><math><mi>F</mi></math></span> is a family of <em>k</em>-subsets of an <em>n</em>-element set <em>X</em> for <span><math><mi>k</mi><mo>≤</mo><mi>n</mi><mo>/</mo><mn>2</mn></math></span> such that every pair of subsets in <span><math><mi>F</mi></math></span> has a nonempty intersection, then <span><math><mi>F</mi></math></span> can be no bigger than the trivially intersecting family obtained by including all <em>k</em>-subsets of <em>X</em> that contain a fixed element <span><math><mi>x</mi><mo>∈</mo><mi>X</mi></math></span>. This family is called the <em>star</em> centered at <em>x</em>. In this paper, we formulate and prove an EKR theorem for intersecting families of subgraphs of the perfect matching graph. This can be considered a generalization not only of the aforementioned EKR theorem but also of a <em>signed</em> variant of it, first stated by Meyer <span><span>[9]</span></span>, and proved separately by Deza–Frankl <span><span>[3]</span></span> and Bollobás–Leader <span><span>[1]</span></span>. The proof of our main theorem relies on a novel extension of Katona's beautiful <em>cycle method</em>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 7","pages":"Article 114460"},"PeriodicalIF":0.7,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511944","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":"Well-Posedness of Degenerate Initial-Boundary Value Problems to a Hyperbolic-Parabolic Coupled System Arising from Nematic Liquid Crystals","authors":"Yanbo Hu,&nbsp;Yuusuke Sugiyama","doi":"10.1007/s00205-025-02093-0","DOIUrl":"10.1007/s00205-025-02093-0","url":null,"abstract":"<div><p>This paper is focused on the local well-posedness of initial-boundary value and Cauchy problems to a one-dimensional quasilinear hyperbolic-parabolic coupled system with boundary or far field degenerate initial data. The governing system is derived from the theory of nematic liquid crystals, which couples a hyperbolic equation describing the crystal property and a parabolic equation describing the liquid property of the material. The hyperbolic equation is degenerate at the boundaries or spatial infinity, which results in the classical methods for the strictly hyperbolic-parabolic coupled systems being invalid. We introduce admissible weighted function spaces and apply the parametrix method to construct iteration mappings for these two degenerate problems separately. The local existence and uniqueness of classical solutions of the degenerate initial-boundary value and Cauchy problems are established by the contraction mapping principle in their selected function spaces. Moreover, the solutions have no loss of regularity and their existence times are independent of the spatial variable.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513360","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":"On the boundary of an immediate attracting basin of a hyperbolic entire function","authors":"Walter Bergweiler,&nbsp;Jie Ding","doi":"10.1112/jlms.70085","DOIUrl":"https://doi.org/10.1112/jlms.70085","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a transcendental entire function of finite order which has an attracting periodic point &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;z&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$z_0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of period at least 2. Suppose that the set of singularities of the inverse of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is finite and contained in the component &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;annotation&gt;$U$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of the Fatou set that contains &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;z&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$z_0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Under an additional hypothesis, we show that the intersection of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$partial U$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with the escaping set of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; has Hausdorff dimension 1. The additional hypothesis is satisfied for example if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; has the form &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mo&gt;∫&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mi&gt;z&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70085","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513563","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}

{"title":"A parameter estimation method for neural mass model based on the improved chimp optimization algorithm and Riemannian geometry","authors":"Shaoting Yan ,&nbsp;Xiaochu Shi ,&nbsp;Ruiqi Li ,&nbsp;Lipeng Zhang ,&nbsp;Rui Zhang ,&nbsp;Mingming Chen ,&nbsp;Meng Li ,&nbsp;Hui Zhang ,&nbsp;Runtao Li ,&nbsp;Li Shi ,&nbsp;Yuxia Hu","doi":"10.1016/j.chaos.2025.116219","DOIUrl":"10.1016/j.chaos.2025.116219","url":null,"abstract":"<div><div>Neural mass model (NMM) serves as an effective tool for understanding and exploring the complex dynamics of brain systems. Accurately estimating the model parameters of NMM is highly important for building brain models driven by observed electroencephalogram (EEG) data. However, existing methods for comparing model output with observed data primarily focus on one-dimensional linear comparisons, overlooking the high-dimensional nonlinear dynamics and Riemannian geometry characteristics of EEG data. To address this issue, we propose a novel parameter estimation method for NMM based on the improved chimp optimization algorithm (ChOA) and Riemannian geometry. First, ChOA is improved by incorporating the Aquila optimizer (AOChOA) is used to improve the convergence efficiency and accuracy of the nonlinear optimization problem. Then, a novel loss function based on the Riemannian geometry of symmetric positive definite matrices (LRSPD) is constructed to capture the high-dimensional nonlinear dynamics of EEG signals. Finally, we validate the effectiveness of the proposed method by using the model output with fixed model parameters and real EEG signals as observed data, respectively. When using the model output with fixed model parameters, the loss function LRSPD yielded more accurate parameter estimation results compared to others, with the fitted model closely matching the dynamics of the observed data. When using real EEG data, the proposed method successfully recovered differences in EEG dynamics for subjects at different consciousness levels. Additionally, our study reveals the neural mechanisms of decreased consciousness level in patients with disorders of consciousness (DOC), characterized by increased inhibitory neural activity of the brain.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116219"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511413","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":"Some mixed soliton wave interaction patterns and stabilities for Rabi-coupled nonlocal Gross–Pitaevskii equations","authors":"Li Li,&nbsp;Fajun Yu","doi":"10.1016/j.chaos.2025.116171","DOIUrl":"10.1016/j.chaos.2025.116171","url":null,"abstract":"<div><div>Some mixed interactions of the soliton, breather and rogue wave(RW) formations and their dynamics are studied in Rabi-coupled Bose–Einstein condensates(BECs) with spatially varying dispersion and nonlinearity. We consider the 2-component inhomogeneous Rabi-coupled Gross–Pitaevskii (GP) equations through suitable three kinds of rotational and similarity transformations. The effects of inhomogeneity and optical lattice hyperbolic potentials of the RWs are investigated with two different forms of potential strengths, and some oscillating behaviors of dark–bright solitons, RWs and breather solitons with Rabi coupling terms are shown in 2-component condensates. We demonstrate creation of some RWs coexisting with dark–bright soliton part in second component of the 2-component GP equations. We show that some mixed interactions of vector soliton, breather and RW formations by employing parabolic cylinder modulations, and find a striking feature of Rabi coupling with spatial modulation. Further, the RWs can be converted into broad based zero background RW appearing on the top of a bright soliton by introducing spatial modulation in 2-component systems. Some dynamic behaviors of the RW solutions are investigated analytically with the external potentials, and the mixed waves, interaction patterns and stabilities for Rabi-coupled nonlocal GP systems are presented with modulation instability, which can be used to calculate nonautonomous mixed wave interactions and the potential applications for the RW phenomena.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116171"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511414","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":"Distribution of maxima and minima statistics on alternating permutations, Springer numbers, and avoidance of flat POPs","authors":"Tian Han ,&nbsp;Sergey Kitaev ,&nbsp;Philip B. Zhang","doi":"10.1016/j.jcta.2025.106034","DOIUrl":"10.1016/j.jcta.2025.106034","url":null,"abstract":"<div><div>In this paper, we find distributions of the left-to-right maxima, right-to-left maxima, left-to-right minima and right-to-left-minima statistics on up-down and down-up permutations of even and odd lengths. We recover and generalize a result by Carlitz and Scoville, obtained in 1975, stating that the distribution of left-to-right maxima on down-up permutations of even length is given by <span><math><msup><mrow><mo>(</mo><mi>sec</mi><mo>⁡</mo><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>q</mi></mrow></msup></math></span>. We also derive the joint distribution of the maxima (resp., minima) statistics, extending the scope of the respective results of Carlitz and Scoville, who obtain them in terms of certain systems of PDEs and recurrence relations. To accomplish this, we generalize a result of Kitaev and Remmel by deriving joint distributions involving non-maxima (resp., non-minima) statistics. Consequently, we refine classic enumeration results of André by introducing new <em>q</em>-analogues and <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-analogues for the number of alternating permutations.</div><div>Additionally, we verify Callan's conjecture (2012) that up-down permutations of even length fixed by reverse and complement are counted by the Springer numbers, thereby offering another combinatorial interpretation of these numbers. Furthermore, we propose two <em>q</em>-analogues and a <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-analogue of the Springer numbers. Lastly, we enumerate alternating permutations that avoid certain flat partially ordered patterns.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"213 ","pages":"Article 106034"},"PeriodicalIF":0.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511458","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}