数学最新文献

{"title":"Self-tapping of a liquid crystal elastomer thin beam above a hot plate","authors":"Yong Yu ,&nbsp;Zheng Dai ,&nbsp;Tianyu Li ,&nbsp;Zhijian Wang ,&nbsp;Honghao Ma ,&nbsp;Kai Li","doi":"10.1016/j.chaos.2025.116904","DOIUrl":"10.1016/j.chaos.2025.116904","url":null,"abstract":"<div><div>Thermally-driven self-oscillating systems are able to absorb heat from the environment to maintain their own motion, and therefore have a wide range of applications in the fields of signal processing, robotics and energy harvester. Existing thermally-driven self-oscillating systems are always in contact with a hot surface or in a temperature field with a non-contacting heat source, which makes it difficult to dissipate heat quickly and limits the generation of high-frequency oscillations. By introducing intermittent contact with a hot plate, a self-tapping liquid crystal elastomer (LCE) thin beam is experimentally designed in this paper. Based on the existing mature dynamic LCE model, the theoretical model of the thermally-driven self-tapping LCE beam is established, and the mechanism of self-tapping is elucidated. Numerical calculations show that the system exists in two modes of motion: static mode and self-tapping mode, which is consistent with the experimental results. The LCE beam maintains its self-tapping by absorbing the thermal energy from the hot plate to compensate for the damping dissipation during its motion. In addition, the effects of several key parameters on the amplitude and frequency of self-tapping are investigated in detail. Specially, the frequency of self-tapping exceeds 7 Hz, originating from the rapid heat absorption when contacting the hot plate and the rapid heat dissipation in air. This self-tapping system has the advantages of high oscillation frequency, simple structure, flexible regulation, and stability, and has potential applications in practical application scenarios such as thermal sensors, energy capture and micro-robotics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":""},"PeriodicalIF":5.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748939","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 weak double Roman domination in graphs","authors":"S. Soltani ,&nbsp;H. Abdollahzadeh Ahangar ,&nbsp;M. Chellali ,&nbsp;H. Rahbani ,&nbsp;S.M. Sheikholeslami","doi":"10.1016/j.dam.2025.07.019","DOIUrl":"10.1016/j.dam.2025.07.019","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; be a graph and &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; a function defined from &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&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;mn&gt;3&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; A vertex &lt;span&gt;&lt;math&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of &lt;span&gt;&lt;math&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is said to be doubly unprotected with respect to &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mrow&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;/mrow&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is a set consisting of vertex &lt;span&gt;&lt;math&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and all vertices adjacent to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; The function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is said to be a weak double Roman dominating function (WDRD-function) if for every vertex &lt;span&gt;&lt;math&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&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;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; there is a neighbor &lt;span&gt;&lt;math&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of &lt;span&gt;&lt;math&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;f&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;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; such that the function &lt;span&gt;&lt;math&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; defined by &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mrow&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;f&lt;/mi&gt;&lt;mrow&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;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;\u0000 &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;g&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;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&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;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;g&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;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&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;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for all &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;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;mi&gt;v&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; has no doubly unprotected vertex. The weight of a WDRD-function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is the sum &lt;span&gt;&lt;math&gt;&lt;mrow&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;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and the weak double Roman domination number &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; equals the minimum weight of a WDRD-function on &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; First, we show that the associate decision pr","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 307-315"},"PeriodicalIF":1.0,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750423","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":"Statistical properties and quantum nature of light in optical cavities combining second- and third-order nonlinearities","authors":"H. Jabri ,&nbsp;H. Eleuch","doi":"10.1016/j.chaos.2025.116915","DOIUrl":"10.1016/j.chaos.2025.116915","url":null,"abstract":"<div><div>The squeezing of light is a typical quantum effect arising in nonlinear systems, which is of great importance for quantum sensors and other applications. We investigate a scheme consisting of an optical cavity containing a pair of coupled quantum wells through electronic tunneling. Nonlinear excitonic interactions in the direct and indirect exciton fields are considered. Further, the cavity interacts with an optical parametric oscillator which results in the injection of squeezed photons inside the cavity. We show that the excitonic density in the quantum wells is increased by the external squeezed source. By analytically solving the quantum Langevin equations in the frequency domain and optimizing the noise spectrum of the transmitted light, we show that indirect exciton nonlinearity produces a stronger squeezing than direct exciton nonlinearity. In all scenarios, incorporating the parametric oscillator significantly increase the degree of squeezing. The impact of the second-order nonlinearity is much more noticeable in the weak coupling regime compared to excitonic nonlinearity. Nevertheless, the nonlinearity of the exciton produces higher squeezing than the optical parametric oscillator when the strong coupling regime is reached. We found also that the squeezing effect manifests a high resistance and stability against the thermal baths, in particular in the weak coupling regime. The proposed scheme offers possible applications by significantly reducing noise in a specific frequency range in a compact device.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116915"},"PeriodicalIF":5.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750734","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":"A criterion space search feasibility pump heuristic for solving maximum multiplicative programs","authors":"Ashim Khanal,&nbsp;Hadi Charkhgard","doi":"10.1016/j.disopt.2025.100903","DOIUrl":"10.1016/j.disopt.2025.100903","url":null,"abstract":"<div><div>We study a class of nonlinear optimization problems with diverse practical applications, particularly in cooperative game theory. These problems are referred to as Maximum Multiplicative Programs (MMPs), and can be conceived as instances of “Optimization Over the Frontier” in multi-objective optimization. To solve MMPs, we introduce a feasibility pump-based heuristic that is specifically designed to search the criterion space of their multi-objective optimization counterparts. Through a computational study, we show the efficacy of the proposed method.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"57 ","pages":"Article 100903"},"PeriodicalIF":1.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738317","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":"mGFD: A meshless generalized finite difference method","authors":"Gerardo Tinoco-Guerrero,&nbsp;Francisco Javier Domínguez-Mota,&nbsp;José Alberto Guzmán-Torres,&nbsp;Gabriela Pedraza-Jiménez,&nbsp;José Gerardo Tinoco-Ruiz","doi":"10.1016/j.camwa.2025.07.034","DOIUrl":"10.1016/j.camwa.2025.07.034","url":null,"abstract":"<div><div>This work introduces a novel meshless method, the meshless Generalized Finite Difference (mGFD) scheme, which is derived from an optimization formulation that enforces the consistency condition. This approach eliminates the need for additional weight functions required by other methods, enabling efficient and accurate simulations of complex geometries. The method leverages a flexible, node-based discretization scheme that avoids a predefined mesh, providing enhanced versatility and adaptability in modeling various engineering applications. The proposed method's flexibility and adaptability are demonstrated through numerical solutions of elliptic, parabolic, and hyperbolic partial differential equations in highly irregular domains, providing satisfactory results compared to known exact solutions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 396-418"},"PeriodicalIF":2.5,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748781","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":"On the k-linkage problem for generalizations of semicomplete digraphs","authors":"Jia Zhou ,&nbsp;Jørgen Bang-Jensen ,&nbsp;Jin Yan","doi":"10.1016/j.disc.2025.114700","DOIUrl":"10.1016/j.disc.2025.114700","url":null,"abstract":"&lt;div&gt;&lt;div&gt;A directed graph (digraph) &lt;em&gt;D&lt;/em&gt; is &lt;em&gt;k&lt;/em&gt;&lt;strong&gt;-linked&lt;/strong&gt; if &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, and for any 2&lt;em&gt;k&lt;/em&gt; distinct vertices &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;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of &lt;em&gt;D&lt;/em&gt;, there exist vertex-disjoint paths &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a path from &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;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; to &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; for each &lt;span&gt;&lt;math&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. In 1980, Thomassen conjectured that there exists a function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&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; such that every &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&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;-strong digraph is &lt;em&gt;k&lt;/em&gt;-linked. He later disproved this conjecture by showing that &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; does not exist for general digraphs and proved that the function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&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; exists for the class of tournaments. In this paper we consider a large class &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of digraphs which includes all &lt;strong&gt;semicomplete digraphs&lt;/strong&gt; (digraphs with no pair of non-adjacent vertices) and all &lt;strong&gt;quasi-transitive digraphs&lt;/strong&gt; (a digraph &lt;em&gt;D&lt;/em&gt; is quasi-transitive if for any three vertices &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of &lt;em&gt;D&lt;/em&gt;, whenever &lt;em&gt;xy&lt;/em&gt; and &lt;em&gt;yz&lt;/em&gt; are arcs, then &lt;em&gt;x&lt;/em&gt; and &lt;em&gt;z&lt;/em&gt; are adjacent). We prove that every 3&lt;em&gt;k&lt;/em&gt;-strong digraph &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with minimum out-degree at least 23&lt;em&gt;k&lt;/em&gt; is &lt;em&gt;k&lt;/em&gt;-linked. A digraph &lt;em&gt;D&lt;/em&gt; is &lt;em&gt;l&lt;/em&gt;&lt;strong&gt;-quasi-transitive&lt;/strong&gt; if whenever there is a path of length &lt;em&gt;l&lt;/em&gt; between vertices &lt;em&gt;u&lt;/em&gt; and &lt;em&gt;v&lt;/em&gt; in &lt;em&gt;D&lt;/em&gt; the vertices &lt;em&gt;u&lt;/em&gt; and &lt;em&gt;v&lt;/em&gt; are adjacent. Hence 2-quasi-transitive digraphs are exactly the quasi-transitive digraphs. We prove that there is a function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; so that every &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-strong &lt;em&gt;l&lt;/em&gt;-quasi-transitive digraph is &lt;em&gt;k&lt;/em&gt;-linked. The main new tool in our proofs significantly strengt","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 2","pages":"Article 114700"},"PeriodicalIF":0.7,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749166","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":"Robustness analysis of k-core percolation on asymmetric interdependent networks","authors":"Lili Zhou,&nbsp;Yukun Li,&nbsp;Fei Tan","doi":"10.1016/j.chaos.2025.116910","DOIUrl":"10.1016/j.chaos.2025.116910","url":null,"abstract":"<div><div>Asymmetric interdependency phenomenon is widely present in real networks, but the vast majority of the existing researches are on symmetric interdependent networks, in which when one party is failed and the other one will be failed as well. While in the asymmetric interdependent networks (AINs), the dependency relationships are unidirectional, the failure for one part may not necessarily result in that for the other part. Consequently, the exploration on the robustness of AINs is very important and meaningful. While <span><math><mi>k</mi></math></span>-core percolation theory provides an effective tool on the analysis of network performance, for this paper, we aims to the analysis on robustness of AINs with use of it. A scale gap threshold <span><math><mi>θ</mi></math></span> is defined to analyze the tolerance between dependent nodes. Then the <span><math><mi>k</mi></math></span>-core percolation equation for AINs is derived to analyze the types of phase transition. The simulations on different networks imply that the robustness of networks is improved after the introduction of asymmetric relation. It can be obtained that the reduction of <span><math><mi>θ</mi></math></span> can make the network robustness further improved, and the network exists continuous phase transition only when <span><math><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mspace></mspace><mn>2</mn></mrow></math></span>, while it has a discontinuous phase transition with square root behavior at the critical point when <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>. Finally, based on the characteristics of <span><math><mi>k</mi></math></span>-core structure and asymmetric dependency, and with consideration of the effect upon node failure, an improved edge attack strategy is put forward. Compared with several other attack strategies, the significance for the proposed strategy is proved by experimental simulation. This study will be beneficial for understanding the hierarchical structure of AINs and optimizing the network design, and it also provides a basis for further identifying the key nodes and vulnerable links of AINs.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116910"},"PeriodicalIF":5.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750735","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":"A multi-market model with heterogeneous agents and switching mechanism.","authors":"Serena Brianzoni, Giovanni Campisi","doi":"10.1063/5.0274253","DOIUrl":"https://doi.org/10.1063/5.0274253","url":null,"abstract":"<p><p>This paper presents a multi-market model consisting of two distinct financial markets with one risky asset. The model assumes that each market is populated by two types of interacting traders: fundamentalists and cross-sectional momentum traders. A market maker sets the price based on a nonlinear adjustment mechanism. We prove that, depending on the relative influence of traders' beliefs, the asset dynamics can exhibit large-amplitude fluctuations. Through bifurcation analysis, we derive analytical conditions that show how the intensity of investors' preferences for trading rules and the switching mechanism can destabilize the markets. Furthermore, we show that when investors hold polarized beliefs, it can introduce significant uncertainty in both markets, leading to complex price dynamics.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 8","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144764638","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":"Tale of one emergent game: Opinion formation in dynamical undirected hypergraphs.","authors":"Yakun Wang, Yuan Liu, Bin Wu","doi":"10.1063/5.0283611","DOIUrl":"https://doi.org/10.1063/5.0283611","url":null,"abstract":"<p><p>Opinion dynamics in dynamical hypergraphs, mirroring the dynamical nature of high-order social interactions, are attracting increasing attention. Opinion dynamics on high-order interactions lead to non-trivial dynamical patterns compared with that on pairwise networks. How should we systematically understand the intrinsic differences between opinion dynamics in hypergraphs and that in networks? We establish a voter model in a dynamical hypergraph. We find that both opinion formation and transient topology are captured by a single multi-player game, provided that the hypergraphs evolve sufficiently fast. The Nash equilibrium analysis facilitates us to reveal the intrinsic differences between high-order interactions and pairwise interactions in the empirical system. Furthermore, we perform simulations to show how robust our theoretical results are beyond fast rewiring. Our work provides a game route for opinion dynamics and sheds a hidden connection between opinion formation on dynamical high-order interactions and multi-player games.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 8","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144764645","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":"The Calderón problem for the logarithmic Schrödinger equation","authors":"Bastian Harrach ,&nbsp;Yi-Hsuan Lin ,&nbsp;Tobias Weth","doi":"10.1016/j.jde.2025.113665","DOIUrl":"10.1016/j.jde.2025.113665","url":null,"abstract":"<div><div>We investigate the Calderón problem for a logarithmic Schrödinger-type operator of the form <figure><img></figure>, where <figure><img></figure> denotes the logarithmic Laplacian—formally defined as the derivative <span><math><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>s</mi></mrow></mfrac><msub><mrow><mo>|</mo></mrow><mrow><mi>s</mi><mo>=</mo><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>s</mi></mrow></msup></math></span> of the fractional Laplacian family. This operator exhibits striking nonlocal properties, including unique continuation and a Runge approximation property. Leveraging these tools, we establish uniqueness in the recovery of bounded potentials from the Dirichlet-to-Neumann map. Furthermore, we derive a constructive uniqueness result using the monotonicity method. Our results are valid in arbitrary spatial dimensions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113665"},"PeriodicalIF":2.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748963","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}