数学最新文献

{"title":"Effect of higher-order nonlinearities and dispersions on modulation instability in semiconductor quantum dots","authors":"Nitu Borgohain ,&nbsp;Abhijit Shyam ,&nbsp;Rohit Mukherjee ,&nbsp;Naga Lakshmi Meghana Akula ,&nbsp;Rohit Hazra","doi":"10.1016/j.chaos.2025.116902","DOIUrl":"10.1016/j.chaos.2025.116902","url":null,"abstract":"<div><div>This article presents the theoretical investigation of modulation instability (MI) in a one-dimensional waveguide structure embedded in a lower-index material, featuring a high-density array of InAs cone-shaped quantum dots within bulk GaAs. The system operates under electromagnetically induced transparency (EIT) conditions, wherein a weak probe field and a strong control field interact within a three-level ladder-type semiconductor quantum dot (SQD) system. Giant Kerr, quintic, and septic nonlinearities of the order <span><math><mo>~</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>11</mn></mrow></msup><msup><mi>m</mi><mn>2</mn></msup><mo>/</mo><msup><mi>V</mi><mn>2</mn></msup></math></span>, <span><math><mo>~</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>22</mn></mrow></msup><msup><mi>m</mi><mn>4</mn></msup><mo>/</mo><msup><mi>V</mi><mn>4</mn></msup></math></span> and <span><math><mo>~</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>32</mn></mrow></msup><msup><mi>m</mi><mn>6</mn></msup><mo>/</mo><msup><mi>V</mi><mn>6</mn></msup></math></span> respectively, are identified in the SQD system that exhibit strong tunability under the effect of control field parameters. These giant nonlinearities are employed to control the MI of the probe pulse. The MI gain enhances linearly with input power, when only Kerr nonlinearity is present, while quintic and septic nonlinearities contributes to the stabilization of MI towards the higher power levels. The higher-order dispersions further contribute to the reduction in the MI spectral bandwidth, enabling enhancement of the stability of the probe field against MI. These findings highlight the potential of SQD-based optical devices for controlled nonlinear optical applications and signal modulation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116902"},"PeriodicalIF":5.3,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702876","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":"Solving the second kind Volterra-Fredholm type of two-dimensional integral equations on non-rectangular domains via radial basis functions","authors":"Mohsen Jalalian ,&nbsp;Manochehr Kazemi ,&nbsp;Mohammad Esmael Samei","doi":"10.1016/j.camwa.2025.07.027","DOIUrl":"10.1016/j.camwa.2025.07.027","url":null,"abstract":"<div><div>This research, introduces a method to solve two-dimensional nonlinear Volterra-Fredholm integral equations with non-rectangular domains, numerically, based on radial basis functions. The method doesn't need a background mesh or cell structure in the domain. In the approach, all of the integrals are estimated using Gauss-Legendre quadrature formula. Error analysis and the rate of convergence of this method are also investigated. Numerical examples are included to demonstrate the validity and efficiency of this method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 265-279"},"PeriodicalIF":2.9,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703833","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":"Minimum embedded-link-cut split k-ary n-cubes","authors":"Yuxing Yang,&nbsp;Kaiyue Meng","doi":"10.1016/j.dam.2025.07.031","DOIUrl":"10.1016/j.dam.2025.07.031","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Given two integers &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, a &lt;span&gt;&lt;math&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-&lt;em&gt;embedded-link-cut&lt;/em&gt; of an &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-dimensional recursive interconnection network &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a set of links whose removal separates &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and each node still lies in a &lt;span&gt;&lt;math&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-dimensional subnetwork &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; in the resulting network. A &lt;em&gt;minimum embedded-link-cut split&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the resultant network obtained by removing all the links in a minimum embedded-link-cut from &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. And &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is said to be &lt;em&gt;super&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;em&gt;-embedded link connected&lt;/em&gt; (super-&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;) if each minimum embedded-link-cut split &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; has exactly two components, one of which is isomorphic to &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. The &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-ary &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cube &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; is a leading interconnection network for the multiprocessor system, which takes the hypercube (i.e., the binary &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cube) as a special case. Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; be the number of nodes in &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;. In this paper, we provide an &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&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;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; algorithm to obtain a minimum &lt;span&gt;&lt;math&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-embedded-link-cut for &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-ary &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cubes with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; or odd &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;k&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;, and prove that both the binary &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cube with &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; and the ternary &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-cube with &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;/sp","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 210-215"},"PeriodicalIF":1.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703914","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":"An infinite family of normal 5-edge colorable superpositioned snarks","authors":"Wenjuan Zhou ,&nbsp;Rong-Xia Hao ,&nbsp;Rong Luo ,&nbsp;Yilun Luo","doi":"10.1016/j.dam.2025.07.032","DOIUrl":"10.1016/j.dam.2025.07.032","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi></math></span> be a cubic graph. For a proper edge coloring <span><math><mi>π</mi></math></span> of <span><math><mi>G</mi></math></span>, an edge <span><math><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> is normal if the number of colors of all edges incident to endvertices of <span><math><mi>e</mi></math></span> is 3 or 5. A normal <span><math><mi>k</mi></math></span>-edge coloring of <span><math><mi>G</mi></math></span> is a proper edge coloring with <span><math><mi>k</mi></math></span> colors such that each edge of <span><math><mi>G</mi></math></span> is normal. The normal chromatic index of <span><math><mi>G</mi></math></span>, denoted by <span><math><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>N</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, is the smallest integer <span><math><mi>k</mi></math></span> such that <span><math><mi>G</mi></math></span> admits a normal <span><math><mi>k</mi></math></span>-edge coloring. Jaeger conjectured that <span><math><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>N</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mn>5</mn></mrow></math></span> for every bridgeless cubic graph <span><math><mi>G</mi></math></span>, and he also proved that this conjecture is equivalent to the Petersen coloring conjecture. The normal 5-edge coloring conjecture has been verified for some families of snarks, such as, generalized Blanuša snarks, Goldberg snarks, flower snarks and Loupekhine snarks. Sedlar et al. proved that this conjecture holds for two families of superpositioned snarks. In this paper, we present a construction of superpositioned snarks whose normal chromatic indices equal to 5, which implies the normal 5-edge coloring conjecture for large families of snarks.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 259-269"},"PeriodicalIF":1.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703915","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":"Construction of bubbling solutions of the Brezis–Nirenberg problem in general bounded domains (I): The dimensions 4 and 5","authors":"Fengliu Li,&nbsp;Giusi Vaira,&nbsp;Juncheng Wei,&nbsp;Yuanze Wu","doi":"10.1112/jlms.70246","DOIUrl":"https://doi.org/10.1112/jlms.70246","url":null,"abstract":"<p>In this paper, we consider the Brezis–Nirenberg problem\u0000\u0000 </p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144705140","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":"A well-posedness theory for the MHD boundary layer equations in three space variables","authors":"Zhonger Wu","doi":"10.1016/j.jde.2025.113650","DOIUrl":"10.1016/j.jde.2025.113650","url":null,"abstract":"<div><div>We study the well-posedness theory for the MHD boundary layer equations in three space variables by energy method. The local-in-time existence and uniqueness of solutions for the MHD boundary layer equations are established under a special structural assumption. Moreover, we also show that this solution is linearly stable for any smooth three-dimensional perturbation.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"447 ","pages":"Article 113650"},"PeriodicalIF":2.4,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702384","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":"Hodge theory on the Harmonic Gasket and other fractals","authors":"Ugo Bessi","doi":"10.1016/j.na.2025.113892","DOIUrl":"10.1016/j.na.2025.113892","url":null,"abstract":"<div><div>S. Kusuoka has proven that, on many fractals <span><math><mrow><mi>G</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span>, it is possible to build a natural bilinear form on the vector space of Borel fields of one-forms on <span><math><mi>G</mi></math></span>. A variant of this construction yields a bilinear form on Borel fields of <span><math><mi>q</mi></math></span>-forms; it is tempting to ask (and several authors have done it) whether some features of Hodge theory survive in this setting. In this paper we define a weak version of the codifferential on fractals and we show that, for one-forms on the Harmonic Sierpinski Gasket, a Hodge decomposition theorem holds. As a further example, we calculate the codifferential of 2-forms and 1-forms on a fractal of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> which is the product of the harmonic Sierpinski gasket with the interval <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113892"},"PeriodicalIF":1.3,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702222","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":"Multi-scale dynamics of a singularly perturbed piecewise-smooth predator–prey model with weak predator interference","authors":"Xiao Wu,&nbsp;Mengyuan Shi,&nbsp;Feng Xie","doi":"10.1016/j.chaos.2025.116895","DOIUrl":"10.1016/j.chaos.2025.116895","url":null,"abstract":"<div><div>In this paper, we focus on the dynamics of a piecewise-smooth predator–prey model with weak predator interference. By non-dimensional transformation, the model can be rewritten as a regular-singular system with a regularly perturbed system for <span><math><mrow><mi>u</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span> and a singularly perturbed system for <span><math><mrow><mi>u</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. Based on the analysis, the regular-singular system has two saddle boundary equilibriums and at most three positive equilibriums. When the positive equilibrium with <span><math><mrow><mi>u</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span> is a stable focus, the system undergoes a saddle–node bifurcation and a boundary equilibrium bifurcation. Furthermore, as the parameters cross the bifurcation curves, the system has a small-amplitude hyperbolically unstable limit cycle, which is surrounded by a stable relaxation oscillation cycle, a homoclinic cycle and a heteroclinic cycle, respectively. Finally, we provide the phase portraits to illustrate our theoretical results.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116895"},"PeriodicalIF":5.3,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702867","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":"Hollow cylindrical droplets in a very strongly dipolar condensate","authors":"S.K. Adhikari","doi":"10.1016/j.chaos.2025.116887","DOIUrl":"10.1016/j.chaos.2025.116887","url":null,"abstract":"<div><div>A harmonically trapped Bose–Einstein condensate (BEC) leads to topologically trivial compact states. Because of the long-range nonlocal dipole–dipole interaction, a strongly dipolar BEC revealed many novel phenomena. Here we show that in a strongly dipolar BEC one can have a hollow cylindrical quasi-one-dimensional metastable droplet with ring topology while the system is trapped only in the <span><math><mi>x</mi></math></span>-<span><math><mi>y</mi></math></span> plane by a harmonic potential and a Gaussian hill potential at the center and untrapped along the polarization <span><math><mi>z</mi></math></span> axis. In this numerical investigation we use the imaginary-time propagation of a mean-field model where we include the Lee–Huang–Yang interaction, suitably modified for dipolar systems. Being metastable, these droplets are weakly stable and we use real-time propagation to investigate its dynamics and establish stability.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116887"},"PeriodicalIF":5.3,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702868","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 multi-graph spatio-temporal learning for citywide traffic flow prediction in transportation systems","authors":"Ahmad Ali,&nbsp;H.M. Yasir Naeem,&nbsp;Amin Sharafian,&nbsp;Li Qiu,&nbsp;Zongze Wu,&nbsp;Xiaoshan Bai","doi":"10.1016/j.chaos.2025.116898","DOIUrl":"10.1016/j.chaos.2025.116898","url":null,"abstract":"<div><div>The complexity and dynamic nature of urban traffic systems necessitate efficient resource management for accurate traffic flow forecasting, enabling real-time adaptation and optimized resource allocation. Recent advancements in multi-graph spatio-temporal graph neural networks (STGNN) have demonstrated their capability to capture spatio-temporal correlations at multiple scales, significantly improving prediction accuracy. However, a persistent challenge lies in effectively aggregating neighborhood information for node representation learning, particularly in scenarios with sparse connectivity. To address this limitation, we propose an Attention-based Dynamic Multi-Graph Module (ADMGM) for traffic prediction, integrating Federated Learning (FL) within a Multi-Access Edge Computing (MEC) architecture. Our approach incorporates an Adaptive Enhancement Module (AEM) deployed at the edge, pre-trained to process high-volume, heterogeneous data from IoT devices. The ADMGM model comprises four key components: closeness, daily, weekly, and an external branch, each contributing to a comprehensive spatio-temporal representation of traffic dynamics. The AEM leverages long-term historical data at each node, capturing inter-node dependencies to generate enriched feature representations while enhancing the model ability to generalize across diverse traffic patterns. Furthermore, we introduce a clustered feature correlation graph to uncover latent relationships within long-term time series data, thereby strengthening spatio-temporal modeling. Extensive experiments on the TaxiBJ and BikeNYC datasets demonstrate that our model significantly reduces prediction errors, achieving state-of-the-art performance in traffic forecasting.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116898"},"PeriodicalIF":5.3,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702871","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}