Applied Mathematics and Computation最新文献

{"title":"The numerical solution of epidemic models on moving domains using combined masses","authors":"Katerina Christou","doi":"10.1016/j.amc.2025.129691","DOIUrl":"10.1016/j.amc.2025.129691","url":null,"abstract":"<div><div>The application of a moving mesh finite difference method, based on mass conservation, is described for epidemic models, integrating cross- and self-diffusion to represent social distancing and self-isolation. A significant feature of the models is the moving boundary which describes the spread of the disease in the domain. Numerical illustrations emphasise the influence of social interactions on transmission and infection rates. Notably, simulations show containment of disease spread within a small initial infected radius despite a high reproductive parameter. The results affirm the efficacy of the moving mesh approach for multi-population systems in epidemic models.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"509 ","pages":"Article 129691"},"PeriodicalIF":3.4,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144916382","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":"Super edge-connectivity of transitive hypergraphs","authors":"Shuang Zhao,&nbsp;Xiaomin Hu,&nbsp;Weihua Yang","doi":"10.1016/j.amc.2025.129698","DOIUrl":"10.1016/j.amc.2025.129698","url":null,"abstract":"<div><div>The properties of fragments and superatoms, first arose in the work of Mader et al., have turned out to be powerful tools in the study of graph connectivity. We generalize the concept of an edge fragment and an edge superatom to hypergraphs and reveal that these generalizations share features with the common concepts. As applications of these properties, we investigate the super edge-connectivity of uniform linear vertex transitive hypergraphs, uniform linear <span><math><mi>t</mi></math></span>-Cayley hypergraphs and linear edge transitive hypergraphs, and derive the main result of Burgess et al. [J. Graph Theory, 105(2024)252–259] as a corollary.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"509 ","pages":"Article 129698"},"PeriodicalIF":3.4,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144916381","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":"Šoltés problem for the Kirchhoff index of a graph","authors":"Kurt Klement Gottwald ,&nbsp;Snježana Majstorović Ergotić ,&nbsp;Tomislav Došlić","doi":"10.1016/j.amc.2025.129694","DOIUrl":"10.1016/j.amc.2025.129694","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The Kirchhoff index &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; of a connected graph &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is defined as the sum of resistance distances between all pairs of vertices in &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. We say that &lt;span&gt;&lt;math&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;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is a &lt;em&gt;good vertex&lt;/em&gt; if the Kirchhoff index remains unchanged when &lt;span&gt;&lt;math&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is removed, i.e. &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&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;/math&gt;&lt;/span&gt;. In 1991, Šoltés studied the Wiener index of a graph and posed the problem of identifying graphs for which the removal of an arbitrary vertex preserves the Wiener index. In this paper, we explore a similar concept: identifying &lt;em&gt;Kirchhoff Šoltés graphs&lt;/em&gt;, i.e. graphs in which all vertices are good vertices. We show that the cycle &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a Kirchhoff Šoltés graph. Due to the challenge of finding more examples of such graphs, we shift our focus to several relaxed versions of the Kirchhoff Šoltés problem, where the primary objective is to identify graphs containing at least one good vertex. One of them is the &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-&lt;em&gt;Kirchhoff Šoltés problem&lt;/em&gt;, which seeks to find an infinite family of graphs in which the proportion of good vertices is at least &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&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;/mrow&gt;&lt;/math&gt;&lt;/span&gt; being a specified rational number. Another one involves constructing infinite families of graphs where the proportion of good vertices increases and asymptotically approaches a given real number &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&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;/mrow&gt;&lt;/math&gt;&lt;/span&gt; as the order of the graph grows. We demonstrate that both relaxed versions have infinitely many solutions. In particular, we prove the existence of infinitely many graphs for which the proportion &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of good vertices, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; tends to a certain irrational number. Furthermore, we prove the existence of infinitely many graphs with half good vertices, and for each &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, we construct an infinite family of graphs whose proportion of good vertices tends to &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;. These findings could be pivotal in addressing the original problem of determining whether there are additional solutions beyond &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/msub&gt;&lt;","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129694"},"PeriodicalIF":3.4,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911788","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":"Enumerating the number of k-matchings in successively amalgamated graphs","authors":"Simon Grad ,&nbsp;Sandi Klavžar","doi":"10.1016/j.amc.2025.129703","DOIUrl":"10.1016/j.amc.2025.129703","url":null,"abstract":"<div><div>In this paper, the transfer matrix technique using the <span><math><mi>k</mi></math></span>-matching vector is developed to compute the number of <span><math><mi>k</mi></math></span>-matchings in an arbitrary graph which can be constructed by successive amalgamations over sets of cardinality two. This widely extends known methods from the literature developed for computing the number of <span><math><mi>k</mi></math></span>-matchings in benzenoid chains, octagonal chains, cyclooctatetraene chains, and arbitrary cyclic chains. Two examples demonstrating how the present method can be applied are given, one of them being an elaborated chemical example.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129703"},"PeriodicalIF":3.4,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911889","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":"Convergence of a positivity preserving logarithmic truncated EM method for SDEs with discontinuous drift coefficients","authors":"Amir Haghighi","doi":"10.1016/j.amc.2025.129704","DOIUrl":"10.1016/j.amc.2025.129704","url":null,"abstract":"<div><div>In this paper, a class of nonlinear stochastic differential equations with positive solutions and discontinuous drift coefficients is studied, considering both theoretical and computational aspects. The theoretical results focus on the existence of a unique positive solution for such SDEs via the approach introduced by Müller-Gronbach et al. (2022), and the computational aspect utilises the truncated Euler-Maruyama method proposed by Li et al. (2023) together with a logarithmic transformation that ensures a positive approximation to the original solution. The convergence of the numerical method is investigated, and the boundedness of the <span><math><mi>p</mi></math></span>-th moment is obtained. Finally, the proposed method is used to verify the convergence with the help of some numerical examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129704"},"PeriodicalIF":3.4,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917262","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 C++ implementation of the discrete adjoint sensitivity analysis method for explicit adaptive Runge-Kutta methods enabled by automatic adjoint differentiation and SIMD vectorization","authors":"Rui Martins,&nbsp;Evgeny Lakshtanov","doi":"10.1016/j.amc.2025.129699","DOIUrl":"10.1016/j.amc.2025.129699","url":null,"abstract":"<div><div>A C++ library for sensitivity analysis of optimisation problems involving ordinary differential equations (ODEs) enabled by automatic differentiation (AD) and SIMD (Single Instruction, Multiple data) vectorization is presented. The discrete adjoint sensitivity analysis method is implemented for adaptive explicit Runge-Kutta (ERK) methods. Automatic adjoint differentiation (AAD) is employed for efficient evaluations of products of vectors and the Jacobian matrix of the right hand side of the ODE system. This approach avoids the low-level drawbacks of the black box approach of employing AAD on the entire ODE solver and opens the possibility to leverage parallelization. SIMD vectorization is employed to compute the vector-Jacobian products concurrently. We study the performance of other methods and implementations of sensitivity analysis and we find that our algorithm presents a small advantage compared to equivalent existing software.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129699"},"PeriodicalIF":3.4,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911890","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":"An equitable partition based construction of graphs with the same spectral radius","authors":"Milica Anđelić ,&nbsp;Carlos M. da Fonseca ,&nbsp;Zoran Stanić","doi":"10.1016/j.amc.2025.129696","DOIUrl":"10.1016/j.amc.2025.129696","url":null,"abstract":"<div><div>An equitable partition of a graph is a remarkable tool that provides valuable spectral information. Among other properties, it is known that the spectral radius of the divisor matrix of any equitable partition equals the spectral radius of the graph. Recently, several methods for construction of families of graphs with the same spectral radius emerged in the literature. In this paper, we develop a unified approach to cyclic-graph constructions by formulating a general method for generating families of connected graphs with a common spectral radius, grounded in the theory of equitable partitions.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129696"},"PeriodicalIF":3.4,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903121","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":"Dynamics of two-strain disease transmission with negative vaccine information and vaccination on multiplex networks","authors":"Lun Liu ,&nbsp;Shaorui Geng ,&nbsp;Lilin Wei ,&nbsp;Zhenyong Lu ,&nbsp;Yinghong Ma","doi":"10.1016/j.amc.2025.129701","DOIUrl":"10.1016/j.amc.2025.129701","url":null,"abstract":"<div><div>During the disease transmission, the virus may mutate and novel strains appear. That causes the reduction of the immune effect of the vaccine against the original strain, and the vaccinated individuals may also be infected, which would lead to the generation and dissemination of negative vaccine information. However, the coupled dynamics of multi-strain disease and negative vaccine information has not yet been comprehensively investigated. In this paper, we consider both the original and mutant strains of the disease and introduce vaccination behavior in the propagation process to expand the classic susceptible-infectious-susceptible (SIS) model into five states: susceptible, vaccinated, infected by original strain, infected by mutant strain and recovered. Then, a two-layer network model is proposed to describe the coupled propagation dynamics of the negative vaccine information and the two-strain disease, and the epidemic outbreak thresholds of the two-strain disease are derived by using the Microscopic Markov Chain Approach (MMCA). Subsequently, the numerical results derived from the MMCA are compared with those from Monte-Carlo (MC) simulation to validate the correctness of the former. Finally, the phase diagrams and time history curves are presented to conduct parametric studies on the epidemic thresholds and information-disease transmission dynamics, such as the vaccination cost, vaccine effectiveness and the negative vaccine information. This research demonstrates that reducing the vaccination cost and enhancing the positive publicity of vaccine can effectively prevent the disease spreading when the infection rate of the mutant strain is low. If this infection rate is large, the effective measure is developing specific vaccines against the mutant strain to improve the vaccination efficacy. Those findings provide valuable strategies for the authorities to make appropriate disease prevention measures.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129701"},"PeriodicalIF":3.4,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893270","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":"Secure observer-driven synchronization for complex networks constrained by partial information exchange and limited communication bandwidth","authors":"Yan Li ,&nbsp;Qirun Hang ,&nbsp;Lijuan Zha ,&nbsp;Jinliang Liu","doi":"10.1016/j.amc.2025.129693","DOIUrl":"10.1016/j.amc.2025.129693","url":null,"abstract":"<div><div>This paper addresses the observer-driven secure synchronization control issue for partial information-based complex networks (CNs) subject to bandwidth constraints. Firstly, given that the complete data transmission between CN nodes can not be always realized in practice, the system model of CNs with partial information exchange is specifically introduced. Then, considering the limitation of communication bandwidth, weighted try-once-discard (WTOD) protocol is utilized to enhance the signal transmission efficiency within each node. The delivery of the data adhered to WTOD protocol is further assumed to be compromised by false-data-injection (FDI) attack, which is a well-recognized risk in communication networks. Afterward, distributed secure observer-based synchronization controllers are designed accordingly. Based on defining the observation and synchronization errors, an augmented system model is then established, and the gain matrices for observers and controllers are obtained through an analysis of the stability conditions of the augmented system. Lastly, a numerical example is provided to validate the proposed method’s effectiveness.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129693"},"PeriodicalIF":3.4,"publicationDate":"2025-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893271","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":"Causal state feedback representation for infinite horizon LQ problems of fractional systems","authors":"Jianping Huang ,&nbsp;Huacheng Zhou","doi":"10.1016/j.amc.2025.129692","DOIUrl":"10.1016/j.amc.2025.129692","url":null,"abstract":"<div><div>In this paper, we consider the feedback representation problem of the optimal control for infinite horizon linear quadratic optimal control problems of fractional systems. By employing the characterization of the optimal control pair and a family of projection operators, we derive the causal state feedback representations which depend only on the history value of the state and does not rely on further state value. Finally, two illustrative examples are included.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129692"},"PeriodicalIF":3.4,"publicationDate":"2025-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893272","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}