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Asymptotic distribution of the final size of a stochastic SIR epidemic on heterogeneous networks 异构网络上随机 SIR 流行病最终规模的渐近分布
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-26 DOI: 10.1016/j.aml.2024.109317
Xiaojie Jing , Guirong Liu , Zhen Jin
{"title":"Asymptotic distribution of the final size of a stochastic SIR epidemic on heterogeneous networks","authors":"Xiaojie Jing ,&nbsp;Guirong Liu ,&nbsp;Zhen Jin","doi":"10.1016/j.aml.2024.109317","DOIUrl":"10.1016/j.aml.2024.109317","url":null,"abstract":"<div><div>In this paper, a Markovian SIR model on a heterogeneous network is considered. The law of large numbers and the central limit theorem of the epidemic process in a large population are provided. Further, the asymptotic distribution of the final size is given. Finally, by numerical and stochastic simulations, it is clear to show that our method performs well in approximation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109317"},"PeriodicalIF":2.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142329710","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}
引用次数: 0
T-product based ℓ1-norm tensor principal component analysis and a finite-step convergence algorithm 基于 T 产物的 ℓ1 准则张量主成分分析和有限步收敛算法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-26 DOI: 10.1016/j.aml.2024.109318
Xianpeng Mao , Yuning Yang
{"title":"T-product based ℓ1-norm tensor principal component analysis and a finite-step convergence algorithm","authors":"Xianpeng Mao ,&nbsp;Yuning Yang","doi":"10.1016/j.aml.2024.109318","DOIUrl":"10.1016/j.aml.2024.109318","url":null,"abstract":"<div><div>T-product based tensor principal component analysis (<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-tPCA) was used for dimensionality reduction, data preprocessing, compression, and visualization of multivariate data. However, <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-tPCA may amplify the influence of outliers and large-magnitude noise. To explore robustness against heavily corrupted third-order data, we consider the <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-norm tPCA model (<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-tPCA). We develop an effective proximal alternating maximization method and prove that within finitely many steps, the algorithm stops at a point satisfying certain optimality conditions. Numerical experiments on color face reconstruction and recognition demonstrate the efficiency of the proposed algorithms, confirming that <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-tPCA is more resilient to outliers compared to <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-tPCA.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109318"},"PeriodicalIF":2.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327558","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}
引用次数: 0
A modified multi-directional iterative mirroring method for SH waves propagation in rectangular sealed plate with a circular surface crack 带圆形表面裂纹的矩形密封板中 SH 波传播的改进型多方向迭代镜像法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-26 DOI: 10.1016/j.aml.2024.109321
Zhiyu Fan, Hui Qi, Jing Guo
{"title":"A modified multi-directional iterative mirroring method for SH waves propagation in rectangular sealed plate with a circular surface crack","authors":"Zhiyu Fan,&nbsp;Hui Qi,&nbsp;Jing Guo","doi":"10.1016/j.aml.2024.109321","DOIUrl":"10.1016/j.aml.2024.109321","url":null,"abstract":"<div><div>This study proposes an exact analytical approach for investigating the steady-state and transient wave dynamic propagation characteristics in frequency and time domain of rectangular sealed plate with a circular surface crack under anti-plane point source wave dynamic load. By introducing revised factor, a modified multi-directional iterative mirroring method is proposed to address the partial differential governing equations of wave propagation with boundary value conditions. Based on wave function expansion method, the scattering wave function is derived after decoupling the governing equation. Fourier integral expansion method is used to solve the infinite linear algebraic boundary equation composed of boundary value conditions. The accuracy of analytical method is verified by numerical calculation and finite element simulation. The results show that the sealed coupled waves have significant effects on dynamic stress concentration and abrupt displacement change.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109321"},"PeriodicalIF":2.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428466","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}
引用次数: 0
N-periodic wave solutions of the N=2 supersymmetric KdV equation N=2超对称KdV方程的N周期波解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-23 DOI: 10.1016/j.aml.2024.109313
Zhaohua Li, Zhonglong Zhao
{"title":"N-periodic wave solutions of the N=2 supersymmetric KdV equation","authors":"Zhaohua Li,&nbsp;Zhonglong Zhao","doi":"10.1016/j.aml.2024.109313","DOIUrl":"10.1016/j.aml.2024.109313","url":null,"abstract":"<div><div>In this paper, the <span><math><mi>N</mi></math></span>-periodic wave solutions of the <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math></span> supersymmetric KdV equation are studied by combining the super Hirota bilinear form with the super Riemann-theta function, which can be used to describe new phenomena on super quasi-periodic waves with the fermionic field. With the aid of the Gauss–Newton method, the three-periodic and four-periodic wave solutions are obtained. In particular, these quasi-periodic waves can produce parallel, crossed and degenerated patterns. The analytical method related to the characteristic lines is used to analyze the dynamic characteristics of the three-periodic and four-periodic waves. In addition, it has been indicated that <span><math><mi>N</mi></math></span>-periodic waves can exist in the supersymmetric integrable systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109313"},"PeriodicalIF":2.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322453","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}
引用次数: 0
A high-order energy stable method for the MBE models with slope selection by using Lagrange multiplier approach 利用拉格朗日乘法器方法为具有斜率选择功能的 MBE 模型提供高阶能量稳定方法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-23 DOI: 10.1016/j.aml.2024.109316
Nan Wang, Binbin Jiang, Meng Li
{"title":"A high-order energy stable method for the MBE models with slope selection by using Lagrange multiplier approach","authors":"Nan Wang,&nbsp;Binbin Jiang,&nbsp;Meng Li","doi":"10.1016/j.aml.2024.109316","DOIUrl":"10.1016/j.aml.2024.109316","url":null,"abstract":"<div><div>In this work, we develop high-order convex splitting implicit–explicit Runge–Kutta methods for Molecular Beam Epitaxy (MBE) model with slope selection, which plays key roles in materials science and physics for describing various phenomena, such as phase transitions, interactions and interfacial dynamics. Since the epitaxy surface height evolution equation is viewed as a dynamical form of a <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-gradient flow, MBE has the highly similar growing processes as the growing facets in phase-ordering process in magnetic systems. Within this context, we focus our attention on the systems with multiple components possess greater physical significance than their classical (single-component) counterparts. We rigorously prove that the proposed schemes both preserve the energy dissipation and mass conservation. Finally, the accuracy and efficiency of proposed schemes are demonstrated by some numerical experiments.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109316"},"PeriodicalIF":2.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142320207","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}
引用次数: 0
Modelling collective invasion with reaction–diffusion equations: When does domain curvature matter? 用反应扩散方程模拟集体入侵：域曲率何时重要？
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-21 DOI: 10.1016/j.aml.2024.109315
J.J. Pollacco , R.E. Baker , P.K. Maini
{"title":"Modelling collective invasion with reaction–diffusion equations: When does domain curvature matter?","authors":"J.J. Pollacco ,&nbsp;R.E. Baker ,&nbsp;P.K. Maini","doi":"10.1016/j.aml.2024.109315","DOIUrl":"10.1016/j.aml.2024.109315","url":null,"abstract":"<div><div>Real-world cellular invasion processes often take place in curved geometries. Such problems are frequently simplified in models to neglect the curved geometry in favour of computational simplicity, yet doing so risks inaccuracies in any model-based predictions. To quantify the conditions under which neglecting a curved geometry is justifiable, we explore the dynamics of a system of reaction–diffusion equations (RDEs) on a two-dimensional annular geometry analytically. Defining <span><math><mi>ϵ</mi></math></span> as the ratio of the annulus thickness <span><math><mi>δ</mi></math></span> and radius <span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> we derive, through an asymptotic expansion, the conditions under which it is appropriate to ignore the domain curvature for a general system of reaction–diffusion equations. To highlight the consequences of these results, we simulate solutions to the Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) model, a paradigm nonlinear RDE typically used to model spatial invasion, on an annular geometry. Thus, we quantify the size of the deviation from an analogous simulation on the rectangle, and how this deviation changes across the width of the annulus. We further characterise the nature of the solutions through numerical simulations for different values of <span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><mi>δ</mi></math></span>. Our results provide insight into when it is appropriate to neglect the domain curvature in studying travelling wave behaviour in RDEs.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109315"},"PeriodicalIF":2.9,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357970","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}
引用次数: 0
Operator splitting for coupled linear port-Hamiltonian systems 耦合线性端口-哈密尔顿系统的算子拆分
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-19 DOI: 10.1016/j.aml.2024.109309
Jan Lorenz, Tom Zwerschke, Michael Günther, Kevin Schäfers
{"title":"Operator splitting for coupled linear port-Hamiltonian systems","authors":"Jan Lorenz,&nbsp;Tom Zwerschke,&nbsp;Michael Günther,&nbsp;Kevin Schäfers","doi":"10.1016/j.aml.2024.109309","DOIUrl":"10.1016/j.aml.2024.109309","url":null,"abstract":"<div><p>Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms preserve the dissipative structure of the overall system and are convergent of second order. Numerical results for coupled mass–spring–damper chains illustrate the computational efficiency of the splitting methods compared to a straight-forward application of the implicit midpoint rule to the overall system.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109309"},"PeriodicalIF":2.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S089396592400329X/pdfft?md5=461caa9d621b164ff71cc86835d28bc7&pid=1-s2.0-S089396592400329X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142270639","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}
引用次数: 0
The exploding solitons of the sine–Gordon equation 正弦-戈登方程的爆炸孤子
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-19 DOI: 10.1016/j.aml.2024.109314
Shuzhi Liu , Deqin Qiu
{"title":"The exploding solitons of the sine–Gordon equation","authors":"Shuzhi Liu ,&nbsp;Deqin Qiu","doi":"10.1016/j.aml.2024.109314","DOIUrl":"10.1016/j.aml.2024.109314","url":null,"abstract":"<div><div>In this paper, the hodograph equivalent short pulse (HESP) equations are investigated via the Darboux transformation, we derive the soliton and positon solutions from the “seed” solutions, and then, the decomposition of the lower-order positons into single-solitons is given analytically when time <span><math><mi>T</mi></math></span> is sufficiently large. As a notable new result, we obtain the exploding soliton and positon solutions of the sine–Gordon (SG) equation from the hodograph equivalent short pulse equations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109314"},"PeriodicalIF":2.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311154","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}
引用次数: 0
Threshold dynamics of a degenerated diffusive incubation period host–pathogen model with saturation incidence rate 具有饱和发病率的退化扩散潜伏期宿主-病原体模型的阈值动力学
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-16 DOI: 10.1016/j.aml.2024.109312
Wenjie Li , Liuan Yang , Jinde Cao
{"title":"Threshold dynamics of a degenerated diffusive incubation period host–pathogen model with saturation incidence rate","authors":"Wenjie Li ,&nbsp;Liuan Yang ,&nbsp;Jinde Cao","doi":"10.1016/j.aml.2024.109312","DOIUrl":"10.1016/j.aml.2024.109312","url":null,"abstract":"<div><p>In this paper, we consider an incubation period host–pathogen system with degenerated diffusion. The global compact attractor of the solution of the model is investigated using the <span><math><mi>κ</mi></math></span>-contraction method. Furthermore, the basic reproduction number is defined, and we discuss the dynamic analysis of a degenerated diffusion model. The obtained theoretical results are nontrivial and can be considered a continuation of the work by Wang et al. in 2022.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109312"},"PeriodicalIF":2.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142243781","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}
引用次数: 0
In a river or an ocean: Similarity-reduction work on a (3+1)-dimensional extended shallow water wave equation 在河流或海洋中： (3+1)- 维扩展浅水波方程的相似性还原工作
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-09-13 DOI: 10.1016/j.aml.2024.109310
Xiao-Tian Gao, Bo Tian
{"title":"In a river or an ocean: Similarity-reduction work on a (3+1)-dimensional extended shallow water wave equation","authors":"Xiao-Tian Gao,&nbsp;Bo Tian","doi":"10.1016/j.aml.2024.109310","DOIUrl":"10.1016/j.aml.2024.109310","url":null,"abstract":"<div><div>Researchers have recently become interested in a (3+1)-dimensional extended shallow water wave equation in a river or an ocean. This equation could be used to represent a variety of the physical phenomena that have some impacts on the environment, such as the floods and tsunamis. Two sets of the similarity reductions are discovered for that equation based on the variable coefficients, connected with the potential applications of the equation in a river or an ocean.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109310"},"PeriodicalIF":2.9,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315954","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}
引用次数: 0
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