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An unstructured algorithm for the singular value decomposition of biquaternion matrices 双四元数矩阵奇异值分解的非结构化算法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-21 DOI: 10.1016/j.aml.2024.109436
Gang Wang
{"title":"An unstructured algorithm for the singular value decomposition of biquaternion matrices","authors":"Gang Wang","doi":"10.1016/j.aml.2024.109436","DOIUrl":"10.1016/j.aml.2024.109436","url":null,"abstract":"<div><div>With the modeling of the biquaternion algebra in multidimensional signal processing, it has become possible to address issues such as data separation, denoising, and anomaly detection. This paper investigates the singular value decomposition of biquaternion matrices (SVDBQ), establishing an SVDBQ theorem that ensures unitary matrices formed by the left and right singular vectors, while also introducing a new form for singular values. Additionally, the non-uniqueness of SVDBQ is proven, expanding the theoretical framework of the biquaternion algebra. Building on this foundation, the paper presents a novel, fast, unstructured algorithm based on the isomorphic representation matrices of biquaternion matrices. Unlike existing methods, which are often complex and computationally expensive, the proposed algorithm is structurally simple and significantly faster, making it ideal for real-time signal processing. Numerical experiments validate the efficiency and effectiveness of this new algorithm, demonstrating its potential to advance both research and practical applications in signal processing.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109436"},"PeriodicalIF":2.9,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889256","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
Uniqueness of identifying multiple parameters in a time-fractional Cattaneo equation 时间分数型Cattaneo方程中辨识多参数的唯一性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-21 DOI: 10.1016/j.aml.2024.109438
Yun Zhang, Xiaoli Feng
{"title":"Uniqueness of identifying multiple parameters in a time-fractional Cattaneo equation","authors":"Yun Zhang,&nbsp;Xiaoli Feng","doi":"10.1016/j.aml.2024.109438","DOIUrl":"10.1016/j.aml.2024.109438","url":null,"abstract":"<div><div>This paper addresses an inverse problem involving the simultaneous identification of the fractional order, potential coefficient, initial value and source term in a time-fractional Cattaneo equation. Utilizing the method of Laplace transformation, we demonstrate that the multiple unknowns can be uniquely determined from observational data collected at two boundary points.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109438"},"PeriodicalIF":2.9,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889362","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
On trapped lee waves with centripetal forces 利用向心力研究被困背风波
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-20 DOI: 10.1016/j.aml.2024.109435
Tao Li, JinRong Wang
{"title":"On trapped lee waves with centripetal forces","authors":"Tao Li,&nbsp;JinRong Wang","doi":"10.1016/j.aml.2024.109435","DOIUrl":"10.1016/j.aml.2024.109435","url":null,"abstract":"<div><div>This paper firstly studies exact solutions to the atmospheric equations of motion in the <span><math><mi>f</mi></math></span>-plane and <span><math><mi>β</mi></math></span>-plane approximations while considering centripetal forces. The obtained solutions are shown in Lagrangian coordinates. Additionally, we derive the dispersion relations and perform a qualitative analysis of density, pressure, and vorticity.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109435"},"PeriodicalIF":2.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889363","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
Lyapunov functions for some epidemic model with high risk and vaccinated class 一类具有高风险和接种类的传染病模型的Lyapunov函数
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-19 DOI: 10.1016/j.aml.2024.109437
Ran Zhang, Xue Ren
{"title":"Lyapunov functions for some epidemic model with high risk and vaccinated class","authors":"Ran Zhang,&nbsp;Xue Ren","doi":"10.1016/j.aml.2024.109437","DOIUrl":"10.1016/j.aml.2024.109437","url":null,"abstract":"<div><div>This paper considers the global asymptotic stability of a model with epidemic model with high risk and vaccinated class, and extends the related methods to two case of reaction–diffusion equations. The results presented here generalize those from Movahedi (2024).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109437"},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889364","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
Stability and Turing bifurcation in a non-local reaction–diffusion equation with a top-hat kernel 一类具有顶帽核的非局部反应扩散方程的稳定性和图灵分岔
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-19 DOI: 10.1016/j.aml.2024.109433
Ying Li, Yongli Song
{"title":"Stability and Turing bifurcation in a non-local reaction–diffusion equation with a top-hat kernel","authors":"Ying Li,&nbsp;Yongli Song","doi":"10.1016/j.aml.2024.109433","DOIUrl":"10.1016/j.aml.2024.109433","url":null,"abstract":"<div><div>In the non-local reaction–diffusion equation, the form of the kernel function has an important effect on the dynamics of the equation. In this paper, we study the spatiotemporal dynamics of a class of non-local reaction–diffusion equation where the non-locality is described by the top-hat function with the perceptual radius. The perceptual radius establishes a bridge between the local equation and global equation. It has been shown that the perceptual radius can destabilize the constant steady state via Turing bifurcation and the critical bifurcation value is theoretically determined.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109433"},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889365","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
Lattice Boltzmann method for surface quasi-geostrophic equations with fractional Laplacian 带分数阶拉普拉斯的曲面拟地转方程的点阵Boltzmann方法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-19 DOI: 10.1016/j.aml.2024.109434
Haoyuan Gong , Tongtong Zhou , Baochang Shi , Rui Du
{"title":"Lattice Boltzmann method for surface quasi-geostrophic equations with fractional Laplacian","authors":"Haoyuan Gong ,&nbsp;Tongtong Zhou ,&nbsp;Baochang Shi ,&nbsp;Rui Du","doi":"10.1016/j.aml.2024.109434","DOIUrl":"10.1016/j.aml.2024.109434","url":null,"abstract":"<div><div>The surface quasi-geostrophic equations with fractional Laplacian are important in the field of oceanic and atmospheric dynamics. In this paper, a new lattice Boltzmann model is proposed to solve the equations. We first obtain an approximation of the governing equation based on the Fourier transform and Gaussian quadrature formula. An LBGK model with a suitable equilibrium distribution function is then developed for the problem. Through Chapman–Enskog expansion, the approximated macroscopic equations can be recovered from the lattice Boltzmann model. Numerical simulations are carried out to verify the numerical accuracy and efficiency.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109434"},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929323","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
Global attractor for an age-structured HIV model with nonlinear incidence rate 具有非线性发病率的年龄结构HIV模型的全局吸引子
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-18 DOI: 10.1016/j.aml.2024.109428
Ru Meng , Tingting Zheng , Yantao Luo , Zhidong Teng
{"title":"Global attractor for an age-structured HIV model with nonlinear incidence rate","authors":"Ru Meng ,&nbsp;Tingting Zheng ,&nbsp;Yantao Luo ,&nbsp;Zhidong Teng","doi":"10.1016/j.aml.2024.109428","DOIUrl":"10.1016/j.aml.2024.109428","url":null,"abstract":"<div><div>Using the method of characteristics and defining one auxiliary function, we prove the existence of global attractor for a general age-structured HIV model, which can be used to solve the uniformly persistence problem in the Kumar and Abbas (2022).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109428"},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874398","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
Normalized solutions to HLS lower critical Choquard equation with inverse-power potential and square-root-type nonlinearity 具有反幂势和平方根型非线性的HLS下临界Choquard方程的归一化解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-18 DOI: 10.1016/j.aml.2024.109430
Jianlun Liu , Hong-Rui Sun , Ziheng Zhang
{"title":"Normalized solutions to HLS lower critical Choquard equation with inverse-power potential and square-root-type nonlinearity","authors":"Jianlun Liu ,&nbsp;Hong-Rui Sun ,&nbsp;Ziheng Zhang","doi":"10.1016/j.aml.2024.109430","DOIUrl":"10.1016/j.aml.2024.109430","url":null,"abstract":"<div><div>This paper is concerned with the HLS lower critical Choquard equation with inverse-power potential and square-root-type nonlinearity. After giving a novel proof of subadditivity of the constraint minimizing problem and establishing the Brézis–Lieb lemma for square-root-type nonlinearity, we not only prove the existence of normalized solutions but also give its energy estimate.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109430"},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874397","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 new structure-preserving method for dual quaternion Hermitian eigenvalue problems 对偶四元数厄密特征值问题的一种新的保结构方法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-18 DOI: 10.1016/j.aml.2024.109432
Wenxv Ding , Ying Li , Musheng Wei
{"title":"A new structure-preserving method for dual quaternion Hermitian eigenvalue problems","authors":"Wenxv Ding ,&nbsp;Ying Li ,&nbsp;Musheng Wei","doi":"10.1016/j.aml.2024.109432","DOIUrl":"10.1016/j.aml.2024.109432","url":null,"abstract":"<div><div>Dual quaternion matrix decompositions have played a crucial role in fields such as formation control and image processing in recent years. In this paper, we present an eigenvalue decomposition algorithm for dual quaternion Hermitian matrices. The proposed algorithm is founded on the structure-preserving tridiagonalization of the dual matrix representation of dual quaternion Hermitian matrices through the application of orthogonal matrices. Owing to the utilization of orthogonal transformations, the algorithm exhibits numerical stability. Numerical experiments are provided to illustrate the efficiency of the structure-preserving algorithm.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109432"},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889377","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
Infinitely many positive periodic solutions for second order functional differential equations 二阶泛函微分方程的无穷多正周期解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-12-18 DOI: 10.1016/j.aml.2024.109431
Weibing Wang, Shen Luo
{"title":"Infinitely many positive periodic solutions for second order functional differential equations","authors":"Weibing Wang,&nbsp;Shen Luo","doi":"10.1016/j.aml.2024.109431","DOIUrl":"10.1016/j.aml.2024.109431","url":null,"abstract":"<div><div>In this paper, we study the existence of infinitely many positive periodic solutions to a class of second order functional differential equations which cannot be applied directly to the fixed point theorem in cone. With suitable deformations, we construct the operator whose fixed point is closely related to the periodic solution of the original equation and show that the problem has infinitely many positive periodic solutions under appropriate conditions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109431"},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874326","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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