Pub Date : 2026-03-01Epub Date: 2025-11-24DOI: 10.1016/j.aml.2025.109829
Wenxv Ding
In recent years, dual quaternion matrix decompositions have become indispensable in applications such as formation control and color image processing. We propose a novel method for computing the eigenvalues and associated eigenvectors of a dual quaternion Hermitian matrix, leveraging its specific properties and structure in this paper. Numerical experiments demonstrate that the proposed algorithm achieves significant speedups compared to existing methods. Furthermore, a two-dimensional principal component analysis method modeled on dual quaternion matrices (2D-DQPCA) is successfully established, enabling the integration of the Hue-Saturation-Value (HSV) color model with the RGB model for application in face recognition.
{"title":"Algebraic method for Eigenvalue problems of dual quaternion Hermitian matrices and its application in RGB-HSV-based face representation and recognition","authors":"Wenxv Ding","doi":"10.1016/j.aml.2025.109829","DOIUrl":"10.1016/j.aml.2025.109829","url":null,"abstract":"<div><div>In recent years, dual quaternion matrix decompositions have become indispensable in applications such as formation control and color image processing. We propose a novel method for computing the eigenvalues and associated eigenvectors of a dual quaternion Hermitian matrix, leveraging its specific properties and structure in this paper. Numerical experiments demonstrate that the proposed algorithm achieves significant speedups compared to existing methods. Furthermore, a two-dimensional principal component analysis method modeled on dual quaternion matrices (2D-DQPCA) is successfully established, enabling the integration of the Hue-Saturation-Value (HSV) color model with the RGB model for application in face recognition.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"174 ","pages":"Article 109829"},"PeriodicalIF":2.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145583711","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}
Pub Date : 2026-03-01Epub Date: 2025-11-17DOI: 10.1016/j.aml.2025.109825
Guang-an Zou , Yei Xin Zhu , Jing Xiong , Xiaofeng Yang
Tumor growth models based on a Cahn–Hilliard equation coupled with a reaction–diffusion equation for nutrients lead to strongly nonlinear systems, presenting significant challenges for reliable simulation. We develop a fully discrete finite element scheme that is linear, decoupled, second-order accurate in time, and unconditionally energy-stable, achieved through a combination of BDF2 discretization, finite element approximation, and scalar auxiliary variable (SAV) approach. Rigorous analysis establishes unconditional energy stability, while numerical experiments confirm second-order convergence, robustness, and efficiency. Beyond benchmark accuracy and stability tests, the scheme captures complex morphological patterns of tumor growth, including invasive finger-like structures consistent with experimental observations, demonstrating its potential for biologically relevant tumor simulations.
{"title":"Efficient second-order and energy-stable fully discrete scheme for a diffuse-interface tumor growth model","authors":"Guang-an Zou , Yei Xin Zhu , Jing Xiong , Xiaofeng Yang","doi":"10.1016/j.aml.2025.109825","DOIUrl":"10.1016/j.aml.2025.109825","url":null,"abstract":"<div><div>Tumor growth models based on a Cahn–Hilliard equation coupled with a reaction–diffusion equation for nutrients lead to strongly nonlinear systems, presenting significant challenges for reliable simulation. We develop a fully discrete finite element scheme that is linear, decoupled, second-order accurate in time, and unconditionally energy-stable, achieved through a combination of BDF2 discretization, finite element approximation, and scalar auxiliary variable (SAV) approach. Rigorous analysis establishes unconditional energy stability, while numerical experiments confirm second-order convergence, robustness, and efficiency. Beyond benchmark accuracy and stability tests, the scheme captures complex morphological patterns of tumor growth, including invasive finger-like structures consistent with experimental observations, demonstrating its potential for biologically relevant tumor simulations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"174 ","pages":"Article 109825"},"PeriodicalIF":2.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145535799","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}
Pub Date : 2026-03-01Epub Date: 2025-11-27DOI: 10.1016/j.aml.2025.109833
Chia-Yu Hsieh , Yongting Huang , Jiaqi Ren
We consider the Poisson–Nernst–Planck–Fourier system for the non-isothermal ionic transport. With the presence of permanent charges, the system admits nonconstant equilibria. In this paper, we prove the global well-posedness around nonconstant equilibria of the system.
{"title":"Global existence of solutions to the Poisson–Nernst–Planck–Fourier system near nonconstant equilibria","authors":"Chia-Yu Hsieh , Yongting Huang , Jiaqi Ren","doi":"10.1016/j.aml.2025.109833","DOIUrl":"10.1016/j.aml.2025.109833","url":null,"abstract":"<div><div>We consider the Poisson–Nernst–Planck–Fourier system for the non-isothermal ionic transport. With the presence of permanent charges, the system admits nonconstant equilibria. In this paper, we prove the global well-posedness around nonconstant equilibria of the system.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"174 ","pages":"Article 109833"},"PeriodicalIF":2.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145608812","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}
Pub Date : 2026-02-01Epub Date: 2025-09-23DOI: 10.1016/j.aml.2025.109769
Tao Xu, Yaonan Shan
The ()-dimensional Wazwaz–Kaur–Boussinesq equation, which always describe shallow water wave interactions, is researched by the Wronskian technique. To guarantee the Wronskian determinant solves the objective equation in Hirota bilinear form, we construct some sufficient conditions consisting of linear differential equations. Based on the received Wronskian conditions, the general Wronskian solutions can be successfully derived. Choosing the matrix in the Wronskian conditions as diagonal or Jordan forms, three kinds of exact solutions including -bright, -dark solitons and rational solutions are skillfully reduced from the resulted general solutions.
{"title":"Wronskian solutions for the (3+1)-dimensional Wazwaz–Kaur–Boussinesq equation","authors":"Tao Xu, Yaonan Shan","doi":"10.1016/j.aml.2025.109769","DOIUrl":"10.1016/j.aml.2025.109769","url":null,"abstract":"<div><div>The (<span><math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math></span>)-dimensional Wazwaz–Kaur–Boussinesq equation, which always describe shallow water wave interactions, is researched by the Wronskian technique. To guarantee the Wronskian determinant solves the objective equation in Hirota bilinear form, we construct some sufficient conditions consisting of linear differential equations. Based on the received Wronskian conditions, the general Wronskian solutions can be successfully derived. Choosing the matrix in the Wronskian conditions as diagonal or Jordan forms, three kinds of exact solutions including <span><math><mi>N</mi></math></span>-bright, <span><math><mi>N</mi></math></span>-dark solitons and rational solutions are skillfully reduced from the resulted general solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109769"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158741","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}
Pub Date : 2026-02-01Epub Date: 2025-10-01DOI: 10.1016/j.aml.2025.109780
Yawen Mao , Chen Xu , Jiahe Yu , Feng Ding
This letter proposes a multiple-direction conjugate gradient (MD-CG) iterative algorithm accelerated by Gram–Schmidt -orthogonalization for parameter estimation in nonlinear NARMAX systems. Unlike the traditional CG algorithm that updates along a single conjugate direction per iteration, the MD-CG algorithm generates mutually -orthogonal search directions through a modified Gram–Schmidt process, and the convergence speed increases with increasing . Theoretical analysis shows that the convergence speed of the MD-CG algorithm can reach th power acceleration of the CG algorithm under ideal conditions, and is especially suitable for large-scale systems. A simulation example is provided to verify the superiority of the proposed algorithm in terms of parameter estimation speed and accuracy.
本文提出了一种由Gram-Schmidt a -正交化加速的多方向共轭梯度（MD-CG）迭代算法，用于非线性NARMAX系统的参数估计。与传统CG算法每次迭代沿单一共轭方向更新不同，MD-CG算法通过改进的Gram-Schmidt过程生成p个相互a正交的搜索方向，并且收敛速度随着p的增加而增加。理论分析表明，MD-CG算法的收敛速度在理想条件下可以达到CG算法的p次幂加速度，特别适用于大型系统。仿真实例验证了该算法在参数估计速度和精度方面的优越性。
{"title":"Multiple-direction conjugate gradient method via Gram–Schmidt A-orthogonalization with applications to nonlinear system identification","authors":"Yawen Mao , Chen Xu , Jiahe Yu , Feng Ding","doi":"10.1016/j.aml.2025.109780","DOIUrl":"10.1016/j.aml.2025.109780","url":null,"abstract":"<div><div>This letter proposes a multiple-direction conjugate gradient (MD-CG) iterative algorithm accelerated by Gram–Schmidt <span><math><mi>A</mi></math></span>-orthogonalization for parameter estimation in nonlinear NARMAX systems. Unlike the traditional CG algorithm that updates along a single conjugate direction per iteration, the MD-CG algorithm generates <span><math><mi>p</mi></math></span> mutually <span><math><mi>A</mi></math></span>-orthogonal search directions through a modified Gram–Schmidt process, and the convergence speed increases with increasing <span><math><mi>p</mi></math></span>. Theoretical analysis shows that the convergence speed of the MD-CG algorithm can reach <span><math><mi>p</mi></math></span>th power acceleration of the CG algorithm under ideal conditions, and is especially suitable for large-scale systems. A simulation example is provided to verify the superiority of the proposed algorithm in terms of parameter estimation speed and accuracy.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109780"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268033","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}
Pub Date : 2026-02-01Epub Date: 2025-09-15DOI: 10.1016/j.aml.2025.109759
Wenguang Cheng
In this paper, we study the Cauchy problem for a scalar conservation law with nonlocal source arising in radiation hydrodynamics, which can be rewritten as a hyperbolic-elliptic coupled system. By virtue of the boundedness of the norm of the solution, we give two new sufficient conditions on the initial data to ensure the occurrence of the wave-breaking of strong solutions.
{"title":"Wave-breaking for a scalar conservation law with nonlocal source arising in radiation hydrodynamics","authors":"Wenguang Cheng","doi":"10.1016/j.aml.2025.109759","DOIUrl":"10.1016/j.aml.2025.109759","url":null,"abstract":"<div><div>In this paper, we study the Cauchy problem for a scalar conservation law with nonlocal source arising in radiation hydrodynamics, which can be rewritten as a hyperbolic-elliptic coupled system. By virtue of the boundedness of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the solution, we give two new sufficient conditions on the initial data to ensure the occurrence of the wave-breaking of strong solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109759"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097095","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}
Pub Date : 2026-02-01Epub Date: 2025-09-18DOI: 10.1016/j.aml.2025.109763
Leonid Shaikhet
To readers attention two known theorems on the stabilization of a controlled inverted pendulum under stochastic perturbations in the form of a combination of white noise and Poisson’s jumps are presented. As unsolved problems, a generalization of these theorems is proposed for a mathematical model, described two coupled controlled inverted pendulums.
{"title":"About unsolved problems in stabilization of two coupled controlled inverted pendulums under stochastic perturbations","authors":"Leonid Shaikhet","doi":"10.1016/j.aml.2025.109763","DOIUrl":"10.1016/j.aml.2025.109763","url":null,"abstract":"<div><div>To readers attention two known theorems on the stabilization of a controlled inverted pendulum under stochastic perturbations in the form of a combination of white noise and Poisson’s jumps are presented. As unsolved problems, a generalization of these theorems is proposed for a mathematical model, described two coupled controlled inverted pendulums.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109763"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097038","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}
Pub Date : 2026-02-01Epub Date: 2025-08-30DOI: 10.1016/j.aml.2025.109740
Julia Elyseeva, Natalia Rogozina
In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with separated boundary conditions. In our consideration we do not impose any controllability and strict normality assumptions and omit the Legendre condition for the Hamiltonian. The main results generalize our previous investigations for the Hamiltonian spectral problems with Dirichlet boundary conditions. We prove the local and global oscillation theorems relating the number of left finite eigenvalues of the problem in the given interval with the values of the oscillation numbers at the end points of this interval.
{"title":"Oscillation theorems for linear Hamiltonian systems with nonlinear dependence on the spectral parameter and separated boundary conditions","authors":"Julia Elyseeva, Natalia Rogozina","doi":"10.1016/j.aml.2025.109740","DOIUrl":"10.1016/j.aml.2025.109740","url":null,"abstract":"<div><div>In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with separated boundary conditions. In our consideration we do not impose any controllability and strict normality assumptions and omit the Legendre condition for the Hamiltonian. The main results generalize our previous investigations for the Hamiltonian spectral problems with Dirichlet boundary conditions. We prove the local and global oscillation theorems relating the number of left finite eigenvalues of the problem in the given interval with the values of the oscillation numbers at the end points of this interval.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109740"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005415","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}
Pub Date : 2026-02-01Epub Date: 2025-09-13DOI: 10.1016/j.aml.2025.109758
Weiao Yang, Chen Wang, Yue Shi, Xiangpeng Xin
The Kuralay-II equation, as a typical form of the well-known Heisenberg ferromagnet equation, is an important integrable model. Here, the nonlocal Kuralay-II equation is constructed for the first time by means of symmetry reduction, resulting in an integrable system of partial differential equations. To solve this equation, Darboux transformation method is employed, which transforms the equation form to eliminate the influence of spectral parameters in the denominator and constructs a suitable gauge transformation matrix. Using trivial solutions as seed solutions, exact solutions of the equation are obtained, and the parameter constraint relationships when spectral parameters take real numbers, conjugate complex numbers, and unrelated complex numbers are analyzed, with specific examples given for the first two cases. This research contributes to solving nonlocal partial differential equations and enriches the construction methods of exact solutions in soliton theory.
{"title":"Construction and exact solution of the nonlocal Kuralay-II equation via Darboux transformation","authors":"Weiao Yang, Chen Wang, Yue Shi, Xiangpeng Xin","doi":"10.1016/j.aml.2025.109758","DOIUrl":"10.1016/j.aml.2025.109758","url":null,"abstract":"<div><div>The Kuralay-II equation, as a typical form of the well-known Heisenberg ferromagnet equation, is an important integrable model. Here, the nonlocal Kuralay-II equation is constructed for the first time by means of symmetry reduction, resulting in an integrable system of partial differential equations. To solve this equation, Darboux transformation method is employed, which transforms the equation form to eliminate the influence of spectral parameters in the denominator and constructs a suitable gauge transformation matrix. Using trivial solutions as seed solutions, exact solutions of the equation are obtained, and the parameter constraint relationships when spectral parameters take real numbers, conjugate complex numbers, and unrelated complex numbers are analyzed, with specific examples given for the first two cases. This research contributes to solving nonlocal partial differential equations and enriches the construction methods of exact solutions in soliton theory.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109758"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061171","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}
Pub Date : 2026-02-01Epub Date: 2025-09-27DOI: 10.1016/j.aml.2025.109771
Hongjie Fan , Kai Wang , Yanling Zhu
In this paper, we propose and investigate a stochastic SEQIR epidemic model with Markovian regime-switching. Governmental policies and their implementation efficiency are incorporated by a generalized incidence function of the susceptible class. Using the Lyapunov method, we illustrate the existence and uniqueness of the globally positive solution to the stochastic model. Furthermore, we also analyze the dynamical behaviors of the disease, and derive sufficient conditions for its extinction and persistence in mean. Finally, numerical simulations are presented to verify the theoretical findings.
{"title":"Dynamics analysis of a stochastic regime-switching transmission model with governmental policy","authors":"Hongjie Fan , Kai Wang , Yanling Zhu","doi":"10.1016/j.aml.2025.109771","DOIUrl":"10.1016/j.aml.2025.109771","url":null,"abstract":"<div><div>In this paper, we propose and investigate a stochastic SEQIR epidemic model with Markovian regime-switching. Governmental policies and their implementation efficiency are incorporated by a generalized incidence function of the susceptible class. Using the Lyapunov method, we illustrate the existence and uniqueness of the globally positive solution to the stochastic model. Furthermore, we also analyze the dynamical behaviors of the disease, and derive sufficient conditions for its extinction and persistence in mean. Finally, numerical simulations are presented to verify the theoretical findings.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109771"},"PeriodicalIF":2.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220886","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}
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