Pub Date : 2026-05-01Epub Date: 2025-12-26DOI: 10.1016/j.aml.2025.109858
João Marcos do Ó , José Carlos de Albuquerque , Hugo H.C. Silva
This work establishes a lower bound for the Morse index of radial nodal solutions for a general class of gradient-type elliptic systems. By relating the Morse index to the negative eigenvalues of the associated linearized operator, we construct a set of non-radial eigenfunctions to find negative directions for the quadratic form. The main result shows the Morse index is bounded from below by , where and are the number of nodal domains of the solutions. Furthermore, this work explores how the estimate for the Morse index influences the structural properties of radial and nodal solutions.
{"title":"A lower bound for the Morse index of nodal radial solutions for gradient elliptic systems","authors":"João Marcos do Ó , José Carlos de Albuquerque , Hugo H.C. Silva","doi":"10.1016/j.aml.2025.109858","DOIUrl":"10.1016/j.aml.2025.109858","url":null,"abstract":"<div><div>This work establishes a lower bound for the Morse index of radial nodal solutions for a general class of gradient-type elliptic systems. By relating the Morse index to the negative eigenvalues of the associated linearized operator, we construct a set of non-radial eigenfunctions to find negative directions for the quadratic form. The main result shows the Morse index <span><math><mrow><mi>m</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> is bounded from below by <span><math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>r</mi><mi>a</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>N</mi><mrow><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>N</mi><mrow><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, where <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are the number of nodal domains of the solutions. Furthermore, this work explores how the estimate for the Morse index influences the structural properties of radial and nodal solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109858"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845495","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 : 2026-04-01Epub Date: 2025-12-24DOI: 10.1016/j.aml.2025.109856
Dongxiu Wang, Anmin Mao
This paper investigates the global boundedness of solutions to a mosquito-borne disease system with chemotaxis via new approach. More specifically, by means of the loop arguments, we prove the existence of a unique globally bounded classical solution to the system without any constraint on initial data in any spatial dimension. This result generalizes some relevant results.
{"title":"Global solvability in a mosquito-borne disease system with chemotaxis","authors":"Dongxiu Wang, Anmin Mao","doi":"10.1016/j.aml.2025.109856","DOIUrl":"10.1016/j.aml.2025.109856","url":null,"abstract":"<div><div>This paper investigates the global boundedness of solutions to a mosquito-borne disease system with chemotaxis via new approach. More specifically, by means of the loop arguments, we prove the existence of a unique globally bounded classical solution to the system without any constraint on initial data in any spatial dimension. This result generalizes some relevant results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109856"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822949","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 : 2026-04-01Epub Date: 2025-12-10DOI: 10.1016/j.aml.2025.109848
Shifeng Geng, Pan Zhang
In this paper, we consider the stability problem of the 2D Boussinesq-MHD system with only fractional horizontal magnetic diffusion and thermal diffusivity. By employing the effects of magnetic field, and the decomposition of the horizontal average and oscillatory parts, we prove the global stability of the 2D Boussinesq-MHD system without velocity dissipation. And the result shows the magnetic field has a stabilizing effect on the fluid. Moreover, we obtain exponential decay of the solution in one direction.
{"title":"Stability of the 2D Boussinesq-MHD system with only fractional horizontal magnetic and thermal diffusion","authors":"Shifeng Geng, Pan Zhang","doi":"10.1016/j.aml.2025.109848","DOIUrl":"10.1016/j.aml.2025.109848","url":null,"abstract":"<div><div>In this paper, we consider the stability problem of the 2D Boussinesq-MHD system with only fractional horizontal magnetic diffusion and thermal diffusivity. By employing the effects of magnetic field, and the decomposition of the horizontal average and oscillatory parts, we prove the global stability of the 2D Boussinesq-MHD system without velocity dissipation. And the result shows the magnetic field has a stabilizing effect on the fluid. Moreover, we obtain exponential decay of the solution in one direction.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109848"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731485","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 : 2026-04-01Epub Date: 2025-12-18DOI: 10.1016/j.aml.2025.109853
Qiuxiang Tu , Guangjing Song , Changzhou Dong , Qi Liu
Dual quaternions provide a powerful mathematical tool for robust point cloud registration through their compact and unified representation of three-dimensional rigid transformations. In this paper, we present a dual quaternion matrix formulation for 3D point cloud registration via a dual-complex representation. We reformulate the rigid transformation as a complex linear system, which enables the direct and unified computation of rotation and translation without the need for iterative refinement. Numerical experiments are conducted to verify the robustness and effectiveness of the proposed methods.
{"title":"Dual quaternion matrix formulation for robust 3D point cloud registration","authors":"Qiuxiang Tu , Guangjing Song , Changzhou Dong , Qi Liu","doi":"10.1016/j.aml.2025.109853","DOIUrl":"10.1016/j.aml.2025.109853","url":null,"abstract":"<div><div>Dual quaternions provide a powerful mathematical tool for robust point cloud registration through their compact and unified representation of three-dimensional rigid transformations. In this paper, we present a dual quaternion matrix formulation for 3D point cloud registration via a dual-complex representation. We reformulate the rigid transformation as a complex linear system, which enables the direct and unified computation of rotation and translation without the need for iterative refinement. Numerical experiments are conducted to verify the robustness and effectiveness of the proposed methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109853"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145786037","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 : 2026-04-01Epub Date: 2025-12-23DOI: 10.1016/j.aml.2025.109855
Huiling Du , Fang Li , Bo Xue
A new nonlinear super vector equation is obtained according to a matrix spectral problem with the help of the compatibility condition. When , the corresponding hierarchy of equations is deduced and its Hamiltonian structures are constructed by means of the supertrace identity. Then an -component super CH equation is gained from a negative flow associated with the original matrix spectral problem, which admits exact solutions with -peakons, and a super dynamical system that the potentials evolve with is derived. Moreover, the infinitely many conservation laws of the -component super CH equation are discussed.
{"title":"An n-component super Camassa–Holm equation with N-peakons","authors":"Huiling Du , Fang Li , Bo Xue","doi":"10.1016/j.aml.2025.109855","DOIUrl":"10.1016/j.aml.2025.109855","url":null,"abstract":"<div><div>A new nonlinear super vector equation is obtained according to a <span><math><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mo>×</mo><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> matrix spectral problem with the help of the compatibility condition. When <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span>, the corresponding hierarchy of equations is deduced and its Hamiltonian structures are constructed by means of the supertrace identity. Then an <span><math><mi>n</mi></math></span>-component super CH equation is gained from a negative flow associated with the original matrix spectral problem, which admits exact solutions with <span><math><mi>N</mi></math></span>-peakons, and a super dynamical system that the potentials evolve with is derived. Moreover, the infinitely many conservation laws of the <span><math><mi>n</mi></math></span>-component super CH equation are discussed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109855"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822954","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 : 2026-04-01Epub Date: 2025-12-13DOI: 10.1016/j.aml.2025.109851
Yana Guo , Ming Li
This paper is devoted to the study of the large time behavior to the two-dimensional MHD-Boussinesq equations with linear velocity damping in . By fully exploiting the special structure of the system and using the uniformly bounded generalized Oseen operator, we establish the decay estimates of the solutions to this system.
{"title":"Decay estimates of 2D Boussinesq equations for MHD convection with stratification effects","authors":"Yana Guo , Ming Li","doi":"10.1016/j.aml.2025.109851","DOIUrl":"10.1016/j.aml.2025.109851","url":null,"abstract":"<div><div>This paper is devoted to the study of the large time behavior to the two-dimensional MHD-Boussinesq equations with linear velocity damping in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. By fully exploiting the special structure of the system and using the uniformly bounded generalized Oseen operator, we establish the decay estimates of the solutions to this system.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109851"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731473","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 : 2026-04-01Epub Date: 2025-12-10DOI: 10.1016/j.aml.2025.109847
To Fu Ma , Rodrigo N. Monteiro , Paulo N. Seminario-Huertas
In this paper, we consider a thermoelastic plate of Green–Lindsay type, characterized by two relaxation times and exhibiting finite-speed heat waves. The homogeneous problem was recently studied by Quintanilla et al. (2023). They pointed out that it was not known whether the domain of the semigroup generator is compactly embedded into the energy space. Nevertheless, through a detailed analysis, they established the well-posedness of the system and the exponential stability of its solution semigroup. Our aim is to investigate the asymptotic dynamics of the plate in the presence of a nonlinear foundation. We establish the existence of a finite dimensional global attractor with higher regularity.
本文考虑具有两个松弛时间且具有有限速度热波的Green-Lindsay型热弹性板。最近Quintanilla et al.（2023）研究了齐次问题。他们指出，尚不清楚半群发生器的域是否紧密嵌入到能量空间中。然而，通过详细的分析，他们建立了系统的适定性及其解半群的指数稳定性。我们的目的是研究在非线性基础存在下板的渐近动力学。建立了具有高正则性的有限维全局吸引子的存在性。
{"title":"Dynamics of a thermoelastic Green–Lindsay plate on a nonlinear foundation","authors":"To Fu Ma , Rodrigo N. Monteiro , Paulo N. Seminario-Huertas","doi":"10.1016/j.aml.2025.109847","DOIUrl":"10.1016/j.aml.2025.109847","url":null,"abstract":"<div><div>In this paper, we consider a thermoelastic plate of Green–Lindsay type, characterized by two relaxation times and exhibiting finite-speed heat waves. The homogeneous problem was recently studied by Quintanilla et al. (2023). They pointed out that it was not known whether the domain of the semigroup generator is compactly embedded into the energy space. Nevertheless, through a detailed analysis, they established the well-posedness of the system and the exponential stability of its solution semigroup. Our aim is to investigate the asymptotic dynamics of the plate in the presence of a nonlinear foundation. We establish the existence of a finite dimensional global attractor with higher regularity.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109847"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731486","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 : 2026-04-01Epub Date: 2025-12-12DOI: 10.1016/j.aml.2025.109849
Liqun Qi , Chunfeng Cui , Haibin Chen , Yi Xu
In this paper, we systemically introduce completely positive biquadratic (CPBQ) tensors and copositive biquadratic tensors. We show that all weakly CPBQ tensors are sum of squares tensors, the CPBQ tensor cone and the copositive biquadratic tensor cone are dual cone to each other. We also show that the outer product of two completely positive matrices is a CPBQ tensor, and the outer product of two copositive matrices is a copositive biquadratic tensor. We then study two easily checkable subclasses of CPBQ tensors, namely positive biquadratic Cauchy tensors and biquadratic Pascal tensors. We show that a biquadratic Pascal tensor is both strongly CPBQ and positive definite.
{"title":"Completely positive biquadratic tensors","authors":"Liqun Qi , Chunfeng Cui , Haibin Chen , Yi Xu","doi":"10.1016/j.aml.2025.109849","DOIUrl":"10.1016/j.aml.2025.109849","url":null,"abstract":"<div><div>In this paper, we systemically introduce completely positive biquadratic (CPBQ) tensors and copositive biquadratic tensors. We show that all weakly CPBQ tensors are sum of squares tensors, the CPBQ tensor cone and the copositive biquadratic tensor cone are dual cone to each other. We also show that the outer product of two completely positive matrices is a CPBQ tensor, and the outer product of two copositive matrices is a copositive biquadratic tensor. We then study two easily checkable subclasses of CPBQ tensors, namely positive biquadratic Cauchy tensors and biquadratic Pascal tensors. We show that a biquadratic Pascal tensor is both strongly CPBQ and positive definite.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109849"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731481","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 : 2026-04-01Epub Date: 2025-12-08DOI: 10.1016/j.aml.2025.109845
Yaxiang Li , Jiangxing Wang
We propose a linearized hybridizable discontinuous Galerkin (HDG) method for solving the time-dependent nonlinear Schrödinger equation. By integrating the advantageous features of HDG spatial discretization with the temporal accuracy of a semi-implicit Crank–Nicolson scheme, the proposed method delivers both high-order accuracy and computational efficiency. A rigorous theoretical analysis establishes unconditional optimal error estimates for the numerical solution and its gradient without any restriction imposed between the time-step size and the spatial mesh size. Numerical examples are carried out to verify the theoretical results.
{"title":"Linearly implicit conservative HDG method for the nonlinear Schrödinger equation","authors":"Yaxiang Li , Jiangxing Wang","doi":"10.1016/j.aml.2025.109845","DOIUrl":"10.1016/j.aml.2025.109845","url":null,"abstract":"<div><div>We propose a linearized hybridizable discontinuous Galerkin (HDG) method for solving the time-dependent nonlinear Schrödinger equation. By integrating the advantageous features of HDG spatial discretization with the temporal accuracy of a semi-implicit Crank–Nicolson scheme, the proposed method delivers both high-order accuracy and computational efficiency. A rigorous theoretical analysis establishes unconditional optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> error estimates for the numerical solution and its gradient without any restriction imposed between the time-step size and the spatial mesh size. Numerical examples are carried out to verify the theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109845"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705024","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 : 2026-04-01Epub Date: 2025-12-08DOI: 10.1016/j.aml.2025.109846
Boxuan Zhao, Guotao Wang
This paper investigates the blow-up problem for the -Hessian equation with nonlinear gradient terms: where , are nonnegative constants with , is a smooth, bounded and strictly -convex domain, is a positive function and may be singular near . By the sub-supersolution method, we present the boundary behavior of large solutions to this problem. Our work essentially generalizes the relevant conclusions in Zhang and Feng (2018); Feng and Zhang (2020).
{"title":"Nonexistence and boundary behavior of solutions to the k-Hessian equation with nonlinear gradient terms","authors":"Boxuan Zhao, Guotao Wang","doi":"10.1016/j.aml.2025.109846","DOIUrl":"10.1016/j.aml.2025.109846","url":null,"abstract":"<div><div>This paper investigates the blow-up problem for the <span><math><mi>k</mi></math></span>-Hessian equation with nonlinear gradient terms: <span><math><mrow><msup><mrow><mrow><mo>(</mo><mi>γ</mi><mo>+</mo><mrow><mo>|</mo><mi>D</mi><mi>u</mi><mo>|</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>k</mi><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></mrow></msup><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>h</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><msup><mrow><mi>u</mi></mrow><mrow><mi>α</mi></mrow></msup><msup><mrow><mrow><mo>(</mo><mo>ln</mo><mi>u</mi><mo>)</mo></mrow></mrow><mrow><mi>β</mi></mrow></msup><mo>></mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace><mi>z</mi><mo>∈</mo><mi>D</mi><mo>,</mo><mspace></mspace><mspace></mspace><mi>u</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>∂</mi><mi>D</mi></mrow></msub><mo>=</mo><mo>+</mo><mi>∞</mi><mo>,</mo></mrow></math></span> where <span><math><mrow><mi>p</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi></mrow></math></span> are nonnegative constants with <span><math><mrow><mi>β</mi><mo>≠</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>D</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> <span><math><mrow><mo>(</mo><mi>N</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></math></span> is a smooth, bounded and strictly <span><math><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span>-convex domain, <span><math><mrow><mi>h</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span> is a positive function and may be singular near <span><math><mrow><mi>∂</mi><mi>D</mi></mrow></math></span>. By the sub-supersolution method, we present the boundary behavior of large solutions to this problem. Our work essentially generalizes the relevant conclusions in Zhang and Feng (2018); Feng and Zhang (2020).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109846"},"PeriodicalIF":2.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705030","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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