Pub 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":"2025-12-18","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 : 2025-12-15DOI: 10.1016/j.aml.2025.109852
Songhang Yu , Yisi Wang , Jian Zhang
In this paper, we investigate the nonlinear fractional -Laplace problem with potentials and mass constraint. Under some natural assumptions on the potentials, using minimization techniques together with compactness analysis, we establish new existence results of normalized solutions.
{"title":"Normalized solutions for a nonlinear fractional elliptic problem with potentials","authors":"Songhang Yu , Yisi Wang , Jian Zhang","doi":"10.1016/j.aml.2025.109852","DOIUrl":"10.1016/j.aml.2025.109852","url":null,"abstract":"<div><div>In this paper, we investigate the nonlinear fractional <span><math><mi>p</mi></math></span>-Laplace problem with potentials and mass constraint. Under some natural assumptions on the potentials, using minimization techniques together with compactness analysis, we establish new existence results of normalized solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109852"},"PeriodicalIF":2.8,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145753503","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 : 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":"2025-12-13","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 : 2025-12-13DOI: 10.1016/j.aml.2025.109850
Qiliang Lin, Chenyin Qian
This paper establishes several regularity criteria for the three-dimensional inhomogeneous incompressible Navier–Stokes equations in terms of the horizontal components of the velocity field, allowing for initial densities that contain vacuum. Specifically, we prove that Prodi–Serrin type conditions imposed solely on the horizontal velocity or its gradient in critical spaces ensure regularity of the weak solution, given initial data and .
{"title":"Regularity criteria via horizontal velocity components for 3D inhomogeneous incompressible Navier–Stokes equations with vacuum","authors":"Qiliang Lin, Chenyin Qian","doi":"10.1016/j.aml.2025.109850","DOIUrl":"10.1016/j.aml.2025.109850","url":null,"abstract":"<div><div>This paper establishes several regularity criteria for the three-dimensional inhomogeneous incompressible Navier–Stokes equations in terms of the horizontal components of the velocity field, allowing for initial densities that contain vacuum. Specifically, we prove that Prodi–Serrin type conditions imposed solely on the horizontal velocity <span><math><msup><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msup></math></span> or its gradient <span><math><mrow><mo>∇</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msup></mrow></math></span> in critical spaces ensure regularity of the weak solution, given initial data <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow><mo>∩</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow><mo>∩</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109850"},"PeriodicalIF":2.8,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731478","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 : 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":"2025-12-12","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 : 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":"2025-12-10","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 : 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":"2025-12-10","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 : 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":"2025-12-08","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 : 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":"2025-12-08","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}
Pub Date : 2025-12-04DOI: 10.1016/j.aml.2025.109842
Yujia Zhang , Xin Wu , Zhaohai Ma
This study is devoted to proving the exponential stability of traveling wave solutions in a scalar age-structured model with spatial diffusion. By employing a comparison principle coupled with a weighted-energy approach, we demonstrate that traveling wave solutions are exponentially stable. This analytical conclusion is validated through numerical simulations.
{"title":"Exponential stability of traveling waves for a scalar age-structured equation","authors":"Yujia Zhang , Xin Wu , Zhaohai Ma","doi":"10.1016/j.aml.2025.109842","DOIUrl":"10.1016/j.aml.2025.109842","url":null,"abstract":"<div><div>This study is devoted to proving the exponential stability of traveling wave solutions in a scalar age-structured model with spatial diffusion. By employing a comparison principle coupled with a weighted-energy approach, we demonstrate that traveling wave solutions are exponentially stable. This analytical conclusion is validated through numerical simulations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"175 ","pages":"Article 109842"},"PeriodicalIF":2.8,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689357","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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