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A randomized Achlioptas block residual steepest descent method for large sparse overdetermined linear systems 大型稀疏过定线性系统的随机Achlioptas块残差最陡下降方法
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-11-03 DOI: 10.1016/j.aml.2025.109808
Liang Li, Shu-Rong Liu, Tao Li
Clustering is a popular strategy to improve the performance of the randomized block Kaczmarz methods, but it is unavailable for large-scale linear systems due to the substantial complexity associated with clustering high-dimensional data. However, for high-dimensional datasets, the clustering with dimensionality reduction could overcome the aforesaid drawback while achieving comparable clustering results. The Achlioptas random projection, as a powerful dimensionality reduction method, projects high-dimensional data into a low-dimensional space and preserves distance relationships between data points. In this paper, we propose a fast randomized block residual steepest descent method, built upon the Achlioptas random projection and the Gaussian mixture model, for solving large sparse, overdetermined linear systems. The theoretical analysis of which is also established. Numerical experiments are performed to illustrate the effectiveness of the proposed method compared with some existing ones, especially in computing time.
聚类是提高随机块Kaczmarz方法性能的一种流行策略，但由于与高维数据聚类相关的大量复杂性，它不适用于大规模线性系统。然而，对于高维数据集，降维聚类可以克服上述缺点，同时获得可比较的聚类结果。Achlioptas随机投影作为一种强大的降维方法，将高维数据投影到低维空间中，并保持数据点之间的距离关系。在本文中，我们提出了一种基于Achlioptas随机投影和高斯混合模型的快速随机块残差最陡下降方法，用于求解大型稀疏，过确定的线性系统。并对其进行了理论分析。通过数值实验，与现有方法进行了比较，特别是在计算时间方面，验证了该方法的有效性。
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引用次数: 0
Scattering below the ground state of odd solutions for the focusing INLS in one dimension 一维聚焦INLS奇解在基态下的散射
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-11-01 DOI: 10.1016/j.aml.2025.109820
Zhi-Yuan Cui, Yuan Li, Dun Zhao
We consider the one-dimensional focusing inhomogeneous nonlinear Schrödinger equation i∂tu+Δu=−|x|−b|u|αu, where 0<b<1 and 4−2b<α<∞. Although this problem has been extensively studied for initial data in H1(RN) when N≥2, there were previously no scattering results available for the case N=1 due to the singularity introduced by the term |x|−b. In this paper, by proving a Virial–Morawetz-type estimate for initial data below a certain level, we establish scattering below the ground state with odd initial data in H1(R).
我们考虑一维聚焦非齐次非线性Schrödinger方程i∂tu+Δu=−|x|−b|u|αu，其中0<；b<；1和4−2b<；α<∞。虽然对于N≥2时H1（RN）的初始数据已经进行了广泛的研究，但由于术语|x|−b引入的奇异性，之前没有得到N=1情况下的散射结果。本文通过对低于一定水平的初始数据证明一个virial - morawetz型估计，建立了H1(R)中初始数据为奇数的基态下散射。
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引用次数: 0
Vector nonautonomous nondegenerate soliton solutions in the coupled Gross–Pitaevskii equations 耦合Gross-Pitaevskii方程的矢量非自治非退化孤子解
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-10-30 DOI: 10.1016/j.aml.2025.109804
Jiguang Rao , Lijuan Guo , Jingsong He
This letter investigates vector nonautonomous nondegenerate solitons and their collision dynamics in the coupled Gross–Pitaevskii equations with variable nonlinear coefficients and external potentials. By employing a bilinear representation linked to the KP hierarchy, compact determinant forms of nondegenerate soliton solutions are established. The results reveal several distinct localized waveforms, including single-hump and double-hump solitons, whose propagations follow curved paths dictated by the modulation function r(t). The asymptotic analysis demonstrates two types of collision patterns for double-hump solitons: either retaining their original profiles or undergoing structural transformations. A previously unreported mixed process is also identified, in which one soliton preserves its symmetric profile while the other experiences a symmetry-breaking change. The work provides new insight into controllable nonlinear excitations relevant to vector Bose–Einstein condensates.
本文研究了具有可变非线性系数和外部势的耦合Gross-Pitaevskii方程中的矢量非自治非退化孤子及其碰撞动力学。利用与KP层次相关的双线性表示，建立了非退化孤子解的紧致行列式。结果揭示了几种不同的局域波形，包括单驼峰和双驼峰孤子，其传播遵循由调制函数r(t)决定的弯曲路径。渐近分析证明了双驼峰孤子的两种碰撞模式：要么保持其原始轮廓，要么进行结构转换。还发现了一种以前未报道的混合过程，其中一个孤子保持其对称轮廓，而另一个孤子经历对称破坏变化。这项工作为与矢量玻色-爱因斯坦凝聚相关的可控非线性激励提供了新的见解。
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引用次数: 0
A third-order multiscale analysis and computation for the elliptic problem in arbitrarily heterogeneous domains 任意非均质区域椭圆问题的三阶多尺度分析与计算
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-10-30 DOI: 10.1016/j.aml.2025.109806
Qiang Ma , Junzhi Cui
A new third-order multiscale expansion is proposed for the elliptic problem with mixed boundary conditions in arbitrarily heterogeneous domains. The field variable is expanded in terms of a homogenized solution and its derivatives up to the third order. The so-called first to third-order functions are defined to give the homogenized coefficients and correct the differences between the homogenized and original solution both in the domain and on the boundaries. Error estimations are derived, and a typical numerical example is presented demonstrating the high accuracy of the multiscale model. This multiscale analysis presented in this paper generalizes the asymptotic expansion method and can be extended to other problems in non-homogeneous domains.
针对任意非均质域上具有混合边界条件的椭圆型问题，提出了一种新的三阶多尺度展开式。将场变量展开为均质解及其三阶导数的形式。定义了所谓的一阶到三阶函数，以给出均匀化系数，并在定义域和边界上修正均匀化后的解与原解之间的差异。给出了误差估计，并给出了典型的数值算例，证明了多尺度模型具有较高的精度。本文的多尺度分析推广了渐近展开方法，可推广到其他非齐次域的问题。
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引用次数: 0
Second-order error analysis for FEM of fractional Laplacian on graded meshes via FDM auxiliary 基于FDM辅助的梯度网格分数阶拉普拉斯有限元二阶误差分析
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-10-30 DOI: 10.1016/j.aml.2025.109807
Jianxing Han , Minghua Chen , Yufeng Nie
On graded meshes, the superlinear convergence for fractional Laplacian problem was proved in Borthagaray et al. (2021) by finite element method (FEM). Furthermore, numerical experiments of FEM in Chen, et al. (2021) demonstrate a second-order accuracy on a suitably graded mesh for the 1D case, but a convergence analysis for the proposed scheme remains unavailable. To fill this gap, we provide a second-order error analysis for the resulting FEM algebraic system. Our analysis employs the finite difference method (FDM) as an auxiliary tool based on our previous work [ arXiv:2520.11117], where FEM scheme can be viewed as a modification of the FDM scheme.
Borthagaray et al.（2021）用有限元法证明了分数阶拉普拉斯问题在梯度网格上的超线性收敛性。此外，Chen等人（2021）的有限元数值实验表明，对于一维情况，在适当的分级网格上具有二阶精度，但对所提出方案的收敛性分析仍然不可用。为了填补这一空白，我们对所得到的有限元代数系统进行了二阶误差分析。我们的分析采用有限差分法（FDM）作为辅助工具，基于我们之前的工作[arXiv:2520.11117]，其中FEM方案可以视为FDM方案的修改。
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引用次数: 0
Existence of solutions for damped elastic inclusions with nonconvex-valued perturbations 具有非凸值扰动的阻尼弹性包体解的存在性
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-10-30 DOI: 10.1016/j.aml.2025.109797
Jiangfeng Han , Zhao Jing , Zhenhai Liu
This paper investigates damped elastic inclusion systems subjected to nonconvex-valued perturbations. Our primary contribution lies in establishing an existence theorem for mild solutions under suitable regularity conditions. To illustrate the practical applicability of these abstract findings, we conduct an explicit analysis of solutions in elastic feedback control systems.
本文研究了受非凸值扰动作用下的阻尼弹性包体系统。我们的主要贡献在于建立了适当正则性条件下温和解的存在性定理。为了说明这些抽象发现的实际适用性，我们对弹性反馈控制系统的解决方案进行了明确的分析。
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引用次数: 0
A fourth-order scheme for the exterior Helmholtz problem in polar coordinates 极坐标下外部亥姆霍兹问题的四阶格式
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-10-30 DOI: 10.1016/j.aml.2025.109805
Tingting Wu , Jiayuan Liu
In this paper, a fourth-order finite difference scheme is proposed to solve the exterior Helmholtz problem in polar coordinates. The perfectly matched layer (PML) technique is applied to truncate the unbounded domain into a bounded domain, and absorb the outgoing waves. Using the undetermined coefficient method, a fourth-order finite difference scheme for the Helmholtz equation with PML in polar coordinates is established. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed scheme.
本文提出了一种四阶有限差分格式来解决极坐标下的外部亥姆霍兹问题。采用完全匹配层（PML）技术将无界域截断为有界域，吸收出波。利用待定系数法，建立了极坐标系下带PML的亥姆霍兹方程的四阶有限差分格式。数值结果验证了该方法的有效性和准确性。
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引用次数: 0
Retraction notice to “Analysis on the motion of nonlinear vibration with fractional order and time variable mass” [Appl. Math. Lett. 124 (2022) 107621] 《分数阶、时变质量非线性振动的运动分析》的撤回通知[j]。数学。Lett. 124 (2022) 107621]
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-10-30 DOI: 10.1016/j.aml.2025.109792
Yue Yu , Wenyao Zhou , Zhengdi Zhang , Qinsheng Bi
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引用次数: 0
On the global existence of weak solution for the 3D axisymmetric chemotaxis-Navier–Stokes equations with nonlinear diffusion 三维轴对称非线性扩散趋化- navier - stokes方程弱解的整体存在性
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-10-29 DOI: 10.1016/j.aml.2025.109802
Mingxi Li, Qian Zhang
We study the Cauchy problem for the 3D axisymmetric chemotaxis-Navier–Stokes equations with nonlinear diffusion Δnm. Leveraging the axisymmetric non-swirl flow structure, we extend the range of m to (76,∞) and prove the global existence of weak solutions for this model. Besides we extend the global result from bounded domain (Winkler, 2015) to the entire spaces.
研究了具有非线性扩散的三维轴对称趋化- navier - stokes方程的Cauchy问题Δnm。利用轴对称非旋流结构，将m的取值范围扩展到（76,∞），证明了该模型弱解的全局存在性。此外，我们将有界域的全局结果（Winkler, 2015）扩展到整个空间。
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引用次数: 0
Withdrawal notice to: “Innovations beyond the Classical Framework in the Dual Space D3” [Appl. Math. Lett. 173 (2026) 109786] 退出通知：“超越经典框架的创新在对偶空间D3”[应用程序]。数学。Lett. 173 (2026) 109786]
IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Applied Mathematics Letters
Pub Date : 2025-10-28 DOI: 10.1016/j.aml.2025.109801
Salim Yüce
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引用次数: 0
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