Results in Applied Mathematics最新文献

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Efficient computation for the eigenvalues and eigenfunctions of two-dimensional non-separable linear canonical transform 二维不可分线性正则变换的特征值和特征函数的高效计算

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-09-27 DOI: 10.1016/j.rinam.2025.100645

Yuru Tian, Feng Zhang

The parameter matrix of the two-dimensional non-separable linear canonical transform (2D-NSLCT) determines its specific form and properties. Certain forms of the 2D-NSLCT are consistent with well-known transforms, such as two-dimensional non-separable fractional Fourier transform (2D-NSFrFT), Fresnel transform, and other related transforms. Based on the analysis of the eigenvalues and eigenfunctions of these special transforms, this paper proposes an efficient method for computing the eigenvalues and eigenfunctions of the 2D-NSLCT. Specifically, based on the properties of similar matrices, if the parameter matrix of the 2D-NSLCT is similar to that of a special transform (e.g., 2D-NSFrFT or other transforms), then the eigenvalues of the 2D-NSLCT are identical to those of the special transform. Moreover, the eigenfunctions of the 2D-NSLCT can be computed using the known eigenfunctions of this special transform based on the additivity of the 2D-NSLCT. The detailed derivation is presented in this paper, and some applications of the 2D-NSLCT’s eigenfunction are also discussed.

二维不可分线性正则变换（2D-NSLCT）的参数矩阵决定了它的具体形式和性质。2D-NSLCT的某些形式与众所周知的变换一致，例如二维不可分分数傅里叶变换（2D-NSFrFT）、菲涅耳变换和其他相关变换。在分析这些特殊变换的特征值和特征函数的基础上，提出了一种计算2D-NSLCT特征值和特征函数的有效方法。具体来说，根据相似矩阵的性质，如果2D-NSLCT的参数矩阵与特殊变换（如2D-NSFrFT或其他变换）的参数矩阵相似，则2D-NSLCT的特征值与特殊变换的特征值相同。基于2D-NSLCT的可加性，利用该特殊变换的已知特征函数可以计算2D-NSLCT的特征函数。本文给出了二维nslct特征函数的详细推导过程，并讨论了二维nslct特征函数的一些应用。

引用次数: 0

Bayesian estimation of discretely observed diffusion processes using Wiener chaos expansion 利用维纳混沌展开的离散观测扩散过程的贝叶斯估计

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-09-27 DOI: 10.1016/j.rinam.2025.100644

Fernando Baltazar-Larios , Gabriel Adrián Salcedo-Varela , Francisco Delgado-Vences

We employ a Bayesian inference technique for discretely observed diffusion processes that arise as solutions of stochastic differential equations. Our aim is to estimate the parameters of the stochastic differential equation. To achieve this, we frame the estimation procedure as a missing data problem. In this framework, the complete dataset includes the theoretically continuous-time path between observed points. We propose augmenting the dataset and using a Gibbs sampler to derive Bayesian estimators for the parameters in cases where the diffusion process is observed discretely. The Gibbs sampler is integrated with a diffusion bridge simulation technique based on the Wiener chaos expansion. The methodology and its implementation are demonstrated through examples and simulation studies. We also present an application to actual data.

我们采用贝叶斯推理技术离散观察扩散过程出现作为随机微分方程的解决方案。我们的目的是估计随机微分方程的参数。为了实现这一点，我们将估计过程定义为缺失数据问题。在这个框架中，完整的数据集包含了观测点之间理论上的连续时间路径。我们建议扩大数据集并使用吉布斯采样器在离散观察扩散过程的情况下推导参数的贝叶斯估计。Gibbs采样器集成了基于维纳混沌展开的扩散桥模拟技术。通过实例和仿真研究证明了该方法及其实现。我们也给出了一个实际数据的应用。

引用次数: 0

Isogeometric boundary element method for solving 2D multi-media heat conduction problems 求解二维介质热传导问题的等几何边界元法

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-09-23 DOI: 10.1016/j.rinam.2025.100639

Kunpeng Li , Wei Jiang , Haozhi Li

In this work, we employ the isogeometric boundary element approach to investigate heat transfer mechanisms in various media. We derive and construct integral equations for the interface of different media to address heat transfer issues. Our proposed modeling technique for two-dimensional problems can be dynamically constructed by incorporating control points and weight factors. In comparison to other numerical software, this approach offers high customizability, improves model accuracy, mitigates mesh errors, and seamlessly integrates the advantages of Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) through the isogeometric method. The boundary element approach boasts several advantages, with numerical stability and excellent precision being paramount. The amalgamation of the isogeometric approach with the boundary element method holds promise for future applications in practical engineering. Simultaneously, we address the domain integral using the radial integration approach. The algorithmic results reveal that the isogeometric boundary element method, in contrast to the traditional boundary element method, expands the applicability of the latter while maintaining good stability and robustness. This provides substantial support for further software integration.

在这项工作中，我们采用等几何边界元方法来研究各种介质中的传热机制。我们推导并构造了不同介质界面的积分方程来解决传热问题。我们提出的二维问题建模技术可以通过结合控制点和权重因子来动态构建。与其他数值软件相比，该方法具有较高的可定制性，提高了模型精度，减轻了网格误差，并通过等几何方法无缝集成了计算机辅助设计（CAD）和计算机辅助工程（CAE）的优势。边界元法具有数值稳定性和较高的精度等优点。等几何方法与边界元方法的融合在实际工程中具有广阔的应用前景。同时，我们使用径向积分方法来处理域积分。算法结果表明，与传统边界元方法相比，等几何边界元方法在保持较好的稳定性和鲁棒性的同时，扩大了传统边界元方法的适用性。这为进一步的软件集成提供了实质性的支持。

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引用次数: 0

Mathematical analysis of shallow water wave and the generalized Hirota-Satsuma-Ito models: Soliton solutions and their interactions 浅水波的数学分析与广义Hirota-Satsuma-Ito模型：孤子解及其相互作用

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-09-19 DOI: 10.1016/j.rinam.2025.100641

M. Belal Hossen , Md. Towhiduzzaman , Harun-Or-Roshid , K. M. Abdul A. Woadud

This study investigates the mathematical properties and soliton dynamics of the (2+1)-dimensional extended Shallow Water Wave (eSWW) and the generalized Hirota-Satsuma-Ito (gHSI) models by Hirota bilinear scheme. A comprehensive mathematical analysis is conducted to derive multi-soliton solutions, including 2-soliton and 3-soliton solutions, while breather, rogue and lump solutions derive from 2-soliton. Investigation focuses on soliton interactions under various conditions, with particular attention to special cases like rogue and lump type solutions, highlighting their distinct characteristics and physical significance. Additionally, the analysis extends to the gHSI equation, where long wave limit scheme is applied to attain rogue and lump wave solutions. We analyzed the planar dynamics of the system to assess its sensitivity. These findings enhance our knowledge of nonlinear wave processes, with potential applications in oceanography, fluid mechanics, and related scientific fields.

利用Hirota双线性格式研究了（2+1）维扩展浅水波（eSWW）和广义Hirota- satsuma - ito （gHSI）模型的数学性质和孤子动力学。对多孤子解进行了全面的数学分析，包括2孤子解和3孤子解，而呼吸、流氓和块状解则由2孤子导出。研究重点是各种条件下的孤子相互作用，特别关注流氓型和块状解等特殊情况，突出其独特的特征和物理意义。此外，分析扩展到gHSI方程，其中长波极限格式应用于获得流氓和块波解。我们分析了系统的平面动力学，以评估其灵敏度。这些发现增强了我们对非线性波浪过程的认识，在海洋学、流体力学和相关科学领域具有潜在的应用前景。

引用次数: 0

Weighted Lorentz estimates with a variable power for non-uniformly elliptic two-sided obstacle problems 非均匀椭圆型双边障碍问题的变幂加权Lorentz估计

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-09-15 DOI: 10.1016/j.rinam.2025.100638

Junjie Zhang, Lina Niu

We proved an optimal local Calderón–Zygmund type estimate with a variable power in weighted Lorentz spaces for the weak solution of non-uniformly elliptic two-sided obstacle problems. It is mainly assumed that the nonlinearity satisfies the

(p (x), q (x))

-growth condition and

(δ, R)

-BMO condition, while the exponents

p (x), q (x)

are strong

log

-Hölder continuous functions. The approach of this paper is mainly based on the perturbation technique and maximal function free technique.

在加权洛伦兹空间中，证明了非均匀椭圆型双边障碍问题弱解的最优局部变幂Calderón-Zygmund型估计。主要假设非线性满足(p(x),q(x))-生长条件和（δ，R）-BMO条件，而指数p(x),q(x)是强log-Hölder连续函数。本文的方法主要基于微扰技术和无极大函数技术。

引用次数: 0

Commutators of fractional maximal functions with Lipschitz functions on mixed-norm amalgam spaces 混合范数汞齐空间上带Lipschitz函数的分数极大函数的对易子

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100628

Suixin He , Lihua Zhang , Heng Yang

In this paper, we investigate the commutators of fractional maximal functions on mixed-norm amalgam spaces. Furthermore, we present some new characterizations of Lipschitz functions.

本文研究了混合范数汞齐空间上分数极大函数的对易子。此外，我们还给出了Lipschitz函数的一些新的表征。

引用次数: 0

Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints 具有控制约束的椭圆型最优控制问题的双风不连续Galerkin方法的收敛性分析

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100624

Satyajith Bommana Boyana , Thomas Lewis , Sijing Liu , Yi Zhang

This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which is discretized using the symmetric DWDG approach. We derive error estimates in the energy norm for both the state and the adjoint state, as well as in the

L^{2}

norm of the control variable. Numerical experiments are provided to demonstrate the robustness and effectiveness of the developed scheme.

研究了一类带控制约束的椭圆型最优控制问题的对称双风不连续Galerkin （DWDG）方法。控制约束是一个椭圆型偏微分方程（PDE），采用对称DWDG方法对其进行离散化。我们推导了状态和伴随状态的能量范数以及控制变量的L2范数中的误差估计。数值实验验证了该方法的鲁棒性和有效性。

引用次数: 0

Analysis framework for stochastic predator–prey model with demographic noise 具有人口统计学噪声的随机捕食者-猎物模型分析框架

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100621

Louis Shuo Wang , Jiguang Yu

Most existing studies focus on environmental noise, with few studies focusing on pure demographic noise. We propose an analytical framework that applies stochastic differential equation tools to prove the well-posedness of solutions to such models with pure demographic noise and obtain moment and asymptotic bounds. We use this framework to prove that demographic noise does not lead to population extinction, and numerical results are consistent with it. Our proposed framework fills the gaps in research on the well-posedness and extinction impossibility of models with pure demographic noise and provides a rigorous mathematical framework for addressing a general ecology system in more sophisticated evolutionary setups.

现有的研究大多集中在环境噪声上，很少有研究集中在纯人口噪声上。我们提出了一个应用随机微分方程工具的分析框架，证明了纯人口统计噪声模型解的适定性，并获得了矩界和渐近界。我们使用这个框架来证明人口噪声不会导致种群灭绝，并且数值结果与之一致。我们提出的框架填补了纯人口噪声模型的适位性和灭绝不可能性研究的空白，并为在更复杂的进化设置中解决一般生态系统提供了严格的数学框架。

引用次数: 0

Oscillation of generalized Riemann–Weber type differential equations with delay 广义Riemann-Weber型时滞微分方程的振动性

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100637

Kazuki Ishibashi , Shouki Miyauchi , Housei Sakikawa

In this study, we investigate the oscillatory behavior of a generalized Riemann–Weber type differential equation, incorporating a logarithmically varying perturbation term and a time delay. Specifically, we derive the precise conditions under which all non-trivial solutions of the considered equation oscillate when the effects of time delay and logarithmic perturbation act simultaneously. The oscillation constant, which determines the boundary between oscillatory and non-oscillatory behavior, coincides with that of the classical delayed equation. In particular, in the absence of a time delay, the generalized equation reduces to a known form, ensuring consistency with the existing theory.

在本研究中，我们研究了包含对数变化扰动项和时滞的广义Riemann-Weber型微分方程的振荡行为。具体地说，我们导出了当时滞和对数摄动同时作用时所考虑的方程的所有非平凡解振荡的精确条件。决定振荡和非振荡行为边界的振荡常数与经典延迟方程的振荡常数一致。特别是，在没有时间延迟的情况下，广义方程简化为已知形式，保证了与现有理论的一致性。

引用次数: 0

Smooth solitary waves for the generalized gKdV-4 equation 广义gKdV-4方程的光滑孤立波

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100625

J. Noyola Rodriguez , Cynthia G. Esquer-Pérez , J.C. Hernández-Gómez , Omar Rosario Cayetano

We consider a generalization of KdV-type equations with a quartic nonlinearity

u^{4}

(gKdV-4), which includes dissipation terms similar to those appearing in the Benjamin-Bona-Mahoney equation as well as in the well-known Camassa–Holm and Degasperis-Procesi equations. Our objective is to construct classical solitary wave solutions (solitons-antisolitons) to this equation.

我们考虑了具有四次非线性u4 （gKdV-4）的kdv型方程的推广，它包含与Benjamin-Bona-Mahoney方程以及著名的Camassa-Holm和Degasperis-Procesi方程中出现的耗散项相似的耗散项。我们的目标是构造这个方程的经典孤波解（孤子-反孤子）。

引用次数: 0

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