Results in Applied Mathematics最新文献

英文中文

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

Turing patterns across geometries: A proven DSC-ETDRK4 solver from plane to sphere 跨几何图形的图灵模式：一个经过验证的DSC-ETDRK4从平面到球体的求解器

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100631

Kolade M. Owolabi , Edson Pindza , Eben Maré

This paper presents a unified and robust numerical framework that combines the Discrete Singular Convolution (DSC) method for spatial discretization with the Exponential Time Differencing Runge–Kutta (ETDRK4) scheme for temporal integration to solve reaction–diffusion systems. Specifically, we investigate the formation of Turing patterns – such as spots, stripes, and mixed structures – in classical models including the Gray–Scott, Brusselator, and Barrio–Varea–Aragón–Maini (BVAM) systems. The DSC method, employing the regularized Shannon’s delta kernel, delivers spectral-like accuracy in computing spatial derivatives on both regular and curved geometries. Coupled with the fourth-order ETDRK method, this approach enables efficient and stable time integration over long simulations. Importantly, we rigorously establish the necessary theoretical results – including convergence, stability, and consistency theorems, along with their proofs – for the combined DSC-ETDRK4 method when applied to both planar and curved surfaces. We demonstrate the capability of the proposed method to accurately reproduce and analyze complex spatiotemporal patterns on a variety of surfaces, including the plane, sphere, torus, and bumpy geometries. Numerical experiments confirm the method’s versatility, high accuracy, and computational efficiency, making it a powerful tool for the study of pattern formation in reaction–diffusion systems on diverse geometries.

本文提出了一个统一的、鲁棒的数值框架，该框架结合了用于空间离散化的离散奇异卷积（DSC）方法和用于时间积分的指数时差龙格-库塔（ETDRK4）格式来求解反应扩散系统。具体来说，我们研究了图灵模式的形成-如斑点，条纹和混合结构-在经典模型中，包括Gray-Scott， Brusselator和Barrio-Varea-Aragón-Maini （BVAM）系统。DSC方法采用正则化香农δ核，在计算规则和弯曲几何的空间导数时提供了类似光谱的精度。与四阶ETDRK方法相结合，该方法可以在长时间模拟中实现高效稳定的时间积分。重要的是，我们严格地建立了必要的理论结果-包括收敛性，稳定性和一致性定理，以及它们的证明-当应用于平面和曲面时，DSC-ETDRK4组合方法。我们证明了所提出的方法能够准确地再现和分析各种表面上的复杂时空模式，包括平面、球体、环面和凹凸几何形状。数值实验证实了该方法的通用性、高精度和计算效率，使其成为研究不同几何形状反应扩散系统模式形成的有力工具。

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引用次数: 0

Multiplicity results for non-local operators of elliptic type 椭圆型非局部算子的多重性结果

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100626

Emer Lopera , Leandro Recôva , Adolfo Rumbos

In this paper, we study a class of problems proposed by Servadei and Valdinoci (2013); namely, (1)

(\begin{matrix} - L_{K} u (x) - λ u (x) & = f (x, u), for x \in Ω; \\ u & = 0 in R^{N} ∖ Ω, \end{matrix})

where

Ω \subset R^{N}

is an open bounded set with Lipschitz boundary,

λ \in R

f \in C^{1} (\bar{Ω} \times R, R)

, with

f (x, 0) = 0

for

x \in Ω

, and

L_{K}

is a non-local integrodifferential operator with homogeneous Dirichlet boundary condition. By computing the critical groups of the associated energy functional for problem (1) at the origin and at infinity, respectively, we prove that problem (1) has three nontrivial solutions for the case

λ < λ_{1}

and two nontrivial solutions for the case

λ ⩾ λ_{1},

where

λ_{1}

is the first eigenvalue of the operator

- L_{K}

. Finally, assuming that the nonlinearity

f

is odd in the second variable, we prove the existence of an unbounded sequence of weak solutions of problem (1) for the case

λ ⩾ λ_{1}

. We use variational methods and infinite-dimensional Morse theory to obtain the results.

本文研究Servadei和Valdinoci（2013）提出的一类问题；即(1)−LKu(x)−λu(x)=f(x,u),forx∈Ω；u=0inRN∈Ω，其中Ω∧RN是一个具有Lipschitz边界的开有界集合，λ∈R, f∈C1（Ω¯×R，R），其中对于x∈Ω， f(x,0)=0， LK是一个具有齐次Dirichlet边界条件的非局部积分微分算子。通过分别在原点和无穷远处计算问题(1)的相关能量函数的临界群，我们证明问题(1)对于λ<；λ1的情况有三个非平凡解，对于λ大于或等于λ1的情况有两个非平凡解，其中λ1是算子−LK的第一个特征值。最后，假设非线性f在第二个变量中是奇数，我们证明对于λ大于或等于λ1的情况，问题(1)的弱解的无界序列的存在性。我们使用变分方法和无限维莫尔斯理论来得到结果。

引用次数: 0

Rational and singular points of a family of curves 曲线族的有理点和奇异点

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100630

M.C. Rodríguez-Palánquex

This paper explores the properties of a family of absolutely irreducible projective plane curves, denoted

C_{a, b}

, which are defined over a finite field

F_{m}

of characteristic 2. The curves are explicitly given by the homogeneous equation

Y^{a} Z^{b - a} + Y Z^{b - 1} + X^{b} = 0

, where

a

and

b

are natural numbers satisfying the conditions

a \geq 2

and

b \geq a

. A primary objective of the paper is to determine the number of rational points on these curves.

The work also includes a detailed analysis of the singular points of the curves, providing a classification of these points based on the parameters

a

and

b

. Furthermore, the relationship between the number of rational points and the genus of the curves is investigated, with specific computations carried out for curves defined over the finite field

F_{2^{4}}

. In particular, the paper presents explicit calculations of the number of rational points for curves of the form

C_{2, b}

and

C_{3, b}

over

F_{2^{4}}

, illustrating the connection between these counts and the genus of the curves.

This comprehensive analysis contributes to a deeper understanding of the arithmetic geometry of this family of curves over finite fields.

研究了在特征为2的有限域Fm上定义的绝对不可约平面投影曲线族Ca，b的性质。曲线由齐次方程YaZb−a+YZb−1+Xb=0显式给出，其中a和b是满足条件a≥2和b≥a的自然数。本文的主要目的是确定这些曲线上有理点的个数。该工作还包括对曲线奇异点的详细分析，提供了基于参数a和b的这些点的分类。此外，研究了有理点数量与曲线属数之间的关系，并对有限域F24上定义的曲线进行了具体计算。特别地，本文给出了形式为C2，b和C3，b / F24的曲线的有理点的数目的显式计算，并说明了这些数目与曲线的属之间的联系。这种全面的分析有助于对有限域上这类曲线的算术几何有更深的理解。

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引用次数: 0

Enhanced PINNs for data-driven solitons and parameter discovery for (2+ 1)-dimensional coupled nonlinear Schrödinger systems （2+ 1）维耦合非线性Schrödinger系统中数据驱动孤子的增强pinn和参数发现

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100635

Hamid Momeni , AllahBakhsh Yazdani Cherati , Ali Valinejad

This paper investigates data-driven solutions and parameter discovery to (2+ 1)-dimensional coupled nonlinear Schrödinger equations with variable coefficients (VC-CNLSEs), which describe transverse effects in optical fiber systems under perturbed dispersion and nonlinearity. By setting different forms of perturbation coefficients, we aim to recover the dark and anti-dark one- and two-soliton structures by employing an enhanced physics-based deep neural network algorithm, namely a physics-informed neural network (PINN). The enhanced PINN algorithm leverages the locally adaptive activation function mechanism to improve convergence speed and accuracy. In the lack of data acquisition, the PINN algorithms will enhance the capability of the neural networks by incorporating physical information into the training phase. We demonstrate that applying PINN algorithms to (2+ 1)-dimensional VC-CNLSEs requires distinct distributions of physical information. To address this, we propose a region-specific weighted loss function with the help of residual-based adaptive refinement strategy. In the meantime, we perform data-driven parameter discovery for the model equation, classified into two categories: constant coefficient discovery and variable coefficient discovery. For the former, we aim to predict the cross-phase modulation constant coefficient under varying noise intensities using enhanced PINN with a single neural network. For the latter, we employ a dual-network strategy to predict the dynamic behavior of the dispersion and nonlinearity perturbation functions. Our study demonstrates that the proposed framework holds significant potential for studying high-dimensional and complex solitonic dynamics in optical fiber systems.

本文研究了（2+ 1）维耦合变系数非线性Schrödinger方程（VC-CNLSEs）的数据驱动解和参数发现问题，该方程描述了光纤系统在扰动色散和非线性下的横向效应。通过设置不同形式的扰动系数，我们的目标是利用增强的基于物理的深度神经网络算法，即物理通知神经网络（PINN），恢复暗和反暗的一孤子和双孤子结构。增强的PINN算法利用局部自适应激活函数机制，提高了收敛速度和精度。在缺乏数据采集的情况下，PINN算法将通过将物理信息纳入训练阶段来增强神经网络的能力。我们证明了将PINN算法应用于（2+ 1）维vc - cnlse需要不同的物理信息分布。为了解决这个问题，我们提出了一个基于残差的自适应改进策略的区域特定加权损失函数。同时，对模型方程进行数据驱动的参数发现，分为常系数发现和变系数发现两类。对于前者，我们的目标是使用单个神经网络的增强PINN来预测不同噪声强度下的交叉相位调制常数系数。对于后者，我们采用双网络策略来预测色散和非线性扰动函数的动态行为。我们的研究表明，所提出的框架在研究光纤系统中的高维和复杂孤子动力学方面具有重要的潜力。

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引用次数: 0

Stability analysis of a dynamical model for sustainable Glacier ecotourism 冰川可持续生态旅游动态模型的稳定性分析

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics

Pub Date : 2025-08-01 DOI: 10.1016/j.rinam.2025.100636

Jianbang He , Jiyue Zhang , Mazheze Xu , Zhongxiang Chen

In this paper, we construct a system dynamics model to study the sustainable evolution of glacier ecotourism systems under environmental change. We calculate

R_{C}

based on the carbon-temperature equilibrium and

R_{N}

based on the reproduction number method in epidemiological models, and prove that the zero equilibrium is globally asymptotically stable when

R_{C} < 1

and

R_{N} \leq 1

, and the error dynamics with respect to the positive equilibrium are globally uniformly ultimately bounded when both

R_{C} < 1

and

R_{N} > 1

. Empirical validation based on data from the Mendenhall Glacier is conducted to support the theoretical analysis.

本文通过构建系统动力学模型，研究了环境变化下冰川生态旅游系统的可持续演化。在流行病学模型中，基于碳-温度平衡计算RC，基于复制数法计算RN，并证明了当RC<；1和RN≤1时，零平衡是全局渐近稳定的，当RC<；1和RN>；1时，相对于正平衡的误差动态是全局一致最终有界的。基于Mendenhall冰川的数据进行了实证验证，以支持理论分析。

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