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Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media 解决非均质介质中二维准晶体的弹性力学问题
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-03-25 DOI: 10.21136/AM.2024.0045-23
Meltem Altunkaynak

Initial value problem for three dimensional (3D) elastodynamic system in two dimensional (2D) inhomogeneous quasicrystals is considered. An analytical method is studied for the solution of this problem. The system is written in terms of Fourier images of displacements with respect to lateral variables. The resulting problem is reduced to integral equations of the Volterra type. Finally, using Paley Wiener theorem it is shown that the solution of the initial value problem can be found by the inverse Fourier transform. A numerical example is considered for the comparison of the exact solution with the computed solution obtained by using the method.

考虑了二维(2D)不均匀准晶体中三维(3D)弹性动力系统的初值问题。研究了解决该问题的分析方法。该系统是用相对于横向变量的位移的傅立叶图像写成的。由此产生的问题被简化为 Volterra 型积分方程。最后,利用 Paley Wiener 定理证明,初值问题的解可以通过反傅里叶变换找到。通过一个数值示例,比较了精确解和使用该方法计算得出的解。
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引用次数: 0
On stochastic properties of past varentropy with applications 论过去透明性的随机特性及其应用
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-03-11 DOI: 10.21136/AM.2024.0163-23
Akash Sharma, Chanchal Kundu

To have accuracy in the extracted information is the goal of the reliability theory investigation. In information theory, varentropy has recently been proposed to describe and measure the degree of information dispersion around entropy. Theoretical investigation on varentropy of past life has been initiated, however details on its stochastic properties are yet to be discovered. In this paper, we propose a novel stochastic order and introduce new classes of life distributions based on past varentropy. Further, we illustrate some of its applications in reliability modeling and in the diversity measure of Boltzmann distribution.

精确提取信息是可靠性理论研究的目标。在信息论中,最近提出了熵来描述和测量信息在熵周围的分散程度。有关前世熵的理论研究已经开始,但有关其随机特性的细节仍有待发现。在本文中,我们提出了一种新的随机顺序,并基于过去熵引入了新的生命分布类别。此外,我们还说明了它在可靠性建模和波尔兹曼分布多样性度量中的一些应用。
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引用次数: 0
Erratum to Fourier diffraction theorem for the tensor fields 张量场的傅立叶衍射定理的勘误
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-03-08 DOI: 10.21136/AM.2024.0056-24
Alexander Leonidovich Balandin
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引用次数: 0
Ridge estimation of covariance matrix from data in two classes 从两类数据中对协方差矩阵进行岭式估计
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-02-22 DOI: 10.21136/AM.2024.0157-23
Yi Zhou, Bin Zhang

This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether the data size is larger or smaller than the data dimension. Furthermore, the ridge parameter is tuned through a cross-validation procedure. Lastly, the proposed ridge estimator is verified with better performance than the existing estimator from the data in two classes and the traditional ridge estimator only from the good data.

摘要 本文论述了从两类数据中估计协方差矩阵的问题:(1) 具有相关协方差矩阵的良好数据;(2) 来自具有不同协方差矩阵的高斯分布的污染。为了解决从两类数据模型中估计协方差矩阵所面临的高维挑战,我们引入了脊惩罚。无论数据大小比数据维度大还是小,协方差矩阵的脊估计器都有统一的表达式,并保持正有限性。此外,脊参数还可以通过交叉验证程序进行调整。最后,验证了所提出的脊估计器在两类数据中的性能优于现有估计器,以及仅在良好数据中的传统脊估计器。
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引用次数: 0
Multi-type synchronization of impulsive coupled oscillators via topology degree 通过拓扑度实现脉冲耦合振荡器的多类型同步
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-02-19 DOI: 10.21136/AM.2024.0183-23
Yingjie Bi, Zhidan Cai, Shuai Wang

The existence of synchronization is an important issue in complex dynamical networks. In this paper, we study the synchronization of impulsive coupled oscillator networks with the aid of rotating periodic solutions of impulsive system. The type of synchronization is closely related to the rotating matrix, which gives an insight for finding various types of synchronization in a united way. We transform the synchronization of impulsive coupled oscillators into the existence of rotating periodic solutions in a relevant impulsive system. Some existence theorems about rotating periodic solutions for a non-homogeneous linear impulsive system and a nonlinear perturbation system are established by topology degree theory. Finally, we give two examples to show synchronization behaviors in impulsive coupled oscillator networks.

摘要 同步的存在是复杂动力学网络中的一个重要问题。本文借助脉冲系统的旋转周期解研究脉冲耦合振荡器网络的同步问题。同步类型与旋转矩阵密切相关,这为统一寻找各种类型的同步提供了启示。我们将脉冲耦合振荡器的同步转化为相关脉冲系统中旋转周期解的存在。通过拓扑度理论,我们建立了非均质线性脉冲系统和非线性扰动系统旋转周期解的一些存在定理。最后,我们举了两个例子来说明脉冲耦合振荡器网络中的同步行为。
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引用次数: 0
Exploring the impact of post-training rounding in regression models 探索回归模型中训练后舍入的影响
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-02-15 DOI: 10.21136/AM.2024.0090-23
Jan Kalina

Post-training rounding, also known as quantization, of estimated parameters stands as a widely adopted technique for mitigating energy consumption and latency in machine learning models. This theoretical endeavor delves into the examination of the impact of rounding estimated parameters in key regression methods within the realms of statistics and machine learning. The proposed approach allows for the perturbation of parameters through an additive error with values within a specified interval. This method is elucidated through its application to linear regression and is subsequently extended to encompass radial basis function networks, multilayer perceptrons, regularization networks, and logistic regression, maintaining a consistent approach throughout.

对估计参数进行训练后舍入(也称为量化)是机器学习模型中广泛采用的一种减少能耗和延迟的技术。本理论研究将深入探讨舍入估计参数对统计学和机器学习领域中关键回归方法的影响。所提出的方法允许通过指定区间内的加法误差值对参数进行扰动。该方法通过对线性回归的应用进行阐释,随后扩展到径向基函数网络、多层感知器、正则化网络和逻辑回归,始终保持方法的一致性。
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引用次数: 0
Identification of source term in a nonlinear degenerate parabolic equation with memory 带记忆的非线性退化抛物方程中源项的识别
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-02-07 DOI: 10.21136/AM.2024.0049-23
Soufiane Abid, Khalid Atifi, El-Hassan Essoufi, Abderrahim Zafrar

In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers’ type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness of this approach.

摘要 在这项工作中,我们考虑了一个布尔格斯(Burgers)型非线性抛物方程的反向问题,该方程带有来自最终数据的记忆项。为此,我们首先建立了直接问题的良好拟合。在最优控制框架的基础上,建立了成本函数最小化的存在性和必要条件。根据必要条件推导出最小值的全局唯一性和稳定性。数值实验证明了这种方法的有效性。
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引用次数: 0
A balanced finite-element method for an axisymmetrically loaded thin shell 轴对称加载薄壳的平衡有限元法
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-01-30 DOI: 10.21136/AM.2024.0134-23
Norbert Heuer, Torsten Linss

We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings.

我们分析了描述轴对称负载薄壳的微分方程的有限元离散化。当壳的厚度变小时,问题会受到奇异扰动。我们证明了该方法在平衡规范下的稳健收敛性,该规范捕捉到了解中存在的层。数值结果证实了我们的发现。
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引用次数: 0
Development of small and large compressive pulses in two-phase flow 两相流中大小压缩脉冲的发展
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-01-23 DOI: 10.21136/AM.2024.0107-23
Nishi Deepa Palo, Jasobanta Jena, Meera Chadha

The evolutions of small and large compressive pulses are studied in a two-phase flow of gas and dust particles with a variable azimuthal velocity. The method of relatively undistorted waves is used to study the mechanical pulses of different types in a rotational, axisymmetric dusty gas. The results obtained are compared with that of nonrotating medium. Asymptotic expansion procedure is used to discuss the nonlinear theory of geometrical acoustics. The influence of the solid particles and the rotational effect of the medium on the distortion are investigated. In a rotational flow it is observed that with the increase in the value of rotational parameter, the steepening of the pulses also increases. The presence of dust in the rotational flow delays the onset of shock formation thereby increasing the distance where the shock is formed first. The rotational and the dust parameters are observed to have the same effect on the shock strength.

在方位角速度可变的气体和尘埃粒子两相流中,研究了小型和大型压缩脉冲的演变。使用相对不扭曲波的方法研究了旋转轴对称含尘气体中不同类型的机械脉冲。研究结果与非旋转介质的结果进行了比较。使用渐近展开程序讨论了几何声学的非线性理论。研究了固体颗粒和介质旋转效应对变形的影响。在旋转流中可以观察到,随着旋转参数值的增加,脉冲的陡度也会增加。旋转流中尘埃的存在延迟了冲击的形成,从而增加了冲击首先形成的距离。旋转参数和尘埃参数对冲击强度的影响是相同的。
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引用次数: 0
Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph 连通单环图描述矩阵的极值逆特征值问题
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-01-10 DOI: 10.21136/AM.2024.0084-23
Bijoya Bardhan, Mausumi Sen, Debashish Sharma

In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned spectral data. Spectral data for the problem consist of the smallest and the largest eigenvalues of each leading principal submatrices. Inverse eigenvalue problem (IEP) with this set of spectral data is generally known as the extremal IEP. We use a standard scheme of labeling the vertices of the graph, which helps in getting a simple relation between the characteristic polynomials of each leading principal submatrix. Sufficient condition for the existence of the solution is obtained. The proof is constructive, hence provides an algorithmic procedure for finding the required matrix. Furthermore, we provide the condition under which the same problem is solvable when two particular entries of the required matrix satisfy a linear relation.

在本文中,我们利用一些预先分配的光谱数据来构建对称矩阵,其对应的图是连通的单环图。该问题的谱数据包括每个主次矩阵的最小和最大特征值。使用这组频谱数据的逆特征值问题(IEP)一般称为极值 IEP。我们使用标准的图顶点标注方案,这有助于获得每个前导主次矩阵的特征多项式之间的简单关系。我们得到了解存在的充分条件。该证明是建设性的,因此提供了找到所需矩阵的算法程序。此外,我们还提供了当所需矩阵的两个特定项满足线性关系时同一问题可解的条件。
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引用次数: 0
期刊
Applications of Mathematics
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