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Maxwell-Schrödinger equations in singular electromagnetic field 奇异电磁场中的麦克斯韦-薛定谔方程
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-05-31 DOI: 10.21136/AM.2024.0180-23
Qihong Shi, Yaqian Jia, Jianwei Yang
{"title":"Maxwell-Schrödinger equations in singular electromagnetic field","authors":"Qihong Shi,&nbsp;Yaqian Jia,&nbsp;Jianwei Yang","doi":"10.21136/AM.2024.0180-23","DOIUrl":"10.21136/AM.2024.0180-23","url":null,"abstract":"<div><p>We investigate the Cauchy problem of the one dimensional Maxwell-Schrödinger (MS) system under the Lorenz gauge condition. Different from the classical case, we consider the electromagnetic and electrostatic potentials which are growing at space infinity. More precisely, the electrostatic potential is allowed to grow linearly, while for the electromagnetic potential the growth is sublinear. Based on the energy estimates and the gauge transformation, we prove the global existence and the uniqueness of the weak solutions to this system.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 4","pages":"437 - 450"},"PeriodicalIF":0.6,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Energy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media 导电介质中稳定麦克斯韦方程的能量规范误差估计和收敛分析
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-05-27 DOI: 10.21136/AM.2024.0248-23
Eric Lindström, Larisa Beilina
{"title":"Energy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media","authors":"Eric Lindström,&nbsp;Larisa Beilina","doi":"10.21136/AM.2024.0248-23","DOIUrl":"10.21136/AM.2024.0248-23","url":null,"abstract":"<div><p>The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell’s equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell’s equations also solves the wave equation, which makes computations very efficient. In this way our problem can be considered as a coupling problem, for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 4","pages":"415 - 436"},"PeriodicalIF":0.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2024.0248-23.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving inverse nodal problem with frozen argument by using second Chebyshev wavelet method 用第二切比雪夫小波法解决带冻结参数的反节点问题
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-04-17 DOI: 10.21136/AM.2024.0038-21
Yu Ping Wang, Shahrbanoo Akbarpoor Kiasary, Emrah Yılmaz
{"title":"Solving inverse nodal problem with frozen argument by using second Chebyshev wavelet method","authors":"Yu Ping Wang,&nbsp;Shahrbanoo Akbarpoor Kiasary,&nbsp;Emrah Yılmaz","doi":"10.21136/AM.2024.0038-21","DOIUrl":"10.21136/AM.2024.0038-21","url":null,"abstract":"<div><p>We consider the inverse nodal problem for Sturm-Liouville (S-L) equation with frozen argument. Asymptotic behaviours of eigenfunctions, nodal parameters are represented in two cases and numerical algorithms are produced to solve the given problems. Subsequently, solution of inverse nodal problem is calculated by the second Chebyshev wavelet method (SCW), accuracy and effectiveness of the method are shown in some numerical examples.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"339 - 354"},"PeriodicalIF":0.6,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140691512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula 基于特殊矩阵和乘积公式的对称 Sturm-Liouville 问题和反电势问题的特征值
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-04-08 DOI: 10.21136/AM.2024.0005-21
Chein-Shan Liu, Botong Li
{"title":"The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula","authors":"Chein-Shan Liu,&nbsp;Botong Li","doi":"10.21136/AM.2024.0005-21","DOIUrl":"10.21136/AM.2024.0005-21","url":null,"abstract":"<div><p>The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in a linear space of trial functions by using the Gram-Schmidt orthonormalization technique. Then an <i>n</i>-dimensional matrix eigenvalue problem is derived with a special matrix <b>A</b>:= [<i>a</i><sub><i>ij</i></sub>], that is, <i>a</i><sub><i>ij</i></sub> = 0 if <i>i</i> + <i>j</i> is odd.</p><p>Based on the product formula, an integration method with a fictitious time, namely the fictitious time integration method (FTIM), is developed to obtain the higher-index eigenvalues. Also, we recover the symmetric potential function <i>q</i>(<i>x</i>) in the Sturm-Liouville operator by specifying a few lower-index eigenvalues, based on the product formula and the Newton iterative method.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"355 - 372"},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations 求解复杂对称线性方程的双参数双步分裂迭代法
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-04-05 DOI: 10.21136/AM.2024.0133-23
Beibei Li, Jingjing Cui, Zhengge Huang, Xiaofeng Xie
{"title":"A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations","authors":"Beibei Li,&nbsp;Jingjing Cui,&nbsp;Zhengge Huang,&nbsp;Xiaofeng Xie","doi":"10.21136/AM.2024.0133-23","DOIUrl":"10.21136/AM.2024.0133-23","url":null,"abstract":"<div><p>We multiply both sides of the complex symmetric linear system <i>Ax</i> = <i>b</i> by 1 − i<i>ω</i> to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"311 - 337"},"PeriodicalIF":0.6,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-point oscillatory solutions to system with relay hysteresis and nonperiodic external disturbance 具有中继滞后和非周期性外部干扰的系统的两点振荡解
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-04-02 DOI: 10.21136/AM.2024.0152-22
Alexander M. Kamachkin, Dmitriy K. Potapov, Victoria V. Yevstafyeva
{"title":"Two-point oscillatory solutions to system with relay hysteresis and nonperiodic external disturbance","authors":"Alexander M. Kamachkin,&nbsp;Dmitriy K. Potapov,&nbsp;Victoria V. Yevstafyeva","doi":"10.21136/AM.2024.0152-22","DOIUrl":"10.21136/AM.2024.0152-22","url":null,"abstract":"<div><p>We study an <i>n</i>-dimensional system of ordinary differential equations with a constant matrix, a relay-type nonlinearity, and an external disturbance in the right-hand side. We consider a nonideal relay characteristic. The external disturbance is described by the product of an exponential function and a sine function with an initial phase as a parameter. We assume the matrix of the linear part and the vector at the relay characteristic such that, by a nonsingular transformation, the system is reduced to the form with the diagonal matrix and the vector being opposite to the unit vector. We establish a necessary and sufficient condition for the existence of two-point oscillatory solutions, i.e., the solutions with two fixed points on the hyperplanes of the relay switching in phase space. Also, we give the sufficient conditions under which such solutions do not exist. We provide a supporting example, which demonstrates how to apply the obtained results.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"395 - 414"},"PeriodicalIF":0.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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
Applications of Mathematics Pub Date : 2024-03-25 DOI: 10.21136/AM.2024.0045-23
Meltem Altunkaynak
{"title":"Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media","authors":"Meltem Altunkaynak","doi":"10.21136/AM.2024.0045-23","DOIUrl":"10.21136/AM.2024.0045-23","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"289 - 309"},"PeriodicalIF":0.6,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140383945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applications of Mathematics Pub Date : 2024-03-11 DOI: 10.21136/AM.2024.0163-23
Akash Sharma, Chanchal Kundu
{"title":"On stochastic properties of past varentropy with applications","authors":"Akash Sharma,&nbsp;Chanchal Kundu","doi":"10.21136/AM.2024.0163-23","DOIUrl":"10.21136/AM.2024.0163-23","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"373 - 394"},"PeriodicalIF":0.6,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applications of Mathematics Pub Date : 2024-03-08 DOI: 10.21136/AM.2024.0056-24
Alexander Leonidovich Balandin
{"title":"Erratum to Fourier diffraction theorem for the tensor fields","authors":"Alexander Leonidovich Balandin","doi":"10.21136/AM.2024.0056-24","DOIUrl":"10.21136/AM.2024.0056-24","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"287 - 287"},"PeriodicalIF":0.6,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140077105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Applications of Mathematics Pub Date : 2024-02-22 DOI: 10.21136/AM.2024.0157-23
Yi Zhou, Bin Zhang
{"title":"Ridge estimation of covariance matrix from data in two classes","authors":"Yi Zhou,&nbsp;Bin Zhang","doi":"10.21136/AM.2024.0157-23","DOIUrl":"10.21136/AM.2024.0157-23","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"169 - 184"},"PeriodicalIF":0.6,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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