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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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
Applications of Mathematics Pub Date : 2024-02-19 DOI: 10.21136/AM.2024.0183-23
Yingjie Bi, Zhidan Cai, Shuai Wang
{"title":"Multi-type synchronization of impulsive coupled oscillators via topology degree","authors":"Yingjie Bi,&nbsp;Zhidan Cai,&nbsp;Shuai Wang","doi":"10.21136/AM.2024.0183-23","DOIUrl":"10.21136/AM.2024.0183-23","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129490","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
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
Applications of Mathematics Pub Date : 2024-02-15 DOI: 10.21136/AM.2024.0090-23
Jan Kalina
{"title":"Exploring the impact of post-training rounding in regression models","authors":"Jan Kalina","doi":"10.21136/AM.2024.0090-23","DOIUrl":"10.21136/AM.2024.0090-23","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2024.0090-23.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139962630","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
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