Successive iteration and positive symmetric solution for a Sturm–Liouville-like four-point boundary value problem with a -Laplacian operator

In this paper, we consider the following Sturm–Liouville-like four-point p-Laplacian boundary value problem with the nonlinear term f depending on the first-order derivative subject to the boundary conditions By using a monotone iterative technique, the existence of symmetric positive solutions and corresponding iterative schemes are obtained.     

An iteration regularization for a time-fractional inverse diffusion problem

In the present paper we consider a time-fractional inverse diffusion problem, where data is given at x = 1 and the solution is required in the interval 0 < x < 1. This problem is typically ill-posed: the solution (if it exists) does not depend continuously on the data. We give a new iteration regularization method to deal with this problem, and error estimates are obtained for a priori and a posteriori parameter choice rules, respectively. Furthermore, numerical implement shows the proposed method works effectively.     

光纤分布式测温系统中基于迭代法的高准确度温度解调算法

提出了一种利用喇曼散射原理的光纤分布式测温系统中基于迭代的高准确度温度解调算法.针对于常规的反斯托克斯-斯托克斯双光路比值的温度解调算法,该迭代算法进一步校正了光纤中双光路衰减系数差对温度敏感带来的温度测量误差,尤其适用于中距离且温度场复杂的测温环境,实现了高准确度的温度测量.通过理论分析确定了该迭代法的迭代格式,测量了相应的光纤参量,并在传感样机上编写相应的代码通过实验予以验证,在0～90℃温度范围,5km测量长度输出的测温曲线符合预期的测温效果.     

基于Landweber迭代的图像重建算法

本文尝试将一种新型的基于Landweber迭代算法用于电阻抗断层图像(EIT)重建。该算法与线性反投影算法不同,Landweber算法可以明显地改进图像质量。仿真结果表明,它不仅可以消除噪声干扰,而且能加快收敛速度。     

一类非线性算子的带误差的Ishikawa迭代程序及其稳定性

建立了任意实Banach空间中带误差的Ishikawa迭代程序逼近Lipschitz强伪压缩算子的不动点的一般性定理,指出已被广泛广泛研究的Ishikawa迭代序列的稳定性问题仅是带误差的Ishikawa迭代程序的特例,作为直接的应用,用不同于通常的方法证得任意实Banach空间中的Ishikawa迭代序列关于Lipschitz强伪压缩算子是稳定的,这些推广或发展了近期许多相应的结果。     

Analytic solutions of a nonlinear iterative equation near neutral fixed points and poles

In this paper existence of analytic solutions of a nonlinear iterative equations is studied when given functions are all analytic and when given functions have poles. As well as in many previous works, we reduce this problem to finding analytic solutions of a functional equation without iteration of the unknown function f. For technical reasons, in previous works an indeterminate constant related to the eigenvalue of the linearized f at its fixed point O is required to fulfill the Diophantine condition that O is an irrationally neutral fixed point of f. In this paper the case of rationally neutral fixed points is also discussed, where the Diophantine condition is not required.     

Stability of functional equations in single variable

This paper discusses Hyers-Ulam stability for functional equations in single variable, including the forms of linear functional equation, nonlinear functional equation and iterative equation. Surveying many known and related results, we clarify the relations between Hyers-Ulam stability and other senses of stability such as iterative stability, continuous dependence and robust stability, which are used for functional equations. Applying results of nonlinear functional equations we give the Hyers-Ulam stability of Böttcher's equation. We also prove a general result of Hyers-Ulam stability for iterative equations.     

矩阵方程AXB=C的反对称解和极小范数反对称解

建立了求矩阵方程AXB=C反对称解的迭代方法.使用该方法不仅能够判断反对称解的存在性,而且在有反对称解时,能够在有限步迭代计算之后得到反对称解.选取特殊的初始矩阵,可求得极小范数反对称解.     

A Lotka-Volterra type food chain model with stage structure and time delays

A three-species Lotka-Volterra type food chain model with stage structure and time delays is investigated. It is assumed in the model that the individuals in each species may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators (immature top predators) do not have the ability to feed on prey (predator). By using some comparison arguments, we first discuss the permanence of the model. By means of an iterative technique, a set of easily verifiable sufficient conditions are established for the global attractivity of the nonnegative equilibria of the model.     

关于单调Brown方法的进一步研究

本文引入了一类较为广泛的函数类，提出了一种新的单调Ｂｒｏｗｎ方法，讨论了这种方法的收敛性，非平凡地推广了Ｆｒｍｍｅｒ的相应结果。