二阶椭圆方程的下解及Holder连续的一个新证明(英文)

借助于检试函数和迭代技术,在系数弱光滑性假设条件下,本文研究了二阶椭圆方程的下解和正则性.进一步借助于局部估计和Poincare不等式,我们给出了Holder连续的一个新证明.     

A basic family of iteration functions for polynomial root finding and its characterizations

Let p(x) be a polynomial of degree n?2 with coefficients in a subfield K of the complex numbers. For each natural number m?2, let L_m(x) be the m×m lower triangular matrix whose diagonal entries are p(x) and for each j=1,…,m−1, its jth subdiagonal entries are . For i=1,2, let L_m^i)(x) be the matrix obtained from L_m(x) by deleting its first i rows and its last i columns. L₁⁽¹⁾(x)≡1. Then, the function B_m(x)=x−p(x) defines a fixed-point iteration function having mth order convergence rate for simple roots of p(x). For m=2 and 3, B_m(x) coincides with Newton's and Halley's, respectively. The function B_m(x) is a member of S(m,m+n−2), where for any M?m, S(m,M) is the set of all rational iteration functions g(x) ∈ K(x) such that for all roots θ of p(x), then g(x)=θ+∑_i=m^Mγ_i(x)(θ−x)ⁱ, with γ_i(x) ∈ K(x) and well-defined at any simple root θ. Given g ∈ S(m,M), and a simple root θ of p(x), gⁱ(θ)=0, i=1, …, m−1 and the asymptotic constant of convergence of the corresponding fixed-point iteration is . For B_m(x) we obtain . If all roots of p(x) are simple, B_m(x) is the unique member of S(m,m + n − 2). By making use of the identity , we arrive at two recursive formulas for constructing iteration functions within the S(m,M) family. In particular, the family of B_m(x) can be generated using one of these formulas. Moreover, the other formula gives a simple scheme for constructing a family of iteration functions credited to Euler as well as Schröder, whose mth order member belongs to S(m,mn), m>2. The iteration functions within S(m,M) can be extended to any arbitrary smooth function f, with the uniform replacement of p^(j) with f^(j) in g as well as in γ_m(θ).     

计时电流的因子分析-法拉第电流与充电电流的分离

基于电化学理论电流公式,用迭代目标变换因子分析法对计时电路曲线进行处理,得到分离的法拉第电流和充电电流成分,对于简单的电极过程,分离效果很好,信噪比得到提高,法拉第电流分量可用于定量分析。     

X射线荧光分析中谢尔曼方程逆问题的求解（理论影响系数法 …

本文首先在理论分析基础上,建立多元素样品的重量分数Ｃｉ、Ｘ射线荧光相对强度Ｒｉ与基体效应因子Ｆｉ的代数关系。然后,按照此关系导出两种求解谢尔曼方程逆问题的方法,即理论影响系数法和基本参数法。并用这两种方法分析了６个耐热钢标样,主量、常量元素的平均相对分析误差〈０．５％,对低含量轻元素Ｓｉ、Ｐ、Ｓ的分析也取得良好的结果。     

MONOTONE ITERATION FOR ELLIPTIC PDEs WITH DISCONTINUOUS NONLINEAR TERMS

In this paper, we use monotone iterative techniques to show the existence of maximal or minimal solutions of some elliptic PDEs with nonlinear discontinuous terms. As the numerical analysis of this PDEs is concerned, we prove the convergence of discrete extremal solutions.     

On the structures of generating iterated function systems of Cantor sets

A generating IFS of a Cantor set F is an IFS whose attractor is F. For a given Cantor set such as the middle-3rd Cantor set we consider the set of its generating IFSs. We examine the existence of a minimal generating IFS, i.e. every other generating IFS of F is an iterating of that IFS. We also study the structures of the semi-group of homogeneous generating IFSs of a Cantor set F in under the open set condition (OSC). If dim_HF<1 we prove that all generating IFSs of the set must have logarithmically commensurable contraction factors. From this Logarithmic Commensurability Theorem we derive a structure theorem for the semi-group of generating IFSs of F under the OSC. We also examine the impact of geometry on the structures of the semi-groups. Several examples will be given to illustrate the difficulty of the problem we study.     

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.