求解对流扩散方程的高阶ICT-MMOCAA差分方法

本文利用文[1,2]中的FCT思想，对于对流扩散问题，提出了通过插值较正传输（ICT）的高阶ICT－MMOCAA差分格式，此格式避免了[3]中基于高次（≥2）Lagrange插值的MMOCAA差分格式在解的大梯度附近产生的振荡。本文给出了格式的误差估计及数值例子。     

关于分形插值函数的连续性和可微性

获得了由迭代函数系统(IFS)定义的两类分形插值函数具有Hlder连续性的充分条件,给出了这两类分形插值函数连续可微的充要条件,并证明了可微分形插值函数的导函数是由关联IFS生成的分形插值函数.     

基于LAGRANGE插值的高阶微分中值定理

本文基于LAGRANGE插值，将微积分中非常重要的中值定理推广到了高阶的情形。     

B-值鞅Hardy空间与BMO空间的实内插

研究了B值鞅Hardy空间与BMO空间的实内插，并利用所得结果，讨论了鞅Hardy空间的内插空间的共轭问题。     

Y. Meyer小波的一般形式

首先我们证明了，如果尺度函数有紧支集，来自多尺度分析的小波函数的支集形式，然后我们证明了Y．Meyer小波的尺度函的一般形式。最后给出了它的另外两种形式和对应的Y．Meyer小波。     

复域中高阶Fejér插值的一致收敛性

对于复域中满足某种条件的Jordan区域D和函数f∈B(D),证明了基于Fejer点的高阶Fejer插值多项式一致收敛于对应的函数f(z)于D上.本文中的这些定理推广了某些已知的结果.     

Adaptive Interpolation by Scaled Multiquadrics

We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.     

Degenerate Principal Series Representations of U(p, q) and Spin0(p, q)

Let p>q and let G be the group U(p, q) or Spin₀(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup where

Asymptotic Distribution of Nodes for Near-Optimal Polynomial Interpolation on Certain Curves in R 2

Let E\subset \Bbb R ^s be compact and let d _n ^E denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ _n ={ \bf x _k,n } _k=1 ^dnE , n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R ² . It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore, for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes. November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001.     

Evolutionary Pareto distributions

We consider here i.i.d. variables which are distributed according to a Pareto up to some point x₁ and a Pareto (with a different parameter) after this point. This model constitutes an approximation for estimating extreme tail probabilities, especially for financial or insurance data. We estimate the parameters by maximizing the likelihood of the sample, and investigate the rates of convergence and the asymptotic laws. We find here a problem which is very close to the change point question from the point of view of limits of experiments. Especially, the rates of convergence and the limiting law obtained here are the same as in a change point framework. Simulations are giving an illustration of the quality of the procedure.