加权的Marcinkiewicz－Zygmund不等式

本文证明加Ａｐ权的Ｍａｒｃｉｎｋｉｅｗｉｃｚ－Ｚｙｇｍｕｎｄ不等式，并指出对权所加的Ａｐ条件是必要的，最后还把这些结果应用于Ｌａｇｒａｎｇｅ插值多项式加权平均逼近阶的估计。     

Flexible piecewise approximations based on partition of unity

In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems. AMS subject classification 65N30, 65D05Weimin Han: Corresponding author. The work of this author was partially supported by NSF under grant DMS-0106781.Wing Kam Liu: The work of this author was supported by NSF.     

三次样条插值离子选择电极测定人发中的氟和碘

对同时测定同一底液中的氟和碘进行了探讨，找到了合适的１．０ｍｏｌ／Ｌ柠檬酸钠－１．０ｍｏｌ／Ｌ ＮａＮＯ３ ｐＨ＝５．５的缓冲体系。采用三次样条插值程序可很好地解决曲线的弯曲问题，改善了含氮和碘量低分析结果的准确度、精度官及检测下限。     

Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function – the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough. AMS subject classification 41A05, 41A25, 41A30, 41A63R.A. Brownlee: Supported by a studentship from the Engineering and Physical Sciences Research Council.     

TETRAHEDRAL C~m INTERPOLATION BY RATIONAL FUNCTIONS

1. IntroductionWe consider the problem of constructing Cd (m 2 0) piecewise rational local interpolation tothe data on a domain in m3 that is assumed to have been tessellated icao tetrahedra (we denotethe tessellation by 'T). The scheme requires the following data: The partial derivatives of orders at each vertex for s = 0, 1,'' 5 Zm, partial derivatives of order s at s equally (no necessary)distributed points (excluding the end points) on each edge, and 1 [(m+Zs) (m+Zs -- 1) --3s(8 -- 1)]r…     

A new finite element of C cubic splines

In this paper, we give a new finite element with dimension 16 of C¹ cubic splines which have interpolation schemes on the Morgan-Scott construction ₀ of a triangle.     

基于xL~（a）_（n－1）（x）之零点的（0，1，…，m－2，m）插值

本文给出了基于之零点的（０，１，…，ｍ－２，ｍ）插值的正则性的充要条件，其中为（ｎ－１）次Ｌａｇｕｅｒｒｅ多项式。同时基函数（若存在的话）的明显表达式也在文中给出。再者，还证明了，若该插值问题有无穷多个解，则其解的一般形式为ｆ＿０（ｘ）＋Ｃｆ＿１（ｘ）这里Ｃ为任意常数。     

Algorithm for constructing range restricted histosplines

This paper is concerned with numerical methods in range restricted histopolation. The proposal is to apply splines on refined grids. The ratios of the added split points are considered to be parameters. In this way, by choosing suitable spline classes, range restricted histosplines can always be constructed if the restrictions are compatible with the given histogram. We offer an algorithm for solving the bivariate problem on a rectangular grid which utilizes univariate results as well as tensor product techniques. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Banach couple is determined by the collection of its interpolation spaces

We prove that an arbitrary Banach couple is uniquely determined by the collection of all its interpolation spaces, which extends a result by N. Aronszajn and E. Gagliardo.

     

两类非线性方程的精确解

利用行波约化方法，并借助于一维立方非线性Klein-Gordon方程的精确解，求出了（1+1）维Zakharov方程组、变系数Korteweg-de Vries方程的一些精确解- 关键词： 行波约化方法 一维立方非线性Klein-Gordon方程 （1+1）维Zakharov方程组 变系数Korteweg-de Vries方程