Extreme 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. We characterize the extreme points of the unit ball of the space of 2-homogeneous polynomials on H. We find the exact value of the λ-function for P(² H) and thus we show that its unit ball is the norm closed convex hull of its extreme points. We also describe topological properties of the set of extreme points, making connections between the set of extreme points and Grassmanian manifolds.     

APPROXIMATION PROPERTIES OF LAGRANGE INTERPOLATION POLYNOMIAL BASED ON THE ZEROS OF （1- x^2）cosnarccosx

We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].     

Approximation by generalized MKZ-operators in polynomial weighted spaces

We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

弱电解质解离热力学研究 I. 对硝基苯酚-NaCl-水体系

本文在298.15±0.2K测定了九个恒定离子强度不同PH值缓冲溶液中对硝基苯酚有等吸收点的紫外谱图。在恒定总离子旨度为I=0.1-2.0mol/kg条件下, 利用谱图中的光密度数据和测定的PH值, 根据扩展的Debye-Huckel公式外推得到pK°=7.246。K°为对硝基苯酚的热力学解离常数, 本文又提出了用多项式拟合法确定pK°, 其值为7.308。两者在实验误差范围内一致。