共轭混合型Jacobi级数的收敛速度(英文)

对于有界变差的连续函数，本文给出了其共轭混合型Jacobi级数的收敛速度．     

Extreme points of unit balls in Lipschitz function spaces

We give a new characterization of the set of all extreme points of the unit ball in the Banach space of all Lipschitz functions on a metric space This result is applied to get a total variation characterization of in the particular case when is a convex subset of a Banach space.

     

The limit of the partial sums process of spatial least squares residuals

We establish a functional central limit theorem for a sequence of least squares residuals of spatial data from a linear regression model. Under mild assumptions on the model we explicitly determine the limit process in the case where the assumed linear model is true. Moreover, in the case where the assumed linear model is not true we explicitly establish the limit process for the localized true regression function under mild conditions. These results can be used to develop non-parametric model checks for linear regression. Our proofs generalize ideas of a univariate geometrical approach due to Bischoff [W. Bischoff, The structure of residual partial sums limit processes of linear regression models, Theory Stoch. Process. 8 (24) (2002) 23–28] which is different to that proposed by MacNeill and Jandhyala [I.B. MacNeill, V.K. Jandhyala, Change-point methods for spatial data, in: G.P. Patil, et al. (Eds.), Multivariate Environmental Statistics. Papers Presented at the 7th International Conference on Multivariate Analysis held at Pennsylvania State University, University Park, PA, USA, May 5–9 1992, in: Ser. Stat. Probab., vol. 6, North-Holland, Amsterdam, 1993, pp. 289–306 (in English)]. Moreover, Xie and MacNeill [L. Xie, I.B. MacNeill, Spatial residual processes and boundary detection, South African Statist. J. 40 (1) (2006) 33–53] established the limit process of set indexed partial sums of regression residuals. In our framework we get that result as an immediate consequence of a result of Alexander and Pyke [K.S. Alexander, R. Pyke, A uniform central limit theorem for set-indexed partial-sum processes with finite variance, Ann. Probab. 14 (1986) 582–597]. The reason for that is that by our geometrical approach we recognize the structure of the limit process: it is a projection of the Brownian sheet onto a certain subspace of the reproducing kernel Hilbert space of the Brownian sheet. Several examples are discussed.     

均匀分布U〔θ-1/2,θ+1/2〕中参数θ的四种估计量

给出均匀分布U〔θ-1/2,θ+1/2〕中θ的四种估计量,并分别比较了四种估计量的优劣性.     

Gurarii的凸性模与正规结构

本文研究了Gurarii的凸性模与正规结构的联系.利用关于该模的不等式得出了如果存在ε,1≤ε≤2,使得β(ε)＞ε-1.则空间X具有一致正规结构.     

UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE NONLINEARITIES＊

This article deals with a nonlocal heat system subject to null Dirichlet boundary conditions,where the coupling nonlocal sources consist of mixed type asymmetric nonlinearities.We at first give the cri...     

密度函数垂直表示及在非均匀随机数生成中的应用

本文给出密度函数垂直表示法,以及利用该方法产生给定概率密度函数的随机向量的一般算法。     

关于微分方程解的一致非常稳定性与一致距离有界性

讨论了一般非自治方程解的一致非常稳定性与一致距离有界性.