赋范线性空间中的最佳共逼近(l)

本文考察了赋范线性空间中的最佳共逼近，给出了共Kolmogorov特征定理及其在某些空间中的应用，从而推广了Papini及Singer的相应结论。     

多项式恒等定理的一个初等证明──兼谈多项式恒等式定理在矩阵代数中的应用

本文首先给出了多项式恒等定理的一个初等证明，然后以实例说明用多项式恒等定理处理有关矩阵命题是非常方便的。     

代数学基本定理的推广

将代数学基本定理推广到某类矩阵多项式 ,获得了一类广泛的结果     

西方现代产权理论与我国经济体制改革

产权对社会经济发展有何影响,历来有不同的理解和争议。建立适合经济发展所需的多样化所有制形式,对于社会主义建设和发展具有重要意义。改革中,深入研究产权与经济发展的关系,可以为我国的经济体制改革提供有益的借鉴。     

弥尔曼定理的探讨及应用

对弥尔曼定理进行了推广 ,给只有两个节点的电路分析带来了方便     

n—幂零Hall子群的Wielandt定理

本文证明了类似于Wielandt定理的结果:设G为有限群,H是G的n—幂零Π-Hall子群,若M是G的Π—子群,(|M|,n(1—n))=1,则存在aG使M~a≤H。并对文[2]中定理2.2的证明进行了改进,证法比文[2]更简洁。     

On the limiting distributions of the jackknife statistics for eigenvalues of a sample covariance matrix

The limiting distributions of jackknife statistics for eigenvalues of a sample covariance matrix are derived under the nonnormal situations. Also the numerical examples are given under normal and nonnormal populations.     

Inequalities for the partial sums of elliptical order statistics related to genetic selection

Let X₁,…,X_n be exchangeable normal variables with a common correlation p, and let X₍₁₎ > … > X_(n) denote their order statistics. The random variable σⁿ_i=_n—_k+1x_i, called the selection differential by geneticists, is of particular interest in genetic selection and related areas. In this paper we give results concerning a conjecture of Tong (1982) on the distribution of this random variable as a function of ρ. The same technique used can be applied to yield more general results for linear combinations of order statistics from elliptical distributions.     

(n,p)积分-微分方程边值问题解的存在性

运用Schauder不动点定理和Banach空间中一个相对紧的充要条件,获得了一类(n,p)积分-微分方程边值问题解的存在性.     

Asymptotically valid single-stage multiple-comparison procedures

We establish general conditions for the asymptotic validity of single-stage multiple-comparison procedures (MCPs) under the following general framework. There is a finite number of independent alternatives to compare, where each alternative can represent, e.g., a population, treatment, system or stochastic process. Associated with each alternative is an unknown parameter to be estimated, and the goal is to compare the alternatives in terms of the parameters. We establish the MCPs’ asymptotic validity, which occurs as the sample size of each alternative grows large, under two assumptions. First, for each alternative, the estimator of its parameter satisfies a central limit theorem (CLT). Second, we have a consistent estimator of the variance parameter appearing in the CLT. Our framework encompasses comparing means (or other moments) of independent (not necessarily normal) populations, functions of means, quantiles, steady-state means of stochastic processes, and optimal solutions of stochastic approximation by the Kiefer–Wolfowitz algorithm. The MCPs we consider are multiple comparisons with the best, all pairwise comparisons, all contrasts, and all linear combinations, and they allow for unknown and unequal variance parameters and unequal sample sizes across alternatives.