概率性质的一种有趣证明

概率性质的一种有趣证明王顺钦（南阳师专数学系）概率论中，设概率空间（Ｄ，Ｆ，Ｐ），其中Ω为基本事件空间，Ｆ为由Ω的子集组成的（δ─代数）事件域，Ｐ是定义在Ｆ上的遵从公理（非负，规范，δ─可加）的集函数，在概率产的公理下，容易证明尸还具有以下基本性质：...     

电磁逆散射问题中的泛函方法

用于电磁逆散射问题中关于未知介质分布的非线性积分方程经离散化后，其相应的矩阵方程通常是病态方程。对于病态的矩阵方程，其解或是不存在或是不唯一。这取决于该矩阵方程是超定的还是欠定的。对于这样的不适定问题，可用一些泛函方法使其转化为适定问题。文中介绍了用于电磁逆散射问题中的最小二乘方法、奇异值分解方法、正则化方法和最大熵方法，并对各种方法的优缺点给出评价。     

除环上一个矩阵秩的恒等式的修正

本文修正了除环上一个矩阵秩的恒等式，推广、改进了屠伯项教授的相应结果．     

分层双各向异性媒质中基本振子源的电磁场(英文)

对于观察点不在任意方向放置的,位于分层双各向异性媒质中的基本电磁振子源附近的电磁场,本文给出了明显表达式。利用傅立叶变换谱域中的横向场矢量的矩阵分析,该问题得到了较为方筻的解决。     

单李代数不可约表示的标记

对于n秩单李代数g,当采用Dynkin关于素根的分类时,其不可约表示可以用n个非负整数Λ_(αi)标记,也可通过初等表示的权用数组li来标记。利用Cartan逆矩阵,我们给出了计算Λ_(α_i)与li之间关系的方法。对于B_n、C_n、D_n和F_4,利用Cartan逆矩阵证明了这些li是与采用Cartan关于素根的分类时的Λi是一致的。     

On the block structure of proper block designs

In this paper we consider proper block designs and derive an upper bound for the number of blocks which can have a fixed number of symbols common with a given block of the design. To arrive at the desired bound, a generalization of an integer programming theorem due to Bush (1976) is first obtained. The integer programming theorem is then used to derive the main result of this paper. The bound given here is then compared with a similar bound obtained by Kageyama and Tsuji (1977).     

Yearly variation in recruitment and its effect on population dynamics inYoldia notabilis (Mollusca: Bivalvia), analyzed using projection matrix model

Summary Long-term variation in recruitment was estimated by constructing projection matrices for a marine bivalve,Yoldia notabilis, at two stations in Otsuchi Bay, northeastern Japan, and the effects of its variation on population dynamics were examined using a simple matrix model. The matrix model was developed from the Leslie matrix, in which the population growth rate λ was expressed as a function of recruitment rater ₀. The equilibrium recruitment rater _s, or the recruitment rate required to maintain population at constant size (λ=1), was expressed by the reciprocal of the reproductive value of a newly recruited individual. The estimates ofr _s for the field population were lower at the shallower station than at the deeper station, reflecting higher survivorship and fecundity. Past recruitment rate estimated both by the field samplings for 3 years and by the back-calculation from the current age structure for over 10 years showed large yearly variation, ranging between 0 and 58.6×10⁻⁴. The estimates were larger thanr _s, and hence, large enough to increase population size (λ>1) only in approximately one-third of the estimated years. This suggests that the population has been maintained by occasional successful recruitment occurring once every few years.     

分配格L上方阵的收敛性与伴随矩阵

证明了分配格Ｌ上的准自反矩阵Ａ（满足条件ａ（１１）＝···ａ（ｍｎ）≥ａ（ｉｊ）的矩阵）的伴随矩阵ａｄｊＡ与收敛指数ｉ（Ａ）之间的关系ａｄｊＡ＝Ａ（Ｉ（Ａ）．从而得到Ａ幂等的一个充要条件为Ａ＝ａｄｊＡ及Ａ的伴随矩阵ａｄｊＡ的一些性质。     

不等式｜A＋B｜~s≥｜A｜~s＋｜B｜~s及其应用

给出了一类矩阵的行列式的不等式｜Ａ＋Ｂ｜ｓ≥｜Ａ｜ｓ＋｜Ｂ｜ｓ，而Ｍｉｎｋｏｗｓｋｉ不等式及其推广均可视为这一结果的简单推论．     

Estimation of the MSE matrix of the stein estimator

Uniformly minimum-variance unbiased (UMVU) estimators of the total risk and the mean-squared-error (MSE) matrix of the Stein estimator for the multivariate normal mean with unknown covariance matrix are proposed. The estimated MSE matrix is helpful in identifying the components which contribute most to the total risk. It also contains information about the performance of the shrinkage estimator with respect to other quadratic loss functions.