用矩阵的行、列初等变换同时解S个线性方程组

求解S个具有相同系数矩阵的线性方程组是线性代数常见的问题.本文提出用矩阵的行、列初等变换同时求解S个线性方程组的新方法,并讨论它的应用。     

罗氏三角形内心、重心、旁心存在性的一种证明

罗氏三角形内心、重心、旁心存在性的一种证明马淑云，王阳（南阳师专数学系）欧氏几何中任意三角形存在五心（即内心、外心、重心、垂心和旁心）。罗氏三角形的外心、垂心在文「ｌ］［２］中分别进行了研究，本文用射影几何的观点讨论内心、重心、傍心的存在性。在Ｃａｙ...     

汉字的矢量化技术

本文提出了直接由点阵汉字形成图形矢量汉字的有效处理方法．可对ＧＢ２３１２—８０中（１—８７）区的所有宋体、仿宋体、楷体及黑体点阵汉字以迹线闭环技术进行矢量化处理，自动产生符合国际惯例的单线体（ＭＯＮＯＴＥＸＴ），双线体（ＣＯＭＰＬＥＸ），三线体（ＴＲＩＰＬＥＸ）以及各种填充体（ＦＩＬＬＰＡＴＥＲＮ）等几十种字体的矢量汉字，其数据占用量少，精度高，尺寸任意缩放，可直接写入图形屏幕，也可产生矢量字库，并支持各类打印机及笔式绘图仪．     

运用层次分析法进行银行信贷决策

从层次分析法的基本原理出发,结合案例,阐述了该法在专业银行信贷决策中的具体运用.     

A class of asymmetrical orthogonal resolution-IV designs

The concept of d-resolvability of orthogonal arrays of strength (d+1) is introduced. This is used to construct orthogonal resolution-IV plans of the type $\text{nt·n·2}{}^{\mathrm{n(m?1)}}\text{mn}{}^2\text{t}$. These plans are minimal and a large number of these plans are new.     

JAMES-STEIN RULE ESTIMATORS IN LINEAR REGRESSION MODELS WITH MULTIVARIATE-t DISTRIBUTED ERROR

This paper considers estimation of β in the regression model y =Xβ+μ, where the error components in μ have the jointly multivariate Student-t distribution. A family of James-Stein type estimators (characterised by nonstochastic scalars) is presented. Sufficient conditions involving only X are given, under which these estimators are better (with respect to the risk under a general quadratic loss function) than the usual minimum variance unbiased estimator (MVUE) of β. Approximate expressions for the bias, the risk, the mean square error matrix and the variance-covariance matrix for the estimators in this family are obtained. A necessary and sufficient condition for the dominance of this family over MVUE is also given.     

Some determinant optimality aspects of main effect fold-over designs

Saha and Mohanty (1970) presented a main effect fold-over design consisting of 14 treatment combinations of the 24×33 factorial, which had the nice property of being even balanced. Calling this design DSM, this paper establishes the following specific results: (i) DSM is not d-optimal in the subclass Δe of all 14 point even balanced main effect fold-over designs of the 24×33 factorial; (ii) DSM is not d-optimal in the subclass $\text{Δ}{}^1\text{?Δ}{}^{\mathrm{e}}$ of all 14 point even and odd balanced main effect fold-over designs of the 24×33 factorial; (iii) DSM is even optimal in $\text{Δ}{}^1$ and Δe. In addition to these results two 14 point designs in $\text{Δ}{}^1$ are presented which are d-optimal and via a counter example it is shown that these designs are not odd optimal. Finally, several general matrix algebra results are given which should be useful in resolving d-optimality problems of fold-over designs of the kn11×kn22 factorial.     

Fuzzy数学在评价函授教学质量中的应用

函授教学质量的评价是一个较复杂的问题。本文根据 Fuzzy 数学的原理,采用了一种综合评价的处理方法,试图通过严密的数学运算,获得较科学的定量化的评价结果,以避免质量评价中的主观偏向,从而为函授教学的管理提供了一个科学的方法。     

On necessary and sufficient condition for superiority of ridge estimator over least squares estimator

The necessary and sufficient condition is obtained such that ridge estimator is better than the least squares estimator relative to the matrix mean square error.     

四元数矩阵之迹的几个不等式

给出了广义西空间的概念,并利用其中向量内积的性质及四元数体上方阵的酉相似理论,建立了几个自共轭四元数矩阵之迹的不等式.