线性次序

In this paper, we use the convex function to form the order statistic and the linear rank statistic, and the asymptotic normality of the statistics are proved.

本文用凸函数构造了线性次序统计量和线性秩统计量，并证明了它们的渐近正态性。

In 1960's, the famous statist,named Moore, proved the asymptotic normality of one kind of linear order statistic. While Hajek gained the equational condition of the asymptotic normality of rank statistic.

早在二十世纪六十年代，Moore构造了一种较为一般的线性次序统计量，并证明了它的渐近正态性，而Hajek也得出了著名的Hajek基本定理，找出了线性秩统计量渐近性的一个充要条件。

Linear order statistic and linear rank statistic are two kinds of important statistics in the mathematical statistics. They are used widely and a lot of the other statistics belonging to them.

线性次序统计量和线性秩统计量是数理统计中两类很重要的统计量，在应用上经常使用，很多形式的统计量都是属于这两类统计量。

In this progress, the order of the picture is non-linear and the picture pixel is discrete.

在这过程中，画面次序是非线性的，画面像素是离散的。

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

If the pattern has a low rate of convergence, the time of the human and machines will be wasted and the answer are not surely attainable.So,we must look for the patterns with the high rate of convergence or try to settle some parameters of the iteration patterns (for instance the overrelaxation parameter of SOR iterative method).

本文第二章针对AOR迭代法考察了当线性方程组的系数矩阵A为(1，1)相容次序矩阵且其Jacobi特征值为纯虚数或零时的迭代收敛范围，最优参数(即最优松弛因子和最优加速因子)及与之相应的谱半径，并将此最优谱半径与相应的SOR的进行比较，定量的给出在不同条件下，AOR和SOR迭代法各有其优越性，从而圆满的解决了在这两种迭代法之间如何适当的选择最佳迭代法的问题。

The basis of a typographic system is the unequal distribution of coded and normative signs in linear sequence within a closed space.

字体编排系统的根本是：在一个封闭的空间内，按照线性的次序，对有编码的或是标准化的一些符号进行有区别的分布。

List the specific storage that is:① with a group of arbitrary memory cell to store the node linear form (this group of storage units can be continuous, it can also be a discontinuity)② node in the chain of physical and logical order of priorities are not necessarily the same.

名单上的具体存储是：①与一组任意的存储单元来存储节点的线性形式（这组存储单位，可以连续，它也可以成为间断）②节点链中的物理和逻辑的优先次序不一定是相同的。

Singular linear systems; Iterative methods;AOR method; JOR method; Rank deficient least squares problems;Semiconvergence; Optimum parameters; P-cyclic matrix; Consistently ordered matrix; Preconditioning; Matrix pencil; Eigenvalue bounds; Support number

奇异线性方程组；迭代法；AOR 方法；JOR方法；亏秩最小二乘问题；半收敛性；最优参数；P-循环矩阵；相容次序矩阵；预处理；矩阵对；特征界；支撑数

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。