矩阵

Group testing; d—separable matrix;—separable matrix; d—disjunct matrix; error-tolerant matrix; construction of separating matrices; transversal design; probabilistic method; Las Vegas algorithm; line graph; competition number

基础科学，数学，代数、数论、组合理论群试理论； d-可分矩阵矩阵；-可分矩阵； d-分离矩阵；容错矩阵；横向设计；概率方法； Las Vegas算法；线图；竞赛数

Firstly, based on the stability criterion for the nominal discrete singular time-delay system, a sufficient condition for the existence of the static output feedback controller in terms of linear matrix inequality with linear matrix equality constraint is established, which ensures that the resulting closed-loop system is regular, causal and robustly asymptotically stable, and the static output feedback controller is designed by the feasible solution of the linear matrix inequality with linear matrix equality constraint.

首先基于标称离散广义时滞系统的稳定条件，以受限线性矩阵不等式形式，得到闭环离散广义时滞系统正则、因果且渐近稳定的充分条件，同时利用受限矩阵不等式的可行解给出静态输出反馈控制器的设计方法；然后采用矩阵的正交补，把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式的可行解；最后的数值实例说明了所给方法的有效性和正确性。

How to judge whether judgement matrix has weak consistency or not is proposed, and the theory and algorithm to find equivalent consistency matrix of weak consistency judgement matrix is designed.

从寻求灰色判断矩阵的所有一致性白化阵、灰元的最小灰域的角度出发，去给出灰色判断矩阵的弱一致性和一致性定义，证明了一致性灰阵中所含信息均为一致性信息，并给出了判定矩阵是否具有弱一致性和寻求弱一致性判断矩阵的等价一致性矩阵的定理和算法。

With proving the isomorph between the function matrix algebra systems and the Boolean algebra s disjunction-conjunction systems,a method of extending the function matrix is proposed,and the expanding theorem of the extended function matrix is proven.

提出了功能矩阵的概念，在证明功能矩阵的代数系统与布尔代数析取合取代数系统同构的基础上，对功能矩阵进行扩展，并证明了扩展功能矩阵的展开定理；利用扩展功能矩阵逐步展开与约简，实现了功能的求解算法。

Zhan has determined the maximum and minimum numbers of positive entries of imprimitive irreducible nonnegative matrices with a given imprimitivity index. In this paper, we prove that if a positive integer is between the maximum and minimum numbers, then there exists an irreducible nonnegative matrix A with the given imprimitivity index and with the given number of positive entries.

非负矩阵是矩阵论中研究比较活跃的领域，不可约非负矩阵是比较重要的非负矩阵，本文分两部分，一部分主要在詹兴致教授的研究基础上研究了给定非本原性指标的不可约非负矩阵中非零元个数的连续性，肯定地回答了詹兴致提出的一个自然的问题。

This is the so-called Duerlite algorithms: from the bottom row of the matrix A do elementary transformation, the diagonal elements into the bottom left of zero, and then show the effect of these lines is equivalent to transform the left by a unit lower triangular matrix, this series of unit lower triangular matrix inverse is the product of L matrices, it is also a unit lower triangular matrix.

这正是所谓的杜尔里特算法：从下至上地对矩阵A做初等行变换，将对角线左下方的元素变成零，然后再证明这些行变换的效果等同于左乘一系列单位下三角矩阵，这一系列单位下三角矩阵的乘积的逆就是L矩阵，它也是一个单位下三角矩阵。

Among thses matrices, bidiagonal matrix and approximately lower triangular array matrix have determinate construction and can provide linear encoding algorithm, and both subscript matrices, masking matrix and permutation matrix need to be redesigned.

其中双对角线矩阵和近似下三角阵列矩阵是确定结构的，具有高速线性编码的功能；而两种下标矩阵、模板矩阵和置换矩阵均具有类随机结构特征，可以根据需要进行再设计。

Finally, the fact is proved using mathematical induction and the character of stochastic matrix.

首先介绍了防御矩阵的概念、物理意义、重要性质及计算方法，分析了防御矩阵满足乘法交换律的重要意义，最后综合运用数学归纳法和随机矩阵性质证明了防御矩阵满足乘法交换律的事实，此结论无论对于多层防御系统的防御效用值研究连是矩阵理论研究都有一定的指导作用。

Necessary and sufficient conditions for the existence and the expressions of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, and skewbisymmetric solution to 4 kinds of systems of linear matrix equations over a regular ring with an involutorial antiautomorphism are given.

利用矩阵技巧和所建立的矩阵理论，给出了正则环上五类矩阵方程组有解的若干充要条件和一般解的表达公式。这些矩阵方程组除了它们在理论上有重要的意义外，还有重要的应用价值。在具有对合反自同构的正则环上，给出了四类矩阵方程组有双对称解，中心对称解，斜中心对称解，广自共轭解，斜广自共轭解，自共轭解以及斜自共轭解的充要条件及其这些解的具体表达式。

To solve the second problem, an approach of irregular QC LDFC codes is proposed. The proposed approach is to replace some sub-matrices by zero matrices and identity matrices at special positions in the given sparse parity-check matrix so as to get a nonsingular square matrix for the construction of the generator matrix.

为解决第二个问题，提出一种不规则准循环LDPC码的设计方法，该方法将校验矩阵中的特定位置的子矩阵用零矩阵和循环矩阵置换，获得一非奇异方阵，用于构造生成矩阵。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。