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In Chapter 3, the generalized skew-symmetric solutions of the matrix equation A~TXA = B on the linear manifold S ={X e GKSR~|||XY - Z}}= min, Y, Z∈ R~}, using the canonical correlation decomposition of a matrix pair, the necessary and sufficient conditions for the existence and the expressions for the generalized skew-symmetric solutions of matrix equation A~TXA — B on the linear manifold are established.

利用矩阵对的标准相关分解，给出了这类线性流形上矩阵方程A~TXA=B存在广义次对称解的充要条件及其通解表达式，并且导出了极小Frobenius范数广义次对称解的表达(来源：d7d7A7dBC论文网www.abclunwen.com)式。

The elemental weight ratios (Na, K, Mg, Ca, Fe, Al, Ti, Mn, Ni)/Si of Ningqiang matrix are within the range of the corresponding ratios of CV chondrite matrix, Ca/Si and Al/Si ratios are high relative to those in the other CV chondrite matrix.

宁强基质的元素重量比值（Na、K、Mg、Ca、Fe、Al、Ti、Mn、Ni）/Si处于CV球粒陨石相应比值的变化范围之内，而Ca/Si、Al/Si值相对于其它CV陨石基质的同样比值较高。

In cinematograph kind the matrix stack that offers through OpenGL in implementation, obtain commutation matrix directly, avoided code of many matrix operation write, be in simplify calculative at the same time, improved the moving efficiency of the program.

在摄影机类的实现中通过OpenGL提供的矩阵堆栈，直接获得变换矩阵，避免了大量矩阵运算代码的编写，并在简化计算的同时，提高了程序的运行效率。

Through the definition of symmetric circulant matrix, the nature of the study, we discuss a class of n-order symmetric circulant matrix of eigenvalues and eigenvectors, and parity check on n different values are given for the matrix eigenvalue and the characteristics of vector formula.

通过对称循环矩阵的定义、性质的学习，我们讨论了一类n阶对称循环矩阵的特征值和特征向量，并分别就n取奇偶等不同数值时，给出了求该矩阵的特征值和特征向量的公式。

A fast algorithm for calculating the inverse and Moore-Penrose inverse of the permutation factor circulant matrix is presented. Then, a fast algorithm for the product of the permutation factor circulant matrix is given. Finally, The least-square solutions of inverse problems and the optimal approximation problems for the permutation factor circulant matrix are discussed.

首先给出了一种求n阶置换因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法，然后给出了计算两n阶置换因子循环矩阵之乘积阵的一种快速算法，最后给出了其反问题的最小二乘解的存在性定理及它的一般表示，并证明了逼近矩阵的存在唯一性且给出它的具体表达式。

This artic le researches a fast algorithm which extends the system matrix of JD into b lock circulant ma-trix,then uses block Fourier transform and block circulant matrix to perform matrix inversion and operation s.

提出一种快速算法，将联合检测的系统矩阵扩展成块循环矩阵，利用块FFT和块循环矩阵进行快速矩阵求逆和简化矩阵运算。

In view of practical problem during Sulige gas field development, this paper complete follow study content. Study material balance theory of two district compound gas reservoir. Carry out stress sensitivity experiment on matrix rock and labor created fracture core from Sulige gas field with America Core Company high pressure high temperature flow experimental instrument to study stress sensitivity change rule of different permeability matrix rock and created fracture core at the condition of time and again switch on and off well and different drawdown pressure. Carry out depletion experiment on matrix rock of different permeability serial combination with different kinds of allocation, using double core clamper serial connected experimental apparatus, to study gas well production performance of bi-zonal compound low permeability reservoir during low pressure production stage. At the basis of experimental study, establish single well simulation model to analyze development index infection caused by stress sensibility and production performance infection rule caused by inner formation and outer formation of bi-zonal compound gas reservoir permeability variation while considering stress sensitivity.

针对苏里格低渗气田开发中存在的实际问题，完成以下研究内容；研究了两区复合气藏物质平衡原理；利用美国岩芯公司高温高压流动实验仪，对取自苏里格气田基质岩芯和人工造缝岩芯进行应力敏感实验，研究不同渗透率基质岩芯和造缝岩芯在多次开关井和不同生产压差条件下的应力敏感变化规律；采用双岩芯夹持器串联实验装置，对不同渗透率串联组合的基质岩芯进行各种配产条件下的衰竭实验，研究两区复合的低渗储层气井在低压生产阶段的生产动态特征；在实验研究的基础上，建立单井模拟模型分析储层应力敏感性和非均质性对开发指标的影响，研究考虑应力敏感时两区复合气藏储层中内区和外区渗透率变化对开发动态的影响规律。

Some basic properties of σ- LFSR over F4 are studied, such as nonlinearity, cycle structure distribution of state graph, the largest period and counting problem related. The conclusions are as follows:The coefficient ring of σ-LFSR is isomorphic to the matrix ring over F,. The cycle structure of σ- LFSR is consistent with that of the determinant of the corresponding polynomial matrix if and only if the feedback polynomial of - LFSR does not contain nontrivial factor over F2,. The counting formula of the number of σ- LFSR with inconsistent cycle structure is also showed in that part. The period of σ-LFSR with degree n is maximum if and only if the determinant of the corresponding polynomial matrix is the primitive polynomial with order 2n over F2,.

本文研究了有限域F_4上的σ-LFSR的一些基本性质，如非奇异性、状态图的圈结构的分布、最大圈的充要条件及相关的计数问题等，得到以下结论：σ-LFSR的系数环同构于F_2上的矩阵环；σ-LFSR的状态图的圈结构与对应的多项式矩阵的行列式的圈结构一致的充要条件为σ-LFSR的反馈多项式不含有非平凡的F_2上的因式，给出了圈结构不一致的σ-LFSR的计数公式； n次σ-LFSR周期达到最大，当且仅当对应多项式矩阵的行列式为F_2上的2n次本原多项式。

In this paper, for m× n Loewner-type matrix or symmetric Loewner-type matrix with full column rank, we form special block matrix firstly and research their triangular factorization or of its inverse, and then get the fast algorithm of the minimal norm least squaresolution .

本文对于秩为n的m×n阶Loewner型或对称Loewner型矩阵L，通过构造特殊分块矩阵并研究其逆的三角分解或自身三角分解，进而得到了线性方程组Lx=b的极小范数最小二乘解快速算法，计算复杂度为O+O(n~2)，而一般方法的计算复杂度为O(mn~2)+O(n~3)。

A new fast algorithm of the minimal norm least squares solution for the linear system whose coefficient matrix is an m×n Loewner-type matrix with full column rank is given by forming a special block matrix and researching its triangular factorization.

通过构造特殊分块矩阵及其三角分解给出了求秩为n的m×n阶Loewner型矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法，该算法的计算复杂度为O+O(n2)，而一般方法的计算复杂度为O(mn2)+O(n3)。

The witness also told the jury at the Royal Courts of Justice in London that he saw a paparazzo fighting with a member of the public who was trying to stop him taking pictures in the minutes before the emergency services arrived.

他还告诉在伦敦皇家法庭的陪审团，在急救服务到来之前，他当时看见一个狗仔队正和一群阻止他拍照的人打架。

The entire N／C program on a tape is made up of an accumulation of these successive data blocks.

纸带上的整个数控程序由这些连续数据单元连接而成。