矩阵代数

Each weight function is a composite function of a generalized Chebyshev polynomial and a linear function, only algebraic calculation is needed, and no requirement is involved for the calculation such as the steepest descent-like algorithms or matrix calculation.

权函数是广义Chebyshev多项式和线性函数的复合函数，只需要通过代数计算就可以求得，不需要梯度下降计算或者矩阵计算。

Each weight function is a composite function of a generalized Chebyshev polynomial and a linear function, only algebraic calculation is needed, and no requirement is involved for the calculation such as the steepest descentlike algorithms or matrix calculation.

权函数是广义Chebyshev多项式和线性函数的复合函数，只需要通过代数计算就可以求得，不需要梯度下降计算或者矩阵计算。

A C++ program is developed for composing the stiffness matrix of the temperature field, saving it in changing bandwidth method and calculating the linear algebraic function group through using the Gauss eliminating method. A module for drawing the color fringe of tire temperature field is created, which makes the result more visual. Taking the 9.00-20 cross-ply tire on CA1092 as an example, the finite element numerical simulation analysis of automobile tire 2-D steady temperature field is completed. Through comparing the result with the analysis data by ANSYS, this software is proved to be capable of the modeling, calculating and post-processing of FEA of automobile tire 2-D steady temperature field.

采用C++语言完成了温度刚度矩阵的总体合成及其一维变带宽存贮，以及线性代数方程组高斯消去法求解等工作，采用C++语言实现了汽车轮胎二维稳态温度场云纹图的绘制，使得计算结果更加直观，也更能形象地显示汽车轮胎二维稳态温度场的分布状况，以CA1092（原CA142）五吨载货汽车用9.00-20尼龙斜交胎为例，进行了汽车轮胎二维稳态温度场有限元数值仿真分析，通过与ANSYS分析结果进行比较，说明所开发的有限元建模、求解以及后处理软件能够用于汽车轮胎二维稳态温度场有限元分析。

In the light of the complex, high-level and non-linear feature of the mathematical model which describe the transport of the coalbed methane, this paper study the fully-implicit solving method of the mathematical model in detail. Based on the complexity of the algebraic equations which are formed eventually, according to the alternating direction implicit difference pattern, this paper use the iterative method and the fully main element Gauss-Jordan eliminating method to solve equations, which is to use the iterative method to determine coefficient matrix and use the fully main element Gauss-Jordan method to solve th linear algebraic equation group, at the same time of studying the solving method of the mathematical model, according to the devising requirement of FORTRAN77 program structure, this paper draw up computer program and form the corresponding computer model, and verify the validity and reliability of the model in theory by operating the model.

重点研究了模型内、外边界及有关参数的处理，针对描述煤层甲烷运移的数学模型是一个复杂、高阶非线性数学模型的特点，详细研究了模型的全隐式求解方法，根据最后形成的代数方程组的复杂性，按交替方向隐式差分格式，采用迭代与全选主元高斯约当消去法相结合的方法求解方程：即确定系数矩阵采用迭代法，求解线性方程组时采用全选主元高斯约当消去法，在研究模型解法的同时按FORTRAN结构化程序设计的要求，编制计算机程序，形成相应的CBMRS计算机模型，并通过模型的运行从理论上证明了模型的正确性与可靠性。

For implementing the encryption/decryption and information hiding for digital multimedia, and aiming to generate enough large cipher key space, the accurate period of high dimension random matrix scrambling transformation is studied with the help of number theory and algebraic theory.

为了适合数字多媒体特性，实施多媒体加密与信息隐藏，生成充分大的密钥空间，使用了数论、近世代数、算法分析等工具，对高维随机矩阵置乱变换的精确周期进行了研究。

But it demands the higher computational accuracy. Time-dependent LU-SGS method and close coupled full implicit finite volume scheme are used. The AUSMPW+ based on the three-order MUSCL difference scheme is used for the inviscid operator, and the maximum eigenvalue splitting method is used to convert matrix operation to algebraic operation in order to shorten the computing time.

运用时间相关的LU-SGS方法，采用强耦合的全隐式有限体积进行离散，其中无粘对流项采用三阶MUSCL型差分的AUSMPW+格式，并应用最大特征值分裂，将矩阵运算转化为代数运算，大大缩短了计算时间。

In the linear algebraic the coefficient of polynomial and the corresponding relation of the farmnla of multi-line matrix could be built,thus seck the maximum common factor of the polynomial through making use of primary transformation of line.

在线性代数中，可以建立多项式的系数与多行矩阵表示式之间的对应关系，从而利用初等行变换求多项式的最大公因式。

The practically oriented treatment of dynamic structural buckling is undoubtely be hampered by two problems, how to adopte a existed criterion or advance a new criterion of dynamic stability in general sense, and how to develope a simple and appealing algebraic representation in terms of singularity of the tangental stiffness matrix .

实际解决动力稳定问题的进程无疑受碍于怎样选用已有的或发展新的一般意义上的动力稳定性判定准则，以及怎样发展简洁的富有吸引力的切线刚度矩阵奇异性的代数描述方法。

We first obtained the algebraic structure when M band wavelet transform was performed to Toeplitz matrix.

首先研究了Toeplitz矩阵在多进制小波变换下的代数结构。

When F is an algebraically closed field char F≠2, A is similar over F to an orthogonal matrix if and only if ( 1 ) the invariant factors of A aer self-reciprocal (2) the elementary divi sors of A of the form x...

ii当F为一个代数闭域且char≠2时，F相似于一个正交矩阵的充要条件为(1)A的不变因子是自反的。(2)A的形为(X±1)~(2k)的初等因子出现偶数次。

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。