向量方程

The new method is a combination of characteristic approximation to handle the convection part, to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion, a smaller time truncation is gained at the same time, and a mixed finite elementspatial approximation to deal with the diffusion part, the sealer unknown and the adjoint vector function are approximated optimally and simultaneously.

此方法即为对方程的对流项沿流体流动的方向即特征方向进行离散，从而保证格式在流动锋线前沿逼近的高稳定性，消除了数值弥散现象，并得到了较小的时间截断误差；另一方面，对方程的扩散项采用混合元离散，可同时高精度逼近未知函数及其伴随向量函数，理论分析表明，此方法是稳定的，具有最优的L~2逼近精度。

The research fields are calculus of single variables functions and several variables functions, space analytic geometry, series, differential equation.

通过本课程的学习，使学生掌握一元函数微积分、向量代数和空间解析几何、多元函数微积分、无究级数、常微分方程等方面的基本概念、基本理论和基本运算技能，为学习后继课程和进一步获得数学知识奠定必要的数学基础。

7 Matrix Exponentials and Linear Systems The solution vectors of a homogeneous linear system Can be used to construct a matrix = that satisfies the matrix differential equation associated with Eq.

5.7 指数矩阵和线性系统借助等式（1），齐次线性系统的解向量可以被用来构造一个满足矩阵微分方程的矩阵。

In the predicted process, the forward simplification is used to get the interface equation, meanwhile taking the voltage of the concentrated grid as control vector to solve the control step length; in the correction process, by means of forward simplification and back substitution the Newton linearization incremental equations of both concentrated computational grid and contracted nodes are solved alternately.

进行计算时，通过前向简化形成预估环节的接口方程，同时以浓缩网络的电压为控制电压向量求出控制步长；校正环节通过双向迭代方法交替实现对浓缩网络和收缩节点的牛顿法线性增量方程的求解。

The generalized deformation equations and the distribution function of branch vector are derived, and the mathematical characteristics of fabric tensor N are also discussed.

在此基础上导出了形变方程的一般形式，对技向量的分布函数进行了理论上的推导，还对组构张量N的一般数学特征进行了讨论。

Of the fundamental matrix in (2) satisfies the differential equation =A , it follows that the matrix = itself satisfies the matrix differential equation Because its column vectors are linearly independent, it also follows that the fundamental matrix is nonsingular, and therefore has inverse matrix .

基本矩阵的求解由于（2）中的基本矩阵的列向量满足微分方程A，进而这个矩阵本身就满足矩阵微分方程。

In which the second order degenerate equations associated with square sum operators of Hormander vector fields are the most important classes. People are used to calling them subelliptic operators because they have properties similar to that of classical Laplacian.

由于该算子具有与经典Laplace算子类似的次椭圆性质，人们习惯上把由向量场构成的二阶线性及非线性算子通称为次椭圆算子，相应的方程称为次椭圆方程。

Firstly, kinetic energy and potential energy expressions are obtained by a series of derivation, considering the extrinsic momentum. In the symplectic system, control equations of longitude and transverse coupling vibrations of rotating elastic structures, or Hamilton canonical equations are described. So the solution of the problem is boiled down to the eigenvalues and eigensolutions in the symplectic space.

首先，从能量的观点出发，通过一系列的理论推导，给出旋转结构的动能和势能表达式，并考虑外动量的影响，从而得到在辛体系中描述旋转结构纵向和横向耦合振动的控制方程，即哈密顿正则方程，于是将问题归结为辛几何空间的本征值和本征向量问题。

In this equation, A is the area normal vector of face f directed from cell c0 to c1, ds is the distance between the cell centroids, and ~es is the unit normal vector in this direction.

在这个方程中A是从单元格c0 指向单元格c1 的表面f的标准向量围成的面积，ds 是两个单元格重心间的距离， s 是这个方向的单元向量。

"Transform",The Laplace transform can be used to solve the state equations for the state and output vectors.

&，&拉普拉氏转换可以用来解状态方程的状态向量和输出向量。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。