数值方程

The model was solved by the Ritz method, and the orthogonal polynomials generated by the Gram-Schmidt process were employed as admissible function for both disk and blades. With this approach, the matrix derived from kinetic energies becomes diagonal and numerical manipulation can become easy and stable.

采用Gram-Schmidt方法生成正交多项式作为李兹容许函数进行模型的离散化，简化了所得到的频率方程求解过程，有利於求解过程的数值稳定性，并可方便地通过对方程系数性质的分析了解结构振动模态的性质。

This paper first analyses the stress acting on the cable by means of tiny segment analytical methods, establishes cable's stress equation, and finds out the relation between the tethered aerostat's position and its stress acting by cable; then, based on the momentum and moment of momentum theorem, the longitudinal nonlinear dynamic equation is established; Finally a numerical simulation of dynamic responses of the balloon and cable to gust are carried out.

本文首先通过微段分析法对缆绳进行受力分析，建立缆绳的受力方程，找出了系留气球在空中的位置同系留气球所受缆绳拉力的关系；然后根据动量和动量矩定理建立了球体的纵向非线性运动方程；最后通过数值仿真计算，对系留气球的纵向动态响应特性进行了分析。

A pressure correction equation is established by use of the finite volume method on nonorthogonal collocated grids, and its algebraic form is also given. The equation is applied to simulation of the flow field in an equilateral cavity and an inclined cavity with a tilt angle of 45°.

利用有限体积法建立了非正交同位网格系统中的压力校正方程，详细给出了压力校正方程的离散形式，并对正方腔及倾斜角为45°的斜方腔内流场进行了数值模拟计算。

If the surface isrepresented by an implicit algebraic equation,the mapping can be constructed bythe theory of parametrization of algebraic surfaces;If the surface is represented byan parametric equation,the parameter values on the parameter plane can be solvedby numerical method or Grobner Basis method.

若曲面由代数隐式方程给出，可通过代数曲面参数化理论构造映射；若曲面由参数方程给出，可通过数值方法或Grobner基方法求解参数型值点。

For the radiation transfer equation, both the spatial domain and the angular domain is discretized, and the finite volume method is used to solve the equation in an explicit way.

把一种新的三维热辐射计算方法应用到高超声速非平衡流场的数值模拟过程中：在非结构网格上对高超声速化学非平衡流场的数值模拟过程中，耦合了辐射输运方程来求解辐射热流。

In this paper the theory and computation of finite element method is discussed for solving seismic response in anisotropic viscoelastic media, the relations between the attenuation factor and viscosity are presented.

本文论述准各向异性粘弹波动方程有限元数值解地震波响应的原理与计算方法，并给出地震衰减因子与方程中粘滞系数的计算关系式。

Considering the numerically more stable properties of Normal Equation with Constraints and Hachtel's augmented matrix method for SE, all telemetered and virtual measurements are classified reasonably. Using blocked and sparse matrices technology, a new SE algorithm with computing speediness and numerical stability is proposed.

借鉴WLS估计中带等式约束的正规方程法和Hachtel法数值稳定性更强的优点，将遥测量和虚拟量测合理分类，并采用分块和稀疏矩阵技术形成了一种计算速度快、数值稳定性好的状态估计改进算法。

The program developed with the formula enable the coordinates for points and the parametric formula for curves in the orthographic projection to be transferred into ones in the axonometric projection, which can be directly displayed on the screen. In addition, except for assigned different values to elastic coefficient of the axial direction and the angles of the axes, it is generally adapted in drawing any of the axonometric projections.

用它编程，可以把正投影中点的坐标或曲线的参数方程，转换成屏幕上能够直接显示点的轴测投影的坐标或曲线的轴测投影的参数方程，而且除了赋轴向伸缩系数和轴间角的大小、正负不同的参数值外，对绘任一种轴测投影和相应正投影都具有通用性。

The correct rate of back substitution of discriminating is 100%. The contents of copper, iron and magnesium of other fruits such as Chinese goosebery and guava were put into the mathematic model, and the results indicated that the mathematic model is suitable for discriminate the nature of fruits.

得到数模为Y=-10.19173X_8~(-1)。42593X_5+0.14975X_4，即100 克水果可食部中X(8铜)、X5和X4的含量代入以上方程，如果函数值在温热性区间(-0.6423171，0.5275019)，则该水果属于温热性，如果函数值在寒凉性区间(-∞，-0.6423171)或(0.5275019，+∞)，则该水果属于寒凉性。

Because the derivation of the extended system has a block lower triangular form, the method of splitting iteration is applied to compute simple bifurcation point, not only computational work is reduced, but also local quadratic convergence is achieved.

由于所构造的扩充系统的导数具有分块下三角形式，采用分块迭代的方法进行数值求解，不仅减少了计算量，而且是二次收敛的，从而为Navier-Stokes方程非退化简单分歧点的数值逼近提供了有效的算法。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。