数值方程

The improved e-N method can also yield results well agree with those obtained by DNS.4 The transition prediction for boundary layers on cones with different key parameters such as angle of attack, cone half angle and the Mach number of the coming flow, have been made, to show the reliability of the modified e-N method.5 For the calculation of base flow, boundary layer equations can be used in the case of small angle of attack.

但是它要依赖于对初始扰动的正确预估，这显然又取决于更多飞行数据的积累和分析。e-N方法的转捩预测结果与直接数值模拟得到的结果也吻合较好。4通过对不同来流攻角、不同半锥角和不同马赫数的三维圆锥边界层的转捩位置进行预测，证实了改进的e-N方法对于三维边界层转捩预测是可靠的。5对于基本流的计算，边界层方程可以用于小攻角的情况，其计算量远远小于直接数值模拟，但背风面的剖面不可靠。

In sphere approximate, GPS/Gravity-BVP is Neumann problem over exterior spherical domains. Then the natural boundary reduction, suggested by Feng and Yu, is applied to deal with the three dimensional problems. By expansion in spherical harmonics, the natural integral equations of harmonic problems over exterior spherical domains are obtained. Meanwhile, a numerical method for solving geodetic BVP is developed.

在球近似下将GPS-边值问题转化为Neumann外问题，用自然边界元法进行自然边界归化，得到自然边界积分方程，再求自然边界积分方程的数值解，与其他边界元方法相比，自然边界元法的计算量大大减小，并且具有很好的逼近性质，能有效地处理奇异积分，是求解GPS-边值问题有效方法。

The equations for the helicoid and cross section of a ballscrew are worked out and a numerical integral method for the computation of the moment of inertia of the cross section is proposed.

建立了滚珠丝杠的螺旋面方程及横截面方程，提出一种精确计算滚珠丝杠横截面惯性矩的数值积分法，计算结果表明，传统的简化方法将造成20％以上的计算误差。

Sobolev equation is widely used in many areas, such as hydromechanics, thermodynamics and so on.

中文摘要： Sobolev方程是在流体力学，热力学等领域应用广泛的一类方程，其有限元数值方法研究已有很多工作，如[5]中提出了位移有限元法，[9]中建立了特征混合元方法，[7]提出了H1-Galerkin混合有限元方法，[10]中提出了最小二乘混合元方法。

Numerical experiments show that because Navier-Stokes equations at highReynolds number are a hyperbolic system,the boundary conditions are appli-cable to prescribe their boundary problems.

数值实验表明，在高Reynolds数下，由于Navier-Stokes方程呈现出很强的双曲型方程的性质，上述经过某些线性化处理得到的无反射边界条件是可以用来指定其边界值问题的。

Chapter 3 is arranged in the following sequence to acquire the refractive index of the Iceland crystal for different values of the wavelength and the temperature.

在可见光区将四组不同的波长和对应的折射率代入常数表达式中，然后通过重复的迭代得到最佳的常数值；使用线形插值的办法得到了不同波长的折射率温度系数，从而可得出不同温度的 S el line i e r方程常数值，这样可以很容易求出各个温度下各波长所对应的折射率值。

The values of Joule-Thomson coefficient derived from VDW and RK equations and the correction formula of state equation of ideal gas are compared with he measured values and the values obtained by conventional methods.

对采用VDW、RK方程直接求导法和理想气体状态方程的修正式求导法求得的焦耳－汤姆邀系数值与实测值、常规方法所得的值进行了对比。

Based on viscous, stable and impressible Navier-Stokes equation and k-s turbulent model, the aerodynamic characteristics and the fluid field around the maglev vehicle are simulated by means of the finite element analysis software ANSYS.

本文以粘性定常不可压Navier-Stokes方程以及k-ε双方程湍流模型理论为基础，利用大型有限元分析软件ANSYS对磁悬浮列车的空气动力特性和外部流场进行数值分析研究。

The flow of incompressible viscous fluid is controlled by Navier-Stokes Equations.The qualititave analysis of the solutions of the equation is important to the studies of bifurcation problems and numerical solutions of the equations.

对于描述不可压缩粘性流体流动的Navier-Stokes方程，其解的定性分析结果对于该方程的数值求解及其分歧问题的研究都是十分重要的。

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we define δ-fine partitions for infinite interval and integral of vector-valued functions on infinite interval, and discuss the properties of integral, and characterize its primitives...

主要包括以下五部分内容：在第一部分中，我们介绍了本文所用到的基本概念和引理；在第二部分中，通过定义无穷区间上δ-精细的分法，我们给出了无穷区间上向量值函数的积分的定义，并讨论其性质，还给出了原函数的刻划；在本文的第三部分中，我们着重讨论了无穷区间上向量值函数积分的收敛定理；在本文的在第四部分中，我们首先应用无穷区间上向量值函数积分的收敛定理给出了常微分方程整体广义解的存在性定理，其次应用强积分对Banach空间常微分方程广义解进行了讨论；最后，在第五部分中，我们将模糊积分推广到无穷区间上并给出了其数值计算方法。

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。