近似方法

For free oscillation of various nonlinear conservative systems, the analytical approximate periods and the corresponding periodic solutions were established and they are valid for small as well as large amplitude of oscillation.

提出了结构参数发生较大变化时，计算结构的静力响应，固有频率与固有振型的高效的、适用范围广的方法；对非线性保守系统的自由振动，建立了既适用于小振幅又适用于大振幅的近似解析解法。

In the method, the mathematic model of parameter identification is frequency response function.

本方法中，参数识别的数学模型是系统的一阶近似频率响应函数。

However, combining image plane DHM with the phase-shifting in-line technique, the complex amplitude of reconstructed image can be obtained without using Fresnel integral, moreover the approximate error of reconstruction calculation is easily eliminated and the signal-to-noise ratio of reconstructed image is significantly improved.

理论分析和实验证明，用这种方法无需使用菲涅尔积分即可直接获得再现像的复振幅，提高了再现像的信噪比，避免了再现中的近似误差。

Then time-dependent invariant is introduced and a kind of method to solve the Schrodinger equation explicitly called Gauge transformation method.

稍后引入含时不变量的定义，以及精确求解薛定谔方程的含时规范变换方法，再次讨论了Aharonov-Bohm效应，Berry相位和绝热近似。

In the article, the Shape Function in the Finite Element Method is used. And a surface is evatuated by integral using the Gauss Legendre Quadrature over a triangle.

在这两种模拟中，使用线性分布法会比近似声源法及高阶分布法好，故在此方法的比较里较推荐使用线性分布声源法。

Among them, former polynomial expansion detection algorithm based on the classic conclusion ,Gauss－Seidel iterative method which will introduce the same time. Inverse matrix will eventually form into a Taylor series approximation.

其中，前一种算法立足多项式扩展检测的经典结论，同时将Gauss－Seidel迭代方法引入其中，最终将矩阵求逆转化为泰勒级数近似的形式。

The distribution of the transform domain data is analysed, and it is approximated by Gaussian distribution.

该方法对直扩通信系统接收信号变换域数据的分布特点进行了分析，并采用高斯分布对其作了近似。

Chapter 2、When treat propagate problem of high power laser beams, ordinary assume beam to be ideal plane wave or Gaussian. Actually, beams is not ideal Gaussian or plane wave. The reason is that is phase aberraed and intensity nonuniform. In this chapter, we have developed a method on frequency conversion of aberrated beam. Based on statistical optics method and within the limits of thin crystal, we have studies on second harmonic generation of the phase aberrted beam. And the phase aberration is assumed to be a Gaussian random variable.

第二部分：在处理高功率光束传输问题中，通常假设光束为理想平面波或高斯型，而实际光束都不可能是理想的高斯光束或平面波，均会有一定的位相畸变及光强不均匀，本部分从统计光学的观点出发，在薄晶体近似下，建立了具有高斯型随机相位畸变光束倍频转换的一种统计描述方法，并对倍频转换光束的横向空间特性进行了分析。

Based on the method that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, the propagation characteristics of a Gaussian beam passing through apertured spatial filter systems are analysed and the corresponding analytical formulae are obtained respectively.

根据矩形函数可以展开为有限复高斯函数之和的方法，从柯林斯衍射积分公式出发，对高斯光束通过受限空间滤波器传输特性进行分析，得到了相应的近似解析式。利用Matlab对其解析式进行数值模拟，得出一组直观的结果。

In order to study the propagation of partially coherent modified Bessel-Gaussian beams passing through a paraxial ABCD optical system with hard-edge aperture,the approximate analytical propagation equation was derived with the hard-edged aperture function expanded into a finite sum of complex Gaussian functions.

为了对部分相干修正贝塞尔－高斯光束通过有硬边光阑近轴4BCD光学系统的传输进行研究，采用将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，得到了近似的解析传输公式。

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。