格林函数

In order to expand half space Green's functions with addition theorem, a high order approximation method is proposed for evaluation of reflection term of half-space Green's functions with far interactions.

采用高阶拟合方法将远区相互作用单元的半空间空域格林函数用级数表示，对高阶拟合项作加法定理展开，进而应用多层快速多极子算法。

Inchapter three,the one dimension spin chain with alternating spins 1 and 1/2 is studiedby Green Function's decoupling approximate method.

第三章是用格林函数切断近似方法来研究一维自旋链。

In 10-20s period band, the sources of ambient seismic noise has a very clear seasonal variability.

由于短周期面波强烈的衰减和吸收效应，提取出的这一周期段的瑞利面波格林函数的信噪比较低。

In order to avoid the singularity in the integration, the integrand was expressed to be sum of complex exponential terms by using discrete complex image method. With generalized pencil of function method introduced, the number, location and intensity of images were obtained without extracting the quasi-static and surface wave terms in the integrand, which makes DCIM more efficient for multi-layered media.

为了避免积分中的奇异性，利用离散复镜像法将积分核用复镜像的指数求和式表示，引入广义函数束方法，可以在不提取积分核中表面波项的条件下，采用数值方法提取准静态项，给出复镜像点的数目、位置和强度，使得该方法在多层介质情况下对格林函数的计算更为有效。

A Green function expression and an equivalent generalized Fourier expansion with corresponding Sturm-Liouville eigenfunctions and eigenvalues are given.

给出了用格林函数表示的普遍解和相应的Sturm-Liouville本征函数及本征值。

On the basic of NNLSE and the Poisson equation, using the Green function approach, we obtain the response function of the lead glass of finite-size, which is a strong nonlocal medium. Starting with the paraxial ray equation, we obtain the analytical solutions of the oscillation trajectory and period of the beam.

基于非局域非线性薛定谔方程以及热传导的泊松方程，采用格林函数法求出了强非局域介质铅玻璃的响应函数和临界功率；从光线方程出发得到了偏离材料中心入射的光束中心振荡轨迹以及周期的解析解。

In chapter four, we developed a direct approach for soliton perturbation based on the Green function, This approch get rid of the proof of orthognality for eigenfunctions in a direct approch for soliton perturbation developed by Yan Jiaren etal.

第四章，发展了一种基于格林函数的孤子微扰理论，克服了颜家壬教授微扰直接法中本征函数正交性证明的困难。

In this paper, a Green quasi-function is firstly set up by using the basic solution of Poisson's equation.

利用Poisson方程的基本解构造一个准格林函数，这个函数满足Poisson方程的齐次边界条件。

The method is to add a term into the original singular kernel while it subtracts its analytical solution from the original equation. Since the singularity of Green's function can be eliminated by such a mathematical technique, shape function does not need to be supposed while solving the unknown. The calculation can be directly applied to the real shape of the object by taking the integral points distributed on the object as nodes that satisfy boundary conditions.

由於格林函数的奇异性经过数学上的技巧加以消除，因此当求解未知数时已经不需要再假设形状函数，即可直接使用物体真实的外型来做计算，也就是直接将物体上分布的积分点视为满足边界条件的节点。

In this paper we studied the general forms and properties of tensor Green functions in waveguides with the methods of eigenfunctions expansion.

本文以本征函数展开的方法，研究了波导管中格林函数的一般性质和形式。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。