格林定理

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。

This result is a higher-dimentional analogue of the Fundamental Theorem of Calculus: it expresses the integral over D of some kind of derivative of P and Q in terms of an integral of P and Q over the boundary of.

格林公式建立了曲线积分和二重积分的关系 O 这是微积分基本定理在高维情形的推广：它将上P、Q某种形式的导数的积分用的边界上 P、 Q 的积分表示出来。

Applying the Green′s theorem and a moving oscillating source, an integral equation method is developed for predicting wave height on a shoal in current. The integral equation is discretized by a higher order element method.

利用格林定理和移动脉动源建立了一个积分方程方法，并利用高阶方法对积分方程进行了离散和求解，用于计算波浪和水流在浅滩上发生的绕射现象。

First, based upon the fields in the single cavities, open and short modes are constructed, whose coupling holes on disks are shorted magnetically and electrically respectively. Second, the whole field in the chain is expanded with the short and open modes. With the Galerkin method and the second vector Green theorem, it is possible to describe the physics problem by a simple general eigenvalue matrix equation. Here, the dispersion curves in periodical structures are available.

它首先利用有限元等方法计算各加速单腔中的电磁场，根据一定规则构造成所需的开模和闭模，然后把整个长腔链加速结构中的场用这些开模和闭模展开，再利用伽略金方法和第二矢量格林定理进行数学变换，考虑各模式在加速腔壁和腔间耦合孔处的边界条件后，就能把加速结构中电磁场用数学上的广义本征值矩阵问题描述，从而能够得到所求的色散曲线和电磁场形态。

In the first part, first, the operational principle of Varivec Propeller is explained. Secondly, the mathematical model for predicting longitudinal and transverse movement hydrodynamic characteristics of Varivec Propeller under steady or unsteady condition are present, based on the general propeller lifting-surface theory, potential flow theory and Green theorem. Thirdly, theoretical calculation methods for predicting hydrodynamic characteristics when the influence of paraboloidal boss on the performance of Varivec Propeller is or isn't considered are present, based on The finite basic solution method, the unsteady vortex lattice method and Hess-Smith method Different rake angle is adopted according to different desire in practical application.

在理论计算部分，本文首先给出了全方向推进器的工作原理，然后基于常规螺旋桨升力面理论、势流理论和格林定理建立了定常和非定常状态下全方向推进器纵向、横向运动的水动力性能计算的数学模型，并利用有限基本解法、非定常涡格法和Hess-smith方法分别对考虑和不考虑桨毂影响时的全方向推进器纵向、横向运动水动力性能进行了数值预报。

By use of the average value way and Green formula,oscillation theorems for such equation satisfying two kinds of boundary value conditions is obtained.

考虑一类非线性抛物泛函微分方程的强迫振动性，利用平均值法和格林公式，在两类边值条件下得到这类方程的振动性定理。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。