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At last,for the double integral which the boundary curve of its domain of integration is denoted by the panameter equation, we will supply a directed method which do not eliminate the parameter.

对积分区域的边界曲线由参数方程表示的二重积分，我们也将给出两种不经消参数而直接计算的方法。

The dissertation is mainly concerned with research of necessary and sufficient boundary integral equations and nonsingular boundary element method.

本文主要研究充要边界积分方程和无奇异边界元方法。

Compared with Finite Element Method and Finite Difference Method, Boundary Integral Equation Method is computationally more efficient.

与有限元法和有限差分法相比，该方法具有更高的计算效率。

The boundary integral method is applied to the analysis of opening displacement and stress intensity factor of surface crack.

用边界积分方法，分析表面裂纹的张开位移和应力强度因子。

Applied Green's function, the differential equations will be transformed into the equivalent of integral equations, sufficient conditions for existence and uniqueness of positive solutions for fourth-order nonlinear singular continuous boundary value problems with p-Lapacian operator are obtained.

文中，利用格林函数，将微分方程转化成等价解的积分方程，给出了该奇异非线性四阶p-Lapacian微分方程边值问题的正解的存在及惟一性的一个充要条件。

After the boundary integral operator is decomposed into the sum of a monotonous Hammerstein operator and a compact mapping by the Sidi rule, we construct the nonlinear discrete equations.

积分算子被分解成单调的Hammerstein算子和一个紧算子后，运用Sidi求积公式，建立了非线性离散方程组。

In performing the numerical analysis of unsteady seepage problem, it is necessary to calculate the integral on free surface boundary.

在三维非恒定渗流有限元计算中，不可避免地需计算自由面上的边界积分项。

In this paper,a proof is made of the equivalence in three definitions of the integral of bounded function in finite set measure.

关于Lebesgue积分，文献有不同的定义，本文给出了测度有限集上有界函数 Lebesgue积分三种不同定义的等价性的一种证明。

Finally we show that the discrete fra-ctional integral operator〓is bounded on〓.

本章还证明了离散分数次积分算子〓在〓上的有界性。

By using the integral equation and the Schauder fixed point theorem, through considering the height of nonlinear term on some bounded set, a new existence theorem is established.

利用积分方程和Schauder不动点定理，通过考察非线性项在某些有界集合上的高度建立了一个新的存在定理。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。