线积分

About the research of this, this paper enumerates four kinds of different types of real integral, which can be calculated by contour integral.

关于这方面的研究，本文列举了四种不同类型的实积分，可用周线积分来计算。

But, in fact, the application of contour integral is more important, its application in integral calculus, physics and engineering science is quite extensive.

但更重要的是其应用，周线积分在积分学、力学、工程学方面应用相当广泛。

This paper probes into its application in integral calculus especially--- utilizing contour integral to calculate relational real integral.

本文重点探讨它在积分学当中的应用——利用周线积分计算有关的实积分。

When the stress and displacement fields in a specimen are calculated by finite element method, the stress intensity factors K and K of mixed-mode crack can be obtained immediately by a contour integral.

此方法与积分路径的选择无关，用有限元法计算出远离裂纹尖端的位移场和应力场，就可通过计算绕裂端的围线积分，精确地给出混合型裂纹的应力强度因子KⅠ和KⅡ的数值解。

In this paper,the boundary singular kernel method in Reproducing Kernel Paicle Method has been applied to impose the essential boundary conditions in EFGM by revising the MLS shape function.The stress field and the displacement field are analysed by linear elastic theory.The contour integral method is used to calculate the J-integral,then the stress intensity factors of mixed-mode crack is acquired.The correctness and the validity of the method are validated.

本文将再生核质点方法中的边界奇异权方法引入EFGM中，通过对MLS形函数进行修正实现了本质边界条件在节点处的精确施加；运用线弹性断裂理论分析裂纹板的应力应变场，采用围线积分法计算J积分，给出了复合型裂纹板的应力强度因子的无网格伽辽金方法。

By applying contour integral method and high-order displacement functionsof MM,we obtain the accurate stress intensity factors of mixed-mode crack.Then,the open crack propagation of the mixed mode I and II is simulated by means oftheories of linear elastic fracture mechanics.This provides a simple and effectivenumerical way for crack evolvement studying.

接着，文中采用围线积分法和流形方法的高阶位移函数来计算得到比较准确的混合型裂纹尖端的应力强度因子，然后基于线弹性断裂力学的裂纹扩展准则，用流形方法实现了平面I-II混合型张裂纹扩展的数值模拟，为数值方法研究裂纹的演化行为提供了一条简单而有效的途径。

This paper puts forward the triangle element method for calculating gravity anomaly of three-dimensional sphere-coronal model by using the divergence theorem. In this study, the volume integration was changed into surface integral, a series of triangles were used to fit the surface, and then the Green's formula was adopted to change surface integral into line integral. At the same time, a reasonable calculation program was given.

提出利用高斯公式将体积分变成包围该积分域的全表面积，应用一系列三角形拟合计算表面，然后通过格林公式把对每个三角形的面积分变成对三角形每边的线积分之和的三角元法来计算三度体球冠模型重力异常，同时给出了合理的计算方案。

Numerical integration of ordinary integrals and line integrals.

一般的积分以及线积分的数值积分。

Our conclusion is : For general transport equation and some special transport equations (slab geometry, spherical symmetry, pillar symmetry) we can evaluate some relevant physical quantities and geometrical properties from the exiting photon flux. The method we will use is to transform the transport equation into integral equation by integrating it along its characteristics, then we prove the nonlinear operator K is monotone and continuous with respect to its arguments and obtain the existence of K~-1. Consequently, we can evaluate some relevant physical quantities and geometrical property of the medium.

我们得到的结论是：无论对于一般的迁移方程，还是当介质具有某种对称性时(板对称、球对称、柱对称)的迁移方程，我们都可以根据泄漏的光子流估计介质各种相关物理量和几何特性，所用方法都是将迁移方程通过沿特征线积分转化为积分方程的形式，然后证明非线性算子K关于自变量的单调性和连续性，从而得到逆算子K~(-1)存在，进而达到估计介质各种相关物理量和几何特性的目的。

Beamlet transform is a multiscale geometric analysis based on dyˉ adicallyˉoriginazed collection of line segments.

先通过线积分计算各分块的Beamlet变换，再利用广义似然比检验寻找保留符合条件的 Beamlet，提取线特征。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。