积分因子

Using the perturbation method and Stroh's formula, a nonideal crack, which is mathematically sharp and the opposing crack faces still have a gap in which a stiffless dielectric fills, the two-field problem is reduced to a standard Riemann-Hilbert problem. The internal electric field distribution is obtained by solving a singular integral equation, and then the full field both inside and outside the crack is obtained and the electro-mechanical intensity factors to the first order of accuracy are given.

采用摄动方法对裂尖理想尖锐而裂纹面又具有一定张开的非理想裂纹进行分析，裂隙内含有无刚度的各向同性电介质，利用Stroh公式，将二域问题化为标准的Riemann-Hilbert问题，裂隙内电场分布通过解一个奇异积分方程获得，从而得到裂纹内外的力电全场分布，进而给出一阶精度下的力电强度因子的表达式。

B Using the basic solutions of single inclusion and single crack, singular integral equations of plane interaction problem of line inclusion and line crack have been deduced. Numerical method is set up. Expresesions of stress intensity factor of both inclusion and crack and interface stress of the inclusion are given.

使用单夹杂和单裂纹的基本解，导出了线夹杂与线裂纹相互作用平面问题的奇异积分方程，并为其建立了数值法，给出了夹杂与裂纹端点的应力强度因子及夹杂两侧界面应力的表达式。

C Taking the short-fiber reinforced and inhomogeneity spreaded composite materials as engineering background, singular integal equations of plane problem of interaction between line inclusion and circular inclusion are deduced, and some particular cases are analysed.

以短纤维和颗粒弥散体复合材料为背景，导出了线夹杂与圆夹杂相互作用平面问题的奇异积分方程，并对一些特殊情形作了退化分析，建立了数值法，给出了圆夹杂和线夹杂两侧的界面应力及线夹杂端点的应力强度因子表达式，同时作了具体的数值计算。

The 3-D thermal weight function method was proposed, in which the works ussually done for finite element stress analyses for every time instants could be avoided, and the transient stress intensity factor of a body subjected to thermal shock can be calculated through direct integration of products of temperature fields and TWF.

在国际上首次以三维热权函数法为核心，绕过对每一时刻有限元应力分析这一步，直接通过温度场与热权函数的乘积的积分来计算热冲击应力强度因子K的过渡过程，极大地提高了计算效率。

To assure astringency, sometechnologies have been used such as iterative penality function methods,assemblage mass matrix, reduced integration algoritlun, NeWton iteration methodwith parameters for non-linear equation set, introducing relax factors and doublesteps solution and so on, and an algorithIn for solving the nonlinear equation set offlow field by FEM has been presented.

基于有限元法建立了流场求解列式，为保证其收敛性，采用了迭代罚函数法，集中质量矩阵，缩减积分计算，带参数的Newton迭代求解，引入松驰因子及双层解法等技术，提出了一套适合流场有限元方程计算的非线性方程求解方法。

To find the prefactor, evaluate the infinite product of gaussian integrals using the formula

为了找出前因子，用公式估算高斯积分的无限连乘

With β= 1/T . Assuming that the levels En are closely spaced, so that the sum over n can bereplaced by an integral, and ignoring the energy dependence of the prefactor An, show that the maximum in the sum corresponds to the energy E for which

其中β = 1/T 。假设能级En 是接近等间距的，因此对n求和可以用积分代替，并忽略能量对前因子An，的依赖，证明和的最大值对应能量E有

Methods The bile duct of rabbit was excided and a pipe supporting bile duct was inserted through duodenal major papilla to establish a model. V.G staining and TGF-beta 1 immunohistochemistry staining on tubal wall of rabbit bile duct in different times were used to determine quantitatively the intensity of light TGF-beta 1 positive area and the relationship between the integral-optical density of bile duct tissue collagen content and time.

切开兔胆管并自十二指肠乳头行胆管内支撑方法建立模型，将不同时期梗阻段胆管壁进行V.G染色和β1型转化生长因子（transforming growth factor beta 1，TGF-β1）免疫组化染色，测定TGF-β1阳性区域的光度以及胆管组织胶原含量积分光密度随时间变化关系。

On the basis of DSC curves of B/KNO_3 igniter powder,the apparent activation energy E of thermal decomposition is calculated with Kissinger′s methods and the probable mechanism function is available from master plot method.

利用差示扫描量热法得到B/KNO3的热分解曲线，用K iss inger方程估算了B/KNO3的表观活化能，用标准作图法得到最可几热分解机理函数，再用积分法求得不同升温速率下热分解的动力学参数活化能E和指前因子A。

In order to simulate the gradual expansion of the crack in ductile material which should take the affect of elastic-plastic and geometric nonlinearity into account, the EWK damage model was used as the fracture criterion to instead of stress intensity factors or J integral theory in this paper.

为解决裂纹稳态扩展的有限元数值仿真，舍弃应力强度因子和$J$积分理论，考虑韧性金属的弹塑性效应和几何非线性效应，采用基于损伤理论的EWK模型作为断裂判据。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。