查询词典 cauchy inequality

The Green's function in complex domain is introduced to turn the mixed boundary value problems of the fluid potential to the problems of Cauchy's dual integral equation.

文中采用了复域内格林函数解法，将势函数的Herbert问题转化为对Cauchy型奇异积分方程的求解。

Based on the complex variable theory of sectioally holomorphic function, Cauchy type integral and Riemann boundary problem, the solution is derived from relationship of the sections.

通过将复变函数的分区全纯函数理论、Cauchy型积分和Riemann边值问题相结合，求得各分区之间的解析关系，获得了问题的温度场。

A direct method is implemented for computing the free-term coefficient and the Cauchy principal value integral in the higher-order boundary element method for potential flow.

采用直接数值计算方法计算了势流问题高阶边界元方法中的自由项系数和柯西主值积分，建立了波浪与结构物作用的一种高阶边界元方法。

By matching the traction along the cracks, Cauchy singular integral equations for the branch cracks in the circular region were derived.

通过裂纹面上的应力边界条件，建立一组以位错密度为未知函数的Cauchy型奇异积分方程。

By using Muskhelishvili complex function methods, the problem of bimaterial incline crack was induced to the solving of Cauchy singular integral equations, in which the unknown functions are the dislocation density functions.

采用 Muskhelishvili复变函数的方法，将两相材料倾斜裂纹问题归结为以裂纹表面位错密度函数为未知量的 Cauchy型奇异积分方程的求解。

Furthermore, it can be changed into singular integral equations with Cauchy kernel by introducing Sherman transformation. Then , the numerical example of the elastic welding problem with symmetric cracks is given, and the stress intensity factors can be obtained.

通过应用平面弹性复变方法，把满足已知边界条件的弹性平衡问题转化为解析函数的边值问题，再通过引入Sherman变换，把边值问题化为Cauchy核的奇异积分方程组。

With the methods of conformal mapping and the Cauchy integral, two cases of crack geometries are studied: one is for a crack emanating from a circular hole and the other is for two symmetric cracks emanating from a circular hole.

利用保角变换和 Cauchy 积分的方法，对含有圆孔孔边单裂纹和双裂纹的压电弹性体分别进行了分析。

By using the Muskhelishvili complex methods, the issue of interaction between bimaterial incline crack s was reduced to solve the Cauchy singular integral equations, in which the unknown functions are the dislocation density functions.

采用 Muskhelishvili复变函数方法，研究两相材料中两根倾斜裂纹应力强度因子的相互影响，将问题归结为求解一组 Cauchy型奇异积分方程，对倾斜裂纹端点的应力强度因子作了数值求解。

Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented.

对结构声辐射的边界积分方程的内部形式与外部形式进行了详细的推导，给出了角点系数的计算方法与边界积分方程的形式，在此基础上，分析了奇异积分产生的原理及其对数值计算的重要性，提出了一种计算奇异积分的非等参(来源：Ae8a8BC论文网www.abclunwen.com)单元的变换方法，该方法给Helmholtz 声学边界积分方程中的弱奇异积分与Cauchy 奇异积分的计算以及编程提供了极大便利。

The edge internal branch crack of half-plane can be considered as a superposition of many single cracks, thus a set of Cauchy singular integral equations can be formulated, where the distributing dislocation density serves as the unknown function.

将半平面边缘内分又裂纹问题看作是许多单裂纹问题的叠加，建立了以分布位错密度为未知函数的Cauchy型奇异积分方程组。

To the user, having competition is meddlesome forever of course.

对于用户而言，有竞争当然永远都是好事。

It endures, unperishing, forever.

它持久忍受，没有消灭，永远。