核函数

The boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function uses Cauchy integral formula as the foundation . The singularity of the Cauchy

广义解析函数的Riemann-Hilbert边值问题的边界元方法是以Cauchy公式为基础，Cauchy核具有奇性，这是所面临的困难，可以设法利用Cauchy主值积分来解决，最后给出问题的解。

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。

The diagonalization of the Cauchy kernel is one of the most important theorems in the theory of symmetric functions.

Cauchy核的对角化是对称函数理论中最重要的定理之一。

This function satisfies the homogeneous boundary condition of Poisson's equation.

应用格林函数将边值问题化为积分方程，并通过建立一个规范化的边界方程来表示问题的边界，以克服积分方程核的奇异性。

Weapply the kernel methods of regression functions and conditional density functions to obtain aseries ofβas the estimators ofβ.

回归函数核估计方法中，又分别提出了在选定连续样本点和离散样本点时的两种非参数估计模型，并对这两种模型做了详细的阐述。

The confidence of each region of target image is calculated according to its discriminative power between the tracking target and local background, and the target and candidate models are characterized by LBP feature probability density function weighted by region confidence and distance.

根据目标各区域对背景的区分能力不同，提出了目标各区域置信度的评价方法，用基于区域置信度及空间距离核加权的LBP特征概率密度函数，构造了目标及候选目标的特征模型。

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。

According to the connective equation of normal distribution function of these parameters, the paper proposes a simple and practical method for the reliability design of involute cylindric gear transmission, and derives a design formula and a proofread formula.

根据这些参数的正态分布函数的联接方程，提出了渐开线圆柱齿轮传动可靠性设计的一种简单适用的方法，并推导出了设计公式和校核公式。

A theoretical study on magneto-structural correlation for binuclear Cu complexes bridged by single N-N group from diazine has been investigated by using broken-symmetry approach within the framework of density functional theory.

在密度泛函数理论的框架下，应用对称性破损方法，研究了以N-N基团为单桥的二嗪类双核Cu体系的磁耦合强度及磁-结构关联。

In this paper we will focus our interesting on the concrete physical character of the dielectric functions of nuclear matter.

在本文的后一部分，我们将讨论核物质系统的介电函数的一些特征。

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。