函数的积分

The mutual coherence and angular correlation function of scattered wave from two dimensional rough surfaces is derived with Integral Equation Model and then calculated for perfectly conducting rough surfaces, then the scattering of incident pulse wave with different shape is calculated and the shape of scattered pulse is presented.

采用积分方程法推导出了二维粗糙面的双频互相关和角相关函数，数值计算了具有不同粗糙度的良导体粗糙面的双频互相关函数，在此基础上分别计算了二维粗糙面对δ脉冲、Gaussian脉冲和矩形脉冲的散射，并给出了散射脉冲的波形。

In this paper ,on one hand ,we establish the weakly asymptotic order of the classical Bernstein interpolation sequence approximate functionin the Wiener space(or 1-fold integrated Wiener space),on the other hand,we discuss the asymptotically order for the average error of Lagrange interpolation sequence, Hermite-Fejer interpolation sequence and Hermite interpolation sequence based on the Chebyshev nodes on the 1-fold integrated Wiener space.

本文一方面确定了经典的Bernstein多项式算子列逼近函数时在Wiener空间(或1-重积分Wiener空间)下的平均误差的弱渐近阶；另一方面确定了基于第一类Chebyshev多项式零点的Lagrange插值算子列、Hermite-Fejer插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差的弱渐近阶。

By means of plane elastic complex variable method and theory of boundary value problems and integral equation.

利用平面弹性复变方法和解析函数边值问题以及积分方程的基本理论，研究不同材料的各向同性弹性长条与半平面的焊接问题，给出了弹性体应力函数封闭形式的

Zhang's works. The integral method is proposed by Prof. Zheng in 1978. The method has a global convergence criterion, and only requires a the continuity of objective and constraint function.

郑权等于1978年提出了积分水平集求总极值的方法，其主要特点有判别总极值的收敛准则，且仅需假定目标函数与约束函数为连续的。

Firstly, illustrate the fundamentals (differential-integral optimizing theory) of the category of algorithms briefly in the sight of differential and integral calculus. Then two examples of the category of algorithms are listed.

首先从函数逼近的角度论述了数值积分与全局最优化的关系，随后从微积分的基本原理和定积分的定义出发对该类算法的几何意义和数学基础作了简要论述；在此基础上给出了该类算法的几个具体实现。

When computing the diagonal elements of the Galerkin matrix, one will encounter the integral of Hankel function, the Green's function of 2-dimensional Helmholtz equation and the cosine weighting function, whose integrand is singular in the integration range. A new approach is proposed to deal with this kind of singular integrals, which is pivotal but have not been reported so far.

首先建立了透镜边缘上任一点的电场满足的边界积分方程，然后选择适当的正交模式函数展开端口上的电场分布，采用边界元法的思路及Galerkin法将该积分方程离散化为—矩阵方程求解即可得到透镜的多模式散射参数。

With the help of the concepts of Lebesgue measure and Lebesgue integral in real function,the mathematics model of concurrent design of life-oriented progressive die is advanced. Which were the Lebesgue measure and Lebesgue integral of die substructures and a general mathematics model of the relation between progressive die structure and die substructures.

运用实变函数中的Lebesgue测度和Lebesgue积分的概念，结合面向寿命的级进冲模并行设计的特点，建立了面向寿命的级进冲模并行设计数学模型—模具子结构的Lebesgue测度和Lebesgue积分，提出了级进冲模结构与模具子结构关系的一般数学表达式。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

The advantages and limitations of every kind of methods for calculating the failure probability is reviewed. The frist order reliability method, the second order reliability method and many kinds of boundary method have achieved remarkable success and formed nature fields of reliability. However, the precision of these methods decrease as the increase of complexity of problem. The numrical methods are versatile, except numerical intergration is only adaptable to special problems which have small number variables and regular intergral domain. Particularly, the advanced variance reduction techniques own the following character: high precision and a small amount computation. But some questions remain to study in the future because only an initial work about these techniqes is developed.

全面评述了计算失效概率各种方法的优点和局限性，其中经典的解析法包括一次可靠性方法、二次可靠性方法、一阶边界法、Vanmarcke上边界、PENT上边界和Ditlevsen二阶窄边界法，这些方法对于多设计点、变量较多且相关、密度函数不是正态以及极限状态方程较复杂的情况，其计算精度较差；而已有的数值方法却是具有较好的通用性，其中除数值积分法只对变量较少、积分域较规则的特殊问题适用外，各种数值模拟方法均具有较广的适应性，特别是各种改进的方差减小技术，精度高、计算量小，但由于其处在研究的初级阶段，还有许多问题有待于解决。

The learning algorithm utilizes shape functions to approximate influence functions in integral transforms and estimate the control input to reduce repetitive error.

学习法则的补偿项是使用形状函数来趋近积分项中的影响函数，并且估测控制输入。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。