积分的

By use of symmetry of integral domain to coordinate surface, coordinate axis and coordinate origin, some useful formula to compute the integral are constructed, which are illustrated very useful and effective.

通过对积分区域的对称性和被积函数的奇偶性的讨论，从积分区域关于坐标平面、坐标轴和坐标原点对称出发，建立了简化各类积分计算的常见公式，并用例于展示了公式的有效性。

Then interpolating cubature formulae is given based on Lagrange interpolation formulae. Secondly it make use of the cubature formula on the triangle to construct cubature formulae on the correspondent spherical triangle.

通过把其定义域上的积分化为平面单纯形{u =(u1， u2， u3)： u1 + u2 + u3 = 1， u1， u2， u3〉0}上的积分，然后利用平面单纯形上数值积分公式给出其在球面三角形上的对d次齐次多项式精确成立的Gauss求积公式的构造方法。

The former is a theoretical foundation of the "probability language" compared with the Daniell Integral; and the later, as will be seen in the following chapter, offered the main methods for Daniell Integral.

并且介绍Daniell积分在定义无穷维空间积分中的应用。第四章我们首先按照Wiener 1923年文章中的方法考察Brown运动的数学描述，说明Daniell积分，特别是Daniell[5]中的方法，在Wiener工作中的重要

These issues are mostly difficult to solve according to the general study of mathematical models, but the Monte-carlo method is very convenient for calculating Multiple Integral of low dimension in regular domain of integration or complex range or even non-connected region.

这类问题绝大多数按数学的研究处理模式出发，都是难以解决的，而蒙特卡罗方法对计算高维空间中维数不很高且积分区域是规则的积分、以及复杂区间甚至不连通的区域上的积分都却是很方便的。

In order to avoid the singularity in the integration, the integrand was expressed to be sum of complex exponential terms by using discrete complex image method. With generalized pencil of function method introduced, the number, location and intensity of images were obtained without extracting the quasi-static and surface wave terms in the integrand, which makes DCIM more efficient for multi-layered media.

为了避免积分中的奇异性，利用离散复镜像法将积分核用复镜像的指数求和式表示，引入广义函数束方法，可以在不提取积分核中表面波项的条件下，采用数值方法提取准静态项，给出复镜像点的数目、位置和强度，使得该方法在多层介质情况下对格林函数的计算更为有效。

However, for exterior problem, in order to ensure the uniqueness of the solution, the behavior of the solution at infinity must be specified, thus the modification for the expression of the solution and the constraint for the solution of boundary integral equation are needed.

对外边值问题，考虑到二维Dirichlet问题的解应当在无穷远处有界，故解的边界积分表达式要做修正，对积分方程的解要有约束，这样去解边界积分方程得出的解才等同于原问题的解。

Fast Line Integral Convolution with constant filter kernels as well as with triangular filter kernels are presented,which are faster than the original Line Integral Convolution approach about an order of magnitude in rendering actual vector fields.

针对这个问题实现了基于常数滤波卷积核的快速线积分卷积算法，提出并论证了基于三角形滤波卷积核的快速线积分卷积算法，对于实际矢量场，上述两种方法均将运算速度提高了一个数量级，而基于三角形滤波卷积核的快速线积分卷积算法的结果使图像更加平滑。

Thirdly,incorporated into A-stability theory of recursion schemes,the A-stability ofthe precise integration schemes with high(＞2)order precision is proved, not only implicitintegral schemes,but also explicit integral schemes.

通过讨论递推格式的A稳定性，证明了精细积分格式不仅具有A稳定的隐式积分格式，而且具有A稳定的显式积分格式，且其阶数都存在超过2的形式。

The integral with respect to scattering angle is separated andcan be carried out exactly without meeting the usual divergent difficulty. The five-foldBoltzmann integral is reduced to a simple three-fold integral.

通过一种变量变换的方法，成功地将玻耳兹曼碰撞项中的有关散射角积分，分离并解析地积出，将五重积分形式的玻耳兹曼碰撞项化为较简单的三重积分。

The equation of time constant of an integrating sphere is derived.

用分析方法推导了积分球时间常数的一般表达式、积分球对δ函数形式的功率波形的变换表达式、积分球对任意光功率波形的变换表达式及其反变换表达式。

The reasons of iron ions content overproof in grade Ⅱ desalting water system,such as variation water quality,contamination of regenerant , operation adjustment of pretreatment system and switching operation of bed were discussed.

对二级脱盐水系统中铁离子含量超标的原因，如来水水质发生波动、再生剂受到污染、预处理系统操作调整、床体运行切换等进行了论述。

You were hired to drum up new business, so go and do it.

公司雇你招徕新业务，你就做你的事好了。