积分的

We prove the fuzzy set-valued characteristicfunction of a compact Baire fuzzy set can be approached by fuzzy set-valuedcontinuous functions with fuzzy compact support sets,the integral of integrablesimple Baire fuzzy set-valued function can be approached not only by the integralsof integral simple fuzzy set-valued functions,but also by the integrals of fuzzy set-valued continuous function with fuzzy compact support sets.

定义了诱导空间上具有模糊紧支集的模糊集值连续函数，说明了它与分明的具有紧支集的连续函数的关系，证明了紧贝尔模糊集的模糊集值特征函数可以用具有模糊紧支集的连续函数列来逼近，可积简单贝尔模糊集值函数的积分可以用可积简单模糊集值函数的积分来逼近，还可以用具有模糊紧支集的模糊集值连续函数的积分来逼近。

First, we discuss the noncharacteristic Cauchy problem for 1-D heat equation.

首先，对一维的热传导方程的非特征Cauchy问题，我们利用边界积分方法将问题的求解转化成解积分方程组的问题，再对积分方程组进行离散化来数值求解，最后的数值结果表明我们的算法是有效的。

A variable-step modified Euler time integration method is proposed and analyzed. Four major factors that affect the efficiency of the variable-step modified Euler time integration method are discussed. These include stability and accuracy analysis for the damped fix-step modified Euler integration formula, adjustment method of the fix-step basic integration formula to accommodate step-size changes, suitable range of the step-size selection strategy based on truncation error concept and development of the step-size selection strategy based on apparent frequency concept to satisfied the specified error bound and stability condition.

提出了变步长修正Euler时间积分法，详细讨论了影响变步长修正Euler时间积分算法效率的四个主要因素，它们包括：有阻尼问题的修正Euler法的稳定性和精度分析，调整固定步长的基本积分公式使之容纳步长大小变化的研究，基于截断误差概念的步长大小选择策略适用范围的讨论，同时满足规定误差界和稳定性条件的、基于表观频率概念的步长大小选择策略的建立。

The characteristic of this method lies in transforming improper integral into the usual one. Thus various kinds of usual approximate integrals can be used, and the observed data may be calculated directly and conveniently to obtain necessary numerical accuracy.

该方法的特点是把Abel变换的广义积分变化成通常的积分，这样就能够使用各种通常的近似积分公式直接从实验数据计算到所要求的数据精度。

The research achievement are acquired as follows: 1From mathematical models for inverse scattering in two dimensional homogenous media including Dirichlet, Neumann, Robin,all kinds of probable mixed boundaries and cracks, direct and inverse scattering are discussed, and ill-posed integral equation and indicator function method are formulated for the diverse of boundary identification. It is shown that the kernel of the integral equation characters the boundary of scatterer, which is determined by solving it by virtual of regularity method, meanwhile, some numerical tests are given.

本研究取得了如下研究成果： 1）在二维均匀介质逆散射各种边界识别的数学模型（包括Dirichlet，Neumann，Robin，各种可能的混合边界问题，裂纹问题）下，分别考虑了正散射问题和逆散射问题，推导了上述各种边界识别的不适定积分方程以及指示函数方法，由于积分方程的核充分表征了散射物的边界，由此说明只要利用正则化方法求解该积分方程，就可以确定散射物的边界，并给出了一些数值实验。

In order to test the feasibility of spectral element methods, time integral methods and absorbing boundary conditions for aeroacoustics, several programs based of Microsoft Visual C++ are presented for different time integral methods and boundary consitions.

为验证本文的谱元方法、时间积分方法和吸收边界条件对于求解气动声学问题的可行性，本文基于Microsoft Visual C++平台编制了分别采用不同时间积分方法和边界条件的谱元算法程序，计算结果证明了谱元方法的高精度以及两种时间积分方法的可行性。

Like the green jersey, the mountains jersey also requires consistency, but not in the same way. Most of the time, a rider wanting the dots will get in a breakaway on one of the first big mountain stages and win most of the points. The defense of it usually requires another long breakaway, but polka dot contenders don't have to concentrate on every single bonus like the sprinters do, because the big climbs are worth so much more than the small ones.

要想取得圆点衫，往往需要长距离的攻击，形成单飞之后逐一拿下爬坡赛点，与冲刺积分不同的是，爬坡积分会因爬坡赛点等级的不同而不同，一个S级的赛点会比4级的赛点积分高出很多，所以圆点衫的争夺要到山地赛段开始之后才会真正展开。

For the regular curves, we find two Killing fields for the purpose of integrating the structural equations of the p-elastic curves and express the p-elastica by quadratures in a system of cylind...

对于正则曲线的情形，我们发现了两个用于求解p-弹性曲线的结构方程的Killing向量场并用积分将p-弹性曲线在一个柱面坐标系中表示出来，而对仿射星形曲线的情形，我们用积分方法解出了欧拉-拉格朗日方程，利用Killing向量场及线性李代数s1(2，R)、s1(3，R)和s1(4，R)的分类将高阶结构方程降为一阶线性方程，因此我们用积分完全解出了中心仿射p-弹性曲线。

For the regular curves, we find two Killing fields for the purpose of integrating the structural equations of the p-elastic curves and express the p-elastica by quadratures in a system of cy...

对于正则曲线的情形，我们发现了两个用于求解p-弹性曲线的结构方程的Killing向量场并用积分将p-弹性曲线在一个柱面坐标系中表示出来，而对仿射星形曲线的情形，我们用积分方法解出了欧拉-拉格朗日方程，利用Killing向量场及线性李代数s1(2，R)、s1(3，R)和s1(4，R)的分类将高阶结构方程降为一阶线性方程，因此我们用积分完全解出了中心仿射p-弹性曲线。

For the regular curves, we find two Killing fields for the purpose of integrating the structural equations of the p-elastic curves and express the p-elastica by quadratures in a syste...

对于正则曲线的情形，我们发现了两个用于求解p-弹性曲线的结构方程的Killing向量场并用积分将p-弹性曲线在一个柱面坐标系中表示出来，而对仿射星形曲线的情形，我们用积分方法解出了欧拉-拉格朗日方程，利用Killing向量场及线性李代数s1(2，R)、s1(3，R)和s1(4，R)的分类将高阶结构方程降为一阶线性方程，因此我们用积分完全解出了中心仿射p-弹性曲线。

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。