积分的

As to its computing methods, this paper synthesizes six kinds, they are: utilizing a general integral method of complex function directly; utilizing Cauchy integral theorem; utilizing Cauchy integral formula; utilizing Cauchy high-level differential coefficient; utilizing Cauchy residue theorem; utilizing the residual of logarithm.

关于周线积分的计算方法，本文综合了六种，它们分别是：直接利用一般的复变函数积分的方法；利用柯西积分定理；利用柯西积分公式；利用柯西高阶导数公式；利用柯西留数定理；利用对数留数。

The paper states the distinctions between Riemann integral and Lebesgue integral from the aspects of the definition of integral,the continuity of integrable function,the additivity of integral,integral limitation theorems and Newton-Leibnitz formula.

从积分的定义，可积函数的连续性，积分的可加性，积分极限定理，牛顿-莱布尼兹公式五个方面阐述了黎曼积分与勒贝格积分的区别。

In calculation of definite integral,beginners tend to use three methods of calculation:(1)Leibniz formula,(2)integration by substitution of definite integral,(3)integration by parts of definite integral.

在定积分计算中初学者常用的计算方法有三种：(1)利用牛顿-莱布尼兹公式，(2)定积分的换元积分法，(3)定积分的分部积分法。

According to the precise time-integration method, this paper discusses the parallel algorithm for whole domain and subdomain precise integration of diffusion equation.

讨论了一维扩散方程的全域精细积分和子域精细积分的并行算法，给出了对流扩散方程的子域精细积分并行算法，其精度优于单点精细积分法。

In this paper, starting from the double integral, double integral first introduced the basic concept and calculation method, the re - Top songs integral cylinder volume and surface area, for example in the application, as well as the double integral in the application of mechanics.

本文从二重积分入手，首先介绍了二重积分的基本概念和计算方法，二重积分计算曲顶柱体体积和曲面面积的在应用举例，以及二重积分在力学中的应用。

Integral of one variable functions, improper integral and its convergence properties.

本课程的主要内容包括：1 各种极限运算，其中包括数列极限、函数极限以及上、下极限；2 一元函数的微分学，包括微分和导数的运算法则、微分中值定理及其应用等；3 一元函数的积分和广义积分及其收敛性；4 级数及其收敛性，包括数值级数的收敛性和函数项级数的各种运算和性质；5 多元函数的微分学及其应用，其中很多方面与一元函数的微分学近似，需要注意它们之间的区别；6 多元函数的积分学，包括多重积分的性质与计算，多重积分的的应用等；7 曲线、曲面积分及其应用；8 含参变量积分的计算与性质；9 Fourier 级数及其应用，等等。

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we define δ-fine partitions for infinite interval and integral of vector-valued functions on infinite interval, and discuss the properties of integral, and characterize its primitives...

主要包括以下五部分内容：在第一部分中，我们介绍了本文所用到的基本概念和引理；在第二部分中，通过定义无穷区间上δ-精细的分法，我们给出了无穷区间上向量值函数的积分的定义，并讨论其性质，还给出了原函数的刻划；在本文的第三部分中，我们着重讨论了无穷区间上向量值函数积分的收敛定理；在本文的在第四部分中，我们首先应用无穷区间上向量值函数积分的收敛定理给出了常微分方程整体广义解的存在性定理，其次应用强积分对Banach空间常微分方程广义解进行了讨论；最后，在第五部分中，我们将模糊积分推广到无穷区间上并给出了其数值计算方法。

In this paper,the definition modes of Lebesgue integral of non-negative measurable functions are studied by the way of cutting defining and valued rids,approaching with simple function series.The four definitions of Lebesgue integral of non-negative measurable functions are given.Furthermore,their e- quivalence properties are proved by elementary knowledge.

文献〔1」利用非负可测函数在Ef镇司上积分的极限定义了f在有界可测集E上的L积分；文献[2」利用非负递增简单函数列积分的极限定义了非负可测函数的L积分；文献[3]给出了L积分的一种统一定义；文献〔4一6〕分别证明了测度

Based on the analysis of existed fuzzy integral theories, the notions of the Choquet upper and lower fuzzy integral and rough interval numbers' integral form were proposed; the rough properties of Choquet fuzzy integral and an information fusion method based on rough Choquet fuzzy integral were given.

在分析现有模糊积分理论的基础上，提出了Choquet上、下模糊积分的概念和粗糙区间数的积分形式，给出了Choquet模糊积分的粗糙特性，建立了基于粗糙Choquet模糊积分形式和信息融合方法。

Introduces the notion of Feynman's path integrals and path integrals approach to financial modeling; Derives the path-dependent options pricing formula by making use of the Lagrange form of path integrals; Discusses Ilinski(2003)'s Gauge model which based on path integrals and fibre bundle, and its application for real-options evaluation; Summarizes the general modeling framework of options evaluation, taking advantage of the Hamilton form of path integrals; Applies the Geske-Johnson's analytical approximation in the path integrals form to the real-options evaluation for investment decisions, detailed procedure is presented under the assumption that underlying asset price dynamic follows a geometric Brownian motion, and the integral reduction for multivariate normal integrals and polynomial approximation for real-options evaluation is given.

系统论述了路径积分概念方法及其在期权估值中的应用，利用路径积分方法的Lagrange表述推导了路径依赖期权定价公式：探讨了基于路径积分和纤维丛的Gauge模型思想方法在实物期权价值评估中的应用；利用路径积分的Hamilton表述形式，总结了基于Hamilton表述的期权估值一般化框架；基于路径积分的形式框架建立了一个新的投资期权估值模型，并在具体的估值算法中给出了多重正态积分的降阶计算和期权价值的多项式逼近方法。

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。