微分

The simplified Phillips' differential equation of tension which derived from Hooke's law on the assumption of uniform strip section is conventionally used up to date for the computation of cold tandem rolling.

目前常用的冷连轧张力微分方程dt=E/Lν_b(i+1-ν_dτ是假设机架间的带钢具有均匀的断面，引用等断面直杆虎克定律导出的，故为等断面张力微分方程。

This dissertation is devoted to a very important equation system among differential equation systems------quasi-linear equation system, as is a important topic of equation system(especially when discussed shock wave solution), Often appear in such research fields as Hydrokinetics, the semiconductor establishes in physical theory ,Chemical reaction theory , project, Biology , Communication and Ecology etc.

中文摘要：本论文主要研究了微分方程中的一类很重要的方程组——拟线性方程组，它是微分方程的一个重要的课题，常常出现在流体动力学、半导体设置的物理理论、化学反应理论、工程、生物、通信和生态等研究领域中。

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。

Under some conditions,the effective method in the second kind of line integrals and the differential equation is derived by using the improvising differential method of indefinite integral.

给出了在一定的条件下，利用不定积分的凑微分法得到了第2类曲线积分及微分方程的一些较为方便的解法

"Economic Mathematics" on the function of the limit, derivative and differential, derivative applications, indefinite integral, integral, integral and infinite binary Series and the first order differential equations, and so forth.

经济数学》介绍了函数、极限、导数与微分、导数的应用、不定积分、定积分、二元积分和无穷级数与一阶微分方程等内容。

Proves the calculus basic formula by the relation between function increment and differential,states briefly the intrinsic connection among indefinite integral, definite integral,derivativee and defferential.

利用函数增量与微分的关系证明了微积分基本公式，简洁地阐明了导数、微分、不定积分和定积分的内在联系。

In chapter 4, we first discussed the existence of multiple positive solutions of the second order nonsingular Dirichlet boundary value problem for impulsive differential equations by using the fixed point index theorem in cones . Next, we presented some new existence results for singular boundary value problems for second order impulsive differential equations by using fixed point theorem in cones and Leray-Schauder nonlinear alternative theorem.

第四章我们首先利用锥不动点定理讨论了非奇异二阶脉冲微分方程狄利克莱边值问题多个正解的存在性；其次我们用锥不动点定理和Leray-Schauder型非线性抉择定理，讨论了奇异二阶脉冲微分方程狄利克莱边值问题一个及多个正解的存在性。

In Chapter 4,we consider the problem of totally characteristic type equation,whose indicial exponent takes positive integers.

在第四章中，我们对全特征型微分方程也讨论了一类不满足第二、三章中定理条件的问题，即对全特征型偏微分方程也考虑了Yamane在文[11]中考虑的问题。

Chapter 4,based on strong efficiency rather than efficiency or weak effi-ciency,discusses the similar problem to chapter 3.The concepts of strongsupremum and strong infimum for the set in finite-dimensionalEuclidean space are given,s-conjugate functions and s-subdifferentials theory is developed,by means of which,the duality problem ofmulitobjectivre programming for strong efficient solutions or called absoluteoptimal solutions is analysed,and a new duality theory-s-conjugateduality theory is proposed.

第四章，基于强有效性而不是有效性和弱有效性，给出了类似于第三章的结果，提出了有限维欧氏空间中集合的强上、下确界等概念，研究了点集映象的强共轭函数和强次微分问题，建立了点集映象的s-共轭函数及其s-次微分理论，并借助于这一理论，讨论了多目标规划关于绝对最优解或称强有效解的对偶性问题，建立了基于强有效性的s-共轭对偶理论。

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。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。