无穷小

The product rule and chain rule, the notion of higher derivatives, Taylor series, and analytical were introduced by Isaac Newton in an idiosyncratic notation which he used to solve problems of mathematical physics .

该产品的规则和链的规则，概念，更高的衍生物，泰勒级数，并分析介绍了牛顿的特殊符号，他用来解决问题的数学物理。在他的出版物，牛顿改写他的想法，以适应数学习语的时间，取代的计算几何无穷小的等价论点被认为是无可指责的。

It can be readily measured, however, with an electrometer by using the technique described in Section VI-B

有时候把无穷小量dx和dy描述成正在消失的或者刚出现的量。

The dissertation focuses on performance gradient estimation and SRO algorithm of DES aswell as other related topics,such as modeling of DES and discrete event simulation,performancemeasure Hessian matrix estimation,Stochastic Approximationand so on.General Semi-Markov Processis adapted to describe behaviour of DES and discrete eventsimulation.A general result is obtained and applied to analyze strong consistency of performancegradient Perturbation Analysisestimator.Conditions for effectiveness of InfinitesimalPerturbation Analysisare also discussed.New PA algorithms,such as server PA,PA usingDirac generalized function,job sequence PA etc.,are proposed to deal with discreteparameters.Furthermore,strategies of combining PA algorithms with certain iterative rules areanalyzed widely in order to optimize DES parameters and some SRO algorithms are constructed toslove DES optimization problems.

论文将DES性能分析领域中性能梯度估计和单运行仿真优化作为主要的研究对象，探讨了与性能梯度估计有关的DES和离散事件仿真过程建模、高阶导数估计以及随机逼近等理论和方法；建立了具有一般性的DES和离散事件仿真的广义半Markov过程模型；获得了分析性能梯度估计量强相合性的理论结果和无穷小摄动分析算法应用的条件；提出了诸如服务台数目的摄动分析、奇异摄动分析、串联生产线和加工车间中工件加工序的摄动分析等一系列摄动的思想和算法，对连续参数和离散参数都进行了深入的研究；对摄动分析算法同优化规则结合实现仿真优化的策略也进行了广泛的分析，构造了新型的变界截尾的随机逼近算法，并用于DES的单运行仿真优化研究；最后，给出了DES性能分析方法的实证性研究结果。

According to [2], we know that if X is a reflexive Banach space and T is a strongly continuous semigroup on X with the infinitesimal generator A, then the adjoint semigroup T~* is also a strongly continuous semigroup on X* and its infinitesimal generator is A~*, the ajoint operator of A.

由文献[2]我们知道，如果X是一自反Banach空间，那么X上强连续半群T的对偶半群T~*也是X~*上的强连续半群，并且其无穷小生成元为半群T的无穷小生成元的对偶。

Using this method,we discussed for generalized Burger equation with variable coefficients and linear danping,obtained its symmetry group,simliar reduced equations,infinitesimal generator and Lie algebras;In chapter 6,using the Exp-function method,the generalized solutions of combined KdV-mKdV equation with variable coefficients are discussed.

首先介绍了Lie群分析法的基本思想，其次用Lie群分析法得到了带线性阻尼项的变系数广义Burgers方程的无穷小变换、无穷小算子的李代数结构，并具体求出了带线性阻尼项的变系数广义Burger方程的群不变解和约化方程。

Especially, if we let Φ denote the mininal Q process, and A denote the corresponding infinitestmal operator, then the primary problem is how to describe the infinitesimal operator ,D

特别地 ，记最小Q过程为Φ，对应的无穷小算子为 A ，我们的首要问题是如何刻划最小Q过程的无穷小算子 A ，D

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下："此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。"

From this point of view, calculus is a collection of techniques for manipulating infinitesimals.

但是，这个概念又恢复了20世纪的引入非标准分析和顺利无穷小分析，提供了坚实的基础操纵无穷小。

This paper discusses how to teach students"the product of infinite infinitesimals isn t necessarily infinitesimal" in teaching "advanced mathematics" Or "Mathematical Analysis",and the author provides some new original examples which had not been seen in currently available textbook and riches the teaching content.

文章对&无穷多个无穷小的乘积不一定是无穷小&这一知识点在&高等数学&或&数学分析&的教学中如何讲授给学生进行了一些有益的探讨，并给出了一些在现有教科书及参考书中未曾见过的独创的新例子，从而丰富了教学内容。

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下：&此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。&

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。