函数说明

Chapter one has introduced the background and classification of minimax theorems; Chapter two summarizes several proof method of minimax theorems, which are illustrated with examples; Chapter three has explained the development general situation of minimax theorems for a function and for two functions with chapter four respectively, and according to the classification of the theorem, has illustrated some important conclusionses in quantitative minimax theorems, topological minimax theorems and quantitative-topological minimax theorems separately.

第一章介绍了极大极小定理的背景及其分类；第二章总结了极大极小定理的几种证明方法，并举出例子进行说明；第三章和第四章分别阐述了单函数的极大极小定理和两个函数的极大极小定理的发展概况，在第三章中，按照极大极小定理的分类，分别对数量极大极小定理，拓扑极大极小定理和数量拓扑极大极小定理的一些重要结论作了介绍。

This article is mainly discussed the relation between some important concepts and conclusions about the Limit of Sequence, the Limit, Continuity ,Differentiability, Integrability of Function, the Infinite Series , and the Limit, Continuity, Derivativeness,Differentiability of Multivariable Function ,as well as the Multiple Integral, and Integral with parameter .

本文对数列极限，一元函数的极限、连续性、可微性、可积性，无穷级数，多元函数的极限、连续性、可导性、可微性以及重积分，参变量积分中的一些重要概念和结论之间的关系进行了一些探讨，每一个问题都作了适当说明或举出反例，并对一些相关的内容进行了讨论，得到若干结果。

This PPT introduces covariance function and its formula for calculating the variation function and its formula, Kriging interpolation process, and finally given an example based Kriging interpolation.

详细说明：本PPT介绍了协方差函数及其计算公式，变异函数及其计算公式，克里格插值方法的过程，最后给了一个基于克里金插值的实例。

It is shown that in complex system like L-tyrosine, using a locally dense basis set with a large number of atomic basis functions for the carbon atom of interest and smaller sets of atomic functions for the other atoms can not only save the disk capacity and computing time but also produce satisfactory results.

由从头计算获得的结果与实验值符合较好，说明对于具有复杂结构的多原子体系，对杂原子使用较小的基函数，而对所关心的碳原子使用较大的基函数以提高计算精度，这样可以达到既节省计算机空间与计算时间而不影响计算精度的目的。

Give examples to show that the derivate of elementary function may be unelementary function.

给出实例说明初等函数的导数可以是非初等函数。

Application of differential coefficient in inequation verification;2. It also elaborates what should be pay attention to while making use of this method to obtain differential coefficient .

本章给出了由分段函数直接求导数再取极限求函数在分段点处导数的方法，并就利用该方法求导数时需要注意的问题进行了说明。

This function is not a practical exponentiation routine, since it handles only positive powers of small integers, but it's good enough for illustration.

该函数并非一个实用的求幂函数，它只能处理较小的整数的正整数次幂，但这对于说明问题己足够了。

The use of genetic algorithms achieve about extremal function of problem solving, function has been give.

详细说明：使用遗传算法实现关于函数极值问题的求解，函数已给出。

Function based on genetic algorithm to optimize the use of genetic algorithm function extremum.

详细说明：基于遗传算法的函数优化，利用遗传算法求解函数极值。

Based on the Collins formula, the analytical propagation equations for a Gaussian beam through a multiple spatial filter system are derived by using the methods of the matrix decomposition and expanding the aperture function into a finite sum of complex Gaussian function .

以Collins衍射积分公式为基础，利用A0CD矩阵分解与物理实现的技巧，以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，推导出了高斯光束通过多级空间滤波器系统的传输方程，并用数值计算加以说明。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。