定理

In this paper, the relevant definitions and theorems of function series continuity and function of the carried out a detailed convergence analysis, so that readers of their intrinsic relationship between the more detailed understanding.

本文通过相关定义与定理对函数的连续性及函数项级数的收敛性进行了详细的分析，使读者对它们之间存在的内在关系有更详细的认识。关键词：函数列；函数项级数；连续性；收敛性；一致收敛性

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。

Next, we provide some basal definitions and theories in the second section, such as the maximum principle, Holder continuity, Schauder theory and so on, which are foundation of the later work.

第二节主要给出一些相关的基本概念，定理。主要包括极值原理，Hlder连续性，Schauder理论，这些都是解决后面问题必要的基础知识。

In Chapter 3, by using the continuity theorem of coincidence degree theory, we obtain a sufficient condition for the existence of positive periodic solutions to population models with impusives.

在第三章，利用重合度理论中的连续性定理研究了在脉冲作用下种群模型的全局周期解存在性。

Under some conditions, by using Mawhin continuity theorem and degree theory, the existence of the periodic solution of the periodic neural network is proved.

利用Mawhin连续定理以及拓扑度理论，证明了在一定条件下该周期神经网络系统周期解的存在性。

The paper studied how to structure a kind of counterexample function in the analysis and widespread application emphatically, further pointed out the misunderstandings easily appeared in the concept and theorem of continuity, derivable, integrable, and other analytic properties of the function and gave the corresponding counter-example finally.

研究了一类函数在分析学相关反例构造中的应用，进一步指出有关函数的连续、可导、可积等分析性质的概念与定理中容易出现的误区，并给出相应的反例，希望能引起高校师生对该类函数的重视，进一步提高教学效果。

This article uses the implicit function theorem and the properties of analytic functions,with less limitations for the uniqueness,continuity,continuous differentiability of the implicit functions,and gets the sufficient and necessary conditions of the existence of implicit functions by simplifying them.

从常用隐函数存在性定理出发，放宽对隐函数唯一、连续、连续可微等性质的限制，利用解析函数的性质将其展拓，得到广义隐函数存在的充分必要条件和广义隐函数的分布特征。

In this article the usual method of determining the distribution density of function of one-dimensional continuous random variable——distribution function method.

本文给出了求一维连续型随机变量函数分布密度的一般方法：分布函数法，并用分布函数法对现有文献中的计算公式进行了理论探讨，对现有的定理进行修正拓展，扩大了应用范围。

According to the Scalar theorem, if the marginal distribution is continuous, there exists only one joint distribution.

根据Scalar 定理：当边际分布是连续的则它们存在唯一的联合分布函数（Copula 连接函数）。

Theorem 2 Letbe a continuous function on the interval and, then there is a , such that .

定理 2 设函数在闭区间上连续，且与异号即），那么在开区间内至少有一点使。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新