查询词典 compactification theorem

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。

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。

In chapter one, by using a competely continuous operator on cone and the Krasnoselskii fixed point theorem, we study the existence of positive periodic solutions of differential equations with impulses and delays, and some sufficient conditions will be given.

第一章讨论了一类具脉冲时滞微分方程周期正解的存在性，通过建立锥上的全连续算子，利用Krasnoselskii不动点定理，得到了存在周期正解的若干充分条件。

By using the method of an abstract continuous theorem of k-set contractive operator and some analysis technique. Sufficient conditions are derived for the existence of at least one strictly positive periodic solution of periodic two-species Lotka-Volterra competition dynamics systems with neutral delay and several deviating arguments.

利用k-集压缩算子抽象连续理论和某些分析技术，导出了此具有中立时滞和变差元的周期两种群Lotka-Volterra竞争动力系统至少存在一个严格正的周期解的充分条件。

In view of continuous function problems, it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem. Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收效，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收效的证明。

In view of continuous function problems,it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem.Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收敛，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收敛的证明。

That not only could be extended to the continuous random varia- ble,but also the theorem of maximum information measure could be extended to the continuous random variable, which unified the measurement arithmetic of information between distributed random variable and continuous ran- dom variable,and gave two validating models to the information entropy of the continuous random variable in the last.

用公理化的方法，推导出了有限分布列的离散型随机变量的信息量系，不仅将它推广到连续型随机变量，而且将信息量系的最大信息量定理推广到连续型随机变量，统一了离散型和连续型随机变量的信息度量算法。最后利用得出的结论对连续型随机变量信息熵给出两个验证性算例。

Theorem If and are continuous on an open set S, then at each point of S.

定理 若和在开集S连续，则对于S的每一点有。

The author proves theorem on contracting maps for halfmetric space and the existance of solution and the Continuousness of integral operator integral equation in Orlica space.

证明了半度量空间中的压缩映像原理，并应用其证明了Orlica空间中一类积分方程解的存在性及积分算子的连续性。

Tom: You are right, he worked hard all the time.

你是对的。他一直都是努力工作。

Take shortcomings,failures,and mockings of others as commonplace and a drive to complete oneself,hold your own opinion over the evalution and disscution divested from others,afterwards sink into the state of eliminate mistakes if any or encourge oneself being not being influenced by the sayinngs of others or having no ideas to do.

把缺点、失败及别人的耻笑等看成是一种常事，当成完善自己的动力，对别人的评价和议论自己心中有主见，做到&有则改之，无则加勉&，不为人言所左右或无所适从。