查询词典 normalization theorem

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。

Then it proves a necessary and sufficient condition for anamalgamation of two 3-manifolds with toms boundary with no new incompressible surfaces.Lastly, with the help of the condition and the theorem about the classification of allautomorphisms of a torus, it is proveed that there exists infinitely many 3-manifolds each ofwhich contains no incompressible surfaces besides a torus.

最后，文章给出了以环面作为边界的两个3维流形在作融合积时不产生新的不可压缩曲面的一个充分必要条件，并将这个结果与关于环面到自身的自同胚类的分类的结果相结合，证明了本文的一个核心结论，即存在无穷多个互不同胚的3维流形满足除了一个环面以外不含有其他的不可压缩曲面。

Firstly , using the conditional independence test built the Bayesian network structure , and desensitizes remote sensing data of study area . Secondly , applying Bayesian network theorem as classification principle classifies every single pixel to a pixel of maximum probability sort .

采用贝叶斯网络分类对具有典型干旱特征的库车县土壤盐渍化情况进行监测，首先应用条件独立性测试原理建立贝叶斯网络结构，把研究区遥感数据进行离散化，然后应用贝叶斯定理作为分类原则，将每个像元分为像元最大概率的类别。

Based on the methods and techniques of covering theory, the structure of module category of tame concealed algebra, one-point extension, vector space category, finite enlargement, degeneration theory, stable equivalence and combinatorial method, we will classify all of the three-point algebras with Gabriel quiver the system quiver Q according to representation type. We get the classification theorem: Let A=kQ/I be a three-point algebra given by the system quiver Q.

本文综合利用覆盖理论，tame concealed代数模范畴的结构，单点扩张，向量空间范畴，有限enlargement，退化理论，稳定等价以及组合的方法等多种方法和技巧，将所有由系统箭图Q给出的三点代数按表示型进行分类，得到如下分类定理：Q是系统箭图，I是kQ的一个admissible理想。

The Fary-Milnor theorem states that the total curvature of a knotted simple closed curve in R^3 is greater than 4π.

Fary-Milnor 定理：一条空间中的简单封闭扭结其总曲率必大於4π。

The assertion is known as the closed graph theorem for Hilbert spaces.

这个断语被称为希耳伯特空间的闭图象定理。

X→Y has a closed graph are provided,and the classical closed-graph theorem is generalized.

本文给出了算子T具有闭图象的一些等价条件，并推广了经典的闭图象定理。

Theorem 1 Let be continuous on the closed interval and let be a point in.

如果函数在区间上连续，则积分上限函数=在上可导，并且它的导数是

Theorem 1 If a function is continuous on the closed interval ,it is integrable on .

设在区间上连续，则在上可积。

According to Sarkovskii's theorem, if the continuous self-map f of the closed interval has a 3-periodic orbit, then f must has an n-periodic orbit for any positive integer n But f can not has all n-periodic orbits for some n.

但f不可能有所有类型的n-周期轨。例如：则f仅有两种类型的3-周期轨中的一类。这表明Sarkovskii定理远远没有给出周期轨之间的关系的全部信息。

"The operators will suffer a temporary decrease in the number of consumers and short message services as people may not like having to provide their ID cards for a phone number," Xu Junqi, vice-dean with the Policy-Making Institute of the Telecommunications Research Centre under MII, said yesterday.

信息产业部下属的通信决策研究院副主任徐俊其昨天说：&实行手机实名制后，人们可能不太情愿用身份证注册手机号，所以通信运营商会暂时面临用户减少和短信用户减少的问题。&

I don't believe in make-believe!

我不相信这些虚构的故事。