查询词典 classification theorem

In Chapter 2, we use Zorn lemma and generalized order set general principle [47] to generalize classical Caristi fixed point theorem, respectively, which weaken the condition that the functional is bounded from below.

在第二章中，我们首先分别利用Zorn引理和推广的序集一般原理[47]推广了古典的Caristi不动点定理，削弱了泛函下方有界这个条件。

According to that Caristi fixed point theorem is equivalent to Ekeland variational principle, we weaken the condition that the functional is bounded from below in Ekeland variational principle, then we enlarge the area of the applicable functionals.

鉴于Caristi不动点定理和Ekeland变分原理的等价性，我们对Ekeland变分原理中泛函的下方有界的要求作了相应的削弱，从而扩大了适用泛函的范围。

Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.

定理 2 有界函数与无穷小的乘积是无穷小。

According to Liouville's theorem , any bounded complex analytic function defined on the whole complex plane is constant.

如上所述，实或复解析函数均在实变量的意义上无穷可微。

As a result, we have demonstrated that the best approximating operator and the best approximating of bounded linear operator in H10 and H1a,+∞ are consistent and, at the same time, we have generalized the theorem of the best approximating of bounded linear operator to the more universal H1

然后，我们说明了在这样的索伯列夫空间上定义的样条插值算子和最佳逼近算子是一致的，同时把有界线性算子的最佳逼近定理也推广到了一般的索伯列夫空间H~1a，+∞上去。

We first show some properties of such operators and give an explit description about the image of a linear bounded operator on a linear normed space. Then based on these results, we show the mean ergordic theorem on a C*-bial-gebra and get a sufficient and necessary condition for a linear functional to be Haar measure. Finally we discuss the sufficent conditions for the existence of Haar measure on C*-bialgebras.

本文首先通过考察这样算子的性质和刻画赋范线性空间中连续线性算子的像集的性质，证明了C*－双代数中的一个平均遮历定理，得到了C*－双代数中的线性泛函是 Haar 测度的充分必要条件；利用遍历定理和这个充分必要条件探讨了C*－双代数中 Haar 浏度存在的一些充分条件。

We get the two edge blocking convergencetheorem of sequence of fuzzy numbers and the almost everywhere cut-convergence theorem ofmonotone bounded sequence of fuzzy numbers, and point out that monotone bounded sequenceof fuzzy numbers may not cut-converges and converges.

讨论了模糊数列的收敛、截收敛、几乎处处截收敛性，得到了模糊数列收敛的夹逼定理及单调序有界模糊数列必几乎处处截收敛定理，并指出了单调序有界模糊数列未必截收敛、收敛。

And we also prove the existence theorem of minimizer for the new model by means of Poincares inequality and the lower semi-continuity of bounded variation functions.

根据有界变差泛函中的Poincare不等式和下半连续性，证明了该模型极小值的存在性。

And we also prove the existence theorem of minimizer for the new model by means of Poincare's inequality and the lower semi-continuity of bounded variation functions.

根据有界变差泛函中的Poincare 不等式和下半连续性，证明了该模型极小值的存在性。

The problem of paths with bounded length, being a variation and a generalization of Menger's theorem, is of very important significance in the design and analysis of real-time or fault-tolerant interconnection networks.

设给出了h，ψ-η限长路径问题是图论中的Menger定理的变形和推广，在实时容错网络设计和分析中有重要意义。

The role of the environment is very important.

的作用，环境是非常重要的。

At that time, the High Court of England and Wales Court of Queen's Bench president of William Murray, Lord Mansfield in June 22, 1772 ruling:"No matter then there is the inconvenience, but there must be a decision, I can not say that this case under the law in England are permitted or authorized; are so black should be released."

当时的英格兰及威尔士高等法院王座法庭院长William Murray， Lord Mansfield于1772年6月22日宣判：「无论有那麽不便，但总要有个决定，我不能说这件案在英格兰法律之下是准许或认可；所以黑人是应该被释放。