查询词典 compactification theorem

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 results show that Cauchy's criterion for convergence, sign theorem, and boundedness theorems are kept.

结果表明，柯西收敛准则、符号定理和有界定理仍然成立。我们的结果推广了经典复分析中的已知结论。

A novel phase unwrapping algorithm is presented based on the Goldstein S branch cut algorithm and the residue theorem.

在分析Goldstein枝切法和残差点位置的基础上，提出了一种改进的相位解缠算法。

In chapter 3, by Brouwer's fixed point theorem, we prove existence of the equilibrium point for high-order Cohen-Grossberg neural networks with delay, and investigate global stability of the equilibrium point by Lyapunov method.

第三章主要通过Brouwer's不动点定理证明了具延迟的高阶Cohen-Grossberg神经网络平衡点的存在性，并且用Lyapunov方法研究了平衡点的全局稳定性。

Chinese traditional virtue is humility and wariness,the compliment and praise to the others should be declination

中国人的传统美德是谦虚谨慎，对别人的恭维和夸奖应是推辞。如

We bought this house on the never-never.

我们以分期付款的方式买下这座房子。