定理

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。

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。

Theorem Let be continuous on a bounded closed region in the -plane.(1) If is given by and , where are continuous functions of on, then

定理 设在xy平面上的有界闭区域 D 上连续，(1)若区域由和所给出，其中是上的连续函数，则。

If is continuous on the closed region , then there exists at least a point in such that , where is the area of .

性质 7(二重积分的中值定理)若在闭区域上连续，则在上至少存在一点使得，其中是区域的面积

The closed shell HF SCF calculations have been carried out for the electron transfer systems corresponding to different values of R, then the Koopmans' theorem is applied to estimate the energy level splitting △, and the relatonship between △ and R has been obtained.

对该电子转移体系进行闭壳层的单点计算，并用Koopmans定理计算了体系的分裂能△，得到△随线性反应坐标R的变化关系。

At the same time corresponding theorems are obtaind concerning the closure property of stochastic maximum of the random variable in the up reversed hazard order and the down reversed hazard order.

另外我们还得到了向上和向下反失效率序都关于随机变量的极大具有封闭性等定理。

We give some examples of BiFrobenius algebras based on the extensions of algebras and coalgebras . Let H be a bialgebra of finite dimension . Then T= H⊕H* has an algebra structure and a coalgebra structure also . We discuss the properties of T , and get the necessary and sufficient condition for T to be a BiFrobenius algebra .

然后根据代数余代数的平凡扩张给出一类BiFrobenius代数的例子，设H是有限维双代数， T= H⊕H*既有代数结构也有余代数结构，研究T的性质，给出了T成为BiFrobenius代数的充要条件，即定理3.9。

In recent years, remarkable progress has been made by [23], [24], [39], [41] and [43] in Bernstein type problems of minimal submanifolds with higher codimension and special Lagrangian submanifolds.

由于LawsonOsserman在[31]中所提出的反例，我们不能希望有关高余维的Bernstein型定理在最一般的情况下是正确的。

The performance boundaries are acquired through coding and coding theorem.

通过编码和编码定理得到一些重要的性能界限。

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