定理

In the end , the adaptive prediction algorithm is proved to be globally convergent by using the extended form of Martingales Convergence Theorem .

k。最后用鞅收敛定理的推广形式证明了这一自适应预测算法的全局收敛性。

Then we use Lebesguge s dominated convergence theorem to obtain some sufficient conditions for (2) and study the existence of a bounded positive solution.

接着，利用Lebesgue单调收敛定理给出了方程(2)振动的若干充分必要条件并且研究了正有界解的存在性。

The third chapter mainly verify the weak convergence and strong convergence theorem ofRTRL.

第三章我们主要论证了RTRL算法的弱收敛和强收敛性定理。

Stability and convergence of the model are proven by means of the weak convergence theorem of generalized function and the convolved integration theory.

由广义函数弱收敛定理和卷积理论，证明所提出的非局部连续模型具备收敛性和稳定性。

Fourthly, Broyden iterative method is studied to solve nonlinear equation with parameters and the existence and convergence theorem is also given.

第四章的主要结果：研究用Broyden迭代求解带参数非线性方程，在弱条件下给出Broyden迭代格式的存在性和收敛性定理。

Theorem 1 If the power series is convergent at ,then for any that ,the power series absolutely converges at point ;if the power series is divergent at ,then for any that ,the power series diverges at point .

定理1 如果级数当时收敛，则适当不等式的一切使这幂级数绝对收敛；反之，如果级数当时发散，则适合不等式的一切使这幂级数发散。

Theorem 1 If the sequence is convergent, then its limit is unique.

定理 1 如果数列收敛，那么它的极限唯一。

Theorem 4(Relation of a Convergent Sequence between its Subsequence) If the sequence converges to ,then any of its subsequence is also convergent, and the limit is also .

定理4(收敛数列与其子数列间的关系)如果数列收敛于，那么它的任一子数列也收敛，且极限也是。

Theorem 2 (Boundedness of a Convergent Sequence) If the sequenceis convergent, thenis bounded.

定理 2 如果数列收敛，那么数列必定有界。

Theorem 8 If the series converges absolutely, the series must be convergent.

定理8 如果级数绝对收敛，则级数必定收敛。

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