定理

This paper proves that every probabilistic contraction map from E to E has a unique fixed point, where E is a complete and uniformly local semi-convex probabilistic normed spacer and obtains a fixed point theorem in metric linear spaces.

摘要证明了完备的一致局部半凸概率赋范空间上的概率压缩映象必有唯一不动点，得到了一类度量线性空间中关于伪范数族一致压缩映象的不动点定理。

This paper studies a contractive mapping, obtains the existence and uniqueness of its fixed point.

该文研究了一类压缩型映射，得到其不动点的存在唯一性定理。

This paper presents fixed point results for a kind of generalized contractive maps and generalized contractive homotopy on space with two metics.

主要讨论在具有二个度量的空间上一类广义压缩映射与广义压缩同伦的不动点定理。

In 2D eddy current field computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by the GMT, and solves several real engineering examples of 2D eddy current field boundary-value problems by the MT.

本文从电磁理论和有关数学定理出发，通过引入内极、外极、内交角的概念，建立一种新的电磁场计算体系——电磁场分析中的多极理论；从理论上证明，在电磁场分析中存在一种无穷级数收敛，且有一定普遍性的解析解。

And the radius of the convergence set of the differentiated series is the same as for the orginal series.

定理5 如果幂级数的收敛半径为则其调和函数在内可导，且有逐项求导公式

The radius of convergence can be characterized by the following theorem

收敛半径可以被如下定理刻画

To ensure stability of the NNA, the convergence theorem of the NNA is presented and proved.

为保证该算法的稳定性，提出并证明了该算法的收敛定理。

In chapter 3,we establish convergence theorem under Ostrowski-Kanorovich condition for Newton-like method by using majorizing method.

第三章：通过运用优函数的方法，建立了Newton类迭代法在Ostrowski-Kantorovich条件的收敛性定理，并给出了相应的误差估计。

In the third chapter,we establish a local convergence theorem of the two points Secant method through the use of the recurrence technique.

在第三章中，利用递推法的技巧，我们建立了两点弦截法的局部收敛性定理。

In Chaper 4,we extendthe simple Newton's method to sovle our problems,the convergence theorem is proved.

在第四章，我们将简单Newton方法加以推广，用于求解取值在闭凸锥中的非线性包含问题，建立了一般的收敛性定理。

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