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1·The topologic structure and learning algorithm of the rough neural network are given, and the approximation theorem of the rough neural network is presented.

给出了粗糙神经网络的拓朴结构和学习算法以及粗糙神经网络的逼近定理。

2·Random sequence Random limit logarithmic likelihood ratio Random approximation theorem Random selection Two-order Markov distribution Stochastic dominated sequence.

随机序列随机极限对数似然比随机逼近定理随机选择二重马氏分布机控制序列。

3·On the basis of the central limit theorem and approximation theory, a new implementation of the Gaussian filter by cascaded triangle filters is presented.

在中心极限定理和逼近理论的基础上，提出了一种用三角滤波器的级联来实现高斯滤波器的新方法。

4·Finally, based on the theorem, a polynomial 2 approximation algorithm for the location problem is presented.

最后，基于此定理，给出了选址问题的一个多项式2近似算法。

5·This paper discusses average approximation and proposes four theorems which are the supplement for existence theorem, characteristic theorem and solitariness theorem.

本文讨论了平均逼近，给出了四个定理，是对存在定理、特征定理，唯一性定理的补充。

6·This theorem simplifies greatly the analysis of the function approximation ability of FFMLNN because one needs only to study the one dimensional function approximation ability of FFMLNN.

也就是说我们只需研究其一维函数逼近能力，所得的结论完全适合于多维情形，该定理大大简化了前馈多层神经网络函数逼近问题的分析难度。

7·At first, we prove a theorem of finite element ultra-approximation.

首先，我们利用投影型插值，证明了一个强超逼近定理。

8·This paper gives a class of approximation identity operators on the integer domain of a local field, and a theorem on estimates of their approximation degree.

本文在局部域的整数环上给出了一类逼近恒同核和关于它们的逼近阶估计的定理。

9·The author gave a reverse theorem of uniform approximation for the combination Gauss-Weierstrass operators on a class of functions.

对于一类函数给出了Gauss - Weierstrass算子线性组合一致逼近的定理。