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Proposed in the paper are the ordered monotony property of MFNNs when the transfer function is monotone, the continuous mapping theorem, and non approximation theorem to function.

给出了单调传递函数的 MFNNs按序单调特性、连续映射定理以及非函数一致逼近定理。

Several strong results on neural network approximation capability obtained in this dissertation are important in the approximation theory and applications of neural networks.

本文系统地研究了多层神经网络的非线性逼近能力,给出了多层网络可一致逼近有限维空间R〓紧集上的连续函数、无穷维函数空间紧集上的连续泛函和连续算子以及布尔函数的理论证明。

We introduce the notion of fuzzy-valued continuous function on a compact set K in a metric space, and discuss its properties; On this base, we study the uniformly d∞-convergence of a sequence of fuzzy-valued continuous function on K. We prove that the space of fuzzy-valued continuous functions on K, i.e. C(K, E1), is a complete metric space with respect to the metric D.

引入了定义在某度量空间的紧子集K上的模糊数值连续函数和水平连续函数的概念,讨论了它们的某些性质;在此基础上,研究了K上模糊数值连续函数列的一致d∞-收敛性,证明了K上模糊数值连续函数空间C(K, E1)关于度量 D 构成一个完备的度量空间。

If each term of the series u1+u2+…un+…is continuous on the interval[a,b], and this series is uniformly convergent on[a,b], then its sum function is also continuous on [a,b].

若级数u1+u2+…un+…的每一项在[a,b]上连续,而且这级数在[a,b]上一致收敛,则它的和函数也在[a,b]上连续

If the topology is fixed and time-invariant, the consensus value of discrete-time systems also globally asymptotically converges to the convex combination of initial states, which is identical to continuous systems.

如果多智能体网络系统的拓扑结构没有改变,在离散状态下系统的一致平衡点仍收敛于初始状态的凸组合,并且离散状态下系统的一致平衡点与连续状态下系统的一致平衡点相等。

Second, we prove that consensus value of continuous time-invariant systems converges globally asymptotically to the convex combination of initial states, thus, determining the consensus value of the non-balanced topology.

对于多智能体网络连续系统,该系统的一致平衡点最终收敛于初始状态的凸组合,本文最终确定了非平衡拓扑结构的一致平衡点。

This thesis firstly defines the uniform integrability and absolute continuity of fuzzy variables, discusses their relationships, and provides an approach to checking the uniform integrability of fuzzy variables.

本文首先定义模糊变量序列的一致可积和绝对连续,讨论它们之间的关系并且给出判别一致可积的方法。

Theorem 1 If the general term of the series is continuous on .and is unanimous convergent with the sum function on .

定理 1 如果级数的各项在区间上连续,且在区间上一致收敛于,则在上也连续。

Heating the strip in the furnace via great temperature drop in order to reduce the heat time, to decrease the oxid created on the strip face, to unify the heating and the character of the strip and to increase the efficiency of the furnace and low the consumption of energy.

为了提高连续退火炉的生产效率和节能效果,采用较大的温度落差进行加热,以大大地缩短加热时间,减少带钢氧化,使带钢表面受热均匀一致,以保证带钢组织与性能的均匀一致。

In the first place, the normal flexible body dynamics modelling method of continous system is built based on hamilton principle. And then taking the flexible beam tunning in the horizontal plan for example, in the assumption of Euler-Bernoulli beam,the identical linearilized vibration differential equation is deduced according to geometry constraint conditions .

首先基于Hamilton原理建立起一般柔性体连续系统的动力学建模方法,进而以水平面内作大范围回转运动的柔性梁为例,在Eu1er-Bemoulli梁模型的假设前提下,根据轴向不可伸长的柔性梁的几何约束条件,推导出作大范围刚体运动的柔性梁连续系统的一致线性化振动微分方程。

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