递归性

The description methods of natural scenery was studied based on fractal, that is, recursive method, L-system method, IFS and IFS description method was put forward based on sine or cosine. This method overcomes angularity and consistency of recursive method, L-system method and IFS, and the variety of fractal sculpting consequence can be added and the basis for the later research and the application was provided.

对基于分形的描述自然景物方法，即递归洪、L-系统法、IFS法进行了分析研究，在此基础上，提出基于正余弦的IFS描述法，该方法克服了递归法、L-系统法、IFS法等描述方法的生硬性和一律性，增加了分形造型结果的多样性，为以后的深入研究和应用提供了依据。

Keywords: Machine discovery,recursive function,primitive recursive formula,goal restraint.

递归函数法，该方法把待求函数本身作为唯一的理论项，从而保证了理论项的合适性；其发现能力也有所提高，该方法采用原始递归式定义函数，递归函数在理论上比较完善，故该方法具有很好的理论依据并且便于计算机实现。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

Language is resourceful because of its duality and its recursiveness .

语言具备产能是因为语言具有二重性和递归性。

Logic recursiveness ; the movement of thinking ; the theories of the negation of negation

逻辑递归性；思维运动；否定之否定原理

I.75 What is the difference between conjoining and embedding and recursiveness?

连接、相嵌和递归性有何差别？

Logic recursiveness ; thought movement ; the negation of negation

逻辑递归性；思维运动；否定之否定原理

Logic recursiveness ; thought movement ; negation of negation

逻辑递归性；思维运动；否定之否定原理

Sharing synthesis process ; language recursiveness ; concurrent language ; concurrent composition of paths ; well path

共享合成；语言递归性；并发语言；路径并发合成；良径

First, the Lyapunov functional and variation of constants method are adopted to study the effect that Sigmoid function and the relation of resistance, capacitance and current in Hopfield neural networks have on the stability of networks. The stability criterion constructed by physics parameters is obtained. Thus how the constrained relation of physics parameters affects the stability of Hopfielf neural networks is clear. Based on the study above, the perturbation model of recurrent neural networks is constructed. And the theorems of the existence of solution of perturbation model are presented.

首先，采用Lyapunov泛函法和常数变易法研究Hopfield神经网络中给出的电阻、电容、电流之间的关系以及Sigmoid函数对网络稳定性的影响规律，得出仅由物理模型参数构成的稳定性判据，从而弄清物理模型参数约束关系对Hopfield神经网络稳定性所起的作用，在此基础上，构建了递归神经网络的扰动模型，并通过讨论扰动模型解的存在性问题，给出递归神经网络扰动模型解的存在性定理。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。