递归的

After analyzing the structure of sentences,Tarski found that, it was impossible to define the truth of the calculus of classes directly,but making use of the structure character of sentential functions could give us the approach to escape the dilemma:Firstly,we could defined the concept of satisfaction in sentential functions by means of recursive method;Then,we could regard sentences as a peculiar form of sentential functions;Finally,with the help of the concept of satisfaction,we could defined successfully the truth of the calculus of classes.

通过分析语句的结构，塔斯基发现很难直接定义出类演算语言的真概念，而语句函项所具有的可递归形成的结构性质可以使我们得到脱离困境的办法：先采用递归方法针对语句函项定义出满足概念，然后把语句作为语句函项的特殊形式，借助于满足概念最终可以得到类演算语言的真概念定义。

We study the recursive structure of the twisted-cube connected network sufficiently, and prove that the twisted-cube connected network is an n regular graph with connectivity n: point out that the twisted-cube connected network is a cube-free network, which is an essential distinction with the hypercube and other variations of the hypercube; prove that the diameter of n dimensional twisted-cube connected network is [ (n+1)/2] , which is almost the half of hypercube's.

首先对其结构的递归性进行充分地研究，证明它是连通度为n的n正则图；指出扭立方体连接网络无立方体子图，这是扭立方体连接网络与超立方体及其其它变种的本质差别；证明了n维扭立方体连接网络的直径为[（n+1）/2]，它几乎是超立方体直径的一半；最后，给出超立方体及其变种的等价定义，并对它们的结构递归性、网络参数和拓扑性质等作了简单的分析、综合和比较。

This idea comes from the appearance of the curse of dimension in computational process, for example, in Markov decision processes, its not practical for improving policy computation using the general policy iteration or value iteration method.

当系统的计算出现维数灾难时，比如在Markov决策过程的求解问题中，如果系统的动作空间非常之大，那么利用一般的策略递归算法或值递归算法，来进行策略的改进计算是不实际的。

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。

In this paper, the theories of generation function and recursive relation in combinatorics is used to analyze the time complexity of some special recursive algorithm, with three conclusions reached simultaneously, which is of valuable reference to the analysis and research on algorithm.

提出了用组合数学中的母函数与递推关系理论来分析一些特殊的递归算法的时间复杂度，并同时得出三个推论，在算法的分析与研究方面具有一定的参考价值。

To prepare studying hierarchical intelligent control system of material flows in mineral processing plant further, picturing, transition rulers, analytic methods, relevance matrix and dynamic equation, defect in applying of Petri network, fall short of orient object models applying are discussed after technology of formalization model built, non-formalization built and compound model. And Petri network system with time attribute is expanded opening network system with interface of input and output. The network system expanded with all attributes of basic Petri network model has hierarchy and recursiveness, can be analyzed with mathematical tools of network system and can deal with concurrent and asynchronously also.

为了对选矿厂生产物流递阶智能控制系统的进一步研究奠定基础，本文在讨论了形式化建模技术、非形式化建模技术和复合模型的基础上，研究和分析了Petri网的图形表示、变迁规则、分析方法、关联矩阵与动态方程、Petri网模型应用中的缺陷、面向对象模型应用中的不足，并把采用赋时的Petri网系统扩展成为对外界有输入和输出接口的开放网系统，扩展后的Petri网具有递阶性和递归性，同时保持基本Petri网的所有性质，使模型仍可采用网系统数学工具进行分析，并可处理生产物流系统中的并发性和异步性。

Furthermore, debugging tools and program analyzing tools will be more powerful if an efficient pointer analysis module is embedded Right for the importance of pointer analysis, many studies have been done in order to find an efficient and effective solution to pointer analysis. Many pointer analysis algorithms have been developed too.

正因为指针分析具有诸多非常重要的意义，曾有许多学者对这个问题进行了研究，也提出了多种指针分析的算法，然而以往的指针分析方法存在着如下不足：对赋值语句的指针分析还不够完善，这尤其表现在对结构赋值语句以及对递归数据结构内递归数据域的分析上。

At last, the application of above modeling and control strategies has been demonstrated by the simulations of a nonlinear dc motor control problem. Under this control strategy, system identification phase is not needed, and only a controller based on the recurrent neural network is provided. Because the control and learning laws are designed with stable theory, stability and convergence problems are solved here with rigorous analysis, which can not been analyzed easily when usual BP neural networks are used.

最后通过非线性电机模型的仿真研究，表明了基于上述动态动态递归神经网络模型对非线性系统进行自适应控制的实际可行性，并且采用这种方法不需要对系统进行离线辨识，整个系统只采用了一个基于动态递归神经网络的控制器，由于整个系统是基于稳定性理论设计的，有效地解决了应用BP网络等其它前向网络时系统的稳定性和收敛性难以分析的问题。

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。

Of all the dependence analysis methods, an approach to analyze dependencies of recursive subprograms is one of the main difficulties.

为此 ，该文提出了一种新的递归子程序间的依赖性分析方法，它首先分析子程序内部的各种依赖关系；然后，结合子程序调用图分析子程序参数间的依赖关系；最后，通过模拟递归子程序的执行过程来分析它们之间的依赖关系。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐