rational metamathematics

In field of circuit theory, the conclusion about structure properties of electrical network based on the field of real number is determined by both network structure and the value of element, but structure properties based on the field of rational functions in multi-parameters is only determined by network structure and not by the value of elements (because these elements do not have values).

在电路理论领域内,关于电网络结构性质的研究都是基于实数域上的(描述系统的状态方程系数矩阵都在实数域上),得到的有关网络性质的结论由网络的结构和网络中元件的取值共同决定,但是基于多元有理函数域F(z)上的研究方法所获得的网络的性质只由网络的结构决定而与网络中元件的取值无关(因为这些元件都没有取值),只需观察网络的结构即可知道网络是否能控能观,方法直观简便,特别适合电网络的分析与综合。

The theory of Multiple Rational Function System takes the approach of system theory to study the structure properties of electrical network and takes the method of state space described to get the state equations of electrical networks and does some research such as controllability and observability.

多元有理函数(F(z))系统理论采用系统理论的方法研究电网络的结构性质,借助于状态空间描述的方法得到电网络的状态方程组,并对电网络结构的能控能观性等方面进行研究。

Structural Controllibility Study of Electrical Network over Field F(z) of Rational Functions in Multi-parameters;

多元有理函数域F（z）上电网络结构能控性研究

The Software Design for Founding the State Equation of RLC Electric Network over the Field of the Rational Functions in Multi-parameters;

建立多元有理函数域上RLC电网络状态方程的软件设计

Judgement Method of Irreducible Polynomial in Two Variables

有理数域上二元不可约多项式的判别

Several Immovable Point Theorems about One-Variable Real Function and Complex Function;

有关一元实函数和复函数不动点的几个定理

A BIVARIATE RATIONAL INTERPOLATION BASED ON FUNCTION VALUES AND THE PROPERTIES

一种基于函数值的二元有理插值函数及其性质

An Extending of Cauchy s Mean-Value Theorem on Functions of Several Variables;

Cauchy微分中值定理在多元函数中的推广

WEIERSTRASS APPROXIMATION THEOREM IN THE PROMOTION OF MULTI-FUNCTION

Weierstrass逼近定理在多元函数中的推广

A proof based on the fundamental theorem has no counterpart for functions of several variables.

根据基本定理的证明对于多元函数就没有相似的东西。

The Value Fields of Rational Function y=f(x)/g(x);

有理函数y=f(x)/g(x)的值域

Deviation Theoremes of the Multivariate Function Sequences of Arbitrary Random Variables;

任意随机变量多元函数序列的偏差定理的研究

Some Key Problems to be Dealt with in Teaching the Differential Calculus of the Pluralistic Function;

多元函数微分教学中应处理好的几个关键问题

An estimate of discrete dirivative Green's functions on concave polysonal domain

凹角域上离散导数Green函数有限元超收敛的一个估计

Difference of Integrations of Broad Meaning between One Function and Plural Function;

一元函数与多元函数在广义积分上的差异

Solving Derivation Problem of Power Exponential Function of N Variables from the Point of View of the Function of Many Variables;

从多元函数的角度解决n元幂指函数的求导

Model of Road Roughness in Time Domain Based on Rational Function

基于有理函数的路面不平度时域模型研究

Region Control of a Rational Quadratic Interpolating Curve Based on Function Values

基于函数值的有理二次插值曲线的区域控制

The Existence of the Two Classes of Bivariate Rational Interpolation Function and Its Algorithm;

两类二元有理插值函数存在性及其算法

In this paper, the Rolle's theorem of a variadle function is extended to multiple-variable functions. The paper, then, gives a new and simple proof.

本文将一元函数的罗尔定理推广到多元函数中,并给出了一个简洁、颖的证明。