We get the multivariate generating function for instantaneous joint queue length distribution under any initial condition, and discuss the joint distribution for steady-state queue length and the related property among queueing systems.

This paper discusses some properties for multivariate generating function of graphical sequences, including cutset theorem and some recurrence properties.

In this paper, we define the probability generating functions of r-dimension branching chains in random environment and, by using the probability generating functions, we obtain an exact formula of covariance matrix of r-dimension branching chains in random environment.

Using firstiy the methods of renewal-process (RP), multivariate transition probability flow graphs (MTPFG)and multivariate transition probability generating function (MTPGF),another theoretical study on operating characteristics tunction of sampling L(P)on chsp-1 is presented.

In this paper,we discussed the the extremum of function of several variables,and generalized the result of paper[2],Then we give the method of solving the extrme value of n-component function using first class partial derivative.

The teaching of function of several variables is a difficult point in higher mathematics teaching.

The sufficient condition of the extreme value of function of many variables;

Seeking the maximum and minimum of function is the perpetual topic in the medium-sized mathematics,and the function of many variables are difficulties.