This paper prasents a domain section method of solving the system of two element equations, by which an existent domain of solution of the system can be determined and an approximate solution can beobtained by sectioning the domain.

Using the cone and monotone iterative theory, the existence and uniqueness of solutions for three classes of systems of two binary operator equations in Banach space are discussed, and the error estimations for the convergent iterative sequence are also given.

Using the cone and partial ordering theory and monotone iterative method in some weaker conditions ,the existence of maxmal and minimal solutions for some classes of systems of two binary operator equations are discussed.

By using the cone theory and monotone iterative technique,the existence and uniqueness of the solutions for a kind of nonlinear non-monotone systems of two binary operator equations,and their convergent iterative sequence and error estimations are obtained.

From the application of facility equation to the application of binary linear equation group, distinct teaching content, versus the uniform students, the author used the same mathematical situations to carry out the teaching of 搈athematical situation and posing problems? As the development of cooperative learning between teachers and students, students?problem intention gradually came into being.

The solution of the non-linear duality equation group of material balance in hydrocarbon steam transform reactor was translated into the problem of single variable non-linear optimization by using immune genetic algorithm,and the efficient solution of production technology was acquired rapidly.