In this paper it is proved that there exist neither right triangles nor isosceles triangles with integer sides and medians by the method of descending.

Based on the sensitivity of neural network of system identification, a method of descending neural network sensitivity in control systems is proposed in this paper.

By means of the method of descending dimension for establishing inequalities(see theorem 1 and its corollaries), This paper proves a class of inequalities for symmetric functions.