Based on the above consideration,and according to the character of some elementary functions and basic algebra inequality,some elementary proof methods on Kantorovich elementary proof methods about Kantorovich inequality are proposed.

Through building the elementary model of Boltzmann distribution of electrostatic dust the author calculates the field-potential distribution of electrostatic dust, discusses the empirical formula of dust concentration in the condition of disruption and verifies the effect of the previous conclusion through the issued experiment report.

Improvement on the elementary transformation method of QR decomposition of matrix;

Application of elementary transformation of matrix;

Finding bases for sum and intersection of subspaces in Pn using elementary transformations;

A primary method and a scientific supposition method are used to present a rigorous mathematical derivation and analysis to the Maxwell distribution of molecular speed.

Some interesting identities of parabola cylindrical functions D-n(z) are obtained by primary method according to the quality of parabola cylindrical functions D-n(z).

With the adoptation of properties of Laguerre polynomials and the primary method,some calculation formulas for Laguerre Polynomials and Γ Function are obtained.