In this paper we use knowledge from weak KAM theory and combine with analysis,topology and calculus of variations to Study the relation which is between the Peierls barrier,Ma(?) critical action and viscosity solutions of the time periodic Hamilton-Jacobi equation.

In this paper,by using variational analysis and weak KAM theory,we study the behavior of the energy function and investigate the property of the viscosity solutions of time-periodic Hamilton-Jacobi equations.

The categorizing principle,method and main characteristics of seem roof in shendong mining area are analysed,RMR rock class system is utilized to measure roof parameters,and thin plate theory is utilized to calculate the weighting interval and strenth of roof.

In this paper, the stress distribution of the roof has been studied by use of thin plate theory, and on the basis of maximum stress theory, the formulas for first roof pressure and periodic roof pressure have been derived.

The constitutive equations are derived according to the thin plate theory and solved with trigonometric series for the slab deflection to satisfy boundary conditions.

The application of plate theory in analysing the stability of stope′s false roof;

With the elastic plate theory, the stress distributions of plate in the various control boundaries are calculated and it is found that intensity of wei.