In the finite square potential well a damped particle with a force quadratic in the velocity is studied,and thus it obtains the energy eigenvalues and energy eigenfunctions of the particle with a force quadratic in the velocity in infinitely deep square potential well.

The development of the cubic equations of state is briefly generalized and the characterstics of the cubic equations of the state is recapitulatory recommended.

In view of the metal's plastic flowing description of the fine extruding rounded square profile and the geometrical parameter optimization of similar dies, with the complex conformal mapping theory, a mathematical model expressing the plastic flow, its die parameters and the energy equation of the plastic body were established.