  The two functional forms, D~1/tau and D~T/tau, are usually adopted as the
variants of the Stokes-Einstein relation; where D is the diffusion constant,
tau the relaxation time and T the temperature. The self-consistent generalized
Langevin equation (SCGLE) theory is presented as an analytical tool to predict
the long time dynamics of colloids and molecular liquids. In this work, taking
truncated Lennard-Jones-like liquids as an example, the rationality of the two
variants were tested in the framework of the SCGLE theory. Our results indicate
that D~1/tau is a good variant of the Stokes-Einstein relation in the framework
of SCGLE theory; however, D~T/tau is not a good one but taking a fractional
from as D~(T/tau)^zeta with an exponent zeta is not equal to 1.0 even the
Stokes-Einstein relation is established in SCGLE theory.
