  The equation of motion method (EOM) for Green functions is one of the tools
used in the analysis of quantum dot system coupled with metallic and
superconducting leads. We investigate modified EOM, based on differentiation of
double-time temperature dependent Green functions both after primary time t and
secondary time t'. Our EOM approach allows us to obtain the Abrikosov-Suhl
resonance both in the particle-hole symmetric case but also in the asymmetric
cases. We will apply the irreducible Green functions technique to analyses the
EOM for dot system. This method give a workable decoupling scheme breaking the
infinite set of Green function equations. We apply this technique for
calculating the density of the states and the differential conductance of
single-level quantum dot with Coulomb repulsion attached to one metallic and
one superconducting leads (N-QD-SC). Our results are compared with the
experimental data and previous calculations.
