The paper continues the rigorous investigations of the mean field Green function solution of the effective two-dimensional two-band Hubbard model [N. M. Plakida et al., Phys. Rev. B, Vol.51, 16599 (1995)] of the superconducting phase transitions in c
uprates, started in [Gh. Adam, S. Adam, J. Phys. A: Math. Theor., Vol.40, 11205 (2007)]. Discussion of the $(delta, T)$ phase diagram of the model points to the divergence of the energy spectrum in the limit of vanishing doping $delta$. Finite energy spectra at all possible doping rates $delta$ are obtained provided the hopping part of the effective Hamiltonian is renormalized with an effective factor pointing to the site-pairs availability for fermion hopping processes.
The boundary layer of a finite domain [a, b] covers mesoscopic lateral neighbourhoods, inside [a, b], of the endpoints a and b. The correct diagnostic of the integrand behaviour at a and b, based on its sampling inside the boundary layer, is the firs
t from a set of hierarchically ordered criteria allowing a priori Bayesian inference on efficient mesh generation in automatic adaptive quadrature.
The mean field Green function solution of the two-band singlet-hole Hubbard model for high-$Tsb{c}$ superconductivity in cuprates (Plakida, N.M. et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlati
on functions describing respectively the singlet hopping and the superconducting pairing. Rigorous derivation of their values is reported based on the finding that specific invariant classes of polynomial Green functions in terms of the Wannier overlap coefficients $ usb{ij}$ exist.
