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The boundary layer of a finite domain [ a, b] covers mesoscopic lateral neighborhoods, inside [ a, b], of the endpoints a and b. The correct diagnostic of the integrand behavior at a and b, based on its sampling inside the boundary layer, is the first from a set of hierarchically ordered criteria allowing a priori Bayesian inference on efficient mesh generation in automatic adaptive quadrature. [ABSTRACT FROM AUTHOR]

The mean field Green function solution of the two-band singlet-hole Hubbard model for high- T c superconductivity in cuprates (N.M. Plakida et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlation 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 v ij exist. [ABSTRACT FROM AUTHOR]

A microscopic theory of superconductivity is considered in the framework of the Hubbard p–d model for the CuO[sub 2] plane. The Dyson equation is derived in the nonintersecting diagram approximation using the projection technique for the matrix Green function of the Hubbard operator. The solution of the equation for the superconducting gap shows that interband transitions for Hubbard subbands lead to antiferromagnetic exchange pairing as in the t–J model, while intraband transitions additionally lead to spin-fluctuation pairing of the d-wave type. The calculated dependences of the superconducting transition temperature on the hole concentration and of the gap on the wave vector are in qualitative agreement with experiments. © 2003 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]