  The properties of nanoscopic rings with electronic correlations and
impurities are analyzed numerically by means of two complementary methods.
Namely, we perform exact diagonalization of systems up to several lattice sites
and Bogoliubov-de Gennes-equations studies of systems consisting of a few
hundred sites. We demonstrate how the properties of the systems are affected by
various configurations of impurities for both repulsive and attractive
electron-electron interactions. In the case of attractive interaction we show
that the nanoscopic properties are mainly determined by the competition between
tendencies toward pairing and formation of the density waves. Since the
impurities act as pinning centers for the density waves, their configuration
determines the result of this competition.
