  An accurate numerical consideration of 1D spinless fermion model with
next-nearest neighbour (NNN) interactions is carried out for the electron
concentrations 4/7. It is shown that depending on the parameters of the model
it can be either Luttinger liquid or bipolaron liquid. In the former case
competing interactions can result in a smooth behavior of one-electron
distribution function at the Fermi surface with a divergence in the second
derivative with respect to the quasimomentum (and not in the first one, as
usual). In this connection, uncommon photoemission spectra for some 1D
conductors can be explained qualitatively.
