  Various implications of new, non-perturbative pomeron inspired enhancement of
small-x neutrino-nucleon structure functions for high-energy neutrino
astrophysics are discussed. At x larger than 10^{-5} these functions are given
by perturbative QCD, while at lower x they are determined by a specific
generalization of F_2^{ep}(x,Q^2) description, proposed by A. Donnachie and P.
V. Landshoff (their two-component model comprises hard and soft pomerons), to
neutrino-nucleon scattering case.
  We found that i) such enhancement causes the most rapid growth of
neutrino-nucleon cross-sections at high energies, ii) pomeron effects may be
perceptible in the rates of neutrino induced events in future giant detectors
and iii) the rate of high-energy neutrino flux evolution (due to absorption
(CC+NC) and regeneration (NC)) on its pass through a large column depth of
matter may be subjected to additional influence of hard pomeron. Solving
transport equations for the initially power-law decreasing neutrino spectra, we
have evaluated shadow factors for several column depths and spectrum indices.
The results are compared with analogous calculations, performed within a
trivial small-x extrapolation of structure functions. Hard pomeron enhanced
high-energy shadow factors are found to be many orders of magnitude lower than
those obtained within ordinary perturbative QCD.
