We use a diffusive model for the propagation of Galactic cosmic rays to estimate the charged pion production in interactions with protons of the interstellar medium. Cosmic ray nuclei from proton to iron are considered and the corresponding contribut
ion to the neutrino secondary flux produced as a result of spallation is also estimated.
We present a new treatment of the Earth matter effects on the neutrino oscillations that is valid for an arbitrary density profile. When applied to the the study of the day-night effect on the solar neutrino flux it renders us a simple analytical exp
ression, which is more accurate than those derived by using the perturbation theory and can be extended to higher energies.
