We have performed a reanalysis of the Akeno data on absorption cross section by using different scenarios for the average inelasticity wherein it can alternatively be an increasing or a decreasing function of energy. The proton-proton total cross section and the proton-air inelastic cross section were calculated up to LHC energy scale.

Using the Feynman procedure of ordered exponential operators we solve the evolution equations for a two-neutrino system considering arbitrarily varying matter density and magnetic field along the neutrino trajectory. We show that a large geometrical phase velocity suppresses PL-d" PR transitions unless some stationary trajectory is found along the neutrino path. Concerning the solar neutrino case, if we admit the standard solar model matter distribution, no such trajectory can be found.

We obtain a simple solution for the ondimensional nucleonic diffusion equation in the atmosphere assuming both interaction mean free path and inelasticity BS energy dependent. We also show that a fairly accurate description of nucleonic fluxes is obtained by using the average inelasticity bp an inereasing function of energy.

We calculate the average elasticity considering non-diffractive and single diffractive interactions and perform an analysis of the cosmic-ray flux by means of an analytical solution for the nucleonic diffusion equation. We show that the diffractive contribution is important for the adequate description of the nucleonic and hadronic fluxes in the atmosphere.

We describe charged hadronic energy spectra of the cosmic-ray superfamilies named Ursa Maior and P3'-C1-890, detected by the Chacaltaya and Pamir Emulsion Chamber Collaborations, respectively, using analytical solutions for the di6'usion equations. We obtain a very good description of these events incorporating Feynman scaling breaking in the multiparticle production model of our cascading formalism. Centauro exotic events are also investigated. PACS number(s): 13.85. Tp, 96.40.De