We analyse how the frequency dependence of the dielectric permittivity affects the electromagnetic field radiated by a point charge uniformly moving in a medium. It turns out that a moving charge radiates at every velocity. We study the space distribution of the electromagnetic field and show that its oscillations are due to the time-dependent polarization of the medium induced by the moving charge. Spectral distributions of the radiated energy and the photon number are given. Consequences arising from a choice of polarization different from the usual one are discussed. An analysis of the Kramers-Kronig dispersion relations for the treated problem is given. This consideration may be useful for the experiments recently discussed in the literature.

The basic equations to describe a plain nuclear vortex of nuclear matter are derived in the framework of nuclear hydrodynamics. The evolution of the shape of the vortex is analogous to the propagation in a plane of the nonlinear dispersion wave. Qualitative analysis of the main features of the vortex is done.

Stability with respect to neutron emission is studied for highly neutronexcessive Oxygen isotopes in the framework of Hartree-Fock-Bogoliubov approach with Skyrme forces Sly4 and Ska. Our calculations show increase of stability around 40 O.

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