In this paper, relativistic Cherenkov radiation was studied in a 3-D magneto-dielectric medium. Electric permittivity and magnetic permeability of the medium as functions of frequency, are assumed to satisfy Kramers- Kronig equations. A new interaction Hamiltonian, which is different from Hamiltonian term in non-relativistic state, was introduced by the quantized vector potential field and part...

The most common reaction-diffusion model on a Cayley tree with the nearest neighbor interactions is introduced, and the shock measure on a Cayley tree with the nearest interactions is studied. This can be solved through the full-interval method, the evolution equation of the system can be solved exactly in a closed form. The stationary solutions of such models are discussed and the final config...