We derive closed analytical formulae for the power emitted by moving charged particles in a uniaxial wire medium by means of an eigenfunction expansion. Our analytical expressions demonstrate that, in the absence of material dispersion, the stopping power of the uniaxial wire medium is proportional to the charge velocity, and that there is no velocity threshold for the Cherenkov emission. It is...

We investigate the existence of principal eigenvalues, i.e., values of λ for which the corresponding eigenfunction is positive, for the problem −∆u(x) = λg(x)u(x) for x ∈ lR where g is a smooth function which may change sign, Unlike most previous studies the eigenfunction is not required to → 0 as |x| → ∞. It is shown that there may exist a closed interval of principal eigenvalues [λ∗, λ ] and ...