No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

A new$q$-binomial theorem for Macdonald polynomials is employed to prove an A_{$n$}analogue of the celebrated Selberg integral. This confirms the $ \mathfrak{g} ={\rm{A}}_{n}$ case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra $ \mathfrak{g} $ .

In this paper, we study a time-domain spherical cloaking model recently introduced by Zhao and Hao (2009). This model is quite complicated and is composed of four coupled differential equations. Here we first prove the existence and uniqueness of a solution for this model. Then we obtain a stability result, which analysis is quite involved due to the coupling between the four variables. To our best knowledge, this is the first well-posedness study carried out for the time-domain cloaking model with metamaterials.