Self-amplified Emission of Cherenkov Radiation from a Relativistic Particle Inside Layered Dielectric-filled Waveguide

It is shown that in some special cases the Cherenkov radiation from a charged particle moving along the axis of cylindrical waveguide filled with a semi-infinite material consisting of dielectric plates alternated with vacuum gaps is many times stronger than that in the waveguide filled with semi-infinite solid dielectric without vacuum gaps.Comment: 1 page, abstract submitted to 4th International Conference "Channeling 2010", Ferrara, Italy, October 3-8, 201

Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi