3,470 research outputs found
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
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