Stacey Crossed Products Associated to Exel Systems

There are many different crossed products by an endomorphism of a C*-algebra, and constructions by Exel and Stacey have proved particularly useful. Here we consider Exel crossed products associated to transfer operators which extend to be unital on the multiplier algebra. We show that every Exel crossed product is isomorphic to a Stacey crossed product, though by a different endomorphism of a different C*-algebra. We apply this result to a variety of Exel systems, including those associated to shifts on the path spaces of directed graphs.     

Shape transformation of poly(butadiene)‐b‐poly(ethyleneoxide) plus DTAB compound micelles in aqueous solutions

The micellar shape of Poly(butadiene)‐b‐poly(ethyleneoxide) (PB‐PEO) plus Dodecyltrimethylammoniumbromide (DTAB) compound micelles was investigated by light scattering, small‐angle X‐ray scattering and small‐angle neutron scattering in dependence of the molar ratio between block copolymer and surfactant. The given block copolymer forms cylindrical micelles in binary aqueous solution, which transform to spherical aggregates upon the addition of a sufficiently high amount of DTAB. It is interesting to note that the micellar shape seems to be a bistable feature, in the sense that it depends not only on the molar ratio of BCP and DTAB but also in a predictable manner on the preparation procedure of the solution.