Molecular-weight scaling of coexistence curves for monodisperse polymer solutions

The available data for the polymer volume fraction along the coexistence curves for monodisperse solutions of polystyrene in methylcyclohexane are used to derive the exponent z ≈ 0.61 such that the “correct” order parameter is only a function of ?M^Z (M is the polymer's molecular weight while ? is the reduced temperature). It is shown that a knowledge of the “correct” order parameter is unnecessary for a determination of z which is expected to be universal, i.e. independent of the polymer-solvent system.     

A method of proving non-unitarity of representations of p-adic groups I

In this paper we exhibit a new method of proving non-unitarity of representations, based on semi simplicity of unitarizable representations. Non-unitarity is proved for a half of all irreducible representations of classical p-adic groups whose infinitesimal character is the same as the infinitesimal character of a generalized Steinberg representation (as defined in Tadić, Am J Math 120:159–210, 1998). Only the Steinberg representation and its Aubert dual are expected to be unitary here. In this way we partially generalize a result of Casselman to the case of classical groups. Our argument is completely different from Casselman’s argument (which is hard to extend to this case). It requires a very limited knowledge of the inducing cuspidal representation.