No abstract

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II 1 . This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.

We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II 1 factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III 0 factors. Several concrete examples are also studied.

Abstract. We present a simple heuristic method to derive the Painlevé di¤erential equations from the corresponding geometry of rational surfaces.

Abstract. We give an explicit determinant formula for a class of rational solutions of the Painlevé V equation in terms of the universal characters.