THE VISCOSITY OF A COMPRESSED GAS IS A FUNCTION OF THREE VARIABLES: (1) the degree of crowding of the molecules; (2) their capacity, by reason of softness, flexibility, or rotational inertia, to absorb the vector momentum applied to cause flow; (3) the resistance to this vector momentum offered by the randomly oriented thermal momenta, which becomes significant when the liquid expands sufficien...

Elementary smooth functions (beyond contact) are employed to construct pair correlation functions that mimic jammed disordered sphere packings. Using the g_{2} -invariant optimization method of Torquato and Stillinger [J. Phys. Chem. B 106, 8354 (2002)], parameters in these functions are optimized under necessary realizability conditions to maximize the packing fraction varphi and average numbe...

We show that for any abelian topological group G and arbitrary diffused submeasure μ, every continuous action of L0(μ,G) on a compact space has a fixed point. This generalizes earlier results of Herer and Christensen, Glasner, Furstenberg and Weiss, and Farah and Solecki. This also answers a question posed by Farah and Solecki. In particular, it implies that if H is of the form L0(μ,R), then H ...

We associate Popa systems (= standard invariants of subfactors, cf. [P3],[P4]) to the finite dimensional representations of compact quantum groups. We characterise the systems arising in this way: these are the ones which can be “represented” on finite dimensional Hilbert spaces. This is proved by an universal construction. We explicitely compute (in terms of some free products) the operation o...

We will discuss the motivating background leading to the consideration of the concept of amenability for von Neumann subfactors of nite Jones index and respectively for the combinatorial objects associated with them (standard graphs, standard lattices, paragroups, etc). Then we will review some of the results related to these notions of amenability, outlining the papers 20]{{25] and the lecture...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signicance of any solutions to them to the development of the eld.