A countable group is C∗-simple if its reeduced C∗-algebra is a simple algebra. Since Powers recognised in 1975 that non-abelian free groups are C∗-simple, large classes of groups which appear naturally in geometry have been identified, including non-elementary Gromov hyperbolic groups and lattices in semisimple groups. In this exposition, C∗-simplicity for countable groups is shown to be an ext...

It is generally accepted that knowledge based systems would be smarter if they can manage uncertainty. In this paper we extend Description Logics, well-known logics for managing structured knowledge, towards the management of uncertainty. We allow to express that a sentence is not just true or false, but certain to some degree, which is taken from a certainty lattice.

An important exercise in the study of rational approximants is to derive their metric, especially in relation to the corresponding quasicrystal or the underlying clusters. Kuo’s model has been the widely accepted model to calculate the metric of the decagonal approximants. Using an alternate model, the metric of the approximants and other complex structures with the icosahedral cluster are expl...

One of the classical problems concerning the peg solitaire game is the feasibility issue. Tools used to show the infeasibility of various peg games include valid inequalities, known as pagoda-functions, and the so-called rule-of-three. Here we introduce and study another necessary condition: the solitaire lattice criterion. While the lattice criterion is shown to be equivalent to the rule-ofthr...

This letter discusses the problem of optimizing a lattice-based signal constellation for signaling over a partial response channel. The objective is to minimize the probability of error which is determined by the combined effects of the additive Gaussian noise and channel memory.

We study the influence of short range antiferromagnetic correlations between local f -electrons on the transport and thermodynamic properties of Kondo insulators. We use a Kondo lattice model with an additional Heisenberg interaction between nearest neighboring f-moments, as first proposed by Coqblin et al.[1] for metallic heavy fermions. The inter-site magnetic correlations produce an effectiv...