We introduce the concept of a geometric categorical sl2 action and relate it to that of a strong categorical sl2 action. The latter is a special kind of 2-representation in the sense of Rouquier. The main result is that a geometric categorical sl2 action induces a strong categorical sl2 action. This allows one to apply the theory of strong sl2 actions to various geometric situations. Our main e...

We deal here with colorings of the pair (µ + , µ), when µ is a strong limit and singular cardinal. We show that there exists a coloring c, with no refinement. It follows, that the properties of identities of (µ + , µ) when µ is singular, differ in an essential way from the case of regular µ.

Constant entropy rate (conditional entropies must remain constant as the sequence length increases) and uniform information density (conditional probabilities must remain constant as the sequence length increases) are two information theoretic principles that are argued to underlie a wide range of linguistic phenomena. Here we revise the predictions of these principles to the light of Hilberg’s...

This paper characterizes the first cohomology group H(G,M) where M is a Banach space (with norm || ||M) that is also a left CG module such that the elements of G act on M as continuous C-linear transformations. We study this group for G an infinite, finitely generated group. Of particular interest are the implications of the vanishing of the group H(G,M). The first result is that H(G,CG) imbeds...

A remarkable similarity in the behaviour of the US S&P500 index from 1996 to August 2002 and of the Japanese Nikkei index from 1985 to 1992 (11 year shift) is presented, with particular emphasis on the structure of the bearish phases. Extending a previous analysis of Johansen and Sornette on the Nikkei index ‘antibubble’ based on a theory of cooperative herding and imitation working both in bul...

Let Ω be an open set of R and let f : Ω × R × R be a nonnegative continuous function, convex with respect to ξ ∈ R. Following the well known theory originated by Serrin [14] in 1961, we deal with the lower semicontinuity of the integral F (u,Ω) = ∫ Ω f (x, u(x), Du(x)) dx with respect to the Lloc (Ω) strong convergence. Only recently it has been discovered that dependence of f (x, s, ξ) on the ...

We address the class of fully-observable nondeterministic (FOND) planning problems where non-deterministic actions are not guaranteed to display fair behaviour. Typical solutions to FOND planning problems either guarantee goal reachability with a bounded number of transitions (so-called strong acyclic solutions), or are predicated on a fairness assumption that presumes each action effect occurs...

The magnetoresistivity of a disordered metallic system is derived using the a2KF-scatteringo theory in terms of a generalized Boltzmann equation with magnetic field B included. The behaviour is complex but in the limit of weak fields (which are experimentally quite strong) we find a negative contribution to the relaxation time proportional to B which gives rise to a positive magnetoconductivity...

We study the corrections to ǫ/ǫ in the minimal supersymmetric model at the leading order in QCD and QED. Supersymmetry can increase the standard model prediction for ǫ/ǫ by at most 40% for mt = 174 GeV, an enhancement which is indistinguishable from the present theoretical uncertainties. The most conspicuous effect of supersymmetry is a strong depletion of ǫ/ǫ. For certain choices of supersymme...