We prove that the dimension of the harmonic measure of the complementary of a translation-invariant type of Cantor sets as a continuous function of the parameters determining these sets. This results extend a previous one of the author and do not use ergodic theoretic tools, not applicable to our case.

In this paper we classify all 4+1 cosmological models where the spatial hypersurfaces are connected and simply connected homogeneous Riemannian manifolds. These models come in two categories, multiply transitive and simply transitive models. There are in all five different multiply transitive models which cannot be considered as a special case of a simply transitive model. The classification of...

It is shown that perturbations around backgrounds with one non-homogeneous dimension, namely of co-homogeneity 1, can be canonically simplified, a property that is shown to hold to any order in perturbation theory. Recalling that the problem naturally reduces to 1d, a procedure is described whereby for each gauge function in 1d two 1d fields are eliminated from the action – one is gauge and can...

Recently, we have introduced spaces of splines deened on trian-gulations lying on the sphere or on sphere-like surfaces. These spaces arose out of a new kind of Bernstein-B ezier theory on such surfaces. The purpose of this paper is to contribute to the development of a constructive theory for such spline spaces analogous to the well-known theory of polynomial splines on planar triangulations. ...

The concept of graph partition dimension was introduced by Chartrand et al. (1998). Let G = (V, E) be a connected graph. For every v ∈ V (G) and L ⊆ V (G), define the distance from v to L as d(v, L) = min{d(v, w)|w ∈ L}. Let Π = {L1, L2, · · · , Lk} be a partition of V (G). The representation of a vertex v with respect to Π is defined as r(v|Π) = (d(v, L1), d(v, L2), · · · , d(v, Lk)). The part...

The simple modules with homogeneous characters are considered, their dimension formulas are determined.