A combinatorial proof of Marstrand's Theorem for products of regular Cantor sets

In 1954 Marstrand proved that if K is a subset of R^2 with Hausdorff dimension greater than 1, then its one-dimensional projection has positive Lebesgue measure for almost-all directions. In this article, we give a combinatorial proof of this theorem when K is the product of regular Cantor sets of class C^{1+a}, a>0, for which the sum of their Hausdorff dimension is greater than 1.Comment: 9 pages, 1 figure, referee suggestions incorporated, to appear in Expositiones Mathematica

Generating hierarchial scale free graphs from fractals

Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal $\Lambda$. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. Using our (deterministic) fractal $\Lambda$ we generate random graph sequence sharing similar properties.Comment: 4 figure

Videndeling i og mellem communities of practice

Der tales i stigende grad om de sociale faktorers betydning for videnledelse og videndeling. Artiklen følger sporene af denne tradition og argumenterer for, at communities of practice i mange henseender udgør ideelle arenaer for videndeling. Communities of practice muliggør, at videndeling integreres som en naturlig del af det daglige arbejde, hvilket forbedrer betingelserne for en mere effektiv udførelse af virksomhedens arbejdsopgaver. Med baggrund i undersøgelser af videndeling i IBM Danmark gives eksempler på, hvordan videndeling foregår både i og mellem communities of practice. Videndeling gennem communities of practice giver en række fordele, men samtidig også centrale ledelsesmæssige udfordringer: Communities of practice må kortlægges, faciliteres og koordineres med henblik på at give dem gode interne vilkår og samtidig sikre, at de kan komplementere hinanden og udgøre en samlet helhed i virksomheden