A unifying approach to the Margolis–Meakin and Birget–Rhodes group expansion

Let G be a group. We show that the Birget–Rhodes prefix expansion \(G^{Pr}\) and the Margolis–Meakin expansion M(X; f) of G with respect to \(f:X\rightarrow G\) can be regarded as inverse subsemigroups of a common E-unitary inverse semigroup P. We construct P as an inverse subsemigroup of an E-unitary inverse monoid \(U/\zeta \) which is a homomorphic image of the free product U of the free semigroup \(X^+\) on X and G. The semigroup P satisfies a universal property with respect to homomorphisms into the permissible hull C(S) of a suitable E-unitary inverse semigroup S, with \(S/\sigma _S=G\), from which the characterizing universal properties of \(G^{Pr}\) and M(X; f) can be recaptured easily.     

An isoperimetric inequality related to a Bernoulli problem

Given a bounded domain Ω we look at the minimal parameter Λ(Ω) for which a Bernoulli free boundary value problem for the p-Laplacian has a solution minimising an energy functional. We show that amongst all domains of equal volume Λ(Ω) is minimal for the ball. Moreover, we show that the inequality is sharp with essentially only the ball minimising Λ(Ω). This resolves a problem related to a question asked in Flucher et al. (Reine Angew Math 486:165–204, 1997).     

A Dynamical Zeta Function for Pseudo Riemannian Foliations

We investigate a generalization of geodesic random walks to pseudo Riemannian foliations. The main application we have in mind is to consider the logarithm of the associated zeta function as grand canonical partition function in a theory unifying aspects of general relativity, quantum mechanics and dynamical systems. Partially supported by DFG, SFB 478.     

Balaton Symposium 2009

JPC – Journal of Planar Chromatography – Modern TLC -     

Tandem olefin metathesis/hydrogenation at ambient temperature: activation of ruthenium carbene complexes by addition of hydrides

Sodium hydride activates ruthenium carbene complexes to catalyze hydrogenation reactions subsequent to ring closing olefin metathesis. Under these conditions, hydrogenation of cyclopentenols proceeds smoothly at ambient temperature and under 1 atm of hydrogen in toluene. An alternative protocol was developed that involves the formation of hydrogen in situ by reaction of excess sodium hydride with protic functional groups and water.