Moment inequalities and central limit properties of isotropic convex bodies

The object of our investigations are isotropic convex bodies , centred at the origin and normed to volume one, in arbitrary dimensions. We show that a certain subset of these bodies – specified by bounds on the second and fourth moments – is invariant under forming ‘expanded joinsrsquo;. Considering a body K as above as a probability space and taking , we define random variables on K. It is known that for subclasses of isotropic convex bodies satisfying a ‘concentration of mass property’, the distributions of these random variables are close to Gaussian distributions, for high dimensions n and ‘most’ directions . We show that this ‘central limit property’, which is known to hold with respect to convergence in law, is also true with respect to -convergence and -convergence of the corresponding densities. Received: 21 March 2001 / in final form: 17 October 2001 / Published online: 4 April 2002     

Automated parallel anionic polymerizations: Enhancing the possibilities of a widely used technique in polymer synthesis

Anionic polymerization techniques have been implemented successfully in a commercial automated synthesizer. The main problems for a successful adaptation of the experimental technique in the automated synthesizer are addressed, as well as some simple potential applications, such as the anionic polymerization of styrene, isoprene, and methyl methacrylate. The obtained results were reproducible and in concordance with literature knowledge. The apparent rate constant of the anionic polymerization of styrene in cyclohexane initiated by sec‐butyllithium could be determined at two different concentrations of the monomer and initiator in a temperature range of 10–60 °C. All the synthesis and characterization experiments of the polymers were performed within a short time period. Moreover, the syntheses of poly(styrene‐b‐isoprene) and poly(styrene‐b‐methyl methacrylate) block copolymers were also successfully carried out within the automated synthesizer. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4151–4160, 2005     

Bounds on Weights of Nearby Cycles and Wakimoto Sheaves on Affine Flag Manifolds

We study certain nearby cycles sheaves on an affine flag manifold which arise naturally in the Beilinson–Gaitsgory deformation of the affine flag manifold to the affine Grassmannian. We study the multiplicity functions we introduced in an earlier paper, which encode the data of the Jordan-Hölder series. We prove the multiplicity functions are polynomials in q, and we give a sharp bound for their degrees. Our results apply as well to the nearby cycles in the p-adic deformation of Laumon–Haines–Ngô, and also to Wakimoto sheaves.     

A polyhedron of genus 4 with minimal number of vertices and maximal symmetry

We construct a symmetric polyhedron of genus 4 in R ³ with 11 vertices. This shows that for given genus g the minimal numbers of vertices of combinatorial manifolds and of polyhedra coincide in the first previously unknown case g=4 also. We show that our polyhedron has the maximal symmetry for the given genus and minimal number of vertices.