Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

The Co-Entrapment of a Homogeneous Catalyst and an Ionic Liquid by a Sol-gel Method: Recyclable Ionogel Hydrogenation Catalysts

Molecular hydrogenation catalysts have been co-entrapped with the ionic liquid [Bmim]NTf(2) inside a silica matrix by a sot-gel method. These catalytic ionogels have been compared to simple catalyst-doped glasses, the parent homogeneous catalysts, commercial heterogeneous catalysts, and Rh-doped mesoporous silica. The most active ionogel has been characterised by transmission electron microscopy, X-ray photoelectron spectroscopy, and solid state NMR before and after catalysis. The ionogel catalysts were found to be remarkably active, recyclable and resistant to chemical change.

Systematic Usage of Embedded Modelling Languages in Automated Model Transformation Chains

Annotation of programs using embedded Domain-Specific Languages (embedded DSLs), such as the program annotation facility for the Java programming language, is a well-known practice in computer science. In this paper we argue for and propose a specialized approach for the usage of embedded Domain-Specific Modelling Languages (embedded DSMLs) in Model-Driven Engineering (MDE) processes that in particular supports automated many-step model transformation chains. It can happen that information defined at some point, using an embedded DSML, is not required in the next immediate transformation step, but in a later one. We propose a new approach of model annotation enabling flexible many-step transformation chains. The approach utilizes a combination of embedded DSMLs, trace models and a megamodel. We demonstrate our approach based on an example MDE process and an industrial case study.