The first total synthesis of (R)-convolutamydine A

The first total synthesis of (R)-convolutamydine A has been achieved by the organocatalytic addition of acetone to 4,6-dibromoisatin. The absolute configuration was determined by single crystal X-ray diffraction. DFT studies were used to model the transition states for the aldol reaction and equilibrium geometries of the post-aldol reaction intermediates. The DFT study revealed that the aldol bond forming reaction was considerably endothermic.     

Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.     

The core of zero-dimensional monomial ideals

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.     

Photopolymers for Rapid Prototyping of Soluble Mold Materials and Molding of Cellular Biomaterials

To substitute cross-linked photopolymers in rapid prototyping of mold materials and therefore extend the range of materials which can be casted, organo-soluble photopolymers were developed. Branched bisalkylacrylamides were suitable as base component for such formulations, due to their high reactivity, good mechanical properties, and excellent solubility of the formed polymers. These molding materials were used to prepare cellular biocompatible materials which could be used as bone replacement materials. Biocompatible crosslinkers based on methacrylates from hydrolyzed gelatine or lactic acid ethyleneglycol blockcopolymers and commercially available reactive diluents are the base components of such a formulation. Biocompatibility was investigated by osteoblast-like cells. Cellular biocompatible parts were obtained by thermal polymerization in soluble mould materials prepared by 3D-photoshaping.