On nearly parallel G2-structures

A nearly parallel G₂-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G₂-manifolds with large symmetry group and in particular all homogeneous nearly parallel G₂-structures.     

Limited stability of the pH reference material sodium tetraborate decahydrate (“borax”)

Thermogravimetric and X-ray powder diffraction analyses revealed that the pH reference material sodium tetraborate decahydrate (“borax”) is not a stable substance but, loosing some of its water of crystallization, transforms slowly into the pentahydrate. The connected pH changes of the solutions are opposite to and larger than, those expected according to the dilution value of the decahydrate as shown by differential potentiometric measurements. The transformation rate depends on the storing time in the closed original container, the time of and after the first exposure of the material to the atmosphere, the frequency of and the relative humidity during subsequent exposures, and the temperature. The transformation reaction is not understood in detail. However, the experiments showed that sodium tetraborate decahydrate is a reliable pH reference material, whose pH is constant within ΔpH=±0.005 within at least two years after preparation, even if occasionally exposed to the atmosphere. Further work will show whether this time limit can be somewhat extended.     

On false branch points of incompressible branched immersions

We prove that a branched immersion of a surface with boundary into a differentiable manifold has no false branch points (in fact, no ramified points) if the immersion induces an isomorphism of fundamental groups and some other natural hypotheses are satisfied. This result has immediate applications to Plateau's problem.Work done while the first author was a visiting member of the Max-Planck-Institut für Mathematik at Bonn. Both authors acknowledge the support of Max-Planck-Institut für Mathematik, Bonn and Schwerpunkt Geometrie at Mathematisches Institut, University of Heidelberg     

Schwingungsspektren und Kraftkonstanten von Hexamethyldisilan,Hexaphenyldisilan und 1,1,1-Trimethyl-2,2,2-triphenyldisilan

The Raman and infrared spectra of (CH₃)₃SiSi(CH₃)₃ (I), (CD₃)₃SiSi(CD₃)₃, (C₆H₅)₃SiSi(C₆H₅)₃ (II), (CH₃)₃SiSi(C₆H₅)₃ (III), and (CD₃)₃SiSi(C₆H₅)₃ are reported. Assignments are based on symmetry G ₃₆ ⁺ (free internal rotation) forI, D_3d forII, and C_3v forIII. Normal coordinate treatment has been done using some simplifications in the phenyl coordinates. The SiSi stretching force constant inI amounts to 1,65 N/cm. In compoundsII andIII strong vibrational coupling is elucidated byPED calculations.     

Multiparametric microsensor chips for screening applications

The identification of drug targets for pharmaceutical screening can be greatly accelerated by gene databases and expression studies. The identification of leading compounds from growing libraries is realized by high throughput screening platforms. Subsequently, for optimization and validation of identified leading compounds studies of their functionality have to be carried out, and just these functionality tests are a limiting factor. A rigorous preselection of identified compounds by in vitro cellular screening is necessary prior to using the drug candidates for the further time consuming and expensive stage, e.g. in animal models. Our efforts are focused to the parallel development, adaptation and integration of different microelectronic sensors into miniaturized biochips for a multiparametric, functional on-line analysis of living cells in physiologically environments. Parallel and on-line acquisition of data related to different cellular targets is required for advanced stages of drug screening and for economizing animal tests.     

High facial diastereoselectivity in intra- and intermolecular reactions of chiral benzylic cations

Chiral carbenium ions can be attacked by arene nucleophiles with high facial diastereoselectivity (dr >/= 94/6). Benzylic cations, such as 2, were generated under acidic conditions and reacted with arenes in intra- and intermolecular Friedel-Crafts alkylation reaction. The depicted reaction 1 --> 3 represents one example for the unprecedented, highly diastereoselective intermolecular Friedel-Crafts alkylation reactions which were observed in this study.