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     

On static and radiative space-times

The conformal constraint equations on space-like hypersurfaces are discussed near points which represent either time-like or spatial infinity for an asymptotically flat solution of Einstein's vacuum field equations. In the case of time-like infinity a certain radiativity condition, is derived which must be satisfied by the data at that point. The case of space-like infinity is analysed in detail for static space-times with non-vanishing mass. It is shown that the conformal structure implied here on a slice of constant Killing time, which extends analytically through infinity, satisfies at spatial infinity the radiativity condition. Thus to any static solution exists a certain radiative solution which has a smooth structure at past null infinity and is regular at past time-like infinity. A characterization of these solutions by their free data is given and non-symmetry properties are discussed.     

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.