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.     

Rheological analysis of triblock copolymer-microemulsion networks

The rheological properties of microemulsion-triblock copolymer [poly(oxyethylene)-b-polyisoprene-b-poly(oxyethylene)] networks were studied by oscillatory shear measurements. The principal viscoelastic pattern of our systems stays the same whether the surfactant is ionic or nonionic. A closer examination shows, however, the enormous influence of the respective phase behavior of the underlying microemulsions. Also, specific interactions between the surfactants and the hydrophilic poly(oxyethylene) blocks lead to a significant effect on the formation of network structures.Characteristic rheological data such as plateau moduli and relaxation times for a series of different samples were derived differing in polymer or droplet concentrations, apart from the molecular weights of the poly-(oxyethylene) and the polyisoprene blocks. Finally, we could construct polymer and droplet concentration invariant master — mastercurves using the temperature invariant mastercurves.