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.     

XPS investigations of ink‐jet printed paper

Different ink‐jet printed paper materials were investigated using X‐ray photoelectron spectroscopy (XPS) yielding the elemental composition of the near‐surface region of the papers. We found significant differences with respect to the detected elements and their atomic concentrations in the different inks studied here. Two different groups of inks could be identified by means of a lower ratio of the O and C atomic concentrations and lower concentrations in specific trace elements like Mg, Na and Si. High‐resolution spectra of C 1s and O 1s core levels allowed a detailed determination of the chemical state of the respective elements. On the basis of a detailed deconvolution of these XPS signals, significant differences between all the investigated ink‐jet printed papers were found, thereby allowing their discrimination. The applicability of the measurements and, more generally, the XPS technique for forensic investigations of paper are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Hg2(OH)[BF4], the First Basic Mercurous Tetrafluoroborate

The first basic mercurous tetrafluoroborate, Hg₂(OH)[BF₄], was obtained through a synproportionation reaction of red mercuric oxide, HgO, and elemental mercury in a 35% solution of HBF₄ in water as colourless single crystals. The crystal structure (orthorhombic, Pbca, Z = 8, a = 985.0(1), b = 991.0(1), c = 1141.0(2) pm) contains [(HO)_1/2—Hg—Hg—(OH)_1/2]⁺ zig‐zag chains that are further connected via weak Hg—OH interchain interactions to layers between which the [BF₄]^— are located in an up and down fashion.     

GnRH binding RNA and DNA Spiegelmers: a novel approach toward GnRH antagonism

Mirror-image oligonucleotide ligands (Spiegelmers) that bind to the pharmacologically relevant target gonadotropin-releasing hormone I (GnRH) with high affinity and high specificity have been identified using the Spiegelmer technology. GnRH is a decapeptide that plays an important role in mammalian reproduction and sexual maturation and is associated with several benign and malignant diseases. First, aptamers that bind to D-GnRH with dissociation constants of 50-100 nM were isolated out of RNA and DNA libraries. The respective enantiomers of the DNA and RNA aptamers were synthesized, and their binding to L-GnRH was shown. These Spiegelmers bind to L-GnRH with similar affinity to that of the corresponding aptamers that bind to D-GnRH. We further demonstrated dose-dependent inhibition of GnRH-induced Ca(2+) release in Chinese hamster ovary cells that were stably transfected with the human GnRH receptor.