Zur Theorie der Chiralitätsfunktionen

The Algebraic Theory of Chirality Functions is derived by means of exclusively qualitative considerations. Hence, the significance of quantitative results is questionable. Moreover the construction of “Näherungsansätze” (”Approximation-Ansatz”), which may be interpreted as semiempirical methods, is achieved on the basis of plausibility and mathematical simplicity. Since physical arguments are not included, the consistency or inconsistency of “Näherungsansätze” with experimental results do not justify direct physical conclusions.     

X-ray diffraction/Calorimetry coupling

Polymorphism of trilaurin mixed with 4% of cholesterol was studied with a setup coupling calorimetry and phase characterisation by in-situ X-ray diffraction (Microcalix). Four polymorphic forms were identified. Monotropic and enantiotropic transitions were identified from the reconstruction of Gibbs free energy diagram which allows the control of trilaurin polymorphism. This revised version was published online in July 2006 with corrections to the Cover Date.     

Darstellung und Kristallstruktur von HgPb2O(OH)Br3

Inhaltsübersicht. Die erstmals dargestellte Verbindung HgPb₂O(OH)Br₃ kristallisiert orthorhombisch in der Raumgruppe Aba2 (Nr. 41) mit den Gitterkonstanten a = 14,652(3) Å, b = 14,6491(8) Å, c = 7,782(2) Å und Z = 8. Die Bestimmung der Kristallstruktur mit Einkristallmethoden zeigte “isolierte”, verzerrt würfelförmige Baugruppen der Zusammensetzung [Hg₂Pb₄O₂(OH)₂]. Diese Einheiten werden von Bromidionen umhüllt. HgPb₂O(OH)Br₃ stellt damit hinsichtlich des strukturellen Aufbaus ein Bindeglied zwischen den Verbindungen [Pb₄(OH)₄](ClO₄)₄ · 2H₂O [1] und Pb₉O₄Br₁₀ [2] dar. Preparation and Crystal Structure of HgPb₂O(OH)Br₃ The new compound, HgPb₂O(OH)Br₃ was prepared and investigated by X-ray crystal structure analysis. Crystals of orthorhombic symmetry show space group Aba2 (No. 41) with lattice parameters a = 14.652(3) Å, b = 14.6491(8) Å, c = 7.782(2) Å, and Z = 8. Remarcable structural units with heterocubane skeleton were found. The [Hg₂Pb₄O₂(OH)₂] group forms a new member of the structural class between [Pb₄(OH)₄] and [Pb₈O₄] units with the relating compounds [Pb₄(OH)₄)](ClO₄)₄ · 2 H₂O [1] und Pb₉O₄Br₁₀ [2].     

Synthese und Kristallstruktur von Blei(II)‐oxidhalogenid‐Alkoholaten mit unterschiedlichen Verknüpfungsvarianten von Pb4O4‐Heterokubaneinheiten

Synthesis and Crystal Structure Determination of Lead(II) Oxide Halide Alcoholates with Different Connectivity of Pb₄O₄ Heterocubane‐like Subunits The reaction of red lead(II) oxide (Litharge) and lead(II) halide (Cl^? and Br^?) with diethylene glycole at a temperature of 180 °C leads to the isotypic compounds [Pb₆(C₄H₈O₃)O₂Cl₆] (1) and [Pb₆(C₄H₈O₃)O₂Br₆] (2) . In a similar synthesis with PbI₂ as educt at temperature of 160 °C the two modifications β‐[Pb₆(C₄H₈O₃)O₂I₆] (3) and α‐[Pb₆(C₄H₈O₃)O₂I₆] (4) were found, whereas at a reaction temperature of 180 °C [Pb₉(C₂H₄O₂)(C₄H₈O₃)O₃I₈] (5) was surprisingly obtained as product. The X‐ray diffraction data show that at a temperature of 180 °C a splitting of the ether took place. The cited compounds show cubane like subunits built by lead and oxygen atoms. These fragments are connected by alkoholate molecules. In 5 additionally an I₆ octahedra centered by lead is observed.     

All NSR-models in terms of bosonic strings: An explicit derivation

We construct the open and closed string NSR-models in terms ofD15 bosonic string theories. All anticommuting NSR-operators are obtained after fermionizing 4 bosonic dimensions, and the NSR-Hilbert spaces are embedded as linear subspaces of the bosonic Hilbert spaces. We thus show the existence of various 10D supersymmetric sectors of the state spaces ofD=26 consistent bosonic strings.     

Preparation of peptide-like bicyclic lactams via a sequential Ugi reaction--olefin metathesis approach

Bicyclic lactams, suitable for incorporation into conformationally restricted peptide mimics, can be synthesized by using olefinic starting materials for the Ugi multicomponent reaction, setting up an olefin metathesis reaction, that is easily carried out with the Grubbs catalyst. The influence of the different starting materials is evaluated. In addition, the utilization of chiral, nonracemic amines is described.