Eine Methode zur Construction des Osculationskreises der ebenen Curven dritter Ordnung mit einem Doppelpunkte

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Note über einige besondere inverse Flächen des Cayley'schen Cylindroids

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Beitrag zur Kenntniss des Kobalts

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Eine Verbesserung an Wassertrockenschr?nken mit Gasheizung

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Peptide sequence mediated self-assembly of molybdenum blue nanowheel superstructures

The precise control over the formation of complex nanostructures, e.g. polyoxometalates (POMs), at the sub-nanoscale is challenging but critical if non-covalent architectures are to be designed. Combining biologically-evolved systems with inorganic nanostructures could lead to sequence-mediated assembly. Herein, we exploit oligopeptides as multidentate structure-directing ligands via metal-coordination and hydrogen bonded interactions to modulate the self-assembly of POM superstructures. Six oligopeptides (GH, AH, SH, G₂H, G₄H and G₅H) are incorporated into the cavities of Molybdenum Blue (MB) POM nanowheels. It is found that the helicity of the nanowheel can be readily switched (Δ to Λ) by simply altering the N-terminal amino acid on the peptide chain rather than their overall stereochemistry. We also reveal a delicate balance between the Mo-coordination and the hydrogen bonds found within the internal cavity of the inorganic nanowheels which results in the sequence mediated formation of two unprecedented asymmetrical nanowheel frameworks: {Mo₁₂₂Ce₅} and {Mo₁₂₆Ce₄}.

Peptide sequence can be used to control the self-assembly and structures of nanoscale molybdenum blue polyoxometalate (POM) wheel-shaped clusters.     

Geometric Structures on the Complement of a Projective Arrangement

Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (= finite union of hyperplanes) whose Levi-Civita connection is of Dunkl type. Interesting examples are obtained from the arrangements defined by finite complex reflection groups. We determine a parameter interval for which the metric is locally of Fubini-Study type, flat, or complex-hyperbolic. We find a finite subset of this interval for which we get a complete orbifold or at least a Zariski open subset thereof, and we analyze these cases in some detail (e.g., we determine their orbifold fundamental group).In this set-up, the principal results of Deligne-Mostow on the Lauricella hypergeometric differential equation and work of Barthel-Hirzebruch-Höfer on arrangements in a projective plane appear as special cases. Along the way we produce in a geometric manner all the pairs of complex reflection groups with isomorphic discriminants, thus providing a uniform approach to work of Orlik-Solomon.     

Beiträge zur Methodik der chemischen Analyse der Uranpechblenden

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Zur Theorie der bilinearen Formen

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Ein neues Herzgift, das Vernonin

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