Ueber Resultanten und Discriminanten von ϑ-Functionen höheren Grades

Ohne Zusammenfassung     

Graphical unitary group approach to arbitrary spin representations

A graph theoretic approach to the representation of N particle systems involving arbitrary single-particle spin is presented. The method is a generalization of the Distinct Row Table (DRT ) technique employed by Shavitt in developing the graphical unitary group approach (GUGA ) to electronic spin-orbitals. A detailed analysis of the DRT and GUGA representations is presented based on several theoretical considerations and computer-tested implementations. The use of the representation to establish rules concerning the evaluation of the matrix elements of the group generators is also discussed.     

Doppeloktaeder-Cluster [V2O9] in der Kristallstruktur von Vanadium(III)-diphosphat,V4(P2O7)3

Double-Octahedra Clusters [V₂O₉] in the Crystal Structure of Vanadium (III) Diphosphate, V₄(P₂O₇)₃ . As the first example for M^III diphosphates the crystal structure of V₄(P₂O₇)₃ (“ I ”) has been determined by means of X-ray diffraction of single crystals. I – according to [7] obtainable by thermal interaction of V₂O₅, H₃PO₃, and H₃PO₄ – crystallizes orthorhombically (data see above); in the unit cell two kinds of isolated doubleoctahedra (clusters) [V₂O₉], having the symmetry C_s, exist. Due to a mutual face-connection of the octahedra, within these clusters relatively short V–V distances are resulting: 2.774(8) and 3.026(7) Å. The diphosphate anions, O₃POPO₃^4? (three kinds; each having the symmetry C_s and staggered conformation), exhibit POP bond angles of 170°, being remarkably large for non-centrosymmetry. Because of the [M₂^IIIO₉] clusters in I , and also in the isostructural diphosphates Cr₄(P₂O₇)₃ and Fe₄(P₂O₇₃), magnetic investigations seem to be challenged.     

Zur Bestimmung der elektrolytischen Leitf?higkeit w?ssriger L?sungen

Ohne Zusammenfassung     

Fast Biosynthesis of GFP Molecules: A Single‐Molecule Fluorescence Study

It's not easy being green : Real‐time visualization of labeled ribosomes and de novo synthesized green fluorescent protein molecules using single‐molecule‐sensitive fluorescence microscopy demonstrates that the mutant GFPem is produced with a characteristic time of five minutes. Fluorescence of the fastest GFP molecules appears within one minute (see picture).

     

Supermanifolds and sequences of computable structures: a link via a nonstandard extension of differential geometry

Using a generalized theory of manifolds, based on the ideas and techniques of nonstandard analysis, a link is established between sequences of computable structures converging to a classical manifold and certain manifold-like structures involving anticommuting variables. The supermanifolds appearing here may be interpreted as a kind of representation of sequences of computable structures.