Preparation and Crystal Structures of Ruthenium and Osmium Oxide Tetrahalides

RuOF₄ as the highest valence oxide fluoride exist as a molecular compound (a = 606.0(1), b = 836.1(1), c = 626.3(1) pm, β = 91.637(3), Z = 4; P2₁/n) as well as fluorine bridged polymer (a = 547.7(2), b = 928.5(3), c = 1252.4(3) pm, Z = 8, P2₁2₁2₁). A reproducible method for pure, deep blue OsOF₄ is given. Pure OsOF₄‐I is isostructural to the fluorine bridged polymeric RuOF₄ (a = 554.6(1), b = 955.4(2), c = 1278.4(2), Z = 8, P2₁2₁2₁). OsOF₄‐II is also a fluorine bridged polymer (a = 537.8(2), b = 1274.8(4), c = 555.2(2), β = 117.716(6)°, Z = 4, P2₁/c). OsOCl₄ again is a molecular species (a = 938.9(2), b = 561.3(1), c = 1192.0(2), β = 109.944(4)°, Z = 4, P2₁/c).     

Hilbert space representations of cross product algebras

Hilbert space representations of cross product *-algebras of the Hopf *-algebras with the coordinate algebras and of quantum vector spaces, and of with the coordinate algebras and of the corresponding quantum spheres, are investigated and classified. Invariant states on the coordinate *-algebras are described by two variants of the quantum trace.     

Zur Differentialgeometrie der Linienkomplexe

Ohne Zusammenfassung     

Abundant singularities

We show that a generic Euler flow or a generic ideal magnetostatic equilibrium contains an intricate structure of tangential discontinuities which are vortex sheets or current sheets, respectively. The discontinuities are present at all spatial scales and are dense at least in some parts of the volume occupied by the fluid. Possible implications for the energy dissipation in turbulent flows and for the structure of equilibria in tokamaks are discussed.     

Functionalized Proline‐Rich Peptides Bind the Bacterial Second Messenger c‐di‐GMP

c‐di‐GMP is an attractive target in the fight against bacterial infections since it is a near ubiquitous second messenger that regulates important cellular processes of pathogens, including biofilm formation and virulence. Screening of a combinatorial peptide library enabled the identification of the proline‐rich tetrapeptide Gup‐Gup‐Nap‐Arg, which binds c‐di‐GMP selectively over other nucleotides in water. Computational and CD spectroscopic studies provided a possible binding mode of the complex and enabled the design of a pentapeptide with even higher binding strength towards c‐di‐GMP. Biological studies showed that the tetrapeptide inhibits biofilm growth by the opportunistic pathogen P. aeruginosa.     

Combinatorics and Algorithms for Augmenting Graphs

The notion of augmenting graphs generalizes Berge’s idea of augmenting chains, which was used by Edmonds in his celebrated solution of the maximum matching problem. This problem is a special case of the more general maximum independent set (MIS) problem. Recently, the augmenting graph approach has been successfully applied to solve MIS in various other special cases. However, our knowledge of augmenting graphs is still very limited and we do not even know what the minimal infinite classes of augmenting graphs are. In the present paper, we find an answer to this question and apply it to extend the area of polynomial-time solvability of the maximum independent set problem.