Ueber rationale Functionen vonnElementen und die allgemeine Theorie der algebraischen Gleichungen

Ohne Zusammenfassung     

Lee–Yang Problems and the Geometry of Multivariate Polynomials

We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by Pólya–Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee–Yang type problems in statistical mechanics, combinatorics, and geometric function theory.     

Crystallization in organo-mineral micro-domains in the crossed-lamellar layer of Nerita undata (Gastropoda, Neritopsina)

Crossed-lamellar shell microstructure consists of a sophisticated arrangement of interspersed lamellae, which is very commonly found in Gastropoda or Bivalvia shell layers. Its smallest constitutive microstructural units are usually described as sub-micrometric fibers, or rods, and form very ordered and regular patterns. Atomic force microscopy (AFM) and transmission electron microscopy (TEM) imaging confirms the presence of even smaller building units in the form of organo-mineral granules, and we further investigate their internal structure within aragonite crossed-lamellar internal layer of Nerita undata (Gastropoda, Neritopsina) shell. Their coalescence may have controlled anisotropically the propagation of the crystallographic coherence through this complex microstructure, as suggested by the propagation of the microtwinning pattern between neighboring granules.     

Synthesis, NMR conformational analysis and pharmacological evaluation of 7,7a,13,14-tetrahydro-6H-cyclobuta[b]pyrimido[1,2-a:3,4-a']diindole analogues as melatonin receptor ligands

A structure for the self-condensation product of 2-(1H-indol-2-yl)ethyl tosylate 2a, previously proposed as 6,7,14,15-tetrahydro-15aH-azocino[1,2-a:6,5-b]diindole 3a, was revised based on the (13)C-2D-INADEQUATE experiment, and proved to be 7,7a,13,14-tetrahydro-6H-cyclobuta[b]pyrimido[1,2-a:3,4-a']diindole 4a. A mechanism for the unexpected formation of this novel hexacyclic heterocycle was proposed and its NMR solution structure was elucidated. Five derivatives of the title ring skeleton 12-16 designed as melatonin receptor ligands were synthesized and their affinities for the human MT(1) and MT(2) receptors were determined. Both butyramides 13 and 15, as well as the non-methoxy acetamide 12 exhibited micromolar binding affinities for both receptors being slightly MT(2) selective. The methoxy acetamide 14 showed the best pharmacological profile exhibiting a five times higher affinity for MT(1) (K(i) = 49 nM) than for MT(2) (K(i) = 246 nM) receptor.     

Protein recognition by a self-assembled deep cavitand monolayer on a gold substrate

This paper details the first use of a self-folding deep cavitand on a gold surface. A sulfide-footed deep, self-folding cavitand has been synthesized, and its attachment to a cleaned gold surface studied by electrochemical and SPR methods. Complete monolayer formation is possible if the cavitand folding is templated by noncovalent binding of choline or by addition of space-filling thiols to cover any gaps in the cavitand adsorption layer. The cavitand is capable of binding trimethylammonium-tagged guests from an aqueous medium and can be deposited in 2 × 2 microarrays on the surface for characterization by SPR imaging techniques. When biotin-labeled guests are used, the cavitand:guest construct can recognize and immobilize streptavidin proteins from aqueous solution, acting as an effective supramolecular biosensor for monitoring protein recognition.     

A light controlled cavitand wall regulates guest binding

Here we report a cavitand with a photochemical switch as one of the container walls. The azo-arene switch undergoes photoisomerization when subjected to UV light producing a self-fulfilled cavitand. This process is thermally and photochemically reversible. The reported cavitand binds small molecules and these guests can be ejected from the cavitand through this photochemical process.