Homogene Räumek-affinoider Gruppen

Ohne Zusammenfassung     

A scaling property in critical spectra of discrete systems

Power spectra of discrete dynamical systems at the threshold of chaos contain line series obeying S_ω ∞ ω$\text{μ}$ for small ω. We explain $\text{μ}$ in terms of the Feigenbaum rescaling parameter α. Another parameter β related to the noise strength of states of periodic chaos and recently numerically determined by Huberman and Zisook is related to α as well.     

Enantioselective synthesis of (--)-gilbertine via a cationic cascade cyclization

Described is the first enantioselective synthesis of (-)-gilbertine (2), a member of the uleine-type family, and the determination of the absolute configuration of this natural product is reported. The key step employs a cationic cascade reaction for a tetrahydropyrane and piperidine ring formation and the construction of the pentacyclic framework in one step. The synthetic strategy utilizes the Shibasaki reaction to build up the first stereogenic center. A formylation reaction of a 3-substituted cyclohexanone derivative was achieved, giving only the desired regioisomer. The Japp-Klingemann Fischer indole protocol was used successfully as a convergent synthetic approach for the construction of the desired tetrahydrocarbazole (20). Furthermore, an unexpected behavior of this 2,3-disubstituted cyclohexanone derivative during an epimerization process was investigated, resulting in different chemical behavior of the enantiomers and the racemate. The diastereomeric resolution was achieved via the cationic cascade reaction, demonstrating the versatility of this approach. Significantly, the synthetic 17-step sequence was easy to execute, giving (-)-gilbertine in 5.5% overall yield.     

Optical properties of passivated silicon nanoclusters: the role of synthesis

The effect of preparation conditions on the structural and optical properties of silicon nanoparticles is investigated. Nanoscale reconstructions, unique to curved nanosurfaces, are presented for silicon nanocrystals and shown to have lower energy and larger optical gaps than bulk-derived structures. We find that high-temperature synthesis processes can produce metastable noncrystalline nanostructures with different core structures than bulk-derived crystalline clusters. The type of core structure that forms from a given synthesis process may depend on the passivation mechanism and time scale. The effect of oxygen on the optical of different types of silicon structures is calculated. In contrast to the behavior of bulklike nanostructures, for noncrystalline and reconstructed crystalline structures surface oxygen atoms do not decrease the gap. In some cases, the presence of oxygen atoms at the nanocluster surface can significantly increase the optical absorption gap, due to decreased angular distortion of the silicon bonds. The relationship between strain and the optical gap in silicon nanoclusters is discussed.     

Going-down functors, the Künneth formula, and the Baum-Connes conjecture

We study the connection between the Baum-Connes conjecture for a locally compact group G with coeefficient A and the Künneth formula for the K-theory of tensor products by the corresponding crossed product . The main tool for this is obtained by an application of a general reduction procedure which allows us to analyze certain functors connected to the topological K-theory of a group in terms of their restrictions to compact subgroups. We also discuss several other interesting applications of this method, including a general extension result for the Baum-Connes conjecture.     

Syntheses and characterization of two dioxygen-reactive dinuclear macrocyclic schiff-base copper(I) complexes

The dinuclear copper(I) complex [Cu(2)L(1)(CH(3)CN)(2)](ClO(4))(2) (1, L(1) = 3,6,9,17,20,23-hexaazatricyclo[23.3.1.1]triaconta-1(29),2,9,11(30),12(13),14,16,23,25,27-decaene) has been structurally characterized. As previously described, intramolecular ligand hydroxylation (at the aromatic ring) was observed when 1 was reacted with dioxygen. A stopped-flow analysis of the reaction of 1 with dioxygen under different conditions did not allow a "dioxygen intermediate" to be spectroscopically detected. Detailed NMR and electrochemical data on 1 are also presented and evaluated for the first time. No copper(II) complexes of L(1) could be characterized due to hydrolysis of the compounds. In contrast, complex 2-differing from 1 only in an increase in the size of the chelate rings-did not undergo intramolecular hydroxylation when it was oxidized. The crystal structure of 2 is also described.