Kooperative Rotationsisomerie in Polymeren

Colloid and Polymer Science - Das Schmelzen von linearen Polymeren wird als Umwandlung vom Kristall in einen Zustand hoher Kinkdichte mit Nahordnung theoretisch beschrieben. Dabei kann die laterale...     

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.     

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.