Zur Wasserbindung im Halloysit

Ohne ZusammenfassungMit 2 Abbildungen.     

Total Synthesis and Structural Revision of the Antibiotic Tetrapeptide GE81112A

The total synthesis of the naturally occurring antibiotic GE81112A, a densely functionalized tetrapeptide, is reported. Comparison of spectral data with those of the natural product and the lack of biological activity of the synthesized compound led us to revise the published configuration of the 3‐hydroxypipecolic acid moiety. This hypothesis was fully validated by the synthesis of the corresponding epimer.     

Time-dependent photoionization of azulene: competition between ionization and relaxation in highly excited states

Pump-probe photoionization has been used to map the relaxation processes taking place from highly vibrationally excited levels of the S(2) state of azulene, populated directly or via internal conversion from the S(4) state. Photoelectron spectra obtained by 1+2(') two-color time-resolved photoelectron imaging are invariant (apart from in intensity) to the pump-probe time delay and to the pump wavelength. This reveals a photoionization process which is driven by an unstable electronic state (e.g., doubly excited state) lying below the ionization potential. This state is postulated to be populated by a probe transition from S(2) and to rapidly relax via an Auger-like process onto highly vibrationally excited Rydberg states. This accounts for the time invariance of the photoelectron spectrum. The intensity of the photoelectron spectrum is proportional to the population in S(2). An exponential energy gap law is used to describe the internal conversion rate from S(2) to S(0). The vibronic coupling strength is found to be larger than 60+/-5 microeV.     

Uniform factorization for compact sets of operators

We prove a factorization result for relatively compact subsets of compact operators using the Bartle and Graves Selection Theorem, a characterization of relatively compact subsets of tensor products due to Grothendieck, and results of Figiel and Johnson on factorization of compact operators. A further proof, essentially based on the Banach-Dieudonné Theorem, is included. Our methods enable us to give an easier proof of a result of W.H. Graves and W.M. Ruess.

     

The Finite Cell Method for large deformation analysis

The Finite Cell Method (FCM) combines the fictitious domain approach with high-order finite elements and adaptive integration. For linear elastic problems with smooth solution, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. In this contribution, the FCM idea is combined with standard finite element technology for the solution of geometrically nonlinear problems. In particular, a modified FCM formulation is introduced, which resets the deformed configuration of the fictitious domain to the deformation-free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis with very small values of the penalty parameter, while the accuracy of the geometrically nonlinear solution within the physical domain remains unaffected. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)