On the Integrated Density of States for Schrödinger Operators on ℤ2 with Quasi Periodic Potential

In this paper we consider discrete Schr?dinger operators on the lattice ℤ² with quasi periodic potential. We establish new regularity results for the integrated density of states, as well as a quantitative version of a “Thouless formula”, as previously considered by Craig and Simon, for real energies and with rates of convergence. The main ingredient is a large deviation theorem for the Green's function that was recently established by Bourgain, Goldstein, and the author. For the integrated density of states an argument of Bourgain is used. Finally, we establish certain fine properties of separately subharmonic functions of two variables that might be of independent interest. Received: 13 February 2001 / Accepted: 21 May 2001     

Ueber die Methoden der Zuckerbestimmung

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Structural investigation and elucidation of new communesins from a marine‐derived Penicillium expansum Link by liquid chromatography/electrospray ionization mass spectrometry

Penicillium expansum is a ubiquitous species for which there are only few reports for chemical investigation in marine environments. Among the numerous secondary metabolites produced by this species, communesins represent a new class of cytotoxic and insecticidal indole alkaloids. In this study, we investigated a marine P. expansum strain exhibiting neuroactivity on a Diptera larvae bioassay. Bio‐guided purification led to the isolation and the identification of communesin B as the main active compound by HRMS and ¹H and ¹³C NMR. Liquid chromatography analyses with detection by electrospray ionization coupled with tandem mass spectrometry (LC/ESI‐MS/MS) and high‐resolution tandem mass spectrometry (LC/HRMS/MS) allowed the identification and characterization of four other known communesins (A, D, E and F) in the crude extract. A fragmentation model for dimethyl epoxide communesins was proposed after detailed interpretation of their MS/MS spectra. Further analyses of the extract using the modelled fragmentations led to the detection of seven new communesins found as minor compounds. Chemical structural elucidation of these new derivatives is discussed based on their fragmentation characteristics. Copyright © 2009 John Wiley & Sons, Ltd.     

Über die Geometrie von Laguerre

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