On the Parametrized Integral of a Multifunction: The Unbounded Case

Integration of set-valued maps (alias multifunctions) depending on a parameter is revisited. Results of Artstein, and of Saint-Pierre and Sajid are extended to the case of set-valued maps whose values may be unbounded. In the general case, this is achieved assuming that the transition probabilities involved in the integration procedure are absolutely continuous with respect to some fixed probability measure. However, when the integrating probability measure does not depend on the parameter this hypothesis is shown to be unnecessary. On the other hand, an alternative proof of a result of Saint-Pierre and Sajid is provided for convex compact-valued multifunctions. An application is given to the control of chattering systems. It is an extension of a result of Artstein to the case of set-valued maps with unbounded values. The proof of the main results is simple and essentially relies on measurable selections arguments.      

Spectral shape of the 2E1 decay from 2s state in He-like tin

The two-photon 2E1 transition from the singlet 2s state of heliumlike tin was measured. An alternative experimental approach was adopted in the present investigation where the two-photon emission results from the decay of the 2s state by selective K-shell ionization of Li-like tin ions in relativistic collisions with a low-Z gaseous target, which allowed for a measurement of the undistorted two-photon spectral shape. The measured 2E1 energy distribution was compared with fully relativistic calculations, which predict a Z dependence of the distribution. The preliminary results indicate the best agreement with the relativistic many body calculations for tin, and thus confirm the sensitivity on Z. Detailed data analysis is still in progress.     

Beiträge zur Theorie der mehrfach perspectiven Dreiecke und Tetraeder

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Die Bestimmung des Aschengehaltes der Schiessbaumwolle

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Schmiermittel

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Seltene Erden

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Evaluation of dialysis as a technique for the removal of lipids prior to the GC determination of ortho- and non-ortho-chlorobiphenyls, using 14C-labelled congeners.

Dialysis was evaluated as a non-destructive clean-up technique to isolate chlorobiphenyls (CBs) from fish-oil prior to further analysis. 14C-CBs were used to study the transfer processes of the CBs across polyethylene membranes. Single step processes using equilibrium dialysis were compared to a dynamic method of refluxing solvent. The dynamic method reduced the duration of the separation to 8 h. The transfer of CBs and the lipids was dependent on temperature and nature of the analyte with smaller molecules being dialysed substantially faster than larger molecules. An optimised dynamic method was used to compare the dialytic clean-up with a traditional method using sulfuric acid-impregnated silica for the determination of CBs in a laboratory reference material. Labelled recovery standards for each individual congener are recommended in combination with dialysis as a method for clean-up.