Jordan homomorphisms,chain geometries and the fundamental theorem

This research was supported by M.P.I. (R.S. 40%).     

Microbial Baeyer-Villiger Oxidation of Ketones by Cyclohexanone and Cyclopentanone Monooxygenase – A Computational Rational for Biocatalyst Performance

Summary. Recombinant Escherichia coli overexpressing Pseudomonas sp. NCIMB 9872 cyclopentanone monooxygenase (CPMO, EC 1.14.13.16) and Acinetobacter sp. NCIMB 9871 cyclohexanone monooxygenase (CHMO, EC 1.14.13.22) have been utilized in whole-cell Baeyer-Villiger biotransformations of prochiral bicycloketones. A significant difference in substrate acceptance and stereoselectivity was observed for bicyclo[3.3.0] and bicyclo[4.3.0] substrates. A plausible mechanism of these transformations was established by means of high level DFT/B3LYP calculations suggesting an essential difference in electronic requirements for a successful enzymatic conversion, which was similarly encountered in recombinant whole-cell mediated biooxidations. Some of the lactones produced in the biocatalytic Baeyer-Villiger oxidation represent key intermediates for the synthesis of indole alkaloids.     

Low energy positron scattering from atoms in and on solids observed with low energy positron diffraction and reemission microscopy

The present status of low energy positron diffraction (LEPD) and positron reemission microscopy (PRM) is reviewed in the context of unanswered questions regarding the elastic scattering of positrons in the 1–300 eV energy range from atoms in solids and at solid surfaces. Recent LEPD studies yield an agreement between theoretical and experimental diffraction intensities for semiconductors that has never been equalled in electron diffraction studies. This situation is discussed in terms of the repulsive interaction between the positron and the embedded atomic potential and the lack of exchange with the nonspherically distributed valence electrons. The scattering of re-emitted positrons in PRM from atoms chemisorbed or physisorbed on the re-emitting surface has not yet received the same theoretical attention as scattering from embedded atoms in LEPD. Possible ways in which positron scattering from overlying atomic structures manifests itself in PRM as well as positron re-emission holography are discussed, both from the practical viewpoint of observing these structures and in the context of fundamental questions regarding the positron re-emission process itself.     

Solving Sequences of Refined Multistage Stochastic Linear Programs

Multistage stochastic programs with continuous underlying distributions involve the obstacle of high-dimensional integrals where the integrands' values again are given by solutions of stochastic programs. A common solution technique consists of discretizing the support of the original distributions leading to scenario trees and corresponding LPs which are – up to a certain size – easy to solve. In order to improve the accuracy of approximation, successive refinements of the support result in rapidly expanding scenario trees and associated LPs. Hence, the solvability of the multistage stochastic program is limited by the numerical solvability of sequences of such expanding LPs. This work describes an algorithmic technique for solving the large-scale LP of refinement ν based on the solutions at the previous ν?1 refinements. Numerical results are presented for practical problem statements within financial applications demonstrating significant speedup (depending on the size of the LP instances).