Asymmetric hydrogenation of alkyl(vinyl)thioethers: a promising approach to α-chiral thioethers

This paper describes the enantioselective hydrogenation of vinylthioethers. We show that thioether derivatives of maleic esters can be hydrogenated with full conversion and up to 60% ee, and that α-thioether cinnamic acids can be hydrogenated in 51% ee with modest conversion.     

Contingent epiderivatives and set-valued optimization

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.     

Low-energy fission investigated in reactions of 750 AMeV 238U-ions on 208Pb. II: Isotopic distributions

Projectile fission of 750 AMeV ²³⁸U-ions interacting with a Pb target was studied by means of the spectrometer FRS, GSI-Darmstadt. One of the two fission fragments was detected with a transmission of few percent and identified in mass and charge. Low-energy fission (E^* < 25 MeV) events were selected by their magnetic rigidity. Whereas the production of asymmetric fission events is dominated by the GDR excitation, very asymmetric fission and symmetric fission take place after a GQR or DGDR excitation or after a nuclear interaction. Cross sections of more than 250 isotopes were measured. Isotopic distributions of low-energy fission were reconstructed for elements from Se to Te. The fission modes SI, SII and SL were clearly shown in these distributions and in the mass and TKE distributions. Charge polarization and mass dispersion were deduced for each fission mode. Finally, the characteristics of the low-energy fission process explain the production rates of neutron-rich species. Received: 14 July 1997 / Revised version: 6 October 1997     

Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in derL p -Theorie

Zusammenfassung Die Hörmander-Klassen _1, ⁰ (0<1) von Pseudodifferentialoperatoren sind -Algebren. Insbesondere ist die Inverse eines inL(L ^p ( ⁿ )) invertierbaren Pseudodifferentialoperators der Klasse _1, ⁰ selbst wieder ein Pseudodifferential-operator derselben Klasse.Der Beweis beruht auf den von R. Beals, R. R. Coifman, Y. Meyer und H. O. Cordes entwickelten Methoden zur Charakterisierung von Algebren von Pseudodifferentialoperatoren.     

Asymmetric Diels-Alder reactions with 5-menthyloxy-2-(5H)-furanone

A new class of chiral dienophiles, 5-alkoxy-2(5H)-furanones, has been developed. Both enantiomers of 5-menthyloxy-2(5H)-ftiranone are readily available in enantiomerically pure form, starting from furfural and d- or l-menthol. Excellent diastereoselectivities (d.e. β99%) are obtained in thermal Diels-Alder reactions with several cyclic and acyclic dienes. The use of silyl dienol ethers has resulted in new routes to enantiomerically pure cyclohexanones in a highly regioselective manner.     

EPR-untersuchungen an carbonsäureestern—II : Radikalanionen der thion- und dithiobenzoesäureester

Alkyl thione (2) and dithiobenzoates (3) as well as their aryl substituted derivatives 4 and 5 may be converted into radical anions by in situ electroreduction.—The EPR spectra of 2–5 are measured. Conclusions about the spin density distribution within the aromatic ring and the functional group are drawn from the hyperfine structure coupling constants, g-values and polarographic half wave potentials, whereby the effect of ortho substituents (twisting of the two halves of the molecule) is especially considered.—The results agree sufficiently with MO calculations of the McLachlan type.Inspection of the alkyl coupling constants

shows that the alkyl groups exhibit conformations of minimum steric hindrance of the thiocarbonyl group.     

The "invisible" 13C NMR chemical shift of the central carbon atom in [(Ph3PAu)6C]2+: a theoretical investigation

The experimental 13C NMR chemical shift of the central carbon atom in the octahedral [(Ph3PAu)6C]2+ cluster was investigated on the basis of relativistic density functional calculations. In order to arrive at independent model conclusions regarding the value of the chemical shift, a systematic study of the dependence of the cluster structure on the phosphine ligands, the chosen density functionals, and the basis set size was conducted. The best structures obtained were then used in the NMR calculations. Because of the cage-like cluster structure a pronounced deshielding of the central carbon nucleus could have been expected. However, upon comparison with the 13C NMR properties of the related complex [C{Au[P(C6H5)2(p-C6H4NMe2)]}6]2+, Schmidbaur et al. have assigned a signal at delta=135.2 ppm to the interstitial carbon atom. Our calculations confirm this value in the region of the aromatic carbon atoms of the triphenylphosphine ligands. The close-lying signals of the 108 phenyl carbon atoms can explain the difficulties of assigning them experimentally.