Observables on hypergraphs

Observables on hypergraphs are described by event-valued measures. We first distinguish between finitely additive observables and countably additive ones. We then study the spectrum, compatibility, and functions of observables. Next a relationship between observables and certain functionals on the set of measures M(H) of a hypergraph H is established. We characterize hypergraphs for which every linear functional on M(H) is determined by an observable. We define the concept of an effect and show that observables are related to effect-valued measures. Finally, we define operational transformations from M(H) to itself and show that they can be described as a certain combination of effects.On leave from University of Berne, Institute of Mathematical Statistics, Sidlerstrasse 5, CH-3012 Berne, Switzerland.     

Bindungsverhältnisse und Elektronenverteilung im Br 4 2− -Ion

The linear ions Br ₄ ^2– which has been discovered for the first time by Siepmann and Schnering [13] in W₆Br₁₆ have been studied theoretically using the free electron model for the valence electrons. Electronic structure, binding energy and charge distribution show that Br ₄ ^2– is a typical electron deficient compound stabilized by a 4c-6e bond.

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Herrn Prof. Dr. H. Dunken bin ich für sein stetes Interesse und die rege Anteilnahme an diesen Modellrechnungen zu großem Dank verpflichtet.     

The role of triplet states in dye sensitization of ZnO electrodes

The quantum efficiency of photooxidation of a number of xanthene dyes at ZnO single crystal electrodes has been found to depend on the solution concentration of a triplet quenching agent, FeCN^4?₆, providing evidence for triplet state participation in the oxidation reaction.     

Hydrogenation without a transition-metal catalyst: on the mechanism of the base-catalyzed hydrogenation of ketones

The hydrogenation of unsaturated organic substrates such as olefins and ketones is usually effected by homogeneous or heterogeneous transition-metal catalysts. On the other hand, a single case of a transition-metal-free and purely base-catalyzed hydrogenation of ketones was reported by Walling and Bollyky some 40 years ago. Unfortunately, the harsh reaction conditions (ca. 200 degrees C, >100 bar H(2), potassium tert-butoxide as base) limit the substrate spectrum of this reaction to robust, nonenolizable ketones such as benzophenone. We herein present a mechanistic study of this process as a basis for future rational improvement. The base-catalyzed hydrogenation of ketones was found to be irreversible, and it shows first-order kinetics with respect to the substrate ketone, hydrogen, and catalytic base. The rate of the reaction depends on the type of alkali ion present (Cs > Rb - K > Na > Li). Using D(2) instead of H(2) revealed a rapid base-catalyzed isotope exchange/equilibration between the gas phase and the solvent as a concomitant reaction. The degree of deuteration of the product alcohols did not indicate a significant kinetic isotope effect. It is proposed that both ketone reduction and isotope exchange proceed via similar six-membered cyclic transition states involving the H(2)(D(2))-molecule, the alkoxide base, and the ketone (solvent alcohol in the case of isotope exchange). Mechanistic analogies are pointed out which apparently exist between the base-catalyzed hydrogenation of ketones studied here and the Ru-catalyzed asymmetric ketone hydrogenation developed by Noyori. In both cases, heterolysis of the hydrogen molecule appears to be assisted by a Br?nsted-base (i.e., alkoxide), the latter being bound to the substrate ketone or the catalyst ligand, respectively, by a bridging Lewis-acidic alkali ion.     

Determination of low dose concentration profiles in solids by means of (n,p) and (n, α) reactions

The isotopes³He,⁶Li,⁷Be and¹⁰B exhibit extremely large cross sections, between 1 and 48 kilobarn, for (n, p) or (n, α) reactions with thermal neutrons. Together with now available extracted thermal neutron fluxes of 10⁽ n·cm⁻²·sec⁻¹ or more, these reactions present a highly sensitive method of detecting the mentioned light elements in any heavy matrix material. Through the experimentally determined energy losses of the emitted protons or α-particles, also well resolved depth profiles can be obtained, as demonstrated here for some relevant examples from semiconductor and fusion technology.     

The Absolute Configuration of 1-Methylindane

It is shown unequivocally by chemical correlations (cf. Schemes 1--3) and Raman optical activity spectra (cf. Fig. 1 and 2) that the (R)-configuration has to be attributed to (+)-1-methylindane ((+)- 1 ). This is in contradiction to an earlier assignment of the (R)-configuration to (?)- 1 [2] which was based on the (R)-configuration of (+)-indane-1-carboxylic acid ( 3 ) [11].     

Hydroxybromierung und Methoxybromierung von (Z)-Cycloocten

In addition totrans-2-bromocyclooctanol andtrans-1,2-dibromocyclooctane,cis-4-bromocyclooctanol,cis-1,4-dibromocyclooctane,trans-1,4-dibromocyclooctane, and (Z)-5-bromocyclooctene are obtained, when (Z)-cyclooctene is treated with N-bromosuccinimide in the presence of water. Similarly the methoxybromination of (Z)-cyclooctene gives transanular products.