Some analytical semigroups occurring in probability theory

One-parameter semigroups occurring in operator-limit distributions are investigated. The topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup.     

Stochastic dominance with nonadditive probabilities

Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.     

First structural characterization of binary AsIII and SbIII azides

The highly explosive molecules As(N(3))(3) and Sb(N(3))(3) were obtained in pure form by the reactions of the corresponding fluorides with (CH(3))(3)SiN(3) in SO(2) and purification by sublimation. The crystal structures and (14)N NMR, infrared, and Raman spectra were determined, and the results compared to ab initio second-order perturbation theory calculations. Whereas Sb(N(3))(3) possesses a propeller-shaped, pyramidal structure with perfect C(3) symmetry, the As(N(3))(3) molecule is significantly distorted from C(3) symmetry due to crystal packing effects.     

OPTICAL EXCITATION OF THE EOSIN-HUMAN SERUM ALBUMIN COMPLEX*

Abstract The excitation of the eosin-human serum albumin complex has been investigated with spectral and photochemical techniques. Measurements of the changes in absorption and fluorescence spectra induced by complexing have shown that the first eosin molecule is held more strongly than the next few and that multiple binding leads to an enhanced fluorescence self-quenching. Flash photolytic measurements indicate that dye-dye quenching interactions enhance triplet eosin formation, and that oxygen quenching of the triplet is suppressed when the dye is singly bound. The quantum yield for aerobic photobleaching of the complex has been measured and is interpreted in terms of these findings.     

Preparation and properties of insoluble films of cyclodextrin condensation polymers

The preparation and properties of smooth and stable films of cyclodextrin polymers are described. The commercially available water soluble prepolymers of-, -, and-cyclodextrin of low molecular masses were crosslinked with glutaric dialdehyde. Side-chain unreacted aldehyde groups were reduced with sodium borohydride. For the-cyclodextrin polymer, optimum film performance was found for a 1:10 mass ratio of glutaric dialdehyde to prepolymer, which corresponds to a molar ratio of glutaric dialdehyde to cyclodextrin units of about 1.75: 1. Such films, of thickness 2.4 µm, were prepared on metallic or glassy-carbon substrates for characterization by scanning-electron microscopy, and for studies with the electrochemical quartz-crystal microbalance.     

Versuche zur Herstellung eines «Bis(triasterans)» und Synthese des heterocyclischen (Tricyclo[4.4.1.01,6]undeca-3,8-dien-11,11-dimethyl)sulfits

Tentative Synthesis of ‘Bis(triasterane)’ and Synthesis of the Heterocyclic (Tricyclo[4.4.1.0^1,6]undeca-3,8-diene-11,11-dimethyl)sulfite The synthesis of the bis(triasterane) ( 1 ) has been tried; the reaction of ‘isotetraline’ (1,4,5,8-Tetrahydronaphthalene; 2 ) with diazomalonate yielded the tricyclic systems 5 and 6 , and not 4 . Hydrolysis of 5 gave the monocarboxylic acid 7 , and not the dicarboxylic acid 9 . The latter could be obtained from the dibromoderivative 8 , but 9 couldn't be converted to the acyl chloride 10 . The reduction of 9 with LiAlH₄ yielded the crystalline diol 11 , which was cyclized with SOCl₂ to the heterocycle 12 . The spectral data of the new compounds 5, 6, 7, 11 and 12 are reported and discussed.