Ring-closing metathesis as a tool for the efficient preparation of chiral spirocyclic ethers from homoallylic alcohols

The preparation of chiral spirocyclic ethers via allylic etherification/olefin metathesis of homoallylic alcohols is investigated. This reaction sequence transforms the enantiopure substrate alcohols, synthesized by a one-pot asymmetric rhodium-catalyzed conjugate addition/metal-mediated allylation procedure, into the desired spiro ethers with full conversions and in excellent isolated yields. The synthetic sequence provides an efficient means for a rapid construction of functionalized spiro ethers in a stereoselective manner.     

The unitary irreducible representations of the quantum heisenberg algebra

The goal of this work is to describe the irreducible representations of the quantum Heisenberg algebra and the unitary irreducible representation of one of its real forms. The solution of this problem is obtained through the investigation of theleft spectrum of the quantum Heisenberg algebra using the result about spectra of generic algebras of skew differential operators (cf. [R]).     

Physico-chemical forms of radiostrontium in simulated freshwaters

A method for the analysis of the physico-chemical forms of radiostrontium in waters is described and applied to the simulated lake and groundwaters to which were later added clay minerals and humus substances. The simulated water samples were fractionated using filtration and ultrafiltration: particulates, colloids and dissolved species. The dissolved species were further separated into three fractions using ion exchange: cations, anions and non-ionic species. The physico-chemical forms of radiostrontium do not appreciable change when humus substances or clay mineral or both are added to the water samples. Only about 1–6% of added radiostrontium was found in particulate and colloid fractions. The greatest amount of⁸⁵Sr was always found in the dissolved fraction, cations (>87%). Radiostrontium was never found in the dissolved fraction, anions or non-ionic species.     

Minimal surfaces in R3 with one end¶and bounded curvature

We study complete minimal surfaces M immersed in R ³, with finite topology and one end. We give conditions which oblige M to be conformally a compact Riemann surface punctured in one point, and we show that M can be parametrized by meromorphic data on this compact Riemann surface. The goal is to prove that when M is also embedded, then the end of M is asymptotic to an end of a helicoid (or M is a plane). Received: 13 January 1997 / Revised version: 15 September 1997