The Absolute Configuration of β-Bisabolol

From bergamot oil (Citrus bergamia RISSO), (?)-(4S, 8R)-8-epi-α-bisabolol ( 2 ) and (?)-(4R, 8S)-4-epi-β-bisabolol ( 3 ) were isolated. The absolute configuration of their stereoisomers 4 and 5 was established by an enantioselective synthesis starting from (?)-(S)-p-mentha-1,8-dien-4-ol.     

The Reaction of Bicyclo [3.2.1] octenyl Halides with Metal Hydrides

Reduction of 2-phenyl- and 2-methyl-exo-3,4-dichlorobicyclo[3.2.1]oct-2-enes with lithium aluminium hydride (LAH) or tributyltin hydride (TBTH) gave endo-2-phenyl-3-chlorobicyclo[3.2.1]oct-3-ene, 2-phenyl-3-chlorobicyclo[3.2.1]oct-2-ene and their methyl analogues. The action of both reagents on 2-phenyl-exo-3, 4-dibromobicyclo[3.2.1]oct-2-ene similarly resulted in reductive monodebromination to give normal and allylically rearranged products. Additionally, further reduction occurred to give endo-2-phenylbicyclo[3.2.1]oct-3-ene and 2-phenylbicyclo[3.2.1]-oct-2-ene. In all cases, LAH gave mainly the allylic rearrangement product whereas TBTH gave mostly unrearranged product. The reason for these differences could have been due either to the intervention of allylic radicals in the TBTH reduction or to differences in nucleophilicity. The results also show that LAH is equally efficaceous as TBTH in the reduction of these allylic halides and equally selective in the reduction of the vinyl bromides. The stereochemistry of the allylic rearrangement was shown to be synfacial in that hydride replaced halide on the same face of the molecule.     

Non-singular space-times with a negative cosmological constant: V. Boson stars

We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.     

FPIV study of gas entrainment by a hollow cone spray submitted to variable density

The gas entrainment in a hollow cone spray submitted to variable density is studied experimentally in order to better understand the effect on mixture formation. Particle image velocimetry on fluorescent tracers, associated with a specific processing of the instantaneous velocity fields have been applied to obtain measurement in the close vicinity of the spray edge. In the “quasi-steady” region of the spray, important effect of the ambient density on the mass flow rate of entrained gas have been pointed out. The axial evolution of is in good agreement with an integral model that takes the momentum exchange between phases into account.     

Studies of Some Curvature Operators in a Neighborhood of an Asymptotically Hyperbolic Einstein Manifold

On an asymptotically hyperbolic Einstein manifold (M,g₀) for which the Yamabe invariant of the conformal structure on the boundary at infinity is nonnegative, we show that the operators of Ricci curvature, and of Einstein curvature, are locally invertible in a neighborhood of the metric g₀. We deduce in the C^∞ case that the image of the Riemann-Christoffel curvature operator is a submanifold in a neighborhood of g₀.     

Non-Singular,Vacuum, Stationary Space-Times with a Negative Cosmological Constant

We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant. Submitted: December 12, 2005. Accepted: May 22, 2006.     

Manifold structures for sets of solutions of the general relativistic constraint equations

We construct manifold structures on various sets of solutions of the general relativistic initial data sets.     

The transfrmation of difluorocarbene into 3,3-diflurocyclopropene

The addition of difluorocarbene to benzobarrelene gives the syn and anti 1,2 mono-adducts. Heating of either of them at 200°C in hexadeuteriobenzene generates naphthalene and 3,3-difluorocyclopropene.