The synthesis of some complexed ketones or sulfones by oxidation of η-arene-η-cyclopentadienyliron cations or η-arenedi-η-cyclopentadienyliron dications

Di-η⁵-cyclopentadienyliron complexed dications of 9,10-dihydroanthracene, xanthene, thioxanthene and diphenylmethane derived from ligand exchange reactions but without their prior isolation were oxidized with KMnO₄ to give, respectively, the dications of anthraquinone, xanthone, thioxanthone and benzophenone, isolated as their dihexafluorophosphate salts. Cyclopentadienyliron complexes of arenes containing a sulfide function were oxidized by m-chloroperbenzoic acid to the corresponding complexed sulfones, and sulfones prepared in this way include the hexafluorophosphate salt of the η⁶-p-tolysulfonylbenzene, thioxanthene-10,10-dioxide, 9,9-dimethylthioxanthene-10,10-dioxide or dibenzothiophene-9,9-dioxide-η⁵-cyclopentadienyliron cation.     

Bengazoles C-G from the Sponge Jaspis sp. Synthesis of the Side Chain and Determination of Absolute Configuration

Five new antifungal bengazoles (C-G) were isolated and fully characterized from a marine sponge of the genus Jaspis sp. Bengazoles C-G, together with the known bengazoles A and B, comprise a homologous series of n, iso, and anteiso fatty acid esters (C(13)-C(16)) of the same heterocyclic bis(oxazolyl)methanol parent. The complete relative and absolute configurations of the bengazoles were determined by application of the modified Mosher method and interpretation of exciton coupling in the CD spectra of the tetra-p-bromobenzoate derivatives of bengazole A and that of a model tetrol synthesized in seven steps from L-fucose.     

Synthesis of some heterocyclic systems from nucleophilic substitution reactions with η6-o-dichlorobenzene-η5-cyclopentadienyliron hexafluorophosphate

A method for the synthesis of heterocylic systems related to 9,10-dihydroanthracene with two hetero-atoms at the 9,10-positions is described. It involves the nucleophilic substitution reaction of η⁶-o-dichlorobenzene-η⁵-cyclopentadienyliron hexafluorophosphate with two nucleophilic groups (OH, SH and/or NH₂) located in the 1,2-positions of a benzene ring to give a cyclopentadienyliron complexed heterocycle. Upon pyrolytic sublimation of the complex, the free heterocyclic compound is then obtained.     

Young modules and filtration multiplicities for Brauer algebras

We define permutation modules and Young modules for the Brauer algebra B _k (r,δ), and show that if the characteristic of the field k is neither 2 nor 3 then every permutation module is a sum of Young modules, respecting an ordering condition similar to that for symmetric groups. Moreover, we determine precisely in which cases cell module filtration multiplicities are well-defined, as done by Hemmer and Nakano for symmetric groups. Supported by the European Community through Marie Curie fellowship MCFI 2002-01325 Supported by EPSRC grant GR/S18151/01     

(Semi-)Riemannian geometry of (para-)octonionic projective planes

We use reduced homogeneous coordinates to construct and study the (semi-)Riemannian geometry of the octonionic (or Cayley) projective plane , the octonionic projective plane of indefinite signature , the para-octonionic (or split octonionic) projective plane and the hyperbolic dual of the octonionic projective plane . We also show that our manifolds are isometric to the (para-)octonionic projective planes defined classically by quotients of Lie groups.     

Turbulence time scales in mixing box experiments

Laboratory experiments are performed to examine eddy time scales in turbulence generated by an oscillating grid in homogeneous fluid using tanks with varying depth and fixed high aspect ratio horizontal cross-section. For high ratios of depth to width, a mean circulation develops in the form of a pair of counter-rotating vortices. In a new technique, pearlescent dye is employed to measure eddy time scales and to determine their power law scaling dependence on the distance from the oscillating grid. Two scaling regimes are observed, one near the source of turbulence and one at intermediate depths. At intermediate depths, the scaling exponent is found to increase if the total fluid depth is larger. We discuss the significance of these results on the use of the law-of-the-wall scaling in the upper oceanic mixed layer.