Studies towards the total synthesis of novel dolabellane-type diterpenoids: construction of the 5,11-fused bicyclic framework

An oxy-Cope protocol has been grafted on to a previously crafted hydroazulenic system to provide a facile entry into the 5,11-fused bicyclic skeleton present in the novel neodolabellane diterpenoids. Formation of a novel tricyclic diterpenoid framework, generated through a transannular cyclization in the 11-membered ring present in the neodolabellane skeleton and embodying a bridged cycloheptatriene moiety, has also been encountered.     

A total synthesis of guanacastepene C

A total synthesis of the structure corresponding to the novel tricyclic diterpene guanacastepene C has been realized in which a Knoevenagel cyclization serves as a key step to annulate the six-membered C-ring on a stereochemically secured bicyclic hydroazulene precursor.     

Biology-oriented synthesis of stereochemically diverse natural-product-derived compound collections by iterative allylations on a solid support

A strategy aiming at the introduction of stereocenters into polymer-bound natural-product-derived and -inspired compound collections is presented. Treatment of immobilized aldehydes with Brown's pinene-derived allylboranes results in the stereoselective formation of homoallylic alcohols with up to 89 % ee (ee=enantiomeric excess). Subsequent iterative ozonolysis-allylation sequences with up to three allylations on a solid support give access to 1,3-polyols with different relative configurations. Esterification with acryloyl chloride and final ring-closing metathesis yields alpha,beta-unsaturated delta-lactones with multiply oxygenated side chains, a substructure found in a group of natural products with a broad range of biological activity. The flexibility of the approach is exemplified by the parallel synthesis of all eight diastereomers of cryptocarya diacetate on a solid support. The individual isomers are obtained in overall yields of 40-60 % over 10 steps and with 63-85 % diastereoselectivity for the major isomer.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Radial oscillations of neutron stars in strong magnetic fields

The eigen frequencies of radial pulsations of neutron stars are calculated in a strong magnetic field. At low densities we use the magnetic BPS equation of state (EOS) similar to that obtained by Lai and Shapiro while at high densities the EOS obtained from the relativistic nuclear mean field theory is taken and extended to include strong magnetic field. It is found that magnetized neutron stars support higher maximum mass whereas the effect of magnetic field on radial stability for observed neutron star masses is minimal.     

Stereocomplementary synthesis of a natural product-derived compound collection on a solid phase

Enantiocomplementary allylation of solid phase-bound aldehydes gives rise to a natural product-derived compound collection, including all stereoisomers of cryptocarya diacetate.