BF3 x Et2O-mediated cascade cyclizations: synthesis of schweinfurthins F and G

The total synthesis of the natural stilbene (+)-schweinfurthin G (8) has been accomplished through a sequence based on an efficient cationic cascade cyclization. This cascade process is initiated by Lewis acid promoted ring opening of an epoxide and terminated through a novel reaction with a phenolic oxygen "protected" as its MOM ether. Several Lewis acids have been examined for their ability to induce this new reaction, and BF3 x Et2O was found to be the most effective. The only major byproduct under these conditions was one where the expected secondary alcohol was found as its MOM ether derivative (e.g., 30). While this byproduct could be converted to the original target compound through hydrolysis, it also could be employed as a protected alcohol to allow preparation of a benzylic phosphonate (43) without dehydration of the secondary alcohol. The resulting phosphonate was employed in a Horner-Wadsworth-Emmons condensation with an aldehyde representing the right half of the target compounds, an approach complementary to previous studies based on condensation of a right-half phosphonate and a left-half aldehyde.     

Synthesis of the schweinfurthin hexahydroxanthene core through Shi epoxidation

Use of a Shi epoxidation for introduction of chirality in a key epoxide intermediate, together with revised protecting group tactics, has allowed an efficient synthesis of the hexahydroxanthene subunit common to the natural schweinfurthin F and the synthetic analogue 3-deoxyschweinfurthin B.     

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.     

Synthesis of the cis-fused hexahydroxanthene system via cationic cascade cyclization

The cis-fused hexahydroxanthene system can be obtained through a cascade cyclization initiated by Lewis acid-mediated epoxide opening and terminated by reaction with a MOM-protected phenol. Only a single diastereomer of the product was obtained with stereochemistry verified by diffraction analysis. This demonstrates the viability of this approach to natural products containing the cis-fused hexahydroxanthene skeleton, and supports preparation of more complex targets through a similar strategy.