Galactic Metrics

The paths of stars in galaxies have circular velocity independent of their distance from the centre of the galaxy. Newtonian mechanics with a logarithmic potential has such paths. In relativity these paths can be taken to be geodesics and this requirement places a restricting equation on the spacetime metric. This equation has a non-unique spherically symmetric solution that in the Newtonian limit has a logarithmic potential. It also can be solved in terms of a conformal factor. In particular it has solutions which are conformal to the vacuum-Einstein solutions and such spacetimes are solutions to the vacuum-Bach equations. Therefore it is suggested that the Bach equations describe dynamics on galactic length scales.     

Sugar conjugates of fulvestrant (ICI 182,780): efficient general procedures for glycosylation of the fulvestrant core

We have prepared glucose and cellobiose conjugates at the phenolic 3- and hydroxylic 17-positions of the pure anti-estrogenic compound fulvestrant (ICI 182,780), which has recently been approved in the USA for the treatment of advanced postmenopausal breast cancer. Glycosylation at the 17-position was achieved most effectively using pivaloyl protection of the sugar imidates employed, which we found suppressed the competing transacylation reaction and led to improved yields of the product glycosides.     

Microwave frequency shifting using photon acceleration

Using a Bostick Gun as a plasma source, we have been investigating the effects of a moving plasma front on the frequency of an incident R.F. signal. We have been able to measure frequency shifts of 10 MHz frequency with a 2.6 GHz signal. The density is such that the plasma frequency is well above the transmitter frequency 1.3 meters from the plasma source. No magnetic field is used.     

Randomized UMD Banach spaces and decoupling inequalities for stochastic integrals

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

     

Nitroxyl free radical binding to Si(1 0 0): a combined scanning tunneling microscopy and computational modeling study

The ultra-high vacuum scanning tunneling microscope (UHV-STM) was used to investigate the addition of the 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) radical to the Si(1 0 0) surface. Room temperature studies performed on clean Si(1 0 0)-2 × 1 confirm the proposed binding of the unpaired valence electron associated with the singly occupied molecular orbital (SOMO) of the molecule with a Si dangling bond. A strong bias dependence in the topography of isolated molecules was observed in the range of −2.0 to +2.5 V. Semiempirical and density functional calculations of TEMPO bound to a three-dimer silicon cluster model yield occupied state density isosurfaces below the highest occupied (HOMO) and unoccupied state densities isosurfaces above the lowest unoccupied molecular orbital (LUMO) which trend in qualitative agreement with the bias dependent STM topography. Furthermore, the placement of TEMPO molecules on dangling bonds was controlled with atomic precision on the monohydride Si(1 0 0) surface via electron stimulated desorption of H, demonstrating the compatibility of nitroxyl free radical binding chemistries with nanopatterning techniques such as feedback controlled lithography.