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.     

Semi-asymptotic evaluation of certain three-center two-electron integrals

Two-electron repulsion integrals between a two-center charge distribution and a charge distribution about a third center, which do not appreciably interpenetrate, are shown to be given to useful accuracy by numerical differentiation of certain three-center one-electron integrals. This method also may be used to evaluate integrals of this type for which the Mulliken or Sklar approximations are inapplicable.Supported by Contract SD-102 with the Advanced Research Projects Agency.     

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.     

Reduction of disulfides in the milligram range with hypophosphorous acid and organic phosphites

A number of organic disulfides in the milligram range were reduced to the corresponding thiol by reaction with hypophosphorous acid at elevated temperatures in aqueous solvents. Reduction is extensive after several hours. Aromatic disulfides were reduced by triethyl phosphite and triphenyl phosphite at room temperature. Products were deterimned by polarographic and amperometric titration techniques.     

Determination of submicrogram-per-liter concentrations of caffeine in surface water and groundwater samples by solid-phase extraction and liquid chromatography

A method for determining submicrogram-per-liter concentrations of caffeine in surface water and groundwater samples has been developed. Caffeine is extracted from a 1 L water sample with a 0.5 g graphitized carbon-based solid-phase cartridge, eluted with methylene chloride-methanol (80 + 20, v/v), and analyzed by liquid chromatography with photodiode-array detection. The single-operator method detection limit for organic-free water samples was 0.02 microgram/L. Mean recoveries and relative standard deviations were 93 +/- 13% for organic-free water samples fortified at 0.04 microgram/L and 84 +/- 4% for laboratory reagent spikes fortified at 0.5 microgram/L. Environmental concentrations of caffeine ranged from 0.003 to 1.44 micrograms/L in surface water samples and from 0.01 to 0.08 microgram/L in groundwater samples.