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 and characterization of polyethylenimine backbone polynucleotide models

Nucleic acid analogs with a PEI backbone and uracil- and thymine-containing pendants and their monomer and dimer models have been synthesized and characterized by means of 360-MHz ¹H-NMR as well as 90- and 20-MHz ¹³C-NMR. ¹³C-NMR was particularly useful in characterizing the primary structures of the polymers. While data from the monomer and dimer models can be assumed transferable to the polymers, some unique features of the ¹H and ¹³C spectra of the polymers compared to the model compounds, give insight to the polymer structures.     

Spectroscopic examination of polyethylenimine backbone polynucleotide models

The UV absorptions of nucleic acid analogs with a polyethylenimine (PEI) backbone and uracil- and thymine-containing pendants have been examined. For the solvents used (water, basic aqueous solutions, and DMSO), significant hypochromicity is observed. The uracil-containing polymers have been shown to interact with polyA in an aqueous solvent at pH 7 (tris buffer). The interaction is proportional to the size of the polymer. A correlation is attempted between the properties of the analogs and their biological activity.     

Field experience with ambient-level flame-photometric sulphur detectors

Carbon dioxide exhaled by the operators produces increased levels of this gas inside the trailers used for housing monitoring equipment for use in the field. These levels can be high enough to produce serious calibration errors in flame photometric detectors used for measuring ambient concentrations of gaseous sulphur products. Quantitative measurement of the carbon dioxide interference in the sulphur emission is reported, as well as a method of estimating the extent of quenching agent pollution.