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.     

Characterization of radiation-induced aging in silica-reinforced polysiloxane composites

Changes in crosslink density and chemical structure of silica-reinforced silicone polymer composites due to aging in gamma radiation environments were examined in this study. Solvent swelling was utilized to determine the individual contributions of the matrix polymer and filler phase to the overall crosslink density of silica-reinforced silicone polymer composites. The results show how polymer–filler hydrogen bonding dominates the overall crosslink density of the material. Air-irradiated samples displayed decreased hydrogen bonding at the polymer–filler interface, while vacuum irradiation revealed the opposite effect. These results were supported by solid-state NMR experiments that correlated the motional dynamics of the polymer chains with crosslink density through T₂ relaxation time measurements. GC/MS analysis was used to identify degradation products formed as a result of irradiation and speculate upon likely degradation mechanisms.     

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.     

The development of a thermal neutron activation (TNA) system as a confirmatory non-metallic land mine detector

In order to detect and locate buried landmines for peacekeeping, the Canadian Department of National Defence (DND), under the Improved Landmine Detection Project, is developing a vehicle-mounted, two-phase mine detection system. The first phase constitutes a suite of detectors used to indicate the possibility of a mine at a particular location (to ±30 cm in accuracy). In the second phase a Thermal Neutron Activation (TNA) system is used to confirm the presence of explosives via detection of the 10.83 MeV gamma-ray associated with nitrogen decay. The TNA system developed for this uses a 100 μg²⁵²Cf neutron source surrounded by four 3″×3″ NaI(Tl) detectors. Combining the use of state-of-the art radiation transport codes for design, judicious choice of specialized shielding materials and development of high-rate, fast-pulse processing electronics, has led to a system which can; (i) confirm the presence of all surface- or lightly-buried anti-tank mines in a few seconds to a minute (depending on mass of explosive), (ii) confirm the presence of anti-tank mines down to 20 cm depth in less than 5 minutes, (iii) confirm the presence of large (>100 g nitrogen) anti-personnel mines in less than five minutes, (iv) operate in adverse climatic conditions. These results have been verified in field trials and the system is due to be fielded in 1999.     

Possible tests for the mechanisms of ligand exchange in solids: The deaquation-anation of [Cr(NH3)5(H2O)]X3 salts

The possibility of using correlations of ΔH⁺ and ΔH, and of ΔH⁺ and ΔS⁺ to gain insight into the mechanisms of ligand-exchange reactions in solids are discussed. These correlations are tested using literature values for the deaquation-anation reactions of [Cr(NH₃)₅(H₂O)]X₃, where X^? = Cl^?, Br^?, I^? or NO^?₃. The poor agreement in the activation parameters reported in the literature precluded a meaningful test of the ΔH?ΔH^* correlation. This poor agreement suggests that these activation parameters are strongly influenced by experimental factors that have not been controlled in studies to date. nevertheless, there is a linear correlation of ΔH² and ΔS² which gives an isokinetic temperature of 367 ± 11 K. This isokinetic behavior suggests that the same mechanism is operative throughout the series.