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.     

Ultrafast laser fabrication of submicrometer pores in borosilicate glass

We demonstrate rapid fabrication of submicrometer-diameter pores in borosilicate glass using femtosecond laser machining and subsequent wet-etch techniques. This approach allows direct and repeatable fabrication of high-quality pores with diameters of 400-800 nm. Such small pores coupled with the desirable electrical and chemical properties of glass enable sensitive resistive-pulse analysis to determine the size and concentration of macromolecules and nanoparticles. Plasma-enhanced chemical vapor deposition allows further reduction of pore diameters to below 300 nm.