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.     

Comparison of near-wall treatment methods for high Reynolds number backward-facing step flow

A comparison of near-wall treatment methods using different turbulence models for flow over a backward-facing step is presented. A Reynolds number (Re) of about 38,000 (U _∞ = 44.2 m/s), based on the step height and the mean stream velocity, was considered. An appropriate near-wall treatment method is critical to the choice of turbulence model used to predict wall-bounded flow. Predictions were obtained by applying standard wall functions, non-equilibrium wall functions and a two-layer model with six different turbulence models. These results were compared with data by Driver and Seegmiller (“Backward-facing step with inclined opposite wall—experiments by driver and seegmiller”, 1985a, http://cfd.me.umist.ac.uk/ercoftac [2003, Jan 31]). Non-equilibrium wall functions with modified k ? ? models predicted the closest reattachment length. However, the two-layer model gave results more representative of the entire flow pattern. The predictions show that a proper combination of turbulence models and near-wall treatment methods give reliable results.     

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.     

Biological production of acetaldehyde from ethanol using non-growingPichia pastoris whole cells

Acetaldehyde has been produced biologically using whole-cellPichia pastoris in a semibatch fermentor. Ethanol and air were fed continuously, and the product, acetaldehyde, was removed by the air stream. Operation of the reactor exceeded 100 h, maintaining high alcohol oxidase activity. Low cell-mass concentration (9.9 g/L) minimized product inhibition. Ethanol concentration in the broth, oxygen concentration in the air, and pH were evaluated for their effects on the fermentation process.