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.     

Wide-frequency-range dielectric response of polystyrene latex dispersions

In this work we analyze the dielectric properties of dilute colloidal suspensions of nonconducting spherical particles with a thin electrical double layer from experimental data obtained by performing impedance spectroscopy experiments over a broad frequency range, from 20 Hz to 1 GHz. The electrode polarization correction was made by fitting a circuit model in the complex impedance plane (impedance spectrum) using a constant phase angle (CPA) element to fit the electrode polarization in series with the sample impedance. This simple procedure is found to be effective in eliminating the electrode contribution. The dielectric response shows two different dispersions, the alpha relaxation (counterion relaxation) that occurs at low kilohertz frequencies, and the delta relaxation (Maxwell-Wagner effect) found in the MHz range. These are reasonably well fitted over a broad frequency range by the theoretical expressions given by a simplified standard model (not including anomalous conduction) and a generalized model (including anomalous conduction) for the low-frequency dispersion, plus Maxwell-Wagner-O'Konski theory for the delta relaxation in the mid-frequency range. An analysis was also made of the need to include, for these latices, the effects of ion mobility in the Stern layer in order for the values of the zeta-potential obtained from electrophoretic and dielectric data to be compatible with each other.     

高T_c超导体YBCO磁通钉扎的计算机模拟研究

临界电流密度Jc是影响高温超导体在强电领域应用的一个重要参数,在实际应用中,特别在外加磁场下,临界电流密度与超导材料的磁通钉扎性质密切相关.因此,磁通钉扎一直是高温超导体研究中的一个重要领域.由于高温超导体磁通钉扎力密度Fp的标度律存在,本文根据D.Dew-Hughes总结的钉扎力函数,主要存在两种主要作用类型(正常相和△K).我们将D.Dew-HugBes给出的钉扎力密度Fp标度函数改进为一个简化的具有物理意义的函数表达式.结合文献中已有的实验数据,我们对YBcO进行了计算机模拟,确定了它的磁通钉扎类型,模拟的研究结果与实际情况比较吻合.