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.     

Investigation of fungal deterioration of synthetic paint binders using vibrational spectroscopic techniques

The deterioration of synthetic polymers caused by biological process is usually evaluated by visual inspection and measuring physical effects. In contrast to this approach, we have applied vibrational spectroscopies to study the biodegradation of the synthetic resins. 29 synthetic resins used as paint binding media, including acrylic, alkyd and poly(vinyl acetate) polymers, were examined for potential susceptibility to fungal degradation using the standard method ASTM G21-96(2002). In addition, the degraded resins were analysed by Raman spectroscopy, FT-IR and FT-IR photoacoustic spectroscopy. Almost all the acrylic resins studied proved to be resistant to microbial attack, while all alkyd resins and some poly(vinyl acetates) turned out to be biodegradable. Within a few days of inoculation Aspergillus niger was the most copious fungus on the biodegraded resins. A comparison of the IR and Raman spectra of control and biodegraded resins did not show any differences, but photoacoustic spectroscopy revealed additional bands for the fungal-degraded resins, consistent with the presence of fungal-derived substances. The additional bands in the photoacoustic spectra were due to the presence of Aspergillus niger and melanin, a fungal pigment. Since IR photoacoustic spectroscopy can be also a suitable technique for the chemical characterisation of binding media, the same spectroscopic analysis can be employed to both characterise the material and obtain evidence for fungal colonization. Microbial growth on Sobral 1241ML (alkyd resin) after 28 d (growth rating 4) compared with the non-inoculated resin.     

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.     

高Tc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.