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.     

Keeping PASE with WEFT: SHWEFT–PASE pulse sequences for 1H NMR spectra of highly paramagnetic molecules

Metalloproteins are a category of biomolecules in which the metal site is usually the locus of activity or function. In many cases, the metal ions are paramagnetic or have accessible paramagnetic states, many of which can be studied using NMR spectroscopy. Extracting useful information from ¹H NMR spectra of highly paramagnetic proteins can be difficult because the paramagnetism leads to large resonance shifts (~400 ppm), extremely broad lines, extreme baseline nonlinearity, and peak shape distortion. It is demonstrated that employing polychromatic and adiabatic shaped pulses in simple pulse sequences, then combining existing sequences, leads to significant spectral improvement for highly paramagnetic proteins. These sequences employ existing technology, with available hardware, and are of short duration to accommodate short nuclear T₁ and T₂. They are shown to display uniform excitation over large spectral widths (~75 kHz), accommodate high repetition rates, produce flat baselines over 75 kHz while maintaining peak shape fidelity, and can be used to reduce spectral dynamic range. High‐spin (S = 5/2) metmyoglobin, a prototypical highly paramagnetic protein, was used as the test molecule. The resulting one‐dimensional (1D) pulse sequences combine shaped pulses with super‐water elimination Fourier transform, which can be further combined with paramagnetic spectroscopy to give shaped pulses with super‐water elimination Fourier transform–paramagnetic spectroscopy. These sequences require, at most, direct current offset correction and minimal phasing. The performance of these sequences in simple ¹H 1D, 1D NOE, and two‐dimensional NOESY experiments is demonstrated for metmyoglobin and Paracoccus denitrificans Co²⁺‐amicyanin (S = 3/2), and employed to make new heme hyperfine resonance assignments for high‐spin metBjFixLH_151–256, the heme sensing domain of Bradyrhizobium japonicum FixL. Copyright © 2013 John Wiley & Sons, Ltd.     

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.