Experimental probes of emergent symmetries in the quantum Hall system

Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry Γ₀(2)${\Gamma }_0(2)$. We briefly review this evidence and show that, for the lowest temperatures, the experimental determination of the position of the quantum critical points agrees to the parts per mille   level with the prediction from Γ₀(2)${\Gamma }_0(2)$. We present evidence that experiments giving results that deviate substantially from the symmetry predictions are not cold enough to be in the quantum critical domain. We show how the modular symmetry extended by a non-holomorphic particle–hole duality leads to an extensive web of dualities related to those in plateau–insulator transitions, and we derive a formula relating dual pairs (B,Bd)$(B,B_d)$ of magnetic field strengths across any transition. The experimental data obtained for the transition studied so far is in excellent agreement with the duality relations following from this emergent symmetry, and rule out the duality rule derived from the “law of corresponding states”. Comparing these generalized duality predictions with future experiments on other transitions should provide stringent tests of modular duality deep in the non-linear domain far from the quantum critical points.     

基于VxWorks新型映像的三模冗余启动机制研究

针对VxWorks启动映像依赖于ROM地址,不能适应航天型号中三模存储要求的缺点,利用VxWorks自带的压缩算法,按照航天型号软件任务要求设计了一种基于VxWorks内存型映像的新型压缩映像,实现了软件映像与ROM区地址无关。并且实现了新型压缩映像的三模冗余引导启动,启动时每一个bit数据都从三份映像获取,并进行三取二判断,将最后结果拷贝到内存作为目的映像的bit数据,目的映像启动后能够回写正确数据自动纠正空间环境下可能发生的单粒子翻转错误,为软件的可靠启动建立了基础。     

广义对角占优阵的一个等价条件

给出了实方阵为广义对角占优阵的充要条件,同时给出了判断广义对角占优阵可靠,可行,较简单方法。     

The computation of the representation matrices of the generators of the unitary group

A method is presented for the efficient computation of the representation matrices of the unitary group, U(n) in the Gelfand—Tsetlin basis (corresponding to the usual spin-symmetry adapted basis for an N electron CI). The present scheme is conceptually and computationally attractive in that it is formulated directly in terms of Weyl tableaux and also that it permits simultaneous basis vector generation and matrix element evaluation. In addition the basis vectors are ordered so that subsequent restriction to the three dimensional rotation group is facilitated. An illustrative example is also presented.Taken in part from a thesis submitted to the University of London in partial fulfilment of the requirements for the degree of PhD.     

An empirical retention model for the optimization of on-line normal-phase LC-GC for the multi-analyte determination of hydrophobic compounds in fatty samples

Summary Normal-phase LC (NPLC) is a powerful method for the clean-up of fatty samples in the determination of organochlorine pesticides (OCPs). The injected sample deactivates the stationary phase and the triglyceride matrix therefore serves as a polarity modifier in the NPLC separation. Thus, the amount of sample injected is the key to both selectivity and sensitivity in matrixmodified LC coupled to capillary GC. In coupled LC-GC the NPLC separation becomes particularly critical because only a limited amount of the LC eluent can be transferred to the GC and the triglyceride matrix must be prevented from entering the GC, because it degrades the performance of the injector and the column. In previous applications method development was seriously hampered by these boundary conditions and tedious and lengthy trial-and-error experiments were required to determine suitable experimental conditions. In this study an empirical model was developed that describes the NPLC separation process in terms of column dimensions and fat loadability. The output is given as the probability of achieving successful LC-GC analysis of a particular set of analytes, thus furnishing a useful tool for the development of new applications in the field of exposure assessment and analysis of residues of apolar compounds in fatty samples. The limitations of current procedures—maximum transfer volumes and minimal separation—are also discussed.     

Quantitative separation of zinc traces from cadmium matrices by solid-phase extraction with polyurethane foam

A system for separation of zinc traces from large amounts of cadmium is proposed in this paper. It is based on the solid-phase extraction of the zinc in the form of thiocyanate complexes by the polyurethane foam. The following parameters were studied: effect of pH and of the thiocyanate concentration on the zinc extraction, shaking time required for quantitative extraction, amount of PU foam necessary for complete extraction, conditions for the separation of zinc from cadmium, influence of other cations and anions on the zinc sorption by PU foam, and required conditions for back extraction of zinc from the PU foam. The results show that zinc traces can be separated from large amounts of cadmium at pH 3.0±0.50, with the range of thiocyanate concentration from 0.15 to 0.20 mol l⁻¹, and the shaking time of 5 min. The back extraction of zinc can be done by shaking it with water for 10 min. Calcium, barium, strontium, magnesium, aluminum, nickel and iron(II) are efficiently separated. Iron(III), copper(II) and cobalt(II) are extracted simultaneously with zinc, but the iron reduction with ascorbic acid and the use of citrate to mask copper(II) and cobalt(II) increase the selectivity of the zinc extraction. The anions nitrate, chloride, sulfate, acetate, thiosulphate, tartarate, oxalate, fluoride, citrate, and carbonate do not affect the zinc extraction. Phosphate and EDTA must be absent. The method proposed was applied to determine zinc in cadmium salts using 4-(2-pyridylazo)-resorcinol (PAR) as a spectrophotometric reagent. The result achieved did not show significant difference in the accuracy and precision (95% confidence level) with those obtained by ICP–AES analysis.     

Infrared spectra of M+NO 3 − contact ion pairs in aprotic solvents and matrix isolated in the corresponding glasses

Studies of the vibrational spectra of matrix-isolated M⁺NO ₃ ^– ion pairs have been extended to glassy aprotic solvents. The deuterated form of the solvents DMSO, THF, and ACN have windows through the 7- nitrate ionv ₃(e) mode infrared region, so it was possible to clearly observe the splitting of the degeneracy of this mode,v ₃, produced by the contacting, but solvated, alkali metal cation. Primary attention has been directed to the extent to which this splitting is reduced relative to the argon matrix values. This reduction, which reflects electron-density transfer from the solvating molecules to the ion pairs, is comparable to that observed for H₂O and NH₃ matrices as the splitting is reduced to 20–35% of the argon-matrix values. The extent of reduction ofv ₃ for the different solvents has been related to Gutmann's donicity number scale with the correlation holding well for solvent molecules of comparable size, DMSO, THF and DMF, but breaking down for the smaller linear ACN, apparently because of more molecules in the cation solvation sphere. The matrix data have also been used, through comparison with spectra for saturated liquid solutions of Li⁺NO ₃ ^– , to show that the contact ion pair is the dominant species in liquid THF and ACN, whereas the ions are largely solvent separated in DMSO.     

六配位与八配位Oh对称晶场中Mn2+光谱及基态立方零场分裂研究

CaF₂晶体掺入Mn²⁺后,Mn²⁺取代了Ca²⁺,受到8个邻近的F^-所产生的八配位立方O_h对称晶场作用,Mckeever等计锋了Mn²⁺的吸收谱,其基态立方零场分裂参量α已有实验观测值。