On the characteristic polynomial of the almost Mathieu operator

Let be the rotation C*-algebra for angle . For with and relatively prime, is the sub-C*-algebra of generated by a pair of unitaries and satisfying . Let

be the almost Mathieu operator. By proving an identity of rational functions we show that for even, the constant term in the characteristic polynomial of is .

     

Determination of ethyl-glucuronide in hair for heavy drinking detection using liquid chromatography-tandem mass spectrometry following solid-phase extraction

The detection of ethyl-β-d-6-glucuronide (EtG), a stable phase II metabolite of ethanol, is of interest in both clinical and forensic contexts with the aim of monitoring alcohol abuse. We present a liquid chromatography-electrospray ionisation-tandem mass spectrometry method for the detection and quantification of EtG in hair. Thirty milligrams of washed and cut hair were cleaned up using solid-phase extraction graphite cartridges. Separation was then performed using an Uptisphere-3SI column, and the detection was operated in the negative mode. After validation, the method was applied to hair samples taken from four fatalities (F) with documented excessive drinking habits, 12 heavy drinkers (HD) and seven social drinkers (SD). The method exhibits limits of detection and quantification of 4 and 10 pg/mg, respectively. Intra- and inter-assay standard deviation and relative bias were less than 20% over the calibrating range (10 to 3,000 pg/mg). EtG hair concentrations in SD were <10 pg/mg and >50 pg/mg for F and HD (range, 54 to 497 pg/mg). The present assay appears convenient to carry out owing to the very small quantity of hair samples required to determine an effective heavy alcohol consumption (EtG hair concentration >50 pg/mg).     

Photoionization cross sections for isoelectronic sequences of Ne,Ne+, Ne++

The evolution of the behaviour of photoionization cross sections relative to 2p subshell inside some isoelectronic sequences (Ne, Ne⁺, Ne⁺⁺) is pointed out, using a single electron model, with a central and non Coulombian potential.     

Efficient syntheses of streptocarpone and (±)-α-dunnione

An efficient divergent synthesis of both streptocarpone and racemic α-dunnione from lawsone are described. A one-pot, formal [3+2] cyclization to form a furanonaphthoquinone directly provided a common intermediate.     

Polarizable empirical force field for nitrogen‐containing heteroaromatic compounds based on the classical Drude oscillator

The polarizable empirical CHARMM force field based on the classical Drude oscillator has been extended to the nitrogen‐containing heteroaromatic compounds pyridine, pyrimidine, pyrrole, imidazole, indole, and purine. Initial parameters for the six‐membered rings were based on benzene with nonbond parameter optimization focused on the nitrogen atoms and adjacent carbons and attached hydrogens. In the case of five‐member rings, parameters were first developed for imidazole and transferred to pyrrole. Optimization of all parameters was performed against an extensive set of quantum mechanical and experimental data. Ab initio data were used for the determination of initial electrostatic parameters, the vibrational analysis, and in the optimization of the relative magnitudes of the Lennard‐Jones (LJ) parameters, through computations of the interactions of dimers of model compounds, model compound‐water interactions, and interactions of rare gases with model compounds. The absolute values of the LJ parameters were determined targeting experimental heats of vaporization, molecular volumes, heats of sublimation, crystal lattice parameters, and free energies of hydration. Final scaling of the polarizabilities from the gas‐phase values by 0.85 was determined by reproduction of the dielectric constants of pyridine and pyrrole. The developed parameter set was extensively validated against additional experimental data such as diffusion constants, heat capacities, and isothermal compressibilities, including data as a function of temperature. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits

We report on a fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms for 8-point functions. The measured visibility of the 8-path interferometer is about 97.5%. Potential applications of our setup to quantum communication or cryptographic protocols using several qubits are discussed.     

Experimental error filtration for quantum communication over highly noisy channels

Error filtration is a method for encoding the quantum state of a single particle into a higher dimensional Hilbert space in such a way that it becomes less sensitive to noise. We have realized a fiber optics demonstration of this method and illustrated its potentialities by carrying out the optical part of a quantum key distribution scheme over a line whose phase noise is too high for a standard implementation of BB84 to be secure. By filtering out the noise, a bit error rate of 15.3% +/- 0.1%, which is beyond the security limit, can be reduced to 10.6% +/- 0.1%, thereby guaranteeing the cryptographic security.     

Polarizable empirical force field for aromatic compounds based on the classical drude oscillator

The polarizable empirical CHARMM force field based on the classical Drude oscillator has been extended to the aromatic compounds benzene and toluene. Parameters were optimized for benzene and then transferred directly to toluene, with parameters for the methyl moiety of toluene taken from the previously published work on the alkanes. Optimization of all parameters was performed against an extensive set of quantum mechanical and experimental data. Ab initio data was used for determination of the electrostatic parameters, for the vibrational analysis, and in the optimization of the relative magnitudes of the Lennard-Jones parameters. The absolute values of the Lennard-Jones parameters were determined by comparing computed and experimental heats of vaporization, molecular volumes, free energies of hydration, and dielectric constants. The newly developed parameter set was extensively tested against additional experimental data such as diffusion constants, heat capacities at constant pressure, and isothermal compressibilities including data as a function of temperature. Moreover, the structures of liquid benzene, liquid toluene, and solutions of each in water were studied. In the case of benzene, the computed and experimental total distribution function were compared, with the developed model shown to be in excellent agreement with experiment.