Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

Specific mass fragmentographic assay for 25,26-dihydroxyvitamin D in human plasma using a deuterated internal standard

A specific mass fragmentographic assay for the measurement of 25,26-dihydroxyvitamin D3 [25,26(OH)2D3] in human plasma, using a stable isotope labelled internal standard ([26,27-2H5]25,26(OH)2D3), is described. Plasma samples (5 ml) were extracted with acetonitrile and applied to a C18 Sep-Pak cartridge, from which the vitamin D metabolites were eluted with methanol. The metabolites were then applied to a Sep-Pak SIL cartridge and three fractions were collected. The most polar fraction, containing the polyhydroxylated metabolites, was further purified by high-performance liquid chromatography on Zorbax SIL. The eluent containing 25,26(OH)2D3 was collected, and the 25,26-n-butylboronate cyclic ester 3-trimethylsilyl ether derivative was formed. Gas chromatography-mass spectrometry was carried out, monitoring the intensities of the ions at m/z 449 and m/z 454 (for the internal standard). These ions represent the loss of a methyl group and the 3-silanol group, (M-90-15)+. The minimum limit of detection of the assay was estimated to be approximately 0.05 microgram/l. Inter-assay (3.7%) and intra-assay (8.0%) precision was acceptable and added 25,26(OH)2D3, over the concentration range 0.5-1.5 microgram/l, was recovered quantitatively. The plasma 25,26(OH)2D3 level was estimated in 26 healthy volunteers and ranged from 0.05 to 1.30 microgram/l, with a mean value of 0.54 microgram/l.     

Sigma,pi, and delta wavefunction forms for the hydrogen molecule

Using variational Monte Carlo methods, we examine simple, explicitly‐correlated trial wavefunction forms for the X¹Σ, B¹Σ, a³Σ, b³Σ, I¹Π_g, C¹Π_u, i³Π_g, c³Π_u, J¹Δ_g, and j³Δ_g states of the hydrogen molecule. The energies produced by our best wavefunctions are slightly above the best values in the literature. When we combine our trial wavefunction forms with the generalized Feynman‐Kac path integral method, our results are in excellent agreement with the best nonrelativistic values for these systems except for the I¹Π_g state. Our best energy for this state, ?0.65951554(6), is lower by several microhartrees than that obtained by Wolniewicz [J Mol Spectrosc 1995, 169, 329]. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Determination of dithiocarbamate pesticides in occupational hygiene sampling devices using the isooctane method and comparison with an automatic thermal desorption (ATD) method

Two new methods for the determination of dithiocarbamate pesticides in occupational hygiene sampling devices are described. Dithiocarbamate spiked occupational hygiene sampling devices, consisting of glass fibre (GF/A) filters, cotton pads, cotton gloves and disposable overalls, were reduced under acidic conditions and the CS2 evolved as a decomposition product was extracted into isooctane. The isooctane was then analysed using gas chromatography with mass spectrometry, for CS2, which provided a quantitative result for dithiocarbamates. Recoveries obtained were generally within a 70-110% range and reproducibilities better than 15% RSD were typically achieved. The method has been successfully applied to samples collected during occupational exposure surveys. A second method employing automatic thermal desorption-gas chromatography-mass spectrometry (ATD-GC-MS) has also been developed and applied to the direct analysis of GF/A (airborne) samples. The method relies on the thermal degradation of dithiocarbamates to release CS2, which is used to quantify the analytes. Thiram spiked GF/A filters gave an average recovery of 107% with an RSD of 4%. The performance of the two analytical methods were directly compared by analysing sub-portions of GF/A filters collected during a survey to evaluate occupational exposures to thiram during seed treatment operations. Both methods performed well for the analysis of airborne (GF/A) samples and produced results in good agreement. ATD-GC-MS is the preferred method for studies involving GF/A (airborne) samples only. Because of the wider applicability of the isooctane method for other sampling devices, it is the preferred choice when carrying out surveys which require a dermal as well as respirable exposure assessment.     

The lowest order relativistic corrections for the hydrogen molecule

We have calculated the lowest order relativistic corrections for the X ¹Σ, B¹Σ, a³Σ, b³Σ, I¹Π_g, C¹Π_u, i³Π_g, c³Π_u, J¹Δ_g, and j³Δ_g states of the hydrogen molecule using variational Monte Carlo methods and compact, explicitly correlated trial wavefunctions. Our values are in good agreement with earlier calculations on the X¹Σ and B¹Σ states. For the other states, our work provides the first estimate of these properties. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Vibrational energies of H2+ using fully nonadiabatic wavefunctions

Using variational Monte Carlo methods, we examine a number of fully nonadiabatic trial wavefunctions to determine which features best describe the lowest several vibrational states of H₂⁺. Our final energies are in excellent agreement with previous calculations. © 2012 Wiley Periodicals, Inc.     

Properties of the finite-mass helium ground state

ABSTRACT

We describe a simple method of incorporating the finite mass of the nucleus directly into atomic variational Monte Carlo calculations. To test this algorithm we computed the energy and 20 other properties of ⁴He. We then compared these values with those obtained from our earlier infinite nuclear mass algorithm. All of our expectation values are in excellent agreement with previous results on this system.