Analysis of 19-norandrosterone in human urine by gas chromatography–isotope-dilution mass spectrometry: method adopted by LGC for participation in the Comité Consultatif pour la Quantité de Matière (CCQM) Pilot Study P68

The method used at LGC for analysis of “total” 19-norandrosterone (19-norandrosterone glucuronide plus “free” 19-norandrosterone) in urine for the Comité Consultatif pour la Quantité de Matière Pilot Study (CCQM-P68) is described. The analytical method used was a modified version of the method developed at the National Measurement Institute of Australia, which used a hydrolysis and derivatisation procedure first described by the German Sports University. This method is routinely used by World Anti-Doping Agency-accredited laboratories for sports drug testing. The main modifications made to the method were the use of 19-norandrosterone glucuronide as a calibration standard and 19-norandrosterone glucuronide-d4 as an isotopically labelled internal standard, and the use of a bench-top quadrupole gas chromatograph–mass spectrometer. The results produced by LGC (2.14 ± 0.15 ng g⁻¹ expanded uncertainty, coverage factor k = 2) were in excellent agreement with those from other participating national metrology institutes and thus further validates the exact-matching isotope-dilution mass spectrometric procedures used at LGC for a wide range of reference measurement applications, including measurement of ng g⁻¹ levels of steroids in a biological matrix.     

Calculation of the proton affinities of polyfluorobenzenes and the activation energies for 1,2-hydrogen shifts in their carbocations

Isolated polyfluorobenzene (PFB) molecules and their protonated forms are investigated by the AM1 method with full geometry optimization. The proton affinities of PFB are estimated for different protonated positions. The proton affinity of PFB averaged over all isomers is shown to decrease monotonically as the number of fluorine atoms in the molecule increases. The relative populations of different isomers of arenonium ions (AI) formed by PFB protonation are determined. From the calculated data, the value of ⁺ for the F atom in theipso-position is estimated as 1.00. The activation energies of the 1,2-hydrogen shifts in AI are calculated. The dependences of the proton affinity and the activation energies of 1,2-hydrogen shifts on the number of halogen atoms are found to have distinct characters for PFB and polychlorobenzenes. The physical reasons for these difference are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1878–1882, November, 1993.     

Kinetic model ofCO oxidation on nonuniform surface analyzed regardingCOads spillover, 2. homotopic method. Effect ofm1 surface portion

The homotopic method has been used to analyze the kinetic model of three-stageCO oxidation on two nonuniform surface patches conjugated byCO ₂ spillover. Diagrams of steady states depending on the portion of surface patchm ₁ at various temperatures and pressure ratiosP(O ₂)/P(CO) have been constructed. The ratios of different type patches corresponding to the maximum overall reaction rate have been found.     

Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

An intermediate spherical model of a ferromagnet

A one-parameter family of partition functions is considered which for zero value of the parameter reduces to the spherical model of a ferromagnet. The model for > 0 is closer to the usual discrete lattice spin model of a ferromagnet than is the spherical model. The first four terms in of the limiting value of the partition function are calculated above and below the critical temperature for arbitrary interactions using the saddle point method to calculate certain correlation functions for the spherical model. These calculations indicate that the critical temperature is independent of for small and certain interactions.Part of this research appeared in the author's doctoral thesis.⁽³⁾     

Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.     

The optimization of silica gel synthesis from chemical bottle waste using response surface methodology

To reduce the amount of hazardous chemical bottle waste in the environment, we report the optimization research of silica extraction in chemical bottle waste into silica gel. Alkali fusion and sol–gel process were utilised to prepare silica gel effectively. The alkali fusion process was carried out by adding sodium hydroxide to produce sodium silicate. Afterwards, silica gel was prepared by the sol–gel method using hydrochloric acid. Box-Behnken Design (BBD) was applied to Optimisation factors the poptimiseactors affecting the silica recovery. The factors that optimised mass ratio, particle size, and temperature. The optimum recovery of silica gel was obtained by SiO₂: NaOH mass ratio of 1:3, the particle size of 63–74 µm, and a temperature of 800 °C. The purity of silica gel optimum is 63.74% characterised using X-ray fluorescence. The structure of silica gel is the appearance of amorphous peaks at 2θ 20-30° characterised using an x-ray diffractogram. The silica gel surface was characterises using scanning electron microscopy-energy dispersive x-ray. It showed an irregular surface and characteristic showed that silica gel had a radius of 15.74 nm and a specific surface area of 297.08 m².     

Electrophoresis simulations using Chebyshev pseudo-spectral method on a moving mesh

We present the implementation and demonstration of the Chebyshev pseudo-spectral method coupled with an adaptive mesh method for performing fast and highly accurate electrophoresis simulations. The Chebyshev pseudo-spectral method offers higher numerical accuracy than all other finite difference methods and is applicable for simulating all electrophoresis techniques in channels with open or closed boundaries. To improve the computational efficiency, we use a novel moving mesh scheme that clusters the grid points in the regions with poor numerical resolution. We demonstrate the application of the Chebyshev pseudo-spectral method on a moving mesh for simulating nonlinear electrophoretic processes through examples of isotachophoresis (ITP), isoelectric focusing (IEF), and electromigration-dispersion in capillary zone electrophoresis (CZE) at current densities as high as 1000 A/m. We also show the efficacy of our moving mesh method over existing methods that cluster the grid points in the regions with large concentration gradients. We have integrated the adaptive Chebyshev pseudo-spectral method in the open-source SPYCE simulator and verified its implementation with other electrophoresis simulators.     

Synthesis and absolute configuration of (1S,8S)-as-hydrindacene-1,8-diol as determined by the circular dichroism exciton chirality method

2,3,6,7-Tetrahydro-as-indacene-1,8-dione 4 was prepared in 4 steps starting from 2-methyl-furan by modification of a literature procedure. Appliance of Noyori’s asymmetric transfer hydrogenation, resulted in (1S,8S)-1,2,3,6,7,8-hexahydro-as-indacene-1,8-diol 5 in high yield (81%) and excellent enantioselectivity (>99% ee) or (8S)-8-hydroxy-3,6,7,8-tetrahydro-2H-as-indacen-1-one 6 in moderate yield (58%) and equally high enantioselectivity (98.5% ee), depending on the conditions. The asymmetric reduction was expected to yield the (S)-alcohols using the (S,S)-Ts-DPEN ligand, which was confirmed by the appliance of the exciton chirality method on the corresponding bis(p-dimethylamino)benzoate 7.     

GRECP/MRD‐CI calculations on the Hg atom and HgH molecule

Multireference single‐ and double‐excitation configuration interaction (MRD‐CI) calculations of transition energies for the Hg atom and spectroscopic constants for the HgH molecule are carried out with the generalized relativistic effective core potential (GRECP) method. A new selection criterium for the reference configurations is discussed. The calculated spectroscopic constants are compared with experimental data and results of calculations of other groups. Improvement of accuracy is mainly observed for bond lengths from the GRECP/MRD‐CI calculations (without applying the T = 0 correction) with respect to the results of other groups. Analysis of the quality of the approximations employed is carried out. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002