On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

A Method for Establishing Optimality Conditions for a Nonsmooth Vector-Valued Minimax Problem

Using a method of uniform approximations, necessary and sufficient conditions for a nonsmooth constrained vector-valued minimax problem are established in terms of Mordukhovich subdifferentials.     

High-precision sub-pixel interpolation in particle image velocimetry image processing

The task of image interpolation and re-sampling for particle image velocimetry (PIV) is investigated, which is used for window shifting with sub-pixel accuracy and image or window deformation. A new interpolation scheme based on a Gaussian filter is introduced and compared with commonly used and widely accepted interpolation techniques in terms of the achievable root mean square deviation of the displacement estimates.     

Improved synthesis of tocopherol fatty alcohols and analogs: microglial activation modulators

The synthesis of tocopherol fatty alcohols (TFAs), potent microglial activation modulators, was achieved via C-alkylation of trimethylhydroquinone. Several analogs, in particular water-soluble prodrugs, have been synthesized using a Wittig reaction and their antioxidant activities have been evaluated.     

Renormalization Effects in the Spectrum of a Coherently Driven Exciton–Biexciton System

Starting from the total Hamiltonian of an excited exciton–biexciton system, nonresonant renormalizations in the electronic spectrum of a coherently driven direct semiconductor are considered. Stringent group-theoretical inclusion of the particle spin in the Hamiltonian allows one to account for the dependence of different renormalization effects on polarizations of the incident laser fields. On the example of circularly polarized driving and probing pulses it is shown that the kind of observed renormalization is defined by the pump-and-probe polarization geometry. Thus, the exciton optical Stark effect must appear in the case of co-circular pump-and-probe, whereas a mixing of the polariton and biexciton spectra is possible only in the case of counter-circular pump-and-probe. The polariton--biexciton dispersion renormalization may manifest itself as synchronous splittings of the exciton--polariton and biexciton spectra under resonant pumping at a frequency of the polariton--biexciton transition, or in their shifts in opposite directions under near-resonant pumping. The mechanisms of both kinds of renormalization effects are analyzed, and the dependence of their characteristics on the pump parameters and microscopic parameters of the exciton–biexciton–photon system is established. An evaluation of the characteristics shows that the effect of polariton–biexciton dispersion renormalization dominates in the spectra of semiconductors with stable biexciton formation. Results of the theoretical study provide an adequate explanation of available experimental data.     

Determination of phosphate in hydroponic nutrient solutions using flow injection potentiometry and a cobalt-wire phosphate ion-selective electrode

The direct flow injection potentiometric (FIP) analysis of phosphate in hydroponic nutrient solution has been carried out using a cobalt-wire ion-selective electrode (ISE). Synthetic hydroponic nutrient solution, commercial hydroponic nutrient solution and working hydroponic farm nutrient solution were analysed for phosphate using the FIP technique. It is shown that FIP results compare favourably to standard methods of analysis such as spectrophotometry and indirect photometric ion-pair chromatography. Reproducible FIP response curves with a slope of −(47.57±0.03) mV per decade and intercept of −(169.7±0.1) mV were obtained for four separate calibrations in the concentration range 5.0×10⁻⁴–1.0×10⁻² M H₂PO₄⁻. Anion corrections for interferences by Cl⁻, NO₃⁻ and SO₄²⁻ were applied to all samples using the selectivity coefficients determined independently using a fixed interference method. Nevertheless, it was found that anion corrections were not necessary, as the deviations fell within the bounds of experimental error for the cobalt-wire ISE technique (i.e.±2–5% R.S.D.). The proposed FIP method enables the direct determination of phosphate in hydroponic nutrient solutions.     

Estimation of precision and efficiency mass transfer steps for the determination of pesticides in vegetables aiming at the expression of results with reliable uncertainty

A 'bottom-up' approach for the expression of results obtained from analytical methods that include analytical steps with recovery inherently different from 100% [mass transfer steps (MTS): extraction, evaporation, clean-up procedures, digestion, etc.] is presented. The estimation of the combination of all MTS uncertainty involves the comparison of the experimental dispersion of replicated analyses of spiked samples with the estimation of the uncertainty obtained for the combination of all uncertainty sources except MTS ones ('incomplete' estimation). The estimation of MTS uncertainty by difference is performed after evaluating the statistical difference between the 'incomplete' estimation and the experimental dispersion (F-test). When the two estimations are statistically equivalent, the MTS uncertainty is considered to be negligible in relation to the other sources budget. The assumption of constancy of MTS performance within the analytical range is tested through single analyses at several concentration levels and is evaluated by the inclusion of the expected values at the intervals resulting from the combination of the MTS uncertainty estimation performed at one concentration level and the 'incomplete' estimation. The developed methodology can also be useful for method optimisation and validation and for the detection of small trends in results. The determination of pesticides in sweet peppers by GC-NPD was used to explore the above concepts.     

Transpositions a etapes multiples d'epoxydes sesquiterpeniques—I : Action de l'acide formique sur l'epoxyde de cyperene. Correlation entre le cyperene et l'α-cedrene

Cyperene epoxide 2, on treatment with formic acid, gives about ten products of which the two major ones have been isolated and characterised. The allylic alcohol 3 is the product of an allylic rearrangement. The diol 5 is produced by a multistep rearrangement, the mechanism of which is remarkable in that the first elementary step cannot be concerted. The structure of the diol 5 has been confirmed by correlation with α-cedrene.     

Raman microscopy of selected tungstate minerals

A series of tungstate bearing minerals including scheelite, stolzite, ferberite, hübnerite, wolframite, russellite, tungstenian wulfenite and cuprotungstite have been analyzed by Raman microscopy. The results of the Raman spectroscopic analysis are compared with published data. These minerals are closely related and often have related paragenesis. Raman microscopy enables the selection of individual crystals of these minerals for spectroscopic analysis even though several of the minerals can be found in the same matrix because of the pargenetic relationships between the minerals. The Raman spectra are assigned according to factor group analysis and related to the structure of the minerals. These minerals have characteristically different Raman spectra. The nu1(Ag) band is observed at 909 cm(-1) and although the corresponding nu1(Bu) vibration should be inactive a minor band is observed around 894 cm(-1). The bands at 790 and 881 cm(-1) are associated with the antisymmetric and symmetric Ag modes of terminal WO2. The band at 695 cm(-1) is interpreted as an antisymmetric bridging mode associated with the tungstate chain. The nu4(Eg) band was absent for scheelite. The bands at 353 and 401 cm(-1) are assigned as either deformation modes or as r(Bg) and delta(Ag) modes of terminal WO2. The band at 462 cm(-1) has an equivalent band in the infrared at 455 cm(-1) assigned as delta(as)(Au) of the (W2O4)n chain. The band at 508 cm(-1) is assigned as nu(sym)(Bg) of the (W2O4)n chain.     

The chemistry of thujone. IX. Thujone as a chiral synthon for the synthesis of optically active steroid analogues. The vinylpicoline route

The thujone-derived enone 1 , upon base-catalyzed reaction with 2-methyl-6-vinylpyridine is converted to the pyridine analogue 5 (Scheme 1). Catalytic reduction of the latter to 6 generates two new centers of chirality which eventually become C(8) and C(14) in the ultimate synthetic steroid analogue 12 . An X-ray analysis of 6 establishes the structure and absolute configuration so as to determine its suitability in subsequent synthetic studies. The acetal derivative 7 , via Birch reduction, hydrolysis, and internal aldol cyclization, is converted into the cyclohexenone analogue 10 (Scheme 2). This ‘one-pot’ process affords an efficient conversion of the pyridine ring into a cyclohexenone system required for A-ring construction of the steroid skeleton. Finally, conversion of 10 , via the unsaturated diketone 11 , provides the chiral steroid analogue 12 .