Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac

We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.Preprint Université de Bourgogne-mai 1990     

Two Other Interpretations of the Entringer Numbers

The Entringer's integers were introduced to enumerate the down-up (or up-down) permutations according to the first term. In a previous paper these integers are shown to enumerate André's trees according to two parameters. In this paper we prove that they enumerate the direct alternative permutations according to the absolute value of the first two terms and also according to a specified term.     

Supercritical fluid extraction for liquid chromatographic determination of carotenoids in Spirulina Pacifica algae: a chemometric approach

An experimental design procedure was used to investigate the effects of some operating parameters on the supercritical fluid extraction of carotenoids beta-carotene, beta-cryptoxanthin and zeaxanthin from Spirulina Pacifica algae, a carotenoid-rich dietary product. Variables tested were temperature and pressure of the supercritical fluid, dynamic extraction time and percentage of ethanol added as the modifier. Each variable was tested at three levels; 31 experiments were performed in random order. Analyses of the extracts were performed by high-performance liquid chromatography with UV-Vis photodiode array detection. Analytical responses (chromatographic peak areas) were processed by using a stepwise multiple regression analysis, in order to find polynomial functions describing the relationships between variables and responses. For all the analytes the experimental conditions providing the highest extraction yield inside the experimental domain considered were found. Supercritical fluid extraction results obtained in these conditions were compared with those obtained by performing solvent extraction in order to evaluate the effectiveness of the supercritical fluid extraction procedure.     

Wavelength independence of Eu quantum yields

A quantitative comparison between the excitation and absorption spectra of Eu³⁺ in aqueous solution is given which leads to the conclusion that fluorescence quantum yields are independent of the excitation wavelength. Use is made therefore of the series of homologous lines ⁵D₃, ⁵D₂, ⁵D₁, ⁵D₀ → ⁷F₁.     

Generalization of a result of Matsuo and Cherednik to the Calogero-Sutherland-Moser integrable models with exchange terms

A few years ago, Matsuo and Cherednik proved that from some solutions of the Knizhnik-Zamolodchikov (KZ) equations, which first appeared in conformal field theory, one can obtain wave functions for the Calogero integrable system. In the present communication, it is shown that from some solutions of generalized KZ equations, one can construct wave functions, characterized by any given permutational symmetry, for some Calogero-Sutherland-Moser integrable models with exchange terms. Such models include the spin generalizations of the original Calogero and Sutherland ones, as well as that with -function interaction.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995     

Detection of banned meat and bone meal in feedstuffs by near-infrared microscopic analysis of the dense sediment fraction

In this paper we present an alternative method for detection of meat and bone meal (MBM) in feedstuffs by near-infrared microscopic (NIRM) analysis of the particles in the sediment fraction (dense fraction (d >1.62) from dichloroethylene) of compound feeds. To apply this method the particles of the sediment fraction are spread on a sample holder and presented to the NIR microscope. By using the pointer of the microscope the infrared beam is focussed on each particle and the NIR spectrum (1112–2500 nm) is collected. This method can be used to detect the presence of MBM at concentrations as low as 0.05% mass fraction. When results from the NIRM method were compared with the classical microscopic method, a coefficient of determination (R²) of 0.87 was obtained. The results of this study demonstrated that this method could be proposed as a complementary tool for the detection of banned MBM in feedstuffs by reinforcement of the monitoring of feeds.     

Fluorescence study of the sol-gel process in hybrid precursors: evidence of concentration fluctuations at the local scale

Hybrid sol-gel materials have been prepared by hydrolytic polycondensation of an alkoxysilane. The sol-gel process of methacryloxypropyltrimethoxysilane (MAPTMS) has been followed by fluorescence spectroscopy with 2-naphthol as a probe. The experimental results showed that this photoprobe was dramatically sensitive to the microenvironment polarity. Spectroscopic studies revealed fluctuations of the maximum emission intensity and wavelength as a function of time. These fluctuations were attributed to the amphiphilic behavior of the hydrolyzed precursor. The maximum emission wavelength of the probe corresponding to its protonated form was higher than in pure water. All the results suggest that the presence of water molecules, tightly bonded to the polar head of the silanols, increased locally the sol polarity and induced a red-shifted emission. Fluorescence spectroscopy emphasized the reversibility of monomeric silanol aggregates and the changes in hydroxy group number of the silica network during the sol maturation. The behavior of this system upon shaking confirmed this statement.