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.     

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     

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.     

Can magnetic circular dichroism tackle the problem of site symmetry in solutions?

A new approach to unravel the site symmetry of lanthanides in solutions is presented. The magnetic circular dichroism spectra of Eu³⁺ in the symmetries D_3h, C_4v and D_2d are simulated. In these simulations, the main idea is to introduce the magnetic field along a 3-fold axis, being the resultant of the three equivalent X-, Y- and Z-direction of a cube. This implies that the parallel and perpendicular Zeeman effects are taken into account simultaneously.     

Sterospecific Syntheses and Spectroscopic Properties of Isomeric 2,4,6,8-Undecatetraenes. New Hydrocarbons from the Marine Brown Alga Giffordia mitchellae. Part IV.

Giffordene (=(2Z,4Z,6E,8Z)-2,4,6,8-undecatetraene; 9f ) and five steroisomers are new C₁₁H₁₆ hydrocarbons from the marine brown alga Giffordia mitchellae. Their synthesis is based on non-stereoselective Wittig reactions of (E)-2-alkenals with appropriate acetylenic phosphoranes and subsequent chromatographic separation of the resulting (E/Z)-pairs. The uniform enynes (>98% purity) are then stereospecifically reduced to (Z)-alkenes with Zn(Cu/Ag) in aq. MeOH at r.t. ¹³C- and ¹ H-NMR data of the new tetraenes are presented. Biosynthetically, giffordene ( 9f ) originates from dodeca-3,6,9-trienoic acid via an unstable (3Z,5Z,8Z)-1,3,5,8,-undecatetraene followed by a thermally allowed antarafacial 1,7-sigmatropic hydrogen shift to the (2Z,4Z,6E,8Z)-isomer 9f .