The Webster scalar curvature problem on the three dimensional CR manifolds

In this paper, we prove some existence results for the Webster scalar curvature problem on the three dimensional CR compact manifolds locally conformally CR equivalent to the unit sphere S³ of C². Our methods are based on the techniques related to the theory of critical points at infinity.     

Isolation and structure determination of a novel furanic ester from the aerial part of Prasium majus

The aerial part of Prasium majus provided a new furanic ester, 2-2-[(5-formyl-6[(5-formylfuran-2-yl)methoxy] succinic acid dimethyl ester, (+/-)-hiziprafuran. Its structure was principally established by one- and two-dimensional NMR spectroscopy.     

Bayesian Unsupervised Learning for Source Separation with Mixture of Gaussians Prior

This paper considers the problem of source separation in the case of noisy instantaneous mixtures. In a previous work [1], sources have been modeled by a mixture of Gaussians leading to an hierarchical Bayesian model by considering the labels of the mixture as i.i.d hidden variables. We extend this modelization to incorporate a Markovian structure for the labels. This extension is important for practical applications which are abundant: unsupervised classification and segmentation, pattern recognition and speech signal processing. In order to estimate the mixing matrix and the a priori model parameters, we consider observations as incomplete data. The missing data are sources and labels: sources are missing data for observations and labels are missing data for incomplete missing sources. This hierarchical modelization leads to specific restoration maximization type algorithms. Restoration step can be held in three different manners: (i) Complete likelihood is estimated by its conditional expectation. This leads to the EM (expectation-maximization) algorithm [2], (ii) Missing data are estimated by their maximum a posteriori. This leads to JMAP (Joint maximum a posteriori) algorithm [3], (iii) Missing data are sampled from their a posteriori distributions. This leads to the SEM (stochastic EM) algorithm [4]. A Gibbs sampling scheme is implemented to generate missing data. We have also introduced a relaxation strategy into these algorithms to reduce the computational cost which is due to the exponential influence of the number of source components and the number of the mixture Gaussian components.     

Self-adjointness of the perturbed wave operator on

We give classes of unbounded real-valued for which is self-adjoint on , , where is the wave operator defined on .

     

Electronic passivation of silicon surfaces by halogens

We report the electronic passivation of a silicon surface by iodine termination. The resulting surface recombination velocity on Si(100) is less than 1 cm/s which is better than that obtained in concentrated hydrofluoric acid (HF). We have produced a surface recombination velocity of 20 cm/s using bromine. We present a simple model for these phenomena of a surface coverage of Si-X where X is a monovalently bonded halogen atom. The effectiveness of the passivation by halogens is shown to be limited by the oxidation of halogens by dissolved oxygen in solution. We demonstrate the use of halogen:methanol solutions as an alternative to HF for the control of silicon surface chemistry.     

Structure-antibacterial activity relationship of secondary metabolites from Ajuga pseudoiva Rob. leaves

A selection of steroids, glycerides, clerodane diterpenoids, and a beta-hydroxy fatty acid methyl ester, all previously isolated from Ajuga pseudoiva leaves, were tested for their antibacterial activity toward three Gram- rods and one Gram+ coccus using the dilution method; MIC values were determined. The results suggested some importance for a free beta-hydroxy group in the fatty acid ester and also in the glycerides and clerodane derivatives; the absolute configurations of the latter, notably at C2, had little influence on activity.     

Echiofruzine, a novel naringenin diglycoside from Echiochilon fruticosum growing in Tunisia

The aerial parts of the Tunisian plant Echiochilon fruticosum yielded a novel flavonol diglycoside: naringenin-5-O-beta-D-glycopyranoside-3-O-alpha-L-rhamnopyranoside, named Echiofruzine (1), together with the known compounds vomifoliol-9-O-beta-D-glucopyraroside (2), 1-oxo-alpha-ionyl-9-O-beta-D-glucopyranoside (3) and 1-O-[beta-D-xylopyranosyl(1 --> 6)-beta-D-glucopyranosyl] eugenol (4), described for the first time in the indicated plant. The structures of the four isolated compounds were established on the basis of chemical and spectroscopic evidence.