Produits1 de Kontsevich sur le fibré cotangent d'un groupe de Lie et formules intégralesKontsevich star products on the cotangent bundle of a Lie group and integral formulae

We describe a large class of natural star products on the cotangent bundle $\text{T}{}^1\text{G}$ of a Lie group G and we characterize these star products by integral formulae. To cite this article: K. Tounsi, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 783–786.     

Equations des variétés de Kummer

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Electroluminescence from a current-emitting nanostructured silicon device

A three-dimensional silicon based nanodevice mainly consisting of two conductive silicon cantilevers was fabricated out of silicon-on-insulator material by electron beam lithography, reactive ion etching, and fluoride based wet chemical etching. One of the cantilevers is bent and sticks to the silicon substrate while the other one is freely suspended. We observed electroluminescence in the visible range when a voltage of any polarity is dropped across both levers. The measured spectra covered the range 400–950 nm peaking at about 650 nm. The current applied to the device could tune the intensity of the electroluminescence spectrum. Light powers ranging from 160 fW to some pW were measured at frequencies up to 17 kHz. The origin of the electroluminescence is discussed in comparison to porous silicon and spark-processed silicon.     

Polarographic reduction and tautomeric structure of 2-amino-5-arylazothiazoles

The polarographic behaviour of a series of 2-amino-4-phenyl-5-arylazothiazoles has been investigated at a dropping mercury electrode. Each of the compounds studied exhibits one wave which was shown to correspond to the reductive cleavage of the azo linkage by a 4e irreversible step. On the basis of the polarographic data, it was concluded that the compounds exist only in one tautomeric form, namely the aminoazo structure 1 . The results of E_1/2 — σ_X correlations and HMO calculations of bonding energies of the various possible tautomeric forms 1–3 indicate that the aminoazo form 1 is the most stable structure of the compounds examined.     

Sun-reactive Skin Type in 4912 French adults participating in the SU.VI.MAX study

Phototype classifications were initially developed in an attempt to predict the skin reactions of patients to phototherapy and are now widely used to advise individuals with regard to sun protection. A transversal study was conducted on the SU.VI.MAX cohort to estimate the frequency of sun-reactive skin features in a large, general adult population-based sample, and to describe the associations between these features. The data were collected 3 years after the beginning of the SU.VI.MAX nutritional intervention study on 4912 volunteers (2868 women aged 35-60 years and 2044 men aged 45-60 years). A multiple correspondence analysis was performed to study the associations between the features. The results showed that these features correspond to a one-dimensional phenomenon, which allowed us to establish a score to summarize skin sensitivity to sun exposure. Furthermore, we found a link between gender and phototype using the Césarini classification (phototype > or = IV: 37% of women, 47% of men). The analysis of the relationship with sun-reactive skin features and the score revealed the same trend. Phenotypic evaluation appears to be a good estimator of skin sensitivity to sun exposure for clinical screening or for use in research, and is easy to collect at a lower cost. Moreover, the sun sensitivity difference between gender should be considered in education about photoprotection.     

Phytochemical study and cytotoxicity evaluation of Colchicum stevenii Kunth (Colchicaceae): a Jordanian meadow saffron

Isolation, characterization, and biological evaluation of active components of Colchicum stevenii Kunth (Colchicaceae) are described. Colchicum stevenii is an unexplored Jordanian specie with toxic reputation. Directed by brine shrimp lethality test (BST), methanolic extraction, liquid-liquid partition, preparative TLC, and semi-preparative HPLC, it resulted in the isolation of six cytotoxic compounds. The compounds, reported for the first time from this specie, are: (-)-colchicine (1), 2-demethyl-(-)-colchicine (2), (-)-cornigerine (3), beta-lumicolchicine (4), (-)-isoandrocymbine (5) and (-)-O-methylandrocymbine (6). A new, in-house developed, acidic-based reverse-phase gradient semi-preparative HPLC method for the separation of colchisides is presented here. Structural elucidation was based on spectroscopic techniques principally; 1H-NMR and low resolution EIMS. Based on BST results, reported as LC50 values in microg mL(-1) (ppm) with 95% confidence intervals, (-)-colchicine (2.5 ppm) and (-)-cornigerine (2.7 ppm) were the most potent.     

Calculating slow-motional electron paramagnetic resonance spectra from molecular dynamics using a diffusion operator approach

A number of groups have utilized molecular dynamics (MD) to calculate slow-motional electron paramagnetic resonance (EPR) spectra of spin labels attached to biomolecules. Nearly all such calculations have been based on some variant of the trajectory method introduced by Robinson, Slutsky and Auteri (J. Chem. Phys. 1992,96, 2609-2616). Here we present an alternative approach that is specifically adapted to the diffusion operator-based stochastic Liouville equation (SLE) formalism that is also widely used to calculate slow-motional EPR line shapes. Specifically, the method utilizes MD trajectories to derive diffusion parameters such as the rotational diffusion tensor, diffusion tilt angles, and expansion coefficients of the orienting potential, which are then used as direct inputs to the SLE line shape program. This approach leads to a considerable improvement in computational efficiency over trajectory-based methods, particularly for high frequency, high field EPR. It also provides a basis for deconvoluting the effects of local spin label motion and overall motion of the labeled molecule or domain: once the local motion has been characterized by this approach, the label diffusion parameters may be used in conjunction with line shape analysis at lower EPR frequencies to characterize global motions. The method is validated by comparison of the MD predicted line shapes to experimental high frequency (250 GHz) EPR spectra.     

Magnetic properties of RE0.7Ca0.3Mn0.95Fe0.05O3 (RE=Sm and Gd) manganites at low temperature

The magnetic properties of RE_0.7Ca_0.3Mn_0.95Fe_0.05O₃ perovskite with rare-earth cations (RE=Sm and Gd) were investigated by means of X-ray diffraction, Mössbauer spectroscopy, and low temperature (4.2-266 K) magnetization measurements. Structural characterization of these compounds shows that they both have orthorhombic (Pbnm) structure. The Mössbauer spectra show clear evidence of local structural distortion of the Mn(Fe)O₆ octahedron, which is based on the non-zero nuclear quadrupole interactions for high-spin Fe³⁺ ions. It was found that the local structural distortion increases significantly when Sm³⁺ is replaced by Gd³⁺. This distortion is attributed to the Jahn-Teller coupling strength as estimated from the Mössbauer effect results. The magnetic results indicate that the Curie temperature decreases as a result of replacing Sm by Gd. This is due to the decrease of the average A-site cationic radius 〈r_A〉. The rapid increase of magnetization at low temperature indicates the magnetic ordering of rare earth ions at the A-site.     

A sharper decay rate for a viscoelastic wave equation with power nonlinearity

We consider a viscoelastic wave equation with power nonlinearity. First, we construct a local solution by the Faedo-Galerkin approximation scheme and contraction mapping theorem. Next, we continue the local solution to the global one by a priori estimates obtained from a decreasing energy. Finally, we discuss the decay rate of the global solution by assuming that the kernel function is convex.