Continuous Data Assimilation Using General Interpolant Observables

We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible two-dimensional Navier–Stokes equations. These ideas are motivated by the fact that dissipative dynamical systems possess finite numbers of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages which govern their long-term behavior. Therefore, our algorithm allows the use of any type of measurement data for which a general type of approximation interpolation operator exists. Under the assumption that the observational measurements are free of noise, our main result provides conditions, on the finite-dimensional spatial resolution of the collected data, sufficient to guarantee that the approximating solution, obtained by our algorithm from the measurement data, converges to the unknown reference solution over time. Our algorithm is also applicable in the context of signal synchronization in which one can recover, asymptotically in time, the solution (signal) of the underlying dissipative system that is corresponding to a continuously transmitted partial data.     

Effect of Hibiscus sabdariffa and its anthocyanins on some reproductive aspects in rats

An aqueous extract of Hibiscus sabdariffa L. is a common beverage in many parts of the world. Reports on its effect on reproduction are conflicting, with anecdotal evidence that the plant is an aphrodisiac, while others report that it is estrogenic, and adversely affects spermatogenesis in rats. We have studied the effect of different concentrations of aqueous extracts of H. sabdariffa calyces (10%, 15% and 20%) used as drinking water for 10 consecutive weeks, and its anthocyanins (50, 100, 200 mg/kg for 5 days, orally) on the weight and histology of the testis, and on some biochemical constituents in testicular homogenates, in addition to the plasma concentrations of testosterone, luteinizing hormone and estradiol. The possible presence of an estrogenic effect of the extract and anthocyanins on the uteri of immature female rats was also tested. Neither the H. sabdariffa extract nor the anthocyanins significantly altered either testicular weight and histology, or uterus weight. Plasma concentrations of the three hormones studied, the testicular concentrations of protein, reduced glutathione and total cholesterol, and superoxide dismutase activity were all insignificantly affected by either the extract or the anthocyanins, except for a slight, but statistically significant, decrease in testicular protein concentration caused by the 15% aqueous extract when compared with controls. These results suggest that H. sabdariffa exerts no adverse effect on the male reproductive system. Consumption of H. sabdariffa aqueous extract inhibited the growth of the rats compared with the controls.     

Structure, microstructure and ionic conductivity of the solid solution LiTi2−xSnx(PO4)3

The Nasicon compounds with the composition LiTi_2−xSn_x(PO₄)₃ (x=0-1.8) were synthesised by the solid state reaction. Their structures were determined from X-ray powder diffraction using Rietveld analysis. All the compositions present the space group R-3c. The refinements show that the Ti and Sn cations are statistically distributed over the same position while the Li ones are exclusively located on the M1 site. The lattice constants a and c exhibit linear variation over the whole composition range. The bond lengths are in accordance with those of other Nasicon structures. The SEM micrographs of the samples show relative porous microstructures. The ionic conductivity is about 10⁻⁴-10⁻⁵ S cm⁻¹; for the activation energy, a typical value of 0.32 eV is obtained for x=0.6 composition whereas significant deviation from linearity in the temperature dependence of the dc conductivity, is observed for the Sn-rich ones. This tendency is discussed along with the structural features.     

ADSORPTION DU COLLAGENE TYPE I SUR UNE APATITE PHOSPHOCALCIQUE DEFICIENTE

L'interaction d'un phosphate de calcium déficient, de structure apatitique, avec le collagéne hydrosoluble en milieu ayant les paramètres physico-chimiques équivalents à ceux du liquide physiologique montre que la fixation du collagène est un phénomène très rapide. Elle est régit par le modèle d'adsorption de Langmuir. L'étude en fonction des configurations probables de la molécule de collagène et des surfaces occupées correspondantes montre que l'adsorption du collagène se fait de façon préférentielle selon la position longitudinale.

The interaction of an apatitic, poorly crystallized calcium phosphate with water-soluble collagen in physiological NaCl solution shows that the fixation of collagen is very fast. It can be described by the Langmuir model. The adsorption of collagen occurs preferably in longitudinal position on the calcium phosphate surface.     

A mild and selective method for the N-Boc deprotection by sodium carbonate

A cleavage of N-tert-butyloxycarbonyl protection by Na₂CO₃ is reported. The N-free products are obtained in excellent yields. The compatibility of the method with the presence of acidic or basic groups is demonstrated. The reactions were performed on indole, azaindole, indazole, pyrazole, indolinone, quinolinone, and oxazolone.     

The photophysical properties of short, linear arrays of ruthenium(II) tris(2,2′-bipyridine) complexes

A series of linear polynuclear ruthenium(II) tris(2,2′-bipyridine) complexes has been synthesized whereby individual chromophores are separated by 1,4-diethynylenebenzene subunits bearing alkoxy groups for improved solubility. These arrays contain two, three, four or five metal centers. The compounds are reasonably soluble in polar organic solvents and they possess optical absorption spectral properties that are dominated by transitions associated with the polytopic ligand. Weak luminescence is observed for each complex in deoxy genated acetonitrile at room temperature that appears to be characteristic of emission from a metal-to-ligand charge-transfer triplet state. The emission lifetime is essentially independent of temperature, at least over a modest range. There is no indication for interaction between close-lying triplet states and no obvious sign of a low-energy τ, τ^* triplet associated with the polytopic ligand. The photophysical properties suggest that the longer arrays are segmented.     

Synthesis of cyclopentathiophenacetic acid derivatives. Reactivity of methyl 6-oxo-4,5-dihydro-6H-cyclopenta[b]thiophen-4-acetate

Oxodihydrocyclopentathiophenacetic acids 4 , 5 and 6 were synthesized from suitable 2- or 3-formylthiophenes. Reactivity of the carbonyl group or the carboxylic group of these bicyclic systems was investigated. The Beckmann rearrangement of methyl 6-oximino4,5-dihydro-6H-cyclopenta[b]thiophen-4-acetate 12 is an interesting route to methyl 7-oxo-4,5,6,7-tetrahydrothieno[2,3-c]pyridin-4-acetate ( 13 ).     

Sur les graphes 2-reconstructibles

Let k be an integer (k?1) and G=(V,E) a graph with more than k vertices, a graph G′=(V,E′) is a k-reconstruction of G if, for any subset W of V with k elements, the subgraphs G(W) and G′(W) induced by W are isomorphic. The graph G is k-reconstructible when each k-reconstruction of G is isomorphic to G. Lopez (Z. Math. Logik Grundlag. Math. 24 (1978) 303–317) proved that any graph is 6-reconstructible. For k=3,4 and 5, the k-reconstructible graphs were studied in Boudabbous and Lopez (Eur. J. Combin. 23 (2002) 507–522; C. R. Acad. Sci. Paris, Sér. I 329 (1999) 845–848). In this Note, we introduce a permutations group allowing for the interpretation of the 2-reconstructibility and we characterize the graphs which are embedded in a 2-reconstructible graph. To cite this article: A. Boussairi, A. Chaichaa, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

A new sorbent for europium nitrate extraction: phosphonic acid grafted on polystyrene resin

A new chelating polymeric sorbent has been developed using polystyrene resin grafted with phosphonic acid. After characterization by FTIR and elementary analysis, the new resin has been investigated in liquid–solid extraction of europium(III). The results indicated that phosphonic resin could adsorb Eu(III) ion effectively from aqueous solution. The adsorption was strongly dependent on pH of the medium with enhanced adsorption as the pH value of 6.5. The influence of other analytical parameters including contact time, amount of resin, metal ion concentration, and ionic strength were investigated. The maximum uptake capacity of Eu(III) ions was 122.6 mg/g grafted resin at ambient temperature, at an initial pH value of 6.50. The overall adsorption process was best described by pseudo first-order kinetic. When Freundlich and Langmuir isotherms were tested, the latter had a better fit with the experimental data. Furthermore, Eu(III) could be eluted by using 1.0 mol/L H₂SO₄ solution and the grafted resin could be regenerated and reused.