Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

New access to H-phosphonates via metal-catalyzed phosphorus-oxygen bond formation

A novel approach to H-phosphonates from hypophosphorous acid using a transfer hydrogenation process was developed. This method is atom-economical, environmentally friendly, catalytic, and efficient, leading easily to H-phosphonate monoesters or ammonium salt in moderate to good yields.     

THE PHOTOTOXICITY OF 2,5-DIPHENYLOXAZOLE (POP) AND 1,4-BIS(5-PHENYLOXAZOL-2-YL)BENZENE (POPOP)

Abstract 2,5-Diphenyloxazole (POP) is widely used for the determination of radioactivity by scintillation counting. It has been found to be phototoxic to the yeasts Saccharomyces cerevisiae and Candida utilis , to the first instar larvae of the mosquito Aedes aegypti , to the crustaceans Daphnia magna and Artemia salida , as well as to the eggs of Drosophila melanogaster . The related molecule 1,4-bis(5-phenyloxazol-2-yl)benzene (POPOP) is also phototoxic, but to a lesser degree. Both POP and POPOP can sensitize the formation of singlet oxygen.     

Expedient synthesis of substituted imidazoles from nitriles

Expedient and practical new methodology for the synthesis of substituted imidazoles was developed to provide a rapid access to a variety of 2-substituted, 1,2-disubstituted and 1,2,4-trisubstituted imidazoles by the direct CuCl-mediated reaction of nitriles with α-amino acetals in an intermolecular as well as intramolecular fashion.     

Size, shape, and structural control of metallic nanocrystals

In this review, we show that chemical reduction in colloidal assemblies favors the formation of size- and shape-controlled metallic nanoparticles. The key parameters that make possible the size control of spherical nanoparticles produced in spherical reverse micelles are the degree of hydration of the reactants, the dynamic character of the micelles, the capping with the surfactant, and the reducing agent concentration. The particle shape can be controlled by combining the strategy of the surfactant-based template and the capping of salts or molecules. Proof of the quality of the samples is given by the observation of two- and three-dimensional spontaneous self-organizations.     

Complexation of Al(III) by 8-Hydroxyquinoline and Drastic Fluorescence Enhancement in Reverse Micelles

Complexation of Al^IIIby 8-hydroxyquinoline and fluorescence behavior of the quinolinate(s) were studied in reverse micellar systems at low water content, and compared to aqueous media. Two surfactants were used: one was cationic (CTAC: cetyltrimethylammonium chloride) and the other was anionic (AOT: sodium bis(2-ethylhexyl)sulfosuccinate). The results obtained in the CTAC/dichloromethane system (W= [H₂O]/[surfactant] = 0.9) showed that complexation occurred very likely in the oil phase and no micellar effect was observed. On the contrary, in the presence of AOT, specific micellar effects were observed due to the presence of the anionic polar heads: stabilization of the positively charged 1:1 and 1:2 chelates, at the expense of the neutral water-insoluble 1:3 chelate which is formed in aqueous solutions under similar conditions;drastic fluorescence enhancement factorsof 120 and 100 in AOT/heptane (W= 1.5) and AOT/dichloromethane (W= 1.6), respectively. Such factors have never been reported so far in either hydroorganic or direct micellar systems. In return, the length of time for the production of the complex(es) is increased because of the microheterogeneity of the medium and the small sizes of the water pools.     

Probing the glycosidic linkage: UV and IR ion-dip spectroscopy of a lactoside

The beta(1-->4) glycosidic linkage found in lactose is a prevalent structural motif in many carbohydrates and glycoconjugates. Using UV and IR ion-dip spectroscopies to probe benzyl lactoside isolated in the gas phase, we find that the disaccharide unit adopts only a single, rigid structure. Its fully resolved infrared ion-dip spectrum is in excellent agreement with that of the global minimum structure computed ab initio. This has glycosidic torsion angles of phi(H) (H1-C1-O-C4') approximately 180 degrees and psi(H) (C1-O-C4'-H4') approximately 0 degrees which correspond to a rotation of approximately 150 degrees about the glycosidic bond compared to the accepted solution-phase conformation. We discuss the biological implications of this discovery and the generality of the strategies employed in making it.     

Glycoconjugate libraries accessed by multicomponent reactions

Glycobiology opens a wide field for new therapeutic approaches. However, the complexity and unavailability of various carbohydrate test compounds has excluded this class of natural products from modern screening systems. Alternatively, glycomimetics are considered to be more drug-like candidates for development. By means of multicomponent condensations (MCCs) utilizing suitable carbohydrate synthons, rapid and effective access to glycoconjugate libraries can be obtained. The flexibility of MCCs allows the assembly of diverse carbohydrate containing libraries. It may be assumed that MCCs containing carbohydrate moieties will play an important role in glycomimetic chemistry and biology.