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.     

RSOS Models and Jantzen–Seitz Representations of Hecke Algebras at Roots of Unity

A special family of partitions occurs in two apparently unrelated contexts: the evaluation of one-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras H_m. We provide an explanation of this coincidence by showing how the irreducible H_m-modules which remain irreducible under restriction to H_{m_1} (Jantzen–Seitz modules) can be determined from the decomposition of a tensor product of representations sl_n.     

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).     

Gas-phase ion/molecule reactions between dimethoxyphosphonium ions and aromatic hydrocarbons

Ion/molecule reactions between O=P(OCH(3))(2)(+) phosphonium ions and six aromatic hydrocarbons (benzene, toluene, 1,2,4-trimethylbenzene, naphthalene, acenaphthylene and fluorene) were performed in a quadrupole ion trap mass spectrometer. The O=P(OCH(3))(2)(+) phosphonium ions, formed by electron impact from neutral trimethyl phosphite, were found to react with aromatic hydrocarbons (ArHs) to give (i) an adduct [ArH, O=P(OCH(3))(2)](+) and (ii) for ArHs which have an ionization energy below or equal to 8.14 eV, a radical cation ArH(+ *) by charge transfer reaction. Collision-induced dissociation experiments, which produce fragment ions other than the O=P(OCH(3))(2)(+) ions, indicate that the adduct ions are covalent species. Isotope-labeled ArHs were used to elucidate fragmentation mechanisms. The charge transfer reactions were investigated using density functional theory at the B3LYP/6-311 + G(3df,2p)//B3LYP/6-31G(d,p) level of theory. The potential energy surface obtained from B3LYP/6-31G(d,p) calculations for the reaction between O=P(OCH(3))(2)(+) and benzene is described.     

Calcul théorique des énergies de divers arrangements géométriques de la molécule (η5-C5H5)2TiCl2

The molecular energy of the complex (η⁵-C₅H₅)₂TiCl₂ has been calculated for experimental geometry and for several hypothetical forms by a semi-empirical CNDO/2 approach. The energy difference between experimental (quasi-tetrahedral) geometry and a planar geometry is ca. 20 kcal mol^?1. This difference is sufficiently high to explain the difficulty of the inversion process.     

The reaction of amines with phthalimide derivatives a convenient synthesis of isoxazolidine

The reaction of tert-butylamine, isoxazolidine and hydrazine with N-[(3-chloropropyl)oxy]phthalimide is investigated. A convenient synthesis of oxazolidine is described.     

Differentiation of isomeric 5- and 7-oxo derivatives of tetrahydrothiazolo[3,2-a]pyrimidine by electron impact mass spectrometry

The electron impact mass spectra of two series of 5-oxo-tetrahydro-5H-thiazolo [3,2-a]pyrimidine-6-ethylcarboxylates and 7-oxo-tetrahydro-7H-thiazolo [3,2-a]pyrimidine-6-ethylcarboxylates were measured and fragmentation patterns examined. Structures were assigned from analysis of oxo molecular ion fragmentations. Compounds of the 5-oxo series gave an [M – CO₂C₂H₅]⁺ fragmentation whereas compounds of the 7-oxo series gave three characteristic cleavages. This decomposition was confirmed for one pair of isomers by high-resolution mass spectrometry and unimolecular mass-analysed ion kinetic energy spectrometry. Electron impact mass spectrometry is a convenient method for assigning structures of 5- and 7-oxo regioisomers of tetrahydrothiazolo[3,2-a]pyrimidine-6-carboxylates.     

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.     

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.