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.     

Colorimetric determination of macrolide antibiotics using ferric ion

Macrolide antibiotics such as erythromycin, oleandomycin, spiromycin, and tylosin are found to react with Fe(3+) in the presence of an acetic acid-sulfuric acid mixture to form a colored product having a useful absorption band at 592 nm. Troleandomycin forms only a weakly colored product upon reaction. The molar absorptivity is about 2900 1 mol(-1) cm(-1) for erythromycin and the detection limit is 5 mug ml(-1). This colorimetric method permits the analysis of fermentation broths containing either erythromycin or tylosin without a separation step.     

Photoelectrochemistry on Ru(II)-2,2'-bipyridine-phosphonate-derivatized TiO2 with the I3-/I- and quinone/hydroquinone relays. Design of photoelectrochemical synthesis cells

Photocurrent measurements have been made on nanocrystalline TiO2 surfaces derivatized by adsorption of a catalyst precursor, [Ru(tpy)(bpy(PO3H2)2)(OH2)]2+, or chromophore, [Ru(bpy)2 (bpy(PO3H2)2)]2+ (tpy is 2,2':6',2' '-terpyridine, bpy is 2,2'-bipyridine, and bpy(PO3H2)2 is 2,2'-bipyridyl-4,4'-diphosphonic acid), and on surfaces containing both complexes. This is an extension of earlier work on an adsorbed assembly containing both catalyst and chromophore. The experiments were carried out with the I3-/I- or quinone/hydroquinone (Q/H2Q) relays in propylene carbonate, propylene carbonate-water mixtures, and acetonitrile-water mixtures. Electrochemical measurements show that oxidation of surface-bound Ru(III)-OH2(3+) to Ru(IV)=O(2+) is catalyzed by the bpy complex. Addition of aqueous 0.1 M HClO4 greatly decreases photocurrent efficiencies for adsorbed [Ru(tpy)(bpy(PO3H2)2)(OH2)]2+ with the I3-/I- relay, but efficiencies are enhanced for the Q/H2Q relay in both propylene carbonate-HClO4 and acetonitrile-HClO4 mixtures. The dependence of the incident photon-to-current efficiency (IPCE) on added H2Q in 95% propylene carbonate and 5% 0.1 M HClO4 is complex and can be interpreted as changing from rate-limiting diffusion to the film at low H2Q to rate-limiting diffusion within the film at high H2Q. There is no evidence for photoelectrochemical cooperativity on mixed surfaces containing both complexes with the IPCE response reflecting the relative surface compositions of the two complexes. These results provide insight into the possible design of photoelectrochemical synthesis cells for the oxidation of organic substrates.     

Some applications of thermomagnetometry to the study of chromindur alloys

Thermomagnetic experiments are shown to be a useful and rapid technique for studying phase changes involving magnetic materials. Particular examples are chosen from Chromindur II (Fe28Cr10.5Co) alloys having different thermal histories. The Curie temperature of the single phase alloy is found to be ～650°C and the metastable spinodal decomposition boundary is at essentially the same temperature. The Cr-rich near equilibrium decomposition product is less magnetic and has a lower T_c, while the Cr-deficient product is more magnetic, with a T_c ? 720°C.Comparisons are made at different heating and cooling rates between temperatures measured using magnetic standards and those measured by a thermocouple in close proximity to the sample.     

The mechanisms of decomposition of the 1- and 2-phenyltetralin radical cations

Mechanisms for decomposition of 1- and 2-phenyltetralins were investigated using low resolution mass spectrometry and metastable ion techniques. Four primary decompositions were observed for 1-phenyltetralin radical cations: (1) the loss of C₆H₆ via a 1,4-elimination; (2) the elimination of ethene via competing losses from carbons 3 + 4 and carbons 2 + 3; (3) the loss of C₈H₈, probably through a stepwise Diels-Alder cycloreversion to expel styrene; and (4) the loss of methyl radical involving carbon 2 and possibly carbon 4. Three major decompositions were observed for 2-phenyltetralin radical cations: (1) the loss of C₈H₈, possibly through a Diels-Alder cycloreversion to expel styrene; (2) the loss of C₆H₆ via a 1,3 elimination; and (3) the loss of methyl radical from carbon 1. Various exchange reactions occur prior to these losses, but they proved to be incomplete even for metastable ions.     

Effect on topical 5-methoxypsoralen on tumorigenesis induced in albino and pigmented hairless mouse skin by UV irradiation

A new line of the Skh:HRII hairless pigmented mouse (black juvenile coat) is described which has been selectively bred for the capacity to respond consistently to simulated solar UV radiation with a continuous and strong tan. This mouse demonstrates a degree of protection from chronic UV-induced tumorigenesis when compared with the Skh:HRI hairless albino mouse, and has been used here to study the effect of induced melanogenesis on phototumorigenesis. Mice were irradiated for 10 weeks with incremental doses of simulated solar UV radiation (UVA + B) from a fluorescent tube source which induced tumours in 100% of albino mice and 93% of black mice by 200 days (minimally oedemal), or with 60% of this dose (sub-oedemal) which induced tumours in 85% of albino mice and 65% of black mice. Mice were also exposed to the UVA component of these radiation sources, obtained by window glass filtration. The effect of topical 5-methoxypsoralen (5-MOP) was examined, at either 0.003% with minimally oedemal UVA + B or its UVA component alone, or at 0.01% with sub-oedemal UVA + B or its UVA component alone, in both albino and black mice. The 5-MOP concentrations were selected as the maximum concentration which did not increase the erythema and oedema responses after a single exposure to minimally oedemal or sub-oedemal UVA + B. At 200 days, the tumorigenic response to sub-oedemal UVA + B was significantly increased by topical 5-MOP, to 100% in albinos and 93% in black mice. In contrast, tumorigenesis in response to minimally oedemal UVA + B was unaffected by topical 5-MOP. The UVA component alone of either irradiation regime was not tumorigenic under these conditions. When combined with topical 5-MOP, the UVA of minimally oedemal UVA + B became moderately tumorigenic, and resulted in a tumour incidence of 23% in albinos and 14.5% in black mice. However, the UVA component of sub-oedemal UVA + B, when combined with topical 5-MOP, was highly tumorigenic specifically in albino mice, inducing tumours in 93% of albino mice but in only 27% of black mice. Tan intensity resulting from minimally oedemal UVA + B was not enhanced by topical 5-MOP, and its UVA component combined with 5-MOP resulted in only a minimal tan. However, the tan intensity resulting from sub-oedemal UVA + B with topical 5-MOP was strongly increased, although its UVA component combined with 5-MOP did not produce a perceptible tan.(ABSTRACT TRUNCATED AT 400 WORDS)