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.     

Synthesis of Functionalized (2-Thienylcarbonyl)thiazoles and 4-(2-Thienyl)pyridines by Reaction of (2-Thienylcarbonyl)thioacetanilides and their Enamine Derivatives

Summary. The condensation of two molecules of 2-(2-thienylcarbonyl)thioacetanilides catalyzed by piperidine yielded thiazole derivatives as confirmed by X-ray crystal structure analysis. The reaction of malononitrile with 3-morpholino-3-(2-thienyl)acrylic acid thioanilides furnished 6-amino-1-aryl-4-(2-thienyl)-1,2-dihydro-2-thioxopyridine-5-carbonitriles. A similar reaction of malononitrile with 3-morpholino-3-(2-thienyl)acrylic acid anilides provided 2-oxopyridine-5-carbonitriles.     

Thermal oxidation of cellulose investigated by chemiluminescence. The effect of magnesium and calcium carbonates and of different pHs

Whatman cellulose impregnated with calcium and magnesium carbonates was oxidized and chemiluminescence accompanying this oxidation has been measured. It was shown that magnesium ions in deacidified cellulose pulp promote the light emission significantly. On the other hand, acid papers give the more pronounced light signals at temperatures close to ambient. The relation between chemiluminescence runs and paper degradation has been implicated, with an attempt to extrapolate half-lives of paper samples to conditions close to ambient. To cite this article: J. Rychlý et al., C. R. Chimie 9 (2006).     

Die Reduktion von Ammoniumpolyuranat zu Urandioxid

Zusammenfassung Es werden die Resultate des isothermen Zerfalles und der Reduktion vonstandardisiertem Ammoniumpolyuranat im Bereich von 285 bis 463° C (in Wasserstoff) wiedergegeben. Der Zerfall zu UO₃ wurde schon bei einer Temp. unter 290° C festgestellt, diese Phase blieb jedoch darauf stabil bis 320° C. Zwischen 320° C und 380° C verläuft die Reduktion zu U₃O₈, über 380° C aber zu UO₂. Die Aktivierungsenergien bei der Reduktion von UO₃ zu U₃O₈ und von U₃O₈ zu UO₂ wurden berechnet, und zwar 32,2 kcal/g-mol und 41,7 kcal/g-mol. Die Ergebnisse können mit den Literaturangaben für die Reduktion der einzelnen Phasen UO₃ und U₃O₈ verglichen werden. Die beobachteten Unterschiede weisen auf den Einfluß der Aktivität der Präparate hin.

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The isothermal decomposition and reduction of ammonium polyuranate (ADU) was investigated in the temperature interval 285–463° C in hydrogen. The formation of UO₃ was noticed below 290° C and this product was stable up to 320° C. U₃O₈ was stable from this temperature on up to 380° C, where the reduction to UO₂ was observed. The activation energies 32,2 Kcal/mole and 41.7 Kcal/mole were calculated for the reduction of UO₃ to U₃O₈ and for the reduction of U₃O₈ to UO₂, respectively. The results are comparable with the published data on reduction of separate phases UO₃ and U₃O₈. Some differences noticed show the influence of the activities of the products.

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Mit 4 Abbildungen     

Determination of the complex formation constants for some water-soluble polymers with trivalent metal ions by differential pulse polarography

The formation of metal complexes between water-soluble polymers, poly(vinyl alcohol) [PVA], poly(N-vinylpyrrolidone) [PVP], poly(acrylamide) [PAAm] and poly(ethylene oxide) [PEO] with trivalent metal ions, Fe³⁺, Cr³⁺, and V³⁺ were studied by using differential pulse polarography (DPP). The general experimental observation is the shift of totally reversible reduction peaks (M³⁺+Hg+e^–M²⁺+Hg) towards more negative potentials when the complexing water-soluble polymers are added to the solution of trivalent metal ions. The negative shift in potential permitted the determination of complex formation constants (K_f) between trivalent metal ions and water soluble polymers. The complex formation constants for Fe³⁺, Cr³⁺, and V³⁺ ions with these polymers increased in the order of V³⁺>Cr³⁺>Fe³⁺.     

Sampling procedure and a radio-indicator study of mercury determination in whole blood by using an AMA 254 atomic absorption spectrometer

A sampling procedure appropriate for the determination of mercury in whole blood was tested by using both inactive controls and a ¹⁹⁷Hg mercury radio-indicator. To exclude the influence of the instrumental device (an AMA 254 single-purpose mercury atomic absorption spectrometer) on the determination of mercury in whole blood, the function of the instrument was checked by using rat blood with metabolised ¹⁹⁷Hg. The measurement procedure was found to be free of errors. However, the study showed that the material used for the sampling vessels is a crucial parameter for obtaining accurate analytical results. The stability of solutions and samples was tested towards polyethylene (PE) and polypropylene (PP) vessels. PE displayed a time-dependent increase in the mercury content both in the samples and in the blood control material. The probable cause of this increase was direct contamination from the material of the vessel and/or diffusion of mercury from the environment through the vessel walls related to a strong complexing affinity of the sample matrix. This assumption was confirmed by supplying the vessels with the complexing agent Na₂EDTA (0.05 mol L^–1). Commercial PP vessels for blood sampling (Sarstedt S-Monovette Metall Analytik) did not give rise to statistically significant variations in mercury content in the samples and blood control material over a 30-day period.     

Electrochemical studies and square-wave voltammetric determination of fenofibrate in pharmaceutical formulations

The electrochemical reduction of fenofibrate at a hanging mercury drop electrode (HMDE) was investigated by cyclic voltammetry, square-wave voltammetry, and chronoamperometry. Different buffer solutions were used over a wide pH range (3.0–10.0). The best definition of the analytical signals was found in borate buffer (pH 9.0)–tetrabutylammonium iodide mixture containing 12.5% (v/v) methanol at –1.2 V (versus Ag/AgCl). According to cyclic voltammetric studies, the reduction was irreversible and diffusion controlled. The diffusion coefficient was 2.38×10^–6 cm² s^–1 as determined by chronoamperometry. Under optimized conditions of square-wave voltammetry, a linear relationship was obtained between 0.146–4.96 g mL^–1 of fenofibrate with a limit of detection of 0.025 g mL^–1. Validation parameters such as sensitivity, accuracy, precision, and recovery were evaluated. The proposed method was applied to the determination of fenofibrate in pharmaceutical formulations. The results were compared with those obtained by a published high-performance liquid chromatography method. No difference was found statistically.     

Evaluation of the redox properties and anti/pro-oxidant effects of selected flavonoids by means of a DNA-based electrochemical biosensor

Quercetin and rutin as well as catechin and epigallocatechin gallate were investigated, as widely distributed representatives of flavonols and flavanols, respectively, regarding their anti/pro-oxidant properties. The flavonoids are irreversibly oxidized at a dsDNA-modified screen-printed electrode within 0.368 to 0.449 V vs. SHE without binding to DNA. Using the DNA biosensor the detection scheme of a DNA prevention/degradation exploits the [Co(phen)(3)](3+) complex as an electrochemical DNA marker. Antioxidant activity of flavonoids was tested in a model cleavage mixture composed of 5 x 10(-7) mol L(-1) [Cu(phen)(2)](2+) as the catalyst, 1 x 10(-3) mol L(-1) ascorbic acid as the chemical reductant and atmospheric oxygen as the natural oxidant where reactive oxygen radicals are generated. The antioxidant activity increases with the concentration of flavonoids reaching a maximum where pro-oxidative behaviour becomes of importance. The pro-oxidant potency of flavonoids depends on the presence of atmospheric oxygen and follows the order quercetin>rutin>epigallocatechin gallate>catechin.     

Decomposing total IR spectra of aqueous systems into solute and solvent contributions: a computational approach using maximally localized Wannier orbitals

The theoretical principles underpinning the calculation of infrared spectra for condensed-phase systems in the context of ab initio molecular dynamics have been recently developed in literature. At present, most ab initio molecular dynamics calculations are restricted to relatively small systems and short simulation times. In this paper we devise a method that allows well-converged results for infrared spectra from ab initio molecular dynamics simulations using small systems and short trajectories characteristic of simulations typically performed in practice. We demonstrate the utility of our approach by computing the imaginary part of the dielectric constant epsilon"(omega) for H2O and D2O in solid and liquid phases and show that it compares well with experimental data. We further demonstrate that maximally localized Wannier orbitals can be used to separate the individual contributions of different molecular species to the linear spectrum of complex systems. The new spectral decomposition method is shown to be useful in present-day ab initio molecular dynamics calculations to compute the magnitude of the "continuous absorption" generated by excess protons in aqueous solutions with good accuracy even when other species present in the solutions absorb strongly in the same frequency window.     

Effect of methoxyl groups on the NMR spectra: configuration and conformation of natural and synthetic indanic and tetralinic structures

Here, we studied the influence of the methoxyl groups attached at C‐7 and C‐2′ of natural and synthetic 1‐arylindanes on the chemical shift of the signal of bibenzylic hydrogen and carbon atoms and J_1,2 coupling constants. This influence was also analysed in natural 1‐aryltetralins and related compounds that possess methoxyl and/or hydroxyl groups bound at C‐8 and C‐2′. The methoxyl groups attached at C‐7 in indanes or at C‐8 in tetralins produce a deshielding signal at H‐1 and shield at C‐1 and a strong decrease in the value of J_1,2 due to the pseudoequatorial location adopted by the aryl group bound at C‐1, avoiding an ‘A^1,3 strain’. Furthermore, compounds with hydroxyl or methoxyl groups in C‐2′, in the absence of substituents of C‐7 or C‐8, present a strong deshielding signal at H‐1, strong shield of the C‐1 signal and a decrease in the value of J_1,2. This is attributed to the stereoelectronic effects of the methoxyl or hydroxyl groups, which we have called ‘Asarone effect’. NOESY experiments were conducted to confirm the configuration and conformation of some of the compounds included in this work. This study shows that both effects, A^1,3 strain and Asarone effect, must be taken into account when the structure of natural indanes and tetralins is analysed by using ¹H‐NMR and ¹³C‐NMR spectra. Copyright © 2016 John Wiley & Sons, Ltd.