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.     

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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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.     

The notion of observable and the moment problem for $$*$$∗-algebras and their GNS representations

Letters in Mathematical Physics - We address some usually overlooked issues concerning the use of $$*$$-algebras in quantum theory and their physical interpretation. If $${\mathfrak {A}}$$ is a...     

High-speed energy efficient selective removal of large area copper layer by laser induced delamination

An indirect laser-induced method for selective removal of large copper areas from a printed circuit board is theoretically and experimentally investigated. The results show that the threshold condition for the process involves phase transition of the epoxy-based substrate resin. Optimal parameters for maximizing process speed are found and discussed.     

Isomerization of a peptidic fragment studied theoretically in vacuum and in explicit water solvent at finite temperature

The cis-trans isomerization of N-methylacetamide, a molecular model of the polypeptide chain, is examined via umbrella sampling Car-Parrinello MD and classical MD, in both gas and solution phases at 300 K. A new analysis of the C(O)-N bond interconversion and a full examination of the solvent shell structure are presented.