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.     

Microwave-assisted synthesis of α-ethoxycarbamates

An efficient and reproducible synthesis of various α-ethoxycarbamates is described via a microwave heating mode. Compared to the thermal process, the microwave dielectric heating induces a dramatic reduction of the reaction time and the improvement of the yields. The reaction is general since applicable to aromatic and aliphatic aldehydes with various primary amines. Several examples involving chiral aldehydes have also been considered.     

Dearomatization of 3-Nitroindoles with Highly γ-Functionalized Allenoates in Formal (3+2) Cycloadditions

3-Nitroindoles are easily reacted with highly substituted γ-allenoates in the presence of a commercially available phosphine catalyst. For instance, allenoates derived from biomolecules such as amino and deoxycholic acids are combined for the first time with 3-nitroindole. The corresponding dearomatized (3+2) tricyclic cycloadducts are obtained as α-regioisomers exclusively. DFT computations shed light on this multi-step reaction mechanism and on the selectivities observed in the sequence.     

Deformable two-dimensional photonic crystal slab for cavity optomechanics

We have designed photonic crystal suspended membranes with optimized optical and mechanical properties for cavity optomechanics. Such resonators sustain vibration modes in the megahertz range with quality factors of a few thousand. Thanks to a two-dimensional square lattice of holes, their reflectivity at normal incidence at 1064?nm reaches values as high as 95%. These two features, combined with the very low mass of the membrane, open the way to the use of such periodic structures as deformable end mirrors in Fabry-Perot cavities for the investigation of cavity optomechanical effects.     

1H MRS detection of glycine residue of reduced glutathione in vivo

Glutathione (GSH) is a powerful antioxidant found inside different kinds of cells, including those of the central nervous system. Detection of GSH in the human brain using ¹H MR spectroscopy is hindered by low concentration and spectral overlap with other metabolites. Previous MRS methods focused mainly on the detection of the cysteine residue (GSH-Cys) via editing schemes. This study focuses on the detection of the glycine residue (GSH-Gly), which is overlapped by glutamate and glutamine (Glx) under physiological pH and temperature. The first goal of the study was to obtain the spectral parameters for characterization of the GSH-Gly signal under physiological conditions. The second goal was to investigate a new method of separating GSH-Gly from Glx in vivo. The characterization of the signal was carried out by utilization of numerical simulations as well as experiments over a wide range of magnetic fields (4.0–14 T). The proposed separation scheme utilizes J-difference editing to quantify the Glx contribution to separate it from the GSH-Gly signal. The presented method retains 100% of the GSH-Gly signal. The overall increase in signal to noise ratio of the targeted resonance is calculated to yield a significant SNR improvement compared to previously used methods that target GSH-Cys residue. This allows shorter acquisition times for in vivo human clinical studies.