Rôle de l'espace de Besov B∞−1,∞ dans le contrôle de l'explosion éventuelle en temps fini des solutions régulières des équations de Navier–Stokes

Let $\text{u∈C([0,T}{}^1\text{[;L}{}^{\mathrm{n}}\text{(}\text{R}{}^{\mathrm{n}}\text{)}{}^{\mathrm{n}}\text{)}$ be a maximal solution of the Navier–Stokes equations. We prove that u is C^∞ on $\text{]0,T}{}^1\text{[×}\text{R}{}^{\mathrm{n}}$ and there exists a constant $\text{ε}{}_1\text{>0}$, which depends only on n, such that if $\text{T}{}^1$ is finite then, for all $\text{ω∈S(}\text{R}{}^{\mathrm{n}}\text{)}{}^{\mathrm{n}}\text{,}$ we have To cite this article: R. May, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Poly(ethylene glycol)--oligolactates with monodisperse hydrophobic blocks: preparation, characterization, and behavior in water

Methoxypoly(ethylene glycol)-b-oligo-L-lactate (mPEG-b-OLA) diblock oligomers with monodisperse OLA blocks were obtained by fractionation of polydisperse block oligomers using preparative HPLC. The fractionated oligomers were composed of an mPEG block with a molecular weight of 350, 550, or 750 and an OLA block with a degree of polymerization of 4, 6, 8, or 10. The diblock oligomers with a low PEG content were fully amorphous, with glass transition temperatures ranging from -60 to -20 degrees C, indicating that the blocks were miscible. Upon heating aqueous dispersions of the block oligomers, cloud points, depending on the PEG/OLA ratio of the block oligomer, were observed at temperatures above 40 degrees C. The monodispersity of the hydrophobic block enabled the amphiphilic molecules to form nanoparticles in water with a hydrodynamic radius of 130-300 nm, at concentrations above the critical aggregation concentration (0.4-1 mg/mL), whereas polydisperse mPEG-b-OLAs gave formation of large aggregates. Static light scattering measurements showed that the nanoparticles have a low density (0.6-25 mg/mL), indicating that the particles are highly hydrated. In agreement herewith, the (1)H NMR spectra of nanoparticles in D2O closely resembled spectra in a good solvent for both blocks (CDCl3). It is therefore suggested that the nanoparticles contain a hydrated core of mPEG-b-OLA block oligomers, stabilized by a thin outer PEG layer. The particles were stable for two weeks, except for the mPEG350 series and mPEG750-b-OLA4, indicating that both the PEG block size and the PEG weight fraction of the oligomers determine their stability. The evident self-emulsifying properties of mPEG-b-oligo-l-lactates with monodisperse hydrophobic blocks as demonstrated in this study, together with their expected biocompatibility and biodegradability, make these systems well suitable for pharmaceutical applications.     

Physicochemical characterization of degradable thermosensitive polymeric micelles

Amphiphilic AB block copolymers consisting of thermosensitive poly(N-(2-hydroxypropyl) methacrylamide lactate) and poly(ethylene glycol), pHPMAmDL-b-PEG, were synthesized via a macroinitiator route. Dynamic light scattering measurements showed that these block copolymers form polymeric micelles in water with a size of around 50 nm by heating of an aqueous polymer solution from below to above the critical micelle temperature (cmt). The critical micelle concentration as well as the cmt decreased with increasing pHPMAmDL block lengths, which can be attributed to the greater hydrophobicity of the thermosensitive block with increasing molecular weight. Cryogenic transmission electron microscopy analysis revealed that the micelles have a spherical shape with a narrow size distribution. 1H NMR measurements in D2O showed that the intensity of the peaks of the protons from the pHPMAmDL block significantly decreased above the cmt, indicating that the thermosensitive blocks indeed form the solidlike core of the micelles. Static light scattering measurements demonstrated that pHPMAmDL-b-PEG micelles with relatively large pHPMAmDL blocks possess a highly packed core that is stabilized by a dense layer of swollen PEG chains. FT-IR analysis indicated that dehydration of amide bonds in the pHPMAmDL block occurs when the polymer dissolved in water is heated from below to above its cmt. The micelles were stable when an aqueous solution of micelles was incubated at 37 degrees C and at pH 5.0, where the hydrolysis rate of lactate side groups is minimized. On the other hand, at pH 9.0, where hydrolysis of the lactic acid side groups occurs, the micelles started to swell after 1.5 h of incubation and complete dissolution of micelles was observed after 4 h as a result of hydrophilization of the thermosensitive block. Fluorescence spectroscopy measurements with pyrene loaded in the hydrophobic core of the micelles showed that when these micelles were incubated at pH 8.6 and at 37 degrees C the microenvironment of pyrene became increasingly hydrated in time during this swelling phase. The results demonstrate the potential applicability of pHPMAmDL-b-PEG block copolymer micelles for the controlled delivery of hydrophobic drugs.     

New Applications of the Lithiated Phosphinimine Ph3P=N-Li: Synthesis of α,β-Unsaturated Nitriles and P=N-P Linked Phosphinimines

Abstract

The reaction of Ph₃P-N-Li⁽¹²⁾ with various α,β-unsaturated esters gives access to new N-(α,β-unsaturated acyl) phosphinimines. which can undergo intramolecular aza-Wittig reaction (at 65 - 110°C) to afford the corresponding nitriles.     

A nonlinear inequality and application to global asymptotic stability of perturbed systems

The goal of this work is to present a new nonlinear inequality which is used in a study of the Lyapunov uniform stability and uniform asymptotic stability of solutions to time‐varying perturbed differential equations. New sufficient conditions for global uniform asymptotic stability and/or practical stability in terms of Lyapunov‐like functions for nonlinear time‐varying systems is obtained. Our conditions are expressed as relation between the Lyapunov function and the existence of specific function which appear in our analysis through the solution of a scalar differential equation. Moreover, an example in dimensional two is given to illustrate the applicability of the main result. Copyright © 2014 John Wiley & Sons, Ltd.     

Isolation and Characterization of Two Chalcone Derivatives with Anti-Hepatitis B Virus Activity from the Endemic Socotraen Dracaena cinnabari (Dragon’s Blood Tree)

Hepatitis B virus (HBV) infection is prevalent and continues to be a global health concern. In this study, we determined the anti-hepatitis B virus (HBV) potential of the Socotra-endemic medicinal plant Dracaena cinnabari and isolated and characterized the responsible constituents. A bioassay-guided fractionation using different chromatographic techniques of the methanolic extract of D. cinnabari led to the isolation of two chalcone derivatives. Using a variety of spectroscopic techniques, including ¹H-, ¹³C-, and 2D-NMR, these derivatives were identified as 2,4’-dihydroxy-4-methoxydihydrochalcone (compound 1) and 2,4’-dihydroxy-4-methoxyhydrochalcone (compound 2). Both compounds were isolated for the first time from the red resin (dragon’s blood) of D. cinnabari. The compounds were first evaluated for cytotoxicity on HepG2.2.15 cells and 50% cytotoxicity concentration (CC50) values were determined. They were then evaluated for anti-HBV activity against HepG2.2.15 cells by assessing the suppression of HBsAg and HBeAg production in the culture supernatants and their half maximum inhibitory concentration (IC₅₀) and therapeutic index (TI) values were determined. Compounds 1 and 2 indicated inhibition of HBsAg production in a dose- and time-dependent manner with IC₅₀ values of 20.56 and 6.36 μg/mL, respectively.     

Feedback control design for Rössler and Chen chaotic systems anti-synchronization

The proposed anti-synchronization conditions of coupled chaotic systems are based, in this Letter, on the use of aggregation techniques for the stability study of the error dynamics. The schemes are, successfully, applied to coupled Rössler and Chen chaotic systems making the instantaneous characteristic matrix under the arrow form. Numerical simulations are performed to illustrate the efficiency of the proposed approach.