Convergence analysis of perturbed hemivariational inequalities

We consider the rate of convergence for a class of perturbed hemivariational inequalities in reflexive Banach Spaces. Our results can be viewed as an extension and refinement of some previous known results in this area.     

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).     

Global Weak Solutions for a Parabolic System Modeling a One-Dimensional Miscible Flow in Porous Media

We consider an initial boundary value problem for a nonlinear differential system of two equations. Such a system is formed by the equations of compressible miscible flow in a one-dimensional porous medium. No assumption about the mobility ratio is involved. Under some reasonable assumptions on the data, we prove the existence of a global weak solution. Our basic approach is the semi-Galerkin method. We use the technique of renormalized solutions for parabolic equations in the derivation ofa prioriestimates.     

The Hydraulic Exchanges between the Main Water Reservoirs of the Moroccan Middle Atlas Region Measured by Solid State Nuclear Track Detectors

Uranium and thorium contents were evaluated in water samples collected from different sources of the piedmont of the Middle Atlas mountains by using two types of solid state nuclear track detectors (SSNTD). In addition, the radon (²²²Rn) and thoron (²²⁰Rn) -activities per unit volume of the water samples were also determined. The influence of the water flow rate and altitude on the radon concentration of the water samples belonging to the piedmont of the Middle Atlas mountains was investigated. The hydraulic exchanges between the Middle Atlas water reservoirs and the Turonian aquifer of the neighbouring Tadla plain have been quantified. The results were compared with data given in literature.     

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.     

Synthesis and characterization of active ester-functionalized polypyrrole-silica nanoparticles: application to the covalent attachment of proteins

Novel ester-functionalized polypyrrole-silica nanocomposite particles were prepared by oxidative copolymerization of pyrrole and N-succinimidyl ester pyrrole (50/50% initial concentrations), using FeCl3 in the presence of ultrafine silica nanoparticles (20 nm diameter). The N-succinimidyl ester pyrrole monomer was prepared in aqueous solution using 1-(2-carboxyethylpyrrole) and N-hydroxysuccinimide in the presence of 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide. The resulting nanocomposites (N-succinimidyl ester polypyrrole-silica) are raspberry-shaped agglomerates of silica sol particles "glued" together by the insoluble poly(pyrrole-co-N-succinimidyl pyrrole). The N-succinimidyl ester polypyrrole-silica particles were characterized in terms of their size, density, copolymer content, and polydispersity. Scanning electron microscopy and disk centrifuge sedimentometry confirmed that the nanocomposite particles had narrow size distributions. X-ray photoelectron spectroscopy analysis indicated a silica-rich surface and a high surface concentration of N-succinimidyl ester groups. These nanoparticles exhibited good long-term dispersion stability. The chemical stability of the ester functions in aqueous media after several weeks of storage was monitored by FTIR spectroscopy. The functionalized nanocomposites were tested as bioadsorbents of human serum albumin (HSA). The very high amount of immobilized HSA determined by UV-visible spectroscopy is believed to be due to covalent binding. Incubation of the HSA-grafted nanocomposite with anti-HSA resulted in immediate flocculation, an indication that they are alternative candidates for visual diagnostic assays.     

Yields and average cross sections of recoil charged particle induced reactions on11B,12C,13C,14N,16O and18O

The yield and average cross section for the reactions¹¹B(p, n)¹¹C,¹²C(p, )¹³N,¹³C(p, n)¹³N, ₁₂ ¹² C(d, n)¹³N,¹⁴N(p, )¹¹C,¹⁶O(p, )¹³N,¹⁶O(d, n)¹⁷F,¹⁶O(t, n)¹⁸F, and¹⁸O(p, n)¹⁸F have been measured in different compounds. The charged particles were created in the samples themselves either through recoil by scattering of 14 MeV neutrons off hydrogen and deuterium, or by the (n, t) reaction on⁶Li using thermal neutrons. The yields of reactions¹²C(d, n);¹⁶O(p, );¹⁶O(t, n) and¹⁸O(p, n) have been measured using proton, deuteron and triton spectra generated by 14 MeV neutrons in the reactions D(n, p)2n;⁶Li(n, d);⁷Li(n, d) and¹⁰B(n, d);⁷Li(n, t) and¹⁰B(n, t), respectively.