Feuilletages des espaces temps globalement hyperboliques par des hypersurfaces à courbure moyenne constante

We announce the following result: every maximal globally hyperbolic 3-dimensional spacetime with compact Cauchy surface, and with nonpositive constant curvature admits a unique time function whose fibers are constant mean curvature surfaces. We discuss the extension of this result in higher dimensions. To cite this article: T. Barbot et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Labeled magnetic nanoparticles assembly on polypyrrole film for biosensor applications

In recent years, conducting polymers combined with metallic nanoparticles have been paid more attention due to their potential applications in microelectronics, microsystems, optical sensors and photoelectronic chemistry. The work presented in this paper describes the preparation and characterization of a nanocomposite composed by a thin polypyrrole (PPy) film covered with an assembly of magnetic nanoparticles (NPs). The magnetic particles were immobilized on PPy films under appropriate magnetic field in order to control their organization on the PPy film and finally to improve the sensitivity of the system in potential sensing applications. The electrical properties and morphology of the resulting PPy film and the PPy film/NPs composite were characterized with cyclic voltammetry, impedance spectroscopy (IS), scanning electron microscopy (SEM), atomic force microscopy (AFM) and infra-red spectroscopy (IR). By using streptavidin labeled magnetic particles it was possible to functionalize the NPs assembly with biotin-Fab fragment K47 antibody. The designed biosensor had been successfully applied in rapid, simple, and accurate measurements of atrazine concentrations, with a significantly low detection limit of 5 ng/ml.     

Effect of the intercalated cation on the properties of poly(o-methylaniline)/maghnite clay nanocomposites

A detailed study about the synthesis, characterization and properties of poly(o-methylaniline)(PoMea)/maghnite nanocomposites has been performed. Changes in the characteristics of the nanocomposites, depending on the intercalated cation between the clay layers before the synthesis, have been observed. Intercalated morphology has been detected by TEM in nanocomposites containing copper-treated maghnite (Magh-Cu), while when maghnite treated with strong acids was used (Magh-H); an exfoliated material has been obtained. Also, remarkable differences in the properties of the polymers have been observed by TG-MS and FTIR, suggesting that the polymer produced with Magh-H has a higher degree of branching. The electrochemical behavior of the polymers extracted from the nanocomposites has been studied by cyclic voltammetry. Good electrochemical response has been observed for PoMea grown into Magh-Cu but not for the one polymerized into Magh-H.     

Some Uniqueness Results for Functional Damped Semilinear Differential Equations in Frechet Spaces

A recent nonlinear alternative for contraction maps in Frechet spaces due to Frigon and Granas （Resultats de type Leray-Schauder pour des contractions sur des espaces de Frechet, Ann. Sci. Math. Quebec 22, （2）, 161-168 （1998））, combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first- and second-order functional semi linear and neutral damped differential equations in Frechet space.     

Tentative links between thermal diffusivity and fire-retardant properties in poly(methyl methacrylate)-metal oxide nanocomposites

Possible relationships between fire-retardant properties and thermal diffusivity for poly(methyl methacrylate) (PMMA) filled by melt blending with titanium dioxide (TiO₂), alumina (Al₂O₃) and boehmite (AlOOH) were investigated for a better understanding of the mode of action of metal oxides as fire-retardants (FR) in PMMA. Fire-retardancy was measured with a cone calorimeter and thermal diffusivity (α) by Laser Flash Analysis (LFA). LFA measurements have shown that heat dispersion is higher with titanium dioxide and boehmite than with alumina despite a larger surface area. For thermal diffusivity, discrepancies between the different nanofillers were only visible from 10 wt% onwards. Thermal degradation of PMMA-oxide nanocomposites and their thermal diffusivity could be linked. Moreover, a bi-linear relationship between the peak of heat release rate (pHRR) and the average of heat release rate (AHRR) showed the occurrence of a barrier effect.     

The fluid limit of the multiclass processor sharing queue

Consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or re-enter the queue, possibly as customers of a different class. The server is operating under the egalitarian processor sharing discipline. Building on prior work by Gromoll et al.?(Ann. Appl. Probab. 12:797?C859, 2002) and Puha et al.?(Math. Oper. Res. 31(2):316?C350, 2006), we establish the convergence of a properly normalized state process to a fluid limit characterized by a system of algebraic and integral equations. We show the existence of a unique solution to this system of equations, both for a stable and an overloaded queue. We also describe the asymptotic behavior of the trajectories of the fluid limit.     

Facile synthesis of controlled‐structure primary amine‐based methacrylamide polymers via the reversible addition‐fragmentation chain transfer process

We report here a novel direct method for the syntheses of primary aminoalkyl methacrylamides that requires mild reagents and no protecting group chemistry. The reversible addition‐fragmentation chain transfer polymerization (RAFT) of the aminoalkyl methacrylamide revealed to be highly efficient with 4‐cyanopentanoic acid dithiobenzoate (CTP) as chain transfer agent and 4,4′‐azobis(4‐cyanovaleric acid) (ACVA) as initiator. Cationic amino‐based homopolymers of reasonably narrow polydispersities (M_w/M_n < 1.30) and predetermined molecular weights were obtained without recourse to any protecting group chemistry. A range of block and random copolymers were also synthesized via the RAFT process. The homopolymers and copolymers were characterized by aqueous conventional and triple detection gel permeation chromatography systems. Furthermore, the primary amine‐based methacrylamide monomers and polymers revealed to be highly stable both with the primary amino group in the protonated and deprotonated form. We have also demonstrated that stabilized gold nanoparticles can be generated with the RAFT‐synthesized amine‐based polymers via a photochemical process. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4984–4996, 2008     

Modification of carboxyl‐functionalized single‐walled carbon nanotubes with biocompatible,water‐soluble phosphorylcholine and sugar‐based polymers: Bioinspired nanorods

We report here the successful functionalization of single‐walled carbon nanotubes with bioinspired sugar and phosphocholine polymeric structures via surface‐initiated atom transfer radical polymerization. The surface‐polymer‐coated carbon nanotubes have been systematically analyzed by Raman, infrared, ultraviolet–visible, and nuclear magnetic resonance spectroscopy and high‐resolution transmission electron microscopy, which give strong evidence of successful functionalization. The successful aqueous dispersion of the functionalized carbon nanotubes also indicates that functionalization has been achieved. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6558–6568, 2006     

Lipschitz Regularity in Some Geometric Problems

The Lipschitz regularity is perhaps the most natural, and surely the most geometrical among all the types of regularities. For example, the Lipschitz character of an ordinary differential equation (vector field) is the natural classical sufficient condition for the (unique) integrability of this equation. The goal here is to show that, in some sense, the Lipschitz regularity is also necessary, if one assumes (geometric) individual conditions on the trajectories. In other words, we show that tangential rigidity leads to a transversal regularity.     

Local and global existence and uniqueness results for impulsive functional differential equations with multiple delay

In this paper, we discuss local and global existence and uniqueness results for first-order impulsive functional differential equations with multiple delay. We shall rely on a fixed point theorem of Schaefer and a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent nonlinear alternative of Leray-Schauder type in Fréchet spaces, due to Frigon and Granas [M. Frigon, A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22 (2) (1998) 161-168].