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).     

Exploring physical features of anisotropic quark stars in Brans-Dicke theory with a massive scalar field via embedding approach

The main aim of this study is to explore the existence and salient features of spherically symmetric relativistic quark stars in the background of massive Brans-Dicke gravity. The exact solutions to the modified Einstein field equations are derived for specific forms of coupling and scalar field functions using the equation of state relating to the strange quark matter that stimulates the phenomenological MIT-Bag model as a free Fermi gas of quarks. We use a well-behaved function along with the Karmarkar condition for class-one embedding as well as junction conditions to determine the unknown metric tensors. The radii of strange compact stars viz., PSR J1416-2230, PSR J1903+327, 4U 1820-30, CenX-3, and EXO1785-248, are predicted via their observed mass for different values of the massive Brans-Dicke parameters. We explore the influences of the mass of scalar field \begin{document}$m_{\phi}$\end{document}, coupling parameter \begin{document}$\omega_{\rm BD}$\end{document}, and bag constant \begin{document}${\cal{B}}$\end{document} on state determinants and perform several tests on the viability and stability of the constructed stellar model. Conclusively, we find that our stellar system is physically viable and stable as it satisfies all the energy conditions and necessary stability criteria under the influence of a gravitational scalar field.     

Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces

In this article, a recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas [1998, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22, 161–168] is used to investigate the existence and uniqueness of solutions for fractional order functional differential equations with infinite delay.     

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.     

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.     

Existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite 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 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 M. Frigon and A. Granas [Résultats de type Leray–Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22 (2) (1998) 161–168]. The goal of this paper is to extend the problems considered by A. Ouahab [Local and global existence and uniqueness results for impulsive differential equations with multiple delay, J. Math. Anal. Appl. 323 (2006) 456–472].     

Ab-initio molecular dynamics and vibrational Raman spectroscopy investigations of quartz polymorph at high temperature

Quartz has found a wide range of applications over the past years. In the present work, the temperature dependence of microcrystalline quartz is investigated with Raman spectroscopy and DFT-based molecular dynamics simulations. We aimed to determine the structure at short and medium range distances as a function of the increasing temperature. The dynamics and the structural changes are analysed in terms of time-dependent properties, and the vibrational analysis obtained from calculated dipole trajectory and vibrational density of states (VDOS). The computed data is compared to Raman and infrared spectroscopic measurements. The approach is of a particularly great interest when we focus on the structural behaviour, and the dynamical disorder observed and characterised through geometric and thermodynamic data. The calculations confirm that the infrared and Raman signature as a function of temperature provide a sensitive analysis of the structural behaviour of quartz.     

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