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.     

Existence of Mild Solutions to Stochastic Delay Evolution Equations with a Fractional Brownian Motion and Impulses

In this article, we study the existence of mild solutions to stochastic impulsive evolution equations with time delays, driven by fractional Brownian motion with the Hurst index H > 1/2 via a new fixed point analysis approach.     

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     

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.     

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].     

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).     

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.     

Green Synthesis of Poly(aminomethylenephosphonic) Acids

The reaction of polyamines with phosphorous acid and formaldehyde in water under focused microwave irradiation provides a facile and rapid synthesis of poly(aminomethylenephosphonic) acids.