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.     

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].     

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.     

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.     

Diffusion of polyphosphates into (poly(allylamine)-montmorillonite) multilayer films: flame retardant-intumescent films with improved oxygen barrier

The present paper relies on the original idea to design multifunctional coatings, and in particular highly efficient intumescent flame retardant coatings, based on the diffusion of polyphosphates (PSPs) in exponentially growing "layer-by-layer" films made from montmorillonite (MMT) and poly(allylamine) (PAH). Here, we used polyphosphates as an acid source, polyallylamine as both a carbon source and a swelling agent, and finally clays to reinforce the intumescent char strength and also for their oxygen barrier property. The coatings made from the alternated deposition of n = 60 layer pairs of PAH and MMT reach a considerable thickness of ～18 μm with well-defined ordering of the MMT in the direction parallel to the substrate. Structural, morphological, mechanical, gas barrier, and fire resistance properties of these films have been studied. Excellent oxygen barrier properties and extraordinary fire resistance properties are demonstrated based on the basis of a strong increase of the time to ignition and on a decrease of the heat release rate of polylactide substrates during mass loss calorimeter tests. This new and innovative intumescent flame retardant system based on (PAH-MMT)(n)-PSP coatings is a promising universal treatment for current polymeric materials.