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.     

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.     

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.     

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.     

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).