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].     

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.     

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].     

The condensation of active methylene reagents with salicylaldehyde: Novel synthesis of chromene,azaanthracene, pyrano[3,4‐c]chromene and chromeno[3,4‐c]pyridine derivatives

On heating of the cyanoacetic acid cyclopentylidene hydrazide 1 with salicylaldehyde in the presence of bases the azaanthracene derivative 6 was formed. Also, reaction of 3 with malononitrile and ketones 10a,b afforded the pyrano[3,4‐c]chromene 9 and chromeno[3,4‐c]pyridine 11 respectively. A mechanism for these reactions is proposed.     

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.     

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.