Boundedness and asymptotic behavior of solutions for a diffusive epidemic model

The aim of this paper is to study the existence and the asymptotic behavior of solutions for some reaction–diffusion equations arising in epidemic biology phenomena. We will show that for a rather broad class of nonlinearities, the solutions are global and uniformly bounded, and under suitable assumptions on the parameters of the system, these solutions converge as time goes to infinity to a disease‐free equilibrium point. Copyright © 2016 John Wiley & Sons, Ltd.     

Astrophysical <Emphasis Type="Italic">S</Emphasis>-factor of radiative <Emphasis Type="Italic">p</Emphasis><Superscript>6</Superscript>Li capture at low energies

A possibility of describing experimental data for the astrophysical S-factor of p⁶Li capture at low energies is discussed within the potential cluster model with forbidden states.     

A nonlinear inequality and application to global asymptotic stability of perturbed systems

The goal of this work is to present a new nonlinear inequality which is used in a study of the Lyapunov uniform stability and uniform asymptotic stability of solutions to time‐varying perturbed differential equations. New sufficient conditions for global uniform asymptotic stability and/or practical stability in terms of Lyapunov‐like functions for nonlinear time‐varying systems is obtained. Our conditions are expressed as relation between the Lyapunov function and the existence of specific function which appear in our analysis through the solution of a scalar differential equation. Moreover, an example in dimensional two is given to illustrate the applicability of the main result. Copyright © 2014 John Wiley & Sons, Ltd.     

Plasmonic Pollen Grain Nanostructures: A Three-Dimensional Surface-Enhanced Raman Scattering (SERS)-Active Substrate

A new route has been developed to design plasmonic pollen grain-like nanostructures (PGNSs) as surface-enhanced Raman scattering (SERS)-active substrate. The nanostructures consisting of silver (Ag) and gold (Au) nanoparticles along with zinc oxide (ZnO) nanoclusters as spacers were found highly SERS-active. The morphology of PGNSs and those obtained in the intermediate stage along with each elemental evolution has been investigated by a high-resolution field emission scanning electron microscopy. The optical band gaps and crystal structure have been identified by UV-vis absorption and X-ray powder diffraction (XRD) measurements, respectively. For PGNSs specimen, three distinct absorption bands related to constituent elements Ag, Au, and ZnO were observed, whereas XRD peaks confirmed the existence of Ag, Au, and ZnO within the composition of PGNSs. SERS-activity of PGNSs was confirmed using Rhodamine 6G (R6G) as Raman-active dyes. Air-cooled solid-state laser kits of 532 nm were used as excitation sources in SERS measurements. SERS enhancement factor was estimated for PGNSs specimen and was found as high as 3.5×10⁶. Finite difference time domain analysis was carried out to correlate the electromagnetic (EM) near-field distributions with the experiment results achieved under this investigation. EM near-field distributions at different planes were extracted for s-, p- and 45° of incident polarizations. EM near-field distributions for such nanostructures as well as current density distributions under different circumstances were demonstrated and plausible scenarios were elucidated given SERS enhancements. Such generic fabrication route as well as correlated investigation is not only indispensable to realize the potential of SERS applications but also unveil the underneath plasmonic characteristics of complex SERS-active nanostructures.     

Removal of Cd(II), Cu(II), and Pb(II) by adsorption onto natural clay: a kinetic and thermodynamic study

In this work, we study the elimination of three bivalent metal ions (Cd²⁺, Cu²⁺, and Pb²⁺) by adsorption onto natural illitic clay (AM) collected from Marrakech region in Morocco. The characterization of the adsorbent was carried out by X-ray fluorescence, Fourier transform infrared spectroscopy and X-ray diffraction. The influence of physicochemical parameters on the clay adsorption capacity for ions Cd²⁺, Cu²⁺, and Pb²⁺, namely the adsorbent dose, the contact time, the initial pH imposed on the aqueous solution, the initial concentration of the metal solution and the temperature, was studied. The adsorption process is evaluated by different kinetic models such as the pseudo-first-order, pseudo-second-order, and Elovich. The adsorption mechanism was determined by the use of adsorption isotherms such as Langmuir, Freundlich, and Temkin models. Experiments have shown that heavy metals adsorption kinetics onto clay follows the same order, the pseudo-second order. The isotherms of adsorption of metal cations by AM clay are satisfactorily described by the Langmuir model and the maximum adsorption capacities obtained from the natural clay, using the Langmuir isotherm model equation, are 5.25, 13.41, and 15.90 mg/g, respectively for Cd(II), Cu(II), and Pb(II) ions. Adsorption of heavy metals on clay is a spontaneous and endothermic process characterized by a disorder of the medium. The values of ΔH are greater than 40 kJ/mol, which means that the interactions between clay and heavy metals are chemical in nature.     

Stokes instability in inhomogeneous membranes: application to lipoprotein suction of cholesterol-enriched domains

We examine the time-dependent distortion of a nearly circular viscous domain in an infinite viscous sheet when suction occurs. Suction, the driving force of the instability, can occur everywhere in the two phases separated by an interface. The model assumes a two-dimensional Stokes flow; the selection of the wavelength at short times is determined by a variational procedure. Contrary to the viscous fingering instability, undulations of the boundary may be observed for enough pumping, whatever the sign of the viscosity contrast between the two fluids involved. We apply our model to the suction by lipoproteins of cholesterol-enriched domains in giant unilamellar vesicles. Comparison of the number of undulations given by the model and by the experiments gives reasonable values of physical quantities such as the viscosities of the domains.     

2- and 2,7-Substituted para-N-Methylpyridinium Pyrenes: Syntheses,Molecular and Electronic Structures,Photophysical, Electrochemical,and Spectroelectrochemical Properties and Binding to Double-Stranded (ds) DNA

Two N-methylpyridinium compounds and analogous N-protonated salts of 2- and 2,7-substituted 4-pyridyl-pyrene compounds were synthesised and their crystal structures, photophysical properties both in solution and in the solid state, electrochemical and spectroelectrochemical properties were studied. Upon methylation or protonation, the emission maxima are significantly bathochromically shifted compared to the neutral compounds, although the absorption maxima remain almost unchanged. As a result, the cationic compounds show very large apparent Stokes shifts of up to 7200 cm⁻¹. The N-methylpyridinium compounds have a single reduction at ca. −1.5 V vs. Fc/Fc⁺ in MeCN. While the reduction process was reversible for the 2,7-disubstituted compound, it was irreversible for the mono-substituted one. Experimental findings are complemented by DFT and TD-DFT calculations. Furthermore, the N-methylpyridinium compounds show strong interactions with calf thymus (ct)-DNA, presumably by intercalation, which paves the way for further applications of these multi-functional compounds as potential DNA-bioactive agents.