Numerical solution of an inverse initial boundary-value problem for the full time-dependent Maxwell's equations in the presence of imperfections of small volume

We consider the numerical solution, in a three-dimensional bounded domain, of the inverse problem for identifying the location of small electromagnetic imperfections in a medium with homogeneous background. Our numerical algorithm is based on the coupling of a discontinuous Galerkin method for the time-dependent Maxwell's equations, on the exact controllability method and on a Fourier inversion. Several numerical results are given with one and two imperfections and the robustness and accuracy of the numerical method used for the dynamic detection problem are shown.     

Treatment of anionic dye aqueous solution using Ti,HDTMA and Al/Fe pillared bentonite. Essay to regenerate the adsorbent

In this study, the adsorption removal of an anionic dye (Congo red) by a local bentonite before and after modification was studied. The modification of the bentonite was made by organophilisation using surfactant (HDTMA) and by pillaring process to obtain a bentonite with Ti pillars and with mixed pillars of Fe/Al. The various synthesized materials are characterized by different techniques such as DRX, MET, N₂ adsorption-desorption, Zeta potential measurement. Results show the development of the texture and the structure of the bentonite after modification. The various adsorbents synthesized show an increase in the adsorption capacity of Congo Red compared to the initial bentonite. Adsorption isotherms are described by the Langmuir model in all cases except that for Ti pillared bentonite, the Freundlich model is more suitable. Pseudo-second order is better for describing the adsorption process. Also, regeneration of the adsorbent is approached in this study by photochemical way and the results show a total regeneration of the adsorbent.     

On the integro-differential equations with reflection

In this paper, by developing important properties on the composition of functions with reflection, using some exponential dichotomy properties and an application of the fixed-point theorem, several new sufficient conditions for the existence and the uniqueness of an pseudo almost automorphic solutions with measure for some general-type reflection integro-differential equations. We suppose that the nonlinear part is measure pseudo almost automorphic and in which we distinguish the two constant and variable cases for the Lipschitz coefficients of the functions associated with this part. It is assumed that the linear part of the equation considered admits an exponential dichotomy. Finally, an application is given on the very interesting model of Markus and Yamabe.     

Echiofruzine, a novel naringenin diglycoside from Echiochilon fruticosum growing in Tunisia

The aerial parts of the Tunisian plant Echiochilon fruticosum yielded a novel flavonol diglycoside: naringenin-5-O-beta-D-glycopyranoside-3-O-alpha-L-rhamnopyranoside, named Echiofruzine (1), together with the known compounds vomifoliol-9-O-beta-D-glucopyraroside (2), 1-oxo-alpha-ionyl-9-O-beta-D-glucopyranoside (3) and 1-O-[beta-D-xylopyranosyl(1 --> 6)-beta-D-glucopyranosyl] eugenol (4), described for the first time in the indicated plant. The structures of the four isolated compounds were established on the basis of chemical and spectroscopic evidence.     

Multiple Solutions for a Class of Nonhomogeneous Fractional Schrödinger Equations in $$\mathbb {R}^{N}$$

This paper is concerned with the following fractional Schrödinger equation

$$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s} u+u= k(x)f(u)+h(x) \text{ in } \mathbb {R}^{N}\\ u\in H^{s}(\mathbb {R}^{N}), \, u>0 \text{ in } \mathbb {R}^{N}, \end{array} \right. \end{aligned}$$

where \(s\in (0,1),N> 2s, (-\Delta )^{s}\) is the fractional Laplacian, k is a bounded positive function, \(h\in L^{2}(\mathbb {R}^{N}), h\not \equiv 0\) is nonnegative and f is either asymptotically linear or superlinear at infinity. By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two positive solutions for the problem under consideration, provided that \(|h|_{2}\) is sufficiently small.

     

Theoretical study of the electronic structure of LiNa and LiNa<Superscript>+</Superscript> molecules

Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels of the lowest electronic states of the alkali dimer LiNa molecule dissociating into Na (3s, 3p, 4s, 3d, and 4p) + Li (2s, 2p, 3s, and 3p) in ^1,3Σ, ^1,3Π, and ^1,3Δ symmetries are presented. Adiabatic results are also reported for ²Σ, ²Π, and ²Δ electronic states of the molecular ion LiNa⁺ dissociating into Li (2s, 2p, 3s, and 3p) + Na⁺ and Li⁺  + Na(3s, 3p, 4s, 3d, and 4p). We use an ab initio approach involving a non-empirical pseudopotential for the Li (1s²) and Na (1s²2s²2p⁶) cores and core valence correlation correction. A very good agreement is obtained for some lowest states of the LiNa and LiNa⁺ molecules for spectroscopic constants with the available theoretical works. The existence of numerous avoided crossings between electronic states of ²Σ and ²Π symmetries is related to the charge transfer process between the two ionic systems Li⁺Na and LiNa⁺.     

Non-isothermal model-free predictions

Suitable thermal treatment of metal organic precursors is a key process to obtain oxide films. To this purpose, non-isothermal model-free predictions are specially suited. In this article we will explore the ability of these methods to provide an accurate prediction of the evolution of the decomposition of yttrium trifluoroacetate, a precursor used in the synthesis of YBaCuO superconducting thin-films. A good agreement has been obtained between the predicted and the measured reaction courses.     

Evolution of yttrium trifluoroacetate during thermal decomposition

A detailed analysis of the thermal decomposition of yttrium trifluoroacetate under different atmospheres is presented. Thermogravimetry, differential thermal analysis, and evolved gas analysis have been used for this in situ analysis. Solid residues at different stages have been characterized by means of X-ray diffraction, elemental analysis, Fourier transform infrared spectroscopy, and scanning electron microscopy. The first decomposition stage (310 °C) is exothermic and involves the complete removal of carbon (organic part) and the formation of yttrium fluoride. This process is characterized by a fast mass loss rate. Afterwards, yttria (Y₂O₃) is formed at 1200 °C through a slow process controlled by the out diffusion of fluorine that involves the formation of yttrium oxyfluoride as an intermediate. The evolution of the mass during the decomposition and the structure of the yttria particles is not affected by the presence of oxygen or water. However, when the oxygen (water) partial pressure is as low as 0.02% (<0.002%), the kinetics and final particle structure are strongly affected.