Unique continuation for the elastic transversely isotropic dynamical systems and its application

In this paper we prove the unique continuation property of the solution for the elastic transversely isotropic dynamical systems with smooth coefficients satisfying some conditions and apply it to extending the Dirichlet to Neumann map. The proof is based on the localized Fourier-Gauss transformation and Carleman type estimate.     

Multifractal Formalism for Selfsimilar Functions Expanded in Singular Basis

Selfsimilar functions can be written as the superposition of similar structures, at different scales, generated by a function g. Their expressions look like wavelet decompositions. In the case where g is regular, the multifractal formalism has been proved for the corresponding selfsimilar function, for Hölder exponents smaller than the regularity of g. In this paper, we show, in the case where g is the Schauder function (or the Haar function or a spline-type wavelet), that for larger Hölder exponents, the singularities of g can disturb the Hölder exponents of the associated selfsimilar function, modify the shape of the spectrum of singularities, and finally affect the validity of the multifractal formalism.     

Synthesis of New Heterocycles from Reactions of 1‐Phenyl‐1H‐pyrazolo[3,4‐b]pyridine‐5‐carbonyl Azides

Two individual examples of pyrazolo[3,4‐b]pyridine‐5‐carbonyl azides and hydrazides were reacted with various nucleophilic reagents. Different unexpected behaviors was observed. NMR, IR, mass spectra together with elemental analyses and X‐ray structure analyses, were used to prove the structure of the obtained products.     

Impact of Tween 60 on physicochemical properties and stability of Pistacia lentiscus fruit oil-in-water emulsion at a semi-low temperature

This study shows the effects of the Tween 60 emulsifier at different concentrations on the aqueous emulsion containing 5% of Pistacia lentiscus fruit oil. The rheological behavior and the droplet size distribution of cosmetic oil-in-water emulsions were investigated. This investigation was carried out by analyzing the shear flow and dynamic oscillatory followed by microscopic analysis and physical stability study for 24?hours and 4 months. During the period of 4 months, the emulsions were stored in a refrigerator at a semi-low temperature 12?°C. The physical stability test showed that the sample not emulsified yielded a creaming process after a short aging time. Flow curves of emulsions prepared with TW 60 exhibited a non-linear relationship between the shear stress σ and shear rate γ ?, which implies that the Herschel–Bulkley rheological model was the appropriate model for the shear flow. The increase of emulsifier quantities leading to an increase in the internal structure coherence, whereas the excess quantity affects the structure. Therefore, the optimal quantity proposed was 3.47%. Furthermore, the storage time at a semi-low temperature performed the stability and maintain the structure of emulsions.     

Distribution of Resonances and Decay Rate of the Local Energy for the Elastic Wave Equation

We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle with Neumann or Dirichlet boundary conditions. We prove that there exists an exponentially small neighborhood of the real axis free of resonances. Consequently we prove that for regular data, the energy for the elastic wave equation decays at least as fast as the inverse of the logarithm of time. According to Stefanov–Vodev ([SV1, SV2]), our results are optimal in the case of a Neumann boundary condition, even when the obstacle is a ball of ℝ³. The main difference between our case and the case of the scalar Laplacian (see Burq [Bu]) is the phenomenon of Rayleigh surface waves, which are connected to the failure of the Lopatinskii condition. Received: 22 February 2000 / Accepted: 28 June 2000     

Numerical simulation of the anisotropic elastic field generated by a misfit dislocations along a NiSi2/Si/(001)GaAs heterotwin interface

The purpose of this work is the numerical resolution, in the case of anisotropic elasticity, of the problem of a misfit dislocation located between an infinite substrate and two-layer composite. This case is obtained where the period of a network of misfit dislocations is taken as much greater than the thickness of the two foils. As a result, in the vicinity of the dislocation, the limiting boundary conditions will be close to those of Volterra translation dislocation. The elastic fields of displacement and stress are calculated for various orientations of the burger's vector, by inversion of a 30 x 30 computed matrix. Before this calculation, we tested the precision of the results of the program by comparing the interfacial relative displacement obtained from it with the results of the analytical expression describing this same displacement. The composite NiSi2/Si/(001)GaAs the subject of several investigations, is treated as an example.     

Inhibitive Effect of Butyltin Trichloride on Dissolution and Localized Corrosion of Aluminium in Sodium Hydroxide and Hydrochloric Acid

The dissolution of aluminium in sodium hydroxide and hydrochloric acid in the presence of butyltin trichloride as corrosion inhibitor has been studied by hydrogen evolution and thermometric methods. Experimental findings indicate that the inhibition effect of butyltin trichloride takes place through an adsorption mechanism following the Frumkin's isotherm. Butyltin trichloride acts as a weakly adsorbed inhibitor in NaOH and as a strongly adsorbed inhibitor in hydrochloric acid medium.