On Elliptic System Involving Critical Sobolev Exponent and Weights

This paper is devoted to the existence and nonexistence of positive solutions for a semilinear elliptic system involving critical Sobolev exponent and weights. We study the effect of the behavior of weights near their minima on the existence of solutions for the considered problem.     

One-loop generated anomalous gauge couplings

We compute, at one loop, the CP-violating anomalous trilinear gauge-boson form factors which couple theW (or theZ) to the photon and theZ. In order to see which form factors are generated by which types of underlying interactions, we work with as general an underlying model as is possible. After identifying which form factors can arise at one loop in a completely general renormalizable model of spin-half and spin-zero particles, we provide explicit formulae for the induced form factors in a very broad class of such models. Our results include some previous calculations as special cases, and we identify errors in some of these.     

Mathematical homogenization of inelastic dissipative materials: a survey and recent progress

In this paper, a review of papers on mathematical homogenization of dissipative composites under small strains and on the interplay between homogenization procedure and dissipation due to mechanical work is presented. Moreover, a critical survey on the links between mathematical homogenization and computational homogenization is attempted.     

X-ray and DFT Crystal Structure Determination and Conformational Analysis of a Pyrethroid Compound

The structure of （E）-N-[（E）-3-[（lR,2R）-2-（3,4-dibromo-phenyl）-l-fluro-cyclopropyl]- allylidene]-2-0-tolyl-acetamide （C21HIsONFBrz, Mr = 479.18） has been determined by X-ray single- crystal diffraction and theoretical calculations to establish the configuration, stereochemistry and a stable conformation of the molecule. The compound crystallizes in the monoclinic space group P21/c, a = 28.3452（10）, b = 4.9311（10）, c = 14.257（2） A, fl = 102.7654（10）, V = 1943.5（5） A3 and Z = 4. The structure has been refined to the final R = 0.05 for the observed structure factors with 1 〉 30（/）. Theoretical calculations in the ground state have been carried out for the compound studied using the Hartree-Fock （HF） and density functional theory （DFT） （B3LYP） with 6-31G（d,p） basis sets. The results show that the studied compound prefers the keto form. The compound involves intra- and intermolecular hydrogen bonding of C-H.-.O and C-H-..F types, which further stabilize the structure and display a trans configuration for the C=N and C=C double bonds. The calculated results show that the predicted geometry can well reproduce the structural parameters.     

Solubility study of sodium, potassium and calcium sulfates and chlorides, in ammonia

Solubility of sodium, potassium and calcium sulfates and chlorides in 28% ammonia solution was determined through monitoring conductivity measurements and kinetics of solids dissolution as a function of temperature and stirring time. The major findings of the present study show that Na₂SO₄ and K₂SO₄ solutions conductivity follow straight linear segments with different slopes. However, in case of NaCl, KC1, CaCl₂ and CaSO₄ · 2H₂O, conductivity curves were continuous, monotonous and reach constants maximum values. The hypothesis of complex formation or dissolution via intermediaries such as NaNH₄SO₄ and KNH₄SO₄ salts seams to be true, through X-ray diffraction study of resulting deposits. Furthermore, the dissolution rates at 25°C of potassium and calcium chlorides in ammonia solution are higher than that reported in the literature for water. In fact, ammonia significantly reduces the solubility of K₂SO₄; conversely, a slight increase in this parameter was observed for CaSO₄.     

Antireflective sol–gel TiO2 thin films for single crystal silicon and textured polycrystal silicon

In this paper, antireflective TiO₂ thin films have been prepared on single crystal silicon, and textured polycrystal silicon by sol–gel route using the dip-coating technique. The thickness and the refractive index of the films have been optimised to obtain low reflexion in the visible region, by controlling both the concentration of the titanium isopropoxide (Ti(ⁱOPr)₄), and the annealing temperature. We showed that the use of a TiO₂ single layer with a thickness of 64.5 nm, heat-treated at 450 or 300 °C, reduces the reflection on single crystal silicon at a level lower than 3% over the broadband spectral ranges 670–830 nm and 790–1010 nm, respectively. In order to broaden the spectral minimum reflectance as much as possible, we have proposed to texture polycrystal silicon wafers, and to coat these wafers by a TiO₂ single layer with a thickness of 73.4 nm. In this case, the reflectance has been reduced from 27 to 13% in the spectral range 460–1000 nm.