Global Weak Solutions for a Parabolic System Modeling a One-Dimensional Miscible Flow in Porous Media

We consider an initial boundary value problem for a nonlinear differential system of two equations. Such a system is formed by the equations of compressible miscible flow in a one-dimensional porous medium. No assumption about the mobility ratio is involved. Under some reasonable assumptions on the data, we prove the existence of a global weak solution. Our basic approach is the semi-Galerkin method. We use the technique of renormalized solutions for parabolic equations in the derivation ofa prioriestimates.     

Accuracy and CPU time of JE-TLM,PLRC-TLM and CRC-TLM methods for plasma medium

The current density (JE), the piecewise linear recursive convolution (PLRC) and the constant convolution recursive (CRC) techniques are developed and integrated into the transmission line matrix (TLM) algorithm. A comparison of these three schemes according to the criteria of accuracy and CPU time is presented. Numerical experiments show that JE provides the most accurate solution and requires the least CPU time; PLRC is nearly as accurate but consumes more CPU time than CRC.     

Simplification of the 1H NMR spectra of enantiomers dissolved in chiral liquid crystals, combining variable angle sample spinning and selective refocusing experiments

This work presents a technique to simplify overcrowded proton spectra in chiral liquid crystal solvents using rotation of the sample near the magic angle, VASS, combined with homonuclear selective refocusing 2D NMR experiments, SERF. This methodology provides a powerful tool to visualise enantiomers out of unresolved proton spectra. A modified SERF sequence is presented where the resulting 2D spectrum can be phased to increase the resolution. Accurate enantiomeric excesses are determined that are not possible to measure on static samples. Two examples are presented.     

Ultrasound-assisted one-pot synthesis of anti-CML nucleosides featuring 1,2,3-triazole nucleobase under iron-copper catalysis

A simple and efficient synthesis of modified 1,2,3-triazole nucleosides was developed. The strategy involved sequential one-pot acetylation-azidation-cycloaddition procedure and was found to be highly effective under a cooperative effect of ultrasound activation and iron/copper catalysis. The reactions were carried out under both conventional and ultrasonic irradiation conditions. In general, improvement in rates and yields were observed when reactions were carried out under sonication compared with conventional conditions. This one-pot procedure provides several advantages such as operational simplicity, high yield, safety and environment friendly protocol. The resulting substituted nucleosides were evaluated for their anticancer activity against K562 chronic myelogenous leukemia (CML) cell line.     

New insights on testing the efficiency of methods of pricing and hedging American options

With reference to the evaluation of the speed–precision efficiency of pricing and hedging of American Put options, we present and discuss numerical results obtained on the basis of four different large enough random samples according to the relevance of the American quality (relative importance of the early exercise opportunity) of the options. Here we provide a comparison of the best methods (lattice based numerical methods and an approximation of the American Premium analytical procedure) known in literature along with some key methodological remarks.     

Synthesis of SiO2-TiO2 xerogels by sol-gel process

A new method to synthesize SiO₂-TiO₂ gels by sol-gel process has been developed. This technique uses tetraisopropylorthotitanate [Ti(O ⁱ Pr)₄] and tetraethylorthosilicate [TEOS]: they are mixed in the same solvent and then directly hydrolysed. This one-step reaction is possible because of the use of 2-methoxyethanol, a protic polar solvent. This alcohol plays two different specific roles: it acts as a solvent as well as a stabilizer of titanium alkoxide towards the hydrolysis-precipitation reaction. So, by an accurate adjustment of the quantity of methoxyethanol in the mixture, we can control the reactivity of the titanium precursor.Monolithic and transparent xerogels were obtained whatever the composition. Three monolithic SiO₂-TiO₂ gels containing 20, 50 and 75 mol% of TiO₂ were prepared and studied in details.By using the TG-DSC analysis, we can follow the evolution of the loss of water and organic residues.The structural evolution of gels during calcination is characterized by IR spectroscopy and X-Ray diffraction.     

Silica-zirconia monoliths from gels

Zirconium propoxide and tetraethylorthosilicate were hydrolyzed in methoxyethanol which acts as stabilizer of zirconium and in presence of formamide or dimethylformamide as Drying Control Chemical Additives in order to obtain zirconia silica gels. The gels were dried at 70°C to get monolithic xerogels. The influence of zirconium content and DCCA on texture was determined. The evolution of these xerogels was investigated as a function of temperature between 70°C and 1000°C by thermogravimetry, differential scanning calorimetry, I.R. spectroscopy and R.X. diffractometry.