Classes polaires associées aux distributions holomorphes de sous-espaces tangents*

Résumé. Nous définissons des classes polaires associées à une distribution holomorphe singulière de sous-espaces tangents d’une variété projective lisse. Nous prouvons que ces classes polaires peuvent être calculées en fonction des classes de Chern-Mather du faisceau tangent de la distribution et réciproquement. Nous utilisons leurs degrés pour borner les degrés de certaines classes polaires associés à une variété invariante. *Ce travail a été soutenu par l’Accord de Coopération France-Brésil (CNRS/CNPq) et par la Fondation CAPES-Brésil.     

A higher resolution edge‐based finite volume method for the simulation of the oil–water displacement in heterogeneous and anisotropic porous media using a modified IMPES method

In this article, we present a higher‐order finite volume method with a ‘Modified Implicit Pressure Explicit Saturation’ (MIMPES) formulation to model the 2D incompressible and immiscible two‐phase flow of oil and water in heterogeneous and anisotropic porous media. We used a median‐dual vertex‐centered finite volume method with an edge‐based data structure to discretize both, the elliptic pressure and the hyperbolic saturation equations. In the classical IMPES approach, first, the pressure equation is solved implicitly from an initial saturation distribution; then, the velocity field is computed explicitly from the pressure field, and finally, the saturation equation is solved explicitly. This saturation field is then used to re‐compute the pressure field, and the process follows until the end of the simulation is reached. Because of the explicit solution of the saturation equation, severe time restrictions are imposed on the simulation. In order to circumvent this problem, an edge‐based implementation of the MIMPES method of Hurtado and co‐workers was developed. In the MIMPES approach, the pressure equation is solved, and the velocity field is computed less frequently than the saturation field, using the fact that, usually, the velocity field varies slowly throughout the simulation. The solution of the pressure equation is performed using a modification of Crumpton's two‐step approach, which was designed to handle material discontinuity properly. The saturation equation is solved explicitly using an edge‐based implementation of a modified second‐order monotonic upstream scheme for conservation laws type method. Some examples are presented in order to validate the proposed formulation. Our results match quite well with others found in literature. Copyright © 2016 John Wiley & Sons, Ltd.     

A simple protocol for the preparation of β-enamino ketones catalyzed by NbOPO4 under solvent free conditions

A novel application of the highly stable niobium oxide phosphate (NbOPO₄) as an efficient catalyst for the synthesis of β-enamino ketones under solvent-free conditions is described. This protocol, exhibits attractive yields, short reaction periods, lower loading of catalyst and high chemoselectivity.     

Assessment of pharmacokinetic interaction between piracetam and l‐carnitine in healthy subjects

A rapid, sensitive and specific method for quantifying piracetam in human plasma using Piracetam d‐8 as the internal standard (IS) is described. The analyte and the IS were extracted from plasma by one‐step precipitation of protein using an acetonitrile (100%). The extracts were analyzed by high‐performance liquid chromatography coupled with electrospray tandem mass spectrometry (HPLC‐MS/MS). The method had a chromatographic run time of 3.8 min and a linear calibration curve over the range 0.5–50 µg/mL (r > 0.99). This LC‐MS‐MS procedure was used to assess the bioavailability of two piracetam formulations: piracetam + l‐carnitine (Piracar®; 270/330 mg tablet) and piracetam (Nootropil®; 800 mg tablet) in healthy volunteers of both sexes. The geometric means with corresponding 90% confidence interval (CI) for test/reference percentage ratios were 88.49% (90% CI = 81.19 – 96.46) for peak concentration/dose and 102.55% (90% CI = 100.62 – 104.51) for AUC_inf/dose. The limit of quantitation of 0.5 µg/mL is well suited for pharmacokinetic studies in healthy volunteers. It was concluded that piracetam (Piracar®; 270/330 mg tablet) has a bioavailability equivalent to the piracetam (Nootropil®; 800 mg tablet) formulation with regard to both the rate and the extent of absorption. Copyright © 2015 John Wiley & Sons, Ltd.     

Ultrasound promoted synthesis of thioesters from 2-mercaptobenzoxa(thia)zoles

An ultrasound-enhanced method has been developed for the synthesis of a variety of thioesters from benzoyl chlorides and 2-mercaptobenzoxa(thia)zoles. Applying this methodology, 14 compounds were synthesized in excellent yields.     

Exact Gaussian expansions of Slater-type atomic orbitals

Three exact Slater-type function (STO) integral transforms are presented. The STO-NG basis set can then be developed using either only 1s Gaussian functions, the same Gaussian exponents for each shell, or using the first Gaussian of each symmetry. The use of any of these three alternatives depends only on appropriate numerical integration techniques.     

Influence of attenuation on the behavior of refracted elastic waves at the interface between anisotropic media

During the ultrasonic non-destructive evaluation of complex materials, like multilayer or composite materials, the behavior of the ultrasonic waves at the interface of samples is strongly dependent upon the anisotropy as well as the attenuation characteristics of the propagation media. In the generally arbitrary case, the incident wave is assumed to be inhomogeneous. Therefore the application of the Snell-Descartes laws requires to consider the real as well as the imaginary parts of all the quantities encountered during the study. In that aim, we use a representation of the complex slowness curves so-called slowness interface curves which point out the evolution of the interaction of the waves at the interface with the inhomogeneity factors, i.e. the imaginary part of the slowness vectors. The continuous distortion of the curves with the inhomogeneity factor increasing is an interesting approach of these complicated phenomena.