Vapour pressures and excess functions of N, N, N′, N′-tetramethylalkanediamine + cyclohexane. A group contribution study of the N---N proximity effect

The vapour pressuresof liquid cyclohexane + N, N, N′, N′-tetramethylalkanediamine, (CH₃)₂ N(CH₂)_uN(CH₃)₂ (u = 1,2) + cyclohexane mixtures were measured by a static method between 303.15 and 343.15 K at 10 K intervals. The excess molar enthalpies at 303.15 K were also measured.

The molar excess Gibbs energies, calculated from the vapour-liquid equilibrium data, and the molar excess enthalpies compare satisfactorily with group contribution (DISQUAC) predictions.

The proximity effect of N atoms produces a regular decrease of the interactional parameters.     

Stabilization of linear systems with saturation: a Sylvester equation approach

A new methodology of the partial eigenstructure assignmentby state feedback via Sylvester equation is used to obtain asolution of the constrained regulator problem for linear continuous-timeand discrete-time systems by using the reduced-order technique.     

Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations

Summary. A nonlinear Galerkin method using mixed finite elements is presented for the two-dimensional incompressible Navier-Stokes equations. The scheme is based on two finite element spaces and for the approximation of the velocity, defined respectively on one coarse grid with grid size and one fine grid with grid size and one finite element space for the approximation of the pressure. Nonlinearity and time dependence are both treated on the coarse space. We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin solution is of the order of $H^2$, both in velocity ( and pressure norm). We also discuss a penalized version of our algorithm which enjoys similar properties. Received October 5, 1993 / Revised version received November 29, 1993     

Evaluation of antioxidant activities of the edible and medicinal Acacia albida organs related to phenolic compounds

This study compared phenolic contents and antioxidant activity in different organs of Acacia albida (leaves and bark) and focuses on identification of phenolic compounds of leaves by HPLC-DAD. The analysed organs exhibited differences in total polyphenol contents (100 and 59.5 mg GAE g^? 1 DW). Phenolic contents of leaves were two times higher than those in bark. Ethanolic extracts exhibited good antioxidant activities with IC₅₀ = 26 μg mL^? 1 for DPPH and EC₅₀ = 50 μg mL^? 1 for FRAP. Identification by HPLC-DAD revealed the presence of nine phenolic compounds known for their high antioxidant activity. The results suggested that this species can be used as source of natural antioxidants.     

Chemical composition and antibacterial activity of Lavandula coronopifolia essential oil against antibiotic-resistant bacteria

The aim of this study was to analyse the composition of the essential oil (EO) of Lavandula coronopifolia from Morocco and to evaluate its in vitro antibacterial activity against antibiotic-resistant bacteria isolated from clinical infections. The antimicrobial activity was assessed by a broth micro-well dilution method using multiresistant clinical isolates of 11 pathogenic bacteria: Klebsiella pneumoniae subsp. pneumoniae, Klebsiella ornithinolytica, Escherichia coli, Enterobacter cloacae, Enterobacter aerogenes, Providencia rettgeri, Citrobacter freundii, Hafnia alvei, Salmonella spp., Acinetobacter baumannii and methicillin-resistant Staphylococcus aureus. The main compounds of the oil were carvacrol (48.9%), E-caryophyllene (10.8%) and caryophyllene oxide (7.7%). The oil showed activity against all tested strains with minimal inhibitory concentration (MIC) values ranging between 1% and 4%. For most of the strains, the MIC value was equivalent to the minimal bactericidal concentration value, indicating a clear bactericidal effect of L. coronopifolia EO.     

Isolation of berberine tannate using a chromatography activity-guided fractionation from root bark of Berberis hispanica Boiss. & Reut.

Root bark of Berberis hispanica Boiss. & Reut. constitutes an important source of alkaloids and is traditionally used in Algeria and Morocco in many herbal formulations particularly for the treatment of stomach infections and colon cancer. Activity-guided fractionation of Berberis extract is developed by step-gradient elution on column chromatography followed by preparative HPLC to isolate the most antistaphylococcal compound. Solvent extraction-activity screening indicates that ethanol should be used as the extracting solvent as it has exhibited the highest activity against Staphylococcus aureus(Rosenbach ATCC6538) followed by water extract, whereas no activity is recorded for acetone and hexane extracts. Screening of collected fractions from chromatographic separations indicates that the fraction presenting the highest antistaphylococcal activity is identified as berberine tannate by UV spectrum, melting point measurement and confirmed by liquid chromatography coupled to mass spectrometry (LC/MS). The minimal inhibition concentration value of berberine tannate against S. aureus is evaluated at 5?µg?mL^?1.     

Global Behavior of Positive Solutions of a Generalized Lane–Emden System of Nonlinear Differential Equations

In this paper we discuss the existence and the global behavior of positive solutions of the following generalized Lane–Emden system of differential equations:

$$\begin{aligned} -u''= & {} a(x)u^{\alpha }\,v^{r}\quad \text{ in } (0,1), \\ -v''= & {} b(x)u^{s}\,v^{\beta }\quad \, \text{ in } (0,1), \\ u'(0)= & {} v'(0)=0; \quad \, u(1)=v(1)=0, \end{aligned}$$

where \(r,\,s\in {\mathbb {R}}\), \(\alpha ,\,\beta <1\) such that \(\gamma :=(1-\alpha )(1-\beta )-rs>0\) and the nonnegative functions \(a,\,b\) satisfy some conditions related to the Karamata regular variation theory.

     

Continuity in law with respect to the Hurst index of some additive functionals of sub-fractional Brownian motion

In this article, first, we prove some properties of the sub-fractional Brownian motion introduced by Bojdecki et al. [Statist. Probab. Lett. 69(2004):405–419]. Second, we prove the continuity in law, with respect to small perturbations of the Hurst index, in some anisotropic Besov spaces, of some continuous additive functionals of the sub-fractional Brownian motion. We prove that our result can be obtained easily, by using the decomposition in law of the sub-fractional Brownian motion given by Bardina and Bascompte [Collect. Math. 61(2010):191–204] and Ruiz de Chavez and Tudor [Math. Rep. 11(2009):67–74], without using the result of Wu and Xiao [Stoch. Proc. Appl. 119(2009):1823–1844] by connecting the sub-fractional Brownian motion to its stationary Gaussian process through Lamperti’s transform. This decomposition in law leads to a better understanding and simple proof of our result.     

An optimisation method for separating and rebuilding one-dimensional dispersive waves from multi-point measurements. Application to elastic or viscoelastic bars

When using a classical SHPB (split Hopkinson pressure bar) set-up, the useful measuring time is limited by the length of the bars, so that the maximum strain which can be measured in material testing applications is also limited. In this paper, a new method with no time limits is presented for measuring the force and displacement at any station on a bar from strain or velocity measurements performed at various places on the bar. The method takes the wave dispersion into account, as must inevitably be done when making long time measurements. It can be applied to one-dimensional and single-mode waves of all kinds propagating through a medium (flexural waves in beams, acoustic waves in wave guides, etc.). With bars of usual sizes, the measuring time can be up to 50 times longer than the time available with classical methods. An analysis of the sensitivity of the results to the accuracy of the experimental data and to the quality of the wave propagation modelling was also carried out. Experimental results are given which show the efficiency of the method.     

Identification de la relation de dispersion dans les barresIdentification of the dispersion relation in rods

Dispersion and attenuation of longitudinal waves in elastic or weakly viscoelastic rods are measured by analysing the resonant frequencies present in the strain spectrum due to an unknown loading. The method takes the finite measuring time of the test into account. It is applied to an aluminium bar, in which the dispersion relation is identified very accurately at frequencies up to 60 kHz. To cite this article: R. Othman et al., C. R. Mecanique 330 (2002) 849–855.