Decay estimates for second order evolution equations with memory

This paper develops a unified method to derive decay estimates for general second order integro-differential evolution equations with semilinear source terms. Depending on the properties of convolution kernels at infinity, we show that the energy of a mild solution decays exponentially or polynomially as t→+∞. Our approach is based on integral inequalities and multiplier techniques.These decay results can be applied to various partial differential equations. We discuss three examples: a semilinear viscoelastic wave equation, a linear anisotropic elasticity model, and a Petrovsky type system.     

A DFT study of inclusion complexes of the antituberculosis drugs pyrazinamide and isoniazid with cucurbit[7]uril

A photoactive system, (2E)-3-{3-[(Z)-naphthalen-1-yldiazenyl] phenyl} prop-2-enoic acid, was synthesized and incorporated on to beta-cyclodextrin (β-CD) core through esterification of the hydroxyl groups of β-CD with the free carboxyl moiety of the chromophoric system by DCC coupling. The silver nanoparticle was synthesized by the reduction reaction executed on silver acetate in presence of dodecyl amine. The silver nano particles were dispersed in β-CD aggregates modified with photoactive system by phase transfer mechanism. The products were characterized by elemental analysis, melting point determination, UV–visible, FT-IR and NMR (¹H and ¹³C) spectral methods and SEM and TGA-DTG thermal studies. The thermal studies shows that the silver nanoparticle dispersed functionally modified beta cyclodextrin exhibited enhanced thermal stability compared to the functionalised β-CD.     

Hydrogen Bonding Complexes of Poly(styrene-co-2-hydroxyethyl acrylate) and Poly (styrene-co-4-vinylpyridine)

Summary: Random copolymers of poly(styrene-co-4-vinylpyridine) (S4VP) and poly (styrene-co-2-hydroxyethyl acrylate) (SHEA) of different compositions were prepared and characterized. An investigation of the effects of solvent and densities of the interacting species incorporated within these copolymers showed that novel and various hydrogen bonding interpolymer complexes of different structures were elaborated when these copolymers are mixed together. The specific interactions that occurred within the SHEA copolymers and the elaborated complexes were evidenced by FTIR qualitatively from the appearance of a new band at 1604 cm⁻¹ and quantitatively using appropriate spectral curve fitting in the carbonyl and pyridine regions. The intermolecular hydrogen bonding interactions that occurred between the hydroxyl groups of the SHEA and the nitrogen atom of the pyridine groups in the S4VP are stronger than the self-associations within the SHEA. In the solid state, a DSC analysis showed that the variation of the glass transition temperatures of these materials with the composition behaved differently with the densities of interacting species and were analyzed quantitatively. A thermal stability study of the synthesized copolymers and of their different mixtures carried by thermogravimetry confirmed a similar behaviour.     

Analytical Determination of Flow Patterns in a Double Porosity Medium Containing Ellipsoidal Occluded Macro-Voids

This article presents the analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, occluded macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for the pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its size is characterized by the macro-porosity. Confrontations are made with numerical solutions in order to investigate the applicability of the analytical pressure and velocity solutions to microstructures of finite size.     

Vitesse de convergence en norme p-intégrale et normalité asymptotique de l'estimateur crible de l'opérateur d'un ARB(1)

The autoregressive model in a Banach space (ARB) allows to represent many continuous time processes used in practice (see, for example, D. Bosq, Linear Processes in Function Spaces: Theory and Applications, 2000, Springer, p. 150). In this Note we study an estimator of the operator in ARB(1) by the least squares method, when the operator is strictly p-integral, $p\in ]1,\infty [$, and we use Grenander's method of sieves (From U. Grenander, Abstract Inference, Wiley, 1981). We show consistency of the sieve estimator and we derive a central limit theorem for this estimator. To cite this article: F. Rachedi, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Donor atom dependent geometric isomers in mononuclear oxo-molybdenum(V) complexes: implications for coordinated endogenous ligation in molybdoenzymes

We have previously demonstrated that the complex [(L1O)MoOCl(2)], where L1OH = (2-hydroxy-3-tert-butyl-5-methylphenyl)bis(3,5-dimethylpyrazolyl)methane, exists as both cis and trans isomers (Kail, B.; Nemykin, V. N.; Davie, S. R.; Carrano, C. J.; Hammes, B. S.; Basu, P. Inorg. Chem. 2002, 41, 1281-1291). Here, the cis isomer is defined as the geometry with the heteroatom in the equatorial position, and the trans isomer is designated as the geometry with the heteroatom positioned trans to the terminal oxo group. The trans isomer represents the thermodynamically more stable geometry as indicated by its spontaneous formation from the cis isomer. In this report, we show that for complexes of [(LO)MoOCl(2)], where LOH is the sterically less restrictive (2-hydroxyphenyl)bis(3,5-dimethylpyrazolyl)methane, only the trans isomer could be isolated, while in the corresponding thiolate containing ligand (2-dimethylethanethiol)bis(3,5-dimethylpyrazolyl)methane (L3SH) only the cis isomer could be observed. In addition, we have isolated and structurally characterized the complex [(L1O)MoO(OPh)(Cl)], a rare example of a species possessing both cis and trans phenolates. Using DFT calculations, we have investigated the origins of the differences in stability between the cis and trans isomers in these complexes and suggest that they are related to the trans influence of the oxo-group. Crystal data for [(LO)MoOCl(2)] (1) include that it crystallizes in the triclinic space group P(-)1 with cell dimensions a = 8.9607 (12) A, b = 10.596 (4) A, c = 13.2998 (13) A, alpha = 98.03 (2) degrees, beta = 103.21 (2) degrees, gamma = 110.05(2) degrees, and Z = 2. [(L1O)MoO(OPh)Cl].2CH(2)Cl(2) (2.2CH(2)Cl(2)) crystallizes in the triclinic space group P(-)1 with cell dimensions a = 12.2740 (5) A, b = 13.0403 (5) A, c = 13.6141 (6) A, alpha = 65.799 (2) degrees, beta = 64.487 (2) degrees, gamma = 65.750 (2) degrees, and Z = 2. [(L3S)Mo(O)Cl(2)] (3) crystallizes in the orthorhombic space group Pna2(1), with cell dimensions a = 13.2213 (13) A, b = 8.817 (2) A, c = 15.649 (4) A, and Z = 4. The implications of these results on the function of mononuclear molybdoenzymes such as sulfite oxidase, and the DMSO reductase, are discussed.     

Electrochemical determination of Cd<Superscript>2+</Superscript> at a titanium electrode modified with a lead film by square wave anodic stripping voltammetry

The modified titanium electrode with lead film (PbTiE) was used for determination of trace levels of cadmium using square wave anodic stripping voltammetry (SWASV). The measurement of cadmium on the PbTiE has the best reply under the following conditions of PbTiE preparation: 10^–3 mol L^–1 Pb²⁺ in HCl (pH 1.0), deposition potential of–1.40 V vs. Ag/AgCl/KCl_sat and deposition time of 300 s. The PbTiE reveals highly linear behavior in the concentration range 5 × 10^–8 to 10^–6 mol L^–1, with a limit of detection of 2 × 10^–9 mol L^–1. Interference of nine ionic species was evaluated. The measurements were carried out without removing dissolved oxygen from the solution.     

Simulations of sooting turbulent jet flames using a hybrid flamelet/stochastic Eulerian field method

The stochastic Eulerian field method is applied to simulate 12 turbulent C₁?C₃ hydrocarbon jet diffusion flames covering a wide range of Reynolds numbers and fuel sooting propensities. The joint scalar probability density function (PDF) is a function of the mixture fraction, enthalpy defect, scalar dissipation rate and representative soot properties. Soot production is modelled by a semi-empirical acetylene/benzene-based soot model. Spectral gas and soot radiation is modelled using a wide-band correlated-k model. Emission turbulent radiation interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modelled using the optically thin fluctuation approximation. Model predictions are found to be in reasonable agreement with experimental data in terms of flame structure, soot quantities and radiative loss. Mean soot volume fractions are predicted within a factor of two of the experiments whereas radiant fractions and peaks of wall radiative fluxes are within 20%. The study also aims to assess approximate radiative models, namely the optically thin approximation (OTA) and grey medium approximation. These approximations affect significantly the radiative loss and should be avoided if accurate predictions of the radiative flux are desired. At atmospheric pressure, the relative errors that they produced on the peaks of temperature and soot volume fraction are within both experimental and model uncertainties. However, these discrepancies are found to increase with pressure, suggesting that spectral models describing properly the self-absorption should be considered at over-atmospheric pressure.     

Antibacterial and antioxidant potency of floral honeys from different botanical and geographical origins

In order to assess their physicochemical and antioxidant properties as well as their antimicrobial potency, four varieties of honey from different botanical and geographical origins were used. The agar incorporation method was used to determine the antimicrobial potency of honeys. The total phenol content was determined by a modified Folin-Ciocalteu method and the free radical scavenging activity by the Fe³⁺ reducing power (FRAP) assay. Manuka honey was the most effective against Staphylococcus aureus Oxa R and S. aureus Oxa S with a Minimum Inhibitory Concentration (MIC) of 6% and 7%, respectively, whereas wild carrot honey was the most effective against Pseudomonas aeruginosa, with a MIC of 12%. Lavender honey was the least effective against all tested strains, even though was found to have the lowest pH and water content. Manuka honey had the highest content of polyphenols, with 899.09 ± 11.75 mg gallic acid/kg, whereas lavender honey had the lowest, with 111.42 ± 3.54 mg gallic acid/kg. A very significant correlation (r value was 0.9079 at P < 0.05) was observed between the total polyphenolic content and the Fe²⁺ content formed in the presence of the honey antioxidants. The differences between honey samples in terms of antibacterial and antioxidant activity could be attributed to the natural variations in floral sources of nectar and the different locations.