Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré

We study the relationship between two classical approaches for quantitative ergodic properties: the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one based on functional inequalities (of Poincaré type). We show that they can be linked through new inequalities (Lyapunov-Poincaré inequalities). Explicit examples for diffusion processes are studied, improving some results in the literature. The example of the kinetic Fokker-Planck equation recently studied by Hérau and Nier, Helffer and Nier, and Villani is in particular discussed in the final section.     

Fix-Mahonian Calculus, II: Further statistics

Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistributed either with the triplet (fix, des, maj), or the pair (fix, maj), where “fix,” “des” and “maj” denote the number of fixed points, the number of descents and the major index, respectively.     

Aqueous Foams: A Field of Investigation at the Frontier Between Chemistry and Physics

This paper reviews the properties of aqueous foams. The current state of knowledge is summarized briefly and the interdisciplinary aspects of this field of investigation are emphasized. Many phenomena are controlled by physical laws, but they are highly dependent upon the chemicals used as foam stabilizers: surfactants, polymers, particles. Most of the existing work is related to surfactants and polymer foams, and little is known yet for particle foams although research in this field is becoming popular. This article presents the general concepts used to describe the monolayers and the films and also some of the recent advances being made in this area.     

Combined Poly(alkyl cyanoacrylate)/Cyclodextrin Nanoparticles

The use of nanoparticles is of great interest for oral or parenteral administration. In fact, nanoparticles not only can protect the active ingredient, but they confer on it a large contact surface with biological membranes and a possible improvement in bioavailability. Biodegradability of nanoparticles, which can be considered as a pre-requisite in the case of parenteral administration     

Bayes minimax estimators of the mean of a scale mixture of multivariate normal distributions

Bayes estimation of the mean of a variance mixture of multivariate normal distributions is considered under sum of squared errors loss. We find broad class of priors (also in the variance mixture of normal class) which result in proper and generalized Bayes minimax estimators. This paper extends the results of Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264] in a manner similar to that of Maruyama [Admissible minimax estimators of a mean vector of scale mixtures of multivariate normal distribution, J. Multivariate Anal. 21 (2003) 69-78] but somewhat more in the spirit of Fourdrinier et al. [On the construction of bayes minimax estimators, Ann. Statist. 26 (1998) 660-671] for the normal case, in the sense that we construct classes of priors giving rise to minimaxity. A feature of this paper is that in certain cases we are able to construct proper Bayes minimax estimators satisfying the properties and bounds in Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264]. We also give some insight into why Strawderman's results do or do not seem to apply in certain cases. In cases where it does not apply, we give minimax estimators based on Berger's [Minimax estimation of location vectors for a wide class of densities, Ann. Statist. 3 (1975) 1318-1328] results. A main condition for minimaxity is that the mixing distributions of the sampling distribution and the prior distribution satisfy a monotone likelihood ratio property with respect to a scale parameter.     

Expressing Forest Origins in the Chemical Composition of Cooperage Oak Woods and Corresponding Wines by Using FTICR‐MS

A non‐targeted, ultra‐high‐resolution mass spectrometric, direct analysis of oak‐wood extracts from two species (Quercus robur L. and Quercus petraea Liebl.) from three French forests, and of a wine aged in barrels derived therefrom has been performed to identify families of metabolites that could discriminate both the species and the geographical origin of woods. From 12 T ultra‐high‐resolution Fourier transform ion cyclotron resonance mass spectra of wood extracts, hundreds of mass signals were identified as possible significant biomarkers of the two species, with phenolic and carbohydrate moieties leading the differentiation between Q. robur and Q. petraea, respectively, as corroborated by both FTMS and NMR data. For the first time, it is shown that oak woods can also be discriminated on the basis of hundreds of forest‐related compounds, and particular emphasis is put on sessile oaks from the Tronçais forest, for which sugars are significantly discriminant. Despite the higher complexity and diversity of wine metabolites, forest‐related compounds can also be detected in wines aged in related barrels. It is only by using these non‐targeted analyses that such innovative results, which reveal specific chemodiversities of natural materials, can be obtained.     

1D to 3D NMR study of microporous alumino‐phosphate AlPO4‐40

From one‐ to two‐ and three‐dimensional MAS NMR solid‐state experiments involving ³¹P and ²⁷Al, we show that the structure of microporous alumino‐phosphate AlPO₄‐40 contains at least four times more sites than expected, and we attribute two types of Al_IV sites. The newly described ²⁷Al‐³¹P MQ‐HMQC opens new possibilities of describing details of three‐dimensional bounded networks. Copyright © 2009 John Wiley & Sons, Ltd.     

Dendriform equations

We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota–Baxter operators, e.g. the Riemann integral map or Jackson's q-integral.     

Influence of surface chemistry on the adsorption of oxygenated hydrocarbons on activated carbons

The objective of this work was to study the adsorption of different oxygenated hydrocarbons (methanol, ethanol, 1 and 2-butanol, methyl acetate) on activated carbons from organic mixtures with cyclohexane. Three activated carbons prepared by thermal and chemical treatments of a commercial carbon were employed for this purpose. Their textural properties were found to be similar, whereas their surface chemistries were modified, as shown by temperature-programmed desorption coupled to mass spectrometry (TPD-MS) and X-ray photoelectron spectroscopy (XPS). The adsorption isotherms were obtained by depletion method, and the analysis of adsorbed species was evaluated by TPD-MS to obtain new insight into the interactions between the different hydrocarbons and the carbon surface. Ethanol leads to a high-energy interaction between its hydroxyl function and the oxygenated surface groups and also to a lower energy interaction between the aliphatic part of the molecule and the carbon material. The desorption activation energy for this hydrophilic interaction is high (50 to 105 kJ/mol), and it is related to the nature of the carbon surface groups. The relative importance of these two interactions depend on the size of the alcohol/methanol is similar to ethanol, whereas butanols lead to more dispersive interactions. Methyl-acetate cannot undergo this kind of strong interaction and behaves like cyclohexane, having desorption activation energies ranging between 25 and 45 kJ/mol no matter the molecule and the carbon surface chemistry.