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.     

Untersuchung von Vitaminen

Ohne Zusammenfassung     

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.     

Selen

Ohne Zusammenfassung     

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     

Production of large quantities of “Janus” nanoparticles using wax-in-water emulsions

For the first time, large amount of Janus silica particles as small as 100 nm in diameter were prepared through a simple method based on the elaboration of Pickering emulsions of wax-in-water. Controlling the kinetic stabilization of wax droplets allows the fabrication of gram-sized quantities of regular asymmetric inorganic particles with high yield. In fact, our method is based on a limited coalescence process, which allows one to predict the quantity of interface which is produced when working with a known mass of wax, and thus to be sure that all introduced silica particles are adsorbed on the wax surface. To this end, the hydrophilic surface of the silica particles was made partially hydrophobic by adsorbing a known amount of surfactant: cetyltrimethylammonium bromide (CTAB). Varying the concentration in surfactant results in tuning the penetration rate of the particles in the wax droplets, leading to various dimension of the modified area. The broken spherical symmetry of the particle surface was thereafter revealed by the selective adsorption of gold nanoparticles on the amino-modified surface.