Riemann-measurable selections

LetX be a Polish space equipped with a -finite regular Borel measure . IfE is a metric space andF a set-valued function:X 2 ^E with complete values, and ifF is lower semicontinuous at almost all points ofX, we prove that there exists a Riemann-measurable selections ofF.     

On a minimax theorem

The aim of this note is to prove the following statement. It gives an extension of the theorem proved by O. Y. Borenshtein and V. S. Shul'man in [1].     

Synthesis of Glux based polymers for removal of benzene derivatives and pesticides from water

In this study, biomass‐derived Glux was used as a monomer in the polymerization of a novel semi‐aromatic polyethersulfone and polyester. The characterization of the synthesized polymers was carried out by means of MALDI‐TOF and NMR spectroscopy, differential scanning calorimetry, and thermogravimetric analysis. These two polymers were tested as sorbent phases of two families of pollutants (benzene derivatives and pesticides) in water. The analysis of the target hydrophilic pollutants was successfully achieved using high performance liquid chromatography meanwhile gas chromatography was applied for the detection of the hydrophobic pollutants. The adsorption data demonstrate that the novel polyethersulfone based on Glux can effectively remove the studied organic pollutants (polar and non polar, 90% to 100%) at environmental concentration (tested concentration: 1 mg L^?1) simultaneously when present in mixtures.     

Multivariate dynamic model for ordinal outcomes

Individual or stand-level biomass is not easy to measure. The current methods employed, based on cutting down a representative sample of plantations, make it possible to assess the biomasses for various compartments (bark, dead branches, leaves, …). However, this felling makes individual longitudinal follow-up impossible. In this context, we propose a method to evaluate individual biomasses by compartments when these are ordinals. Biomass is measured visually and observations are therefore not destructive. The technique is based on a probit model redefined in terms of latent variables. A generalization of the univariate case to the multivariate case is then natural and takes into account of dependency between compartment biomasses. These models are then extended to the longitudinal case by developing a Dynamic Multivariate Ordinal Probit Model. The performance of the MCMC algorithm used for the estimation is illustrated by means of simulations built from known biomass models. The quality of the estimates and the impact of certain parameters, are then discussed.     

Determination of the interactions in confined macroscopic Wigner islands: theory and experiments

Macroscopic Wigner islands present an interesting complementary approach to explore the properties of two-dimensional confined particles systems. In this work, we characterize theoretically and experimentally the interaction between their basic components, viz., conducting spheres lying on the bottom electrode of a plane condenser. We show that the interaction energy can be approximately described by a decaying exponential as well as by a modified Bessel function of the second kind. In particular, this implies that the interactions in this system, whose characteristics are easily controllable, are the same as those between vortices in type-II superconductors.