Non-porous reference carbon for N2 (77.4 K) and Ar (87.3 K) adsorption

A new non-porous carbon material from granular olive stones has been prepared to be used as a reference material for the characterization of the pore structure of activated carbons. The high precision adsorption isotherms of nitrogen at 77.4 K and argon at 87.3 K on the newly developed sample have been measured, providing the standard data for a more accurate comparative analysis to characterize disordered porous carbons using comparative methods such as t- and αS-methods.

Non-covalent immobilization of RhDuphos on carbon nanotubes and carbon xerogels

The immobilization of the chiral complex RhDuphos, by electrostatic or π–π (adsorption) interactions, on carbon nanotubes and carbon xerogels is investigated. To promote such interactions, the supports were either oxidized or heat treated to create carboxylic type surface groups or an apolar surface, respectively. The catalysts were tested in the hydrogenation of methyl 2-acetamidoacrylate. The prepared hybrid catalysts are less active than the homogeneous RhDuphos, but most of them show a high enantioselectivity and the one prepared with the oxidized carbon xerogel is also reusable, being able to give a high substrate conversion, keeping as well a high enantioselectivity. The anchorage by electrostatic interactions is more interesting than the anchorage by π–π interactions, as the π–π adsorption method produces a modification of the metal complex structure leading to an active hybrid catalyst but without enantioselectivity. The creation of carboxylic groups on the support surface has led to some hindering of the complex leaching.

Cost sharing solutions defined by non-negative eigenvectors

The problem of sharing a cost M among n individuals, identified by some characteristic ci∈R+,ci∈R+, appears in many real situations. Two important proposals on how to share the cost are the egalitarian and the proportional solutions. In different situations a combination of both distributions provides an interesting approach to the cost sharing problem. In this paper we obtain a family of (compromise) solutions associated to the Perron’s eigenvectors of Levinger’s transformations of a characteristics matrix A. This family includes both the egalitarian and proportional solutions, as well as a set of suitable intermediate proposals, which we analyze in some specific contexts, as claims problems and inventory cost games.