On the stability of Voronoi cells

Let T be a given subset of ℝ n , whose elements are called sites, and let s∈T. The Voronoi cell of s with respect to T consists of all points closer to s than to any other site. In many real applications, the position of some elements of T is uncertain due to either random external causes or to measurement errors. In this paper we analyze the effect on the Voronoi cell of small changes in s or in a given non-empty set P⊂T\{s}. Two types of perturbations of P are considered, one of them not increasing the cardinality of T. More in detail, the paper provides conditions for the corresponding Voronoi cell mappings to be closed, lower and upper semicontinuous. All the involved conditions are expressed in terms of the data.

Steam reforming of ethanol over bimetallic RhPt/La2O3: Long-term stability under favorable reaction conditions

Recently, the steam reforming of biofuels has been presented as a potential hydrogen source for fuel cells. Because this scenario represents an interesting opportunity for Colombia (South America), which produces large amounts of bioethanol, the steam reforming of ethanol was studied over a bimetallic RhPt/La2O3 catalyst under bulk mass transfer conditions. The effect of temperature and the initial concentrations of ethanol and water were evaluated at space velocities above 55,000 h−1 to determine the conditions that maximize the H2/CO ratio and reduce CH4 production while maintaining 100% conversion of ethanol. These requirements were accomplished when 21 mol% H2O and 3 mol% C2H5OH (steam/ethanol molar ratio = 7) were reacted at 600 °C. The catalyst stability was assessed under these reaction conditions during 120 h on stream, obtaining ethanol conversions above 99% during the entire test. The effect of both H2 and air flows as catalyst regeneration treatments were evaluated after 44 and 67 h on stream, respectively. The results showed that H2 treatment accelerated catalyst deactivation, and air regeneration increased both the catalyst stability and the H2 selectivity while decreasing CH4 generation. Fresh and spent catalyst samples were characterized by TEM/EDX, XPS, TPR, and TGA. Although the Rh and Pt in the fresh catalyst were completely reduced, the spent samples showed a partial oxidation of Rh and small amounts of carbonaceous residue. A possible Rh–Pt–Rh2O3 structure was proposed as the active site on the catalyst, which was regenerated by air treatment.

Pt- and Ru-Doped SnO2–Sb Anodes with High Stability in Alkaline Medium

Different Pt- and Ru-doped Ti/SnO2–Sb electrodes were synthesized by thermal decomposition. The effect of the gradual substitution of Sb by Ru in the nominal composition on the physicochemical and electrochemical properties were evaluated. The electrochemical stability of the electrodes was estimated from accelerated tests at 0.5 A cm–2 in 1 M NaOH. Both as-synthesized and deactivated electrodes were thoroughly characterized by scanning electron microscopy (SEM), energy-dispersive X-ray microanalysis (EDX), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS) and X-ray diffraction analysis (XRD). The incorporation of a small amount (about 3 at. %) of both Pt and Ru into the SnO2–Sb electrodes produced a 400-times increase in their service life in alkaline medium, with no remarkable change in the electrocatalysis of the oxygen evolution reaction (OER). It is concluded that the deactivation of the electrodes is promoted by alkaline dissolution of metal species and coating detachment at high potentials. The introduction of Pt has a coating compacting effect, and Ru(IV), at low amounts until 9.75 at. %, replaces the Sn(IV) cations in the rutile-like SnO2 structure to form a solid solution that strongly increases the stability of the electrodes. The observed Ru segregation and decreased stability for larger Ru contents (x > 9.75 at. %), together with the selective dissolution of Ru after deactivation, suggest that the formation of a homogeneous (RuδSn1−δ)O2 single-phase is crucial for the stabilization of these electrodes.

Stability in Linear Optimization Under Perturbations of the Left-Hand Side Coefficients

This paper studies stability properties of linear optimization problems with finitely many variables and an arbitrary number of constraints, when only left hand side coefficients can be perturbed. The coefficients of the constraints are assumed to be continuous functions with respect to an index which ranges on certain compact Hausdorff topological space, and these properties are preserved by the admissible perturbations. More in detail, the paper analyzes the continuity properties of the feasible set, the optimal set and the optimal value, as well as the preservation of desirable properties (boundedness, uniqueness) of the feasible and of the optimal sets, under sufficiently small perturbations.