Lower semicontinuity of the feasible set mapping of linear systems relative to their domains

This paper deals with stability properties of the feasible set of linear inequality systems having a finite number of variables and an arbitrary number of constraints. Several types of perturbations preserving consistency are considered, affecting respectively, all of the data, the left-hand side data, or the right-hand side coefficients.

On the stability of the Motzkin representation of closed convex sets

A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. This paper analyzes the continuity properties of the set-valued mapping associating to each couple (C,D) formed by a compact convex set C and a closed convex cone D its Minkowski sum C + D. The continuity properties of other related mappings are also analyzed.

Behavior of different soot combustion catalysts under NOx/O2. Importance of the catalyst–soot contact

Four different catalysts (Pt/Al2O3, Ce0.8Zr0.2O2, PrO2−x and SrTiCuO3) have been investigated on a laboratory scale to evaluate their potential as diesel soot combustion catalysts under different experimental conditions, which simulate the situation found in a continuous regeneration technology trap (dual-bed configuration of catalyst and soot) or a catalyst-coated filter system (single-bed configuration, both catalyst and soot particles mixed under loose-contact mode). Under dual-bed configuration, the behavior of the catalysts towards soot combustion are very similar, despite the differences observed in the NO2 production profiles. However, under single-bed configuration, there are important differences in the soot combustion activities and in the NO2 slip profiles. The configurations chosen have an enormous impact on CO/(CO + CO2) ratios of combustion products as well. The most active catalyst under NOx + O2 is PrO2−x combining a high contribution of active oxygen-assisted soot combustion as well as high NO2 production activity along the catalytic bed.

Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

Students’ understanding of the function-derivative relationship when learning economic concepts

The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.