Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields

We provide normal forms and the global phase portraits in the Poincaré disk for all the Hamiltonian linear type centers of linear plus cubic homogeneous planar polynomial vector fields.     

A networking method to compare theories: metacognition in problem solving reformulated within the Anthropological Theory of the Didactic

An important role of theory in research is to provide new ways of conceptualizing practical questions, essentially by transforming them into scientific problems that can be more easily delimited, typified and approached. In mathematics education, theoretical developments around ‘metacognition’ initially appeared in the research domain of Problem Solving closely related to the practical question of how to learn (and teach) to solve non-routine problems. This paper presents a networking method to approach a notion as ‘metacognition’ within a different theoretical perspective, as the one provided by the Anthropological Theory of the Didactic. Instead of trying to directly ‘translate’ this notion from one perspective to another, the strategy used consists in going back to the practical question that is at the origin of ‘metacognition’ and show how the new perspective relates this initial question to a very different kind of phenomena. The analysis is supported by an empirical study focused on a teaching proposal in grade 10 concerning the problem of comparing mobile phone tariffs.     

Spectrophotometric analysis of mixtures of two components with extensively or completely overlapping spectra by the H-point standard additions method

Summary This paper discusses the requirements and scope of application of the H-Point Standard Additions Method (HPSAM) for resolving binary mixtures. Various mixtures of dyes with extensively or completely overlapping spectra were assayed with accurate, precise results. The method thus developed was also applied to the spectrophotometric resolution of binary mixtures of phenol and o-cresol, the absorption bands of which lie in similar positions and feature similar absorptivities.