We consider numeration systems based on a d-tuple U=(U_1,...,U_d) of sequences of integers and we define (U,K)-regular sequences through K-recognizable formal series, where K is any semiring. We show that, for any d-tuple U of Pisot numeration systems and any commutative semiring K, this definition does not depend on the greediness of the U-represe...
Nous nous intéressons à l'enseignement de la statistique descriptive au niveau de la TSU (Transition Secondaire-Université). Nous présentons un modèle didactique sous forme d'un graphe dont les sommets (ou pôles) sont relatifs aux savoirs en jeu (c'est-à-dire au savoir savant, au savoir à enseigner, au savoir enseigné et au savoir appris), tandis q...
The notion of b-regular sequences was generalized to abstract numeration systems by Maes and Rigo in 2002. Their definition is based on a notion of S-kernel that extends that of b-kernel. However, this definition does not allow us to generalize all of the many characterizations of b-regular sequences. In this paper, we present an alternative defini...
We consider the space C^1(K) of real-valued continuously differentiable functions on a compact set K ⊆ Rd. We characterize the completeness of this space and prove that the restriction space C^1(Rd|K) ={f|K : f ∈ C1(Rd)} is always dense in C1(K). The space C1(K) is then compared with other spaces of differentiable functions on compact sets.
In this presentation, I introduce the notions of subshifts, S-adic representations and dendric subshifts. I then give a method to obtain an S-adic representation of any dendric subshift and briefly explain how to find a set of S-adic representations which characterises the ternary dendric subshifts.
Cluster analysis is one of the most applied methods which help researchers to find a structure in their dataset by dividing observations into necessary homogeneous groups such that observations in each group have similar properties and different characteristics in separate groups. A general and non-avoidable challenge in real-world data analysis, w...
We consider the regularity of p-adic Davenport series and some related functions.
Nous étudions les fonctions qui admettent une différentielle, au sens de Fréchet, sur un ensemble compact. On s'intéresse notamment à diverses propriétés topologiques de l'espace regroupant ces fonctions, muni d'une norme naturelle. Entre autres, la complétude de ce dernier est caractérisée et la densité des jets de Whitney est établie. Les espaces...
Peer reviewed
