editorial reviewed / In this work, we present several generalized functional spaces, primarily the $T_p^u$ spaces, originally introduced in essence by Calderón and Zygmund through the lens of Boyd functions. We provide conditions that relate functions belonging to these spaces with their wavelet coefficients. Subsequently, we propose a multifractal...
peer reviewed / In this presentation, we introduce the notion of eventual φ-stability in return groups. It provides a general framework that extends notions previously explored in a variety of studies. While it would be difficult to single out a main result, the significance of this property lies in its applications to known concepts. We have highl...
peer reviewed
In combinatorics on words, for two finite words u and v, the binomial coefficient of u and v is the number of times v appears as a subsequence of u (also called (scattered) subword). For example, with u = alphalpha and v = al, there are = 36 ways to select 2 2 letters among 9, but only 3 of them give back v. Generalizing famous binomial coefficient...
This thesis deals with the theory of complex hyperbolicity, which studies the geometry of entire curves in complex manifolds, and more generally value distribution of meromorphic mappings between complex manifolds. The contributions of this memoir concerns two main questions. First, we wish to extend concepts and results of Nevanlinna theory of val...
La physique-chimie est une matière qui fait son apparition dès le collège. Comme la plupart des matières scientifiques, cette discipline requiert des compétences mathématiques, il s’agit d’une matière pluridisciplinaire. L’utilisation des outils mathématiques est un indispensable en science-physique. Les élèves ont parfois beaucoup de mal à disting...
We study normalisation as a rewriting system in the framework of two-way alternate bases. In this framework, nonnegative real numbers are represented by right-infinite words with a decimal point. A number may have multiple representations, among which one is distinguished unsing a greedy algorithm and called the expansion. The problem of normalisat...
In combinatorics on words, the well-studied factor complexity function $\rho_{\bf x}$ of a sequence ${\bf x}$ over a finite alphabet counts, for any nonnegative integer $n$, the number of distinct length-$n$ factors of ${\bf x}$. In this paper, we introduce the \emph{reflection complexity} function $r_{\bf x}$ to enumerate the factors occurring in ...
Deux visions s’opposent concernant les objectifs principaux de l’enseignement préscolaire, la manière dont les jeunes enfants apprennent et les pratiques pédagogiques à privilégier (Russell, 2011). Ces deux visions semblent avoir une incidence sur la conceptualisation et la mesure des connaissances pédagogiques de contenu (PCK - pedagogical content...
