https://luck.synhera.be/handle/123456789/168 2026-04-18T09:30:25Z https://luck.synhera.be/handle/123456789/2662 Approaching proof in geometry by folding problems with pre-service teachers NINOVE, Laure This study focuses on the geometric thinking of first-year pre-service middle school mathematics teachers and the potential contribution of folding prob lems to improving their geometric thinking regarding proofs. A significant propor tion of these students do not work with the level of geometric thinking that might be expected: When asked to prove a geometric property, they base their argumen tation partly on observations or measurements on the geometric diagram, whereas an answer based solely on deductive reasoning is required. To foster the entry of these students into deductive geometry, while at the same time offering to every student a first discovery of concepts related to the teaching and learning of plane geometry, we designed and experimented a teaching sequence based on folding problems. 2024-01-01T00:00:00Z https://luck.synhera.be/handle/123456789/1148 The T-PageRank : a Model of Self-Validating Effects of Web Surfing Akian, Marianne; Gaubert, Stéphane; NINOVE, Laure We model the behaviour of a surfer who makes a walk on the webgraph favouring webpages with high ranking. 2006-01-01T00:00:00Z https://luck.synhera.be/handle/123456789/1145 Affine iterations on nonnegative vectors Blondel, Vincent; NINOVE, Laure; Van Dooren, Paul In this paper we consider three different iterations and and analyze their fixed points and ate of convergence. The initial vector x0 is positive, and the vectors b and y and the iteration matrix A are all nonnegative. 2004-01-01T00:00:00Z https://luck.synhera.be/handle/123456789/1144 Multiple equilibria of nonhomogeneous Markov chains and self-validating web rankings Akian, Marianne; Gaubert, Stéphane; NINOVE, Laure PageRank is a ranking of the web pages that measures how often a given web page is visited by a random surfer on the web graph, for a simple model of web surfing. It seems realistic that PageRank may also have an influence on the behavior of web surfers. We propose here a simple model taking into account the mutual influence between web ranking and web surfing. Our ranking, the T-PageRank, is a nonlinear generalization of the PageRank. It is defined as the limit, if it exists, of some nonlinear iterates. A positive parameter T, the temperature, measures the confidence of the web surfer in the web ranking. We prove that, when the temperature is large enough, the T-PageRank is unique and the iterates converge globally on the domain. But when the temperature is small, there may be several T-PageRanks, that may strongly depend on the initial ranking. Our analysis uses results of nonlinear Perron-Frobenius theory, Hilbert projective metric and Birkhoff's coefficient of ergodicity. 2008-01-01T00:00:00Z