Analyse des problemes de geometrie et apprentissage de la preuve au secondaire

Résumé

Le présent article rend compte de l'élaboration d'une grille d'analyse des problèmes de géométrie, et de sa mise à l'épreuve par la classification des problèmes et exercices de géométrie synthétique dans une collection de manuels du secondaire parmi les plus utilisées au Québec. Le cadre conceptuel sur lequel s'appuie cette élaboration s'inspire principalement des travaux de Balacheff (1987), Barbin (1988), Brousseau (1998), Hanna (1995) et Rouche (1989), et débouche sur une typologie des preuves de géométrie. La classification des problèmes à partir de cette grille et l'analyse qui en découle nous a permis de conclure sur les aspects de l'apprentissage de la preuve que nous évaluons comme mal ? gérés ? dans la collection : transition non suffisamment graduelle du sensible au formel (peu de problèmes qui sollicitent une validation hybride, niveau de formalisation trop longtemps stationnaire), prépondérance des applications directes et des déductions locales sur les séquences déductives, intérêt et mode de présentation des résultats qui ne favorisent pas une ? attitude de preuve ?.     

Complete Classifications for the Communication Complexity of Regular Languages

We show that every regular language L has either constant, logarithmic or linear two-party communication complexity (in a worst-case partition sense). We prove similar classifications for the communication complexity of regular languages for the simultaneous, probabilistic, simultaneous probabilistic and Mod_p-counting models of communication.     

Regular Languages Defined by Generalized First-Order Formulas with a Bounded Number of Bound Variables

Abstract. We consider generalized first-order sentences over < using both ordinary and modular quantifiers. It is known that the languages definable by such sentences are exactly the regular languages whose syntactic monoids contain only solvable groups. We show that any sentence in this logic is equivalent to one using three variables only, and we prove that the languages expressible with two variables are those whose syntactic monoids belong to a particular pseudovariety of finite monoids, namely the wreath product of the pseudovariety DA (which corresponds to the languages definable by ordinary first-order two-variable sentences) with the pseudovariety of finite solvable groups. This generalizes earlier work of Thérien and Wilke on the expressive power of two-variable formulas in which only ordinary quantifiers are present. If all modular quantifiers in the sentence are of the same prime modulus, this provides an algorithm to decide if a regular language has such a two-variable definition.     

Tracking the mind during reading via eye movements: Comments on Kliegl, Nuthmann, and Engbert (2006).

R. Kliegl, A. Nuthmann, and R. Engbert (see record 2006-01956-002) reported an impressive set of data analyses dealing with the influence of the prior, present, and next word on the duration of the current eye fixation during reading. They argued that outcomes of their regression analyses indicate that lexical processing is distributed across a number of words during reading. The authors of this comment question their conclusions and address 4 different issues: (a) whether there is evidence for distributed lexical processing, (b) whether so-called parafoveal-on-foveal effects are widespread, (c) the role of correlational analyses in reading research, and (d) problems in their analyses because they use only cases in which words are fixated exactly once. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Collaborative Localization for Multi-Robot System with Fault Detection and Exclusion Based on the Kullback-Leibler Divergence

Multi-robot system attracted attention in various applications in order to replace the human operators. To achieve the intended goal, one of the main challenges of this system is to ensure the integrity of localization by adding a sensor fault diagnosis step to the localization task. In this paper, we present a framework able, in addition of localizing a group of robots, to detect and exclude the faulty sensors from the group with an optimized thresholding method. The estimator has the informational form of the Kalman Filter (KF) namely Information Filter (IF). A residual test based on the Kullback-Leibler divergence (KLD) between the predicted and the corrected distributions of the IF is developed. It is generated from two tests: the first acts on the means and the second deals with the covariance matrices. Thresholding using entropy based criterion and Receiver Operating Characteristics (ROC) curve are discussed. Finally, the validation of this framework is studied on real experimental data from a group of robots.     

Gain control by concerted changes in I(A) and I(H) conductances

Stability of intrinsic electrical activity and modulation of input-output gain are both important for neuronal information processing. It is therefore of interest to define biologically plausible parameters that allow these two features to coexist. Recent experiments indicate that in some biological neurons, the stability of spontaneous firing can arise from coregulated expression of the electrophysiologically opposing I(A) and I(H) currents. Here, I show that such balanced changes in I(A) and I(H) dramatically alter the slope of the relationship between the firing rate and driving current in a Hodgkin-Huxley-type model neuron. Concerted changes in I(A) and I(H) can thus control neuronal gain while preserving intrinsic activity.     

Hydrodynamic blood plasma separation in microfluidic channels

The separation of red blood cells from plasma flowing in microchannels is possible by biophysical effects such as the Zweifach–Fung bifurcation law. In the present study, daughter channels are placed alongside a main channel such that cells and plasma are collected separately. The device is aimed to be a versatile but yet very simple module producing high-speed and high-efficiency plasma separation. The resulting lab-on-a-chip is manufactured using biocompatible materials. Purity efficiency is measured for mussel and human blood suspensions as different parameters, such as flow rate and geometries of the parent and daughter channels are varied. The issues of blood plasma separation at the microscale are discussed in relation to the different regimes of flow. Results are compared with those obtained by other researchers in the field of micro-separation of blood.     

Numerical solution of transport equations for plasmas with transport barriers

An approach to solve numerically transport equations for plasmas with spontaneously arising and arbitrarily located transport barriers, regions with a strongly reduced transfer of energy, is proposed. The transport equations are written in a form conserving heat flux and solved numerically by using piecewisely exact analytical solutions of linear differential equations. Compared to standard methods, this approach allows to reduce significantly the number of operations required to obtain a converged solution with a heat conductivity changing abruptly at a critical temperature gradient and to use large time steps in modeling the formation and dynamics of transport barriers. Computations for the tokamak JET are done.     

A rapid h.p.l.c. method for the determination of methionine hydroxy analogue free acid in supplemented feeds

Two methods are described for determining methionine hydroxy analogue free acid (HMB) in supplemented poultry feeds. The procedure is based on extraction of analogue from the feed, followed by high-pressure liquid chromatographic measurement of the HMB directly after extraction or, more rigorously, after extraction and hydrolysis of oligomers to monomer. Recoveries of HMB over the supplementation range 0.08–0.25% (by wt) are 98% with coefficients of variation of 5.4% in commercial poultry feeds. A 98% correlation coefficient is obtained when the analyses are compared with the gas chromatographic method.