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 ?.     

Theoretical Modelling of Film-Forming Mechanisms Under Transient Conditions: Application to Deceleration and Experimental Validation

This paper proposes an analytical model for line (1D) and point contacts (2D), based upon the Ertel’s hypothesis to predict the evolution of film thickness in steady-state and transient conditions in elastohydrodynamic lubrication. This theoretical approach, applied to a velocity ramp at constant deceleration, is perfectly supported by experimental results in terms of film thickness distribution during the deceleration process and in terms of central film thickness at the vanishing of the entrainment velocity. This work emphasizes the role of the transport effects of the lubricant at the instantaneous entrainment velocity on the time and length scales at which the film thickness disturbances induced by the deceleration process occur until the complete halting of the surfaces.     

Investigation of the Influence of Heat Balance Shifts on the Freeze Microstructure and Composition in Aluminum Smelting Bath System: Cryolite-CaF2-AlF3-Al2O3

Metallurgical and Materials Transactions B - In an aluminum electrolysis cell, the side ledge forms on side walls to protect it from the corrosive cryolitic bath. In this study, a series of...     

Community energy planning in Canada: The role of renewable energy

An emerging trend in Canada is the creation of community energy plans, where decisions that used to be left to regional level energy agencies or private individuals are now being considered at the community level. A desire to reduce greenhouse gas emissions and to become more energy self-sufficient is driving this change. Theoretically, local level management is desirable because it achieves these goals through improvements in the three areas of energy efficiency, energy conservation and switching to renewable energy sources. The analysis of 10 of the first community energy plans in Canadian communities, ranging in population size from 500 to one million, finds that communities are choosing policies and programs centred on increasing energy efficiency and conservation while renewable energy receives much less attention. Municipal operations were called upon to set higher targets than the general community. Communities that recognized the substantial potential of renewable energy often focused on technologies that the municipal sector could implement, such as bio-fuels for their transportation fleet. Wind, passive solar design, solar photovoltaics and solar thermal options were only recommended in a few cases. Overall, only one of the five larger communities (Calgary) recommended implementing multiple renewable energy technologies while three of the five smaller communities proposed multiple renewable energy sources. The implication is that smaller and more remote communities may be the most willing to lead in the planned introduction of renewable energy systems.     

Relation between microstructure and glass transition temperature of poly[(methyl methacrylate)‐co‐(ethyl acrylate)]

The glass transition temperature of a series of samples of the poly[(methyl methacrylate)‐co‐(ethyl acrylate)] copolymer, synthesized at low conversion, were calculated theoretically using the equations of Barton and Johnston. The values obtained are more precise when the probabilities of the compositional diads are derived from the ¹³C NMR data instead of the classical method utilizing reactivity ratios. This can be observed more clearly when the copolymer samples are synthesized at high conversion. Introduction of configuration (tacticity) at the diad level confirms the above observations and slightly improves the calculated values of T_g compared to the initial formulae which were only taking into account the compositional sequences of the copolymer. © 2001 Society of Chemical Industry     

Conversion of amorphous TiO2 coatings into their crystalline form using a novel microwave plasma treatment

Crystalline titanium dioxide (TiO₂) coatings have been widely used in photo-electrochemical solar cell applications. In this study, TiO₂ and carbon-doped TiO₂ coatings were deposited onto unheated titanium and silicon wafer substrates using a DC closed-field magnetron sputtering system. The resultant coatings had an amorphous structure and a post-deposition heat treatment is required to convert this amorphous structure into the photoactive crystalline phase(s) of TiO₂. This study investigates the use of a microwave plasma heat treatment as a means of achieving this crystalline conversion. The treatment involved placing the sputtered coatings into a 2.45 GHz microwave-induced nitrogen plasma where they were heated to approximately 550 °C. It was observed that for treatment times as short as 1 min, the 0.25-μm thick coatings were converted into the anatase crystalline phase of TiO₂. The coatings were further transformed into the rutile crystalline phase after treatments at higher temperatures. The doping of TiO₂ with carbon was found to result in a reduction in this phase transformation temperature, with higher level of doping (up to 5.8% in this study) leading to lower anatase-to-rutile transition temperature. The photoactivity performance of both doped and un-doped coatings heat-treated using both furnace and microwave plasma was compared. The carbon-doped TiO₂ exhibited a 29% increase in photocurrent density compared to that observed for the un-doped coating. Comparing carbon-doped coatings heat-treated using the furnace and microwave plasma, it was observed that the latter yielded a 19% increase in photocurrent density. This enhanced performance may be correlated to the differences in the coatings' surface morphology and band gap energy, both of which influence the coatings' photoabsorption efficiency.     

Supervisory fault‐tolerant control with mutual performance optimization

The problem of active fault‐tolerant control with reconfiguration mechanism for uncertain linear systems with external disturbances is addressed applying the supervisory control approach. A key feature of the proposed approach is establishment of a set of conditions providing mutual performance in the sense of taking into account the interaction of the fault detection, isolation, and accommodation subsystems in order to achieve global fault‐tolerance performance with guaranteed global stability. The efficiency of the approach is demonstrated in an example of computer simulation for a flight system benchmark. Copyright © 2012 John Wiley & Sons, Ltd.     

PCA3 and PCA3-Based Nomograms Improve Diagnostic Accuracy in Patients Undergoing First Prostate Biopsy

While now recognized as an aid to predict repeat prostate biopsy outcome, the urinary PCA3 (prostate cancer gene 3) test has also been recently advocated to predict initial biopsy results. The objective is to evaluate the performance of the PCA3 test in predicting results of initial prostate biopsies and to determine whether its incorporation into specific nomograms reinforces its diagnostic value. A prospective study included 601 consecutive patients addressed for initial prostate biopsy. The PCA3 test was performed before ≥12-core initial prostate biopsy, along with standard risk factor assessment. Diagnostic performance of the PCA3 test was evaluated. The three available nomograms (Hansen’s and Chun’s nomograms, as well as the updated Prostate Cancer Prevention Trial risk calculator; PCPT) were applied to the cohort, and their predictive accuracies were assessed in terms of biopsy outcome: the presence of any prostate cancer (PCa) and high-grade prostate cancer (HGPCa). The PCA3 score provided significant predictive accuracy. While the PCPT risk calculator appeared less accurate; both Chun’s and Hansen’s nomograms provided good calibration and high net benefit on decision curve analyses. When applying nomogram-derived PCa probability thresholds ≤30%, ≤6% of HGPCa would have been missed, while avoiding up to 48% of unnecessary biopsies. The urinary PCA3 test and PCA3-incorporating nomograms can be considered as reliable tools to aid in the initial biopsy decision.     

Tie‐simplex based compositional space parameterization: Continuity and generalization to multiphase systems

A theoretical analysis is provided of the continuity of multiphase compositional space parameterization for thermal‐compositional reservoir simulation. It is shown that the tie‐simplex space changes continuously as a function of composition, pressure, and temperature, and this justifies the Compositional Space Adaptive Tabulation (CSAT) framework, in which a discrete number of tie‐simplexes are constructed, tabulated, and reused in the course of a simulation. The CSAT is extended for thermal‐compositional displacements for mixtures that can form an arbitrary number of phases. In particular, the construction is described of three‐phase tie‐simplex tables, and it is shown how the degeneration of multiphase regions can be accurately captured over wide ranges of temperature and pressure. Several challenging multiphase examples are used to demonstrate the accuracy and effectiveness of phase‐state identification using tabulated tie‐simplexes. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1684–1701, 2013