Generación de modelos de enseñanza–aprendizaje en álgebra lineal

Dos de las dificultades más importantes y frecuentes que encontramos en el aprendizaje del álgebra lineal, tenemos la conceptualización y la formalización. Los contenidos de la materia son, en gran medida, formulados a partir de la definición de vectores, espacios vectoriales, bases, transformaciones lineales, etc. En los primeros capítulos de un curso de álgebra lineal, es frecuente acudir a la visualización geométrica en R2 y R3 como ayuda pedagógica para ilustrar las representaciones vectoriales y sus operaciones. Pero esto no siempre es así, la noción “visual” de otros conceptos, su enseñanza parte solamente de la definición formal la cual frecuentemente carece de alguna “justificación plausible” del porqué es así. Ejemplos de ellos son las definiciones de espacios vectoriales o de espacios con producto interno. Algunas investigaciones en torno a las dificultades en el aprendizaje del álgebra lineal comienzan con la descripción de tres tipos de lenguaje (geométrico, aritmético y algebraico) que se maneja en el álgebra lineal. En estas investigaciones, las dificultades en el aprendizaje tienen entre otros orígenes, la falta de articulación entre estos lenguajes

Suppression of viscous fluid fingering: a piecewise constant-injection process

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are quite undesirable. In this letter we propose an efficient and easily reproducible way to restrain these instabilities based on a simple piecewise constant pumping protocol. It results in a reduction in the size of the viscous fingers by one order of magnitude.Comment: Published in Phys. Rev.

The Effects of the Brazilian ADRs Program on Domestic Market Efficiency

This paper examines the impact on Brazilian stocks following American Depositary Receipts (ADRs) listing in the U.S. stock markets. Evidence suggests that a systematic change has taken place in the post-listing period as the multivariate variance ratio statistics have significantly decreased if compared to the pre-listing period, which indicates a move toward a more efficient domestic stock market. This empirical evidence is robust to the use of dollar and local currency-denominated returns. These results add to the literature that finds evidence on changes in domestic volatility and abnormal returns around listing dates.

Causality and Cointegration in Stock Markets: The Case of Latin America

This paper analyzes causality and cointegration relationships among stock markets for Latin America and the United States. Within a simple framework causality and cointegration is tested for Argentina, Brazil, Chile, Colombia, Mexico, Peru, Venezuela and the US. We found no evidence of cointegration among these stock markets but short-run causality could not be rejected. Furthermore, we use impulse response functions to analyze the relative impact of shocks in the US stock index (Dow Jones) on Latin American indexes. Evidence suggests that the responses differ significantly among these countries. These findings imply that there are valuable opportunities to international investors from diversifying in US and Latin American stocks.

Exchange Rate Dynamics and the Relationship between the Random Walk Hypothesis and Official Interventions

This paper examines the empirical evidence that official interventions are associated with periods of high predictability in exchange rate markets. We employ a block bootstrap methodology to build critical values for the Variance Ratio statistics and test for predictability within moving windows of fixed length sizes for major developed countries currencies. Empirical results suggest that interventions are indeed associated to periods of increase in predictability and that time varying risk premium may, at least partially, explain such results.