El aprendizaje del concepto de integral

El propósito de este artículo es presentar una propuesta didáctica de la integral definida para la educación secundaria obligatoria y bachillerato a través de unas secuencias de aprendizaje que ayuden al estudiante a captar las ideas fundamentales del cálculo integral, del concepto de integral y del proceso de integración.

Para qué tantas hipótesis en el criterio de la integral

Se repasa el planteo tradicional del criterio de la integral para la convergencia de series (con las hipótesis de que la función en cuestión sea continua, positiva y decreciente, y la conclusión de que la serie y la integral impropia convergen ambas o divergen ambas). Se muestran ejemplos en los que fallan una o más de las hipótesis y la conclusión del criterio falla. Se demuestra que son innecesarias las hipótesis de continuidad y positividad, y finalmente que basta con una condición aún más débil que la de que la función sea decreciente. Los resultados se aplican tanto a la equivalencia entre la convergencia de la serie y la convergencia de la integral impropia como a la fórmula para la cota del error en las sumas parciales cuando la serie converge.

[Book Review] Noel Starkey (ed), Connectionist Natural Language Processing: Readings from 'Connection Science'

Review of: Noel Starkey (ed), Connectionist Natural Language Processing: Readings from 'Connection Science'

Philosophy and Politics in the 20th in Argentina. Readings of Italian Idealism

The transition from a positivist matrix to an idealistic one in Argentinean academic philosophy can be read as a result of a gradual and problematic pollution. It was, also, heavily traversed by considerations that exceeded the theoretical aspects. Based on the willingness to explore this transit, the article pays attention to one of the episodes of this contamination: how the Revista de Filosofía reads Croce and Gentile’s philosophy. Observing there some possibility of dialogue between positivist assumptions, with which the journal takes a position, and the idealism the article analyze how this dialogue and its limits were given from a political consideration. If the idealism was condemned, it is centrally owed to its performance during the first years of the government of Mussolini. If, meanwhile, it was some to rescue of that philosophy, it was that it contributed to think the revolutionary change.

Path-integral study of a two-dimensional Lennard-Jones glass

The glass transition in a quantum Lennard-Jones mixture is investigated by constant-volume path-integral simulations. Particles are assumed to be distinguishable, and the strength of quantum effects is varied by changing h from zero (the classical case) to one (corresponding to a highly quantum-mechanical regime). Quantum delocalization and zero point energy drastically reduce the sensitivity of structural and thermodynamic properties to the glass transition. Nevertheless, the glass transition temperature T-g can be determined by analyzing the phase space mobility of path-integral centroids. At constant volume, the T-g of the simulated model increases monotonically with increasing h. Low temperature tunneling centers are identified, and the quantum versus thermal character of each center is analyzed. The relation between these centers and soft quasilocalized harmonic vibrations is investigated. Periodic minimizations of the potential energy with respect to the positions of the particles are performed to determine the inherent structure of classical and quantum glassy samples. The geometries corresponding to these energy minima are found to be qualitatively similar in all cases. Systematic comparisons for ordered and disordered structures, harmonic and anharmonic dynamics, classical and quantum systems show that disorder, anharmonicity, and quantum effects are closely interlinked.