Construcción de la recta tangente variacional a traves de los usos del conocimiento del siglo XVII y XVIII

El presente trabajo es una investigación en curso. Una fuente de dificultades didácticas es la interpretación geométrica de la derivada, en donde la recta tangente no se considera como objeto de estudio. Nuestro planteamiento es que al construir la recta tangente desde una perspectiva variacional puede servir como una introducción a la derivada desde un punto de vista gráfico, lo cual implica también un rediseño del Discurso Matemático Escolar. Utilizamos la teoría de la Socioepistemología, en la cual se plantea que el uso de herramientas matemáticas para resolver actividades organizadas intencionalmente con la intención de resolver un problema, son una práctica, normadas por una práctica social. El escenario histórico nos ha servido para reconocer la práctica de la tangente variacional. Actualmente hemos implementado un método para obtener nuestros datos el cual nos servirá para que un futuro próximo podamos analizarlos y obtener conclusiones.

Saber calcular no es saber matemática

Un poco de historia. Los cálculos eran la preocupación principal de nuestros antepasados, que promovieron el desarrollo de las matemáticas. Así nacieron los logaritmos, en los últimos años del siglo XVII. Decía Laplace en aquello años, “el uso de los logaritmos, acortó el trabajo y duplicó la vida de los astrónomos”. En los últimos años de la década 1970 a 1980 se popularizaron las calculadoras. Que no son tan viejas. Yo, no las use. En 1972 entre a la facultad de química y no tenía calculadora. Un año antes, me compre una de las mejores reglas de cálculo. Para usarla deberíamos saber tanto, que nos calificarían de genio en la actualidad ¿Cuál es entonces la premisa de mi pensamiento? “Saber matemática no es saber hacer cuentas”

Códigos numéricos para la vida

Es un hecho indudable que vivimos en una sociedad que nos requiere, cada vez más, interactuar con una serie de códigos numéricos. En este trabajo se pretende analizar las características de algunos de estos códigos -DNI-NIF, códigos de barras, códigos ISBN, códigos ISSN, códigos de tarjetas de crédito, de cuentas bancarias, de cheques bancarios- haciendo especial hincapié en los algoritmos que permiten calcular su carácter de control a partir de los demás elementos del código y en la forma que tienen estos códigos de hacer frente a los errores más frecuentes en la transmisión de los mismos. Además se estudian sus posibilidades didácticas y se ofrece una aplicación informática al aula de secundaria a través de una WebQuest, creada por el autor, sobre el tema.

Mientras hay vida hay esperanza

Este clip va dedicado a la esperanza. Por supuesto no se trata de interferir en la política de la comunidad de Madrid, ni de hacer una reflexión sobre virtudes cristianas, ni de reconocer en público que esta palabra forma parte de nuestros sentimientos más nobles cuando estamos dando clase. Lo que nos proponemos es hacer referencia a tres casos muy concretos de esperanza matemática.

Electron impact excitation of Ar XVII

Energies for the lowest 49 levels among the 1s(2) and 1snl (n = 2-5) configurations of Ar XVII have been calculated using the GRASP code of Dyall et al. (1989, Comput. Phys. Comm., 55, 424). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Furthermore, collision strengths have also been calculated for all the 1176 transitions among the above 49 levels using the Dirac Atomic R-matrix Code (DARC) of Norrington & Grant (2005, Comput. Phys. Commun., in preparation), over a wide energy range up to 580 Ryd. Resonances have been resolved in the threshold region, and effective collision strengths have been obtained over a wide temperature range up to log T-e = 7.2 K. Comparisons are made with the limited results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 0.1%, whereas results for other parameters are probably accurate to better than 20%.

Radiative rates for transitions in Fe XVII

Energies of the lowest 157 levels belonging to the (1s(2)) 2s(2)2p(6), 2s(2)p(5)3l, 2s(2)2p(5)4l, 2s(2)2p(5)4l, 2s2p(5)5l, 2s2p(6)4l and 2s2p(6)5l configurations of Fe XVII have been calculated using the GRASP code of Dyall et al. (1989). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E I), magnetic dipole (M I), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Comparisons are made with the results already available in the literature, and the accuracy of the data is assessed. Our energy levels are expected to be accurate to better than M whereas results for other parameters are probably accurate to better than 20%.

Energy levels and radiative rates for transitions in Ni XIII-Ni XVI

Energy levels and radiative rates for fine-structure transitions in nickel ions (Ni XIII-XVI) have been calculated using the GRASP code. Configuration interaction and relativistic effects have been included, and comparisons are made with available data. Energy levels and radiative rates are tabulated for transitions among the 48, 43, 32, and 84 levels of Ni XIII, Ni XIV, Ni XV, and Ni XVI, respectively. The energy levels are assessed to be accurate to better than 5% for a majority of levels, while oscillator strengths for all strong transitions are accurate to better than 20%. (C) 2003 Published by Elsevier Inc.

Oscillator strengths for transitions in C-like ions between K XIV and Mn XX

Energy levels and oscillator strengths (transition probabilities) have been calculated for transitions among 46 fine-structure levels of the (1s(2)) 2s(2) 2p(2), 2s2p(3),2p(4), 2s(2)2p3s, 2s(2) 2p3p and 2s(2)2p3d configurations of C-like K XIV, Sc XVI, Ti XVII, V XVIII, Cr XIX and Mn XX using the GRASP code. Configuration interaction and relativistic effects have been included while generating the wavefunctions. Calculated values of energy levels agree within 3% with the experimentally compiled results, and the length and velocity forms of oscillator strengths agree within 20% for a majority of allowed transitions.

Energy levels, radiative rates, and collision strengths for transitions in Fe XVII

Energy levels and radiative rates have been calculated for fine-structure transitions among the lowest 89 levels of the (1s(2)) 2s(2)2p(6), 2s(2) 2p(5) 3 l, 2s(2) 2p(5) 4l, 2s2p(6) 3 l, and 2s2p(6)4l configurations of Fe XVII using the GRASP code of Dyall et al. Collision strengths have also been calculated, for transitions among the lowest 55 levels, using the recently developed Dirac atomic R-matrix code (DARC) of Norrington & Grant. The results are compared with those available in the literature, and the accuracy of the data is assessed.

Emission lines of Na-like ions in spectra obtained with the Solar EUV Research Telescope and Spectrograph (SERTS)

Theoretical emission-line ratios involving transitions in the 236-412 Angstrom wavelength range are presented for the Na-like ions Ar viii, Cr xiv, Mn xv, Fe xvi, Co xvii, Ni xviii and Zn xx. A comparison of these with an extensive data set of the solar active region, quiet-Sun, subflare and off-limb observations, obtained during rocket flights by the Solar EUV Research Telescope and Spectrograph (SERTS), reveals generally very good agreement between theory and experiment. This indicates that most of the Na-like ion lines are reliably detected in the SERTS observations, and hence may be employed with confidence in solar spectral analyses. However, the features in the SERTS spectra at 236.34 and 300.25 Angstrom, originally identified as the Ni xviii 3p (2) P-3/2 -3d (2) D- 3/2 and Cr xiv 3p (2) P-3/2 -3d (2) D-5/2 transitions, respectively, are found to be due to emission lines of Ar xiii (236.34 Angstrom) and possibly S v or Ni vi (300.25 Angstrom). The Co xvii 3s (2) S-3p (2) P-3/2 line at 312.55 Angstrom is always badly blended with an Fe xv feature at the same wavelength, but Mn xv 3s (2) S-3p (2) P-1/2 at 384.75 Angstrom may not always be as affected by second-order emission from Fe xii 192.37 Angstrom as previously thought. On the other hand, we find that the Zn xx 3s (2) S-3p (2) P-3/2 transition can sometimes make a significant contribution to the Zn xx/Fe xiii 256.43- Angstrom blend, and hence care must be taken when using this feature as an Fe xiii electron density diagnostic. A line in the SERTS-89 active region spectrum at 265.00 Angstrom has been re-assessed, and we confirm its identification as the Fe xvi 3p (2) P-3/2 -3d (2) D-3/2 transition.

Inner-shell photoexcitation of Fe XV and Fe XVI

The configuration-interaction method as implemented in the computer code CIV3 is used to determine energy levels, electric dipole radiative transition wavelengths, oscillator strengths and transition probabilities for inner-shell excitation of transitions in Fe XV and Fe XVI. Specifically, transitions are considered of the type 1s(2) 2s(2) 2p(6) 3s(2) -1s(2) 2s(2) 2p(5) 3l3l' 3l" (l, l' and l" = s,p or d) in FeXV and 1s(2) 2s(2) 2p(6) 3s- 1s(2) 2s(2) 2p(5) 3l3l' (l and l' = s,p or d) in FeXVI, using the relativistic Breit-Pauli approach. An assessment of the accuracy of the derived atomic data is performed.

Energy levels and radiative rates for Li-like Ar XVI and Fe XXIV

Energy levels for transitions among the lowest 24 fine- structure levels belonging to the 1s(2)nl(n greater than or equal to 5) configurations of Li-like Ar XVI and Fe XXIV have been calculated using the fully relativistic GRASP code. Oscillator strengths, radiative rates and line strengths have also been generated among these levels for the four types of transitions: electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2). Comparisons are made for the electric dipole transitions with other available results, and the accuracy of the present data is assessed.

Electron impact excitation of Fe XVI: radiative and excitation rates

Aims. In this paper we report calculations for energy levels, radiative rates, collision strengths, and effective collision strengths for transitions in Fe XVI. Methods. For energy levels and radiative rates we have used the General purpose Relativistic Atomic Structure Package ( grasp), and for the compuations of collision strengths the Dirac Atomic R-matrix Code (darc) has been adopted. Results. Energies for the lowest 39 levels among the n