Comprensión de la sintaxis del álgebra en tangentes a las cónicas con el método de descartes

Este artículo forma parte de la investigación maestría de la autora. En este artículo se identifican qué tendencias cognitivas presentan estudiantes de bachillerato cuando se enfrentan al tema de tangentes a las cónicas en un curso de Geometría Analítica (UNAM, 1996). También se analiza si este curso permite una mejor comprensión de la sintaxis algebraica.

Prediciendo con la regla de los signos de Descartes

En este reporte se discute, desde la socioepistemología, una experiencia realizada con estudiantes de bachillerato respecto de la Regla de los signos de Descartes, aquella que permite determinar el número de raíces positivas que una función polinómica podría presentar. El diseño de la secuencia de aprendizaje requirió el uso de la Ingeniería Didáctica como metodología, aunque no buscábamos validar la actividad de aprendizaje, sino analizar las herramientas que los estudiantes evocaran o construyeran en la experiencia.

El método de Descartes para trazar normales a curvas

El trabajo que hemos desarrollado en este artículo es un estudio de un método histórico desarrollado por Descartes para calcular la recta normal a una curva, y que puede ser aprovechado para calcular derivadas puntuales y generales de funciones. El método, requiere de la resolución de ecuaciones algebraicas y transcendentes, que en principio pueden ser complicadas (por eso ha caído en el olvido), pero que permite introducir en el aula una gran cantidad de aspectos docentes. Además, la idea en la que se fundamenta el método de Descartes puede ser aprovechada para calcular la distancia de un punto a una recta o un plano.

On-line algorithms for single machine scheduling with family setup times

The paper considers an on-line single machine scheduling problem where the goal is to minimize the makespan. The jobs are partitioned into families and a setup is performed every time the machine starts processing a batch of jobs of the same family. The scheduler is aware of the number of families and knows the setup time of each family, although information about a job only becomes available when that job is released. We give a lower bound on the competitive ratio of any on-line algorithm. Moreover, for the case of two families, we provide an algorithm with a competitive ratio that achieves this lower bound. As the number of families increases, the lower bound approaches 2, and we give a simple algorithm with a competitive ratio of 2.

The Richit-Richards family of distributions and its use in forestry

Johnson's SB and the logit-logistic are four-parameter distribution models that may be obtained from the standard normal and logistic distributions by a four-parameter transformation. For relatively small data sets, such as diameter at breast height measurements obtained from typical sample plots, distribution models with four or less parameters have been found to be empirically adequate. However, in situations in which the distributions are complex, for example in mixed stands or when the stand has been thinned or when working with aggregated data, then distribution models with more shape parameters may prove to be necessary. By replacing the symmetric standard logistic distribution of the logit-logistic with a one-parameter “standard Richards” distribution and transforming by a five-parameter Richards function, we obtain a new six-parameter distribution model, the “Richit-Richards”. The Richit-Richards includes the “logit-Richards”, the “Richit-logistic”, and the logit-logistic as submodels. Maximum likelihood estimation is used to fit the model, and some problems in the maximum likelihood estimation of bounding parameters are discussed. An empirical case study of the Richit-Richards and its submodels is conducted on pooled diameter at breast height data from 107 sample plots of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.). It is found that the new models provide significantly better fits than the four-parameter logit-logistic for large data sets.

An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times

We consider the problem of scheduling families of jobs in a two-machine open shop so as to minimize the makespan. The jobs of each family can be partitioned into batches and a family setup time on each machine is required before the first job is processed, and when a machine switches from processing a job of some family to a job of another family. For this NP-hard problem the literature contains (5/4)-approximation algorithms that cannot be improved on using the class of group technology algorithms in which each family is kept as a single batch. We demonstrate that there is no advantage in splitting a family more than once. We present an algorithm that splits one family at most once on a machine and delivers a worst-case performance ratio of 6/5.

Family, community and politics: the fertile legacy of Michael Young

The Institute of Community Studies was set up by Michael Young in order to carry out research on politically relevant social issues, in a context free from direct political control. A research method was devised for it whereby researchers made their own values and objectives very explicit, while staying as close as possible in their reports to the concerns and language of respondents themselves. This method has often been criticized by professional sociologists: but it reflects quite well the nature of social knowledge. It has produced reports which help to increase public understanding of social processes, and provide useful guidance to policy makers. Professional sociology on the other hand has tried to develop a rigorously value-free method. As a result, though, it often seems to be tied implicitly to values shared among researchers but not more universally. Arguably this makes it harder for the general public to understand, and accept, its findings.

Insolvency: ordering a sale of the family home

Comments on the Chancery Division ruling in Nicholls v Lan on whether the interests of a bankrupt husband's creditors prevailed over those of the wife, despite her circumstances being exceptional within the meaning of the Insolvency Act 1986 s.335A on account of her suffering from chronic schizophrenia, where the wife was the joint owner of another property which could be realised to buy out the trustee in bankruptcy's half share in the equity of the matrimonial home.

But no one in my family has been to university - aiming higher: school students attitudes to higher education

In this paper, we present findings from the second stage of a three year longitudinal study involving 3,570 students aged 13-18 in a London Borough looking at the impact of Widening Participation (WP) on the attitudes of students. We outline findings from a previous stage and then focus specifically on two cohorts of Year 10 students (aged 14-15) in two consecutive years. The students completed the specially designed Attitudes to Higher Education Questionnaire (AHEQ) and provided information on WP activities in which they had participated. Data on the students' academic attainment and social backgrounds were also included. There were significant sex and cohort differences and interactions which were found to be related to WP activities specifically aimed at increasing the participation of socially disadvantaged students in higher education. The implications of findings are discussed in relation to theories of social identity and self concept and the implementation of strategies to increase participation in Higher Education