Bivariate second--order linear partial differential equations and orthogonal polynomial solutions

In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially self--adjoint and of hypergeometric type. General formulae for all these properties are obtained explicitly in terms of the polynomial coefficients of the partial differential equation, using vector matrix notation. Moreover, Rodrigues representations for the polynomial eigensolutions and for their partial derivatives of any order are given. Finally, as illustration, these results are applied to specific Appell and Koornwinder orthogonal polynomials, solutions of the same partial differential equation.Comment: 27 page

Linear partial divided-difference equation satisfied by multivariate orthogonal polynomials on quadratic lattices

In this paper, a fourth-order partial divided-difference equation on quadratic lattices with polynomial coefficients satisfied by bivariate Racah polynomials is presented. From this equation we obtain explicitly the matrix coefficients appearing in the three-term recurrence relations satisfied by any bivariate orthogonal polynomial solution of the equation. In particular, we provide explicit expressions for the matrices in the three-term recurrence relations satisfied by the bivariate Racah polynomials introduced by Tratnik. Moreover, we present the family of monic bivariate Racah polynomials defined from the three-term recurrence relations they satisfy, and we solve the connection problem between two different families of bivariate Racah polynomials. These results are then applied to other families of bivariate orthogonal polynomials, namely the bivariate Wilson, continuous dual Hahn and continuous Hahn, the latter two through limiting processes. The fourth-order partial divided-difference equations on quadratic lattices are shown to be of hypergeometric type in the sense that the divided-difference derivatives of solutions are themselves solution of the same type of divided-difference equations.Comment: 36 page

Preliminary reflections on the activity theory and the development of educational software

Se presenta una síntesis de la teoría de la actividad, para establecer el marco de referencia y sus posibles aportes en la ingeniería del software educativo. El trabajo se compone de cinco secciones. La primera, expone los fundamentos que sustentan el trabajo. La segunda resume consideraciones de la teoría de la actividad y de la ingeniería del software, enfocándose en el software educativo. En la tercera, la metodología aplicada para elaborar el trabajo. En la cuarta se exponen las aproximaciones propuestas, atendiendo al contexto socio cultural y la dialéctica hegeliana. Finalmente, se mencionan las conclusiones y futuras líneas de trabajo.The paper presents a synthesis of activity theory, considering the viewpoints from different authors. It attempts to set the framework and the potential contributions of that theory in software engineering education. This paper is composed of five sections which describe foundations of the work; summarize aspects of activity theory and software engineering as well as applied methodology; present the first approaches proposed to link the activity theory and the development of educational software, and finally mention the conclusions and future work lines

On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions

AbstractIn this paper we classify the bivariate second-order linear partial difference equations, which are admissible, potentially self-adjoint, and of hypergeometric type. Using vector matrix notation, explicit expressions for the coefficients of the three-term recurrence relations satisfied by monic orthogonal polynomial solutions are obtained in terms of the coefficients of the partial difference equation. Finally, we make a compilation of the examples existing in the literature belonging to the class analyzed in this paper, namely bivariate Charlier, Meixner, Kravchuk and Hahn orthogonal polynomials

Mortalidad atribuible al alcohol en Cataluña: 1994

Fundamento: El objetivo de este estudio es evaluar la contribución del consumo de alcohol a la mortalidad en Cataluña durante 1994, así como su contribución a las muertes prematuras. Métodos: En este estudio se han utilizado los datos de las causas de muerte en Cataluña durante 1994 del Servei d’Informació i Estudis de la Direcció General de Recursos Sanitaris del Departament de Sanitat I Seguretat Social de Catalunya. Las fracciones atribuibles al alcohol están basadas en las utilizadas en el estudio de la mortalidad relacionada con el alcohol en Estados Unidos en 1987. Resultados: El 5,3% de las muertes en Cataluña durante 1994 estuvieron relacionadas con el consumo de alcohol. Esta mortalidad fue del 6,5% entre los hombres y del 3,9% entre las mujeres. La categoría diagnóstica que más contribuyó al número de muertes fue la de las neoplasias malignas (29,3%). El estudio de las muertes prematuras muestra que los accidentes no intencionales son la causa más importante (52,3%). En esta categoría diagnóstica los accidentes con vehículos a motor son los principales responsables de los años potenciales de vida perdidos (APVP). La media de APVP por cada muerte atribuible al alcohol hasta la edad de 65 fue de 7,5. Conclusiones: Este estudio muestra la magnitud que tiene el alcohol como problema de salud pública en Cataluña.BACKGROUND: The objective of this study was to asses the contribution of alcohol consumption to mortality in Catalonia (Spain) during 1994, as well as its importance in premature death. METHODS: In this study we have used the data of causes of death from Servei d'Informació i Estudis de la Direcció General de Recursos Sanitaris del Departament de Sanitat i Seguretat Social de Catalunya. The alcohol-related fractions are based in fractions used to estimate alcohol-related mortality in the United States in 1987. RESULTS: 5.3% of the deaths in Catalonia in 1994 were related to alcohol consumption. This mortality was 6.5% among males and 3.9% among females. The diagnostic category that most contributed to the number of deaths was malignant neoplasm (29.3%). The study of premature death shows that unintentional injuries are the most important cause (52.3%). In this diagnostic category, motor vehicle accidents were responsible for most of the years of potential life lost (YPLL). On average, each alcohol-related death was associated with 7.5 YPLL before age 65. CONCLUSIONS: The results shows the magnitude that alcohol has as a problem of public health in Catalonia