On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.Comment: 6 pages, submitted to the Proceedings of the "International Conference on High Energy and Mathematical Physics", Morocco, Marrakech, April 200

On special quadratic birational transformations of a projective space into a hypersurface

We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by quadratic forms by showing that there are only four examples having general hyperplane sections of Severi varieties as base loci.Comment: Accepted for publication in Rendiconti del Circolo Matematico di Palerm

Development of Scientific Competences in Chemistry Courses

Enseñar química en los primeros años de educación universitaria es clave en la formación de futuros profesionales, puesto que, además de proveer los conocimientos que aportan las ciencias básicas, contribuye al desarrollo de competencias científicas para que el estudiante resuelva problemas reales, a partir de la búsqueda adecuada de información en fuentes confiables y su lectura, con el propósito de desarrollar habilidades analíticas, críticas y creativas. Es por esto que, como estrategia de innovación pedagógica, el Departamento de Ciencias Básicas de la Universidad de La Salle ha venido implementando desde el año 2016 la formulación de un proyecto de investigación en los cursos de química. En el marco de esta estrategia, desde el II-2018 las autoras se abocaron a la reflexión e implementación de la estrategia didáctica que propende por el desarrollo de competencias científicas en los cursos de Química General, Química Orgánica y Bioquímica desde tareas, investigación y aprendizaje de problemáticas vigentes en Colombia y en el mundo.Abstract: Teaching chemistry in the first years of university education is key in the training of future professionals since, in addition to providing the knowledge of the basic sciences, it contributes to the development of scientific skills that lead to the student to solve real problems, starting from the appropriate search of information in reliable sources and its reading with the purpose of developing analytical, critical and creative skills. Therefore, as a pedagogical innovation strategy, the formulation of a research project in chemistry courses has been implemented since 2016 by the Department of Basic Sciences of the Universidad de La Salle. Within the framework of this strategy, from II-2018 the authors focused on the reflection and implementation of the didactic strategy that depends on the development of scientific competences in the courses of General Chemistry, Organic Chemistry and Biochemistry from tasks, research and learning of current problems in Colombia or in the world

From linear recurrence relations to linear ODEs with constant coefficients

Linear Ordinary Differential Equations (ODEs) with constant coefficients are studied by looking in general at linear recurrence relations in a module with coefficients in an arbitrary Z-algebra. The bridge relating the two theories is the notion of formal Laplace transform associated to a sequence of invertibles. From this more economical perspec- tive, generalized Wronskians associated to solutions of linear ODEs will be revisited, mentioning their relationships with Schubert Calculus for Grassmannians