Dual Formulation of the Lie Algebra S-expansion Procedure

The expansion of a Lie algebra entails finding a new, bigger algebra G, through a series of well-defined steps, from an original Lie algebra g. One incarnation of the method, the so-called S-expansion, involves the use of a finite abelian semigroup S to accomplish this task. In this paper we put forward a dual formulation of the S-expansion method which is based on the dual picture of a Lie algebra given by the Maurer-Cartan forms. The dual version of the method is useful in finding a generalization to the case of a gauge free differential algebra, which in turn is relevant for physical applications in, e.g., Supergravity. It also sheds new light on the puzzling relation between two Chern-Simons Lagrangians for gravity in 2+1 dimensions, namely the Einstein-Hilbert Lagrangian and the one for the so-called "exotic gravity".Comment: 12 pages, no figure

Aplicación forestal del método AHP de toma de decisiones mediante el software MPC©

We present an example of the application of the AHP decision-making approach to forest management, by use of MPC© 2.0 software. The example considered is that of a forest services company interested in buying a timber harvester. The company had preselected four different machines as possible alternatives, and established 11 different criteria involved in the decision, grouped into four categories (economic, environmental, social and technical). The decision-making process was undertaken using MPC© 2.0 software tools, which enable establishment of criteria on two levels, independent pairwise comparison of criteria (first phase) and of alternatives under each criterion (second phase), repetition of the decision-making process by the same or different users, graphical display of the results on the computer screen, and sensitivity analysis.En este trabajo se presenta un ejemplo de aplicación a la gestión forestal del método AHP de toma de decisiones mediante el software MPC© 2.0. Se considera el ejemplo de una empresa de servicios forestales interesada en adquirir una procesadora para la corta de madera, habiendo preseleccionado cuatro diferentes máquinas como posibles alternativas, y estableciendo 11 diferentes criterios implicados en la decisión, agrupados a su vez en cuatro categorías: económicos, ambientales, sociales y técnicos. Se presentan con el ejemplo las utilidades del programa MPC© 2.0, entre las que destacan la posibilidad de establecer un esquema de criterios en dos niveles, la realización independiente de la comparación por pares de criterios (primera fase) y de alternativas bajo cada criterio (segunda fase), la posibilidad de incluir diferentes repeticiones de la decisión por un mismo o diferentes usuarios, un interface gráfico para la exposición de los resultados y el análisis de sensibilidad de los mismos

Effects of Coulomb interactions on the splitting of luminescence lines

We study the splitting between the right-hand and left-hand circularly polarized luminescence lines in a quantum dot under relatively weak confinement regime and resonant high-power excitation. When the dot is populated with an even number of electron-hole pairs (biexciton and higher excitations), the splitting measures basically the Zeeman energy. However, in the odd number of pairs case, we have, in addition to the Zeeman and Overhauser shifts, a contribution to the splitting coming from Coulomb interactions. This contribution is of the order of a few meV, and shows distinct signatures of shell-filling in the quantum dot.Comment: Submitted for publicatio