Volumen 14 (2010) No. 2
Volumen 14 (2010) No. 2 
A note on distributional equations in discounted risk processes
Gerardo Hernández del Valle and Carlos G. Pacheco González
Resumen:
In this paper we give an account of the classical discounted risk processes and their limiting distributions. For the models considered, we set the Markov chains embedded in the continuous-time processes; we also set distributional equations for the limit distributions. Additionally, we mention some applications regarding ruin probabilities and optimal premium.
Cohomology groups of configuration spaces of pairs of points in real projective spaces
Jesús González and Peter Landweber
Resumen:
The Stiefel manifold of $V_{m+1,2}$ of 2-frames in $\mathbb{R}^{m+1}$ is acted upon by the orthogonal group $O(2)$. By restriction, there are corresponding actions of the dihedral group of order 8, $D_8$, and of the rank-2 elementary 2-group $\mathbb{Z}_2 \times \mathbb{Z}_2$. We use the Cartan-Leray spectral sequences of these actions to compute the integral homology and cohomology groups of the configuration spaces $B(P^m, 2)$ and $F(P^m, 2)$ of (unordered and ordered) pairs of points on the real projective spaces $P^m$.
An upper bound on the size of irreducible quadrangulations
Gloria Aguilar Cruz and Francisco Javier Zaragoza Martinez
Resumen:
Let $S$ be a closed surface with Euler genus $\gamma (S)$. A quadrangulation $G$ of a closed surface $S$ is irreducible if it does not have any contractible face. Nakamoto and Ota gave a linear upper bound for the number $n$ of vertices of $G$ in terms of $\gamma (S)$. By extending Nakamoto and Ota's method we improve their bound to $n \leq 159.5 \gamma (S) - 46$ for any closed surface $S$.