Volumen 05 (2001) No. 1

Geometry and dynamics of the residue theorem

Jesús Muciño-Raymundo and Carlos Valero-Valdés

Resumen:

Using singular flat metrics associated to meromorphic differential forms on Riemann surfaces, a converse of the classical residue theorem is due. Also a dynamical interpretation of residues using real geodesic flows is given.

Descargar

The equations of the cone associated to the Rees algebra of the ideal of square-free $k$-products

Adrián Alcántar

Resumen:

In this paper we determine the equations of the polyhedral cone generated by the exponent vectors of the monomials defining the Rees algebra of the ideal generated by the square-free monomials of degree $k$ in $n$ variables. Some applications are presented to show the relevance of the computation of these equations.

Descargar

Algebra generada por la proyeccióon de Bergman y operadores de multiplicación por funciones continuas a trozos

Maribel Loaiza Leyva

Resumen:

Sea $D = \{z \in \mathbb{C} | \; |z| < 1\}$ y $\mathcal{L}$ una colección finita de curvas suaves en $D$. Se estudia el álgebra $\mathcal{R}$ generada por la proyección de Bergman de $D$ y los operadores de multiplicación por funciones continuas en $D \setminus \mathcal{L}$. Se considera el caso en que en un punto $z_0 \in \partial D$ convergen dos o más curvas de $\mathcal{L}$ y se describe el álgebra de Calkin de $\mathcal{R}$ .

Descargar

Existence of optimal strategies for zero-sum stochastic games with discounted payoff

Francisco Ramírez-Reyes

Resumen:

This work deals with zero-sum stochastic games with Borel state and action spaces, and unbounded payoff function. We consider finite-horizon as well as infinite-horizon discounted problems. Our main purpose is to give conditions for the existence of the game value and for the existence of optimal strategies for both players. The infinite-horizon case is analyzed using the approach of successive approximations.

Descargar