Volume 04 (2000) No. 1
Volume 04 (2000) No. 1 
The eta invariant, connective $K$-theory and the Gromov-Lawson-Rosenberg conjecture
Egidio Barrera-Yánez
Abstract:
Let $\ell=2^\nu \ge 2$. Let $M$ be an even dimensional manifold with cyclic fundamental group $\mathbb{Z}_\ell$. Assume the universal cover $\tilde M$ is spin. We shall define $N(M)=(\tilde M \times \tilde M)/{\mathbb{Z}_{2\ell}}$ and express the eta invariant of $N(M)$ in terms of the eta invariant of $M$. We use this computation to determine certain equivariant connective $K$ theory groups and establish the Gromov-Lawson-Rosenberg conjecture for some special cases in the non-orientable setting.
An stochastic consumption-investment problem with unbounded utility function
Heliodoro D. Cruz-Suárez
Abstract:
This paper is concerned with a discrete-time, infinite-horizon consumption and investment problem, which is formulated as a Markov Decision Process with unbounded utility of consumption, and the total discounted reward criterion. The conditions given in the paper permit to obtain explicit expressions for both the optimal policy and the optimal value function $V^*$. Moreover, we find a bound for the difference between $V^*$ and a rolling-horizon reward function $\hat{V}$, that is, the discounted reward value when using a rolling-horizon policy.
Solvability of the general capacity problem in metric spaces
J. Rigoberto Gabriel
Abstract:
Conditions are given under which the general capacity problem in metric spaces is solvable.
Algebra generada por la proyección de Bergman y un operador de translación II
Josué Ramírez Ortega
Abstract:
En este artículo se calcula el índice de los operadores de Fredholm del álgebra $C^*$ generada por un operador de traslación, la proyección de Bergman de un dominio $G \subset \mathbb{C}$ del plano complejo y los operadores de multiplicación de funciones continuas en la cerradura de $\overline{G}$.