Volumen 07 (2003) No. 2
Volumen 07 (2003) No. 2 
When Does a Manifold admit a Metric with Positive Scalar Curvature?
Egidio Barrera-Yáñez and José Luis Cisneros-Molina
Resumen:
The scalar curvature is the weakest geometric invariant in a Riemannian manifold. M. Gromov, B. Lawson Jr. and J. Rosenberg conjectured that a Riemannian manifold admits a metric with positive scalar curvature if and only if certain topological invariant called $\widehat{A}$-genus vanishes. This is known as the Gromov-Lawson-Rosenberg conjecture. In this article we explain this conjecture and give a brief survey of some results related to it.
A Survey on Modular Hadamard Matrices
Shalom Eliahou and Michel Kervaire
Resumen:
We provide constructions of 32-modular Hadamard matrices for every size $n$ divisible by 4. They are based on the description of several families of modular Golay pairs and quadruples. Higher moduli are also considered, such as 48, 64, 128 and 192. Finally, we exhibit infinite families of circulant modular Hadamard matrices of various types for suitable moduli and sizes.
Application of Modularity to Optimal Resource Allocation with Risk Sensitivity
Guadalupe Ávila-Godoy
Resumen:
An optimal allocation problem with a risk-sensitive controller is modelled by a controlled Markov chain with exponential total cost criterion. Some general results recently obtained are applied to show that the particular model studied here has a monotone optimal policy and monotone optimal value function. Moreover, it is shown that under certain conditions, the allocation problem with both risk-neutral and risk-sensitive performance criteria has an optimal policy of the threshold type.