Volumen 07 (2003) No. 1
Volumen 07 (2003) No. 1 
The Lagrange approach to constrained Markov control processes: a survey and extension of results
Raquiel R. López-Martínez and Onésimo Hernández-Lerma
Resumen:
This paper considers constrained Markov control processes in Borel spaces, with unbounded costs. The criterion to be minimized is the expected total discounted cost and the constraints are imposed on similar criteria. Conditions are given for the constrained problem to be equivalent to a convex program. We present a saddle-point theorem for the Lagrange function associated with the convex program, which is used to obtain the existence of an optimal solution to the constrained problem. In addition, we show that there exists an optimal policy for the constrained problem which is also Pareto optimal for a certain multiobjective Markov control processes.
Representaciones discretas en tiempo-frecuencia y el problema de la selección de frecuencias
Alin Andrei Carsteanu Manitiu
Resumen:
El artículo presenta la problemática general de la obtención de bases en $\mathrm{R}^n$ con significado de frecuencia. También se presenta el efecto sobre la característica de contraste de una base, de la minimización de una función objetivo aditiva (tal como lo sería una función de costo), definida sobre los elementos de aquella base. Se discuten varios algoritmos de optimización, basados en el paquete de ondículas. Finalmente, se propone una solución novedosa a lo que es el problema del cálculo de un espectro energético significativo de la representación de una señal en una base obtenida a partir del paquete de ondículas.
Generalized tilings with height functions
Olivier Bodini and Matthieu Latapy
Resumen:
In this paper, we introduce a generalization of a class of tilings which appear in the literature: the tilings over which a height function can be defined (for example, the famous tilings of polyominoes with dominoes). We show that many properties of these tilings can be seen as the consequences of properties of the generalized tilings we introduce. In particular, we show that any tiling problem which can be modelized in our generalized framework has the following properties: the tilability of a region can be constructively decided in polynomial time, the number of connected components in the undirected flip-accessibility graph can be determined, and the directed flip-accessibility graph induces a distributive lattice structure. Finally, we give a few examples of known tiling problems which can be viewed as particular cases of the new notions we introduce.
On Anosov energy levels that are of contact type
Osvaldo Osuna-Castro
Resumen:
In this work we prove that given an autonomous Lagrangian $L$ on a closed manifold $M$, if an Anosov energy level $k$ can be reparametrized to make it of contact type, then $k >c_0(L)$, the critical value of $L$ associated with the abelian covering.