Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

About the Stabilization of a Nonlinear Perturbed Difference Equation

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

Los determinantes de la rentabilidad primaria de los bonos de titulización hipotecaria: la influencia de las estructuras multitramo

[ES] Este artículo analiza los determinantes de la rentabilidad primaria de los bonos de titulización hipotecaria (conocidos en la literatura como mortgage backed securities, o MBS) emitidos en España durante el periodo 1993-2011, periodo en el que el mercado español llegó a convertirse en el más importante de Europa continental. Los resultados obtenidos sobre el análisis de la población completa de MBS emitidos (262 tramos configurados sobre 94 fondos de titulización) indican que la estructuración multitramo de los MBS ha ayudado a reducir el riesgo percibido global de las emisiones de MBS, mediante la generación de mercados más completos y la reducción de los problemas derivados de la existencia de asimetrías informativas implícitas en el proceso de selección de los activos transmitidos por parte de la entidad cedente. Esta reducción del riesgo percibido ha tenido un efecto directo sobre la rentabilidad ofrecida por los bonos de titulización emitidos. Además, no se encuentran evidencias de que la emisión de MBS persiga la transmisión efectiva de riesgos, más bien al contrario. Las Entidades de crédito, por lo general, han retenido los tramos de primeras pérdidas, lo que ha contribuido a mantener en niveles muy bajos (por debajo de la rentabilidad de la deuda soberana) la rentabilidad ofrecida por los MBS. Precisamente, el escaso diferencial ofrecido por los bonos de titulización se debe a que los tramos retenidos no han ofrecido primas de rentabilidad ajustadas al riesgo inherente.

Stability analysis and observer design for discrete-time SEIR epidemic models

This paper applies Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points is discussed for the discrete-time case. Afterwards, the design of a state observer for this discrete-time SEIR epidemic model is tackled. The analysis of the model along with the observer design is faced in an implicit way instead of obtaining first an explicit formulation of the system which is the novelty of the presented approach. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast in the form of a LMI. The feasibility of the matrix inequality is proved, while some simulation examples show the operation and usefulness of the observer.