Invariance principles for switched systems with restrictions

In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems.Comment: 29 pages, 2 Appendixe

The conformal transformation's controversy: what are we missing?

An alternative interpretation of the conformal transformations of the metric is discussed according to which the latter can be viewed as a mapping among Riemannian and Weyl-integrable spaces. A novel aspect of the conformal transformation's issue is then revealed: these transformations relate complementary geometrical pictures of a same physical reality, so that, the question about which is the physical conformal frame, does not arise. In addition, arguments are given which point out that, unless a clear statement of what is understood by "equivalence of frames" is made, the issue is a semantic one. For definiteness, an intuitively "natural" statement of conformal equivalence is given, which is associated with conformal invariance of the field equations. Under this particular reading, equivalence can take place only if the metric is defined up to a conformal equivalence class. A concrete example of a conformal-invariant theory of gravity is then explored. Since Brans-Dicke theory is not conformally invariant, then the Jordan's and Einstein's frames of the theory are not equivalent. Otherwise, in view of the alternative approach proposed here, these frames represent complementary geometrical descriptions of a same phenomenon. The different points of view existing in the literature are critically scrutinized on the light of the new arguments.Comment: 17 pages, no figures. version accepted by General Relativity and Gravitation journa

El fondo antiguo de la biblioteca

En este curso se presentan los diferentes aspectos que presenta los fondos antiguos que se conservan en las bibliotecas, como un aspecto del patrimonio cultural de las sociedades. Por tanto se analizan las diversas problemáticas que afectan a los diferentes objetos patrimoniales que se consideran integran ese fondo antiguo.Universidad Nacional Autónoma de Méxic