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.

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.

Behavioral, neurochemical and morphological changes induced by the overexpression of munc18-1a in brain of mice: relevance to schizophrenia

Overexpression of the mammalian homolog of the unc-18 gene (munc18-1) has been described in the brain of subjects with schizophrenia. Munc18-1 protein is involved in membrane fusion processes, exocytosis and neurotransmitter release. A transgenic mouse strain that overexpresses the protein isoform munc18-1a in the brain was characterized. This animal displays several schizophrenia-related behaviors, supersensitivity to hallucinogenic drugs and deficits in prepulse inhibition that reverse after antipsychotic treatment. Relevant brain areas (that is, cortex and striatum) exhibit reduced expression of dopamine D-1 receptors and dopamine transporters together with enhanced amphetamine-induced in vivo dopamine release. Magnetic resonance imaging demonstrates decreased gray matter volume in the transgenic animal. In conclusion, the mouse overexpressing brain munc18-1a represents a new valid animal model that resembles functional and structural abnormalities in patients with schizophrenia.