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.

Stability and Limit Oscillations of a Control Event-Based Sampling Criterion

This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

Chemical contaminants, pathogen exposure and general health status of live and beach-cast Washington sea otters (Enhydra lutris kenyoni)

Analyses of blood and liver samples from live captured sea otters and liver samples from beachcast sea otter carcasses off the remote Washington coast indicate relatively low exposure to contaminants, but suggest that even at the low levels measured, exposure may be indicated by biomarker response. Evidence of pathogen exposure is noteworthy - infectious disease presents a potential risk to Washington sea otters, particularly due to their small population size and limited distribution. During 2001 and 2002, 32 sea otters were captured, of which 28 were implanted with transmitters to track their movements and liver and blood samples were collected to evaluate contaminant and pathogen exposure. In addition, liver samples from fifteen beachcast animals that washed ashore between 1991 and 2002 were analyzed to provide historical information and a basis of reference for values obtained from live otters. The results indicate low levels of metals, butyltins, and organochlorine compounds in the blood samples, with many of the organochlorines not detected except polychlorinated biphenyls (PCBs), and a few aromatic hydrocarbons detected in the liver of the live captured animals. Aliphatic hydrocarbons were measurable in the liver from the live captured animals; however, some of these are likely from biogenic sources. A significant reduction of vitamin A storage in the liver was observed in relation to PCB, dibutyltin and octacosane concentration. A significant and strong positive correlation in vitamin A storage in the liver was observed for cadmium and several of the aliphatic hydrocarbons. Peripheral blood mononuclear cell (PBMC) cytochrome P450 induction was elevated in two of 16 animals and may be potentially related to aliphatic and aromatic hydrocarbon exposure. Mean concentration of total butyltin in the liver of the Washington beach-cast otters was more than 15 times lower than the mean concentration reported by Kannan et al. (1998) for Southern sea otters in California. Organochlorine compounds were evident in the liver of beach-cast animals, despite the lack of large human population centers and development along the Washington coast. Concentrations of PCBs and chlordanes (e.g., transchlordane, cis-chlordane, trans-nonachlor, cis-nonachlor and oxychlordane) in liver of Washington beach-cast sea otters were similar to those measured in Aleutian and California sea otters, excluding those from Monterey Bay, which were higher. Mean concentrations of 1,1,1,- trichloro-2,2-bis(p-chlorophyenyl)ethanes (DDTs) were lower, and mean concentrations of cyclohexanes (HCH, e.g., alpha BHC, beta BHC, delta BHC and gamma BHC) were slightly higher in Washington beach-cast otters versus those from California and the Aleutians. Epidemiologically, blood tests revealed that 80 percent of the otters tested positive for morbillivirus and 60 percent for Toxoplasma, the latter of which has been a significant cause of mortality in Southern sea otters in California. This is the first finding of positive morbillivirus titers in sea otters from the Northeast Pacific. Individual deaths may occur from these diseases, perhaps more so when animals are otherwise immuno-compromised or infected with multiple diseases, but a population-threatening die-off from these diseases singly is unlikely while population immunity remains high. The high frequency of detection of morbillivirus and Toxoplasma in the live otters corresponds well with the cause of death of stranded Washington sea otters reported herein, which has generally been attributable to infectious disease. Washington’s sea otter population continues to grow, with over 1100 animals currently inhabiting Washington waters; however, the rate of growth has slowed over recent years. The population has a limited distribution and has not yet reached its carrying capacity and as such, is still considered at high risk to catastrophic events. (PDF contains 189 pages)

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

12 p.

Defeza ou resposta do Tenente General Graduado Jorge D'Avillez Juzarte de Sousa Tavares

Chegado a Portugal, o general Avilez foi detido e submetido a Conselho de Guerra. A sua defesa relata o seu conflito com D.Pedro e sua retirada do Rio de Janeiro.

Memoires de monsieur du Guay-Trouin, lieutenant general des armees navales de France, et commandeur de l'ordre royal & militaire de Saint Louis

Notas tipográficas retiradas de Brunet, v. 2, col. 1780.

Participação, e documentos dirigidos ao governo pelo general commandante da tropa expedicionaria, que existia na provincia do Rio de Janeiro, chegando a Lisboa e remettidos pelo governo ás Cortes Geraes, Extraordinarias, e Constituintes da Nação Portugueza

Com: Cartas, e mais peças officiaes dirigidas a S. Magestade, o senhor D. João VI pelo principe real, o senhor D. Pedro de Alcantara -- Cartas, e mais peças officiaes dirigidas a sua magestade, o senhor D. João VI pelo principe real, o senhor D. Pedro de Alcantara e junctamente os officios e documentos, que o general commandante da tropa expedicionaria existente na provincia do Rio de Janeiro tinha dirigido ao governo -- Cartas dirigidas a S. Magestade, o senhor D. João VI pelo principe real o senhor D. Pedro de Alcantara.

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.