Sheaves, local homeomorphisms and local sets as Hilbert locale modules

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.

Parâmetros métricos da traqueia e suas correlações com o perímetro torácico, peso e comprimento corporal de cães sem raça definida (Canis familiaris, Linnaeus, 1758)

The present study aimed to analyze metric data from the trachea of dogs and to correlate them with the thoracic girth, body length and weight. We used 48 dogs of unknown breed, 19 males and 29 females. The animals were weighed and then body length, thoracic girth, length and diameter of the trachea, and the number of tracheal rings were measured. The weight of dogs ranged from 4.2 to 21.5 kg, body length from 40.6 to 81.0 cm and thoracic girth from 36.0 to 63.5 cm. The trachea exhibited a total number of tracheal rings between 32 and 43, length between 13.0 and 23.4 cm, diameter of the cervical portion between 11.0 and 23.5 mm and in the thoracic portion between 8.2 and 20.9 mm. We also evaluated the tracheal termination skeletopy, which maintained relations with the 2nd (2.0%), 3 (6.3%), 4 (20.8%) or 5 (12.5%) intercostal spaces, and with the 3rd (6.3%), 4th (35.4%) or 5th (16.7%) ribs. Strong positive correlations of tracheal length with body weight (rS = 0.756, p <0.001), body length (r = 0.808, p <0.001) and thoracic girth (r = 0.735, p <0.001) were found. Therefore, the anatomical study of the trachea provides morphological subsidies for the realization of clinical and surgical procedures in this organ, being an important tool in veterinary practice.

Estimates for the Poisson kernel and Hardy spaces on compact manifolds

We study Hardy spaces on the boundary of a smooth open subset or R-n and prove that they can be defined either through the intrinsic maximal function or through Poisson integrals, yielding identical spaces. This extends to any smooth open subset of R-n results already known for the unit ball. As an application, a characterization of the weak boundary values of functions that belong to holomorphic Hardy spaces is given, which implies an F. and M. Riesz type theorem. (C) 2004 Elsevier B.V. All rights reserved.

Reversibility properties of semigroup actions on homogeneous spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Versão breve da social rhythm metric: um instrumento para avaliar ritmo social de pacientes com acidente vascular cerebral

Stroke is a neurological disorder caused by restriction of blood flow to the brain, which generates directly a deficit of functionality that affects the quality of life of patients. The aim of this study was to establish a short version of the Social Rhythm Scale (SRM), to assess the social rhythm of stroke patients. The sample consisted of 84 patients, of both sexes, with injury time exceeding 6 months. For seven days, patients recorded the time held 17 activities of SRM. Data analysis was performed using a principal components factor analysis with varimax rotation of the full version of SRM in order to determine which activities could compose brief versions of SRM. We then carried out a comparison of hits, the ALI (Level Activity Index) and SRM, between versions, by Kruskal-Walls and the Mann-Whitney test. The Spearman correlation test was used to evaluate the correlation between the score of the full version of SRM with short versions. It was found that the activities of SRM were distributed in three versions: the first and second with 6 activities and third with 3 activities. Regarding hits, it was found that they ranged from 4.9 to 5.8 on the first version; 2.3 to 3.8 in version 2 and 2.8 to 6.2 in version 3, the first the only version that did not show low values. The analysis of ALI, in version 1, the median was 29, in version 2 was 14 and in version 3 was 18. Significant difference in the values of ALI between versions 1 and 2, between 2 and 3 and between versions 1 and 3. The highest median was found in the first version, formed by activities: out of bed, first contact, drink coffee, watch TV in the evening and go to bed. The lowest median was observed in the second version and this was not what had fewer activities, but which had social activities. The medians of the SRM version 1 was 6, version 2 was 4 and version 3 was 6. Significant difference in the values of SRM between versions 1 and 2 and between 2 and 3, but no significant difference between versions 1 and 3. Through analysis, we found a significant correlation only between the full version and the version 1 (R2 = 0.61) (p <0.05), no correlation was found with version 2 (R2 = 0.007) nor with version 3 (R2 = 0.002), this was finally a factor to consider version 1 as the short brazilian version of the Social Rhythm Metric for stroke patients

(Por) entre pedra e tela: a construção de uma memória republicana (Natal - 1906-1919)

This work, from a perspective that thinks the space as a historical category, and especially as a relationship which stresses the role of objects, proposes an analysis of the construction of a Republican memory in the city of Natal in the early twentieth century. This research will focus mainly on two objects: the obelisk opened in 1917, and the Andre de Albuquerque Square on the occasion of the celebration of Frei Miguelinho´s death centenary and the paint Julgamento de Frei Miguelinho ordered by the State Government to the painter Antonio Parreiras, picture that was in the Salão Nobre do Palácio do Poder Executivo of that time. In a geral way this work intend to analyse the construction of this memory as well as the role of these objects in this process. To achieve that, we propose to trace ways and networks to follow the possible associations(between people, events, images, discourses, objects, institutios etc.) in the constitution of mutual belongings. Thus, our procedure was to follow these objects through the pathways in which they became possible, so that in the end we could defend the idea that they are active participants of the process that establish them.

Santo de casa faz milagre: Luíz da Câmara Cascudo, o padroeiro literário da cidade de Natal

Assuming that the subject is a draft work in permanent invention, the biographical texts, memories written by Luís da Câmara Cascudo, between 1967 and 1969 were read as part of a discursive strategy created by the potiguar memorialist regarding the construction of a self-image profoundly connected to the space of his house, which decisively collaborated so that the province teacher and researcher after announcing his official retirement in 1968 was revered in the city where he had been born, grown up and lived throughout his whole life and considered as the prophet of his own country (or rather, as the literary patron of Natal). Our work begins with some reading about the manner as the potiguar memorialist selected, ordered and spatialized his childhood memories. In the following chapter, we problematized the meanings assigned by Câmara Cascudo to his house in Tirol - where the young prince Cascudinho (little Cascudo) used to live - transformed into the neighborhood principality. It finishes with memories from the retired old man with the purpose of making us think about the sacredness process master Cascudo s house has gone through. The space where he had lived for almost forty years of his life and produced a great part of his works, was elected as a monument in his memory, as his own incarnation, as guarantee of his eternity and perenniality, as a sanctuary and place of worship and have been kept by the actions that, still nowadays, institutionalize it as his sacred space

Different origins of green-light photoluminescence emission in structurally ordered and disordered powders of calcium molybdate

A strong greenish-light photoluminescence (PL) emission was measured at room temperature for disordered and ordered powders of CaMoO4 prepared by the polymeric precursor method. The structural evolution from disordered to ordered powders was accompanied by XRD. Raman spectroscopy, and TEM imagery. High-level quantum mechanical calculations in the density functional framework were used to interpret the formation of the structural defects of disorder powders in terms of band diagram and density of states. Complex cluster vacancies [MoO3 center dot V-O(z)] and [CaO7 center dot V-O(z)] (where V-O(z) = V-O(X), V-O(center dot), V-O(center dot center dot)) were suggested to be responsible to the appearance of new states shallow and deeply inserted in the band gap. These defects give rise to the PL in disordered powders. The natural PL emission of ordered CaMoO4 was attributed to an intrinsic slight distortion of the [MoO4] tetrahedral in the short range.

Electrocatalysis of oxidation of hydrogen on platinum ordered intermetallic phases: Kinetic and mechanistic studies

An experimentally based kinetic and mechanistic study of the hydrogen oxidation reaction (HOR) on platinum and platinum ordered intermetallic materials in acid medium is presented. RDE kinetic data were re-evaluated and complemented by Tafel plots obtained from chronoamperometric measurements. Among the materials evaluated, PtSb and PtSn exhibited markedly improved kinetic current densities and exchange current densities, compared to Pt in the same experimental conditions. It is proposed that the intermetallic phase enhanced the adsorptive characteristic of the surface sites and, as a consequence, improved the kinetics of the adsorption steps (Tafel or Heyrovsky) of the mechanism involved. (c) 2006 Published by Elsevier B.V.

Synthesis and Characterization of Ordered Intermetallic Nanostructured PtSn/C and PtSb/C and Evaluation as Electrodes for Alcohol Oxidation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Preparation and characterization of ordered intermetallic platinum phases for electrocatalytic applications

Ordered intermetallic phases of Pt with several transition metals have been prepared and their electrocatalytic properties studied. In light of these tests it is proposed that these catalysts could be used as electrodes in fuel cells, as they combine an excellent capacity to adsorb organic fuels at the Pt sites with low susceptibility to being poisoned by intermediates and reaction products at the transition-metal sites. An experimental procedure used to obtain the four intermetallic phases Pt-M (M = Mn, Pb, Sb and Sn) is described. The phases thus produced were characterized by X-ray diffraction, scanning electron microscopy with surface analysis by energy-dispersive X-ray spectrometry, scanning tunneling microscopy and X-ray photoelectron spectroscopy. The data thus obtained support the conclusion that the method described here is highly effective for the preparation of Pt-M phases featuring a range of structural and electronic modifications that will allow a useful relation to be established between their physicochemical properties and predicted electrocatalytic activity. (C) 2007 Elsevier Ltd. All rights reserved.

Hydrogen oxidation on ordered intermetallic electrodes covered with CO

This describes an experimental evaluation of the electrocatalytic activity of the hydrogen oxidation reaction on electrodes of platinum and the ordered intermetallic phases PtSb and PtSn, on which CO has previously been deposited. The experiments were carried out in perchloric acid solution and the analysis based on steady-state polarization curves and Tafel plots derived from chronoamperometric data. Both intermetallics, PtSb and PtSn, performed better than Pt towards the HOR, when their surface was deliberately covered with CO. It is suggested that the intermetallic surfaces have a lower affinity for CO molecules, causing a lower CO coverage on these surfaces, and/or a weaker surface-CO interaction, compared to Pt under the same conditions. (C) 2007 Elsevier B.V. All rights reserved.

New approaches in W gravities

We devote effort to studying some nonlinear actions, characteristic of W theories, in the framework of the soldering formalism. We disclose interesting new results concerning the embedding of the original chiral W particles in different metrical spaces in the final soldered action; i.e., the metric is modified by the soldering interference process. The results are presented in a weak field approximation for the W-N case when Ngreater than or equal to3 and also in an exact way for W-2. We promote a generalization of the interference phenomenon to W-N theories of different chiralities and show that the geometrical features introduced can yield a new understanding of the interference formalism in quantum field theories.

Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Generalizações do conceito de distância, i-distâncias, distâncias intervalares e topologia

In this dissertation we present some generalizations for the concept of distance by using more general value spaces, such as: fuzzy metrics, probabilistic metrics and generalized metrics. We show how such generalizations may be useful due to the possibility that the distance between two objects could carry more information about the objects than in the case where the distance is represented just by a real number. Also in this thesis we propose another generalization of distance which encompasses the notion of interval metric and generates a topology in a natural way. Several properties of this generalization are investigated, and its links with other existing generalizations