Integrais de linha intervalares: fundamentos e aplicações

A necessidade de uma precisão e de uma aproximação dos resultados numéricos zeram com que diversas teorias surgissem: dentre elas, destacamos a Matemática Intervalar. A Matemática Intervalar surgiu na década de 60 com os trabalhos de pesquisa de Moore (MOORE, 1959) , em que ele propôs trabalhar com uma Matemática baseada na noção de intervalo real e não mais com um número como aproximação. Com isso, surgiu a necessidade de revisitar e reformular os conceitos e resultados da Matemática Clássica utilizando como base a noção de intervalo de Moore. Uma das áreas da Matem ática Clássica que tem tido muitas aplicações em engenharias e ciências é a Análises Numérica, onde um dos seus pilares é o Cálculo Integral e em particular as integrais de linha. Assim, é muito desejável se ter um cálculo integral dentro da própria Matemática Intervalar. No presente trabalho apresenta-se uma noção de Integral de Linha Intervalar baseada na extensão de integração proposta por Bedregal em (BEDREGAL; BEDREGAL, 2010). Para a fundamentação apresenta-se incialmente uma introdução sobre a pespectiva em que o trabalho foi realizado, considerando alguns aspectos histórico-evolutivos da Matemática Clássica. Os conceitos de Integrais de Linha Clássica, bem como algumas das suas aplicações mais importantes. Alguns conceitos de Matemática Intervalar necessários para o entendimento do trabalho. Para nalizar propomos uma aplicação da integral de linha em um experimênto clássico da mecânica quântica (a difração de um elétron em uma fenda) que graças ao fato de ser a Matemática Intervalar utilizada, nos dá um foco mais detalhado e mais próximo da realidade

Análise caracterização da dinâmica da Foz do Rio Apodi, região de Areia Branca/RN, com base na cartografia temática multitemporal de produtos de sensores remotos

The study area islocated in the northern cost of Rio Grande do Norte State, preciselyin a west zone of Apodi-Mossoró River, inclunding Tibau City, Grossos City and part of Mossoró City. Geologicaly, this area is composed by rokcs of Potiguar basin, represented by Cretaceous, Tertiary and Quaternary sediments. This area is characterizer by the intense action of cosatal processes (eolic and costal tranports, generalized erosion, alteration in the sediments balance and coast modification), reponsable for it´s morfological instability, also the antropic interference, where the iol industry is located, next Mossoró City, and also the salt exploration industry and the tendency of expantion of shrimp cultivation. This report had as objective the multitemporalgeoenvorimentalmonitoring of the region by recognizingin the field and analizingimages of orbital sensors of diferents years of last four decades. This analisys was achieved by Digital Images Procesing (DIP) thecnics, com subsidized, in a GIS, the preparion of Thematic Maps of natural resources (Geology, Geomorphology and Use & Ocupatios of Earth) and the Envorimental Sensivity to Oil Spilling, main objective os this project. Such technics constitute important tools of envoriment monitoring and maneging, indicating tendencies of antropic of natural growing, making possible the apropiated planning of development of the region, where the steps can be indicated minimized possibles envorimental impacts caused by antropics interferencies on the region, mainly those related to industrial activities, and oil industry above all. Researchs of this nature are very important to the analisys and ordered manegements of use and ocupation of coastal places

Análise multitemporal dos elementos geoambientais da região da Ponta do Tubarão, área de influência dos campos petrolíferos de Macau e Serra, município de Macau/RN

The study area is inserted in Ponta do Tubarão region, Macau City, setentrional littoral of Rio Grande do Norte State, composed of Tertiary and Quatemary sedimentary rocks and sediments. This region is characterized for the intense action of the coastal processes, causing the morphologic instability in part of the area, beyond the interference of human activities, as the Petroliferous Industrial Polo, salt companies and shrimp farms. This justifies the integration of multidisciplinary and multitemporal detailed scientific studies dealing with the evaluation of the changing behavior of this coastal environment by geoenvironments elements characterization, identifying protected and recuperation areas, mainly those under socioeconomic intervention. The main objective was the coastal monitoring using geoprocessing techniques to prepare thematic maps useful for oil spilling environment risk areas survey. The methodology was based on multitemporal interpretation of remote sensing images and field checking, integrated in a Geographical Information System (GIS). The Geologic, Geomorphologic, Vegetation, Soil and Land Use maps were prepared, and later on they allowed the generation of the Natural Vulnerability and Environmental Vulnerability maps. These maps had been classified in accordance with vulnerability degrees: very low, low, medi um, high and very high. Beyond these maps the GIS allowed the analysis of the shoreline evolution for 10 distinct dates, using Landsat 5 TM and 7 ETM+ and SPOT-HRVIR images. This analysis made possible the attendance of the coastal morphodynamic evolution, where the results had been represented by areasof erosion and accretion (or deposition) of sediments, pointing critical areas under erosive process to the petroliferous industry (Macau and Serra fields). The GIS also provided to prepare the Environmental Sensitivity Maps of Oil Spill (SAO Maps) in operational scale (1: 10.000), according to the norms ofthe Ministério do Meio Ambiente (MMA 2002). The SAO Map in operational scale was based on IKONOS images mosaic where the ESI (Environmental Sensitivity Index) was represented according with two tides phases of theregion. Therewere recognizedfiveESI (3, 4,7,9, 1O) for the low tide; to the high tide the ESI number increased to seven (3, 4, 5, 7, 8, 9, 10). All these information are necessary to the decisions making about oi! spill and its derivatives containment. These techniques application makes possible the optimization and implantation ofnew socioeconomics activities of low environmental impact, indicates areas for better productivity and security exploration, and benefits local communities with fauna and flora preservation. The development of these activities is inserted in the scope of Monitoramento Ambiental de Áreas de Risco a Derrames de Petróleo e Seus Derivados Cooperation Project (Rede 05/01 - PETRORISCO, FINEP/CTPETRO/PETROBRAS) of multidisciplinary and interinstitucional characteristics dealing with subjects involving the environmental monitoring and the petroliferous activity

Análise da sobre-reação e sub-reação nos ativos de primeira e segunda linha do mercado acionário brasileiro

The Behavioral Finance develop as it is perceived anomalies in these markets efficient. This fields of study can be grouped into three major groups: heuristic bias, tying the shape and inefficient markets. The present study focuses on issues concerning the heuristics of representativeness and anchoring. This study aimed to identify the then under-reaction and over-reaction, as well as the existence of symmetry in the active first and second line of the Brazilian stock market. For this, it will be use the Fuzzy Logic and the indicators that classify groups studied from the Discriminant Analysis. The highest present, indicator in the period studied, was the Liabilities / Equity, demonstrating the importance of the moment to discriminate the assets to be considered "winners" and "losers." Note that in the MLCX biases over-reaction is concentrated in the period of financial crisis, and in the remaining periods of statistically significant biases, are obtained by sub-reactions. The latter would be in times of moderate levels of uncertainty. In the Small Caps the behavioral responses in 2005 and 2007 occur in reverse to those observed in the Mid-Large Cap. Now in times of crisis would have a marked conservatism while near the end of trading on the Bovespa speaker, accompanied by an increase of negotiations, there is an overreaction by investors. The other heuristics in SMLL occurred at the end of the period studied, this being a under-reaction and the other a over-reaction and the second occurring in a period of financial-economic more positive than the first. As regards the under / over-reactivity in both types, there is detected a predominance of either, which probably be different in the context in MLCX without crisis. For the period in which such phenomena occur in a statistically significant to note that, in most cases, such phenomena occur during the periods for MLCX while in SMLL not only biases are less present as there is no concentration of these at any time . Given the above, it is believed that while detecting the presence of bias behavior at certain times, these do not tend to appear to a specific type or heuristics and while there were some indications of a seasonal pattern in Mid- Large Caps, the same behavior does not seem to be repeated in Small Caps. The tests would then suggest that momentary failures in the Efficient Market Hypothesis when tested in semistrong form as stated by Behavioral Finance. This result confirms the theory by stating that not only rationality, but also human irrationality, is limited because it would act rationally in many circumstances

Caracterização ambiental de bancos areno-lamosos nos campos petrolíferos de Macau e Serra (RN), como subsídio às medidas mitigadoras ao processo erosivo

On Rio Grande do Norte northern coast the process of sediment transport are intensely controlled by wind and sea (waves and currents) action, causing erosion and shoreline morphological instability. Due to the importance of such coastal zone it was realized the multi-spectral mapping and physical-chemical characterization of mudflats and mangroves aiming to support the mitigating actions related to the containment of the erosive process on the oil fields of Macau and Serra installed at the study area. The multi-spectral bands of 2000 and 2008 LANDSAT 5 TM images were submitted on the several digital processing steps and RGB color compositions integrating spectral bands and Principal Components. Such processing methodology was important to the mapping of different units on surface, together with field works. It was possible to make an analogy of the spectral characteristics of wetlands with vegetations areas (mangrove), showing the possibility to make a restoration of this area, contributing with the environmental monitoring of that ecosystem. The maps of several units were integrated in GIS environment at 1:60,000 scale, including the classification of features according to the presence or absence of vegetation cover. Thus, the strategy of methodology established that there are 10.13 km2 at least of sandy-muddy and of these approximately 0.89 km2 with the possibility to be used in a reforestation of typical flora of mangrove. The physical-chemical characterization showed areas with potential to introduce local species of mangrove and they had a pH above neutral with a mean of 8.4. The characteristic particle size is sand in the fine fractions, the high levels of carbonate, organic matter and major and trace element in general are concentrated where the sediment had the less particles size, showing the high correlation that those elements have with smaller particles of sediment. The application of that methodological strategy is relevant to the better understanding of features behavior and physical-chemical data of sediment samples collected on field allow the analysis of efficiency/capability of sandy-muddy to reforestation with local mangrove species for mitigation of the erosive action and coastal processes on the areas occupied by the oil industry

Análise comparativa entre simuladores de linha de fluxo e diferenças finitas para um reservatório de petróleo submetido a injeção de água

Water injection is the most widely used method for supplementary recovery in many oil fields due to various reasons, like the fact that water is an effective displacing agent of low viscosity oils, the water injection projects are relatively simple to establish and the water availability at a relatively low cost. For design of water injection projects is necessary to do reservoir studies in order to define the various parameters needed to increase the effectiveness of the method. For this kind of study can be used several mathematical models classified into two general categories: analytical or numerical. The present work aims to do a comparative analysis between the results presented by flow lines simulator and conventional finite differences simulator; both types of simulators are based on numerical methods designed to model light oil reservoirs subjected to water injection. Therefore, it was defined two reservoir models: the first one was a heterogeneous model whose petrophysical properties vary along the reservoir and the other one was created using average petrophysical properties obtained from the first model. Comparisons were done considering that the results of these two models were always in the same operational conditions. Then some rock and fluid parameters have been changed in both models and again the results were compared. From the factorial design, that was done to study the sensitivity analysis of reservoir parameters, a few cases were chosen to study the role of water injection rate and the vertical position of wells perforations in production forecast. It was observed that the results from the two simulators are quite similar in most of the cases; differences were found only in those cases where there was an increase in gas solubility ratio of the model. Thus, it was concluded that in flow simulation of reservoirs analogous of those now studied, mainly when the gas solubility ratio is low, the conventional finite differences simulator may be replaced by flow lines simulator the production forecast is compatible but the computational processing time is lower.