The Interval Constructor on classes of ML-algebras

Monoidal logic, ML for short, which formalized the fuzzy logics of continuous t-norms and their residua, has arisen great interest, since it has been applied to fuzzy mathematics, artificial intelligence, and other areas. It is clear that fuzzy logics basically try to represent imperfect or fuzzy information aiming to model the natural human reasoning. On the other hand, in order to deal with imprecision in the computational representation of real numbers, the use of intervals have been proposed, as it can guarantee that the results of numerical computation are in a bounded interval, controlling, in this way, the numerical errors produced by successive roundings. There are several ways to connect both areas; the most usual one is to consider interval membership degrees. The algebraic counterpart of ML is ML-algebra, an interesting structure due to the fact that by adding some properties it is possible to reach different classes of residuated lattices. We propose to apply an interval constructor to ML-algebras and some of their subclasses, to verify some properties within these algebras, in addition to the analysis of the algebraic aspects of them

Em direção a uma representação para equações algébricas :uma lógica equacional local

The intervalar arithmetic well-known as arithmetic of Moore, doesn't possess the same properties of the real numbers, and for this reason, it is confronted with a problem of operative nature, when we want to solve intervalar equations as extension of real equations by the usual equality and of the intervalar arithmetic, for this not to possess the inverse addictive, as well as, the property of the distributivity of the multiplication for the sum doesn t be valid for any triplet of intervals. The lack of those properties disables the use of equacional logic, so much for the resolution of an intervalar equation using the same, as for a representation of a real equation, and still, for the algebraic verification of properties of a computational system, whose data are real numbers represented by intervals. However, with the notion of order of information and of approach on intervals, introduced by Acióly[6] in 1991, the idea of an intervalar equation appears to represent a real equation satisfactorily, since the terms of the intervalar equation carry the information about the solution of the real equation. In 1999, Santiago proposed the notion of simple equality and, later on, local equality for intervals [8] and [33]. Based on that idea, this dissertation extends Santiago's local groups for local algebras, following the idea of Σ-algebras according to (Hennessy[31], 1988) and (Santiago[7], 1995). One of the contributions of this dissertation, is the theorem 5.1.3.2 that it guarantees that, when deducing a local Σ-equation E t t in the proposed system SDedLoc(E), the interpretations of t and t' will be locally the same in any local Σ-algebra that satisfies the group of fixed equations local E, whenever t and t have meaning in A. This assures to a kind of safety between the local equacional logic and the local algebras

Especificação do tipo intervalar parametrizado em CASL

The interval datatype applications in several areas is important to construct a interval type reusable, i.e., a interval constructor can be applied to any datatype and get intervals this datatype. Since the interval is, of certain form, a set of elements limited for two bounds, left and right, with a order notions, then it s reasonable that interval constructor enclose datatypes with partial order. On the order hand, what we want is work with interval of any datatype like this we work with this datatype then. it s important to guarantee the properties of the datatype when maps to interval of this datatype. Thus, the interval constructor get a theory to parametrized interval type, i.e., a interval with generics parameters (for example rational, real, complex). Sometimes, the interval application in some algebras doesn t guarantee the mainutenance of their properties, for example, when we use interval of real, that satisfies the field properties, it doesn t guarantee the distributivity propertie. A form to surpass this problem Santiago introduced the local equality theory that weakened the notion of strong equality, and thus, allowing some properties are local keeped, what can be discard before. The interval arithmetic generalization aim to apply the interval constructor on ordered algebras weakened for local equality with the purpose of the keep their properties. How the intervals are important in applications with continuous data, it s interesting specify that theory using a specification language that supply a system development using intervals of form disciplined, trustworth and safe. Currently, the algebraic specification language, based in math models, have been use to that intention often. We choose CASL (Common Algebraic Specification Language) among others languages because CASL has several characteristics excellent to parametrized interval type, such as, provide parcialiy and parametrization

Litoestratigrafia e deformação cenzóica na região de Icapuí, Ceará, e implicações para a estruturação de campos de petróleo na borda ocidental da bacia Potiguar(NE do Brasil)

This thesis deals with the sedimentological/stratigraphic and structural evolution of the sedimentary rocks that occur in the NW continental border of the Potiguar Basin. These rocks are well exposed along coastal cliffs between the localities of Lagoa do Mato and Icapuí, Ceará State (NE Brazil). The sedimentological/stratigraphic study involved, at the outcrop scale, detailed facies descriptions, profile mapping of the vertical succession of different beds, and columnar sections displaying inferred lateral relationships. The approach was complemented by granulometric and petrographic analyses, including the characterization of heavy mineral assemblages. The data set allowed to recognize two kinds of lithological units, a carbonate one of very restricted occurrence at the base of the cliffs, and three younger, distinct siliciclastic units, that predominate along the cliffs, in vertical and lateral extent. The carbonate rocks were correlated to the late Cretaceous Jandaíra Formation, which is covered by the siliciclastic Barreiras Formation. The Barreiras Formation occurs in two distinct structural settings, the usual one with nondeformed, subhorizontal strata, or as tilted beds, affected by strong deformation. Two lithofacies were recognized, vertically arranged or in fault contacts. The lower facies is characterized by silty-argillaceous sandstones with low-angle cross bedding; the upper facies comprises medium to coarse grained sandstones, with conglomeratic layers. The Tibau Formation (medium to coarse-grained sandstones with argillite intercalations) occurs at the NW side of the studied area, laterally interlayered with the Barreiras Formation. Eolic sediments correlated to the Potengi Formation overly the former units, either displaying an angular unconformity, or simply an erosional contact (stratigraphic unconformity). Outstanding structural features, identified in the Barreiras Formation, led to characterize a neocenozoic stress field, which generated faults and folds and/or reactivated older structures in the subjacent late cretaceous (to paleogene, in the offshore basin) section. The structures recognized in the Barreiras Formation comprise two distinct assemblages, namely a main extensional deformation between the localities of Ponta Grossa and Redonda, and a contractional style (succeeded by oblique extensional structures) at Vila Nova. In the first case, the structural assemblage is dominated by N-S (N±20°Az) steep to gently-dipping extensional faults, displaying a domino-style or listric geometry with associated roll-over structures. This deformation pattern is explained by an E-W/WNW extension, contemporaneous with deposition of the upper facies of the Barreiras Formation, during the time interval Miocene to Pleistocene. Strong rotation of blocks and faults generated low-angle distensional faults and, locally, subvertical bedding, allowing to estimate very high strain states, with extension estimates varying between 40% up to 200%. Numerous detachment zones, parallel to bedding, help to acommodate this intense deformation. The detachment surfaces and a large number of faults display mesoscopic features analoguous to the ones of ductile shear zones, with development of S-C fabrics, shear bands, sigmoidal clasts and others, pointing to a hydroplastic deformation regime in these cases. Local occurrences of the Jandaíra limestone are controled by extensional faults that exhume the pre-Barreiras section, including an earlier event with N-S extension. Finally, WNWtrending extensional shear zones and faults are compatible with the Holocene stress field along the present continental margin. In the Vila Nova region, close to Icapuí, gentle normal folds with fold hinges shallowly pluging to SSW affect the lower facies of the Barreiras Formation, displaying an incipient dissolution cleavage associated with an extension lineation at high rake (a S>L fabric). Deposition of the upper facies siliciclastics is controlled by pull-apart graben structures, bordered by N-NE-trending sinistral-normal shear zones and faults, characterizing an structural inversion. Microstructures are compatible with tectonic deformation of the sedimentary pile, burried at shallow depths. The observed features point to high pore fluid pressures during deformation of the sediments, producing hydroplastic structures through mechanisms of granular flow. Such structures are overprinted by microfractures and microfaults (an essentially brittle regime), tracking the change to microfracturing and frictional shear mechanisms accompanying progressive dewatering and sediment lithification. Correlation of the structures observed at the surface with those present at depth was tested through geophysical data (Ground Penetrating Radar, seismics and a magnetic map). EW and NE-trending lineaments are observed in the magnetic map. The seismic sections display several examples of positive flower structures which affect the base of the cretaceous sediments; at higher stratigraphic levels, normal components/slips are compatible with the negative structural inversion characterized at the surface. Such correlations assisted in proposing a structural model compatible with the regional tectonic framework. The strong neogenepleistocene deformation is necessarily propagated in the subsurface, affecting the late cretaceous section (Açu and Jandaíra formations), wich host the hydrocarbon reservoirs in this portion of the Potiguar Basin. The proposed structural model is related to the dextral transcurrent/transform deformation along the Equatorial Margin, associated with transpressive terminations of E-W fault zones, or at their intersections with NE-trending lineaments, such as the Ponta Grossa-Fazenda Belém one (the LPGFB, itself controlled by a Brasiliano-age strike-slip shear zone). In a first step (and possibly during the late Cretaceous to Paleogene), this lineament was activated under a sinistral transpressional regime (antithetic to the main dextral deformation in the E-W zones), giving way to the folds in the lower facies of the Barreiras Formation, as well as the positive flower structures mapped through the seismic sections, at depth. This stage was succeeded (or was penecontemporaneous) by the extensional structures related to a (also sinistral) transtensional movement stage, associated to volcanism (Macau, Messejana) and thermal doming processes during the Neogene-Pleistocene time interval. This structural model has direct implications to hydrocarbon exploration and exploitation activities at this sector of the Potiguar Basin and its offshore continuation. The structure of the reservoirs at depth (Açu Formation sandstones of the post-rift section) may be controlled (or at least, strongly influenced) by the deformation geometry and kinematics characterized at the surface. In addition, the deformation event recognized in the Barreiras Formation has an age close to the one postulated for the oil maturation and migration in the basin, between the Oligocene to the Miocene. In this way, the described structural cenario represents a valid model to understand the conditions of hydrocarbon transport and acummulation through space openings, trap formation and destruction. This model is potentially applicable to the NW region of the Potiguar Basin and other sectors with a similar structural setting, along the brazilian Equatorial Atlantic Margin

Análise da deformação pós-Rifte na Bacia do Araripe, Nordeste do Brasil

The Araripe Basin is located over Precambrian terrains of the Borborema Province, being part of Northeast Brazil inner basins. Its origin is related to the fragmentation of the Gondwana supercontinent and consequently opening of South Atlantic during early Cretaceous. The basin has a sedimentary infill encompassing four distinct evolution stages, comprising Paleozoic syneclisis, pre-rift, rift and post-rift. The target of this study comprises the post-rift section of the basin focusing deformational styles which affect evaporates from Ipubi Member of the Santana Formation, which is composed by gypsum and anidrite layers interbedded with shales. These units occur widespread across the basin. In the central part of the basin, near Nova Olinda-Santana do Cariri, evaporites are affected by an essentialy brittle deformation tipified by fibrous gypsum filled fractures, cutting massive layers of gypsum and anidrite. Veins with variable orientations and dips are observed in the region distributed over three main populations: i) a dominant NWSE with shallow to moderate NE dipping population, consisting of gypsum filled veins in which fibers are normal to vein walls; i) NE-SW veins with moderate SE dips containing subhorizontal growth fibers; and iii) N-S veins with shallow E-W dips with fibers oblique to vein walls. In the west portion of the basin, near Trindade-Ipubi-Araripina towns, evaporate layers are dominantly constituted by gypsum/anidrite finely stratified, showing a minor density of veins. These layers are affected by a unique style of deformation, more ductile, typified by gentle to open horizontal normal folding with several tens of meters length and with double plunging NW-SE or NE-SW hinges, configuring domic features. In detail, gypsum/anidrite laminae are affected by metre to decimeter scale close to tight folding, usually kinked, with broken hinges, locally turning into box folds. Veins show NE-SW main directions with shallow NE dips, growth fibers are parallel to vein walls, constituting slickenfibers. This region is marked by faults that affect Araripina Formation with NW-SE, NE-SW and E-W directions. The main structural styles and general orientations of structures which affected the post-rift section of Araripe Basin yielded important kinematic information analysis which led us to infer a E-W to NE-SW extension direction to the northeastern part of the Basin, whereas in the southeastern part, extension occurred in N-S direction. Thus, it was possible to determine a regional kinematic setting, through this analysis, characterizing a NE-SW to ENE-WSW system for the post-rift section, which is compatible with the tension settings for the Sout American Plate since Albian. Local variations at the fluid pressure linked (or not) to sedimentary overload variation define local tension settings. This way, at the northeastern portion of the basin, the post-rift deformation was governed by a setting which σ 1 is sub-horizontal trending NE-SW and, σ 3 is sub-vertical, emphasizing a reverse fault situation. At the southwestern portion however there was characterized a strike slip fault setting, featuring σ 1 trending ENEWSW and σ3 trending NNW-SSE

Caracterização geomorfológica e paleogeográfica da plataforma continental adjacente a foz do Rio Apodi-Mossoró, RN/Brasil

The brazilian marginal basins have a huge potential to generate and accumulate petroleum. Incised valleys which are eroded in response to a fall of relative sea level are related to potential reservoir as well, modern drowned-valley estuaries serve as harbors to petroleum and salt industries, fisheries, waste-disposal sites and recreational areas for a significant fraction of the world s population. The combined influence of these factors has produced a dramatic increase in research on modern and ancient incised-valley systems. This research is one expression of this interest. The integrated use of satellites images and high resolution seismic (bathymetry, sides scan sonar) was used on the Apodi River mouth-RN to characterizes the continental shelf This area is located at the Potiguar Basin in the NE Brazilian Equatorial Atlantic margin. Through bathymetric and side scan sonar data processing, a digital Terrain Model was developed, and a detailed geomorphologic analysis was performed. In this way was possible to recognize the geomorphologic framework and differents sismofacies, which may influence this area. A channel extending from the ApodiMossoró river mouth to the shelf edge dominates the investigated area. This structure can be correlated with the former river valley developed during the late Pleistocene sea level fall. This channel has two main directions (NW-SE and NE-SW) probably controlled by the Potiguar Basin structures. The western margin of the channel is relatively steep and pronounced whereas the eastern margin consists only of a gentle slope. Longitudinal bedforms and massive ridges also occur. The first are formed doe to the shelf sediment rework and the reef-like structures probably are relics of submerged beachrock-lines indicating past shoreline positions during the deglacial sea-level rise. The sub-bottom seismic data allow the identification of different sismic patterns and a marcant discontinuity, interpreted as the Upper

Detecção de áreas degradadas na sub-bacia hidrográfica do rio taperoá/pb, utilizando parâmetros físicos dos sensores modis/terra e tm/landsat

This study includes the results of the analysis of areas susceptible to degradation by remote sensing in semi-arid region, which is a matter of concern and affects the whole population and the catalyst of this process occurs by the deforestation of the savanna and improper practices by the use of soil. The objective of this research is to use biophysical parameters of the MODIS / Terra and images TM/Landsat-5 to determine areas susceptible to degradation in semi-arid Paraiba. The study area is located in the central interior of Paraíba, in the sub-basin of the River Taperoá, with average annual rainfall below 400 mm and average annual temperature of 28 ° C. To draw up the map of vegetation were used TM/Landsat-5 images, specifically, the composition 5R4G3B colored, commonly used for mapping land use. This map was produced by unsupervised classification by maximum likelihood. The legend corresponds to the following targets: savanna vegetation sparse and dense, riparian vegetation and exposed soil. The biophysical parameters used in the MODIS were emissivity, albedo and vegetation index for NDVI (NDVI). The GIS computer programs used were Modis Reprojections Tools and System Information Processing Georeferenced (SPRING), which was set up and worked the bank of information from sensors MODIS and TM and ArcGIS software for making maps more customizable. Initially, we evaluated the behavior of the vegetation emissivity by adapting equation Bastiaanssen on NDVI for spatialize emissivity and observe changes during the year 2006. The albedo was used to view your percentage of increase in the periods December 2003 and 2004. The image sensor of Landsat TM were used for the month of December 2005, according to the availability of images and in periods of low emissivity. For these applications were made in language programs for GIS Algebraic Space (LEGAL), which is a routine programming SPRING, which allows you to perform various types of algebras of spatial data and maps. For the detection of areas susceptible to environmental degradation took into account the behavior of the emissivity of the savanna that showed seasonal coinciding with the rainy season, reaching a maximum emissivity in the months April to July and in the remaining months of a low emissivity . With the images of the albedo of December 2003 and 2004, it was verified the percentage increase, which allowed the generation of two distinct classes: areas with increased variation percentage of 1 to 11.6% and the percentage change in areas with less than 1 % albedo. It was then possible to generate the map of susceptibility to environmental degradation, with the intersection of the class of exposed soil with varying percentage of the albedo, resulting in classes susceptibility to environmental degradation

Petrologia e geologia estrutural do plutão granítico Barcelona, província Borborema, NE do Brasil

The Dissertation aimed to advance the geological knowledge of the Barcelona Granitic Pluton (BGP). This body is located in the eastern portion of the Rio Grande do Norte Domain (RND), within the São José do Campestre subdomain (SJC), NE of the Borborema Province. The main goal was to understand the geological evolution of the rocks of the pluton and the tectonic setting of magma generation and its emplacement. The BGP has an assumed Ediacaran age and outcropping area of approximately 260 km2, being composed of three varied petrographic/textural facies: (a) porphyritic biotite monzogranite; (b) dykes and sheets of biotite microgranite; (c) dioritic to quartz-dioritic enclaves. The rocks of the BGP have the following structures: (i) a NE-SW and NW-SE directed magmatic fabric (Sγ), accompanied by a magmatic lineation (Lγ) with gentle dip to NE-SW and NW-SE. In the southern portion, there is the concentric pattern of this foliation with medium to high dip, and (ii) a solid state foliation, in part mylonitic (S3+), mainly on the eastern edge with slightly plunging to west. The integration of structural and gravity data permitted to interpret the emplacement of the BGP as controlled by the transcurrent shear zones systems Lajes Pintadas (LPSZ) and Sítio Novo (SNSZ), both of dextral strike-slip kinematics. Mineral chemistry data show that the amphibole form the porphyritic biotite monzogranite facies is hastingsite with moderate Mg / (Mg + Fe) ratios, indicating crystallization under moderate to high ƒO2 and cristallization pressure of around 5.0-6.0 kbar. The biotite tends to be slightly richer in annite molecule and plots in the transitional field from primary biotite to reequilibrated biotite. In discriminant diagrams of magmatic series, the biotite behave like those of subalkaline affinity, consistent with the potassium calc-alkaline / sub-alkaline geochemical affinity of the hosting rock. The opaque minerals are primarily magnetite, with some crystals martitized to hematite indicating relatively oxidizing conditions during magma evolution that originated the BGP. Zoning in plagioclase, K-feldspar and allanite crystals suggest fractional crystallization process. Lithogeochemical data suggest that the facies described for the BGP have similar magma source, usually plotting in the fields and trends of the subalkaline / high potassium calc-alkaline series.