Estimação paramétrica e não-paramétrica em modelos de markov ocultos

In this work we study the Hidden Markov Models with finite as well as general state space. In the finite case, the forward and backward algorithms are considered and the probability of a given observed sequence is computed. Next, we use the EM algorithm to estimate the model parameters. In the general case, the kernel estimators are used and to built a sequence of estimators that converge in L1-norm to the density function of the observable process

Calculando distância em geometria espacial usando material manipulável como recurso didático

This work presents a proposal for introducing the teaching of Geometry Space study attempts to demonstrate that the use of manipulatives as a teaching resource can be an alternative learning facilitator for fixing the primitive concepts of geometry, the postulates and theorems, position relationships between points, lines and planes and calculating distances. The development makes use of a sequence of activities aimed at ensuring that students can build a more systematic learning and these are divided into four steps

O ensino de funfições trigonometricas através do software geogebra

In this study, we sought to address the weaknesses faced by most students when they were studying trigonometric functions sine and cosine. For this, we proposed the use of software Geogebra in performing a sequence of activities about the content covered. The research was a qualitative approach based on observations of the activities performed by the students of 2nd year of high school IFRN - Campus Caicfio. The activities enabled check some diculties encountered by students, well as the interaction between them during the tasks. The results were satisfactory, since they indicate that the use of software contributed to a better understanding of these mathematical concepts studied

Estudo geológico e geofísico da falha de carnaubais, Bacia Potiguar-RN, e implicações neotectônicas

The segment of Carnaubais Fault located in the southeasthern portion of Guamaré Graben (Potiguar Basin) was studied. Several structures were detected and some of them strongly suggest that the last movements in Carnaubais Fault are of Neotectonic age. The study comprises an integrated interpretation of geologic, geomorphologic and geophysical data (gravimetry, magnetometry, resistivity, and self potential methods). According to the size of the studied areas, two approaches were used in this research. The first approach is of a regional nature and was conducted in an area, hereafter named Regional Area, having approximately 6,000 km2 and localized in the northern portion of Rio Grande do Norte state, around Macau city. The second approach comprises detailled studies of two small areas inside the Regional Area: the Camurupim and São Bento areas. Gravimetric and topographic data were used in the Regional Area. A separation into regional and residual components were conducted both on gravimetric and topographic data. The interpretation of the residual component of the gravimetric data allows a precise mapping of the borders of the Guamaré Graben. The regional component features of the topographic data are controlled by the pair of conjugate faults composed by the Carnaubais Fault (NE direction) and the Afonso Bezerra Fault (NW direction). On the other hand, the residual component of the topographic data shows that river valleis of NW direction are sharply interrupted where they intersect Carnaubais Fault. This fact is interpreted as an evidency that the last significant moviments occured in the Carnaubais Fault. Geologic, geomorphologic and geophysical data (magnetometry, resistivity, and self potential methods) were used in the Camurupim Area. The geologic mapping allows to identify five lithophacies unities. The first two unities (from base to top) were interpreted as composing a marine (or transitional) depositional sequency while the other were interpreted is composing a continental depositional sequence. The two sequences are clearly separated of an erosional discordance. The unities grouped in the marine sequence are composed by calcarenites (Unity A) and mudstones (Unity B). Unity A was deposited in a shalow plataform while Unity B, in a tidal flat. The unities grouped in the continental sequence are composed of conglomerate (Unity C) and sandstones (Unities D and E). Unities C and D are fluvial deposits while unity E is an eolian deposit. Unities A and B can be stratigraphycally correlated with Guamaré Formation. Unities C and D present three possible correlations. They may be correlated with Tibau Formation; or with Barreiras Formation; or with a clastic sediment deposit, commonly found in some rivers of Rio Grande do Norte state, and statigraphycally positioned above Barreiras Formation. Based on the decrease of the grain sizes from base to top both on unities C and D, it is proposed that these unities are correlated with the clastic sediment above mentioned. In this case, these unities would have, at least, Pleistocenic age. Finally, it is proposed that Unity E represent an eolian deposit that sufferred recent changes (at least in the Quaternary). The integrated interpretation of hydrographic, morphologic and geophysical data from Camurupim Area shows that Carnaubais Fault is locally composed by a system of several paralel subvertical faults. The fault presenting the larger vertical slip controls the valley of Camurupim river and separates the area in two blocks; in the nothern block the top of the Jandaira limestone is deeper than in the southern block. In addition, at least one of the faults in the northern block is cutting the whole sedimentary section. Because unities C , D, and/or E may be of Quaternary age, tectonic moviments possibly occured in Carnaubais Fault during this period. Detailled geologic mapping were conducted in beachrocks found in São Bento Area. This area is located at the intersection of the coast line with the Carnaubais Fault. The detected structures in the beachrocks are very similar to those caused by fragile deformations. The structures mapped in the beachrocks are consistent with a stress field with maximun compressional stress in E-W direction and extensional stress in the N-S direction. Since the Carnaubais Fault has a NE direction, it is optimally positioned to suffer tectonic movements under the action of such stress field. In addition, the shape of the coastal line appear to be controlled by the Carnaubais Fault. Furthemore, the observed structures in Camurupim Área are consistent with this stress field. These facts are interpreted as evidences that Carnaubais Fault and beachrocks suffered coupled tectonic movements. These moviments are of Neotectonic age because the beachrocks present ages less than 16,000 years

Arquitetura deposicional e evolução tectono-estratigráfica das sequências pré-rifte e rifte, na porção central do Vale do Cariri, Bacia do Araripe, NE do Brasil

A complex depositional history, related to Atlantic rifting, demonstrates the geological evolution during the late Jurassic and early Neocomian periods in the Araripe Basin NE Brazil. Based on outcrop, seismic and remote sensing data, a new model of the tectono-stratigraphic evolution of the section that covers the stages Dom João, Rio da Serra and Aratu (Brejo Santo, Missão Velha and Abaiara formations) is presented in this paper. In the stratigraphic section studied, ten sedimentary facies genetically linked to nine architectural elements were described, representing depositional systems associated with fluvial, aeolian and deltaic environments. Based on the relationship between the rates of creation of accommodation space and sediment influx (A / S) it was possible to associate these depositional systems with High and Low accommodation system tracks. These system tracks represent two tectono-sequences, separated by regional unconformities. The Tectono-sequence I, which includes lithotypes from the Brejo Santo Formation and is related to the pre-rift stage, is bounded at the base by the Paleozoic unconformity. This unit represents only a High Accommodation System Track, composed by a succession of pelitic levels interbedded with sandstones and limestones, from a large fluvial floodplain origin, developed under arid climatic conditions. The Tectono-sequence II, separated from the underlying unit by an erosional unconformity, is related to the rift stage, and is composed by the Missão Velha and Abaiara Formation lithotypes. Changes in depositional style that reflect variations in the A / S ratio, and the presence of hydroplastic deformation bands, make it possible to divide this tectonosequence into two internal sequences. Sequence IIA, which includes the lower portion of the Missão Velha Formation and sequence IIB, is composed by the upper section of the Missão Velha and Abaiara Formations The Sequence IIA below, composed only by the Low Accommodation System Track, includes crossbedding sandstones interbedded with massive mudstones, which are interpreted as deposits of sandy gravel beds wandering rivers. Sequence IIB, above, is more complex, showing a basal Low Accommodation System Track and a High Accommodation System Track at the top, separated by an expansion surface. The lower System Track, related to the upper portion of the Missão Velha Formation, is composed by a series of amalgamated channels, separated by erosion surfaces, interpreted as deposits of a belt of braided channels. The High Accommodation System Track, correlated with the Abaiara Unit, is marked by a significant increase in the A / S, resulting in the progradation of a system of braided river deltas with aeolic influence. Regarding tectonic evolution, the stratigraphic study indicates that the Tectonosequence Rift in the Araripe basin was developed in two phases: first characterized by a beginning of rifting, related to Sequence IIA, followed by a phase of syndepositional deformation, represented by sequence IIB. The first phase was not influenced by the development of large faults, but was influenced by a sharp and continuous decrease of accommodation space that permitted a change in depositional patterns, establishing a new depositional architecture. In turn, the stage of syndepositional deformation allowed for the generation of enough accommodation space for the preservation of fluvial-lacustrine deposits and conditioned the progradation of a braided river-dominated delta system.

Expressão em superfície do sistema de falhas Poço Verde-caraúbas, Bacia Potiguar

The structural knowledge of the western portion of the Potiguar Basin is still in its infancy, especially these related to NW-trending fault systems. This paper analyzes the Poço Verde-Caraúbas Fault System, which was initially recognized in subsurface. The activities involved in this study correspond to remote-sensing analysis and, in particular, to the geometric and kinematic analysis of post-rift sequences of the basin. In addition, the study aimed to determine the stress fields operating in the area. The studies were carried out in an area of 1,000 km², located in the western portion of Potiguar Basin along the Poço Verde-Caraúbas Fault System, Rio Grande do Norte State. The remote sensing imagery indicates a predominance of NW-SE-trending lineaments, consistent with the fault system under study, followed by the NE-SW, N-S and E-W directions. The tectonic structures mapped were analyzed only in outcrops of the Jandaíra Formantion. They are joints (filled or not) in all directions, but with predominance of the NW-trending joints. Faults are usually N-S-trending normal faults and NW-SE and NE-SW-trending strike-slip faults. Geodynamic analysis identified two tectonic stress fields: the first field, "Field 1" is represented by an N-S-trending horizontal compression and E-W-trending horizontal extension. This field affected the Potiguar Basin at least until the Miocene. The second field, "Field 2", is represented by an E-W-trending horizontal compression and N-S-trending horizontal extension. This is the present-day stress field and has affected the Potiguar basin since the Pliocene

Petrologia do plúton Serra da Macambira, neoproterozóico da faixa seridó, província Borborema (NE do Brasil)

The final stage of Brasiliano/Pan-African orogeny in the Borborema Province is marked by widespread plutonic magmatism. The Serra da Macambira Pluton is an example of such plutonism in Seridó Belt, northeastern Borborema Province, and it is here subject of geological, petrographic, textural, geochemical and petrogenetic studies. The pluton is located in the State of Rio Grande do Norte, intrusive into Paleoproterozoic orthogneisses of the Caicó Complex and Neoproterozoic metassupracrustal rocks of the Seridó Group. Based upon intrusion/inclusion field relationships, mineralogy and texture, the rocks are classified as follows: intermediate enclaves (quartz-bearing monzonite and biotite-bearing tonalite), porphyritic monzogranite, equigranular syenogranite to monzogranite, and late granite and pegmatite dykes. Porphyritic granites and quartz-bearing monzonites represent mingling formed by the injection of an intermediate magma into a granitic one, which had already started crystallization. Both rocks are slightly older than the equigranular granites. Quartz-bearing monzonite has K-feldspar, plagioclase, biotite, hornblende and few quartz, meanwhile biotite-bearing tonalite are rich in quartz, poor in K-feldspar and hornblende is absent. Porphyritic and equigranular granites display mainly biotite and rare hornblende, myrmekite and pertitic textures, and zoned plagioclase pointing out to the relevance of fractional crystallization during magma evolution. Such granites have Rare Earth Elements (REE) pattern with negative Eu anomaly and light REE enrichment when compared to heavy REE. They are slight metaluminous to slight peraluminous, following a high-K calc-alkaline path. Petrogenesis started with 27,5% partial melting of Paleoproterozoic continental crust, generating an acid hydrous liquid, leaving a granulitic residue with orthopyroxene, plagioclase (An40-50), K-feldspar, quartz, epidote, magnetite, ilmenite, apatite and zircon. The liquid evolved mainly by fractional crystallization (10-25%) of plagioclase (An20), biotite and hornblende during the first stages of magmatic evolution. Granitic dykes are hololeucocratic with granophyric texture, indicating hypabissal crystallization and REE patterns similar to A-Type granites. Preserved igneous textures, absence or weak imprint of ductile tectonics, association with mafic to intermediate enclaves and alignment of samples according to monzonitic (high-K calcalkaline) series all indicate post-collisional to post-orogenic complexes as described in the literature. Such interpretation is supported by trace element discrimination diagrams that place the Serra da Macambira pluton as late-orogenic, probably reflecting the vanishing stages of the exhumation and collapse of the Brasiliano/Pan-African orogen.