Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números

The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him

Estudos dos aspectos qualitativos e quantitativos da água e do sedimento no baixo curso do Rio Pitimbu (RN)

Urban growth of metropolitan areas has produced impacts of considerable importance on environment and water resources. Such impacts are in general associated with human activities, such as basin area uncontrolled development. In this context, Pitimbu river watershed, located at Natal metropolitan area, has been affected by uncontrolled development caused by urban expansion. Indeed, such effects have been reflected on water quantity and quality, which may produce social consequences. Pitimbu river is an important water supplier for human consumption, actually supplying a 2600 m3/h water discharge. This study aims to analyze the qualitative and quantitative aspects of water and sediment on Pitimbu river lowland portion. For this purpose, physical-chemical water properties were analyzed, and sediment macro invertebrates benthonic were monitored in two cross sections in a period between November 8th, 2007 and October 3rd, 2008. Monitoring methodology consisted of water and sediment sampling for laboratory analysis. Water quality analysis included Dissolved Oxygen, Oxygen Biochemical Demand, Nitrate, pH and Alkalinity, Suspended and Total Solids. The analysis of heavy metals in the sediment included Cadmium, Cobalt, Copper, Chrome, Silver and Nickel. Dry season water discharge data were measured and used to adjust recession function parameters, whose values reveal quick recession and strong river-aquifer unconfined interaction. Water quality analysis revealed the absence of degradation by organic composites. However, DO and BOD levels indicate that more consistent results could be provided if sampling time interval were reduced. Biomonitoring showed signs of aquatic ecosystem degradation by the absence of sensitive and abundance of resistant benthic organisms. Obtained results demonstrate the urgent need of effective management measures to provide environmental protection. The increase of environmental degradation will certainly make impracticable the use of water for human consumption

Avaliação da produção de sedimento na bacia hidrográfica do rio Potengi através do modelo SWAT

Anthropic disturbances in watersheds, such as inappropriate building development, disorderly land occupation and unplanned land use, may strengthen the sediment yield and the inflow into the estuary, leading to siltation, changes in the reach channel conformation, and ecosystem/water quality problems. Faced with such context, this study aims to assess the applicability of SWAT model to estimate, even in a preliminary way, the sediment yield distribution along the Potengi River watershed, as well as its contribution to the estuary. Furthermore, an assessment of its erosion susceptibility was used for comparison. The susceptibility map was developed by overlaying rainfall erosivity, soil erodibility, the slope of the terrain and land cover. In order to overlap these maps, a multi-criteria analysis through AHP method was applied. The SWAT was run using a five year period (1997-2001), considering three different scenarios based on different sorts of human interference: a) agriculture; b) pasture; and c) no interference (background). Results were analyzed in terms of surface runoff, sediment yield and their propagation along each river section, so that it was possible to find that the regions in the extreme west of the watershed and in the downstream portions returned higher values of sediment yield, reaching respectively 2.8 e 5.1 ton/ha.year, whereas central areas, which were less susceptible, returned the lowest values, never more than 0.7 ton/ha.ano. It was also noticed that in the west sub-watersheds, where one can observe the headwaters, sediment yield was naturally forced by high declivity and weak soils. In another hand, results suggest that the eastern part would not contribute to the sediment inflow into the estuary in a significant way, and the larger part of the sediment yield in that place is due to anthropic activities. For the central region, the analysis of sediment propagation indicates deposition predominance in opposition to transport. Thus, it s not expected that isolated rain storms occurring in the upstream river portions would significantly provide the estuary with sediment. Because the model calibration process hasn t been done yet, it becomes essential to emphasize that values presented here as results should not be applied for pratical aims. Even so, this work warns about the risks of a growth in the alteration of natural land cover, mainly in areas closer to the headwaters and in the downstream Potengi River

Avaliação da disponibilidade hídrica e da demanda hídrica no trecho do Rio Piranhas-Açu entre os açudes Coremas-mãe D´água e Armando Ribeiro Gonçalves

Piranhas-Açu basin is a Federal watershed with a drainage area of 43.681,5 km2, sited at Brazilian northeast semi arid, with 60% of your area in Paraiba State and 40% in Rio Grande do Norte State. The main river, Piranhas-Açu, has strategic importance for development of these states, because it s an essential source for many socio-economics activities developed along watercourse. The river s reach between Coremas-Mãe D`água Dam and Armando Ribeiro Gonçalves Dam has many irrigation projects, and supply many riverside cities. All this activities practiced in this river s reach consumes high water volumes. Due the importance of this stream and the necessity of an adequate management, this work aims for an impartial and detailed evaluation of real water supply conditions in this river s reach, by the application of hydrological modeling, including the arrangement of main dams in tributaries, and storage reservoir water balance. The rainfall-discharge model s applied in each sub-basins it was selected the model MODHISA- Hydrological Model of Semi Arid, that is a concentrated model with easy application. The simulation produced 50 years of inflows into the reservoirs, for which, were constructed the guaranties curves; and produced 50 years of synthetic discharge data in relevant points on the river and on its affluents; so it was constructed the permanence curves. Confronting the available discharge with the current and futures volumes of raw water captured in this river s reach, it was verified that de demands have high guaranties. This work concluded that the MODHISA Model is suitable to reproduce the hydrologic characteristics of Piranhas-Açu sub-basins, and showing good results

Caracterização in situ e diversidade genética de algodoeiros mocós (Gossypium hissutum raça marie galante) da Região Nordeste do Brasil

Brazil is one of the major centers of diversity for polyploid cotton plants; these plants belong to the genus Gossypium, which has three known species: G. hirsutum, G. barbadense and G. mustelinum. The Northeast is the only region where the three species occur, the last group being endemic. Northeast s cotton plants can be important sources of variability for genetic breeding. It is believed that great part of local diversity is being lost, due to economic, political, cultural and agricultural problems. In an attempt to mitigate this loss and delineate conservation strategies it is necessary to know how the species are found where they occur. The objective was to characterize and determine how plants are maintained in situ in the states of Maranhão, Piauí, Ceará, Rio Grande do Norte and Paraíba at the beginning of the XXI century. The in situ characterization of G. hirsutum and G. barbadense was conducted through structured interviews with the cotton plants owners and through the analysis of the environment. The data were collected during expeditions undertaken between the years 2004 to 2005. Twenty-two plants were collected in the state of Paraíba, forty-four in the state of Rio Grande do Norte, one hundred and forty-six in the state of Ceará, forty in the state of Maranhão and ninety-one plants in the state of Piauí. All plants collected in the states of Paraíba and Rio Grande do Norte belonged to moco type. Moco cotton plants also predominated in the other states, representing 92%, 62% and 78% of plants collected in Ceará, Piauí and Maranhão, respectively. The other cotton plants collected belong to the species G. barbadense. The cotton plants were found in situ as dooryard plants, roads side, feral populations, cultivation or local varieties. Great part were dooryard plants (45.2%), being major in Piauí and Maranhão. Cultivation predominated in Ceará; in Rio Grande do Norte feral populations were the most frequent and, in Paraíba, local varieties. The maintenance of moco plants is related, mainly, to the phytotherapic domestic use (20.9%) and to confection of lamp wicks (29.7%). Few inhabitants in Paraíba, Rio Grande do Norte, Piauí and none in Maranhão used harvest the plants, storage the seeds or gin; however, in Ceará, 40.5% of owners affirmed that they harvested and commercialized the fiber. It was found that the maintenance of species is dependent of the fragile cultural habits of local inhabitants, therefore the maintenance in situ is not a suitable way to conservation of genetic resources. The efforts must be directed to the continuity of collections, maintenance and characterization ex situ