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

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