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

Obtenção e conservação de espermatozoides de cutia (Dasyprocta leporina Linneaus, 1753) do semiárido brasileiro

The general objective of this thesis was to stablish protocols to obtain and conserve agouti (Dasyprocta leporina) sperm bred in captivity in the Brazilian semi-arid, aiming its sustainable production. The thesis was divided in three experiments. In the first one, we studied the influence of the interaction between two probes (quadratics and sine waves) and two stimulation protocols (continuous and in series) on the agouti sperm collection by electroejaculation efficiency. The most efficient interaction on this obtainment was the one with probes with rings associated with stimuli in series (4/7; 57%, P<0.05). In the second experiment we compared the cryoprotectant effects of different substances (glycerol, ethyleneglycol, dimethylsulfoxide, dimethylformamide) on epididymis sperm cryopreservation. The highest values on motility (39.5±4.6%), vigor (2.9±0.2) and membrane integrity (30.6±4.5%) were observed on the samples cryopreserved using glycerol when compared to those with ethyleneglycol and dimethylformamide, but there was no difference (P>0.05) when compared to the samples cryopreserved with dimethylsulfoxide. At last, we studied the effects of the methods to obtain sperm (electroejaculation vs epididymal collection) on post thawing sperm quality. The samples obtained by epididymal retrograde flushing showed values for motility of 25.0±10.9% and vigor 2.4±0.8, and those obtained by electroejaculation had 31.2±14.2% of motility and vigor of 2.2±0.7, however, without statistical difference (P>0.05), which shows the possibility to successfully use the epididymal sperm cryopreservation protocol on agouti ejaculated sperm. In conclusion, significant advances on obtainment and processing of agouti sperm were made, allowing the establishment of germplasm banks from sperm samples obtained from the epididymis or by electroejaculation.