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

Aperfeiçoamento no projeto de um protótipo de misturador-decantador à inversão de fases visando aplicação na indústria do petróleo

In the oil industry the mixture oil/water occurs in the operations of production, transportation and refining, as well as during the use of its derivatives. The amount of water produced associated with the oil varies and can reach values of 90% in volume in the case of mature phase of the production fields. The present work deals with the development of new design of the Mixer Settler based on Phase Inversion (MDIF) in a laboratory scale. We envisage this application in industrial scale so the phases of project, construction and operation are considered. The modifications most significant, in comparison with the original prototype, include the materials of construction and the substitution of the equipment used in the mixing stage of the process. It was tested the viability of substitution of the original system of mechanical mixing by a static mixer. A statistical treatment by means of an experimental design of composed central type was used in order to evaluate the behavior of the main variables of the separation process as function of the efficiency of separation for the new device. This procedure is useful to delimit an optimal region of operation with the equipment. The variables of process considered on the experimental design were: oil concentration in the feeding water (mg/L); Total volumetric flow rate (L/h); Ratio organic/water on volumetric basis (O/A). The separation efficiency is calculated by comparison of the content of oil and greases in the inlet and outlet of the equipment. For determination of TOG (Total Oil and Grease), the method used was based in the absorption of radiation in the infra-red region. The equipment used for these determinations was InfraCal® TOG/TPH Model HATR-T2 of the Wilks Enterprise, Incorporation. It´s important to stand out that this method of measure has being used by PETROBRAS S.A. Results of global efficiency of separation oil/water varied from 75.3 to 97.7% for contaminated waters containing up to 1664,1 mg/L of oil. By means of tests carried out with a real sample of contaminated water supplied by PETROBRAS we have got an effluent specified in terms of the legal standards required for discharging. Thus, the new design of equipment constitutes a real alternative for the conventional systems of treatment of produced water in the oil industry