Tropical geometry is an area of mathematics that interfaces algebraic geometry and combinatorics. The main object of study in tropical geometry is the tropical variety, which is the combinatorial counterpart of a classical variety. A classical variety is converted into a tropical variety by a process called tropicalization, thus reducing the problems of algebraic geometry to problems of combinatorics. This new tropical variety encodes several useful information about the original variety, for example an algebraic variety and its tropical counterpart have the same dimension. In this thesis, we look at the some of the computational aspects of tropical algebraic geometry. We study a generalization of Grobner basis theory of modules which unlike the standard Grobner basis also takes the valuation of coefficients into account. This was rst introduced in (Maclagan & Sturmfels, 2009) in the settings of polynomial rings and its computational aspects were first studied in (Chan & Maclagan, 2013) for the polynomial ring case. The motivation for this comes from tropical geometry as it can be used to compute tropicalization of varieties. We further generalize this to the case of modules. But apart from that it has many other computational advantages. For example, in the standard case the size of the initial submodule generally grows with the increase in degree of the generators. But in this case, we give an example of a family of submodules where the size of the initial submodule remains constant. We also develop an algorithm for computation of Grobner basis of submodules of modules over Z=p`Z[x1; : : : ; xn] that works for any weight vector. We also look at some of the important applications of this new theory. We show how this can be useful in efficiently solving the submodule membership problem. We also study the computation of Hilbert polynomials, syzygies and free resolutions.

Submitted by paulo roberto gozzi (paulo.gozzi@gmail.com) on 2014-01-20T14:43:17Z No. of bitstreams: 1 Finanças-Governança Dissertação Final - Participação do Conselheiro Independente.pdf: 3210786 bytes, checksum: ce3979d3f01f43f2efa2a33c6fb9edb1 (MD5) / Rejected by Vera Lúcia Mourão (vera.mourao@fgv.br), reason: Prezado Paulo, o título digitado na BD e no PDF está diferente do que consta em sua Ata e não existe nenhuma informação que deveria ser alterado, portanto estou rejeitando o seu trabalho para que corrija. Caso a banca tenha sugerido ou o seu orientador necessitamos dessa informação com o novo título, o prof. Arthur poderá encaminhar por e-mail para o mestradoprofissional@fgv.br. reforço que se o título for mantido deverá providenciar outra ficha catolografica antes de postar novamente. atenciosamente. Vera tel. 3799 3445 on 2014-01-20T15:12:19Z (GMT) / Submitted by paulo roberto gozzi (paulo.gozzi@gmail.com) on 2014-01-20T16:14:43Z No. of bitstreams: 1 Finanças-Governança Dissertação Final - Participação do Conselheiro Independente.pdf: 3210786 bytes, checksum: ce3979d3f01f43f2efa2a33c6fb9edb1 (MD5) / Approved for entry into archive by Vera Lúcia Mourão (vera.mourao@fgv.br) on 2014-01-20T16:28:03Z (GMT) No. of bitstreams: 1 Finanças-Governança Dissertação Final - Participação do Conselheiro Independente.pdf: 3210786 bytes, checksum: ce3979d3f01f43f2efa2a33c6fb9edb1 (MD5) / Made available in DSpace on 2014-01-20T20:31:58Z (GMT). No. of bitstreams: 1 Finanças-Governança Dissertação Final - Participação do Conselheiro Independente.pdf: 3210786 bytes, checksum: ce3979d3f01f43f2efa2a33c6fb9edb1 (MD5) Previous issue date: 2013-12-19 / The object of this paper is the corporate governance, specifically in relation to the role of the independent board members elected by the companies of Novo Mercado from BMF&Bovespa, by means of a qualitative study in order to verify the participation of the independent board members and the dynamics of decision process within such companies. The purpose of this work is to contribute to the corporate finance and corporate governance areas, specifically to explain several results of quantitative studies that deny a positive correlation between the proportion of independent board members and the financial performance of the companies. The survey was distributed by e-mail which was answered by 30 out of the total 361 independent board members and enabled the identification that the performance tasks of such members are directed by consulting activities and not by controlling activities, demonstrating that the dynamics within the boardroom in the decision process is in the direction of an alignment of interests and not of conflict. Furthermore, the study identified that reduced hours are dedicated in the actual performance of the functions of board members and, therefore, indicate that this may be one of the reasons to justify the lack of positive correlation between the proportion of board members and the financial performance of the companies. Therefore, the study suggests that, in the Brazilian environmental of high concentration of shares within reduced number of shareholders, the regulation authorities should be more active in their supervision functions, as the independent board member does not assume such role. / O tema do presente trabalho é a governança corporativa, especificamente sobre a atuação dos conselheiros independentes das companhias do Novo Mercado da BM&FBovespa por meio de um estudo qualitativo para verificar a forma e a dinâmica da participação dos membros independentes no processo de tomada de decisão das companhias onde atuam. O objetivo é contribuir para o campo de finanças e governança corporativa de modo a explicar resultados de diversos estudos quantitativos que apontam não haver uma correlação significativa entre a proporção de conselheiros independentes e o desempenho financeiro das companhias. O questionário distribuído por e-mail foi respondido por 30 dos 361 conselheiros independentes e possibilitou a constatação de que a atuação dos conselheiros independentes avaliados está atualmente mais voltada para o papel consultivo do que propriamente de fiscalização, demonstrando uma dinâmica de alinhamento e não de conflito no processo decisório do conselho de administração. Além disso, o estudo constatou que os conselheiros independentes disponibilizam pouco tempo no exercício das suas funções, situação que pode constituir fator indicativo para a falta de correlação entre proporção de conselheiros independentes e o desempenho financeiro das companhias, conforme apontada por diversos estudos quantitativos. Dessa forma, o estudo sugere que, no ambiente brasileiro de elevada concentração de ações nas mãos de poucos acionistas, os órgãos reguladores estejam mais atentos à sua função fiscalizadora uma vez que os conselheiros independentes não assumem esse papel.