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

Estratégias midiáticas na aprendizagem do tema DST/AIDS: ações em rede para reduzir vulnerabilidades de adolescentes e jovens da comunidade de Mãe Luiza, Natal-RN

Youngsters and teenagers are still a very vulnerable group of DST/AIDS. In order to combat this vulnerability the community intervention project being developed in Mãe Luiza neighborhood in the city of Natal-RN, entitled Strengthening Community Action Network for Prevention in HIV/AIDS: knowledge and Intervene emerged, popularly known as Project Viva Mãe Luiza. The project develops workshops of educomunication whose approach involves the DST/AIDS subject with the following media: video, photography, and theater playbook. This research integrates the activities of the project and has as main objective to investigate how strategies and practices of media communication developed in Project Viva Mãe Luiza through workshops of educomunication, assisted learning for the prevention of DST/AIDS and contributed to the reduction of vulnerability to DST/AIDS among adolescents and young participants of the project residents of Mãe Luiza community. The methodological basis was based on intervention research, with the technique of gathering daily field data, literature and documentary, in-depth interviews and ethnographic observation. The qualitative analysis was based on the monitoring of video workshops, photography, theater and primer, respectively, crossed by transverse to the prevention of DST/AIDS, conducted between June 2012 and December 2013 issues. Interviews with eight multipliers, aiming to understand their perceptions of vulnerability, prevention, multiplication and use of media that were part of the project were conducted. The analyzes show that learning workshops educomunication community health repercussions both in the development of individual skills in communication as changing perceptions about the vulnerabilities to which they are exposed, the awareness about prevention at the individual and differentiated actions multiplication in the community

Notes on Newton-Euler formulation of robotic manipulators

The equations corresponding to Newton-Euler iterative method for the determination of forces and moments acting on the rigid links of a robotic manipulator are given a new treatment using composed vectors for the representation of both kinematical and dynamical quantities. It is shown that Lagrange equations for the motion of a holonomic system are easily found from the composed vectors defined in this note. Application to a simple model of an industrial robot shows that the method developed in these notes is efficient in solving the dynamics of a robotic manipulator. An example is developed, where it is seen that with the application of appropriate control moments applied to each arm of the robot, starting from a given initial position, it is possible to reach equilibrium in a final pre-assigned position.

Analytical and semi-analytical analysis of an artificial satellite's rotational motion

The rotational motion of an artificial satellite is studied by considering torques produced by gravity gradient and direct solar radiation pressure. A satellite of circular cylinder shape is considered here, and Andoyers variables are used to describe the rotational motion. Expressions for direct solar radiation torque are derived. When the earth's shadow is not considered, an analytical solution is obtained using Lagrange's method of variation of parameters. A semi-analytical procedure is proposed to predict the satellite's attitude under the influence of the earth's shadow. The analytical solution shows that angular variables are linear and periodic functions of time while their conjugates suffer only periodic variations. When compared, numerical and analytical solutions have a good agreement during the time range considered.

GPS Satellites Orbits: Resonance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Conservação dos invertebrados em área de proteção ambiental litorânea no nordeste do Brasil: contribuições da educação ambiental para a sustentabilidade

Today's society is in a real collapse of an environmental nature. The populations are lost due to a dream of development without thinking of the consequences that said development can bring to human populations. Thus, it is necessary that strategies be developed for the purpose of protecting the flora and fauna that is at risk from suffering the pressure to achieve this development. Thus important issues involving the need to conserve nature and the creation of protected areas as these strategies are increasingly being developed in research, whether in the biological and / or social. In this sense, the aim of this research through environmental perception social actors for the formation of significant elements for understanding the relationship between man and nature, and from there to provide actions for sensitization. As well as changing attitudes towards environmental issues, to thereby provide analysis based on Environmental Education in order to provide the production of environmental knowledge as a tool that provides value shift. This area of research was to study the Environmental Protection Area Jenipabu - APA Jenipabu, located in northeastern Brazil. Where, from the environmental perception of students from schools within and around this Nature Conservation Unit notes were made regarding the value and meaning given by students, and how this, the feeling of belonging to these groups. This dissertation is composed of two chapters, the first is titled Environmental perception and feeling of belonging in the area of environmental protection in coastal RN - Brazil, where it makes a diagnosis of how these groups understands and realizes the Unity of Nature Conservation. The second, which is titled Construction of environmental knowledge and conservation of invertebrates in the Environmental Protection Area in the northeast coast of Brazil, specifically developed in the school from within the APA Jenipabu, in order to promote a sense of belonging for those students who become multipliers, in order to realize the importance and necessity of having this unit for Nature Conservation. Looking to the degree of importance of environmental education as a tool to raise awareness on conservation of invertebrates and is all the fauna and flora exists, whether in a conservation of nature or not

Genus Paracoccidioides: Species Recognition and Biogeographic Aspects

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

LEAST ACTION PRINCIPLE and THE INCOMPRESSIBLE EULER EQUATIONS WITH VARIABLE DENSITY

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Superfluid Fermi-Fermi mixture: Phase diagram, stability, and soliton formation

We study the phase diagram for a dilute Bardeen-Cooper-Schrieffer superfluid Fermi-Fermi mixture (of distinct mass) at zero temperature using energy densities for the superfluid fermions in one (1D), two (2D), and three (3D) dimensions. We also derive the dynamical time-dependent nonlinear Euler-Lagrange equation satisfied by the mixture in one dimension using this energy density. We obtain the linear stability conditions for the mixture in terms of fermion densities of the components and the interspecies Fermi-Fermi interaction. In equilibrium there are two possibilities. The first is that of a uniform mixture of the two components, the second is that of two pure phases of two components without any overlap between them. In addition, a mixed and a pure phase, impossible in 1D and 2D, can be created in 3D. We also obtain the conditions under which the uniform mixture is stable from an energetic consideration. The same conditions are obtained from a modulational instability analysis of the dynamical equations in 1D. Finally, the 1D dynamical equations for the system are solved numerically and by variational approximation (VA) to study the bright solitons of the system for attractive interspecies Fermi-Fermi interaction in 1D. The VA is found to yield good agreement to the numerical result for the density profile and chemical potential of the bright solitons. The bright solitons are demonstrated to be dynamically stable. The experimental realization of these Fermi-Fermi bright solitons seems possible with present setups.

Zel'dovich's method of perturbation theory in quantum mechanics

Many years ago Zel'dovich showed how the Lagrange condition in the theory of differential equations can be utilized in the perturbation theory of quantum mechanics. Zel'dovich's method enables us to circumvent the summation over intermediate states. As compared with other similar methods, in particular the logarithmic perturbation expansion method, we emphasize that this relatively unknown method of Zel'dovich has a remarkable advantage in dealing with excited stares. That is, the ground and excited states can all be treated in the same way. The nodes of the unperturbed wavefunction do not give rise to any complication.

On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

Non-linear dynamics of a tower orchard sprayer based on an inverted pendulum model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Um esboço da história do conceito de trabalho virtual e suas aplicações

Neste trabalho abordamos a questão concernente à origem do princípio de trabalho virtual e sua consolidação como um dos conceitos fundamentais no estudo da mecânica analítica e, em particular, dos sistemas em equilíbrio estático. Ênfase foi dada às contribuições seminais de Stevin, Galileu e, sobretudo, as de d'Alembert e Lagrange, no tocante ao conceito de trabalho virtual. Além disso, faz-se um comentário geral sobre vínculos holônomos e deslocamento virtual. Alguns exemplos de emprego da equação de d'Alembert-Lagrange são apresentados, para mostrar como o princípio de trabalho virtual pode ser adequadamente aplicado.

Application of a meshless method in electromagnetics

An improved meshless method is presented with an emphasis on the detailed description of this new computational technique and its numerical implementations by investigating the usefulness of a commonly neglected parameter in this paper. Two approaches to enforce essential boundary conditions are also thoroughly investigated. Numerical tests on a mathematical function is carried out as a means of validating the proposed method. It will be seen that the proposed method is more robust than the conventional ones. Applications in solving electromagnetic problems are also presented.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).