Os artigos de Euler sobre os números amigáveis

Among the many methodological resources that the mathematics teacher can use in the classroom, we can cite the History of Mathematics which has contributed to the development of activities that promotes students curiosity about mathematics and its history. In this regard, the present dissertation aims to translate and analyze, mathematically and historically, the three works of Euler about amicable numbers that were writed during the Eighteenth century with the same title: De numeris amicabilibus. These works, despite being written in 1747 when Euler lived in Berlin, were published in different times and places. The first, published in 1747 in Nova Acta Eruditorum and which received the number E100 in the Eneström index, summarizes the historical context of amicable numbers, mentions the formula 2nxy & 2nz used by his precursors and presents a table containing thirty pairs of amicable numbers. The second work, E152, was published in 1750 in Opuscula varii argument. It is the result of a comprehensive review of Euler s research on amicable numbers which resulted in a catalog containing 61 pairs, a quantity which had never been achieved by any mathematician before Euler. Finally, the third work, E798, which was published in 1849 at the Opera postuma, was probably the first among the three works, to be written by Euler

Efeitos de campos aleatórios e de anisotropias em vidros de spins

Ising and m-vector spin-glass models are studied, in the limit of infinite-range in-teractions, through the replica method. First, the m-vector spin glass, in the presence of an external uniform magnetic field, as well as of uniaxial anisotropy fields, is consi-dered. The effects of the anisotropics on the phase diagrams, and in particular, on the Gabay-Toulouse line, which signals the transverse spin-glass ordering, are investigated. The changes in the Gabay-Toulouse line, due to the presence of anisotropy fields which favor spin orientations along the Cartesian axes (m = 2: planar anisotropy; m = 3: cubic anisotropy), are also studied. The antiferromagnetic Ising spin glass, in the presence of uniform and Gaussian random magnetic fields, is investigated through a two-sublattice generalization of the Sherrington-Kirpaktrick model. The effects of the magnetic-field randomness on the phase diagrams of the model are analysed. Some confrontations of the present results with experimental observations available in the literature are discussed

Efeitos de acoplamentos biquadráticos e campos aleatórios em vidros de spins

In this work we have studied the effects of random biquadratic and random fields in spin-glass models using the replica method. The effect of a random biquadratic coupling was studied in two spin-1 spin-glass models: in one case the interactions occur between pairs of spins, whereas in the second one the interactions occur between p spins and the limit p > oo is considered. Both couplings (spin glass and biquadratic) have zero-mean Gaussian probability distributions. In the first model, the replica-symmetric assumption reveals that the system presents two pha¬ses, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic cou¬plings between the spins. For the case p oo, the replica-symmetric assumption yields again only two phases, namely, paramagnetic and quadrupolar. In both these phases the spin-glass parameter is zero. Besides, it is shown that they are stable under the Almeida-Thouless stability analysis. One of them presents negative entropy at low temperatures. We developed one step of replica simmetry breaking and noticed that a new phase, the biquadratic glass phase, emerge. In this way we have obtained the correct phase diagram, with.three first-order transition lines. These lines merges in a common triple point. The effects of random fields were studied in the Sherrington-Kirkpatrick model consi¬dered in the presence of an external random magnetic field following a trimodal distribu¬tion {P{hi) = p+S(hi - h0) +Po${hi) +pS(hi + h0))- It is shown that the border of the ferromagnetic phase may present, for conveniently chosen values of p0 and hQ, first-order phase transitions, as well as tricritical points at finite temperatures. It is verified that the first-order phase transitions are directly related to the dilution in the fields: the extensions of these transitions are reduced for increasing values of po- In fact, the threshold value pg, above which all phase transitions are continuous, is calculated analytically. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified

Competição entre caminhantes aleatórios

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Conceitos e técnicas da mecânica estatística e termodinâmica aplicados ao estudo dos grafos aleatórios

This dissertation briefly presents the random graphs and the main quantities calculated from them. At the same time, basic thermodynamics quantities such as energy and temperature are associated with some of their characteristics. Approaches commonly used in Statistical Mechanics are employed and rules that describe a time evolution for the graphs are proposed in order to study their ergodicity and a possible thermal equilibrium between them

Melhorando a estimação de pose com o RANSAC preemptivo generalizado e múltiplos geradores de hipóteses

The camera motion estimation represents one of the fundamental problems in Computer Vision and it may be solved by several methods. Preemptive RANSAC is one of them, which in spite of its robustness and speed possesses a lack of flexibility related to the requirements of applications and hardware platforms using it. In this work, we propose an improvement to the structure of Preemptive RANSAC in order to overcome such limitations and make it feasible to execute on devices with heterogeneous resources (specially low budget systems) under tighter time and accuracy constraints. We derived a function called BRUMA from Preemptive RANSAC, which is able to generalize several preemption schemes, allowing previously fixed parameters (block size and elimination factor) to be changed according the applications constraints. We also propose the Generalized Preemptive RANSAC method, which allows to determine the maximum number of hipotheses an algorithm may generate. The experiments performed show the superiority of our method in the expected scenarios. Moreover, additional experiments show that the multimethod hypotheses generation achieved more robust results related to the variability in the set of evaluated motion directions

Processos aleatórios não-markovianos: perfis de memória

One of the mechanisms responsible for the anomalous diffusion is the existence of long-range temporal correlations, for example, Fractional Brownian Motion and walk models according to Elephant memory and Alzheimer profiles, whereas in the latter two cases the walker can always "remember" of his first steps. The question to be elucidated, and the was the main motivation of our work, is if memory of the historic initial is condition for observation anomalous diffusion (in this case, superdiffusion). We give a conclusive answer, by studying a non-Markovian model in which the walkers memory of the past, at time t, is given by a Gaussian centered at time t=2 and standard deviation t which grows linearly as the walker ages. For large widths of we find that the model behaves similarly to the Elephant model; In the opposite limit (! 0), although the walker forget the early days, we observed similar results to the Alzheimer walk model, in particular the presence of amnestically induced persistence, characterized by certain log-periodic oscillations. We conclude that the memory of earlier times is not a necessary condition for the generating of superdiffusion nor the amnestically induced persistence and can appear even in profiles of memory that forgets the initial steps, like the Gausssian memory profile investigated here.

Regulador eletromagnético de frequência aplicado no controle de velocidade de geradores eólicos

The constant necessity for new sources of renewable energy is increasingly promoting the increase of investments in this area. Among other sources, the wind power has been becoming prominent. It is important to promote the search for the improvement of the technologies involved in the topologies of the wind turbines, seeking for alternatives which enhance the gotten performance, despite the irregularity of the wind speed. This study presents a new system for speed control, in this case applied to the wind turbines - the Electromagnetic Frequency Regulator (EFR). One of the most used devices in some topologies is the mechanical gearboxes which, along with a short service life, often represent sources of noise and defects. The EFR does not need these transmission boxes, representing a technological advancement, using for that an adapted induction machine, in which the stator becomes mobile, supportive to the axis of the turbine. In the topology used in this study, the EFR also allows us to leave out the usage of the eletronic converters to establish the coupling between the generator and the electrical grid. It also the reason why it provides the possibility of obtaining the generation in alternating current, with constant voltage and frequency, where there is no electrical grid. Responsable for the mechanical speed control of the generator, the EFR can be useful in other transmission systems in which the mechanical speed control output is the objective. In addition, the EFR operates through the combination of two inputs, a mechanical and other electrical. It multiplies the possibilities of application because it is able to synergistic coupling between different arrays of energy, and, for such reasons, it enables the various sources of energy involved to be uncoupled from the network, being the synchronous generator responsible for the system connection with the electrical grid, simplifying the control strategies on the power injected in it. Experimental and simulation results are presented through this study, about a wind turbine, validating the proposal related to the efficience in the speed control of the system for different wind conditions.

Do encantamento dos números à realidade dos fatos: conciliação entre os balanços patrimonial e social da ALUNORTE

The social balance is turning into an instrument capable of identifying the Organizational Commitment socio-environmental. The objective of the Social Balance is to present the application of company resources on socio-environmental investments internally and externally. The research was developed based on the Balance Social and Sheet from Alumina North Brazil S / A, ALUNORTE, for fiscal years 2008 and 2009, with the purpose of describing the finding of the Balance Social and Sheet from ALUNORTE about social responsibility. To validate the proposal were doing comparisons between accounting and financial datas from Alunorte and Y.Yamada, in order to highlight what they say and indicators confirm the privileges of the first against second