Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem

Caracterização espectral de áreas de gramíneas forrageiras infectadas com a doença mela-das-sementes da braquiária por meio de imagens CCD/CBERS-2

Imagens CCD/CBERS-2, nas bandas espectrais CCD2, CCD3 e CCD4, dos anos de 2004 e 2005, de Mirante do Paranapanema - SP, foram transformadas em reflectância de superfície usando o modelo 5S de correção atmosférica e normalizadas radiometricamente. O objetivo principal foi caracterizar espectralmente áreas de pastagens de Brachiaria brizantha em fase de florescimento, isentas e infectadas com a doença mela-das-sementes da braquiária, possibilitando a sua detecção por meio da comparação entre os valores de reflectância de superfície denominada de Fator de Reflectância Bidirecional de Superfície (FRBS). Teve-se, também, o objetivo de avaliar a eficácia das imagens CCD/CBERS-2 para a obtenção de respostas espectrais de pastagens. Os dosséis sadios e doentes da Brachiaria brizantha foram identificados por meio da análise dos valores de reflectância e dos dados observados no Índice de Estresse Hídrico Acumulativo Relativo da Cultura (ACWSI) obtidos na área de estudo. Os resultados indicaram que as principais diferenças foram a diminuição da reflectância na banda CCD3 e o aumento da reflectância na banda CCD4 nas áreas doentes. A metodologia empregada com o uso de dados do sensor CCD/CBERS-2, associados ao ACWSI, mostrou-se eficaz para discriminar dosséis infectados com a mela-das-sementes da braquiária.

Caracterização espectral da água do reservatório de Itupararanga, SP, a partir de imagens hiperespectrais hyperion e análise derivativa

The current accessibility to hyperspectral images of Hyperion/EO1 orbital sensor has brought new perspectives for studies of aquatic environments for allowing the remote estimative of several optically active constituents (OACs) in water body. The changes in the composition and concentration of OACs cause different patterns of absorption and scattering of electromagnetic radiation, likely to be detected using hyperspectral data. Therefore, an investigation was conducted taking into account the spectral characterization of water of a reservoir intended for public supply (Itupararanga Reservoir), from Hyperion/EO1 images and derivative analysis technique applied to spectral curves generated. Simultaneously to the acquisition of a Hyperion/EO1 image, a field campaign was carried out to collect limnological data in situ in georeferenced points. After radiometric correction of the image, reflectance curves of pixels were extracted for each station and the curves obtained were subjected to the technique of derivative analysis, which revealed features of absorption and scattering mainly associated to the presence of algal pigments. The results obtained show the presence of phytoplankton and algal activity, matching the field observation.

Teoria histórico-cultural e suas implicações na atuação do professor de educação física escolar

This article presents a theoretical search and aims to introduce the main categories of historical-cultural theory and discuss its implications for the physical education teacher's work inside the school and also emphasizes this theory and its methodological proposal as an important way to build the scholar physical education in a critical perspective aiming to change the school and the students conscious and personality. The Vigotskian school of human development it is taken as an important reference to understand the scholars in their vital process of development and helps the teachers in general, and physical education teachers in specific, to consider the activity ( vital activity) as important instrument to get the humanization and liberty of human being, inside the school and inside the contemporary society.

Infografia interativa na redação: o processo de produção no Diário do Nordeste à luz da teoria do jornalismo

The infographics historically experience the process of evolution of journalism, from the incipient models handmade in the eighteenth century to the inclusion of computers and sophisticated software today. In order to face the advent of TV against of the partiality readers of the printed newspaper, or to represent the Gulf War, where not allowed photography, infographics reaches modern levels of production and publication. The technical devices which enabled the infographics to evolve the environment of the internet, with conditions for the manipulation of the reader, incorporating video, audio and animations, so styling of interactive infographics. These digital models of information visualization recently arrived daily in the northeast and on their respective web sites with features regionalized. This paper therefore proposes to explore and describe the processes of producing the interactive infographics, taking the example of the Diário do Nordeste, Fortaleza, Ceará, whose department was created one year ago. Therefore, based on aspects that guide the theory of journalism, as newsmaking, filters that focus on productive routine (gatekeeping) and the construction stages of the news. This research also draws on the theoretical framework on the subject, in concepts essential characteristics of computer graphics, as well as the methodological procedures and systematic empirical observations in production routines of the newsroom who can testify limitations and / or advances

Interpretação e análise do problema da indução sob uma visão fundamentada em teorias de conjuntos e teoria de probabilidades

The following work is to interpret and analyze the problem of induction under a vision founded on set theory and probability theory as a basis for solution of its negative philosophical implications related to the systems of inductive logic in general. Due to the importance of the problem and the relatively recent developments in these fields of knowledge (early 20th century), as well as the visible relations between them and the process of inductive inference, it has been opened a field of relatively unexplored and promising possibilities. The key point of the study consists in modeling the information acquisition process using concepts of set theory, followed by a treatment using probability theory. Throughout the study it was identified as a major obstacle to the probabilistic justification, both: the problem of defining the concept of probability and that of rationality, as well as the subtle connection between the two. This finding called for a greater care in choosing the criterion of rationality to be considered in order to facilitate the treatment of the problem through such specific situations, but without losing their original characteristics so that the conclusions can be extended to classic cases such as the question about the continuity of the sunrise

Aplicações da teoria da percolação à modelagem e simulação de reservatórios de petróleo

In this thesis we study some problems related to petroleum reservoirs using methods and concepts of Statistical Physics. The thesis could be divided percolation problem in random multifractal support motivated by its potential application in modelling oil reservoirs. We develped an heterogeneous and anisotropic grid that followin two parts. The first one introduce a study of the percolations a random multifractal distribution of its sites. After, we determine the percolation threshold for this grid, the fractal dimension of the percolating cluster and the critical exponents ß and v. In the second part, we propose an alternative systematic of modelling and simulating oil reservoirs. We introduce a statistical model based in a stochastic formulation do Darcy Law. In this model, the distribution of permeabilities is localy equivalent to the basic model of bond percolation

Sobre a natureza dos processos físicos de aquecimento da atmosfera de estrelas do tipo solar

In the present work, we have studied the nature of the physical processes of the coronal heating, considering as basis significant samples of single and binary evolved stars, that have been achieved with the ROSAT satellite. In a total of 191 simple stars were studied, classified in the literature as giants with spectral type F, G and K. The results were compared with those obtained from 106 evolved stars of spectral type F, G and K, which belong to the spectroscopic binary systems. Accurate measurements on rotation and information about binarity were obtained from De Medeiros s catalog. We have analysed the behavior of the coronal activity in function of diverse stellar parameters. With the purpose to better clarify the profile of the stars evolution, the HR diagram was built for the two samples of stars, the single and the binary ones. The evolved traces added in the diagram were obtained from the Toulouse-Geneve code, Nascimento et al. (2000). The stars were segregated in this diagram not only in range of rotational speed but also in range of X-ray flux. Our analysis shows clearly that the single stars and the binary ones have coronal activity controlled by physical process independent on the rotation. Non magnetic processes seem to be strongly influencing the coronal heating. For the binary stars, we have also studied the behavior of the coronal emission as a function of orbital parameters, such as period and eccentricity, in which it was revealed the existence of a discontinuity in the emission of X-rays around an orbital period of 100 days. The study helped to conclude that circular orbits of the binary stars are presented as a necessary property for the existence of a higher level ofX-rays emission, suggesting that the effect of the gravitational tide has an important role in the coronal activity level. When applied the Kolmogorov-Smirnov test (KS test ) for the Vsini and FX parameters to the samples of single and binary stars, we could evidence very relevant aspects for the understanding of the mechanisms inherent to the coronal activity. For the Vsini parameter, the differences between the single stars and the binary ones for rotation over 6.3 km/s were really remarkable. We believe, therefore, that the existence of gravitational tide is, at least, one of the factors that most contribute for this behavior. About the X-rays flux, the KS test showed that the behavior of the single and the binary stars, regarding the coronal activity, comes from the same origin

Um estudo na teoria do movimento brownianno com viscosidade variável

In this work we investigate the stochastic behavior of a large class of systems with variable damping which are described by a time-dependent Lagrangian. Our stochastic approach is based on the Langevin treatment describing the motion of a classical Brownian particle of mass m. Two situations of physical interest are considered. In the first one, we discuss in detail an application of the standard Langevin treatment (white noise) for the variable damping system. In the second one, a more general viewpoint is adopted by assuming a given expression to the so-called collored noise. For both cases, the basic diffententiaql equations are analytically solved and al the quantities physically relevant are explicitly determined. The results depend on an arbitrary q parameter measuring how the behavior of the system departs from the standard brownian particle with constant viscosity. Several types of sthocastic behavior (superdiffusive and subdiffusive) are obteinded when the free pamameter varies continuosly. However, all the results of the conventional Langevin approach with constant damping are recovered in the limit q = 1

Teoria cinética não extensiva: efeitos físicos em gases e plasmas

The standard kinetic theory for a nonrelativistic diluted gas is generalized in the spirit of the nonextensive statistic distribution introduced by Tsallis. The new formalism depends on an arbitrary q parameter measuring the degree of nonextensivity. In the limit q = 1, the extensive Maxwell-Boltzmann theory is recovered. Starting from a purely kinetic deduction of the velocity q-distribution function, the Boltzmann H-teorem is generalized for including the possibility of nonextensive out of equilibrium effects. Based on this investigation, it is proved that Tsallis' distribution is the necessary and sufficient condition defining a thermodynamic equilibrium state in the nonextensive context. This result follows naturally from the generalized transport equation and also from the extended H-theorem. Two physical applications of the nonextensive effects have been considered. Closed analytic expressions were obtained for the Doppler broadening of spectral lines from an excited gas, as well as, for the dispersion relations describing the eletrostatic oscillations in a diluted electronic plasma. In the later case, a comparison with the experimental results strongly suggests a Tsallis distribution with the q parameter smaller than unity. A complementary study is related to the thermodynamic behavior of a relativistic imperfect simple fluid. Using nonequilibrium thermodynamics, we show how the basic primary variables, namely: the energy momentum tensor, the particle and entropy fluxes depend on the several dissipative processes present in the fluid. The temperature variation law for this moving imperfect fluid is also obtained, and the Eckart and Landau-Lifshitz formulations are recovered as particular cases

Teoria semi-clássica para super rede magnética formada por materiais ferromagnético e antiferromagnético

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Estudo sistemático de estrelas variáveis na era dos grandes surveys

The interest in the systematic analysis of astronomical time series data, as well as development in astronomical instrumentation and automation over the past two decades has given rise to several questions of how to analyze and synthesize the growing amount of data. These data have led to many discoveries in the areas of modern astronomy asteroseismology, exoplanets and stellar evolution. However, treatment methods and data analysis have failed to follow the development of the instruments themselves, although much effort has been done. In present thesis, we propose new methods of data analysis and two catalogs of the variable stars that allowed the study of rotational modulation and stellar variability. Were analyzed the photometric databases fromtwo distinctmissions: CoRoT (Convection Rotation and planetary Transits) and WFCAM (Wide Field Camera). Furthermore the present work describes several methods for the analysis of photometric data besides propose and refine selection techniques of data using indices of variability. Preliminary results show that variability indices have an efficiency greater than the indices most often used in the literature. An efficient selection of variable stars is essential to improve the efficiency of all subsequent steps. Fromthese analyses were obtained two catalogs; first, fromtheWFCAMdatabase we achieve a catalog with 319 variable stars observed in the photometric bands Y ZJHK. These stars show periods ranging between ∼ 0, 2 to ∼ 560 days whose the variability signatures present RR-Lyrae, Cepheids , LPVs, cataclysmic variables, among many others. Second, from the CoRoT database we selected 4, 206 stars with typical signatures of rotationalmodulation, using a supervised process. These stars show periods ranging between ∼ 0, 33 to ∼ 92 days, amplitude variability between ∼ 0, 001 to ∼ 0, 5 mag, color index (J - H) between ∼ 0, 0 to ∼ 1, 4 mag and spectral type CoRoT FGKM. The WFCAM variable stars catalog is being used to compose a database of light curves to be used as template in an automatic classifier for variable stars observed by the project VVV (Visible and Infrared Survey Telescope for Astronomy) moreover it are a fundamental start point to study different scientific cases. For example, a set of 12 young stars who are in a star formation region and the study of RR Lyrae-whose properties are not well established in the infrared. Based on CoRoT results we were able to show, for the first time, the rotational modulation evolution for an wide homogeneous sample of field stars. The results are inagreement with those expected by the stellar evolution theory. Furthermore, we identified 4 solar-type stars ( with color indices, spectral type, luminosity class and rotation period close to the Sun) besides 400 M-giant stars that we have a special interest to forthcoming studies. From the solar-type stars we can describe the future and past of the Sun while properties of M-stars are not well known. Our results allow concluded that there is a high dependence of the color-period diagram with the reddening in which increase the uncertainties of the age-period realized by previous works using CoRoT data. This thesis provides a large data-set for different scientific works, such as; magnetic activity, cataclysmic variables, brown dwarfs, RR-Lyrae, solar analogous, giant stars, among others. For instance, these data will allow us to study the relationship of magnetic activitywith stellar evolution. Besides these aspects, this thesis presents an improved classification for a significant number of stars in the CoRoT database and introduces a new set of tools that can be used to improve the entire process of the photometric databases analysis

Contribuições da teoria histórico-cultural para o processo de avaliação psicoeducacional

Cet article a comme objectif présenter la contribution de la Psychologie Historique-Culturelle pour l'analyse critique de l'évaluation psychoéducationnel traditionnel et postuler les fondements pour la nouvelle modalité évaluative. Cette proposition se justifie à cause de l'actuelle révitalisation de l'usage des testes padronisés pour la mensuration des fonctions psychologiques, dues à la vulgarisation de la neuropsychologie. Historiquement les testes padronisés servent comme instrument pour attester cientifiquement l'idéologie de l'égalité entre les hommes dans la societé capitaliste que se maintient à travers de l'expropriation et de l'exclusion. En outre, il existe une forte tendence à attendre que les résultats expliquent l'intelligence comme inée ou considèrent les prédispositions héréditaires pour apprendre, ce qu'on oppose à la comprehénsion que les fonctions mentales sont formées dans le proccès de développement historique-social à travers l'appropriation de la culture humaine. Il est nécessaire donc une évaluation qui considère les médiations sociales (des instruments et des signes) comme constituants des fonctions psychologiques encourageant le développement de tous les individus et la non légitimation de l'exclusion sociale.

Uma análise crítica dos ideários pedagógicos contemporâneos à luz da teoria de A. N. Leontiev

O presente artigo objetiva demonstrar o alcance das pedagogias do aprender a aprender (DUARTE, 2001), uma vez que elas fundamentam as propostas educacionais no âmbito nacional e no internacional, na atualidade; bem como apresentar suas principais premissas, que mantêm sua filiação ao pragmatismo e ao irracionalismo e, no limite, submetem o desenvolvimento humano à ordem do capital. Tais proposições se contrapõem ao objetivo humanizador da educação escolar pressuposto na produção teórica do psicólogo soviético Alexis Leontiev. Como resultados, temos que, dessas produções, é possível extrair subsídios para o enfrentamento do processo de esvaziamento do ensino escolar e do papel do professor engendrado pelas referidas pedagogias. Além disso, pretendese evidenciar a impossibilidade de aproximações entre as produções da psicologia histórico-cultural com outras correntes pedagógicas que estão a serviço da legitimação e do revigoramento da sociedade capitalista.

A teoria de Kohlberg sobre o desenvolvimento do raciocínio moral e os instrumentos de avaliação de juízo e competência moral em uso no Brasil

O presente artigo tem por objetivo abordar as bases, finalidades e composição de dois instrumentos de avaliação de juízo moral: a Moral Judgment Interview (MJI) e o Defining Issues Test (DIT), e um de competência moral: o Moral Judgment Test (MJT). Retoma a teoria do desenvolvimento moral de Kohlberg que fundamenta esses instrumentos, assim como os últimos estudos realizados com os mesmos. A MJI é uma entrevista semiestruturada que avalia o nível de juízo moral. O DIT é um teste objetivo que mede a proporção de respostas pós-convencionais. O MJT é um instrumento objetivo, que avalia a competência moral. Destaca-se a crescente utilização desses instrumentos em pesquisas sobre moralidade.