Uma sequencia didática para o ensino da resolução da equação do 2. grau : adequação para o uso com professores

The present study aims to check whether the use of activities mediated by the History of Mathematics can contribute to improve the understanding of resolution the 2nd degree equation for teachers and undergraduates that reproduce methods of solving such equations, uncritically, without domain of the justifications for their actions. For this, we adapted a didactic sequence with activities that aims to cause a rediscovery of resolutive formula of 2nd degree equation through the method known as cut and paste. Finally, we presented the activity module containing the didactic sequence used during the study, as suggestion for use in the classroom, by the math teacher

Cinge a musa o oráculo da tradição: revelações perenes da narrativa em contos de Perrault

Le présent ouvrage comprend des versions comparatives de neuf contes de Perrault, parmi les plus célèbres, publiés dans des éditions intégrales, au Brésil, entre 1934 et 2005. L analyse comparative donne la priorité à l identification des éléments relatifs à l oralité, comme ceux qui appartiennent, selon Ong (1998) et Havelock (1996), à des contextes de cultures antérieures à l épanouissement de l écriture et qui donc élaboraient ses propres structures de pensée et d expression pour interagir dans la vie pratique comme dans la création, dans la transmission et la manutention des coutumes et traditions. Issus des premiers récits, les contes de Perrault, traduits ou adaptés au Brésil, gardent en eux l esprit du langage narratif auquel l auteur français a consagré une attention spéciale, pour transposer dans l écrit quelques récits de la grande expérience humaine née dans le milieu populaire et qui désormais intègrent l espace de l écriture à chaque nouvelle version produite. Les bagages formulaires, comme les épithètes, les interventions du narrateur et la propre relation des signifations de l intrigue avec les structures de l imaginaire toujours présentes dans l humanité, démontrent le rapprochement entre l oralité et écriture. En suivant les discussions théoriques de Zumthor (1993, 1997, 2000) et par l interation du lecteur avec le texte, on constate que ces éléments relatifs à l oralité rendent possibl existence d une performance dans l écrit a partir des impressions cinesthésiques qui chaque lecture provoque chez le lecteur et récepteur d un texte narratif qui revendique, automatiquement, la construction d une ouvrage seulement possible à chaque instant de l interation, par le processus esthétique de la réception. Même au niveau d écrit, ou l intensité de sa présence est diminuée en raison de l absence d un corps physique qui transmet, qui développe, qui opere littéralement le texte par la voix et qui réunit l écoute et la vision de l auditeur, la performance produite s interpose entre le corps du lecteur qui agit sur le texte et en même temps reçoit les sensations lui permettant l expérience esthétique. Ainsi, dans l expérience de la lecture de Contes de Perrault est possible percevoir les éléments qui renvoient à la forme du conte de tradition populaire. Même déjà influencée par l écrit, le lecteur peut identifier, dans cette oeuvre, les possibilités determinantes de la dynamique perpétuel dans la transmission de ses textes: le plaisir de la pratique de l écoute des histoires contées oralement et le plaisir de la pratique de lectures silencieuses et solitaires. Dans ce chemin le lecteur devoit chercher les sens perdus, ici, rencontrés avec l aide des discours littéraires, linguistique, folklorique, anthropologique et psycanalytique sur la surface du texte narratif merveilleux. Outre cela, ces discours collaborent avec le lecteur qui retrouvent les voix emprisonnées par l écrit dans la virtualité et dans émergence d une performance

Uma análise teórica da evolução da rotação estelar

In the past 50 years, large efforts have been made toward the understanding of the stellar evolution. In the observational context, large sets of precise measurements of projected rotational velocity were produced, in particular by the Natal and Geneva groups. From these data, it is now possible to establish the behavior of stellar rotation from the turnoff to the red giant branch. In addition, these data have shown the role of tidal effects on stellar rotation in close binary systems. Nevertheless, relatively little attention has been paid to theoretical studies on the evolution of rotation along the HR Diagram, a topic itself directly associated to the evolution of the stars. Basically, there are two reasons for such a fact, (i) spherical symmetry is not assumed, what leads to a substantial increase in the numerical complexity of equations and (ii) non rotating models have been very successful in explaining relevant observational data, including the mass-luminosity relation and chemical abundances. In spite of these facts, it is clear that considerable work remains to be done on the role of rotation in the later stages of the evolution, where clear disagreements arise from confrontations between theoretical predictions and observations. In the present work we study the evolutionary behavior of stellar rotation along the HR Diagram, taking into account constraint conditions issued from recent observational survey of rotational velocity carried out with high precision procedures and new evolutionary codes

Modelos analíticos para rádio fontes extragalácticas

The great majority of analytical models for extragalactic radio sources suppose self-similarity and can be classified into three types: I, II and III. We have developed a model that represents a generalization of most models found in the literature and showed that these three types are particular cases. The model assumes that the area of the head of the jet varies with the jet size according to a power law and the jet luminosity is a function of time. As it is usually done, the basic hypothesis is that there is an equilibrium between the pressure exerted both by the head of the jet and the cocoon walls and the ram pressure of the ambient medium. The equilibrium equations and energy conservation equation allow us to express the size and width of the source and the pressure in the cocoon as a power law and find the respective exponents. All these assumptions can be used to calculate the evolution of the source size, width and radio luminosity. This can then be compared with the observed width-size relation for radio lobes and the power-size (P-D) diagram of both compact (GPS and CSS) and extended sources from the 3CR catalogue. In this work we introduce two important improvement as compared with a previous work: (1)We have put together a larger sample of both compact and extended radio sources

Dinâmica Estocástica e Cosmologia: alguns resultados analíticos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Filtros acústicos em cristais fonônicos

In this work, we have studied the acoustic phonon wave propagation within the periodic and quasiperiodic superlattices of Fibonacci type. These structures are formed by phononic crystals, whose periodicity allows the raise of regions known as stop bands, which prevent the phonon propagation throughout the structure for specific frequency values. This phenomenon allows the construction of acoustic filters with great technological potential. Our theoretical model were based on the method of the transfer matrix, thery acoustics phonons which describes the propagation of the transverse and longitudinal modes within a unit cell, linking them with the precedent cell in the multilayer structure. The transfer matrix is built taking into account the elastic and electromagnetic boundary conditions in the superllatice interfaces, and it is related to the coupled differential equation solutions (elastic and electromagnetic) that describe each model under consideration. We investigated the piezoelectric properties of GaN and AlN the nitride semiconductors, whose properties are important to applications in the semiconductor device industry. The calculations that characterize the piezoelectric system, depend strongly on the cubic (zinc-bend) and hexagonal (wurtzite) crystal symmetries, that are described the elastic and piezoelectric tensors. The investigation of the liquid Hg (mercury), Ga (gallium) and Ar (argon) systems in static conditions also using the classical theory of elasticity. Together with the Euler s equation of fluid mechanics they one solved to the solid/liquid and the liquid/liquid interfaces to obtain and discuss several interesting physical results. In particular, the acoustical filters obtained from these structures are again presented and their features discussed

Confinamento de fónons ópticos em estruturas piezoelétricas periódicas e quasiperiódicas

We study the optical-phonon spectra in periodic and quasiperiodic (Fibonacci type) superlattices made up from III-V nitride materials (GaN and AlN) intercalated by a dielectric material (silica - SiO2). Due to the misalignments between the silica and the GaN, AlN layers that can lead to threading dislocation of densities as high as 1010 cm−1, and a significant lattice mismatch (_ 14%), the phonon dynamics is described by a coupled elastic and electromagnetic equations beyond the continuum dielectric model, stressing the importance of the piezoelectric polarization field in a strained condition. We use a transfer-matrix treatment to simplify the algebra, which would be otherwise quite complicated, allowing a neat analytical expressions for the phonon dispersion relation. Furthermore, a quantitative analysis of the localization and magnitude of the allowed band widths in the optical phonon s spectra, as well as their scale law are presented and discussed

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

Condições de energia de hawking e ellis e a equação de raychaudhuri

In the Einstein s theory of General Relativity the field equations relate the geometry of space-time with the content of matter and energy, sources of the gravitational field. This content is described by a second order tensor, known as energy-momentum tensor. On the other hand, the energy-momentum tensors that have physical meaning are not specified by this theory. In the 700s, Hawking and Ellis set a couple of conditions, considered feasible from a physical point of view, in order to limit the arbitrariness of these tensors. These conditions, which became known as Hawking-Ellis energy conditions, play important roles in the gravitation scenario. They are widely used as powerful tools for analysis; from the demonstration of important theorems concerning to the behavior of gravitational fields and geometries associated, the gravity quantum behavior, to the analysis of cosmological models. In this dissertation we present a rigorous deduction of the several energy conditions currently in vogue in the scientific literature, such as: the Null Energy Condition (NEC), Weak Energy Condition (WEC), the Strong Energy Condition (SEC), the Dominant Energy Condition (DEC) and Null Dominant Energy Condition (NDEC). Bearing in mind the most trivial applications in Cosmology and Gravitation, the deductions were initially made for an energy-momentum tensor of a generalized perfect fluid and then extended to scalar fields with minimal and non-minimal coupling to the gravitational field. We also present a study about the possible violations of some of these energy conditions. Aiming the study of the single nature of some exact solutions of Einstein s General Relativity, in 1955 the Indian physicist Raychaudhuri derived an equation that is today considered fundamental to the study of the gravitational attraction of matter, which became known as the Raychaudhuri equation. This famous equation is fundamental for to understanding of gravitational attraction in Astrophysics and Cosmology and for the comprehension of the singularity theorems, such as, the Hawking and Penrose theorem about the singularity of the gravitational collapse. In this dissertation we derive the Raychaudhuri equation, the Frobenius theorem and the Focusing theorem for congruences time-like and null congruences of a pseudo-riemannian manifold. We discuss the geometric and physical meaning of this equation, its connections with the energy conditions, and some of its several aplications.

Evolução da excentricidade dos sistemas binários com componente evoluída

On this study we have revisited the predicted tidal circularization theory in close binary systems with a evolved component. Close binaries suffer tidal interactions that tend to synchronize periods and circularize the orbits (Zahn 1977, 1989, 1992). According to Zahn s theory we compute the integral that give us the variation of the eccentricity in a binary under the influence of tidal force and we compare the integral results with new observations for 260 binary systems with orbital solutions. Our results confirm the success of the Zahn s theory with a new data and new stellar evolutionary models, on the other hand, our results points to the need for a better description of the role of convection on this theory

Efeitos interfaciais em heteroestruturas quânticas nô-abruptas: GaAs/ALxGa1-xAs

Um minuncioso estudo das propriedades de confinamento em heterostructuras bidimensionais(poços quânticos) GaAs/AlxGa1_xAs, com interfaces graduais é realizado. Um modelo teórico que represente bem a variação da fração molar do alumínio nas interfaces, resultante do aparecimento de micro-rugosidades e ilhas durante os processos de crescimento e recozimento pós-crescimento da amostra, é elaborado. Vários perfis desta fração molar de alumínio nas interfaces são considerados. Soluções analíticas da equação de Schrodinger, na aproximação da massa efetiva constatne nas interfaces, resultando em equações transcendentais, que possibilitam a obtenção dos níveis de energia dos portadores, decorrentes do seu confinamento quântico, são apresentadas. Energias de ligação e de confinamento de excitons 2D, utilizando-se um método analítico e numerérico e a aproximação do potencial efetivo, são também calculadas. Resultados numéricos para os níveis de energia dos portadores e para as energias de ligação e de confinamento dos excitons 2D, em poços quânticos GaAs/Al0.35Ga0.65As não-abruptos, sem e com a presença de campo elétrico aplicado para vários perfis interfaciais da fração de molar, são mostrados. Para a obtenção desses resultados, faz-se uso do método dos degraus múltiplos e da técnica da matriz de transferência, e adota-se, como operador de energia cinética, o de Ben-Daniel e Duque para uma massa efetiva dependente da posição. Conclui-se que um modelo que leva em conta a existência de interfaces não-abruptas e seus diversos perfis é indispensável para uma melhor descrição das propriedades opto-eletrônicas de poços quânticos GaAs/AlxGa1-xAs, enquanto que a aproximação das interfaces abruptas apresenta-se bastante limitada

Evolução top-hat hidrodinâmica em campos de velocidades peculiares primordiais

We investigate the cosmology of the vacuum energy decaying into cold dark matter according to thermodynamics description of Alcaniz & Lima. We apply this model to analyze the evolution of primordial density perturbations in the matter that gave rise to the first generation of structures bounded by gravity in the Universe, called Population III Objects. The analysis of the dynamics of those systems will involve the calculation of a differential equation system governing the evolution of perturbations to the case of two coupled fluids (dark matter and baryonic matter), modeled with a Top-Hat profile based in the perturbation of the hydrodynamics equations, an efficient analytical tool to study the properties of dark energy models such as the behavior of the linear growth factor and the linear growth index, physical quantities closely related to the fields of peculiar velocities at any time, for different models of dark energy. The properties and the dynamics of current Universe are analyzed through the exact analytical form of the linear growth factor of density fluctuations, taking into account the influence of several physical cooling mechanisms acting on the density fluctuations of the baryonic component of matter during the evolution of the clouds of matter, studied from the primordial hydrogen recombination. This study is naturally extended to more general models of dark energy with constant equation of state parameter in a flat Universe

Criação da matéria em cosmologias com velocidade da luz variável e eletrônico não-linear

In this work we obtain the cosmological solutions and investigate the thermodynamics of matter creation in two diferent contexts. In the first we propose a cosmological model with a time varying speed of light c. We consider two diferent time dependence of c for a at Friedmann-Robertson- Walker (FRW) universe. We write the energy conservation law arising from Einstein equations and study how particles are created as c decreases with cosmic epoch. The variation of c is coupled to a cosmological Λ term and both singular and non-singular solutions are possible. We calculate the "adiabatic" particle creation rate and the total number of particles as a function of time and find the constrains imposed by the second law of thermodynamics upon the models. In the second scenario, we study the nonlinearity of the electrodynamics as a source of matter creation in the cosmological models with at FRW geometry. We write the energy conservation law arising from Einstein field equations with cosmological term Λ, solve the field equations and study how particles are created as the magnetic field B changes with cosmic epoch. We obtain solutions for the adiabatic particle creation rate, the total number of particles and the scale factor as a function of time in three cases: Λ = 0, Λ = constant and Λ α H2 (cosmological term proportional to the Hubble parameter). In all cases, the second law of thermodynamics demands that the universe is not contracting (H ≥ 0). The first two solutions are non-singular and exhibit in ationary periods. The third case studied allows an always in ationary universe for a suficiently large cosmological term

Soluções cosmológicas e locais para uma eletrodinâmica modificada

The present work investigates some consequences that arise from the use of a modifed lagrangean for the eletromagnetic feld in two diferent contexts: a spatially homogeneous and isotropic universe whose dynamics is driven by a magnetic feld plus a cosmological parameter A, and the problem of a static and charged point mass (charged black hole). In the cosmological case, three diferent general solutions were derived. The first, with a null cosmological parameter A, generalizes a particular solution obtained by Novello et al [gr-qc/9806076]. The second one admits a constant A and the third one allows A to be a time-dependent parameter that sustains a constant magnetic feld. The first two solutions are non-singular and exhibit in ationary periods. The third case studied shows an in ationary dynamics except for a short period of time. As for the problem of a charged point mass, the solutions of the Einstein-Maxwell equations are obtained and compared with the standard Reissner-Nordstrom solution. Contrary to what happens in the cosmological case, the physical singularity is not removed

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time