Prevalence of refractive errors in students in Northeastern Brazil

To determine the prevalence of refractive errors in the public and private school system in the city of Natal, Northeastern Brazil. Methods: Refractometry was performed on both eyes of 1,024 randomly selected students, enrolled in the 2001 school year and the data were evaluated by the SPSS Data Editor 10.0. Ametropia was divided into: 1- from 0.1 to 0.99 diopter (D); 2- 1.0 to 2.99D; 3- 3.00 to 5.99D and 4- 6D or greater. Astigmatism was regrouped in: I- with-the-rule (axis from 0 to 30 and 150 to 180 degrees), II- against-the-rule (axis between 60 and 120 degrees) and III- oblique (axis between > 30 and < 60 and >120 and <150 degrees). The age groups were categorized as follows, in: 1- 5 to 10 years, 2- 11 to 15 years, 3- 16 to 20 years, 4- over 21 years. Results: Among refractive errors, hyperopia was the most common with 71%, followed by astigmatism (34%) and myopia (13.3%). Of the students with myopia and hyperopia, 48.5% and 34.1% had astigmatism, respectively. With respect to diopters, 58.1% of myopic students were in group 1, and 39% distributed between groups 2 and 3. Hyperopia were mostly found in group 1 (61.7%) as well as astigmatism (70.6%). The association of the astigmatism axes of both eyes showed 92.5% with axis with-the-rule in both eyes, while the percentage for those with axis againstthe- rule was 82.1% and even lower for the oblique axis (50%). Conclusion: The results found differed from those of most international studies, mainly from the Orient, which pointed to myopia as the most common refractive error, and corroborates the national ones, with the majority being hyperopia

Fractais e Percolação na Recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points

Fractais e percolação na recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points. In oil recovery terminology, the given single point can be mapped to an injection well (injector) and the multiple other points to production wells (producers). In the previously standard case of one injection well and one production well separated by Euclidean distance r, the distribution of shortest paths l, P(l|r), shows a power-law behavior with exponent gl = 2.14 in 2D. Here we analyze the situation of one injector and an array A of producers. Symmetric arrays of producers lead to one peak in the distribution P(l|A), the probability that the shortest path between the injector and any of the producers is l, while the asymmetric configurations lead to several peaks in the distribution. We analyze configurations in which the injector is outside and inside the set of producers. The peak in P(l|A) for the symmetric arrays decays faster than for the standard case. For very long paths all the studied arrays exhibit a power-law behavior with exponent g ∼= gl.

Termodinâmica de um gás de fótons no contexto de eletrodinâmicas não-lineares

The objective of this dissertation is the development of a general formalism to analyze the thermodynamical properties of a photon gas under the context of nonlinear electrodynamics (NLED). To this end it is obtained, through the systematic analysis of Maxwell s electromagnetism (EM) properties, the general dependence of the Lagrangian that describes this kind of theories. From this Lagrangian and in the background of classical field theory, we derive the general dispersion relation that photons must obey in terms of a background field and the NLED properties. It is important to note that, in order to achieve this result, an aproximation has been made in order to allow the separation of the total electromagnetic field into a strong background electromagnetic field and a perturbation. Once the dispersion relation is in hand, the usual Bose-Einstein statistical procedure is followed through which the thermodynamical properties, energy density and pressure relations are obtained. An important result of this work is the fact that equation of state remains identical to the one obtained under EM. Then, two examples are made where the thermodynamic properties are explicitly derived in the context of two NLED, Born-Infelds and a quadratic approximation. The choice of the first one is due to the vast appearance in literature and, the second one, because it is a first order approximation of a large class of NLED. Ultimately, both are chosen because of their simplicity. Finally, the results are compared to EM and interpreted, suggesting possible tests to verify the internal consistency of NLED and motivating further developement into the formalism s quantum case

Estimativa de expoentes críticos em Percolação

In Percolation Theory, functions like the probability that a given site belongs to the infinite cluster, average size of clusters, etc. are described through power laws and critical exponents. This dissertation uses a method called Finite Size Scaling to provide a estimative of those exponents. The dissertation is divided in four parts. The first one briefly presents the main results for Site Percolation Theory for d = 2 dimension. Besides, some important quantities for the determination of the critical exponents and for the phase transistions understanding are defined. The second shows an introduction to the fractal concept, dimension and classification. Concluded the base of our study, in the third part the Scale Theory is mentioned, wich relates critical exponents and the quantities described in Chapter 2. In the last part, through the Finite Size Scaling method, we determine the critical exponents fi and. Based on them, we used the previous Chapter scale relations in order to determine the remaining critical exponents

Método de Projeções Ortogonais

The problem treated in this dissertation is to establish boundedness for the iterates of an iterative algorithm in 2, under some technical conditions. However, this paper uses non-trivial intuitive arguments and its proofs lack suficient rigor. In this dissertation we discuss and strengthen the results of this paper, in order to complete and simplify its proofs

Prevalence of refractive errors in students in Northeastern Brazil

To determine the prevalence of refractive errors in the public and private school system in the city of Natal, Northeastern Brazil. Methods: Refractometry was performed on both eyes of 1,024 randomly selected students, enrolled in the 2001 school year and the data were evaluated by the SPSS Data Editor 10.0. Ametropia was divided into: 1- from 0.1 to 0.99 diopter (D); 2- 1.0 to 2.99D; 3- 3.00 to 5.99D and 4- 6D or greater. Astigmatism was regrouped in: I- with-the-rule (axis from 0 to 30 and 150 to 180 degrees), II- against-the-rule (axis between 60 and 120 degrees) and III- oblique (axis between > 30 and < 60 and >120 and <150 degrees). The age groups were categorized as follows, in: 1- 5 to 10 years, 2- 11 to 15 years, 3- 16 to 20 years, 4- over 21 years. Results: Among refractive errors, hyperopia was the most common with 71%, followed by astigmatism (34%) and myopia (13.3%). Of the students with myopia and hyperopia, 48.5% and 34.1% had astigmatism, respectively. With respect to diopters, 58.1% of myopic students were in group 1, and 39% distributed between groups 2 and 3. Hyperopia were mostly found in group 1 (61.7%) as well as astigmatism (70.6%). The association of the astigmatism axes of both eyes showed 92.5% with axis with-the-rule in both eyes, while the percentage for those with axis againstthe- rule was 82.1% and even lower for the oblique axis (50%). Conclusion: The results found differed from those of most international studies, mainly from the Orient, which pointed to myopia as the most common refractive error, and corroborates the national ones, with the majority being hyperopia