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

De solutione problematum diophanteorum per números integros : o primeiro trabalho de Euler sobre equações diofantinas

The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers

Avaliação das pressões respiratórias máximas em crianças e adolescentes da grande Natal: elaboração de uma equação preditiva

The human respiratory system was so designed that would allow efficient ventilation, regardless of variations in the external environment that may hinder the act of breathing, such an act involves dozens of variables, among them we find the respiratory depression, which is nothing more than respiratory muscle strength. The pressures are widely used in several cases: Neuro-muscular; evolution of pulmonary dysfunction and a predictor for discontinuation of mechanical ventilation. Therefore it was proposed to carry out evaluations of these respiratory pressures for children and adolescents aged 10 to 16 years and propose a predictive equation that involves the anthropometric variables age (A, years), body mass (BM, kilograms) and height (H, meters) with maximal respiratory pressures (maximum inspiratory and expiratory pressure). Evaluations were performed in this age group of students in public and private schools of the Grande Natal , measurements were performed using the analogue manometer, were children and adolescents and their parents gave informed consent. 517 samples were taken, and 250 for males (M), 255 for females (F) and 12 were excluded according to our exclusion criteria. The sample was subdivided into three age groups (10-11, 12-13 and 14 to 16 years old). It was found through the student s t test (p ≤ 0.05) for all variables studied, children and male adolescents had higher means than females, except for the MC. For the correlation between the variables found significant correlation (p <0.05) among all the variables when analyzed as pairs except between MIP and height for females. The development of predictive equations (for p ≤ 0.05) based on three types of strategies adopted were restricted to two association between anthropometric variables isolated, resulting in: for males: MIP = -32.29 + (-2.11*A) + (-0.52*BM), MIP = 9.99 + (-0.36*BM) + (-49.40*H); MEP = 18.54 + 3.53*A + 0, 42*BM, MEP = -33.37 + 2.78*A + 52.18* H, MEP = -17.39 + 0.33*BM + 55.04*H; and, for females we find: MEP = 24.32 + 2.59 * A + 0.24*BM

Estimativas de mortalidade para a região nordeste do Brasil em 2010: uma associação do método demográfico equação geral de balanceamento, com o estimador bayesiano empírico

One of the greatest challenges of demography, nowadays, is to obtain estimates of mortality, in a consistent manner, mainly in small areas. The lack of this information, hinders public health actions and leads to impairment of quality of classification of deaths, generating concern on the part of demographers and epidemiologists in obtaining reliable statistics of mortality in the country. In this context, the objective of this work is to obtain estimates of deaths adjustment factors for correction of adult mortality, by States, meso-regions and age groups in the northeastern region, in 2010. The proposal is based on two lines of observation: a demographic one and a statistical one, considering also two areas of coverage in the States of the Northeast region, the meso-regions, as larger areas and counties, as small areas. The methodological principle is to use the General Equation and Balancing demographic method or General Growth Balance to correct the observed deaths, in larger areas (meso-regions) of the states, since they are less prone to breakage of methodological assumptions. In the sequence, it will be applied the statistical empirical Bayesian estimator method, considering as sum of deaths in the meso-regions, the death value corrected by the demographic method, and as reference of observation of smaller area, the observed deaths in small areas (counties). As results of this combination, a smoothing effect on the degree of coverage of deaths is obtained, due to the association with the empirical Bayesian Estimator, and the possibility of evaluating the degree of coverage of deaths by age groups at counties, meso-regions and states levels, with the advantage of estimete adjustment factors, according to the desired level of aggregation. The results grouped by State, point to a significant improvement of the degree of coverage of deaths, according to the combination of the methods with values above 80%. Alagoas (0.88), Bahia (0.90), Ceará (0.90), Maranhão (0.84), Paraíba (0.88), Pernambuco (0.93), Piauí (0.85), Rio Grande do Norte (0.89) and Sergipe (0.92). Advances in the control of the registry information in the health system, linked to improvements in socioeconomic conditions and urbanization of the counties, in the last decade, provided a better quality of information registry of deaths in small areas

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

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

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

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.

Métodos numéricos para resolução de equações diferenciais ordinárias lineares baseados em interpolação por spline

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the traditional solvers such as Runge-Kutta, and avoids root calculations in the linear time invariant case. The method is then applied on a central problem of control theory, namely, the step response problem for linear EDOs with possibly varying coefficients, where root calculations do not apply. We have implemented an efficient algorithm which uses exclusively matrix-vector operations. The working interval (till the settling time) was determined through a calculation of the least stable mode using a modified power method. Several variants of the method have been compared by simulation. For general linear problems with fine grid, the proposed method compares favorably with the Euler method. In the time invariant case, where the alternative is root calculation, we have indications that the proposed method is competitive for equations of sifficiently high order.

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

A relação de Euler para poliedros

In this paper we analyze the Euler Relation generally using as a means to visualize the fundamental idea presented manipulation of concrete materials, so that there is greater ease of understanding of the content, expanding learning for secondary students and even fundamental. The study is an introduction to the topic and leads the reader to understand that the notorious Euler Relation if inadequately presented, is not sufficient to establish the existence of a polyhedron. For analyzing some examples, the text inserts the idea of doubt, showing cases where it is not fit enough numbers to validate the Euler Relation. The research also highlights a theorem certainly unfamiliar to many students and teachers to research the polyhedra, presenting some very simple inequalities relating the amounts of edges, vertices and faces of any convex polyhedron, which clearly specifies the conditions and sufficient necessary for us to see, without the need of viewing the existence of the solid screen. And so we can see various polyhedra and facilitate understanding of what we are exposed, we will use Geogebra, dynamic application that combines mathematical concepts of algebra and geometry and can be found through the link http://www.geogebra.org

Correspondências científicas como uma relação didática entre história e ensino de matemática: o exemplo das cartas de Euler a uma princesa da Alemanha

Lettres àune Princesse d'Allemagne sur divers sujets de physique et de philosophie (Letters to a Princess of Germany on various topics of physics and philosophy) is the work taken as an object of study of this thesis. It is a literary success written in the eighteenth century by the Swiss mathematician and physicist Leonhard Paul Euler (1707-1783) in order to meet a request from the Prussian king, Frederick II, the Great (1712-1786) to accept to guide the intellectual education of his niece, the young princess Anhalt-Dessau (1745-1808). The method of teaching and learning through letters elected to the education of the German monarch resulted in a collection of 234 matches in which Euler theory is about music, Philosophy, Mechanics, Optics, Astronomy, Theology and Ethics among others. The research seeks to point out mathematical content contained in this reference work based on the exploitation and adaptation of original historical works as an articulator of development activities for teaching mathematics in basic education and in accordance with the National Curriculum Parameters of Mathematics (NCP) work. The general objective point out the limits and didactic potential of Lettres à une Princesse d'Allemagne sur divers sujets de physique et de philosophie as a source of support for teachers of basic education in developing activities for teaching mathematics. The discussions raised point to concrete possibilities of entanglement between the extracted mathematical content of the bulge of the work with current teaching methodologies from resizing the use of letters according to Freire's pedagogical perspective of the correspondence, and especially the use of new communication channels in the century XXI, both aimed at dialogue and approximation between those who write and those who read.

Impacto da Estratégia Saúde da Família com equipe de saúde bucal sobre a utilização de serviços odontológicos

PEREIRA, C. R. S. et al. Impacto da estratégia saúde da família com equipe de saúde bucal sobre a utilização de serviços odontológicos. Cad. Saúde Pública, v. 25, n. 5, p.985-996. Maio, 2009. ISSN 0102-311X.

Impacto da Estratégia Saúde da Família com equipe de saúde bucal sobre a utilização de serviços odontológicos

PEREIRA, Carmen Regina dos Santos et al. Impacto da Estratégia Saúde da Família com equipe de saúde bucal sobre a utilização de serviços odontológicos. Cadernos de Saúde Pública, Rio de Janeiro, v. 25, n. 5, p. 985-996, maio 2009.

Análise comparativa e teste empírico da validade dos modelos CAPM tradicional e condicional: o caso das ações da Petrobrás

ALVES, Janaína da Silva. Análise comparativa e teste empírico da validade dos modelos CAPM tradicional e condicional: o caso das ações da Petrobrás. Revista Ciências Administrativas, Fotaleza, v. 13, n. 1, p.147-157, ago. 2007.