Teorema de Pitágoras: aplicações em objetos de aprendizagem

Pós-graduação em Matemática em Rede Nacional - IBILCE

Impact of Quantity of Resin, C-factor, and Geometry on Resin Composite Polymerization Shrinkage Stress in Class V Restorations

Objective: This study evaluated the effect of quantity of resin composite, C-factor, and geometry in Class V restorations on shrinkage stress after bulk fill insertion of resin using two-dimensional finite element analysis.Methods: An image of a buccolingual longitudinal plane in the middle of an upper first premolar and supporting tissues was used for modeling 10 groups: cylindrical cavity, erosion, and abfraction lesions with the same C-factor (1.57), a second cylindrical cavity and abfraction lesion with the same quantity of resin (QR) as the erosion lesion, and then all repeated with a bevel on the occlusal cavosurface angle. The 10 groups were imported into Ansys 13.0 for two-dimensional finite element analysis. The mesh was built with 30,000 triangle and square elements of 0.1 mm in length for all the models. All materials were considered isotropic, homogeneous, elastic, and linear, and the resin composite shrinkage was simulated by thermal analogy. The maximum principal (MPS) and von Mises stresses (VMS) were analyzed for comparing the behavior of the groups.Results: Different values of angles for the cavosurface margin in enamel and dentin were obtained for all groups and the higher the angle, the lower the stress concentration. When the groups with the same C-factor and QR were compared, the erosion shape cavity showed the highest MPS and VMS values, and abfraction shape, the lowest. A cavosurface bevel decreased the stress values on the occlusal margin. The geometry factor overcame the effects of C-factor and QR in some situations.Conclusion: Within the limitations of the current methodology, it is possible to conclude that the combination of all variables studied influences the stress, but the geometry is the most important factor to be considered by the operator.

Investigation of Plasma Immersion Ion Implantation Process in Magnetic Mirror Geometry

Plasma immersion ion implantation (PIII) with low external magnetic field has been investigated both numerically and experimentally. The static magnetic field considered is essentially nonuniform and is generated by two magnetic coils installed outside the vacuum chamber. Experiments have been conducted to investigate the effect of two of the most important PIII parameters: target voltage and gas pressure. In that context, it was found that the current density increased when the external parameters were varied. Later, the PIII process was analyzed numerically using the 2.5-D computer code KARAT. The numerical results show that the system of crossed E x B fields enhances the PIII process. The simulation showed an increase of the plasma density around the target under the operating and design conditions considered. Consequently, an increase of the ion current density on the target was observed. All these results are explained through the mechanism of gas ionization by collisions with electrons drifting in crossed E x B fields.

Boundary identification criteria and geometry analysis of Al 7050 stretch zone from elevation profiles

This article describes the development of a method for analysis of the shape of the stretch zone surface based on parallax measurement theory and using digital image processing techniques. Accurate criteria for the definition of the boundaries of the stretch zone are established from profiles of fracture surfaces obtained from crack tip opening displacement tests on Al-7050 alloy samples. The elevation profiles behavior analysis is based on stretch zone width and height parameters. It is concluded that the geometry of the stretch zone profiles under plane strain conditions can be described by a semi-parabolic relationship. (C) Elsevier B.V., 1999. All rights reserved.

Unscented Kalman Filter Applied to the Spacecraft Attitude Estimation with Euler Angles

The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artificial satellite using real data supplied by attitude sensors that are on board of the CBERS-2 satellite (China Brazil Earth Resources Satellite). The real-time estimator used in this work for attitude determination is the Unscented Kalman Filter. This filter is a new alternative to the extended Kalman filter usually applied to the estimation and control problems of attitude and orbit. This algorithm is capable of carrying out estimation of the states of nonlinear systems, without the necessity of linearization of the nonlinear functions present in the model. This estimation is possible due to a transformation that generates a set of vectors that, suffering a nonlinear transformation, preserves the same mean and covariance of the random variables before the transformation. The performance will be evaluated and analyzed through the comparison between the Unscented Kalman filter and the extended Kalman filter results, by using real onboard data.

Differential geometry of intersection curves in R(4) of three implicit surfaces

We present algorithms for computing the differential geometry properties of intersection Curves of three implicit surfaces in R(4), using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive t, n, b(1), b(2) vectors and curvatures (k(1), k(2), k(3)) for transversal intersections of the intersection problem. (C) 2008 Elsevier B.V. All rights reserved.

Radiographic measurement of tibial joint angles in sheep

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Note on four Dp-branes at angles

In this note we analyse the dynamical potential of a system of four Dp-branes at arbitrary angles. The equilibrium configurations for various values of the relative angles and distances among branes are discussed. The known configurations of parallel branes and brane-antibranes are obtained at extrema of the dynamical potential.

Spinorial field and Lyra geometry

The Dirac field is studied in a Lyra space-time background by means of the classical Schwinger Variational Principle. We obtain the equations of motion, establish the conservation laws, and get a scale relation relating the energy-momentum and spin tensors. Such scale relation is an intrinsic property for matter fields in Lyra background.

Gauge groups from brane-anti-brane systems at angles

We discuss a system formed by two pairs of brane-anti-brane that form an arbitrary angle in a plane. We identify the gauge groups from this system which presumably could be used to construct gauge theories.

Husserl on Geometry and Spatial Representation

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl's ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl.

Aprendizagem de conceitos geométricos pelo futuro professor das séries iniciais do Ensino Fundamental e as novas tecnologias

Com o movimento da Matemática Moderna, a partir de 1950, o ensino da matemática passou a enfatizar o simbolismo e a exigir dos alunos grandes abstrações, distanciando a matemática da vida real. O que se percebe é que o aluno formado por este currículo aprendeu muito pouco de geometria e não consegue perceber a relação deste conteúdo com sua realidade. Por outro lado, o professor que não conhece geometria não consegue perceber a beleza e a importância que a mesma possui para a formação do cidadão. A geometria estimula a criança a observar, perceber semelhanças, diferenças e a identificar regularidades. O objetivo deste trabalho é identificar o nível de conhecimento dos alunos do Centro Específico de Formação e Aperfeiçoamento ao Magistério (CEFAM), futuros professores da 1ª a 4ª séries do Ensino Fundamental do Estado de São Paulo, quanto aos conceitos de ponto, reta, plano, ângulos, polígonos e circunferências e também verificar as contribuições do computador para a construção de conceitos geométricos. Para atingir esses objetivos, foi desenvolvida uma pesquisa com 30 alunos do CEFAM de Presidente Prudente-SP, na qual, com base no diagnóstico das dificuldades de aprendizagem, organizaram e desenvolveram-se os momentos de formação, que utilizaram o computador como ferramenta de aprendizagem e projetos de trabalho tendo como aporte teórico a abordagem construcionista. O futuro professor que não dominar a geometria e não perceber sua relação com a natureza não conseguirá contribuir para o desenvolvimento do pensamento geométrico da criança. Esse pensamento é que permite a criança observar, compreender, descrever e representar, de forma organizada, o mundo em que vive.

Dichloro(cyclohexilidene-1-methylene)(phenyl)Te(IV). Looking for the theoretical treatment

C(13)H(16)Cl(2)Te,M(r)=370.76,P2(1)/a, a = 8.1833(8), b = 8.4163(8), c = 20.787(2) A, beta = 99.52(1)degrees, Z = 4, R(1) = 0,0275. The primary coordination around the Te(IV) atom is consistent with a pseudo-trigonal bipyramidal bond configuration with two Cl atoms occupying axial positions while the C atoms and the lone pair of electrons occupy the equatorial positions. The Te(IV) atom is involved in an intermolecular secondary interaction resulting in the self assembly of zigzag-chains supramolecular array. In order to determine the theoretical basis set for the Te atom which leads to the best agreement with the experimental data, a large series of geometry optimizations were performed on dichloro dimethyl Te(IV), as a model compound, and the results compared with the mean distances and angles obtained from 45 X-ray structures. The Ahlrichs basis set plus the Hay & Wadt ECP was selected and used for a series of calculations performed on the title compound.

Molecular structures and vibrational frequencies for cis-[PdCl2(tmen)] and cis-[Pd(N-3)(2)(tmen)]: A DFT study

Theoretical molecular structures of the complexes cis-[PdCl2(tmen)] and cis-[Pd(N-3)(2)(tmen)] (tmen = N,N,N',N'-tetramethylethylenediamine) were investigated using B3LYP/DFT method. The calculated molecular parameters, bond distances and angles, revealed a square-planar geometry around the metallic center for both compounds with the azide being linear. The theoretical infrared spectra of C, symmetry (electronic state (1)A) of the compounds are in agreement with the experimental data. (C) 2007 Elsevier B.V. All rights reserved.

Numerical simulation of magnetic-field-enhanced plasma immersion ion implantation in cylindrical geometry

Recent studies have demonstrated that the sheath dynamics in plasma immersion ion implantation (PIII) is significantly affected by an external magnetic field. In this paper, a two-dimensional computer simulation of a magnetic-field-enhanced PHI system is described. Negative bias voltage is applied to a cylindrical target located on the axis of a grounded vacuum chamber filled with uniform molecular nitrogen plasma. A static magnetic field is created by a small coil installed inside the target holder. The vacuum chamber is filled with background nitrogen gas to form a plasma in which collisions of electrons and neutrals are simulated by the Monte Carlo algorithm. It is found that a high-density plasma is formed around the target due to the intense background gas ionization by the magnetized electrons drifting in the crossed E x B fields. The effect of the magnetic field intensity, the target bias, and the gas pressure on the sheath dynamics and implantation current of the PHI system is investigated.