Um estudo sobre os conhecimentos geométricos adquiridos por alunos do ensino médio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Os Processos de visualização e de representação dos signos matemáticos no contexto didático-pedagógico

Pós-graduação em Educação Matemática - IGCE

Uma forma quadrática no corpo de condutor primo

Pós-graduação em Matemática - IBILCE

Cúbicas galoisianas

Pós-graduação em Matemática - IBILCE

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Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur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.

Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An efficient Hopfield network to solve economic dispatch problems with transmission system representation

Economic dispatch (ED) problems have recently been solved by artificial neural network approaches. Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. The ability of neural networks to realize some complex non-linear function makes them attractive for system optimization. All ED models solved by neural approaches described in the literature fail to represent the transmission system. Therefore, such procedures may calculate dispatch policies, which do not take into account important active power constraints. Another drawback pointed out in the literature is that some of the neural approaches fail to converge efficiently toward feasible equilibrium points. A modified Hopfield approach designed to solve ED problems with transmission system representation is presented in this paper. The transmission system is represented through linear load flow equations and constraints on active power flows. The internal parameters of such modified Hopfield networks are computed using the valid-subspace technique. These parameters guarantee the network convergence to feasible equilibrium points, which represent the solution for the ED problem. Simulation results and a sensitivity analysis involving IEEE 14-bus test system are presented to illustrate efficiency of the proposed approach. (C) 2004 Elsevier Ltd. All rights reserved.

Framework for analysis and representation of external systems for online reactive-optimisation studies

The paper proposes a framework for the analysis and representation of external systems for online optimisation studies. The basis for this framework is the equivalent OPF (EOPF), an optimisation model obtained by partitioning of the OPF model. The EOPF is mathematically redefined in the paper to accommodate the concept of a buffer zone. The resulting model is more useful for online optimisation, since external information obtained through intercontrol-centre exchange contracts can be used to improve internal control calculation. Numerical results obtained with original studies involving the boundary-matching procedure have provided a conceptual basis for the definition of a buffer zone for optimisation studies with the EOPF. In the proposed framework, the accuracy of the external representation in optimisation studies is evaluated by comparing the controls obtained by an EOPF procedure with those obtained by the reference-optimisation procedure defined in this paper. The framework is then used to evaluate the accuracy of equivalent optimisation studies involving the IEEE 118-bus test system and the Brazilian South Southeast 810-bus system. The results show that the incorporation of a buffer zone improves the external system representation for all optimisation studies performed.

A geometric interpretation for transmission real losses minimization through the optimal power flow and its influence on voltage collapse

This work presents an approach for geometric solution of an optimal power flow (OPF) problem for a two bus system (a slack and a PV busses). Additionally, the geometric relationship between the losses minimization and the increase of the reactive margin and, therefore, the maximum loading point, is shown. The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Improved geometric parameterisation techniques for continuation power flow

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Alternative proposal for Modal Representation of a Non-transposed Three-Phase Transmission Line with a Vertical Symmetry Plane

The objective of this paper is to show an alternative representation in time domain of a non-transposed three-phase transmission line decomposed in its exact modes by using two transformation matrices. The first matrix is Clarke's matrix that is real, frequency independent, easily represented in computational transient programs (EMTP) and separates the line into quasi-modes a, b and zero. After that, Quasi-modes a and zero are decomposed into their exact modes by using a modal transformation matrix whose elements can be synthesized in time domain through standard curve-fitting techniques. The main advantage of this alternative representation is to reduce the processing time because a frequency dependent modal transformation matrix of a three-phase line has nine elements to be represented in time domain while a modal transformation matrix of a two-phase line has only four elements. This paper shows modal decomposition process and eigenvectors of a non-transposed three-phase line with a vertical symmetry plane whose nominal voltage is 440 kV and line length is 500 km.

Evolution of representation of the hands in plastic arts

A interação entre arte e ciência foi intensa durante o Renascimento, sofrendo declínio nos anos posteriores com retomada significativa no século XX, principalmente com o uso de técnicas de identificação, datação de obras de arte e o desenvolvimento de novos materiais. O relacionamento entre artes plásticas e Cirurgia da Mão mantêm-se intenso , sendo freqüente o uso de reproduções artísticas da mão nas ilustrações de textos científicos. Objetivando compreender o papel da mão nas artes plásticas, reproduções de obras de artes (esculturas e pinturas) representativas de vários estilos ou períodos da história da arte foram analisadas com enfoque no estudo das mãos. Detalhes anatômicos, relacionamento com outras estruturas do corpo humano, papel na composição e aspectos simbólicos das mãos foram estudados no contexto histórico e artístico de obras de arte do período paleolítico (pré-história) até o século XX. A representação da mão nas artes plásticas está diretamente relacionada ao estilo ou período da obra e à capacidade individual de interpretação e execução do artista.

Stress Analysis in Simulation Models With or Without Implant Threads Representation

Purpose: This study aimed to evaluate the influence of implants with or without threads representation on the outcome of a two-dimensional finite element (FE) analysis. Materials and Methods: Two-dimensional FE models that reproduced a frontal section of edentulous mandibular posterior bone were constructed using a standard crown/implant/screw system representation. To evaluate the effect of implant threads, two models were created: a model in which the implant threads were accurately simulated (precise model) and a model in which implants with a smooth surface (press-fit implant) were used (simplified model). An evaluation was performed on ANSYS software, in which a load of 133 N was applied at a 30-degree angulation and 2 mm off-axis from the long axis of the implant on the models, The Von Mises stresses were measured. Results: The precise model (1.45 MPa) showed higher maximum stress values than the simplified model (1.2 MPa). Whereas in the cortical bone, the stress values differed by about 36% (292.95 MPa for the precise model and 401.14 MPa for the simplified model), in trabecular bone (19.35 MPa and 20.35 MPa, respectively), the stress distribution and stress values were similar. Stress concentrations occurred around the implant neck and the implant apex. Conclusions: Considering implant and cortical bone analysis, remarkable differences in stress values were found between the models. Although the models showed different absolute stress values, the stress distribution was similar. INT J ORAL MAXILLOFAC IMPLANTS 2009;24:1040-1044

Geographic variation in cranial shape in the Pumpkin Toadlet (Brachycephalus ephippium): A geometric analysis

The description of patterns of variation in any character system within well-defined species is fundamental for understanding lineage diversification and the identification of geographic units that represent opportunities for sustained evolutionary divergence. In this paper, we analyze intraspecific variation in cranial shape in the Pumpkin Toadlet, Brachycephalus ephippium-a miniaturized species composed of isolated populations on the slopes of the mountain ranges of southeastern Brazil. Shape variables were derived using geometric-statistical methods that describe shape change as localized deformations in a spatial framework defined by anatomical landmarks in the cranium of B. ephippium. By statistically weighting differences between landmarks that are not close together (changes at larger geometric scale), cranial variation among geographic samples of B. ephippium appears continuous with no obvious gaps. This pattern of variation is caused by a confounding effect between within-sample allometry and among-sample shape differences. In contrast, by statistically weighting differences between landmarks that are at close spacing (changes at smaller geometric scale), differences in shape within- and among-sample variation are not confounded, and a marked geographic differentiation among population samples of B. ephippium emerges. The observed pattern of geographic differentiation in cranial shape apparently cannot be explained as isolation-by-distance. This study provides the first evidence that the detection of morphological variation or lack thereof, that is, morphological conservatism, may be conditional on the scale of measurement of variation in shape within the methodological formalism of geometric morphometrics.

CP trajectory diagram - a tool for a pictorial representation of CP and matter effects in neutrino oscillations

We introduce a CP trajectory diagram in bi-probability space as a powerful tool for a pictorial representation of the genuine CP and the matter effects in neutrino oscillations. The existence of correlated ambiguity in the B is uncovered. The principles of tuning the beam energy for a determination of CP-violating phase delta and the sign of Deltam(13)(2) given baseline distance are proposed to resolve the ambiguity and to maximize the CP-odd effect. We finally point out, quite contrary to what is usually believed, that the ambiguity may be resolved with similar to 50% chance in the super-JHF experiment despite its relatively short baseline of 300 km. (C) 2003 Elsevier B.V. B.V. All rights reserved.