Usando a história da resolução de alguns problemas para introduzir conceitos: sistemas lineares, determinantes e matrizes.

In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications

Circuitos espaciais de produção da atividade boneleira: o uso dos territórios de Caicó, Serra Negra do Norte e São José do Seridó

Cette étude a été fondée sur la reconaissance, la description et l'analyse du circuit spatial de la production de l activité des fabriques des casquettes dans la région du Seridó Potiguar. L activité des fabriques des casquettes est située dans les villes de Caicó, Serra Negra do Norte e São José do Seridó, qui forment le pôle de fabriques de casquettes, composé de soixante-quatre (64) unités de fabrication, le deuxième plus grand producteur de casquettes au Brésil. Dans la condition de base géographique, l'opérationnalisation du concept de circuits spatiales de la production a été essentielle à la compréhension de l'utilisation du territoire et de l'indivisibilité de l'espace, du fournisseur de matières premières au consommateur final, comprenant les étapes des matières premières, la main-d'oeuvre, le stockage, les transports, le commerce et la consommation dans la période actuelle, dans laquelle les instances de la production, la circulation, la distribution et de la consommation sont spatialement diffus. Sur la base de l'identification et de la localisation de ces étapes et des principaux acteurs impliqués dans la activité des fabriques de casquettes, une configuration de circuit spatial de la production a été élaborée, en s'interprétant l'utilisation des territoires par les instances productives. L'interprétation des étapes de production a identifié que les entreprises liées à l'Association Seridoense des Fabricants de Casquettes agissent plus efficacement sur le territoire que celles nonassociées, alors que toujours elles investissent dans des nouveaux équipements, en augmentant sa puissance technique pour se renforcer avant un marché si compétitif comme celui des casquettes. En examinant la contribution de la fabrication des casquettes à l'utilisation actuelle des territoires de la coupe, nous avons appris que les activités complémentaires et des matières premiéres nécessaires à sa réalisation se trouvent dans leur environnement géographique. Ainsi, la proximité spatiale entre les étapes de la fabrication des casquettes fait entrevoir la matérialité du territoire, conférée dans la coexistence des techniques passées et présentes, et l'ensemble des actions effectuées par un certain nombre de travailleurs sociaux qui collaborent à la création du circuit spatial de la production de l activité des fabriques des casquettes. Cette étude a confirmé que les fabriques des casquettes sont organisées sous la forme de cellules de production, continues ou discontinues, dont les équipements et les machines à coudre industrielles obéissent à la logique d'une production de plus en plus standardisée. Ce circuit spatial de la production contribue à l'utilisation actuelle des territoires de Caicó, Serra Negra do Norte et de São José do Seridó car il amplifie le mouvement du commerce et des relations entre les lieux, à travers la dynamique des flux des personnes, des biens et des produits, en constante circulation, guidées par la division du travail entre les étapes productives

Feira livre e circuitos da economia urbana: um estudo da feira da Pedra, em São Bento (PB)

The Feira da Pedra is an extension of the open fair of São Bento in the State of Paraiba. It is a system of trade in textile goods produced by textile industry in manufacturing of hammocks and derivatives of this industry, present in some cities in the state of Paraiba and Rio Grande do Norte, as a survival strategy, inserted in the list of tertiary and retail of the urban economics of this city. It is thereby aimed to discuss about the urban economics, reflecting on the open fair system from the two circuits of urban economy, mainly in the context of the dynamics of the current period of geographic space, the technical-scientific-informational period, as the specific empirical object, the Feira da Pedra of São Bento (PB). For this, this research was carried out in two stages of operation: a) surveys of secondary data and b) primary data collection which were reported an operational triad: I) literature; II) documentary research, and III) research of field. The presence of the Feira da Pedra in São Bento has shown us one of the most important characteristics of this city, in order to present major economic, social and cultural benefits to the local population, and contribute to (re) production of sertanejo space, making lower part of the circuit of its urban economy. This activity has entailed several dynamics for urban space in this city, mainly because of attracting large numbers of people, carrying typical actions of its relationship with the urban space are são-bentense and built environment. Thus, its importance is not only a local and regional phenomenon, but also a cultural reference of a place in the geographical area of many paraibanos and norte-rio-grandenses subjects, as the case of this activity has brought to its weekly routine, this product resulting from the textile working of this area of Sertão Paraibano and Seridó Potiguar

A Ceasa-RN e os circuitos da economia urbana: a circulação de hortifrutigranjeiros em Natal-RN

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Uma leitura atual do bairro da Ribeira em Natal/RN a partir dos dois circuitos da economia urbana

The present study aims to analyze the spatial organization of the Ribeira district in Natal/ RN from the two circuits of the urban economy. For its realization, was used the bibliographical, documentary and field research. From the information collected in the field research and of secondary data was elaborated the maps, tables, graphics, frames and photographic collections. In the analysis of the results identified the presence of two circuits of the urban economy in the said neighborhood, thus as the predominance of the upper circuit compared to the lower circuit between the surveyed establishments, well as the role that each of the circuits represents to their spatial organization. Some variables such as technology, organization, information, publicity and consumption were important to establish the main differences between the circuits.

Critério de correntropia no treinamento de redes fuzzy wavelet neural networks para identificação de sistemas dinâmicos não lineares

The great interest in nonlinear system identification is mainly due to the fact that a large amount of real systems are complex and need to have their nonlinearities considered so that their models can be successfully used in applications of control, prediction, inference, among others. This work evaluates the application of Fuzzy Wavelet Neural Networks (FWNN) to identify nonlinear dynamical systems subjected to noise and outliers. Generally, these elements cause negative effects on the identification procedure, resulting in erroneous interpretations regarding the dynamical behavior of the system. The FWNN combines in a single structure the ability to deal with uncertainties of fuzzy logic, the multiresolution characteristics of wavelet theory and learning and generalization abilities of the artificial neural networks. Usually, the learning procedure of these neural networks is realized by a gradient based method, which uses the mean squared error as its cost function. This work proposes the replacement of this traditional function by an Information Theoretic Learning similarity measure, called correntropy. With the use of this similarity measure, higher order statistics can be considered during the FWNN training process. For this reason, this measure is more suitable for non-Gaussian error distributions and makes the training less sensitive to the presence of outliers. In order to evaluate this replacement, FWNN models are obtained in two identification case studies: a real nonlinear system, consisting of a multisection tank, and a simulated system based on a model of the human knee joint. The results demonstrate that the application of correntropy as the error backpropagation algorithm cost function makes the identification procedure using FWNN models more robust to outliers. However, this is only achieved if the gaussian kernel width of correntropy is properly adjusted.

Contribuição ao estudo de treliças não lineares considerando efeitos térmicos

This work presents the numerical analysis of nonlinear trusses summited to thermomechanical actions with Finite Element Method (FEM). The proposed formulation is so-called positional FEM and it is based on the minimum potential energy theorem written according to nodal positions, instead of displacements. The study herein presented considers the effects of geometric and material nonlinearities. Related to dynamic problems, a comparison between different time integration algorithms is performed. The formulation is extended to impact problems between trusses and rigid wall, where the nodal positions are constrained considering nullpenetration condition. In addition, it is presented a thermodynamically consistent formulation, based on the first and second law of thermodynamics and the Helmholtz free-energy for analyzing dynamic problems of truss structures with thermoelastic and thermoplastic behavior. The numerical results of the proposed formulation are compared with examples found in the literature.

Implementação da rotina de unfolding para determinação de distribuição de tamanho de grãos esféricos via distribuição de interceptos lineares e de área de seção

Na unfolding method of linear intercept distributions and secction área distribution was implemented for structures with spherical grains. Although the unfolding routine depends on the grain shape, structures with spheroidal grains can also be treated by this routine. Grains of non-spheroidal shape can be treated only as approximation. A software was developed with two parts. The first part calculates the probability matrix. The second part uses this matrix and minimizes the chi-square. The results are presented with any number of size classes as required. The probability matrix was determined by means of the linear intercept and section area distributions created by computer simulation. Using curve fittings the probability matrix for spheres of any sizes could be determined. Two kinds of tests were carried out to prove the efficiency of the Technique. The theoretical tests represent ideal cases. The software was able to exactly find the proposed grain size distribution. In the second test, a structure was simulated in computer and images of its slices were used to produce the corresponding linear intercept the section area distributions. These distributions were then unfolded. This test simulates better reality. The results show deviations from the real size distribution. This deviations are caused by statistic fluctuation. The unfolding of the linear intercept distribution works perfectly, but the unfolding of section area distribution does not work due to a failure in the chi-square minimization. The minimization method uses a matrix inversion routine. The matrix generated by this procedure cannot be inverted. Other minimization method must be used