Cálculo mental com números racionais não negativos: um estudo sobre as estratégias utilizadas por alunos do 4.º ano de escolaridade

Relatório Final apresentado à Escola Superior de Educação de Lisboa para a obtenção de grau de mestre em Ensino do 1.º e 2.º Ciclo do Ensino Básico

Desenvolvimento da fluência no cálculo mental através do uso de estratégias de cálculo: um estudo no 4.º e no 6.º ano de escolaridade

Relatório de estágio de mestrado em Ensino do 1º e 2º Ciclo do Ensino Básico

A brincar e a aprender: a importância das atividades lúdicas em educação pré-escolar e ensino do 1.º ciclo do ensino básico

Relatório de estágio de mestrado em Educação Pré-Escolar e Ensino do 1.º Ciclo do Ensino Básico

Aprendizagem dos números racionais não negativos com alunos do 3.º ano

Este estudo visa compreender as dificuldades que os alunos evidenciam na aprendizagem da noção de número racional não negativo. Ao longo da minha experiência como docente do 2.º ciclo, permitiu-me questionar por que razão os alunos de 5.º e 6.º ano apresentam dificuldades em compreender o conceito de fração nos seus diversos significados: número, partetodo, quociente, medida e operador multiplicativo. Foi no sentido de entender esta dificuldade na apropriação dos conhecimentos matemáticos sobre frações, que resolvi aplicar esta investigação a alunos do 1.º ciclo, nomeadamente a uma turma do 3.º ano, uma vez que é neste ano escolar que o estudo dos números racionais não negativos é aprofundado. A metodologia constou de um estudo de abordagem de carácter qualitativo, de natureza interpretativa. A recolha de dados inclui as produções escritas dos alunos e as gravações de áudio das intervenções verbais dos mesmos. A análise dos resultados realizou-se a partir das estratégias cognitivas que os alunos utilizaram para responderem às tarefas propostas. Os resultados deste estudo mostraram que a construção do sentido de número racional não é de fácil compreensão. É um conceito que requer uma abordagem multifacetada, apoiada com a manipulação de materiais estruturados ou não estruturados, para que os diferentes significados de fração fiquem bem consolidados nas estruturas cognitivas dos alunos.

Local non-negative initial data scalar characterization of the Kerr solution

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

Non-negative matrix decomposition approaches to frequency domain analysis of music audio signals

On étudie l’application des algorithmes de décomposition matricielles tel que la Factorisation Matricielle Non-négative (FMN), aux représentations fréquentielles de signaux audio musicaux. Ces algorithmes, dirigés par une fonction d’erreur de reconstruction, apprennent un ensemble de fonctions de base et un ensemble de coef- ficients correspondants qui approximent le signal d’entrée. On compare l’utilisation de trois fonctions d’erreur de reconstruction quand la FMN est appliquée à des gammes monophoniques et harmonisées: moindre carré, divergence Kullback-Leibler, et une mesure de divergence dépendente de la phase, introduite récemment. Des nouvelles méthodes pour interpréter les décompositions résultantes sont présentées et sont comparées aux méthodes utilisées précédemment qui nécessitent des connaissances du domaine acoustique. Finalement, on analyse la capacité de généralisation des fonctions de bases apprises par rapport à trois paramètres musicaux: l’amplitude, la durée et le type d’instrument. Pour ce faire, on introduit deux algorithmes d’étiquetage des fonctions de bases qui performent mieux que l’approche précédente dans la majorité de nos tests, la tâche d’instrument avec audio monophonique étant la seule exception importante.

Product autoregressive models for non-negative variables

When variables in time series context are non-negative, such as for volatility, survival time or wave heights, a multiplicative autoregressive model of the type Xt = Xα t−1Vt , 0 ≤ α < 1, t = 1, 2, . . . may give the preferred dependent structure. In this paper, we study the properties of such models and propose methods for parameter estimation. Explicit solutions of the model are obtained in the case of gamma marginal distribution

Rational Numbers and Intensive Quantities : Challenges and Insights to Pupils' Implicit Knowledge.'Números racionales y cantidades intensivas: retos y comprensión para el conocimiento implícito de los alumnos'.

Resumen tomado parcialmente de la revista.- El artículo forma parte de un monográfico dedicado a Psicología de las Matemáticas

The system identification and control of Hammerstein system using non-uniform rational B-spline neural network and particle swarm optimization

In this paper a new system identification algorithm is introduced for Hammerstein systems based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a non-uniform rational B-spline (NURB) neural network. The proposed system identification algorithm for this NURB network based Hammerstein system consists of two successive stages. First the shaping parameters in NURB network are estimated using a particle swarm optimization (PSO) procedure. Then the remaining parameters are estimated by the method of the singular value decomposition (SVD). Numerical examples including a model based controller are utilized to demonstrate the efficacy of the proposed approach. The controller consists of computing the inverse of the nonlinear static function approximated by NURB network, followed by a linear pole assignment controller.

A New Class of Non Negative Distributions Generated by Symmetric Distributions

In this article, we study a new class of non negative distributions generated by the symmetric distributions around zero. For the special case of the distribution generated using the normal distribution, properties like moments generating function, stochastic representation, reliability connections, and inference aspects using methods of moments and maximum likelihood are studied. Moreover, a real data set is analyzed, illustrating the fact that good fits can result.

Source terms for calculations of vaporizing and burning fuel sprays with non-unity Lewis numbers in gases with temperature-dependent thermal conductivities

Liquid-fueled burners are used in a number of propulsion devices ranging from internal combustion engines to gas turbines. The structure of spray flames is quite complex and involves a wide range of time and spatial scales in both premixed and non-premixed modes (Williams 1965; Luo et al. 2011). A number of spray-combustion regimes can be observed experimentally in canonical scenarios of practical relevance such as counterflow diffusion flames (Li 1997), as sketched in figure 1, and for which different microscalemodelling strategies are needed. In this study, source terms for the conservation equations are calculated for heating, vaporizing and burning sprays in the single-droplet combustion regime. The present analysis provides extended formulation for source terms, which include non-unity Lewis numbers and variable thermal conductivities.

bioNMF: a versatile tool for non-negative matrix factorization in biology

Medical imaging has become an absolutely essential diagnostic tool for clinical practices; at present, pathologies can be detected with an earliness never before known. Its use has not only been relegated to the field of radiology but also, increasingly, to computer-based imaging processes prior to surgery. Motion analysis, in particular, plays an important role in analyzing activities or behaviors of live objects in medicine. This short paper presents several low-cost hardware implementation approaches for the new generation of tablets and/or smartphones for estimating motion compensation and segmentation in medical images. These systems have been optimized for breast cancer diagnosis using magnetic resonance imaging technology with several advantages over traditional X-ray mammography, for example, obtaining patient information during a short period. This paper also addresses the challenge of offering a medical tool that runs on widespread portable devices, both on tablets and/or smartphones to aid in patient diagnostics.

Mathematical approach for predicting non-negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non-negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non-linear optimization problem. By solving the non-linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non-negativity constraint for the TSVs of the corresponding colours.

Operator's manual : compressor, rotary, air, wheel mounted, pneumatic tires, diesel driven, 600 cfm, 100 psi : (Ingersoll-Rand model DR-6000) non-winterized, serial numbers 600AR 18604 ... winterized ....

"February 1962."

Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.