http://docentes.fct.unl.pt/lblm/files/jbic-2015-20-821.pdf

The usual difficulties of students regarding the choice of an appropriate window when using the graphing calculator in the study of functions and the importance of the teachers’ knowledge to overcoming them, led to this study. The main goal was to characterize the way teachers address the viewing window in the classroom, trying to infer aspects of the Knowledge for Teaching Mathematics with Technology that can justify that practice. The conclusions reached point to the importance of a set of specific knowledge where I highlight the knowledge of the students’ difficulties, the knowledge of mathematical content necessary to understand the impact of the viewing window on the graphic, and the knowledge of teaching strategies that address both the students’ difficulties and the relevant mathematical knowledge.

We prove that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space \(X(\mathbb{R}^n)\) and on its associate space \(X'(\mathbb{R}^n)\) and a maximally modulated Calderón-Zygmund singular integral operator \(T^{\Phi}\) is of weak type \((r,r)\) for all \(r\in(1,\infty)\), then \(T^{\Phi}\) extends to a bounded operator on \(X(\mathbb{R}^n)\). This theorem implies the boundedness of the maximally modulated Hilbert transform on variable Lebesgue spaces \(L^{p(\cdot)}(\mathbb{R})\) under natural assumptions on the variable exponent \(p:\mathbb{R}\to(1,\infty)\). Applications of the above result to the boundedness and compactness of pseudodifferential operators with \(L^\infty(\mathbb{R},V(\mathbb{R}))\)-symbols on variable Lebesgue spaces \(L^{p(\cdot)}(\mathbb{R})\) are considered. Here the Banach algebra \(L^\infty(\mathbb{R},V(\mathbb{R}))\) consists of all bounded measurable \(V(\mathbb{R})\)-valued functions on \(\mathbb{R}\) where \(V(\mathbb{R})\) is the Banach algebra of all functions of bounded total variation.

Abstract A modified Iosipescu specimen is proposed to measure the mode İI\} intralaminar fracture toughness and the corresponding crack resistance curve of fibre reinforced composites. Due to the impossibility of scaling the specimen, a modification of the classical size effect method is proposed. The calculation of the crack driving force curves is performed using the Finite Element Method. The classical Iosipescu shear feature was used and tests were coupled with digital image correlation to support the proposed approach. Experiments were performed on IM7/8552 material system and the R-curve was obtained. The steady-state value of the fracture toughness of the ply is found to be equal to R 0 ss = 34.4  kJ/m2.

Abstract This work addresses the experimental identification of mode I cohesive law of wood bonded joints. The approach combines the double cantilever beam (DCB) test with both digital image correlation (DIC) and embedded fibre Bragg grating (FBG) sensors. The spectrum geometric mean of the \{FBG\} reflected spectral response was determined, and the wavelength evolution was used to define the fracture process zone (FPZ) development phase. This evaluation allowed a consistent selection of experimental range of over which the identification procedure of mode I cohesive law is build up. Mode I crack length, Resistance-curve and cohesive law parameters are characterised and discussed. The strain energy release rate (GI) is determined from the P�d curve by the compliance-based beam method (CBBM). The crack tip opening displacement (wI) is determined by post-processing displacements measured by DIC. The cohesive law in mode I (sI�wI) is then obtained by numerical differentiation of the GI�wI relationship.

Abstract Several analyses of diversity through geological time use global, synoptic databases, and this practice often makes it difficult to distinguish true signals in changing diversity from regional-scale sampling and/or geological artefacts. Here we investigate how echinoid diversity changed through the Mesozoic of the Lusitanian basin in Portugal based on a comprehensive, revised database, and seek to distinguish biological signal from geological or environmental constraints. The observed diversity pattern is far from having a defined trend, showing many fluctuations that appear to be linked with gaps in the geological record. This study revealed that, independently of the method used, whether correlation tests or model fitting, the diversity signal is not completely explained by the studied sampling proxies. Among the different proxies, marine facies variation in combination with outcrop area best explains the palaeodiversity curve.

Supply Chain Design problems often result into multiperiod stochastic mixed integer problems that are hard to solve. In this paper we propose a metaheuristic algorithm as a specialization for two- stage problems of the so-named Fix-and-Relax Algorithm presented previously for solving large- scale multiperiod stochastic mixed 0-1 optimization problems under a time stochastic dominance risk averse strategy, so-named TSD. Some computational experience is presented.

Goal-oriented Requirements Engineering approaches have become popular in the Requirements Engineering community as they provide expressive modelling languages for requirements elicitation and analysis. However, as a common challenge, such approaches are still struggling when it comes to managing the accidental complexity of their models. Furthermore, those models might be incomplete, resulting in insufficient information for proper understanding and implementation. In this paper, we provide a set of metrics, which are formally specified and have tool support, to measure and analyse complexity and completeness of goal models, in particular social goal models (e.g. i⁎). Concerning complexity, the aim is to identify refactoring opportunities to improve the modularity of those models, and consequently reduce their accidental complexity. With respect to completeness, the goal is to automatically detect model incompleteness. We evaluate these metrics by applying them to a set of well-known system models from industry and academia. Our results suggest refactoring opportunities in the evaluated models, and provide a timely feedback mechanism for requirements engineers on how close they are to completing their models.

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http://docentes.fct.unl.pt/lblm/files/jbic-2015-20-181.pdf

http://docentes.fct.unl.pt/lblm/files/jbic-2015-20-287.pdf

Let $G$ be a graph whose edges are coloured with $k$ colours, and $\mathcal H=(H_1,\dots , H_k)$ be a $k$-tuple of graphs. A \emph{monochromatic $\mathcal H$-decomposition} of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms a monochromatic copy of $H_i$ in colour $i$, for some $1\le i\le k$. Let $\phi_{k}(n,\mathcal H)$ be the smallest number $\phi$, such that, for every
order-$n$ graph and every $k$-edge-colouring, there is a monochromatic $\mathcal H$-decomposition with at most $\phi$ elements. Extending the previous results of Liu and Sousa [``Monochromatic $K_r$-decompositions of graphs", \emph{Journal of Graph Theory}76:89-100,2014], we solve this problem
when each graph in $\mathcal H$ is a clique and $n\ge n_0(\mathcal H)$ is sufficiently large.

A tecnologia e o impacto que esta pode ter sobre as diferentes representações utilizadas e, em particular, sobre a representação algébrica são o foco deste artigo. Procura-se assim compreender como é que o professor enquadra a representação algébrica no trabalho em sala de aula e como a procura tornar relevante para os alunos num contexto de utilização da tecnologia. As conclusões alcançadas apontam para a opção por uma estreita articulação entre as representações algébrica e gráfica e para uma criteriosa escolha de tarefas, envolvendo múltiplas abordagens, onde a representação algébrica vem disponibilizar informação fundamental e tendencialmente inacessível a partir de outras representações.