This article focuses the choice and use of examples by two students of the 11th grade to prove or refute a set of statements. The use of representations of sequences and functions is also considered. The study adopts a qualitative approach and data were collected by interviews and documental gathering. The conclusions suggest most of the examples used were well-known sequences or functions. However, the students sought different purposes for the use of examples, such as understanding the conjecture, demonstrate the falsity or truthfulness of the statement and conveying a general argument. The students made a satisfactory articulation between the various types of representations but relied mostly in the cartesian graph.

In this work, the design and operation planning of a multi-period, multi-product closed-loop supply chain is addressed. Recovered end-of-life products from customers are evaluated in disassembly centers and accordingly are sent back to factories for remanufacturing, or leave the network either by being sold to third parties or by being sent to disposal. Typical uncertain parameters are product demand, production cost, and returned product volume and evaluation, among others. So, stochastic optimization approaches should be used for problem solving, where different topology decisions on the timing, location and capacity of some entities (factories, and distribution and sorting centers) are to be considered along a time horizon. A two-stage multi-period stochastic mixed 0–1 bilinear optimization model is introduced, where the combined definition of the available entities at the periods and the products’ flow among the entities, maximizes the net present value of the expected total profit along the time horizon. A version of the mixture of chance-constrained and second order stochastic dominance risk averse measures is considered for risk management at intermediate periods of the time horizon. Given the high dimensions of the model it is unrealistic to look for the optimality of the solution in an affordable computing effort for current hardware and optimization software resources. So, a decomposition approach is considered, namely a Fix-and-Relax decomposition algorithm. For assessing the computational validation of the modeling and algorithmic proposals, pilot cases are taken from a real-life glass supply chain network whose main features are retained.

Failure of structural steel members strengthened with Carbon Fibre Reinforced Polymers (CFRP) may occur at the joints CFRP-steel and this study examines variables that alter or explain the corresponding reduction of load capacity for a specific CFRP laminate, adhesive and steel. Factors and parameters likely to be influential like surface treatment prior to bonding, the bonded length, the glass transition temperature (Tg) of the adhesive, the exposure to aggressive environment, the temperature at service and different types of loading were examined. The experimental program selected double strap CFRP-steel bonded joints under shear for the analysis. The steel surfaces to be bonded were subjected to sand blasting (6.3 bar) or abrasive grinding (6.9 bar) corresponding to thorough blast cleaning Sa2; surfaces rusted after exposure to salt fog at 35 °C were also considered. Differences detected in responses of specimens treated by sand or steel spheres blasting were relatively minor. Tests made at increasing ambient temperatures confirmed that service temperature near and above adhesive Tg caused rapid deterioration of ultimate capacity and change of failure modes. Salt fog cycles (SF) originated the most significant losses of joint capacity. Application of cyclic static loading above the critical loading threshold obtained for unaged joints did not reduce the capacity of joints previously aged by freeze-thaw. The same cyclic loading after salt fog cycles, reduced bond capacity and increase the ultimate slip, suggesting larger effective length. Despite the losses of capacity, microscopic changes of structural nature could not be identified. © 2019 Elsevier Ltd

This article deals with a feedback optimal control problem for the stochastic second grade fluids. More precisely, we establish the existence of an optimal feedback control for the two-dimensional stochastic second grade fluids, with Navier-slip boundary conditions. In addition, using the Galerkin approximations, we show that the optimal cost can be approximated by a sequence of finite dimensional optimal costs, showing the existence of the so-called ϵ−optimal feedback control.

{This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The control acts through an external stochastic force and we search for a control that minimizes a cost functional. We show that the Gateaux derivative of the control to state map is a stochastic process being the unique solution of the stochastic linearized state equation. The well-posedness of the corresponding stochastic backward adjoint equation is also established, allowing to derive the first order optimality condition. (C) 2017 Elsevier B.V. All rights reserved.}

Problem of the reliability increasing of the vehicles electric drives is discussed in context of the reduction of the electric motor heating during variable character of movement. Opportunities of the induction motor stator winding heating reduction by means of the control of the vehicles electric drives in transient and steady state modes of movement are shown. Analytical expressions for dynamic torque, optimal on minimal of the winding temperature rise during acceleration, as well as expressions for dynamic torque and value of the motor torque limitation, optimal on energy consumption during acceleration are presented. It is shown that desire to reduce the stator winding temperature rise by means of dynamic torque optimal value selection or motor torque limitation can lead to the rise of energy consumption. Results of the modeling are presented.

Neste estudo analisamos as perceções que professores do 3.º ciclo e do ensino secundário têm da sua prática no âmbito do ensino de Funções, com o objetivo de as caracterizar e de identificar as diferenças existentes entre estes dois grupos de professores. Um aspeto particularmente relevante se tivermos em conta que se tratam de dois grupos de professores com formações iniciais idênticas. Adotamos uma metodologia mista, com uma vertente quantitativa apoiada na aplicação de questionários e uma vertente qualitativa baseada na realização de entrevistas. As principais conclusões alcançadas apontam para semelhanças nas perceções dos professores, mas também para algumas diferenças em função do ciclo de ensino. Na planificação das aulas os manuais são amplamente utilizados, mas de forma diferente consoante o ciclo de ensino do professor. Os professores de ambos os ciclos de ensino estabelecem conexões entre diferentes representações, mas valorizam de diferentes formas as representações disponíveis. O envolvimento dos alunos nas atividades da aula é outro aspeto destacado pelos professores, mas uma vez mais existem diferenças. Na avaliação o recurso ao teste é enfatizado pelos dois grupos de professores, mas já existem diferenças quanto à importância atribuída ao trabalho de grupo.

A formação e o desenvolvimento profissional do professor são determinantes para as opções que este assume na sala de aula. É o seu conhecimento, aquilo que valoriza e o contexto onde se encontra inserido que determinam as experiências de aprendizagem que proporciona aos seus alunos. Mas esse conhecimento profissional envolve uma multiplicidade de dimensões que decorrem da sua formação inicial e contínua, mas também das experiências que teve ocasião de vivenciar e de processos de socialização, onde a interação com os pares e as oportunidades de desenvolver trabalho colaborativo são elementos importantes. A aula de matemática surge assim como o campo aglutinador do trabalho do professor numa dupla vertente que se une num ciclo único: por um lado a aula de Matemática é o foco do trabalho do professor, onde as opções previamente assumidas são implementadas; e, por outro lado, é um ponto de partida para a reflexão e o desenvolvimento profissional do professor.

Da planificação da aula, onde a escolha das tarefas e a forma de as implementar são aspetos centrais e onde a vertente histórica não deixará de estar presente; à sua implementação, operacionalizando diferentes recursos (nomeadamente os tecnológicos) e assumindo dinâmicas de aula diferenciadas; até à fase de reflexão entre pares, que termina e reinicia um novo ciclo – estas são as grandes etapas em torno das quais este texto se organiza e onde a formação inicial e contínua não deixarão de estar presentes.

This work addresses the reconstruction of strain gradient fields at the wood growth ring scale from full-field deformation measurements provided by digital image correlation. Moreover, the spatial distribution of the earlywood and latewood radial modulus of elasticity is assessed. Meso-scale tensile tests are carried out on Pinus pinaster Ait. wooden specimens oriented in the radial–tangential plane under quasi-static loading conditions. A parametric analysis of the two-dimensional digital image correlation extrinsic and intrinsic setting parameters is performed, in a balance between spatial resolution and resolution. It is shown that the parametric module is an effective way to quantitatively support the choice of digital image correlation parameters in the presence of the high deformation gradient fields generated by the structure–property relationships at the scale of observation. Under the assumption of a uniaxial tensile stress state, the spatial distribution of the radial elastic modulus across the growth rings is obtained. It is observed that the ratio of the radial modulus of elasticity between latewood and earlywood tissues can vary significantly as a function of the digital image correlation parameters. It is pointed out, however, that a convergence value can be systematically established. Effectively, earlywood and latewood stress–strain curves are obtained and elastic properties are determined assuming the converged digital image correlation setting parameters.

Phylogenetic analyses of morphological data are often characterized by missing data due to incomplete operational taxonomic units, as in fossils. This incomplete knowledge derives from various reasons, including—in the case of fossils—the numerous filters an organism has to pass through during taphonomy, fossilization, weathering and collecting. Whereas several methods have been proposed to address issues raised by the inclusion of incomplete terminal taxa, until recently no tool existed to easily quantify the amount of anatomical overlap within a particular clade. The Overlap Indices provide such values and might prove useful for comparative cladistics. We herein describe these new indices and their applications in detail and provide an example file for their calculation. A case study of diplodocid sauropod dinosaurs shows how the Overlap Indices will help to explore and quantify, which one of a number of conflicting tree topologies is supported by more anatomical traits, which skeletal regions are underrepresented in a particular phylogenetic matrix, and which taxon would improve character state score completeness.

The teacher's knowledge of the mathematical fidelity of technology and the impact it has on the teacher’s practice is the focus of this article. Based on the conceptualization of Knowledge for Teaching Mathematics with Technology (KTMT), and involving the teaching of Functions at the 10th grade, we analyze: the situations of lack of mathematical fidelity considered by the teacher in the classes, the way how the teacher manages students' contact with this kind of situations, and how the teacher supports students when they are faced with a lack of mathematical fidelity. The conclusions reached point to: some devaluation of the situations of lack of mathematical fidelity, with only one type of situation being explicitly addressed; a careful selection of tasks, in order to ensure that these situations do not occur too soon; a focus on the identification by the students of this type of situation, suggesting what they can do to confirm the suspicion but without effective implementation of the process. As a consequence, knowledge of mathematical fidelity does not necessarily have a relevant impact on teacher’s practice and it is not easily transformed into a deep teacher’s KTMT.

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The class of finitely presented monoids defined by homogeneous (length-preserving) relations
is considered. The properties of admitting a finite complete rewriting system, having finite derivation type, being automatic, and being biautomatic, are investigated for monoids in this class. The first main result shows that for any possible combination of these properties and their negations there is a homoegenous monoid with exactly this combination of properties. We then extend this result to show that the same statement holds even if one restricts attention to the class of $n$-ary multihomogeneous monoids (meaning every side of every relation has fixed length $n$, and all relations are also content preserving).