Methodological aspects of a mathematical programming model to evaluate soil tillage technologies in a risky environment

In this work we develop a methodology for the economic evaluation of soil tillage technologies, in a risky environment, and to capture the influence of farmer behaviour on his technology choice. The model has short-term activities, that change with the type of year, and long-term activities, in which sets of traction investment activities are included. Although these activities do not change with the type of year, they lead to different availability of resources for each type of year, since the same tractor has different available fieldwork days under different weather conditions. We prove that the model is sensitive to the greater income variability resulting from the use of alternative technologies and to the balance between income and risk, accounting for the probability of occurrence of each state of nature and giving an investment solution that considers the best production plan for each type of year. (c) 2005 Elsevier B.V. All rights reserved.

Equações de 1.º grau : estratégias e erros na resolução e simplificação de equações de 1.º grau

Relatório da prática de ensino supervisionada, Mestrado em Ensino da Matemática, Universidade de Lisboa, 2011

O desenvolvimento do pensamento algébrico de alunos do 4º ano de escolaridade : uma experiência de ensino

Tese de doutoramento, Educação (Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2014

The Impact of Critical Thinking Disposition on Learning Using Business Simulations

This research seeks to determine the relationship between students’ critical thinking disposition and their learning while engaging in a business simulation at a UK higher education institution (HEI). The research informs educators making decisions about the use of simulations as to the value of considering critical thinking dispositions. Previous research has found that simulations are an effective way for students to engage actively in learning, bridging the gap between theory and practice. It has also been found that such simulations can develop students’ critical thinking skills. However, hitherto no research has been undertaken into the role that existing critical thinking disposition has on the learning of students, as measured by the degree to which students perceived that they met the module’s intended learning outcomes. This research offers insights into the role and importance of critical thinking disposition and its component dimensions and how this impacts student learning. The results indicate that the level of critical thinking disposition is positively related to the students’ learning. The implications of the research suggest educators should target business simulations at specific cohorts of students. The relative importance of the critical thinking disposition constructs and the practical educational implications of these findings are discussed.

Abstract thinking: a predictor of modelling ability?

In this paper, we describe a study of the abstract thinking skills of a group of students studying object-oriented modelling as part of a Masters course. Abstract thinking has long been considered a core skill for computer scientists. This study is part of attempts to gather evidence about the link between abstract thinking skills and success in the Computer Science discipline. The results of this study show a positive correlation between the scores of the students in the abstract thinking test with the marks achieved in the module. However, the small numbers in the study mean that wider research is needed.

Mathematical modelling of supercritical CO2 extraction of volatile oils from aromatic plants

The modelling of the experimental data of the extraction of the volatile oil from six aromatic plants (coriander, fennel, savoury, winter savoury, cotton lavender and thyme) was performed using five mathematical models, based on differential mass balances. In all cases the extraction was internal diffusion controlled and the internal mass transfer coefficienty (k(s)) have been found to change with pressure, temperature and particle size. For fennel, savoury and cotton lavender, the external mass transfer and the equilibrium phase also influenced the second extraction period, since k(s) changed with the tested flow rates. In general, the axial dispersion coefficient could be neglected for the conditions studied, since Peclet numbers were high. On the other hand, the solute-matrix interaction had to be considered in order to ensure a satisfactory description of the experimental data.

Fuzzy Monte Carlo mathematical model for load curtailment minimization in transmission power systems

This paper presents a methodology which is based on statistical failure and repair data of the transmission power system components and uses fuzzyprobabilistic modeling for system component outage parameters. Using statistical records allows developing the fuzzy membership functions of system component outage parameters. The proposed hybrid method of fuzzy set and Monte Carlo simulation based on the fuzzy-probabilistic models allows catching both randomness and fuzziness of component outage parameters. A network contingency analysis to identify any overloading or voltage violation in the network is performed once obtained the system states by Monte Carlo simulation. This is followed by a remedial action algorithm, based on optimal power flow, to reschedule generations and alleviate constraint violations and, at the same time, to avoid any load curtailment, if possible, or, otherwise, to minimize the total load curtailment, for the states identified by the contingency analysis. In order to illustrate the application of the proposed methodology to a practical case, the paper will include a case study for the Reliability Test System (RTS) 1996 IEEE 24 BUS.

Inexact restoration approaches to solve mathematical program with complementarity constraints

Mathematical Program with Complementarity Constraints (MPCC) finds applica- tion in many fields. As the complementarity constraints fail the standard Linear In- dependence Constraint Qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ), at any feasible point, the nonlinear programming theory may not be directly applied to MPCC. However, the MPCC can be reformulated as NLP problem and solved by nonlinear programming techniques. One of them, the Inexact Restoration (IR) approach, performs two independent phases in each iteration - the feasibility and the optimality phases. This work presents two versions of an IR algorithm to solve MPCC. In the feasibility phase two strategies were implemented, depending on the constraints features. One gives more importance to the complementarity constraints, while the other considers the priority of equality and inequality constraints neglecting the complementarity ones. The optimality phase uses the same approach for both algorithm versions. The algorithms were implemented in MATLAB and the test problems are from MACMPEC collection.

Numerical experiments with a modified regularization scheme for mathematical programs with complementarity constraints

On this paper we present a modified regularization scheme for Mathematical Programs with Complementarity Constraints. In the regularized formulations the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In our approach both the complementarity condition and the nonnegativity constraints are relaxed. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested.

Desenvolvendo o pensamento algébrico no 2.º ciclo do ensino básico: o sentido dos símbolos e da generalização

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de mestre em Educação Matemática na Educação Pré-escolar e nos 1.º e 2.º Ciclos do Ensino Básico

Dermic diffusion and stratum corneum: a state of the art review of mathematical models

Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives.

Mathematical modeling and simulation of heat flow through pultrusion die assembly system for thermoset composites

Pultrusion is an industrial process used to produce glass fibers reinforced polymers profiles. These materials are worldwide used when performing characteristics, such as great electrical and magnetic insulation, high strength to weight ratio, corrosion and weather resistance, long service life and minimal maintenance are required. In this study, we present the results of the modelling and simulation of heat flow through a pultrusion die by means of Finite Element Analysis (FEA). The numerical simulation was calibrated based on temperature profiles computed from thermographic measurements carried out during pultrusion manufacturing process. Obtained results have shown a maximum deviation of 7%, which is considered to be acceptable for this type of analysis, and is below to the 10% value, previously specified as maximum deviation. © 2011, Advanced Engineering Solutions.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.