International duopoly with unknown costs

We consider two firms, located in different countries, selling the same homogeneous good in both countries. In each country there is a non negative tariff on imports of the good produced in the other country. We suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We analyse the effect of the production costs uncertainty on the profits of the firms and also on the welfare of the governments.

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.

Ecotoxicological aspects related to the presence of pharmaceuticals in the aquatic environment

Pharmaceuticals are biologically active and persistent substances which have been recognized as a continuing threat to environmental stability. Chronic ecotoxicity data as well as information on the current distribution levels in different environmental compartments continue to be sparse and are focused on those therapeutic classes that are more frequently prescribed and consumed. Nevertheless, they indicate the negative impact that these chemical contaminants may have on living organisms, ecosystems and ultimately, public health. This article reviews the different contamination sources as well as fate and both acute and chronic effects on non-target organisms. An extensive review of existing data in the form of tables, encompassing many therapeutic classes is presented.

Optimization process of polyester polymer mortars modified with recycled GFRP waste aggregates – application of factorial experiment design-

Glass fibre-reinforced plastics (GFRP), nowadays commonly used in the construction, transportation and automobile sectors, have been considered inherently difficult to recycle due to both: cross-linked nature of thermoset resins, which cannot be remolded, and complex composition of the composite itself, which includes glass fibres, matrix and different types of inorganic fillers. Presently, most of the GFRP waste is landfilled leading to negative environmental impacts and supplementary added costs. With an increasing awareness of environmental matters and the subsequent desire to save resources, recycling would convert an expensive waste disposal into a profitable reusable material. There are several methods to recycle GFR thermostable materials: (a) incineration, with partial energy recovery due to the heat generated during organic part combustion; (b) thermal and/or chemical recycling, such as solvolysis, pyrolisis and similar thermal decomposition processes, with glass fibre recovering; and (c) mechanical recycling or size reduction, in which the material is subjected to a milling process in order to obtain a specific grain size that makes the material suitable as reinforcement in new formulations. This last method has important advantages over the previous ones: there is no atmospheric pollution by gas emission, a much simpler equipment is required as compared with ovens necessary for thermal recycling processes, and does not require the use of chemical solvents with subsequent environmental impacts. In this study the effect of incorporation of recycled GFRP waste materials, obtained by means of milling processes, on mechanical behavior of polyester polymer mortars was assessed. For this purpose, different contents of recycled GFRP waste materials, with distinct size gradings, were incorporated into polyester polymer mortars as sand aggregates and filler replacements. The effect of GFRP waste treatment with silane coupling agent was also assessed. Design of experiments and data treatment were accomplish by means of factorial design and analysis of variance ANOVA. The use of factorial experiment design, instead of the one factor at-a-time method is efficient at allowing the evaluation of the effects and possible interactions of the different material factors involved. Experimental results were promising toward the recyclability of GFRP waste materials as polymer mortar aggregates, without significant loss of mechanical properties with regard to non-modified polymer mortars.

New end-use application for GFRP recyclates as reinforcement for concrete-polymer materials’

Glass fibre-reinforced plastics (GFRP), nowadays commonly used in the construction, transportation and automobile sectors, have been considered inherently difficult to recycle due to both: cross-linked nature of thermoset resins, which cannot be remolded, and complex composition of the composite itself, which includes glass fibres, matrix and different types of inorganic fillers. Presently, most of the GFRP waste is landfilled leading to negative environmental impacts and supplementary added costs. With an increasing awareness of environmental matters and the subsequent desire to save resources, recycling would convert an expensive waste disposal into a profitable reusable material. There are several methods to recycle GFR thermostable materials: (a) incineration, with partial energy recovery due to the heat generated during organic part combustion; (b) thermal and/or chemical recycling, such as solvolysis, pyrolisis and similar thermal decomposition processes, with glass fibre recovering; and (c) mechanical recycling or size reduction, in which the material is subjected to a milling process in order to obtain a specific grain size that makes the material suitable as reinforcement in new formulations. This last method has important advantages over the previous ones: there is no atmospheric pollution by gas emission, a much simpler equipment is required as compared with ovens necessary for thermal recycling processes, and does not require the use of chemical solvents with subsequent environmental impacts. In this study the effect of incorporation of recycled GFRP waste materials, obtained by means of milling processes, on mechanical behavior of polyester polymer mortars was assessed. For this purpose, different contents of recycled GFRP waste materials, with distinct size gradings, were incorporated into polyester polymer mortars as sand aggregates and filler replacements. The effect of GFRP waste treatment with silane coupling agent was also assessed. Design of experiments and data treatment were accomplish by means of factorial design and analysis of variance ANOVA. The use of factorial experiment design, instead of the one-factor-at-a-time method is efficient at allowing the evaluation of the effects and possible interactions of the different material factors involved. Experimental results were promising toward the recyclability of GFRP waste materials as aggregates and filler replacements for polymer mortar, with significant gain of mechanical properties with regard to non-modified polymer mortars.

Multiple linear and principal component regressions for modelling ecotoxicity bioassay response

The ecotoxicological response of the living organisms in an aquatic system depends on the physical, chemical and bacteriological variables, as well as the interactions between them. An important challenge to scientists is to understand the interaction and behaviour of factors involved in a multidimensional process such as the ecotoxicological response.With this aim, multiple linear regression (MLR) and principal component regression were applied to the ecotoxicity bioassay response of Chlorella vulgaris and Vibrio fischeri in water collected at seven sites of Leça river during five monitoring campaigns (February, May, June, August and September of 2006). The river water characterization included the analysis of 22 physicochemical and 3 microbiological parameters. The model that best fitted the data was MLR, which shows: (i) a negative correlation with dissolved organic carbon, zinc and manganese, and a positive one with turbidity and arsenic, regarding C. vulgaris toxic response; (ii) a negative correlation with conductivity and turbidity and a positive one with phosphorus, hardness, iron, mercury, arsenic and faecal coliforms, concerning V. fischeri toxic response. This integrated assessment may allow the evaluation of the effect of future pollution abatement measures over the water quality of Leça River.

Rhapsody in fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

Desenvolvimento e aplicação de um biossensor para monitorização de creatinina, um biomarcador associado a doenças emergentes

Este trabalho descreve o desenvolvimento de um material sensor para creatinina por impressão molecular em estrutura polimérica (MIP) e a sua aplicação no desenvolvimento de um dispositivo de natureza potenciométrica para a determinação da molécula alvo em fluidos biológicos. A creatinina é um dos biomarcadores mais utilizados no acompanhamento da doença renal, já que é um bom indicador da taxa de filtração glomerular (TFG). Os materiais biomiméticos desenhados para interação com a creatinina foram obtidos por polimerização radicalar, recorrendo a monómeros de ácido metacríclico ou de vinilpiridina e a um agente de reticulação apropriado. De modo a aferir o efeito da impressão da creatinina na resposta dos materiais MIP à sua presença, foram também preparados e avaliados materiais de controlo, obtidos sem impressão molecular (NIP). O controlo da constituição química destes materiais, incluindo a extração da molécula impressa, foi realizado por Espectroscopia de Raman e de Infravermelho com Transformada de Fourrier. A afinidade de ligação entre estes materiais e a creatinina foi também avaliada com base em estudos cinéticos. Todos os materiais descritos foram integrados em membranas selectivas de elétrodos seletivos de ião, preparadas sem ou com aditivo iónico lipófilo, de carga negativa ou positiva. A avaliação das características gerais de funcionamento destes elétrodos, em meios de composição e pH diferentes, indicaram que as membranas com materiais impressos e aditivo aniónico eram as únicas com utilidade analítica. Os melhores resultados foram obtidos em solução tampão Piperazine-N,N′-bis(2- ethanesulfonic acid), PIPES, de pH 2,8, condição que permitiu obter uma resposta quasi-Nernstiana, a partir de 1,6×10-5 mol L-1. Estes elétrodos demonstraram ainda uma boa selectividade ao apresentaram uma resposta preferencial para a creatinina quando na presença de ureia, carnitina, glucose, ácido ascórbico, albumina, cloreto de cálcio, cloreto de potássio, cloreto de sódio e sulfato de magnésio. Os elétrodos foram ainda aplicados com sucesso na análise de amostras sintéticas de urina, quando os materiais sensores eram baseados em ácido metacrilico, e soro, quando os materiais sensores utilizados eram baseados em vinilpiridina.

New modified electrochemical conductive paper support for BSA detection

Chemical sensors and biosensors are widely used to detect various kinds of protein target biomolecules. Molecularly Imprinted Polymers (MIPs) have raised great interest in this area, because these act as antibody-like recognition materials, with high affinity to the template molecule. Compared to natural antibodies, these are also of lower cost and higher stability. There are different types of supports used to carry MIP materials, mostly of these made of gold, favourably assembled on a Screen Printed Electrode (SPE) strategy. For this work a new kind of support for the sensing layer was developed: conductive paper. This support was made by modifying first cellulose paper with paraffin wax (to make it waterproof), and casting a carbon-ink on it afterwards, to turn it conductive. The SPAM approach previously reported in1 was employed herein to assemble to MIP sensing material on the conductive paper. The selected charged monomers were (vinylbenzyl) trimethlammonium chloride (positive charge) or vinylbenzoic acid (negative charge), used to generate binding positions with single-type charge (positive or negative). The non-specific binding area of the MIP layer was assembled by chronoamperometry-assisted polymerization (at 1 V, for 60, 120 or 180 seconds) of vinylbenzoate, cross-linked with ethylene glycol vinyl ether. The BSA biomolecules lying within the polymeric matrix were removed by Proteinase K action. All preparation stages of the MIP assembly were followed by FTIR, Raman spectroscopy and, electrochemical analysis. In general, the best results were obtained for longer polymerization times and positively charged binding sites (which was consistent with a negatively-charged protein under physiological pH, as BSA). Linear responses against BSA concentration ranged from 0.005 to 100 mg/mL, in PBS buffer standard solutions. The sensor was further calibrated in standard solutions that were prepared in synthetic or real urine, and the analytical response became more sensitive and stable. Compared to the literature, the detection capability of the developed device is better than most of the reported electrodes. Overall, the simplicity, low cost and good analytical performance of the BSA SPE device, prepared with positively charged binding positions, seems a suitable approach for practical application in clinical context. Further studies with real samples are required, as well as gathering with electronic-supporting devices to allow on-site readings.

Rhapsody in Fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.