Cálculo flexível e o raciocínio quantitativo aditivo em alunos dos 1.º e 2.º anos

Esta comunicação insere-se no Projeto “Pensamento numérico e cálculo flexível: Aspetos críticos”. Começa por discutir o que se entende por flexibilidade de cálculo e raciocínio quantitativo aditivo, discutindo depois os resultados de entrevistas individuais realizadas com quatro alunos (dois do 1.º ano e dois do 2.º ano) quando lhes foram propostas tarefas onde aqueles aspetos estavam presentes. Trata-se de um estudo exploratório cujo principal objetivo é compreender o raciocínio dos alunos quando resolvem tarefas numéricas envolvendo situações aditivas, e ainda identificar aspetos associados à flexibilidade de cálculo e ao raciocínio quantitativo. Os resultados mostram que, no caso dos alunos do 1.º ano, o seu desempenho parece estar relacionado com o seu desenvolvimento do sentido do número e com as relações que dominam. Para os alunos do 2.º ano, o raciocínio inversivo constituiu um aspeto crítico, que conseguiram mobilizar depois de superadas as dificuldades iniciais. Os resultados sugerem, ainda, que estes alunos concebem a diferença como uma relação invariante numérica.

Determination of tartaric acid in wines by FIA with tubular tartrate-selective electrodes

A flow injection analysis (FIA) system comprising a tartrate- (TAT) selective electrode has been developed for determination of tartaric acid in wines. Several electrodes constructed for this purpose had a PVC membrane with a complex of quaternary ammonium and TAT as anion exchanger, a phenol derivative as additive, and a more or less polar mediator solvent. Characterization of the electrodes showed behavior was best for membranes with o-nitrophenyl octyl ether as solvent. On injection of 500 μL into a phosphate buffer carrier (pH = 3.1; ionic strength 10–2 mol/L) flowing at 3 mL/min, the slope was 58.06 ± 0.6 with a lower limit of linear range of 5.0 × 10–4 mol/L TAT and R2 = 0.9989. The interference of several species, e.g. chloride, bromide, iodide, nitrate, gallic acid, tannin, sucrose, glucose, fructose, acetate, and citrate, was evaluated in terms of potentiometric selectivity coefficients. The Hofmeister series was followed for inorganic species and the most interfering organic ion was citrate. When red and white wines were analyzed and the results compared with those from an independent method they were found to be accurate, with relative standard deviations below 5.0%.

Citrate selective electrodes for the flow injection analysis of soft drinks, beers and pharmaceutical products

Aiming the establishment of simple and accurate readings of citric acid (CA) in complex samples, citrate (CIT) selective electrodes with tubular configuration and polymeric membranes plus a quaternary ammonium ion exchanger were constructed. Several selective membranes were prepared for this purpose, having distinct mediator solvents (with quite different polarities) and, in some cases, p-tert-octylphenol (TOP) as additive. The latter was used regarding a possible increase in selectivity. The general working characteristics of all prepared electrodes were evaluated in a low dispersion flow injection analysis (FIA) manifold by injecting 500µl of citrate standard solutions into an ionic strength (IS) adjuster carrier (10−2 mol l−1) flowing at 3ml min−1. Good potentiometric response, with an average slope and a repeatability of 61.9mV per decade and ±0.8%, respectively, resulted from selective membranes comprising additive and bis(2-ethylhexyl)sebacate (bEHS) as mediator solvent. The same membranes conducted as well to the best selectivity characteristics, assessed by the separated solutions method and for several chemical species, such as chloride, nitrate, ascorbate, glucose, fructose and sucrose. Pharmaceutical preparations, soft drinks and beers were analyzed under conditions that enabled simultaneous pH and ionic strength adjustment (pH = 3.2; ionic strength = 10−2 mol l−1), and the attained results agreed well with the used reference method (relative error < 4%). The above experimental conditions promoted a significant increase in sensitivity of the potentiometric response, with a supra-Nernstian slope of 80.2mV per decade, and allowed the analysis of about 90 samples per hour, with a relative standard deviation <1.0%.

Trimethoprim-selective electrodes with molecularly imprinted polymers acting as ionophores and potentiometric transduction on graphite solid-contact

This work proposes a new biomimetic sensor material for trimethoprim. It is prepared by means of radical polymerization, having trimethylolpropane trimethacrylate as cross-linker, benzoyl peroxide as radicalar iniciator, chloroform as porogenic solvent, and methacrylic acid and 2-vinyl pyridine as monomers. Different percentages of sensor in a range between 1 and 6% were studied. Their behavior was compared to that obtained with ion-exchanger quaternary ammonium salt (additive tetrakis(p-chlorophenyl)borate or tetraphenylborate). The effect of an anionic additive in the sensing membrane was also tested. Trimethoprim sensors with 1% of imprinted particles from methacrylic acid monomers showed the best response in terms of slope (59.7 mV/decade) and detection limit (4.01×10−7 mol/L). These electrodes displayed also a good selectivity towards nickel, manganese aluminium, ammonium, lead, potassium, sodium, iron, chromium, sulfadiazine, alanine, cysteine, tryptophan, valine and glycine. The sensors were not affected by pH changes from 2 to 6. They were successfully applied to the analysis of water from aquaculture.

Maltol determination in food by microwave assisted extraction and electrochemical detection

An electrochemical method is proposed for the determination of maltol in food. Microwave-assisted extraction procedures were developed to assist sample pre-treating steps. Experiments carried out in cyclic voltammetry showed an irreversible and adsorption controlled reduction of maltol. A cathodic peak was observed at -1.0 V for a Hanging Mercury Drop Electrode versus an AgCl/Ag (in saturated KCl), and the peak potential was pH independent. Square wave voltammetric procedures were selected to plot calibration curves. These procedures were carried out with the optimum conditions: pH 6.5; frequency 50 Hz; deposition potential 0.6 V; and deposition time 10 s. A linear behaviour was observed within 5.0 × 10-8 and 3.5 × 10-7 M. The proposed method was applied to the analysis of cakes, and results were compared with those obtained by an independent method. The voltammetric procedure was proven suitable for the analysis of cakes and provided environmental and economical advantages, including reduced toxicity and volume of effluents and decreased consumption of reagents.

FIA potentiometric system based on periodate polymeric membrane sensors for the assessment of ascorbic acid in commercial drinks

Ascorbic acid is found in many food samples. Its clinical and technological importance demands an easyto- use, rapid, robust and inexpensive method of analysis. For this purpose, this work proposes a new flow procedure based on the oxidation of ascorbic acid by periodate. A new potentiometric periodate sensor was constructed to monitor this reaction. The selective membranes were of PVC with porphyrin-based sensing systems and a lipophilic cation as additive. The sensor displayed a near-Nernstian response for periodate over 1.0x10-2–6.0x10-6 M, with an anionic slope of 73.9 ± 0.9 mV decade-1. It was pH independent in acidic media and presented good selectivity features towards several inorganic anions. The flow set-up operated in double-channel, carrying a 5.0x10-4 M IO- 4 solution and a suitable buffer; these were mixed in a 50-cm reaction coil. The overall flow rate was 7 ml min-1 and the injection volume 70 µl. Under these conditions, a linear behaviour against concentration was observed for 17.7–194.0 µg ml-1, presenting slopes of 0.169 mV (mg/l)-1, a reproducibility of ±1.1 mV (n = 5), and a sampling rate of ~96 samples h-1. The proposed method was applied to the analysis of beverages and pharmaceuticals.

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

A divisão no 4º ano de escolaridade

Dissertação apresentada para obtenção do grau de Mestre em Educação Matemática na Educação Pré-Escolar e nos 1.º e 2.º Ciclos do Ensino Básico

The AIDS epidemic in the Amazon region: a spatial case-control study in Rondonia, Brazil

OBJECTIVE To analyze spatial changes in the risk of AIDS and the relationship between AIDS incidence and socioeconomic variables in the state of Rondonia, Amazon region. METHODS A spatial, population case-control study in Rondonia, Brazil, based on 1,780 cases reported to the Epidemiological Surveillance System and controls based on demographic data from 1987 to 2006. The cases were grouped into five consecutive four-year periods. A generalized additive model was adjusted to the data; the dependent variable was the status of the individuals (case or control), and the independent variables were a bi-dimensional spline of the geographic coordinates and some municipality-level socioeconomic variables. The observed values of the Moran’s I test were compared to a reference distribution of values generated under conditions of spatial randomness. RESULTS AIDS risk shows a marked spatial and temporal pattern. The disease incidence is related to socioeconomic variables at the municipal level in Rondônia, such as urbanization and human capital. The highest incidence rates of AIDS are in municipalities along the BR-364 highway and calculations of the Moran’s I test show positive spatial correlation associated with proximity of the municipality to the highway in the third and fourth periods (p = 0.05). CONCLUSIONS Incidence of the disease is higher in municipalities of greater economic wealth and urbanization, and in those municipalities bisected by Rondônia’s main roads. The rapid development associated with the opening up of once remote regions may be accompanied by an increase in these risks to health.

Principal components and generalized linear modeling in the correlation between hospital admissions and air pollution

OBJECTIVE To analyze the association between concentrations of air pollutants and admissions for respiratory causes in children. METHODS Ecological time series study. Daily figures for hospital admissions of children aged < 6, and daily concentrations of air pollutants (PM10, SO2, NO2, O3 and CO) were analyzed in the Região da Grande Vitória, ES, Southeastern Brazil, from January 2005 to December 2010. For statistical analysis, two techniques were combined: Poisson regression with generalized additive models and principal model component analysis. Those analysis techniques complemented each other and provided more significant estimates in the estimation of relative risk. The models were adjusted for temporal trend, seasonality, day of the week, meteorological factors and autocorrelation. In the final adjustment of the model, it was necessary to include models of the Autoregressive Moving Average Models (p, q) type in the residuals in order to eliminate the autocorrelation structures present in the components. RESULTS For every 10:49 μg/m3 increase (interquartile range) in levels of the pollutant PM10 there was a 3.0% increase in the relative risk estimated using the generalized additive model analysis of main components-seasonal autoregressive – while in the usual generalized additive model, the estimate was 2.0%. CONCLUSIONS Compared to the usual generalized additive model, in general, the proposed aspect of generalized additive model − principal component analysis, showed better results in estimating relative risk and quality of fit.

Copper-organic frameworks assembled from in situ generated 5-(4-pyridyl) tetrazole building blocks: synthesis, structural features, topological analysis and catalytic oxidation of alcohols

Two new metal- organic compounds {[Cu-3(mu(3)-4-(p)tz)(4)(mu(2)-N-3)(2)(DMF)(2)](DMF)(2)}(n) (1) and {[Cu(4ptz) (2)(H2O)(2)]}(n) (2) {4-ptz = 5-(4-pyridyl)tetrazolate} with 3D and 2D coordination networks, respectively, have been synthesized while studying the effect of reaction conditions on the coordination modes of 4-pytz by employing the [2 + 3] cycloaddition as a tool for generating in situ the 5-substituted tetrazole ligands from 4-pyridinecarbonitrile and NaN3 in the presence of a copper(II) salt. The obtained compounds have been structurally characterized and the topological analysis of 1 discloses a topologically unique trinodal 3,5,6-connected 3D network which, upon further simplification, results in a uninodal 8-connected underlying net with the bcu (body centred cubic) topology driven by the [Cu-3(mu(2)-N-3)(2)] cluster nodes and mu(3)-4-ptz linkers. In contrast, the 2D metal-organic network in 2 has been classified as a uninodal 4-connected underlying net with the sql [Shubnikov tetragonal plane net] topology assembled from the Cu nodes and mu(2)-4-ptz linkers. The catalytic investigations disclosed that 1 and 2 act as active catalyst precursors towards the microwave-assisted homogeneous oxidation of secondary alcohols (1-phenylethanol, cyclohexanol, 2-hexanol, 3-hexanol, 2-octanol and 3-octanol) with tert-butylhydroperoxide, leading to the yields of the corresponding ketones up to 86% (TOF = 430 h(-1)) and 58% (TOF = 290 h(-1)) in the oxidation of 1-phenylethanol and cyclohexanol, respectively, after 1 h under low power ( 10 W) microwave irradiation, and in the absence of any added solvent or additive.

Halogen-bonded tris (2,4-Bis(trichloromethyl)-1,3,5,triazapentadienato)-M(III) [M = Mn, Fe, Co] complexes and their catalytic activity in the peroxidative oxidation of 1-phenylethanol to acetophenone

One-pot template condensation of CCl3C=N with ammonia on a metal source [MnCl2 center dot 4H(2)O, FeCl3 center dot 6H(2)O or Co(CH3COO)(2)center dot 4H(2)O] in DMSO led to the formation of tris(2,4-bis(trichloromethyl)-1,3,5-triazapentadienato)-M(III) complexes, [M(NH=C(CCl3)NC(CCl3)=-NH}(3)]center dot n(CH3)(2)SO [M = Mn, n = 1 (1); M = Fe, n = 2 (2); M = Co, n = 2 (3)1, which were characterized using elemental analysis, and IR, ESI-MS and single-crystal X-ray analysis. The role of inter- and intramolecular non-covalent halogen and hydrogen bonds in the synthesis of 1-3 is discussed. It is shown that the crystal ionic radii of the metal ions [68.5 (Co) < 69 (Fe) < 72 (Mn), pm] are related to the corresponding Cl center dot center dot center dot Cl distances [3.178 (3) > 3.155 (2) > 3.133 (1) Al. Compounds 1-3 and the related di(triazapentadienato)-Cu(v) complex [Cu(NH=C(CCl3)NC(CCl3)=NH}2]center dot 2(CH3)(2)SO (4) act as catalyst precursors for the additive-free microwave (MW) assisted homogeneous oxidation of 1-phenylethanol with tert-butylhydroperoxide (TBHP), leading to the formation of acetophenone with yields up to 99% and TONs up to 5.0 x 10(3) after 1 h of low power (10 W) MW irradiation.

An SEM investigation of the pozzolanic activity of a waste catalyst oil refinery

The most active phase of the fluid catalytic cracking (FCC) catalyst, used in oil refinery, is zeolite-Y which is an aluminosilicate with a high internal and external surface area responsible for its high reactivity. Waste FCC catalyst is potentially able to be reused in cement-based materials - as an additive - undergoing a pozzolanic reaction with calcium hydroxide (Ca(OH)2) formed during cement hydration [1-3]. This reaction produces additional strength-providing reaction products i.e., calcium silicate hydrate (C-S-H) and hydrous calcium aluminates (C-A-H) which exact chemical formula and structure are still unknown. Partial replacement of cement by waste FCC catalyst has two key advantages: (1) lowering of cement production with the associated pollution reduction as this industry represents one of the largest sources of man-made CO2 emissions, and (2) improving the mechanical properties and durability of cement-based materials. Despite these advantages, there is a lack of fundamental knowledge on pozzolanic reaction mechanisms as well as spatial distribution of porosity and solid phases interactions at the microstructural level and consequently their relationship with macroscopical engineering properties of catalyst/cement blends. Within this scope, backscattered electron (BSE) images acquired in a scanning electron microscope (SEM) equipped with Energy-Dispersive Spectroscopy (EDS) and by X-ray diffraction were used to investigate chemical composition of hydration products and to analyse spatial information of the microstructure of waste FCC catalyst blended cement mortars. For this purpose mortars with different levels of cement substitution by waste catalyst as well as with different hydration ages, were prepared. The waste FCC catalyst used is produced by the Portuguese refinery company Petrogal S.A.

Cobs and stair nesting – segregation and crossing

Stair nesting leads to very light models since the number of their treatments is additive on the numbers of observations in which only the level of one factor various. These groups of observations will be the steps of the design. In stair nested designs we work with fewer observations when compared with balanced nested designs and the amount of information for the different factors is more evenly distributed. We now integrate these models into a special class of models with orthogonal block structure for which there are interesting properties.

Greener Selective Cycloalkane Oxidations with Hydrogen Peroxide Catalyzed by Copper-5-(4-pyridyl)tetrazolate Metal-Organic Frameworks

Microwave assisted synthesis of the Cu(I) compound [Cu(µ4-4-ptz)]n [1, 4-ptz = 5-(4-pyridyl)tetrazolate] has been performed by employing a relatively easy method and within a shorter period of time compared to its sister compounds. The syntheses of the Cu(II) compounds [Cu3(µ3-4-ptz)4(µ2-N3)2(DMF)2]n∙(DMF)2n (2) and [Cu(µ2-4-ptz)2(H2O)2]n (3) using a similar method were reported previously by us. MOFs 1-3 revealed high catalytic activity toward oxidation of cyclic alkanes (cyclopentane, -hexane and -octane) with aqueous hydrogen peroxide, under very mild conditions (at room temperature), without any added solvent or additive. The most efficient system (2/H2O2) showed, for the oxidation of cyclohexane, a turnover number (TON) of 396 (TOF of 40 h−1), with an overall product yield (cyclohexanol and cyclohexanone) of 40% relative to the substrate. Moreover, the heterogeneous catalytic systems 1–3 allowed an easy catalyst recovery and reuse, at least for four consecutive cycles, maintaining ca. 90% of the initial high activity and concomitant high selectivity.