Números complexos: uma proposta de mudança metodológica para uma aprendizagem significativa no ensino médio

This work presents a proposal of a methodological change to the teaching and learning of the complex numbers in the Secondary education. It is based on the inquiries and difficulties of students detected in the classrooms about the teaching of complex numbers and a questioning of the context of the mathematics teaching - that is the reason of the inquiry of this dissertation. In the searching for an efficient learning and placing the work as a research, it is presented a historical reflection of the evolution of the concept of complex numbers pointing out their more relevant focuses, such as: symbolic, numeric, geometrical and algebraic ones. Then, it shows the description of the ways of the research based on the methodology of the didactic engineering. This one is developed from the utilization of its four stages, where in the preliminary analysis stage, two data surveys are presented: the first one is concerning with the way of presenting the contents of the complex numbers in math textbooks, and the second one is concerning to the interview carried out with High school teachers who work with complex numbers in the practice of their professions. At first, in the analysis stage, it is presented the prepared and organized material to be used in the following stage. In the experimentation one, it is presented the carrying out process that was made with the second year High school students in the Centro Federal de Educação tecnológica do Rio Grande do Norte CEFET-RN. At the end, it presents, in the subsequent and validation stages, the revelation of the obtained results from the observations made in classrooms in the carrying out of the didactic sequence, the students talking and the data collection

Estudo de titanatos nanoestruturados obtidos por tratamento hidrotérmico de óxido de titânio em meio alcalino

TiTanate NanoTubes (TTNT) were synthesized by hydrothermal alkali treatment of TiO2 anatase followed by repeated washings with distinct degrees of proton exchange. TTNT samples with different sodium contents were characterized, as synthesized and after heattreatment (200-800ºC), by X-ray diffraction, scanning and transmission electron microscopy, electron diffraction, thermal analysis, nitrogen adsorption and spectroscopic techniques like FTIR and UV-Vis diffuse reflectance. It was demonstrated that TTNTs consist of trititanate structure with general formula NaxH2−xTi3O7·nH2O, retaining interlayer water in its multiwalled structure. The removal of sodium reduces the amount of water and contracts the interlayer space leading, combined with other factors, to increased specific surface area and mesopore volume. TTNTs are mesoporous materials with two main contributions: pores smaller than 10 nm due to the inner volume of nanotubes and larger pores within 5-60 nm attributed to the interparticles space. Chemical composition and crystal structure of TTNTs do not depend on the average crystal size of the precursor TiO2-anatase, but this parameter affects significantly the morphology and textural properties of the nanostructured product. Such dependence has been rationalized using a dissolution-recrystallization mechanism, which takes into account the dissolution rate of the starting anatase and its influence on the relative rates of growth and curving of intermediate nanosheets. The thermal stability of TTNT is defined by the sodium content and in a lower extent by the crystallinity of the starting anatase. It has been demonstrated that after losing interlayer water within the range 100-200ºC, TTNT transforms, at least partially, into an intermediate hexatitanate NaxH2−xTi6O13 still retaining the nanotubular morphology. Further thermal transformation of the nanostructured tri- and hexatitanates occurs at higher or lower temperature and follows different routes depending on the sodium content in the structure. At high sodium load (water washed samples) they sinter and grow towards bigger crystals of Na2Ti3O7 and Na2Ti6O13 in the form of rods and ribbons. In contrast, protonated TTNTs evolve to nanotubes of TiO2(B), which easily convert to anatase nanorods above 400ºC. Besides hydroxyls and Lewis acidity typical of titanium oxides, TTNTs show a small contribution of protonic acidity capable of coordinating with pyridine at 150ºC, which is lost after calcination and conversion into anatase. The isoeletric point of TTNTs was measured within the range 2.5-4.0, indicating behavior of a weak acid. Despite displaying semiconductor characteristics exhibiting typical absorption in the UV-Vis spectrum with estimated bandgap energy slightly higher than that of its TiO2 precursor, TTNTs showed very low performance in the photocatalytic degradation of cationic and anionic dyes. It was concluded that the basic reason resides in its layered titanate structure, which in comparison with the TiO2 form would be more prone to the so undesired electron-hole pair recombination, thus inhibiting the photooxidation reactions. After calcination of the protonated TTNT into anatase nanorods, the photocatalytic activity improved but not to the same level as that exhibited by its precursor anatase

Conciliação entre modelos de mecanismos avançados de oxidação eletroquímica

Many pollutants dumped in waterways, such as dyes and pesticides, have become so ubiquitous that they represent a serious threat to human health. The electrochemical oxidation is presented as an alternative clean, efficient and economic degradation of wastewater containing organic compounds and a number of advantages of this technique is to just not make use of chemical reagents, since only electrical energy is consumed during the removal of pollutants organic. However, despite being a promising alternative, still needs some tweaking in order to obtain better efficiency in the elimination of persistent pollutants. Thus, this study sought a relationship between a recently discovered phenomenon that reflects the participation of dissolved oxygen in solution in the electrochemical oxidation process, as an anomaly, present a kinetic model that shows instantaneous current efficiency (ICE) above 100% limited by theory, manifested for some experiments with phenolic compounds with H2SO4 or HClO4 as supporting electrolyte with electrodes under anodic oxidation on boron doped diamond (BDD). Therefore it was necessary to reproduce the data ICE exposes the fault model, and thus the 2-naphthol was used as phenolic compound to be oxidised at concentrations of 9, 12 and 15 mmol L-1, and H2SO4 and HClO4 to 1 mol L-1 as a supporting electrolyte under a current density of 30 mA cm-2 in an electrochemical reactor for continuous flow disk configuration, and equipped with anodes DDB at room temperature (25 oC). Experiments were performed using N2 like as purge gas for eliminate oxygen dissolved in solution so that its influence in the system was studied. After exposure of the anomaly of the ICE model and investigation of its relationship with dissolved O2, the data could be treated, making it possible for confirmation. But not only that, the data obtained from eletranálise and spectroscopic analysis suggest the involvement of other strongly oxidizing species (O3 (ozone) and O radicals and O2 -), since the dissolved O2 can be consumed during the formation of new strong oxidizing species, not considered until now, something that needs to be investigated by more accurate methods that we may know a little more of this system. Currently the performance of the electrocatalytic process is established by a complex interaction between different parameters that can be optimized, so it is necessary to the implementation of theoretical models, which are the conceptual lens with which researchers see

Aplicação da modelagem estrutural computacional direta na análise da geometria de falhas: exemplo da falha de Baixa Grande (Bacia Potiguar - NE do Brasil)

The Baixa grande fault is located on the edge of the S-SW Potiguar Rift. It limits the south part of Umbuzeiro Graben and the Apodi Graben. Although a number of studies have associated the complex deformation styles in the hanging wall of the Baixa Grande Fault with geometry and displacement variations, none have applied the modern computational techniques such as geometrical and kinematic validations to address this problem. This work proposes a geometric analysis of the Baixa Fault using seismic interpretation. The interpretation was made on 3D seismic data of the Baixa Grande fault using the software OpendTect (dGB Earth Sciences). It was also used direct structural modeling, such as Analog Direct Modeling know as Folding Vectors and, 2D and 3D Direct Computational Modeling. The Folding Vectors Modeling presented great similarity with the conventional structural seismic interpretations of the Baixa Grande Fault, thus, the conventional interpretation was validated geometrically. The 2D direct computational modeling was made on some sections of the 3D data of the Baixa Grande Fault on software Move (Midland Valley Ltd) using the horizon modeling tool. The modeling confirms the influence of fault geometry on the hanging wall. The Baixa Grande Fault ramp-flat-ramp geometry generates synform on the concave segments of the fault and antiform in the convex segments. On the fault region that does not have segments angle change, the beds are dislocated without deformation, and on the listric faults occur rollover. On the direct 3D computational modeling, structural attributes were obtained as horizons on the hanging wall of the main fault, after the simulation of several levels of deformation along the fault. The occurrence of structures that indicates shortening in this modeling, also indicates that the antiforms on the Baixa Grande Fault were influenced by fault geometry