Unicidade e discretização para problemas de valor inicial

This paper has two objectives: (i) conducting a literature search on the criteria of uniqueness of solution for initial value problems of ordinary differential equations. (ii) a modification of the method of Euler that seems to be able to converge to a solution of the problem, if the solution is not unique

Preparação e caracterização de um material híbrido, à base de vermiculita modificada com quitosana, para a remoção de íons de chumbo presentes em efluentes sintéticos

Actually, surveys have been developed for obtaining new materials and methodologies that aim to minimize environmental problems due to discharges of industrial effluents contaminated with heavy metals. The adsorption has been used as an alternative technology effectively, economically viable and potentially important for the reduction of metals, especially when using natural adsorbents such as certain types of clay. Chitosan, a polymer of natural origin, present in the shells of crustaceans and insects, has also been used for this purpose. Among the clays, vermiculite is distinguished by its good ion exchange capacity and in its expanded form enhances its properties by greatly increasing its specific surface. This study aimed to evaluate the functionality of the hybrid material obtained through the modification of expanded vermiculite with chitosan in the removal of lead ions (II) in aqueous solution. The material was characterized by infrared spectroscopy (IR) in order to evaluate the efficiency of modification of matrix, the vermiculite, the organic material, chitosan. The thermal stability of the material and the ratio clay / polymer was evaluated by thermogravimetry. To evaluate the surface of the material was used in scanning electron microscopy (SEM) and (BET). The BET analysis revealed a significant increase in surface area of vermiculite that after interaction with chitosan, was obtained a value of 21, 6156 m2 / g. Adsorption tests were performed according to the particle size, concentration and time. The results show that the capacity of removal of ions through the vermiculite was on average 88.4% for lead in concentrations ranging from 20-200 mg / L and 64.2% in the concentration range of 1000 mg / L. Regarding the particle size, there was an increase in adsorption with decreasing particle size. In fuction to the time of contact, was observed adsorption equilibrium in 60 minutes with adsorption capacity. The data of the isotherms were fitted to equation Freundlich. The kinetic study of adsorption showed that the pseudo second- order model best describes the adsorption adsorption, having been found following values K2=0,024 g. mg-1 min-1and Qmax=25,75 mg/g, value very close to the calculated Qe = 26.31 mg / g. From the results we can conclude that the material can be used in wastewater treatment systems as a source of metal ions adsorbent due to its high adsorption capacity

Ateliês de história e pedagogia da matemática: contribuições para a formação de professores que ensinam matemática nos anos iniciais

This paper presents a discussion about the use of the History of Mathematics as an educational resource and conceptual mediator in the formation of teachers who teach mathematics in the years of elementary school. It was a qualitative action method, in order to show the importance of holding workshops of History and Pedagogy of Mathematics as contribution to overcome the conceptual difficulties of teaching and teachers regarding the content covered in the course of education and afterwards they have to teach in the early of elementary school. We assume that understanding the historical, social and cultural comprehension as a conceptual and didactic focus effectively nurture the pursuit of a teaching and learning of mathematics students safe and justified in order to contribute to overcoming the difficulties of teaching and learning usually occurred in the classroom of the early years. In this sense, we organized a study group formed by students of Bachelors in Education and Mathematics at the University of Piauí. We developed five training workshops in History and Pedagogy of Mathematics, with a workload of 20 hours each and four follow-up sessions and advicement, totalizing 180 hours. The purpose of workshops was to develop studies on the History of Mathematics that could support the formation of a conceptual and didactic group with a view to prepare teaching materials and activities based on information drawn from undertaken historical studies .The products designed were used in formation of the group itself and will later be used in training teachers of public school in Teresina, in the form of workshop of History and Pedagogy of Mathematics in order to overcome problems arising from teaching and conceptual this education degree in Education Based on the obtained informations it was possible to suggest new referrals procedural level of education and university extension that may contribute to the reorientation of initial and continuing training of teachers in the early years elementary school

Estudo e implementação em plantas físicas de um controlador preditivo generalizado com restrições

This work shows a study about the Generalized Predictive Controllers with Restrictions and their implementation in physical plants. Three types of restrictions will be discussed: restrictions in the variation rate of the signal control, restrictions in the amplitude of the signal control and restrictions in the amplitude of the Out signal (plant response). At the predictive control, the control law is obtained by the minimization of an objective function. To consider the restrictions, this minimization of the objective function is done by the use of a method to solve optimizing problems with restrictions. The chosen method was the Rosen Algorithm (based on the Gradient-projection). The physical plants in this study are two didactical systems of water level control. The first order one (a simple tank) and another of second order, which is formed by two tanks connected in cascade. The codes are implemented in C++ language and the communication with the system to be done through using a data acquisition panel offered by the system producer

Simulador computacional para poços de petróleo com método de elevação artificial por bombeio mecânico

This work proposes a computer simulator for sucker rod pumped vertical wells. The simulator is able to represent the dynamic behavior of the systems and the computation of several important parameters, allowing the easy visualization of several pertinent phenomena. The use of the simulator allows the execution of several tests at lower costs and shorter times, than real wells experiments. The simulation uses a model based on the dynamic behavior of the rod string. This dynamic model is represented by a second order partial differencial equation. Through this model, several common field situations can be verified. Moreover, the simulation includes 3D animations, facilitating the physical understanding of the process, due to a better visual interpretation of the phenomena. Another important characteristic is the emulation of the main sensors used in sucker rod pumping automation. The emulation of the sensors is implemented through a microcontrolled interface between the simulator and the industrial controllers. By means of this interface, the controllers interpret the simulator as a real well. A "fault module" was included in the simulator. This module incorporates the six more important faults found in sucker rod pumping. Therefore, the analysis and verification of these problems through the simulator, allows the user to identify such situations that otherwise could be observed only in the field. The simulation of these faults receives a different treatment due to the different boundary conditions imposed to the numeric solution of the problem. Possible applications of the simulator are: the design and analysis of wells, training of technicians and engineers, execution of tests in controllers and supervisory systems, and validation of control algorithms

Métodos numéricos para resolução de equações diferenciais ordinárias lineares baseados em interpolação por spline

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the traditional solvers such as Runge-Kutta, and avoids root calculations in the linear time invariant case. The method is then applied on a central problem of control theory, namely, the step response problem for linear EDOs with possibly varying coefficients, where root calculations do not apply. We have implemented an efficient algorithm which uses exclusively matrix-vector operations. The working interval (till the settling time) was determined through a calculation of the least stable mode using a modified power method. Several variants of the method have been compared by simulation. For general linear problems with fine grid, the proposed method compares favorably with the Euler method. In the time invariant case, where the alternative is root calculation, we have indications that the proposed method is competitive for equations of sifficiently high order.

Adsorção de Mn (II) e Zn (II) em soluções aquosas usando perlita expandida revestida com quitosana

In this work, chitosan was used as a coating of pure perlite in order to increase the accessibility of the groups OH- e NH2+the adsorptionof ions Mn2+ e Zn2+.The characterization results of the expanded perlite classified as microporous and whose surface area 3,176 m2 g-1after the change resulted in 4,664 m2g-1.From the thermogravimetry(TG) it was found that the percentage of coating was34,3%.The infrared analysis can prove the presence of groups Si-OH, Si-O e Al-O-Siresulting from the perlite and C=O, NH2and OH characterization of chitosan. The experiments on experiments on the adsorption of Mn and Zn were performed in the concentration range of10 a 50 mgL-1and the adsorption capacity inpH 5,8 e 5,2 was 19,49 and 23,09 mgg-1to 25 oC,respectively.The adsorption data were best fitted to Langmuir adsorption model to Langmuir adsorption model for both metalionsisindicative of monolayer adsorption. The kinetics of adsorption were calculated from the equation of Lagergren fitting the model pseudo-second-order for all initial concentrations, suggesting that adsorption of ions Mn2+ and Zn2+ follows the kinetics of pseudo-second-order and whose constant Speedk2(g/mg.min) are 0,105 e 3,98 and capacity and maximum removal qe 4,326 e 3,348,respectively.In this study we used a square wave voltammetry cathodic stripping voltammetry to quantify the adsorbed ions, and the working electrode glassy carbon, reference electrode silver / silver chloride and a platinum auxiliary electrode. The attainment of the peaks corresponding to ions Mn2+ and Zn2+ was evaluated in and electrochemical cell with a capacity of 30 mL using a buffer system (Na2HPO4/NaH2PO4)at pH 4 and was adjusted with solutionsH3PO4 0,1molL-1and NaOH 0,1 molL-1and addition of the analyte has been a cathodic peak in- 0,873 Vand detection limit of2,55x10-6molL-1para Zn.The dough used for obtaining the adsorption isotherm was 150 mg and reached in 120 min time of equilibrium for both metal ions.The maximum adsorption for 120 min with Mn concentration 20 mgL-1 and Zn 10 mgL-1,was91, 09 e 94, 34%, respectively

Comparação entre técnicas de nitretação em cátodo oco e gaiola catódica na deposição de TiN

The plasma nitriding has been used in industrial and technological applications for large-scale show an improvement in the mechanical, tribological, among others. In order to solve problems arising in the conventional nitriding, for example, rings constraint (edge effect) techniques have been developed with different cathodes. In this work, we studied surfaces of commercially pure titanium (Grade II), modified by plasma nitriding treatment through different settings cathodes (hollow cathode, cathodic cage with a cage and cathodic cage with two cages) varying the temperature 350, 400 and 430oC, with the goal of obtaining a surface optimization for technological applications, evaluating which treatment generally showed better results under the substrate. The samples were characterized by the techniques of testing for Atomic Force Microscopy (AFM), Raman spectroscopy, microhardness, X-ray diffraction (XRD), and a macroscopic analysis. Thus, we were able to evaluate the processing properties, such as roughness, topography, the presence of interstitial elements, hardness, homogeneity, uniformity and thickness of the nitrided layer. It was observed that all samples were exposed to nitriding modified relative to the control sample (no treatment) thus having increased surface hardness, the presence of TiN observed by XRD as per both Raman and a significant change in the roughness of the treated samples . It was found that treatment in hollow cathode, despite having the lowest value of microhardness between treated samples, was presented the lowest surface roughness, although this configuration samples suffer greater physical aggressiveness of treatment

Estudo da eficiência dos adsorventes de Al2O3 e Fe/Al2O3 para remoção de BTX presente em água contaminada com gasolina

Contamination of groundwater by BTX has been featured in recent decades. This type of contamination is due to small and continuous leaks at gas stations, causing serious problems to public health and the environment. Based on these antecedents, the search for new alternatives for treating contaminated water is shown to be essential. Therefore, this study aimed to evaluate the efficiency of removal of BTX by adsorption processes employing commercial alumina (Al2O3) and alumina supported with iron (Fe/Al2O3) as adsorbents. It was prepared by a in a synthetic gasoline solution and distilled water to simulate an actual sample. Initially, the adsorbents were characterized by techniques XRD, TG / DTG, XRF, FTIR and SEM/EDS, several trials, where he was placed synthetic solution to react in the presence of Al2O3 and Fe/Al2O3 in a closed, mechanical stirring system were performed varying the catalyst concentration 2, 4 and 6 g.L-1 every 0, 10, 30 60, 90 and 120 min, aliquots were taken and brought to analysis by gas chromatography flame ionization with headspace extraction. The results indicated that the absorbent which has higher BTX removal capacity was the Fe/Al2O3 at a concentration of 6 g.L-1, pH = 4 and time of 90 minutes reaction, resulting in an efficiency, resulting in a 86,5% efficiency for benzene removal, for the 95,4% toluene, 90,8% for ɱ,ρ- xylene and 93.7% for the θ-xylenes. Subsequently, we performed a kinetic study of the reactions, the values of experimental adsorption capacity (qe) showed agreement with the values of the theoretical adsorption capacity (qc) to the pseudo-second-order model in the adsorption tests using 2 and 6 gL-1 of Al2O3 and assays using 2, 4 and 6 g.L-1 of Fe/Al2O3. A fact corroborated by the R2 values, thus indicating that the chemical interactions are present in the adsorption mechanisms of BTX.