Uma análise dos questionamentos dos alunos nas aulas de números complexos

This work presents a contribution for the studies reffering to the use of the History of Mathematics focusing on the improvement of the Teaching and Learning Process. It considers that the History of Matematics, as a way of giving meaning to the discipline and improve the quality of the Teaching and Learning Process. This research focuses on the questions of the students, classified in three categories of whys: the chronological, the logical and the pedagogical ones. Therefore, it is investigated the teaching of the Complex Numbers, from the questions of the students of the Centro Federal de Educação Tecnológica do Rio Grande do Norte (Educational Institution of Professional and Technology Education from Rio Grande do Norte). The work has the following goals: To classify and to analyse the questions of the students about the Complex Numbers in the classes of second grade of the High School, and to collate with the pointed categories used by Jones; To disccus what are the possible guidings that teachers of Mathematics can give to these questions; To present the resources needed to give support to the teacher in all things involving the History of Mathematics. Finally, to present a bibliographic research, trying to reveal supporting material to the teacher, with contents that articulate the Teaching of Mathematics with the History of Mathematics. It was found that the questionings of the pupils reffers more to the pedagogical whys, and the didatic books little contemplate other aspects of the history and little say about the sprouting and the evolution of methods of calculations used by us as well

O uso pedagógico de uma seqüência didática para a aquisição de algumas idéias relacionadas ao conceito de números complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

Os Polímeros como Sistemas Complexos

Neste trabalho, através de simulações computacionais, identificamos os fenômenos físicos associados ao crescimento e a dinâmica de polímeros como sistemas complexos exibindo comportamentos não linearidades, caos, criticalidade auto-organizada, entre outros. No primeiro capítulo, iniciamos com uma breve introdução onde descrevemos alguns conceitos básicos importantes ao entendimento do nosso trabalho. O capítulo 2 consiste na descrição do nosso estudo da distribuição de segmentos num polímero ramificado. Baseado em cálculos semelhantes aos usados em cadeias poliméricas lineares, utilizamos o modelo de crescimento para polímeros ramificados (Branched Polymer Growth Model - BPGM) proposto por Lucena et al., e analisamos a distribuição de probabilidade dos monômeros num polímero ramificado em 2 dimensões, até então desconhecida. No capítulo seguinte estudamos a classe de universalidade dos polímeros ramificados gerados pelo BPGM. Utilizando simulações computacionais em 3 dimensões do modelo proposto por Lucena et al., calculamos algumas dimensões críticas (dimensões fractal, mínima e química) para tentar elucidar a questão da classe de universalidade. Ainda neste Capítulo, descrevemos um novo modelo para a simulação de polímeros ramificados que foi por nós desenvolvido de modo a poupar esforço computacional. Em seguida, no capítulo 4 estudamos o comportamento caótico do crescimento de polímeros gerados pelo BPGM. Partimos de polímeros criticamente organizados e utilizamos uma técnica muito semelhante aquela usada em transições de fase em Modelos de Ising para estudar propagação de danos chamada de Distância de Hamming. Vimos que a distância de Hamming para o caso dos polímeros ramificados se comporta como uma lei de potência, indicando um caráter não-extensivo na dinâmica de crescimento. No Capítulo 5 analisamos o movimento molecular de cadeias poliméricas na presença de obstáculos e de gradientes de potenciais. Usamos um modelo generalizado de reptação para estudar a difusão de polímeros lineares em meios desordenados. Investigamos a evolução temporal destas cadeias em redes quadradas e medimos os tempos característicos de transporte t. Finalizamos esta dissertação com um capítulo contendo a conclusão geral denoss o trabalho (Capítulo 6), mais dois apêndices (Apêndices A e B) contendo a fenomenologia básica para alguns conceitos que utilizaremos ao longo desta tese (Fractais e Percolação respectivamente) e um terceiro e ´ultimo apêndice (Apêndice C) contendo uma descrição de um programa de computador para simular o crescimentos de polímeros ramificados em uma rede quadrada

Estudo de sistemas complexos com interações de longo alcance : percolação, redes e tráfego

In this thesis we investigate physical problems which present a high degree of complexity using tools and models of Statistical Mechanics. We give a special attention to systems with long-range interactions, such as one-dimensional long-range bondpercolation, complex networks without metric and vehicular traffic. The flux in linear chain (percolation) with bond between first neighbor only happens if pc = 1, but when we consider long-range interactions , the situation is completely different, i.e., the transitions between the percolating phase and non-percolating phase happens for pc < 1. This kind of transition happens even when the system is diluted ( dilution of sites ). Some of these effects are investigated in this work, for example, the extensivity of the system, the relation between critical properties and the dilution, etc. In particular we show that the dilution does not change the universality of the system. In another work, we analyze the implications of using a power law quality distribution for vertices in the growth dynamics of a network studied by Bianconi and Barabási. It incorporates in the preferential attachment the different ability (fitness) of the nodes to compete for links. Finally, we study the vehicular traffic on road networks when it is submitted to an increasing flux of cars. In this way, we develop two models which enable the analysis of the total flux on each road as well as the flux leaving the system and the behavior of the total number of congested roads

Estudo de propriedades críticas em sistemas complexos: método de procura automática em sistemas tipo Ising e percolação de longo alcance

The new technique for automatic search of the order parameters and critical properties is applied to several well-know physical systems, testing the efficiency of such a procedure, in order to apply it for complex systems in general. The automatic-search method is combined with Monte Carlo simulations, which makes use of a given dynamical rule for the time evolution of the system. In the problems inves¬tigated, the Metropolis and Glauber dynamics produced essentially equivalent results. We present a brief introduction to critical phenomena and phase transitions. We describe the automatic-search method and discuss some previous works, where the method has been applied successfully. We apply the method for the ferromagnetic fsing model, computing the critical fron¬tiers and the magnetization exponent (3 for several geometric lattices. We also apply the method for the site-diluted ferromagnetic Ising model on a square lattice, computing its critical frontier, as well as the magnetization exponent f3 and the susceptibility exponent 7. We verify that the universality class of the system remains unchanged when the site dilution is introduced. We study the problem of long-range bond percolation in a diluted linear chain and discuss the non-extensivity questions inherent to long-range-interaction systems. Finally we present our conclusions and possible extensions of this work

Representações espectrais de sistemas complexos: aplicações à síntese de superfícies brownianas fracionárias anisotrópicas, filtragem de sinais e identificação de correlações

In this thesis, we study the application of spectral representations to the solution of problems in seismic exploration, the synthesis of fractal surfaces and the identification of correlations between one-dimensional signals. We apply a new approach, called Wavelet Coherency, to the study of stratigraphic correlation in well log signals, as an attempt to identify layers from the same geological formation, showing that the representation in wavelet space, with introduction of scale domain, can facilitate the process of comparing patterns in geophysical signals. We have introduced a new model for the generation of anisotropic fractional brownian surfaces based on curvelet transform, a new multiscale tool which can be seen as a generalization of the wavelet transform to include the direction component in multidimensional spaces. We have tested our model with a modified version of the Directional Average Method (DAM) to evaluate the anisotropy of fractional brownian surfaces. We also used the directional behavior of the curvelets to attack an important problem in seismic exploration: the atenuation of the ground roll, present in seismograms as a result of surface Rayleigh waves. The techniques employed are effective, leading to sparse representation of the signals, and, consequently, to good resolutions

A percepção dos docentes da UFRN sobre o programa de apoio a planos de reestruturação e ampliação das universidades federais - REUNI

In recent decades higher education in Brazil has gone through several changes. The Programa de Reestruturação e Expansão das Universidades Federais REUNI has been the greatest overhaul performed by the government in public universities in the last years. REUNI is presented as the biggest reform in tertiary education in contemporary times, having as the main goal a gradual increase in the average rate of conclusion in live learning graduation courses up to 90%, as well as a rate expansion of graduating students in face to face classes per professor. This research aims at studying the perception of professors from UFRN concerning the REUNI program in execution from 2008 until 2012. The study seeks to understand how professors evaluate the program and what the dimensions that most influence in this evaluation are. The study made use of a research tool (survey) which was sent through the internal system of the university, SIGAdmin, to all professors of superior teaching from UFRN. The answers generated by the survey were processed using SPSS statistical software (Statistical Package for Social Science). Factorial Analysis and Multiple Linear Regression were used as an analysis technique. 180 answers were obtained, reaching all UFRN Centers and some academic units, as well as some campuses in the countryside of the state. Through the research was possible to analyze how professors from UFRN perceive the REUNI program implemented in the institution. The results point to the program approval by the professors. Statistical tests showed that the average values obtained in the Centers and academic units are basically the same. It was demonstrated that the extent that most influenced in the answers is linked to practical outcomes of the program, whereas the knowledge of REUNI goals was the least that impacted on the marks given to the program. Another dimension which influenced the perception of professors relates to the influence of REUNI in their activities. It was observed that professors from UFRN don t see REUNI as an impediment to them

Análise de sedimento de fundo: uma amostragem representativa do estuário Potengi/RN

The aim of this study is to quantify the presence of major and minor elements in the sediments of estuary Potengi. Four georeferenced sampling points were used in the study, at which sediment samples were collected in the channel of the river and on the right and left banks. In addition, dissolved oxygen, salinity and water conductivity were taken in situ at the time of sample collection. The percentage of organic matter, determined by gravimetry, and granulometric analysis of the sediment samples were conducted in the laboratory. To quantify the major and minor elements a prior test to open the sample was conducted with standard NIST 1646ª estuarine sediment to choose the best methodology to be adopted. The sediment samples were dissolved in microwaves with nitric acid and chloridric acid, according to methodology proposed by US EPA 3051ª. Quantitative analyses of the elements Al, Fe, Cd, Cr, Cu, Mn, Ni, Pb and Zn were conducted by inductively coupled plasma optical emission spectrometry (ICPOES). The results showed that the partial concentrations of the elements analyzed are below average worldwide shale levels, the standard described by Turekian and Wedepohl (1961)

Complexos metálicos de cobalto, níquel e cobre com a Pirazina-2-carboxamida e 4- hidrazida ácida piridincarboxílica: síntese e caracterização

This work involved the synthesis, characterization and proposing the molecular structure of coordination compounds involving ligands pyrazine-2-carboxamide (PZA) and 4- hydrazide acidic pyridine carboxylic (INH) and metals of the first transition series (M = Co2+, Ni2+ and Cu2+). For the characterization of the compounds used were analytical techniques such as infrared absorption spectroscopy average (FT-IR) molar conductivity measurements, CHN elemental analysis, EDTA Complexometric, measurement of melting point, X-ray diffraction by powder method, Thermogravimetry (TG) and Differential Thermal Analysis (DTA) and Simultaneous Differential Scanning Calorimetry (DSC). The absorption spectra in the infrared region suggested that the ligand coordination to the metal center occurs through the carbonyl oxygen atom and nitrogen alpha pyrazine ring to those complexes formed with PZA. For INH complexes with metal-ligand coordination is through the carbonyl oxygen and nitrogen of the terminal hydrazide grouping. The conductivity measurements of the complexes in aqueous solution they suggest to all behavior of the type 1:2 electrolytes, and conduct of non-electrolytes in acetonitrile. The results obtained by CHN elemental analysis and EDTA Complexometric allowed to infer the stoichiometry of the compounds synthesized. For all of the complexes obtained was possible to record the melting points, neither of which melted near the melting temperature of the free ligands. The X-ray diffraction showed that the complexes of pyrazinamide exhibited diffraction lines, suggesting that these compounds are crystalline, while compounds of isoniazid, with the exception of cobalt, exhibited diffraction lines, indicating that they are crystalline. The results from the TG-DTA and DSC allowed information regarding the dehydration and thermal decomposition of these complexes

Síntese, caracterização e estudo fotofísico de complexos de 4,4- diaminoestilbeno-2,2-dissulfonato com íons lantanídeos

This is a work involving fundamental studies of chemistry where the synthesis and structural characterization, as well as a possible future application of these new compounds as luminescent sensors or sunscreen agents, complexes with 4,4 diaminostilbene-2,2-disulfonic (DSD) and trivalent lanthanide ions La3+, Nd3+, Eu3+, Gd3+ and Yb3+, were synthesized in the ratio of 3 mmol: 1 mmol (DSD: lanthanides). The complexes obtained with these ions were present in powder form and were characterized by complexometric titration with EDTA CHN Elemental analysis, molecular absorption spectroscopy in the ultraviolet region, the absorption spectroscopy in the infrared, thermal analysis (TG / DTG), Nuclear Magnetic Resonance - NMR 1H and Luminescence Spectroscopy. The complexometric titration and CHN analysis, confirmed the TG / DTG which suggest that these complexes have the following general chemical formulas: [La2(C14H12S2O6N2)2(H2O)2Cl2].7H2O,[Nd2(C14H12S2O6N2)2(H2O)2Cl2].6H2O,[Eu2(C14 H12S2O6N2)2(H2O)2Cl2].7H2O,[Gd2(C14H12S2O6N2)2(H2O)2Cl2].4H2O e [Yb2(C14H12S2O6N2)2(H2O)2].6H2O. The disappearance of the bands in the infrared spectrum at 2921 cm-1 and 2623 cm-1 and the displacement of the bands in the spectra of the amine complex indicate that the lanthanide ion is coordinated to the oxygen atoms and the sulfonate groups of the nitrogens amines, suggesting the formation of the dimer. The disappearance of the signal and the displacement signal SO3H amines in the 1H NMR spectrum of this complex are also indicative coordination and dimer formation. The Thermogravimetry indicates that the DSD is thermally stable in the range of 40º to 385°C and their complexes with lanthanide ions exhibit weight loss between 4 and 5 stages. The Uv-visible spectra indicated that the DSD and complexes exhibit cis isomers. The analysis of luminescence indicates that the complexes do not exhibit emission in the region of the lanthanides but an intense emission part of the binder. This is related to the triplet states of the ligand, which are in the lowest energy state emitting lanthanide ions, and also the formation of the dimer that suppress the luminescence of ion Eu3+. The formation of dimer was also confirmed by calculating the europium complex structure using the model Hamiltonian PM6 and Sparkle

Obtenção de dispersões de complexos polieletrolíticos à base de quitosana e poli(ácido metacrílico) e análise de adsorção de albumina bovina sérica

Dispersions composed of polyelectrolyte complexes based on chitosan and poly(methacrylic acid), PMAA, were obtained by the dropping method and template polymerization. The effect of molecular weight of PMAA and ionic strength on the formation of chitosan/poly(methacrylic acid), CS/PMAA, complexes was evaluated using the dropping method. The increase in molecular weight of PMAA inhibited the formation of insoluble complexes, while the increase in ionic strength first favored the formation of the complex followed by inhibiting it at higher concentrations. The polyelectrolyte complexation was strongly dependent on macromolecular dimensions, both in terms of molecular weight and of coil expansion/contraction driven by polyelectrolyte effect. The resultant particles from dropping method and template polymerization were characterized as having regions with different charge densities: chitosan predominating in the core and poly(methacrylic acid) at the surface, the particles being negatively charged, as a consequence. Albumin was adsorbed on templatepolymerized CS/PMAA complexes (after crosslinking with glutardialdehyde) and pH was controlled in order to obtain two conditions: (i) adsorption of positively charged albumin, and (ii) adsorption of albumin at its isoelectric point. Adsorption isotherms and zeta potential measurements showed that albumin adsorption was controlled by hydrogen bonding/van der Waals interactions and that brushlike structures may enhance adsorption of albumin on these particles

O Serviço Social nas operadoras de planos privados de assistência à saúde: demandas, atribuições e respostas profissionais

The present study deals with the exercise of professional social workers in private health care plans registered with the Regional Council of Medicine/RN, in the city of Natal/RN, with regards to the demands/tasks, work conditions, and the professional response, given the climate of restructuring the capital. The set of socio-historical transformations, as a results of the dynamic capitalist, is a process of new configurations in relation to state and society that interfere directly in relation to working conditions, social rights historically won by workers. In this context, the operator of health plans arises as a possibilities to provide services in health, through the logic of the market, in which the subjects of law, become consumers contributing to the displacement of the responsibilities of the State. Obligating workers to lessen the burden with the reproduction of their workforce. This involves changing societal context for social service, since it is one of the professions that are active in terms of the immediate social issue, and come as part of the collective worker. From qualitative research based on a theoretical and methodological perspective and critical dialectics, it was possible to unveil some features and trends of the exercise of(a) social operators in private health care plans. The survey results indicated that : a) the demands and duties for certain social service, are associated with the redevelopment of the capital, whose requirements and responsibilities professionals have with their needs, particularly the guarantee of profit, services rendered; b) in the conditions of work there is a trend of insecurity uncertainty and dismantling of professionals; c) the answers professionals suffer the limits and contradictions present in the daily training, mainly depending one the characteristics of management and operation of the operators, which has professional relative autonomy

Lógica BDI fuzzy

Intendding to understand how the human mind operates, some philosophers and psycologists began to study about rationality. Theories were built from those studies and nowadays that interest have been extended to many other areas such as computing engineering and computing science, but with a minimal distinction at its goal: to understand the mind operational proccess and apply it on agents modelling to become possible the implementation (of softwares or hardwares) with the agent-oriented paradigm where agents are able to deliberate their own plans of actions. In computing science, the sub-area of multiagents systems has progressed using several works concerning artificial intelligence, computational logic, distributed systems, games theory and even philosophy and psycology. This present work hopes to show how it can be get a logical formalisation extention of a rational agents architecture model called BDI (based in a philosophic Bratman s Theory) in which agents are capable to deliberate actions from its beliefs, desires and intentions. The formalisation of this model is called BDI logic and it is a modal logic (in general it is a branching time logic) with three access relations: B, D and I. And here, it will show two possible extentions that tranform BDI logic in a modal-fuzzy logic where the formulae and the access relations can be evaluated by values from the interval [0,1]

Estudo de Fractalidade e Evolução Dinâmica de Sistemas Complexos

In this work, the study of some complex systems is done with use of two distinct procedures. In the first part, we have studied the usage of Wavelet transform on analysis and characterization of (multi)fractal time series. We have test the reliability of Wavelet Transform Modulus Maxima method (WTMM) in respect to the multifractal formalism, trough the calculation of the singularity spectrum of time series whose fractality is well known a priori. Next, we have use the Wavelet Transform Modulus Maxima method to study the fractality of lungs crackles sounds, a biological time series. Since the crackles sounds are due to the opening of a pulmonary airway bronchi, bronchioles and alveoli which was initially closed, we can get information on the phenomenon of the airway opening cascade of the whole lung. Once this phenomenon is associated with the pulmonar tree architecture, which displays fractal geometry, the analysis and fractal characterization of this noise may provide us with important parameters for comparison between healthy lungs and those affected by disorders that affect the geometry of the tree lung, such as the obstructive and parenchymal degenerative diseases, which occurs, for example, in pulmonary emphysema. In the second part, we study a site percolation model for square lattices, where the percolating cluster grows governed by a control rule, corresponding to a method of automatic search. In this model of percolation, which have characteristics of self-organized criticality, the method does not use the automated search on Leaths algorithm. It uses the following control rule: pt+1 = pt + k(Rc − Rt), where p is the probability of percolation, k is a kinetic parameter where 0 < k < 1 and R is the fraction of percolating finite square lattices with side L, LxL. This rule provides a time series corresponding to the dynamical evolution of the system, in particular the likelihood of percolation p. We proceed an analysis of scaling of the signal obtained in this way. The model used here enables the study of the automatic search method used for site percolation in square lattices, evaluating the dynamics of their parameters when the system goes to the critical point. It shows that the scaling of , the time elapsed until the system reaches the critical point, and tcor, the time required for the system loses its correlations, are both inversely proportional to k, the kinetic parameter of the control rule. We verify yet that the system has two different time scales after: one in which the system shows noise of type 1 f , indicating to be strongly correlated. Another in which it shows white noise, indicating that the correlation is lost. For large intervals of time the dynamics of the system shows ergodicity

Grafico misto de controle da media com amostragem em dois estagios

This paper proposes a new control chart to monitor a process mean employing a combined npx-X control chart. Basically the procedure consists of splitting the sample of size n into two sub-samples n1 and n2 determined by an optimization search. The sampling occur in two-stages. In the first stage the units of the sub-sample n1 are evaluated by attributes and plotted in npx control chart. If this chart signs then units of second sub-sample are measured and the monitored statistic plotted in X control chart (second stage). If both control charts sign then the process is stopped for adjustment. The possibility of non-inspection in all n items may promote a reduction not only in the cost but also the time spent to examine the sampled items. Performances of the current proposal, individual X and npx control charts are compared. In this study the proposed procedure presents many competitive options for the X control chart for a sample size n and a shift from the target mean. The average time to sign (ATS) of the current proposal lower than the values calculated from an individual X control chart points out that the combined control chart is an efficient tool in monitoring process mean.