Desempenho e qualidade de frutos de tomateiro em cultivo protegido com diferentes números de hastes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

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

Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem

Os artigos de Euler sobre os números amigáveis

Among the many methodological resources that the mathematics teacher can use in the classroom, we can cite the History of Mathematics which has contributed to the development of activities that promotes students curiosity about mathematics and its history. In this regard, the present dissertation aims to translate and analyze, mathematically and historically, the three works of Euler about amicable numbers that were writed during the Eighteenth century with the same title: De numeris amicabilibus. These works, despite being written in 1747 when Euler lived in Berlin, were published in different times and places. The first, published in 1747 in Nova Acta Eruditorum and which received the number E100 in the Eneström index, summarizes the historical context of amicable numbers, mentions the formula 2nxy & 2nz used by his precursors and presents a table containing thirty pairs of amicable numbers. The second work, E152, was published in 1750 in Opuscula varii argument. It is the result of a comprehensive review of Euler s research on amicable numbers which resulted in a catalog containing 61 pairs, a quantity which had never been achieved by any mathematician before Euler. Finally, the third work, E798, which was published in 1849 at the Opera postuma, was probably the first among the three works, to be written by Euler

Prevalência e susceptibilidade antimicrobiana de Staphylococcusspp. em quadros de saúde e doença periodontal

The aim of this study was determine the prevalence and antimicrobial susceptibility of Staphylococcus spp. from patients with periodontal disease and periodontally healthy, correlate them with factors to host, local environment and traits of the diseases. To this, thirty adults from 19 to 55 years old were selected. They had not periodontal treatment and no antibiotic or antimicrobial was administered during three previous months. From these individuals, sites periodontally healthy, with chronic gingivitis and/or periodontitis were analyzed. Eighteen subgingival dental biofilm samples were collected through sterile paper points being six from each tooth randomly selected, representing conditions mentioned. They were transported to Oral Microbiology laboratory, plated onto Mannitol Salt Agar (MSA) and incubated at 370C in air for 48 h. Staphylococcus spp. were identified by colonial morphology, Gram stain, catalase reaction, susceptibility to bacitracin and coagulase activity. After identification, strains were submitted to the antibiotic susceptibility test with 12 antimicrobials, based on Kirby-Bauer technique. To establish the relation between coagulase-negative Staphylococcus (CSN) presence and their infection levels and host factors, local environment and traits of diseases were used Chi-square, Mann-Whitney and Kruskal-Wallis tests to a confidence level of 95%. 86,7% subjects harbored CSN in 11,7% periodontal sites. These prevalence were 12,1% in healthy sites, 11,7% in chronic gingivitis, 13,5% in slight chronic periodontitis, 6,75% in moderate chronic periodontitis and in sites with advance chronic periodontitis was not isolated CSN, without difference among them (p = 0,672). There was no significant difference to presence and infection levels of CSN as related to host factors, local environm ent and traits of the diseases. Amongst the 74 samples of CSN isolated, the biggest resistance was observed to penicillin (55,4%), erythromycin (32,4%), tetracycline (12,16%) and clindamycin (9,4%). 5,3% of the isolates were resistant to oxacilin and methicillin. No resistance was observed to ciprofloxacin, rifampicin and vancomycin. It was concluded that staphylococci are found in low numbers in healthy or sick periodontal sites in a similar ratio. However, a trend was observed to a reduction in staphylococci occurrence toward more advanced stages of the disease. This low prevalence was not related to any variables analyzed. Susceptibility profile to antibiotics demonstrates a raised resistance to penicillin and a low one to methicillin. To erythromycin, tetracycline and clindamycin was observed a significant resistance

Computabilidade no espaço dos intervalos reais: um modelo BSS intervalar

A matemática intervalar é uma teoria matemática originada na década de 60 com o objetivo de responder questões de exatidão e eficiência que surgem na prática da computação científica e na resolução de problemas numéricos. As abordagens clássicas para teoria da computabilidade tratam com problemas discretos (por exemplo, sobre os números naturais, números inteiros, strings sobre um alfabeto finito, grafos, etc.). No entanto, campos da matemática pura e aplicada tratam com problemas envolvendo números reais e números complexos. Isto acontece, por exemplo, em análise numérica, sistemas dinâmicos, geometria computacional e teoria da otimização. Assim, uma abordagem computacional para problemas contínuos é desejável, ou ainda necessária, para tratar formalmente com computações analógicas e computações científicas em geral. Na literatura existem diferentes abordagens para a computabilidade nos números reais, mas, uma importante diferença entre estas abordagens está na maneira como é representado o número real. Existem basicamente duas linhas de estudo da computabilidade no contínuo. Na primeira delas uma aproximação da saída com precisão arbitrária é computada a partir de uma aproximação razoável da entrada [Bra95]. A outra linha de pesquisa para computabilidade real foi desenvolvida por Blum, Shub e Smale [BSS89]. Nesta aproximação, as chamadas máquinas BSS, um número real é visto como uma entidade acabada e as funções computáveis são geradas a partir de uma classe de funções básicas (numa maneira similar às funções parciais recursivas). Nesta dissertação estudaremos o modelo BSS, usado para se caracterizar uma teoria da computabilidade sobre os números reais e estenderemos este para se modelar a computabilidade no espaço dos intervalos reais. Assim, aqui veremos uma aproximação para computabilidade intervalar epistemologicamente diferente da estudada por Bedregal e Acióly [Bed96, BA97a, BA97b], na qual um intervalo real é visto como o limite de intervalos racionais, e a computabilidade de uma função intervalar real depende da computabilidade de uma função sobre os intervalos racionais

Estudo do leite de éguas sadias ou portadoras de mastite subclínica, pelo teste de Whiteside, análise microbiológica e contagem de células somáticas

Com o objetivo de identificar a microbiota existente no leite de éguas normais ou portadoras de mastite subclínica, coletaram-se amostras (10 a 15 ml) de leite de 38 animais, que foram examinadas pelo teste de Whiteside, após a homogeneização das amostras dos dois tetos de cada animal. Os resultados foram negativos. Os exames microbiológicos realizados em meios de ágar sangue bovino 10% e ágar MacConkey revelaram presença de bactérias do gênero Staphylococcus spp. e Streptococcus spp. A contagem de células somáticas de amostras individuais de cada teto revelou números superiores a 500.000 células/ml de leite em somente 9,3% das 73 amostras de leite examinadas. Os resultados sugerem a realização de novos estudos objetivando-se a padronização do número de células somáticas no leite de éguas.

A revisão do Código Florestal Brasileiro: impactos negativos para a conservação dos anfíbios

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estudo da produção de beta -lactamase e sensibilidade às drogas em linhagens de estafilococos coagulase-negativos isolados de recém-nascidos

Os estafilococos coagulase-negativos (ECN), embora reconhecidos como saprófitas por muito tempo, têm emergido como agentes etiológicos de uma série de infecções, sendo atualmente os principais responsáveis por sepse em UTI neonatal. Tendo em vista estas características, este estudo objetivou a identificação de estafilococos coagulase-negativos isolados de processos infecciosos em recém-nascidos, bem como a determinação da produção de beta-lactamase e sensibilidade às drogas pelas linhagens isoladas. O Staphylococcus epidermidis foi a espécie mais freqüentemente isolada (77,8%). O estudo da produção de beta-lactamase revelou esta característica na maioria das linhagens de ECN isoladas (71,8%). As linhagens de ECN mostraram, ainda, resistência múltipla aos antibióticos utilizados, com 63,2% dos isolados apresentando resistência a cinco ou mais drogas. A elevada transmissibilidade de plasmídios entre estas linhagens e o uso abusivo de drogas antimicrobianas têm-se constituído em importantes fatores na seleção de amostras multirresistentes e na transferência de genes de resistência.

Pesquisa de suínos portadores renais de leptospiras pelo isolamento microbiano e reação em cadeia pela polimerase em amostras de rins de animais sorologicamente positivos e negativos para leptospirose

Com o intuito de se estudar a presença de suínos portadores renais de leptospiras foram colhidas 131 amostras sanguíneas e os respectivos rins de animais durante o abate em abatedouro da região de Botucatu-SP. Pela prova de Soroaglutinação Microscópica obteve-se 48 amostras sorológicas positivas para um ou mais sorovar de Leptospira spp., com uma taxa de ocorrência de anticorpos anti-leptospira de 36,64%, e maior importância para o sorovar icterohaemorrhagiae. Para a pesquisa do agente nos rins, das 88 amostras renais submetidas a cultura em meio de EMJH e analisadas pela prova de PCR, foi isolado e detectado o agente em uma única amostra renal, pertencente a um animal soropositivo. Embora não tenha sido possível a comparação estatística, em termos de sensibilidade e especificidade das duas provas de detecção do agente a partir de amostras renais, a PCR mostrou-se mais rápida e prática na pesquisa de portadores renais. Pelo isolamento obtido, ressalta-se a importância desses animais como possíveis transmissores da doença para trabalhadores de abatedouro e inspetores de carne.