Atividades estruturais de equações polinomiais numa abordagem histórica por meio de e-book

The present study investigates how the inter-relationship of the content of polynomial equations works with structured activities and with the history of mathematics through a sequence of activities presented in an e-book, so that the result of this research will proceed will result in a didactic and pedagogic proposal for the teaching of polynomial equations in a historical approach via the reported e-book. Therefore, we have considered in theoretical and methodological assumptions of the History of Mathematics, in structured activities and new technologies with an emphasis on e-book tool. We used as a methodological approach the qualitative research, as our research object adjusts to the objectives of this research mode. As methodological instruments, we used the e-book as a synthesis tool of the sequence of activities to be evaluated, while the questionnaires, semi-structured interviews and participant observation were designed to register and analyze the evaluation made by the research, participants in the structured activities. The processing and analysis of data collected though the questionnaires were organized, classified and quantified in summary tables to facilitate visualization, interpretation, understanding, and analysis of these data. As for participant observation was used to contribute to the qualitative analysis of the quantified data. The interviews were synthetically transcribed and qualitatively analyzed. The analysis ratified our research objectives and contributed to improve, approve and indicate the use of e-book for the teaching of polynomial equations. Thus, we consider that this educational product will bring significant contributions to the teaching of mathematical content, in Basic Education

Desempenho de diferentes equações antropométricas na predição de gordura corporal excessiva em crianças e adolescentes

OBJETIVO: O objetivo do presente estudo foi analisar a eficiência de diferentes equações antropométricas para a identificação de excesso de gordura corporal entre crianças e adolescentes. MÉTODOS: A amostra foi composta por 1.498 indivíduos (678 meninos e 820 meninas), com idade entre 7 e 17 anos (M=13,7, DP=2,0), da cidade de Presidente Prudente (SP). A massa corporal e a estatura foram mensuradas para o cálculo do Índice de Massa Corporal. Também foi realizada a mensuração da circunferência de cintura e das dobras cutâneas subescapular, tricipital, abdominal e da panturrilha. O percentual de gordura corporal foi calculado por meio de quatro equações: Slaughter et al., Slaughter II et al., Dezenberg et al., e Deurenberg et al.. Para indicar a eficiência das diferentes equações antropométricas na indicação da obesidade, foi utilizada a análise da curva Receiver Operating Characteristic Curve. RESULTADOS: No grupo masculino, foram observados valores de sensibilidade elevados (82,4% a 100,0%) e valores oscilando de baixo a alto, para a especificidade (20,9% a 94,9%). Para o sexo feminino, os valores de sensibilidade variaram entre moderado e alto (72,2% a 99,4%); e os de especificidade apresentaram, também, grande oscilação entre baixo e alto (21,6% a 98,2%). CONCLSÃO: A equação proposta por Deurenberg et al., apresentou o melhor desempenho no diagnóstico tanto da presença como da ausência de obesidade na amostra investigada.

Equações preditivas para as pressões respiratórias máximas de crianças brasileiras

I ntroduction: The assessment of respiratory muscle strength is important in the diagnosis and monitoring of the respiratory muscles weakness of respiratory and neuromuscular diseases. However, there are still no studies that provide predictive equations and reference values for maximal respiratory pressures for children in our population. Aim: The purpose of this study was to propose predictive equations for maximal respiratory pressures in healthy school children. Method: This is an observational cross-sectional study. 144 healthy children were assessed. They were students from public and private schools in the city of Natal /RN (63 boys and 81 girls), subdivided in age groups of 7-8 and 9-11 years. The students presented the BMI, for age and sex, between 5 and 85 percentile. Maximal respiratory pressures were measured with the digital manometer MVD300 (Globalmed ®). The maximal inspiratory pressure (MIP) and maximal expiratory pressures (MEP) were measured from residual volume and total lung capacity, respectively. The data were analyzed using the SPSS Statistics 15.0 software (Statistical Package for Social Science) by assigning the significance level of 5%. Descriptive analysis was expressed as mean and standard deviation. T'Student test was used for unpaired comparison of averages of the variables. The comparison of measurements obtained with the predicted values in previous studies was performed using the paired t'Student test. The Pearson correlation test was used to verify the correlation of MRP's with the independent variables (age, sex, weight and height). For the equations analysis the stepwise linear regression was used. Results: By analyzing the data, we observed that in the age range studied MIP was significantly higher in boys. The MEP did not differ between boys and girls aged 7 to 8 years, the reverse occurred in the age between 9 and 11 years. The boys had a significant increase in respiratory muscle strength with advancing age. Regardless sex and age, MEP was always higher than the MIP. The reference values found in this study are similar to a sample of Spanish and Canadian children. The two models proposed in previous studies with children from other countries were not able to consistently predict the values observed in this studied population. The variables sex, age and weight correlated with MIP, whereas the MEP was also correlated with height. However, in the regression models proposed in this study, only gender and age were kept exerting influence on the variability of maximal inspiratory and expiratory pressures. Conclusion: This study provides reference values, lower limits of normality and proposes two models that allow predicting, through the independent variables, sex and age, the value of maximal static respiratory pressures in healthy children aged between 7 and 11 years old

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.

Em direção a uma representação para equações algébricas :uma lógica equacional local

The intervalar arithmetic well-known as arithmetic of Moore, doesn't possess the same properties of the real numbers, and for this reason, it is confronted with a problem of operative nature, when we want to solve intervalar equations as extension of real equations by the usual equality and of the intervalar arithmetic, for this not to possess the inverse addictive, as well as, the property of the distributivity of the multiplication for the sum doesn t be valid for any triplet of intervals. The lack of those properties disables the use of equacional logic, so much for the resolution of an intervalar equation using the same, as for a representation of a real equation, and still, for the algebraic verification of properties of a computational system, whose data are real numbers represented by intervals. However, with the notion of order of information and of approach on intervals, introduced by Acióly[6] in 1991, the idea of an intervalar equation appears to represent a real equation satisfactorily, since the terms of the intervalar equation carry the information about the solution of the real equation. In 1999, Santiago proposed the notion of simple equality and, later on, local equality for intervals [8] and [33]. Based on that idea, this dissertation extends Santiago's local groups for local algebras, following the idea of Σ-algebras according to (Hennessy[31], 1988) and (Santiago[7], 1995). One of the contributions of this dissertation, is the theorem 5.1.3.2 that it guarantees that, when deducing a local Σ-equation E t t in the proposed system SDedLoc(E), the interpretations of t and t' will be locally the same in any local Σ-algebra that satisfies the group of fixed equations local E, whenever t and t have meaning in A. This assures to a kind of safety between the local equacional logic and the local algebras

Equações de segundo grau e mudança de variáveis

In this work are presented, as a review and in a historical context, the most used methods to solve quadratic equations. It is also shown the simplest type of change of variables, namely: x = Ay + B where A;B 2 R, and some changes of variables that were used to solve quadratic equations throughout history. Finally, a change of variable, which has been used by the author in the classroom as an alternative method, is presented and the result of this methodoly is illustrated by the responses of a test that was done by the students in classroom

Validade das equações preditivas da frequência cardíaca máxima para crianças e adolescentes

FUNDAMENTO: Ausência de estudos na literatura validando equações preditivas da frequência cardíaca máxima (FCmáx) em crianças e adolescentes. OBJETIVO: Analisar a validade das equações preditivas da FCmáx 220 - idade e 208 - (0,7 x idade) em meninos com idades entre 10 e 16 anos. MÉTODOS: Um teste progressivo de esforço máximo foi realizado em 69 meninos com idades entre 10 e 16 anos, aparentemente saudáveis e ativos. A velocidade inicial do teste foi de 9 km/h com incrementos de 1 km/h a cada três minutos. O teste foi mantido até a exaustão voluntária, considerando-se como FCmáx a maior frequência cardíaca atingida durante o teste. A FCmáx medida foi comparada com os valores preditos pelas equações 220 - idade e 208 - (0,7 x idade) através da ANOVA, medidas repetidas. Resultados: Os valores médios da FCmáx (bpm) foram: 200,2 ± 8,0 (medida), 207,4 ± 1,5 (220 - idade) e 199,2 ± 1,1 (208 - (0,7 x idade)). A FCmáx predita pela equação 220 - idade foi significantemente maior (p < 0,001) que a FCmáx medida e que a FCmáx predita pela equação (208 - (0,7 x idade)). A correlação entre a FCmáx medida e a idade não foi estatisticamente significativa (r = 0,096; p > 0,05). CONCLUSÃO: A equação 220 - idade superestimou a FCmáx medida e não se mostrou válida para essa população. A equação 208 - (0,7 x idade) se mostrou válida apresentando resultados bastante próximos da FCmáx medida. Estudos futuros estudos com amostras maiores poderão comprovar se a FCmáx não depende da idade para essa população, situação em que o valor constante de 200 bpm seria mais apropriado para a FCmáx.

Ensaios em parcelas subdivididas delineados em blocos incompletos balanceados. I - Equações normais

Com o objetivo de ampliar o uso dos ensaios com parcelas subdivididas na pesquisa agropecuária, realizou-se um estudo de tais ensaios delineados em blocos incompletos balanceados. Adotou-se, para tanto, o modelo tradicionalmente usado no delineamento completo. Optou-se pela existência de correlação constante entre subparcelas distintas. A obtenção das estimativas para efeitos de blocos ocorreu como nos ensaios em blocos incompletos balanceados, enquanto que as estimativas para efeitos de tratamentos secundários e para a interação tratamentos principais x tratamentos secundários portaram-se como nos ensaios com parcelas subdivididas em blocos (completos), casualizados.

Práticas de gestão da cadeia de suprimentos e seus eventuais relacionamentos com as prioridades competitivas da produção: evidências empíricas do setor eletroeletrônico à luz de modelagem de equações estruturais

Este artigo tem como objetivo identificar as práticas de gestão da cadeia de suprimentos que estão sendo adotadas no setor eletroeletrônico brasileiro e verificar se as prioridades competitivas da produção das empresas desse setor se relacionam com a adoção de tais práticas. Desenvolveu-se uma pesquisa empírica, de cunho quantitativo, a partir da realização de uma pesquisa survey por e-mail com gerentes de empresas do setor eletroeletrônico da Associação Brasileira da Indústria Elétrica e Eletrônica. Técnicas estatísticas descritivas e multivariadas de segunda geração (modelagem de equações estruturais) foram empregadas para analisar os dados obtidos. Como principais resultados deste artigo destacam-se: a) as práticas de gestão da cadeia de suprimentos que estão sendo mais implantadas são voltadas à integração e apoio das atividades de desenvolvimento de produtos com os clientes; e b) não foram verificadas relações significativas entre as prioridades competitivas das empresas estudadas e a adoção de práticas de gestão da cadeia de suprimentos.

Comparações entre equações de predição de consumo de capim-elefante cortado para vacas lactantes

This work aimed to compare intake prediction equations with values obtained by direct methods using chopped elephant-grass offered to crossbreed lactating cows with rumen canulas. The experimental design was a 3 x 3 Latin square (three animals and three cutting ages: 30, 45 and 60 days). The equations used for intake prediction (y) were: (1) y= -1.19 + 0.035(a+b) + 28.5c; (2) y= [%NDF on DM]*[NDF intake]/[(1- a - b)/KP+b/(c+kp)]/24; (3) y= -0.822 + 0.0748(a+b) + 40.7c and (4) equation 2 with values of intake measured directly. The predictions of NDF intake by equations were not different among treatments, instead of the difference among values measured directly: the 30 day-old had lower intake (5.29 kg/day) in relation to 45 (6.57 kg/day) and 60 (7.31 kg/day) day-old grasses. In general, equations overestimated the DM intake in relation to direct measuring (9.0 kg/cow/day), with exception of equation 3 which underestimated the intake (7.7 kg/day). The means of DM intake found by equations 1 and 2 (13.7 and 13.4 kg/cow/day, respectively) were similar between themselves and superior in relation to those found by equation 4 (9.7 kg/cow/day). The intakes measured directly were similar to those found in equation 4 and higher than those found by equation 3. The mean of rumen fill of 7.5 kg was superior to those of 5.2 kg estimated by equation. The prediction equations based on in situ degradability parameters do not supply estimates of DM intake, NDF intake and rumen fill in agreement with values obtained by direct methods.

Proposição e validações de equações para estimativa da erosividade de dois municípios do estado de São Paulo

The equations and extrapolation use to localities whose characteristics of soil and climate, even if partial, distinguish the town to which they were generated, still permeate in studies to estimate the rainfall erosivity (EI 30). This work has objective to propose and validate mathematical equations to estimate the rainfall erosivity of two cities of Sao Paulo State's. The adjusted to estimate obtaining and validate data of equations of erosivity (EI 30) according to values of coefficient of rain (Rc) were obtained from pluviographic and pluviometric rainfall data, respectively, using of distinct historical rainfall series. Mutiple comparisions test and confidence intervals were performed to compare absolute average of EI 30, pluviometric data (Pp), and Rc. The correlation between EI 30 and Rc was verified by of Pearson correlation coefficient. Test of the hypothesis of equality between population variance was used to compare the equations. Pluviometrics data of historical series rainfall data different than those that the models were generated were used to validate and to assess the performance of the equations, proposed of this study and compare them with another equation already consolidated in literature. The results show that for the conditions under which the study was conducted, the simple linear equations, shown to be the most appropriate to estimate the rainfall erosivity these two cities. According to the test of the hypothesis of equality variances between populations, the equations adjusted for each city differ statistically so that the rainfall erosivity of each city must be estimated by their respective equation.

Tópicos de equações diferenciais parciais elípticas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Controle aproximado para sistemas não-lineares de equações diferenciais ordinárias

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Semigrupos de operadores lineares aplicados às equações diferenciais parciais

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