A obra de triangulis omnimodis libri quinque de Johann Müller Regiomontanus (1436 1476): uma contribuição para o desenvolvimento da trigonometria

Trigonometry, branch of mathematics related to the study of triangles, developed from practical needs, especially relating to astronomy, Surveying and Navigation. Johann Müller, the Regiomontanus (1436-1476) mathematician and astronomer of the fifteenth century played an important role in the development of this science. His work titled De Triangulis Omnimodis Libri Quinque written around 1464, and published posthumously in 1533, presents the first systematic exposure of European plane and spherical trigonometry, a treatment independent of astronomy. In this study we present a description, translation and analysis of some aspects of this important work in the history of trigonometry. Therefore, the translation was performed using a version of the book Regiomontanus on Triangles of Barnabas Hughes, 1967. In it you will find the original work in Latin and an English translation. For this study, we use for most of our translation in Portuguese, the English version, but some doubt utterance, statement and figures were made by the original Latin. In this work, we can see that trigonometry is considered as a branch of mathematics which is subordinated to geometry, that is, toward the study of triangles. Regiomontanus provides a large number of theorems as the original trigonometric formula for the area of a triangle. Use algebra to solve geometric problems and mainly shows the first practical theorem for the law of cosines in spherical trigonometry. Thus, this study shows some of the development of the trigonometry in the fifteenth century, especially with regard to concepts such as sine and cosine (sine reverse), the work discussed above, is of paramount importance for the research in the history of mathematics more specifically in the area of historical analysis and critique of literary sources or studying the work of a particular mathematician

Objetiva(ação) da medida e contagem do tempo em práticas socioculturais e educativas

This thesis describes and analyzes various processes established and practiced by both groups about the socio-cultural objective (action) the measurement and timing, mobilized some socio-historical practices as the use of the gnômon of the sundial and reading and interpretation of movements celestial constellations in cultural contexts such as indigenous communities and fishermen in the state of Pará, Brazil. The Purpose of the study was to describe and analyze the mobilization of such practices in the socio-historical development of matrices for teaching concepts and skills related to geometric angles, similar triangles, symmetry and proportionality in the training of mathematics teachers. The record of the entire history of investigation into the socio-historical practice, the formative action was based on epistemological assumptions of education ethnomathematics proposed by Vergani (2000, 2007) and Ubiratan D'Ambrosio (1986, 1993, 1996, 2001, 2004) and Alain Bishop conceptions about mathematics enculturation. At the end of the study I present my views on the practices of contributions called socio-cultural and historical for school mathematics, to give meaning to the concept formation and teaching of students, especially the implications of Education Ethnomatematics proposed by Vergani (2000) for training of future teachers of mathematics

Determinação dos parâmetros do controlador preditivo generalizado com função de pesos variante no tempo através de algoritmos genéticos

The predictive control technique has gotten, on the last years, greater number of adepts in reason of the easiness of adjustment of its parameters, of the exceeding of its concepts for multi-input/multi-output (MIMO) systems, of nonlinear models of processes could be linearised around a operating point, so can clearly be used in the controller, and mainly, as being the only methodology that can take into consideration, during the project of the controller, the limitations of the control signals and output of the process. The time varying weighting generalized predictive control (TGPC), studied in this work, is one more an alternative to the several existing predictive controls, characterizing itself as an modification of the generalized predictive control (GPC), where it is used a reference model, calculated in accordance with parameters of project previously established by the designer, and the application of a new function criterion, that when minimized offers the best parameters to the controller. It is used technique of the genetic algorithms to minimize of the function criterion proposed and searches to demonstrate the robustness of the TGPC through the application of performance, stability and robustness criterions. To compare achieves results of the TGPC controller, the GCP and proportional, integral and derivative (PID) controllers are used, where whole the techniques applied to stable, unstable and of non-minimum phase plants. The simulated examples become fulfilled with the use of MATLAB tool. It is verified that, the alterations implemented in TGPC, allow the evidence of the efficiency of this algorithm

Revisitando o problema de visibilidade para visualização tridimensional

We revisit the problem of visibility, which is to determine a set of primitives potentially visible in a set of geometry data represented by a data structure, such as a mesh of polygons or triangles, we propose a solution for speeding up the three-dimensional visualization processing in applications. We introduce a lean structure , in the sense of data abstraction and reduction, which can be used for online and interactive applications. The visibility problem is especially important in 3D visualization of scenes represented by large volumes of data, when it is not worthwhile keeping all polygons of the scene in memory. This implies a greater time spent in the rendering, or is even impossible to keep them all in huge volumes of data. In these cases, given a position and a direction of view, the main objective is to determine and load a minimum ammount of primitives (polygons) in the scene, to accelerate the rendering step. For this purpose, our algorithm performs cutting primitives (culling) using a hybrid paradigm based on three known techniques. The scene is divided into a cell grid, for each cell we associate the primitives that belong to them, and finally determined the set of primitives potentially visible. The novelty is the use of triangulation Ja 1 to create the subdivision grid. We chose this structure because of its relevant characteristics of adaptivity and algebrism (ease of calculations). The results show a substantial improvement over traditional methods when applied separately. The method introduced in this work can be used in devices with low or no dedicated processing power CPU, and also can be used to view data via the Internet, such as virtual museums applications

Otimização Topológica com Termo-elasticidade Utilizando Elementos Tri3

This work proposes a formulation for optimization of 2D-structure layouts submitted to mechanic and thermal shipments and applied an h-adaptive filter process which conduced to computational low spend and high definition structural layouts. The main goal of the formulation is to minimize the structure mass submitted to an effective state of stress of von Mises, with stability and lateral restriction variants. A criterion of global measurement was used for intents a parametric condition of stress fields. To avoid singularity problems was considerate a release on the stress restriction. On the optimization was used a material approach where the homogenized constructive equation was function of the material relative density. The intermediary density effective properties were represented for a SIMP-type artificial model. The problem was simplified by use of the method of finite elements of Galerkin using triangles with linear Lagrangian basis. On the solution of the optimization problem, was applied the augmented Lagrangian Method, that consists on minimum problem sequence solution with box-type restrictions, resolved by a 2nd orderprojection method which uses the method of the quasi-Newton without memory, during the problem process solution. This process reduces computational expends showing be more effective and solid. The results materialize more refined layouts with accurate topologic and shape of structure definitions. On the other hand formulation of mass minimization with global stress criterion provides to modeling ready structural layouts, with violation of the criterion of homogeneous distributed stress

Estudo histórico e pedagógico sobre ternos pitagóricos à luz de eugène bahier

At the present investigation had the purpose to achieve a descritive analysis pedagogy in the work of Recherche méthodique et propriétés des triangles rectangles en nombres entiers. According to the analysis achieved, we made and applyed the teaching module called Pitagories: one of tools to comprehension Pitagory Theorema, there were studying by public students in mathematic course in the UFRN , the new mathematic teachers in future. The analysis the was made with writen test the was showed that all students got the view comprehension in the teaching approach module, to apointed the difference in the learning qualytative with other reseach that was made with quastionaire and enterview. With this module that was made with the new future teacheres there was more attention the better comprehension with the Pitagory Theorema, that was good focus in the pitagory about the potential historical pedagogyc in the work studied.

Geometrias não-eucludianas como anomalias: implicações para o ensino de geometria e medidas

This present research the aim to show to the reader the Geometry non-Euclidean while anomaly indicating the pedagogical implications and then propose a sequence of activities, divided into three blocks which show the relationship of Euclidean geometry with non-Euclidean, taking the Euclidean with respect to analysis of the anomaly in non-Euclidean. PPGECNM is tied to the line of research of History, Philosophy and Sociology of Science in the Teaching of Natural Sciences and Mathematics. Treat so on Euclid of Alexandria, his most famous work The Elements and moreover, emphasize the Fifth Postulate of Euclid, particularly the difficulties (which lasted several centuries) that mathematicians have to understand him. Until the eighteenth century, three mathematicians: Lobachevsky (1793 - 1856), Bolyai (1775 - 1856) and Gauss (1777-1855) was convinced that this axiom was correct and that there was another geometry (anomalous) as consistent as the Euclid, but that did not adapt into their parameters. It is attributed to the emergence of these three non-Euclidean geometry. For the course methodology we started with some bibliographical definitions about anomalies, after we ve featured so that our definition are better understood by the readers and then only deal geometries non-Euclidean (Hyperbolic Geometry, Spherical Geometry and Taxicab Geometry) confronting them with the Euclidean to analyze the anomalies existing in non-Euclidean geometries and observe its importance to the teaching. After this characterization follows the empirical part of the proposal which consisted the application of three blocks of activities in search of pedagogical implications of anomaly. The first on parallel lines, the second on study of triangles and the third on the shortest distance between two points. These blocks offer a work with basic elements of geometry from a historical and investigative study of geometries non-Euclidean while anomaly so the concept is understood along with it s properties without necessarily be linked to the image of the geometric elements and thus expanding or adapting to other references. For example, the block applied on the second day of activities that provides extend the result of the sum of the internal angles of any triangle, to realize that is not always 180° (only when Euclid is a reference that this conclusion can be drawn)

Relação entre padrão comportamental, estágios do ciclo de muda e atividade de enzimas digestivas proteolíticas em juvenis do camarão marinho Litopenaeus vannamei (Crustacea: Penaeidae)

Shrimp farming in Brazil is a consolidated activity, having brought economical and social gains to several states with the largest production concentrated in the northeast. This fact is also reflected in higher feed intake, necessitating a more efficient feed management. Currently, management techniques already foresee food loss due to molting. In this sense, studies relating shrimp s digestive physiology, molting physiology and behavioral response of shrimp feed can optimize the feed management. Thus, our study aimed to evaluate the behavioral response of the marine shrimp L. vannamei (Crustacea: Penaeidae) in accordance with the stages of moulting cycle and feeding schedules based on higher or lower activity of proteolytic digestive enzymes; also, to investigate the influence of feeding schedule on hepatosomatic index and non-specific and specific protease activity (trypsin). Experiments were carried out at the Laboratory of Shrimp Behavioral Studies at UFRN in partnership with the Laboratory of Enzimology UFPE. Juveniles of L. vannamei weighting 5.25 g (+ 0.25 g) were kept in aquaria at a density of 33 shrimp m -2. In the first experiment, shrimp were fed in the light phase or in the dark phase for 8 days; in the ninth day, the animals were observed for 15 minutes every hour during the 12 hours of each phase of the photoperiod. We recorded the frequency of inactivity, exploration, food intake, burrowing, swimming and crawling behavior. At the end of the 12th observation session, the shrimp were sacrified and classified by the method of setogenesis in the molt cycle stages A, B, C, D0, D1, D2 or D3. We found that the shrimp in A stage show high levels of inactivity. Moreover, the frequency of food intake was very low. The shrimp in D3 stage also had low food intake and high inactivity associated with elevated frequencies of burrowing. In the second experiment, shrimp were kept in physiological acclimation to experimental conditions for 28 days, distributed in 12 treatments in the light phase and 12 treatments in the dark phase. In the end, the animals were sacrified and dissected to assess non-specific and specific protease activity (trypsin) activity. In general, these parameters did not vary among animals fed in the light phase and those fed in the dark phase. However, significant differences were found in the activity of specific and nonspecific proteases in relation to food treatment. In the light phase, the major proteolytic activities converged to 10 hours after the start of the light phase, while the lowest activities converged to 6 hours after the beginning of this phase. In the dark phase, the highest enzyme activity converged to 12 hours after the onset of phase, while the lowest activities converged to 3 hours after the onset of phase. In the third experiment, we sought to evaluate the behavioral responses of shrimp in relation to dietary treatments based on higher or lower activity of proteolytic enzymes, considering the results of the second experiment. The behavioral categories observed were the same as the ones in the first experiment, with observations of 30 minutes (15min before and 15min after food supply). We found variation in behavioral responses as a function of the treatments, with greater intake of food in shrimp fed during the period of greatest activity of proteolytic enzymes, in the light phase. Thus we see that periodic events associated with the shrimp s physiology interfere in their behavioral responses, revealing situations that are more adjustable to the provision of food, and consequently optimizing feeding management

Influência do tamoxifeno associado ao diabete melito na densidade mineral óssea

Considering that osteopenia and osteoporosis are diabetes mellitus complications, and that tamoxifen (TAM) is an anti-estrogenic drug used in breast cancer treatment, this drug may have a beneficial action preventing accentuaded bone loss associated to diabetes. Female Wistar rats (n=60) weighting 180-250g were divided in four groups: Group C, control animals (n=5); Group T, animals treated with TAM (n=5); Group D, diabetic animals (n=5); and Group DT, diabetic animals treated with TAM (n=5). Oestrus cycle was evaluated before the beggining of experimental period to select the animals with regular cycle. This evaluation continued throughout the study period and for all studied groups. Diabetes was induced by a intra perithoneal injection of streptozotocin (STZ) in a concentration of 45 mg/Kg of body weight. Those animals with serum glicose levels 250 mg/dL were considered diabetics. Animals were sacrificed in the periods of 30, 60 and 90 days after diabetes onset. Left femur histomorphometric measurements and serum biochemical analysis (glycemia, alkaline phosphatase, tartaric-resistant acid phosphatase, calcium, phosphorous, magnesium, total proteins, albumin, globulins, urea and creatinine) were done. Histomorphometric results showed a progressive bone loss in Group D animals when compared to those from Group C all over the experimental period, becoming accentuaded in the 90 days period. In relation to Groups T and DT, values approcimated to those obtained for control group were found during the whole period of study. Those data may indicate a bone mass recovery or a diminished bone loss due to diabetes when animals were treated with TAM. During the whole experimental period animals of groups D and DT maintained glycemic levels above 250 mg/dL whereas animals of groups C and T maintained those levels below 150mg/dL. Alkaline phosphatase activity was increased in all study periods for groups D and DT when compared to group C animals over the 90 days period. Tartarate-resistant acid phosphatase activity was showed unaltered in all periods of study and for all groups. Calcium and magnesium results were also unaltered, maintaining reference levels for all groups in all experimental periods. Phosphorous levels were increased in groups D and DT when compared to groups C and T in the 30 days period. However no difference was found in the periods of 60 and 90 days for this test. No difference was found for total proteins levels for groups C, T, D and DT over the study period. Albumin levels were reduced in DT group in the 60 days period and in D and DT groups in the 90 days period. Urea levels were significantly increased in the 30, 60 and 90 days study periods in groups D and DT when compared to groups C and T. Creatinine results showed a significantly increase in the 90 days period for groups D and DT when compared to groups C and T, and maintaining unaltered in the 30 and 60 days periods. These results suggest that the treatment with TAM may reduce bone loss caused by diabetes mellitus

Formulações e algoritmos para o problema das p-medianas heterogêneo livre de penalidade

This work presents a new model for the Heterogeneous p-median Problem (HPM), proposed to recover the hidden category structures present in the data provided by a sorting task procedure, a popular approach to understand heterogeneous individual’s perception of products and brands. This new model is named as the Penalty-free Heterogeneous p-median Problem (PFHPM), a single-objective version of the original problem, the HPM. The main parameter in the HPM is also eliminated, the penalty factor. It is responsible for the weighting of the objective function terms. The adjusting of this parameter controls the way that the model recovers the hidden category structures present in data, and depends on a broad knowledge of the problem. Additionally, two complementary formulations for the PFHPM are shown, both mixed integer linear programming problems. From these additional formulations lower-bounds were obtained for the PFHPM. These values were used to validate a specialized Variable Neighborhood Search (VNS) algorithm, proposed to solve the PFHPM. This algorithm provided good quality solutions for the PFHPM, solving artificial generated instances from a Monte Carlo Simulation and real data instances, even with limited computational resources. Statistical analyses presented in this work suggest that the new algorithm and model, the PFHPM, can recover more accurately the original category structures related to heterogeneous individual’s perceptions than the original model and algorithm, the HPM. Finally, an illustrative application of the PFHPM is presented, as well as some insights about some new possibilities for it, extending the new model to fuzzy environments

Sobre o problema da mentira na filosofia prática de Kant

The research examines the problem lie in the thought of Immanuel Kant. This field of law, of the history of political morality, we seek to investigate the Kantian rejection of falsehood and unconditional obligation to be truthful. Defends the thesis of the exception to lie and not be objectionable in two cases, namely: the torture and before the murderer. Thus, it is demonstrated that it is possible the exception to lie under the law, politics and history, considering the perspective of harmony of external freedoms and the idea of moral progress. In this sense, it is argued that the source of law is established to guarantee the external freedoms. From the point of view of morality, reaffirmed the absoluteness is that for Kant the duty of veracity, but it points to the possibility of a practical rule that allows the lie based on human dignity, weighting values as political equality, respect for rational agents, as well as the principle of humanity which teaches always treat the other as an end in itself.

Plano amostral, ponderação e efeitos do delineamento da Pesquisa Nacional de Saúde Bucal

OBJETIVO: Estimar la prevalencia y la extensión de la caries radicular en la población adulta y anciana de Brasil. MÉTODOS: A partir de los datos de la Investigación Nacional de Salud Bucal (SBBrasil 2010) se examinaron 9.564 adultos y 7.509 ancianos en domicilios de las 26 capitales y en el Distrito Federal y de 150 municipios del interior de cada macro región. Se implementaron criterios de diagnóstico establecidos por la Organización Mundial de la Salud. Para estudio de la prevalencia y de extensión se utilizó el índice de caries radicular y el índice de raíces cariadas y obturadas. RESULTADOS: La prevalencia de caries radicular fue de 16,7% en los adultos y 13,6% en los ancianos; el índice de raíces cariadas y obturadas fue de 0,42 y 0,32 respectivamente, siendo la mayor parte compuesta por caries no tratadas. Se observaron diferencias en la experiencia de caries radicular entre capitales y macro regiones, con valores mayores en capitales del Norte y Noreste. El índice de caries radicular en los adultos varió de 1,4% en Aracaju (SE) a 15,1% en Salvador (BA) y en los ancianos de 3,5% en Porto Velho (RO) a 29,9% en Palmas (TO). Se verificó incremento de caries radicular con la edad y mayor expresividad de la enfermedad en hombres de ambos grupos etarios. CONCLUSIONES: Se identificó una gran variación de la prevalencia y extensión de la caries radicular entre y dentro de las regiones de Brasil, tanto en adultos como en ancianos, y la mayor parte de la caries radicular se encuentra no tratada. Se recomienda la incorporación de este agravio al sistema de vigilancia en salud bucal, debido a su tendencia creciente.

Efeito de diferentes divisões territoriais na flutuação aleatória de indicadores socioeconômicos relacionados à determinação social da saúde

This research aimed to analyse the effect of different territorial divisions in the random fluctuation of socio-economic indicators related to social determinants of health. This is an ecological study resulting from a combination of statistical methods including individuated and aggregate data analysis, using five databases derived from the database of the Brazilian demographic census 2010: overall results of the sample by weighting area. These data were grouped into the following levels: households; weighting areas; cities; Immediate Urban Associated Regions and Intermediate Urban Associated Regions. A theoretical model related to social determinants of health was used, with the dependent variable Household with death and as independent variables: Black race; Income; Childcare and school no attendance; Illiteracy; and Low schooling. The data was analysed in a model related to social determinants of health, using Poisson regression in individual basis, multilevel Poisson regression and multiple linear regression in light of the theoretical framework of the area. It was identified a greater proportion of households with deaths among those with at least one black resident, lower-income, illiterate, who do not attend or attended school or day-care and less educated. The analysis of the adjusted model showed that most adjusted prevalence ratio was related to Income, where there is a risk value of 1.33 for households with at least one resident with lower average personal income to R$ 655,00 (Brazilian current). The multilevel analysis demonstrated that there was a context effect when the variables were subjected to the effects of areas, insofar as the random effects were significant for all models and with different prevalence rates being higher in the areas with smaller dimensions - Weighting areas with coefficient of 0.035 and Cities with coefficient of 0.024. The ecological analyses have shown that the variable Income and Low schooling presented explanatory potential for the outcome on all models, having income greater power to determine the household deaths, especially in models related to Immediate Urban Associated Regions with a standardized coefficient of -0.616 and regions intermediate urban associated regions with a standardized coefficient of -0.618. It was concluded that there was a context effect on the random fluctuation of the socioeconomic indicators related to social determinants of health. This effect was explained by the characteristics of territorial divisions and individuals who live or work there. Context effects were better identified in the areas with smaller dimensions, which are more favourable to explain phenomena related to social determinants of health, especially in studies of societies marked by social inequalities. The composition effects were better identified in the Regions of Urban Articulation, shaped through mechanisms similar to the phenomenon under study.