De solutione problematum diophanteorum per números integros : o primeiro trabalho de Euler sobre equações diofantinas

The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers

Avaliação das equações de predição das exigências de proteína para matrizes pesadas na fase de crescimento

Objetivou-se avaliar as equações para predição das exigências protéicas de matrizes pesadas em crescimento, desenvolvidas em estudos anteriores na Faculdade de Ciências Agrárias e Veterinárias da UNESP, Jaboticabal, tendo como padrão de comparação as recomendações estabelecidas pelo manual de criação da linhagem. Foram utilizadas 288 matrizes pesadas da linhagem Hubbard Hy-Yield, com cinco semanas de idade, em delineamento inteiramente casualizado, com dois tratamentos e seis repetições, sendo 24 aves por unidade experimental até 14 semanas e, de 15 a 20 semanas de idade, 20 aves por unidade experimental. Um tratamento foi representado pelas recomendações protéicas para a linhagem (testemunha) e o outro pelas seguintes equações de predição das exigências de proteína: de 5 a 8 semanas PB (g/ave/dia) = 2,02.P0,75+ 0,350.G, 9 a 14 semanas - PB = 2,02.P0,75 + 0,406.G e de 15 a 20 semanas PB = 2,02.P0,75 + 0,463.G, em que P é o peso corporal (kg) e G, o ganho de peso diário (g). Os resultados indicaram que as equações de predição para proteína, apesar de não comprometerem o peso ou a uniformidade corporal em relação ao tratamento testemunha, determinaram menor porcentagem de peito e maior de gordura abdominal e maior teor de gordura na carcaça, sendo atribuído à menor ingestão de proteína proporcionada pelas equações de predição e, conseqüentemente, deficiência em relação a alguns aminoácidos que não foram suplementados.

Equações de predição da composição química corporal a partir do corte da 9-10-11ª costelas de bovinos castrados Nelore

Objetivou-se obter equações de regressão linear simples para estimativa da composição química corporal de novilhos Nelore a partir da composição química do corte da 9-10-11ª costelas. Foram utilizados 27 bovinos em confinamento, com 21 a 31 meses de idade e 338,0 a 503,6 kg de peso corporal. do total, foram abatidos seis animais (referência) ao início do experimento para estimativa da composição química corporal. A composição química em água, proteína, EE e cinzas foi determinada no corte da 9-10-11ª costelas e nos tecidos corporais. As equações de regressão para estimativa do peso de corpo vazio (PCVZ) a partir dos pesos de jejum (PV) e carcaça quente (PCQ) foram PCVZ = 0,8726 PV - 2,7399 e PCVZ = 1,5350 PCQ + 13,598 (R² = 0,98). O ganho de 1 kg de PCVZ correspondeu a aproximadamente 1,15 kg de PV. A porcentagem de água no corpo vazio (CVz) esteve altamente correlacionada às porcentagens de água (R² = 0,98) e EE (R² = 0,91) no corte das costelas. A equação mais indicada foi a desenvolvida a partir da porcentagem de água no corte das costelas (Sx, y = 0,46). Verificou-se alta correlação entre a porcentagem de EE no CVz e a porcentagem de EE (R² = 0,95) no corte das costelas, portanto, a equação %EE CVz = 0,9662%EE costelas + 1,5294 pode ser utilizada para estimativa da composição do CVz em EE. O mesmo ocorreu para a porcentagem de cinzas, sendo recomendada a equação %MM CVz = 0,5915%MM costelas + 0,7619 (R² = 0,88). A composição química percentual em água, EE e minerais no corte das 9-10-11ª costelas permitiu estimar com acuidade a composição do corpo vazio.

Um sistema para estimação da vazão de gás de poços produzindo por Plunger Lift para vaso separador de teste em plataformas de petróleo

This work intends to analyze the behavior of the gas flow of plunger lift wells producing to well testing separators in offshore production platforms to aim a technical procedure to estimate the gas flow during the slug production period. The motivation for this work appeared from the expectation of some wells equipped with plunger lift method by PETROBRAS in Ubarana sea field located at Rio Grande do Norte State coast where the produced fluids measurement is made in well testing separators at the platform. The oil artificial lift method called plunger lift is used when the available energy of the reservoir is not high enough to overcome all the necessary load losses to lift the oil from the bottom of the well to the surface continuously. This method consists, basically, in one free piston acting as a mechanical interface between the formation gas and the produced liquids, greatly increasing the well s lifting efficiency. A pneumatic control valve is mounted at the flow line to control the cycles. When this valve opens, the plunger starts to move from the bottom to the surface of the well lifting all the oil and gas that are above it until to reach the well test separator where the fluids are measured. The well test separator is used to measure all the volumes produced by the well during a certain period of time called production test. In most cases, the separators are designed to measure stabilized flow, in other words, reasonably constant flow by the use of level and pressure electronic controllers (PLC) and by assumption of a steady pressure inside the separator. With plunger lift wells the liquid and gas flow at the surface are cyclical and unstable what causes the appearance of slugs inside the separator, mainly in the gas phase, because introduce significant errors in the measurement system (e.g.: overrange error). The flow gas analysis proposed in this work is based on two mathematical models used together: i) a plunger lift well model proposed by Baruzzi [1] with later modifications made by Bolonhini [2] to built a plunger lift simulator; ii) a two-phase separator model (gas + liquid) based from a three-phase separator model (gas + oil + water) proposed by Nunes [3]. Based on the models above and with field data collected from the well test separator of PUB-02 platform (Ubarana sea field) it was possible to demonstrate that the output gas flow of the separator can be estimate, with a reasonable precision, from the control signal of the Pressure Control Valve (PCV). Several models of the System Identification Toolbox from MATLAB® were analyzed to evaluate which one better fit to the data collected from the field. For validation of the models, it was used the AIC criterion, as well as a variant of the cross validation criterion. The ARX model performance was the best one to fit to the data and, this way, we decided to evaluate a recursive algorithm (RARX) also with real time data. The results were quite promising that indicating the viability to estimate the output gas flow rate from a plunger lift well producing to a well test separator, with the built-in information of the control signal to the PCV

Software inteligente embarcado aplicado à correção de erro na medição de vazão em gás natural

This study developed software rotines, in a system made basically from a processor board producer of signs and supervisory, wich main function was correcting the information measured by a turbine gas meter. This correction is based on the use of an intelligent algorithm formed by an artificial neural net. The rotines were implemented in the habitat of the supervisory as well as in the habitat of the DSP and have three main itens: processing, communication and supervision

Avaliação de equações de predição de exigências energéticas na alimentação de frangas de postura

O objetivo do presente estudo foi testar a validade de equações de predição de exigências energéticas para frangas de postura, as quais foram determinadas em estudos anteriores realizados na Faculdade de Ciências Agrárias e Veterinárias da UNESP- Jaboticabal. O delineamento experimental utilizado foi o inteiramente casualizado com três tratamentos e seis repetições compostas por 18 aves no período de 3 a 8 semanas, 15 aves de 9 a 12 semanas e 12 aves de 13 a 18 semanas de idade. Os tratamentos consistiram em comparar três diferentes formas de se alimentar as aves: alimentação à vontade, alimentação de acordo com as recomendações para a linhagem e alimentação de acordo com as equações de predição das exigências de energia metabolizável (EM). Os tratamentos foram avaliados por intermédio do desempenho das aves durante o período de crescimento e na fase de produção. No período de 3 a 8 semanas de idade, as aves alimentadas de acordo com as equações de predição de em apresentaram menor consumo de ração e de energia, o que determinou menor peso corporal e uniformidade insatisfatória. em função dos resultados da fase de 3 a 8 semanas de idade, foi adotada uma correção na equação de predição das exigências de em para as fases seguintes, acrescentando-se uma porcentagem de 37% sobre as exigências de em para mantença, valor relativo às atividades das aves. Às 18 semanas de idade, a ingestão de em foi maior para o tratamento à vontade, sendo que as aves de todos os tratamentos apresentaram peso corporal superior ao proposto pelo manual e boa uniformidade. O experimento teve continuidade durante a fase de produção, sendo que os tratamentos aplicados na fase de crescimento não afetaram o desempenho produtivo das aves.

Modelagem de equações estruturais na análise de dados de serviços em comunicações móveis

In recent decades, changes have been occurring in the telecommunications industry, allied to competition driven by the policies of privatization and concessions, have fomented the world market irrefutably causing the emergence of a new reality. The reflections in Brazil have become evident due to the appearance of significant growth rates, getting in 2012 to provide a net operating income of 128 billion dollars, placing the country among the five major powers in the world in mobile communications. In this context, an issue of increasing importance to the financial health of companies is their ability to retain their customers, as well as turn them into loyal customers. The appearance of infidelity from customer operators has been generating monthly rates shutdowns about two to four percent per month accounting for business management one of its biggest challenges, since capturing a new customer has meant an expenditure greater than five times to retention. For this purpose, models have been developed by means of structural equation modeling to identify the relationships between the various determinants of customer loyalty in the context of services. The original contribution of this thesis is to develop a model for loyalty from the identification of relationships between determinants of satisfaction (latent variables) and the inclusion of attributes that determine the perceptions of service quality for the mobile communications industry, such as quality, satisfaction, value, trust, expectation and loyalty. It is a qualitative research which will be conducted with customers of operators through simple random sampling technique, using structured questionnaires. As a result, the proposed model and statistical evaluations should enable operators to conclude that customer loyalty is directly influenced by technical and operational quality of the services offered, as well as provide a satisfaction index for the mobile communication segment

Sistemas de automação e supervisão do laboratório de avaliação dos processos de medição de vazão e BSW

During a petroleum well production process, It is common the slmultaneous oil and water production, in proportion that can vary from 0% up to values close to 100% of water. Moreover, the production flows can vary a lot, depending on the charaeteristies of eaeh reservoir. Thus being, the meters used in field for the flow and BSW (water in the oil) measurement must work well in wide bands of operation. For the evaluation of the operation of these meters, in the different operation conditions, a Laboratory will be built in UFRN, that has for objective to evaluate in an automatic way the processes of flow and BSW petroleum measurement, considering different operation conditions. The good acting of these meters is fundamental for the accuracy of the measures of the volumes of production liquid and rude of petroleum. For the measurement of this production, the petroleum companies use meters that should indicate the values with tha largast possible accuracy and to respect a series of conditions and minimum requirements, estabelished by the united Entrance ANP/INMETRO 19106/2000. The laboratory of Evafuation of the Processes of Measurement of Flow and BSW to be built will possess an oil tank basically, a tank of water, besides a mixer, a tank auditor, a tank for separation and a tank of residues for discard of fluids, fundamental for the evaluation of the flow metars and BSW. The whole process will be automated through the use of a Programmable Logicat Controller (CLP) and of a supervisory system.This laboratory besides allowing the evaluation of flow meters and BSW used by petroleum companies, it will make possible the development of researches related to the automation. Besides, it will be a collaborating element to the development of the Computer Engineering and Automation Department, that it will propitiate the evolution of the faculty and discente, qualifying them for a job market in continuous growth. The present work describes the project of automation of the laboratory that will be built at of UFRN. The system will be automated using a Programmable Logical Controller and a supervisory system. The programming of PLC and the screens of the supervisory system were developed in this work

Uma metodologia para redução de incertezas em sistema de medição de vazão de óleo e gás

The objective of this research is to discuss about the need for implementation of new alternatives for the implementation on the metrological control: on the findings of initial and subsequent measurements, the control procedures of measurement uncertainty applied in assessing the loss or remains found in handling operations of bulk liquids, when used turbine meters used in measuring the tax on the business of Petrobras, due to the current environment of legal metrology and scientific, both domestic and international. We aim, with these alternatives: standardizing the minimization of random and systematic errors, the estimate of the remaining errors, as well as the management control of metrological calibration procedures, control of measurement uncertainty, and contribute to the change in the form of performance of legal metrology and scientific disseminating new information to change management of metrological control, objectively focused on aspects of supervision in implementing these activities in the control of the uncertainties of measurement used in our processes in the fiscal measurement system Petrobras. Results are presented, information and comments on the influence of measurement uncertainty in the current results of the fiscal and transfer of custody. This will emphasize the need, among other things, improvement and expansion of metrological control monitored by setting a better meet demand, calibration equipment and measuring instruments for Petrobras. Finally, we intend to establish the need for improving the method of evaluation of the data meter applied to the current management control of measurement uncertainty by proposing a methodology for addressing the problem, as well as highlighting the expected results.

Estudo da estimativa da incerteza de medição para determinação do BS&W e da vazão aplicado no laboratório de avaliação de medição do petróleo

The considered work presents the procedure for evaluation of the uncertainty related to the calibration of flow measurers and to BS&W. It is about a new method of measurement purposed by the conceptual project of the laboratory LAMP, at Universidade Federal do Rio Grande do Norte, that intends to determine the conventional true value of the BS&W from the total height of the liquid column in the auditor tank, hydrostatic pressure exerted by the liquid column, local gravity, specific mass of the water and the specific mass of the oil, and, to determine the flow, from total height of liquid column and transfer time. The calibration uses a automatized system of monitoration and data acquisition of some necessary largnesses to determine of flow and BS&W, allowing a better trustworthiness of through measurements

Simulação computacional do escoamento em bombas de cavidades progressivas

The use of Progressing Cavity Pumps (PCPs) in artificial lift applications in low deep wells is becoming more common in the oil industry, mainly, due to its ability to pump heavy oils, produce oil with large concentrations of sand, besides present high efficiency when compared to other artificial lift methods. Although this system has been widely used as an oil lift method, few investigations about its hydrodynamic behavior are presented, either experimental or numeric. Therefore, in order to increase the knowledge about the BCP operational behavior, this work presents a novel computational model for the 3-D transient flow in progressing cavity pumps, which includes the relative motion between rotor and stator, using an element based finite volume method. The model developed is able to accurately predict the volumetric efficiency and viscous looses as well as to provide detailed information of pressure and velocity fields inside the pump. In order to predict PCP performance for low viscosity fluids, advanced turbulence models were used to treat, accurately, the turbulent effects on the flow, which allowed for obtaining results consistent with experimental values encountered in literature. In addition to the 3D computational model, a simplified model was developed, based on mass balance within cavities and on simplification on the momentum equations for fully developed flow along the seal region between cavities. This simplified model, based on previous approaches encountered in literature, has the ability to predict flow rate for a given differential pressure, presenting exactness and low CPU requirements, becoming an engineering tool for quick calculations and providing adequate results, almost real-time time. The results presented in this work consider a rigid stator PCP and the models developed were validated against experimental results from open literature. The results for the 3-D model showed to be sensitive to the mesh size, such that a numerical mesh refinement study is also presented. Regarding to the simplified model, some improvements were introduced in the calculation of the friction factor, allowing the application fo the model for low viscosity fluids, which was unsuccessful in models using similar approaches, presented in previous works

Avaliacao de dados de secagem de suspensoes de polpas de frutas em leito de jorro com alimentacao intermitente

The objective of this work was the development and improvement of the mathematical models based on mass and heat balances, representing the drying transient process fruit pulp in spouted bed dryer with intermittent feeding. Mass and energy balance for drying, represented by a system of differential equations, were developed in Fortran language and adapted to the condition of intermittent feeding and mass accumulation. Were used the DASSL routine (Differential Algebraic System Solver) for solving the differential equation system and used a heuristic optimization algorithm in parameter estimation, the Particle Swarm algorithm. From the experimental data food drying, the differential models were used to determine the quantity of water and the drying air temperature at the exit of a spouted bed and accumulated mass of powder in the dryer. The models were validated using the experimental data of drying whose operating conditions, air temperature, flow rate and time intermittency, varied within the limits studied. In reviewing the results predicted, it was found that these models represent the experimental data of the kinetics of production and accumulation of powder and humidity and air temperature at the outlet of the dryer

Modelagem e simulação da solubilização da parafina em tubos circulares e em regime laminar

O óleo produzido nos novos campos de petróleo está cada vez mais parafínico e viscoso, com isso, à medida que o óleo é escoado, parafinas são depositadas sobre as paredes internas do tubo, e ao longo do tempo, tendem a reduzir drasticamente a área transversal ao escoamento. Visando estudar o processo de solubilização da parafina em dutos, esse trabalho objetiva desenvolver modelos matemáticos que represente o processo, com base nos fenômenos envolvidos no mesmo tais como transferência de massa, transferência de energia e equilíbrio sólido-líquido, implementando-os em um ambiente de desenvolvimento VBA (Visual Basic) for Excel ®. O presente trabalho foi realizado em quatro etapas: i) modelagem dos fenômenos de transferência de calor e massa, ii) modelagem da rotina dos coeficientes de atividade através do modelo UNIFAC e modelagem do sistema de equilíbrio sólido-líquido; iii) modelagem matemática do processo de solubilização e cálculo da espessura da parafina ao longo do tempo; iv) implementação dos modelos em um ambiente de desenvolvimento VBA for Excel® e criação de um simulador com uma interface gráfica, para simular o processo de solubilização da parafina depositada em dutos e sua otimização. O simulador conseguiu produzir soluções bastante adequadas, mantendo continuidade das equações diferenciáveis do balanço de energia e de massa, com uma interpretação física viável, sem a presença de dissipação de oscilações nos perfis de temperatura e massa. Além disso, esse simulador visa permitir a simulação nas diversas condições de escoamento, bem como compreender a importância das variáveis (vazão, temperatura de entrada, temperatura externa, cadeia carbônica do solvente). Através dos resultados foram possíveis verificar os perfis de temperatura, fração molar e o de solubilização

Conversão catalítica de clorometano em hidrocarbonetos

Amorphous silica-alumina and modified by incipient impregnation of iron, nickel, zinc and chromium were synthetized in oxide and metal state and evaluated as catalysts for the chloromethane conversion reaction. With known techniques their textural properties were determined and dynamics techniques in programmed temperature were used to find the acid properties of the materials. A thermodynamic model was used to determine the adsorption and desorption capacity of chloromethane. Two types of reactions were studied. Firstly the chloromethane was catalytically converted to hydrocarbons (T = 300 450 oC e m = 300 mg) in a fixed bed reactor with controlled pressure and flow. Secondly the deactivation of the unmodified support was studied (at 300 °C and m=250 g) in a micro-adsorver provided of gravimetric monitoring. The metal content (2,5%) and the chloromethane percent of the reagent mixture (10% chloromethane in nitrogen) were fixed for all the tests. From the results the chloromethane conversion and selectivity of the gaseous products (H2, CH4, C3 and C4) were determined as well as the energy of desorption (75,2 KJ/mol for Ni/Al2O3-SiO2 to 684 KJ/mol for the Zn/Al2O3-SiO2 catalyst) considering the desorption rate as a temperature function. The presence of a metal on the support showed to have an important significance in the chloromethane condensation. The oxide class catalyst presented a better performance toward the production of hydrocarbons. Especial mention to the ZnO/Al2O3-SiO2 that, in a gas phase basis, produced C3 83 % max. and C4 63% max., respectively, in the temperature of 450 oC and 20 hours on stream. Hydrogen was produced exclusively in the FeO/Al2O3-SiO2 catalysts (15 % max., T = 550 oC and 5,6 h on stream) and Ni/SiO2-Al2O3 (75 % max., T = 400 oC and 21,6 h on stream). All the catalysts produced methane (10 à 92 %), except for Ni/Al2O3-SiO2 and CrO/Al2O3-SiO2. In the deactivation study two models were proposed: The parallel model, where the product production competes with coke formation; and the sequential model, where the coke formation competes with the product desorption dessorption step. With the mass balance equations and the mechanism proposed six parameters were determined. Two kinetic parameters: the hydrocarbon formation constant, 8,46 10-4 min-1, the coke formation, 1,46 10-1 min-1; three thermodynamic constants (the global, 0,003, the chloromethane adsorption 0,417 bar-1, the hydrocarbon adsorption 2,266 bar-1), and the activity exponent of the coke formation (1,516). The model was reasonable well fitted and presented a satisfactory behavior in relation with the proposed mechanism

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