Um estudo na teoria do movimento brownianno com viscosidade variável

In this work we investigate the stochastic behavior of a large class of systems with variable damping which are described by a time-dependent Lagrangian. Our stochastic approach is based on the Langevin treatment describing the motion of a classical Brownian particle of mass m. Two situations of physical interest are considered. In the first one, we discuss in detail an application of the standard Langevin treatment (white noise) for the variable damping system. In the second one, a more general viewpoint is adopted by assuming a given expression to the so-called collored noise. For both cases, the basic diffententiaql equations are analytically solved and al the quantities physically relevant are explicitly determined. The results depend on an arbitrary q parameter measuring how the behavior of the system departs from the standard brownian particle with constant viscosity. Several types of sthocastic behavior (superdiffusive and subdiffusive) are obteinded when the free pamameter varies continuosly. However, all the results of the conventional Langevin approach with constant damping are recovered in the limit q = 1

Evolução top-hat hidrodinâmica em campos de velocidades peculiares primordiais

We investigate the cosmology of the vacuum energy decaying into cold dark matter according to thermodynamics description of Alcaniz & Lima. We apply this model to analyze the evolution of primordial density perturbations in the matter that gave rise to the first generation of structures bounded by gravity in the Universe, called Population III Objects. The analysis of the dynamics of those systems will involve the calculation of a differential equation system governing the evolution of perturbations to the case of two coupled fluids (dark matter and baryonic matter), modeled with a Top-Hat profile based in the perturbation of the hydrodynamics equations, an efficient analytical tool to study the properties of dark energy models such as the behavior of the linear growth factor and the linear growth index, physical quantities closely related to the fields of peculiar velocities at any time, for different models of dark energy. The properties and the dynamics of current Universe are analyzed through the exact analytical form of the linear growth factor of density fluctuations, taking into account the influence of several physical cooling mechanisms acting on the density fluctuations of the baryonic component of matter during the evolution of the clouds of matter, studied from the primordial hydrogen recombination. This study is naturally extended to more general models of dark energy with constant equation of state parameter in a flat Universe

Estimativa da profundidade do embasamento na bacia potiguar usando inversão gravimétrica

The gravity inversion method is a mathematic process that can be used to estimate the basement relief of a sedimentary basin. However, the inverse problem in potential-field methods has neither a unique nor a stable solution, so additional information (other than gravity measurements) must be supplied by the interpreter to transform this problem into a well-posed one. This dissertation presents the application of a gravity inversion method to estimate the basement relief of the onshore Potiguar Basin. The density contrast between sediments and basament is assumed to be known and constant. The proposed methodology consists of discretizing the sedimentary layer into a grid of rectangular juxtaposed prisms whose thicknesses correspond to the depth to basement which is the parameter to be estimated. To stabilize the inversion I introduce constraints in accordance with the known geologic information. The method minimizes an objective function of the model that requires not only the model to be smooth and close to the seismic-derived model, which is used as a reference model, but also to honor well-log constraints. The latter are introduced through the use of logarithmic barrier terms in the objective function. The inversion process was applied in order to simulate different phases during the exploration development of a basin. The methodology consisted in applying the gravity inversion in distinct scenarios: the first one used only gravity data and a plain reference model; the second scenario was divided in two cases, we incorporated either borehole logs information or seismic model into the process. Finally I incorporated the basement depth generated by seismic interpretation into the inversion as a reference model and imposed depth constraint from boreholes using the primal logarithmic barrier method. As a result, the estimation of the basement relief in every scenario has satisfactorily reproduced the basin framework, and the incorporation of the constraints led to improve depth basement definition. The joint use of surface gravity data, seismic imaging and borehole logging information makes the process more robust and allows an improvement in the estimate, providing a result closer to the actual basement relief. In addition, I would like to remark that the result obtained in the first scenario already has provided a very coherent basement relief when compared to the known basin framework. This is significant information, when comparing the differences in the costs and environment impact related to gravimetric and seismic surveys and also the well drillings

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

O problema da matéria escura e o teorema do virial na teoria de gravidade Eddington-Born-Infeld

Dark matter is a fundamental ingredient of the modern Cosmology. It is necessary in order to explain the process of structures formation in the Universe, rotation curves of galaxies and the mass discrepancy in clusters of galaxies. However, although many efforts, in both aspects, theoretical and experimental, have been made, the nature of dark matter is still unknown and the only convincing evidence for its existence is gravitational. This rises doubts about its existence and, in turn, opens the possibility that the Einstein’s gravity needs to be modified at some scale. We study, in this work, the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides en alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations and find their solutions to a spherical system of identical and collisionless point particles. Then, we took into account the collisionless relativistic Boltzmann equation and using some approximations and assumptions for weak gravitational field, we derived the generalized virial theorem in the framework of EBI gravity. In order to compare the predictions of EBI gravity with astrophysical observations we estimated the order of magnitude of the geometric mass, showing that it is compatible with present observations. Finally, considering a power law for the density of galaxies in the cluster, we derived expressions for the radial velocity dispersion of the galaxies, which can be used for testing some features of the EBI gravity.

O problema da matéria escura e o teorema do virial na teoria de gravidade Eddington-Born-Infeld

Dark matter is a fundamental ingredient of the modern Cosmology. It is necessary in order to explain the process of structures formation in the Universe, rotation curves of galaxies and the mass discrepancy in clusters of galaxies. However, although many efforts, in both aspects, theoretical and experimental, have been made, the nature of dark matter is still unknown and the only convincing evidence for its existence is gravitational. This rises doubts about its existence and, in turn, opens the possibility that the Einstein’s gravity needs to be modified at some scale. We study, in this work, the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides en alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations and find their solutions to a spherical system of identical and collisionless point particles. Then, we took into account the collisionless relativistic Boltzmann equation and using some approximations and assumptions for weak gravitational field, we derived the generalized virial theorem in the framework of EBI gravity. In order to compare the predictions of EBI gravity with astrophysical observations we estimated the order of magnitude of the geometric mass, showing that it is compatible with present observations. Finally, considering a power law for the density of galaxies in the cluster, we derived expressions for the radial velocity dispersion of the galaxies, which can be used for testing some features of the EBI gravity.

Influência da vermiculita expandida na formulação de pastas leves para evitar a migração de gás em cimentação de poços petrolíferos

The gas migration during the cementing of wells is one of the main problems of oil wells engineering. Its occurrence can cause severe problems since shortly to loss of control of the well after cementation. Recently, 20/04/2010 In an accident of major proportions in the Gulf of Mexico, among other factors, faulty cementing operation provided the gas migration, causing the accident, in which 11 people died and 17 were injured occurred. Besides the serious consequences that can be caused by gas migration, remediation of the problem, which is made by injecting cement in damaged areas, usually involves additional costs and is not always effective. Therefore, preventing gas migration to be preferred. Some methods are used to prevent the migration of the pressurized gas as the annular space, application of pressure pulses, reducing the height of the cement column compressible cement pastes of low permeability, pastes and to control free filtered water, and binders of thixotropic cement expandable and flexible. Thus, the cement pastes used to prevent gas migration must meet the maximum these methods. Thus, this study aimed to formulate a cement paste to prevent gas migration, using the expanded vermiculite, and evaluate the behavior of the folder trials necessary for use in oil wells. Free water content, rheological properties, compressive strength, loss of liquid phase sedimentation of solids, specific weight, thickening time and gas migration: The following tests were performed. The results show that meets the specifications paste formulated for use in oil wells and the use of expanded vermiculite contribute to the absorption of free water, thixotropy and low density. The absorption of free water is proven to result in zero percentage test free water content, thixotropy is observed with the high value of the initial gel strength (Gi) in testing rheological properties and low density is proven in test weight specific

Tenho um problema: não gosto de ler! A formação do leitor literário construção compartilhada do prazer de ler

Esta tesis de maestría es el resultado de una investigación de carácter cualitativo y etnometodológico, realizada entre agosto de 2003 y junio de 2004, en una escuela primaria estatal, ubicada en Natal RN (Brasil). Su objetivo fue investigar la recepción de la lectura de literatura por parte de una maestra a la que, según reveló, no le gustaba leer y no se consideraba lectora de literatura. Se buscó investigar la mediación que le posibilitara llegar a ser lectora, comprender cuáles son los aspectos que influyen en la relación entre el lector en formación y la lectura de literatura, y verificar cómo repercute ese proceso de formación en la práctica docente de la maestra estudiada. Los procedimientos de investigación fueron aplicados con flexibilidad, tomando en cuenta el proceso de formación lectora de la docente. Los principales instrumentos utilizados fueron dos entrevistas semi-estructuradas, realizadas con la maestra, y notas de campo, que adquirieron el formato de un diario de investigación. En la primera etapa, fueron realizadas treinta sesiones de lectura, para posibilitar el acercamiento de la maestra a diferentes textos literarios. En la segunda etapa, fueron realizados tres encuentros de planificación con la maestra y cinco clases de lectura con sus alumnos. El análisis focaliza la recepción de la lectura literaria por parte de la maestra, abordando diferentes aspectos: su historia en relación con la lectura; la identificación, el contrato ficcional y la relación texto-vida; las previsiones y sus verificaciones; la mediación y el andamiaje brindados para introducir a la maestra en la cultura de la lectura. Se focaliza también la relación entre sus roles de lectora y de mediadora de lectores. Los fundamentos teóricos se basan, principalmente, en Coulon (1995a, 1995b), Vigotsky (1989, 1991, 2003), Graves y Graves (1995), Smith (1991), Jauss (2002), Iser (1996, 1999) y Amarilha (1996, 2001). Como resultados de este trabajo, se destacan el interés de la maestra, la manera en que ella se involucró con las historias leídas mediante procesos de identificación con algunos personajes y la relación que estableció entre los textos y su historia; esos procesos indican avances significativos en su vínculo con la lectura de literatura. La mediación ocupó un papel central en la consecución de aquellos avances. Vale destacar que la relación texto-vida fue establecida por la maestra con cierta ingenuidad, lo que le impidió vivenciar lo ficcional como una actividad lúdica. Se considera necesario un contacto más intenso y regular con textos de ficción, para que la docente pueda distanciarse de su vida cotidiana y adquirir la autonomía y la conciencia transformadora que le permitirán ir y volver de la realidad a la ficción, enriqueciéndose, sin confundirlas. Ese contacto no depende sólo de una actitud individual y personal de la maestra, sino del contexto institucional y social en el cual está inmersa. En ese sentido, la segunda etapa del trabajo de campo demostró que el pasaje de la formación lectora inicial a una acción pedagógica adecuada es complejo; los procesos no son lineales y, todavía, queda un largo camino por recorrer

Utilizando processos geométricos da história da matemática para o ensino de equações do 2º grau

The present work had as principal objective to analyze the, 9th grade students understanding about the solutions of an equation of the 2° degree, using geometric processes of the History of the Mathematics. To do so, the research had as base the elaboration and application of a group of teaching activities, based on Jean Piaget's construtivism. The research consisted of a methodological intervention, that has as subjects the students of a group of 9th grade of the State School José Martins de Vasconcelos, located in the municipal district of Mossoró, Rio Grande do Norte. The intervention was divided in three stages: application of an initial evaluation; development of activities‟ module with emphasis in constructive teaching; and the application of the final evaluation. The data presented in the initial evaluation revealed a low level of the students' understanding with relationship to the calculation of areas of rectangles, resolution of equations of the 1st and 2nd degrees, and they were to subsidize the elaboration of the teaching module. The data collected in the initial evaluation were commented and presented under descriptive statistics form. The results of the final evaluation were analyzed under the qualitative point of view, based on Richard Skemp's theory on the understanding of mathematical concepts. The general results showed a qualitative increase with relationship to the students' understanding on the mathematical concepts approached in the intervention. Such results indicate that a methodology using the previous student‟s knowledge and the development of teaching activities, learning in the construtivist theory, make possible an understanding on the part of the students concerning the thematic proposal

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

As ações de controle da tuberculose na atenção primária à saúde: a visão do doente

Tuberculosis is a disease of great impact on the world context today. In Brazil, the disease management was directed to the Primary Health Care, due to the determination of the Ministry of Health to decentralize health actions for primary care. Thus, since the actions of diagnosis, treatment and control of the disease should happen in this context, however, there are still many barriers that may hinder the realization of these determinations. This study aims to analyze the development of tuberculosis control activities conducted in the services of primary health care from the patient's vision. This is a descriptive, cross-sectional and quantitative study. The population consists of 517 tuberculosis patients treated in units of Primary Health Care in the city of Natal-RN; the sample consists of 93 TB patients. The collect instrument is structured, based in The Primary Care Assessment Tool (PCAT), validated in Brazil and adapted to assess attention to TB in Brazil, with modifications. This instrument was divided into blocks: the first one describes the socio-demographic information of patients with TB and the second one describes the health services working in control, diagnosis and treatment of TB, and includes issues related to the dimensions of primary care: access, bond, services, coordination of care, guidance to the community and family focus. For quantitative analysis, were built indicators for each item of the instrument. The response patterns are followed according to the Likert scale, which was assigned a value between one and five meant that the degree of preference relation (or agreement) of the statements. Values between 1 and 3 were considered unsatisfactory for the indicator, between 3 and less than 4, regular, and between 4 and 5, satisfactory. The results indicate that 62.37% of patients are male, 27.96% aged 41 to 50 years old, and 34.41% unemployed, with low education and low family income. It was found that the reference hospital services are the front door to the patient (59.14%), and are also the local diagnosis of the disease (72.04%). On access, the conditions satisfactory found are: the number of times the patients need to pick up the health care issue, the marking and the facility to get a consultancy in the HS, assistance provided without harm to the individual's attendance labor and facilities related to the proximity between the residence and services; were considered unsatisfactory conditions related to travel to the HS, and on hours and days of operation of services. As for the cast of services were satisfactory and regular actions related to the request for examination to become viable in the first HS, the availability of pot to perform smear and medicines for the treatment, as well as consultations control and receiving information about the disease and the treatment performed; it is considered unsatisfactory the performance of the home care for patients with TB by the HS that acts as a front door, for implementation of the Directly Observed Treatment (DOT), home visits during treatment, the provision of transportation allowance to the patient and the existence of groups for TB patients. Regarding the coordination of care, resulted in regular the action of referring the patient to other HS to obtain examinations, and as unsatisfactory referral to obtain medications. The relationship bond between patient and health team were considered satisfactory in the majority or regular. As for the family and community focus, is satisfactory only the indicator relating to questions from professionals to the patient about the existence of respiratory symptoms in the family. It is considered that there is need for greater commitment from government entities to the incentives required to TB control, as well as the availability of necessary inputs and training of human resources working in the PHC in the ongoing quest to strengthen primary care, as a place of broader host needs to contact the user with the actions and health professionals. It is recommended the adoption of management mechanisms possible to expand the capacity of the health PHC, promoting the service delivery to the user and ensuring attention to population health.

Avaliação de economias de escala e escopo no desempenho de equipes de serviços aplicando Análise de Envoltória de Dados DEA: um estudo em Empresa de Telecomunicações no Brasil

This Master s Thesis proposes the application of Data Envelopment Analysis DEA to evaluate economies of scale and economies of scope in the performance of service teams involved with installation of data communication circuits, based on the study of a major telecommunication company in Brazil. Data was collected from the company s Operational Performance Division. Initial analysis of a data set, including nineteen installation teams, was performed considering input oriented methods. Subsequently, the need for restrictions on weights is analyzed using the Assurance Region method, checking for the existence of zero-valued weights. The resulting returns to scale are then verified. Further analyses using the Assurance Region Constant (AR-I-C) and Variable (AR-I-V) models verify the existence of variable, rather than constant, returns to scale. Therefore, all of the final comparisons use scores obtained through the AR-I-V model. In sequence, we verify if the system has economies of scope by analyzing the behavior of the scores in terms of individual or multiple outputs. Finally, conventional results, used by the company in study to evaluate team performance, are compared to those generated using the DEA methodology. The results presented here show that DEA is a useful methodology for assessing team performance and that it may contribute to improvements on the quality of the goal setting procedure.

Algoritmo evolutivo paralelo para o problema de atribuição de localidades a anéis em redes sonet/sdh

The telecommunications play a fundamental role in the contemporary society, having as one of its main roles to give people the possibility to connect them and integrate them into society in which they operate and, therewith, accelerate development through knowledge. But as new technologies are introduced on the market, increases the demand for new products and services that depend on the infrastructure offered, making the problems of planning of telecommunication networks become increasingly large and complex. Many of these problems, however, can be formulated as combinatorial optimization models, and the use of heuristic algorithms can help solve these issues in the planning phase. This paper proposes the development of a Parallel Evolutionary Algorithm to be applied to telecommunications problem known in the literature as SONET Ring Assignment Problem SRAP. This problem is the class NP-hard and arises during the physical planning of a telecommunication network and consists of determining the connections between locations (customers), satisfying a series of constrains of the lowest possible cost. Experimental results illustrate the effectiveness of the Evolutionary Algorithm parallel, over other methods, to obtain solutions that are either optimal or very close to it

Uso de técnicas de otimização baseadas em derivadas como suporte do planejamento operacional de redes de distribuição de energia elétrica

The usual programs for load flow calculation were in general developped aiming the simulation of electric energy transmission, subtransmission and distribution systems. However, the mathematical methods and algorithms used by the formulations were based, in majority, just on the characteristics of the transmittion systems, which were the main concern focus of engineers and researchers. Though, the physical characteristics of these systems are quite different from the distribution ones. In the transmission systems, the voltage levels are high and the lines are generally very long. These aspects contribute the capacitive and inductive effects that appear in the system to have a considerable influence in the values of the interest quantities, reason why they should be taken into consideration. Still in the transmission systems, the loads have a macro nature, as for example, cities, neiborhoods, or big industries. These loads are, generally, practically balanced, what reduces the necessity of utilization of three-phase methodology for the load flow calculation. Distribution systems, on the other hand, present different characteristics: the voltage levels are small in comparison to the transmission ones. This almost annul the capacitive effects of the lines. The loads are, in this case, transformers, in whose secondaries are connected small consumers, in a sort of times, mono-phase ones, so that the probability of finding an unbalanced circuit is high. This way, the utilization of three-phase methodologies assumes an important dimension. Besides, equipments like voltage regulators, that use simultaneously the concepts of phase and line voltage in their functioning, need a three-phase methodology, in order to allow the simulation of their real behavior. For the exposed reasons, initially was developped, in the scope of this work, a method for three-phase load flow calculation in order to simulate the steady-state behaviour of distribution systems. Aiming to achieve this goal, the Power Summation Algorithm was used, as a base for developing the three phase method. This algorithm was already widely tested and approved by researchers and engineers in the simulation of radial electric energy distribution systems, mainly for single-phase representation. By our formulation, lines are modeled in three-phase circuits, considering the magnetic coupling between the phases; but the earth effect is considered through the Carson reduction. It s important to point out that, in spite of the loads being normally connected to the transformer s secondaries, was considered the hypothesis of existence of star or delta loads connected to the primary circuit. To perform the simulation of voltage regulators, a new model was utilized, allowing the simulation of various types of configurations, according to their real functioning. Finally, was considered the possibility of representation of switches with current measuring in various points of the feeder. The loads are adjusted during the iteractive process, in order to match the current in each switch, converging to the measured value specified by the input data. In a second stage of the work, sensibility parameters were derived taking as base the described load flow, with the objective of suporting further optimization processes. This parameters are found by calculating of the partial derivatives of a variable in respect to another, in general, voltages, losses and reactive powers. After describing the calculation of the sensibility parameters, the Gradient Method was presented, using these parameters to optimize an objective function, that will be defined for each type of study. The first one refers to the reduction of technical losses in a medium voltage feeder, through the installation of capacitor banks; the second one refers to the problem of correction of voltage profile, through the instalation of capacitor banks or voltage regulators. In case of the losses reduction will be considered, as objective function, the sum of the losses in all the parts of the system. To the correction of the voltage profile, the objective function will be the sum of the square voltage deviations in each node, in respect to the rated voltage. In the end of the work, results of application of the described methods in some feeders are presented, aiming to give insight about their performance and acuity

Uso de técnicas de otimização baseadas em derivadas como suporte do planejamento operacional de redes de distribuição de energia elétrica

The usual programs for load flow calculation were in general developped aiming the simulation of electric energy transmission, subtransmission and distribution systems. However, the mathematical methods and algorithms used by the formulations were based, in majority, just on the characteristics of the transmittion systems, which were the main concern focus of engineers and researchers. Though, the physical characteristics of these systems are quite different from the distribution ones. In the transmission systems, the voltage levels are high and the lines are generally very long. These aspects contribute the capacitive and inductive effects that appear in the system to have a considerable influence in the values of the interest quantities, reason why they should be taken into consideration. Still in the transmission systems, the loads have a macro nature, as for example, cities, neiborhoods, or big industries. These loads are, generally, practically balanced, what reduces the necessity of utilization of three-phase methodology for the load flow calculation. Distribution systems, on the other hand, present different characteristics: the voltage levels are small in comparison to the transmission ones. This almost annul the capacitive effects of the lines. The loads are, in this case, transformers, in whose secondaries are connected small consumers, in a sort of times, mono-phase ones, so that the probability of finding an unbalanced circuit is high. This way, the utilization of three-phase methodologies assumes an important dimension. Besides, equipments like voltage regulators, that use simultaneously the concepts of phase and line voltage in their functioning, need a three-phase methodology, in order to allow the simulation of their real behavior. For the exposed reasons, initially was developped, in the scope of this work, a method for three-phase load flow calculation in order to simulate the steady-state behaviour of distribution systems. Aiming to achieve this goal, the Power Summation Algorithm was used, as a base for developping the three phase method. This algorithm was already widely tested and approved by researchers and engineers in the simulation of radial electric energy distribution systems, mainly for single-phase representation. By our formulation, lines are modeled in three-phase circuits, considering the magnetic coupling between the phases; but the earth effect is considered through the Carson reduction. Its important to point out that, in spite of the loads being normally connected to the transformers secondaries, was considered the hypothesis of existence of star or delta loads connected to the primary circuit. To perform the simulation of voltage regulators, a new model was utilized, allowing the simulation of various types of configurations, according to their real functioning. Finally, was considered the possibility of representation of switches with current measuring in various points of the feeder. The loads are adjusted during the iteractive process, in order to match the current in each switch, converging to the measured value specified by the input data. In a second stage of the work, sensibility parameters were derived taking as base the described load flow, with the objective of suporting further optimization processes. This parameters are found by calculating of the partial derivatives of a variable in respect to another, in general, voltages, losses and reactive powers. After describing the calculation of the sensibility parameters, the Gradient Method was presented, using these parameters to optimize an objective function, that will be defined for each type of study. The first one refers to the reduction of technical losses in a medium voltage feeder, through the installation of capacitor banks; the second one refers to the problem of correction of voltage profile, through the instalation of capacitor banks or voltage regulators. In case of the losses reduction will be considered, as objective function, the sum of the losses in all the parts of the system. To the correction of the voltage profile, the objective function will be the sum of the square voltage deviations in each node, in respect to the rated voltage. In the end of the work, results of application of the described methods in some feeders are presented, aiming to give insight about their performance and acuity