Competição oligopolística em ambiente de incerteza knightiana

Este artigo aplica um teorema da existência de equilibrios de Nash sob incerteza (Dow & Werlang, 1994) à um problema clássico da Teoria da Competição Oligopolística. Particularmente, mostra como se pode mapear todos os equilibrios de Cournot (que têm, por limite, as soluções de monopólio e de bloqueio total da produção) unicamente em função da aversão à incerteza dos produtores. Os efeitos de variações destes parâmetros sobre as produções de equilibrio são estudados, tanto no curto prazo como no caso da livre entrada no mercado e convergência para o equilibrio competitivo. Também, as soluções de Cournot sob incerteza são comparadas com a solução do monopólio standard. Particularmente, mostra-se que existe um nível de incerteza tal que toda aversão à incerteza (na indústria) superior à este nível, induz os agentes a produzir, agregadamente, quantidades menores que as de monopólio. Enfim, as soluções de equilibrio são particularizadas para os casos da Demanda Linear e do Duopólio de Cournot. A análise do equilibrio competitivo no caso simétrico, permite identificar o coeficiente de aversão à incerteza na indústria como um custo proporcional transferido via preço pelos produtores aos consumidores (índice de Lerner).

Cálculo Diferencial e Integral - Integrais

Neste material é apresentado primeiramente um teorema muito importante que é o teorema do valor médio, com exemplos de aplicação. Na sequência temos a definição de antiderivada ou primitiva de uma função. No segundo tópico segue a definição de integral indefinida e a apresentação de algumas integrais importantes e básicas. Uma tabela de integrais básicas também é disponibilizada. Finalizando, foram listados propriedades e exemplos de integrais.

Integrais definidas e outros métodos de integração

Na este capítulo, é apresentada inicialmente a definição formal de integral, mostrando que a mesma calcula a área sob o gráfico de uma função em um intervalo [a, b]. Na sequência são listadas as propriedades das integrais sem demonstração e também algumas convenções que serão utilizadas. A unidade também traz o teorema fundamental do cálculo e exemplo do cálculo de uma área usando a integral. Também são apresentadas as técnicas de integração por substituição e a técnica de integração por partes, além de vários exemplos resolvidos passo a passo. Finalizando, temos algumas integrais envolvendo funções trigonométricas, fórmulas de redução ou de recorrência e substituições trigonométricas.

Integrais definidas e aplicações

Capítulo 8 do Livro Noções de "Cálculo Diferencial e Integral para Tecnólogos"

Cálculo de integral indefinida por mudança de variável [Audiodescrição]

Versão com menu acessível para leitores de tela e vídeo com audiodescrição.

Método de integração por partes [Audiodescrição]

Versão com menu acessível para leitores de tela e vídeo com audiodescrição.

Divisor e Máximo Divisor Comum

A videoaula traz o teorema da divisão no contexto dos números inteiros e o Máximo Divisor Comum (MDC). Destaca ainda o algoritmo de Euclides, sendo este usado para cálculo do máximo divisor comum.

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

Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números

The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him

Comparação de alguns modelos matemáticos para ajuste à curva de lactação média de um rebanho da raça Caracu

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelo de covariância bayesiana para seleção de protfólios de investimentos

The portfolio theory is a field of study devoted to investigate the decision-making by investors of resources. The purpose of this process is to reduce risk through diversification and thus guarantee a return. Nevertheless, the classical Mean-Variance has been criticized regarding its parameters and it is observed that the use of variance and covariance has sensitivity to the market and parameter estimation. In order to reduce the estimation errors, the Bayesian models have more flexibility in modeling, capable of insert quantitative and qualitative parameters about the behavior of the market as a way of reducing errors. Observing this, the present study aimed to formulate a new matrix model using Bayesian inference as a way to replace the covariance in the MV model, called MCB - Covariance Bayesian model. To evaluate the model, some hypotheses were analyzed using the method ex post facto and sensitivity analysis. The benchmarks used as reference were: (1) the classical Mean Variance, (2) the Bovespa index's market, and (3) in addition 94 investment funds. The returns earned during the period May 2002 to December 2009 demonstrated the superiority of MCB in relation to the classical model MV and the Bovespa Index, but taking a little more diversifiable risk that the MV. The robust analysis of the model, considering the time horizon, found returns near the Bovespa index, taking less risk than the market. Finally, in relation to the index of Mao, the model showed satisfactory, return and risk, especially in longer maturities. Some considerations were made, as well as suggestions for further work

Técnicas de simplificação de redes e otimização multiobjetivo para análise de variações de tensão em regime permanente provocadas por parques eólicos integrados ao sistema elétrico

This study presents a description of the development model of a representation of simplified grid applied in hybrid load flow for calculation of the voltage variations in a steady-state caused by the wind farm on power system. Also, it proposes an optimal load-flow able to control power factor on connection bar and to minimize the loss. The analysis process on system, led by the wind producer, it has as base given technician supplied by the grid. So, the propose model to the simplification of the grid that allows the necessity of some knowledge only about the data referring the internal network, that is, the part of the network that interests in the analysis. In this way, it is intended to supply forms for the auxiliary in the systematization of the relations between the sector agents. The model for simplified network proposed identifies the internal network, external network and the buses of boulders from a study of vulnerability of the network, attributing them floating liquid powers attributing slack models. It was opted to apply the presented model in Newton-Raphson and a hybrid load flow, composed by The Gauss-Seidel method Zbarra and Summation Power. Finally, presents the results obtained to a developed computational environment of SCILAB and FORTRAN, with their respective analysis and conclusion, comparing them with the ANAREDE

Um algoritmo para estimação de estado em alimentadores de distribuição de energia elétrica com base no método da soma de potências

Most algorithms for state estimation based on the classical model are just adequate for use in transmission networks. Few algorithms were developed specifically for distribution systems, probably because of the little amount of data available in real time. Most overhead feeders possess just current and voltage measurements at the middle voltage bus-bar at the substation. In this way, classical algorithms are of difficult implementation, even considering off-line acquired data as pseudo-measurements. However, the necessity of automating the operation of distribution networks, mainly in regard to the selectivity of protection systems, as well to implement possibilities of load transfer maneuvers, is changing the network planning policy. In this way, some equipments incorporating telemetry and command modules have been installed in order to improve operational features, and so increasing the amount of measurement data available in real-time in the System Operation Center (SOC). This encourages the development of a state estimator model, involving real-time information and pseudo-measurements of loads, that are built from typical power factors and utilization factors (demand factors) of distribution transformers. This work reports about the development of a new state estimation method, specific for radial distribution systems. The main algorithm of the method is based on the power summation load flow. The estimation is carried out piecewise, section by section of the feeder, going from the substation to the terminal nodes. For each section, a measurement model is built, resulting in a nonlinear overdetermined equations set, whose solution is achieved by the Gaussian normal equation. The estimated variables of a section are used as pseudo-measurements for the next section. In general, a measurement set for a generic section consists of pseudo-measurements of power flows and nodal voltages obtained from the previous section or measurements in real-time, if they exist -, besides pseudomeasurements of injected powers for the power summations, whose functions are the load flow equations, assuming that the network can be represented by its single-phase equivalent. The great advantage of the algorithm is its simplicity and low computational effort. Moreover, the algorithm is very efficient, in regard to the accuracy of the estimated values. Besides the power summation state estimator, this work shows how other algorithms could be adapted to provide state estimation of middle voltage substations and networks, namely Schweppes method and an algorithm based on current proportionality, that is usually adopted for network planning tasks. Both estimators were implemented not only as alternatives for the proposed method, but also looking for getting results that give support for its validation. Once in most cases no power measurement is performed at beginning of the feeder and this is required for implementing the power summation estimations method, a new algorithm for estimating the network variables at the middle voltage bus-bar was also developed

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