Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais

We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli’s algorithm for square-free denominators; and another for Czichowski’s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work’s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text

Computabilidade no espaço dos intervalos reais: um modelo BSS intervalar

A matemática intervalar é uma teoria matemática originada na década de 60 com o objetivo de responder questões de exatidão e eficiência que surgem na prática da computação científica e na resolução de problemas numéricos. As abordagens clássicas para teoria da computabilidade tratam com problemas discretos (por exemplo, sobre os números naturais, números inteiros, strings sobre um alfabeto finito, grafos, etc.). No entanto, campos da matemática pura e aplicada tratam com problemas envolvendo números reais e números complexos. Isto acontece, por exemplo, em análise numérica, sistemas dinâmicos, geometria computacional e teoria da otimização. Assim, uma abordagem computacional para problemas contínuos é desejável, ou ainda necessária, para tratar formalmente com computações analógicas e computações científicas em geral. Na literatura existem diferentes abordagens para a computabilidade nos números reais, mas, uma importante diferença entre estas abordagens está na maneira como é representado o número real. Existem basicamente duas linhas de estudo da computabilidade no contínuo. Na primeira delas uma aproximação da saída com precisão arbitrária é computada a partir de uma aproximação razoável da entrada [Bra95]. A outra linha de pesquisa para computabilidade real foi desenvolvida por Blum, Shub e Smale [BSS89]. Nesta aproximação, as chamadas máquinas BSS, um número real é visto como uma entidade acabada e as funções computáveis são geradas a partir de uma classe de funções básicas (numa maneira similar às funções parciais recursivas). Nesta dissertação estudaremos o modelo BSS, usado para se caracterizar uma teoria da computabilidade sobre os números reais e estenderemos este para se modelar a computabilidade no espaço dos intervalos reais. Assim, aqui veremos uma aproximação para computabilidade intervalar epistemologicamente diferente da estudada por Bedregal e Acióly [Bed96, BA97a, BA97b], na qual um intervalo real é visto como o limite de intervalos racionais, e a computabilidade de uma função intervalar real depende da computabilidade de uma função sobre os intervalos racionais

O estudo das funções quadráticas e sua relação com o cotidiano

Across the centuries, Mathematics - exact science as it is - has become a determining role in the life of man, which forms to use suprir needs of their daily lives. With this trajectory, is characterized the importance of science as an instrument of recovery not only conteudstica, but also a mathematician to know that leads the apprentice to be a dynamic process of learning ecient, able to find solutions to their real problems. However, it is necessary to understand that mathematical knowledge today requires a new view of those who deal directly with the teaching-learning process, as it is for them - Teachers of Mathematics - desmistificarem the version that mathematics, worked in the classroom, causes difficulties for the understanding of students. On this view, we tried to find this work a methodology that helps students better understand the Quadratic functions and its applications in daily life. Making use of knowledge Ethnomathematics, contextualizing the problems relating to the content and at the same time handling the software GeoGebra, aiming a better view of the behavior of graphs of functions cited

Ambiente computacional paradesenvolvimento de aplicações de controladores lógicos programáveis baseado em linguagens SFC e ST

This work proposes an environment for programming programmable logic controllers applied to oil wells with BCP type method of artificially lifting. The environment will have an editor based in the diagram of sequential functions for programming of PLCs. This language was chosen due to the fact of being high-level and accepted by the international standard IEC 61131-3. The use of these control programs in real PLC will be possible with the use of an intermediate level of language based on XML specification PLCopen T6 XML. For the testing and validation of the control programs, an area should be available for viewing variables obtained through communication with a real PLC. Thus, the main contribution of this work is to develop a computational environment that allows: modeling, testing and validating the controls represented in SFC and applied in oil wells with BCP type method of artificially lifting

Supressão do ruído de rolamento superficial utilizando a transformada Curvelet

Among the many types of noise observed in seismic land acquisition there is one produced by surface waves called Ground Roll that is a particular type of Rayleigh wave which characteristics are high amplitude, low frequency and low velocity (generating a cone with high dip). Ground roll contaminates the relevant signals and can mask the relevant information, carried by waves scattered in deeper regions of the geological layers. In this thesis, we will present a method that attenuates the ground roll. The technique consists in to decompose the seismogram in a basis of curvelet functions that are localized in time, in frequency, and also, incorporate an angular orientation. These characteristics allow to construct a curvelet filter that takes in consideration the localization of denoise in scales, times and angles in the seismogram. The method was tested with real data and the results were very good

Atenuação de ruídos coerentes utilizando decomposição em modos empíricos

The seismic processing technique has the main objective to provide adequate picture of geological structures from subsurface of sedimentary basins. Among the key steps of this process is the enhancement of seismic reflections by filtering unwanted signals, called seismic noise, the improvement of signals of interest and the application of imaging procedures. The seismic noise may appear random or coherent. This dissertation will present a technique to attenuate coherent noise, such as ground roll and multiple reflections, based on Empirical Mode Decomposition method. This method will be applied to decompose the seismic trace into Intrinsic Mode Functions. These functions have the properties of being symmetric, with local mean equals zero and the same number of zero-crossing and extremes. The developed technique was tested on synthetic and real data, and the results were considered encouraging

Dos movimentos sociais às funções institucionais: a Consolidação de uma geração política em Sergipe.

This study was presented to the Post-Graduation Program in Social Sciences at UFRN as part of the requisites for obtaining the title of Master in Social Sciences. It describes the results of the research From social movements to the institutional functions: the consolidation of a generation . Its main objective is to describe the history of a political generation that emerged from the social movements, in the 80 s, in Sergipe, and that nowadays occupies the main governmental positions in the State s political scenario. As its specific objectives, the research described the emerging of social movements in the 80s in Sergipe; it found in the social movements in Sergipe, in the 80s, the beginning of the history of a new political generation, and described the consolidation of this new political generation in institutional positions as the expression of a new group of power in Sergipe s politics. Among the social movements that gained visibility in that period and that projected their leadership into the political scenario of Sergipe, this study highlights: the students movement, teacher s movement, bank clercks movement, miners movement, and rural workers movement. It utilized as methodology the research in sites, magazines, and the use of testimonies from semi-structured interviews. The main leadership of the five movements that were analyzed is, nowadays, governing the state, administering the capital s city hall, and performing legislative work at the Legislative Assembly of Sergipe, and at the Chamber of City Councilmen of Aracaju. This study described the political history of the main leadership of that generation of militants and organizers of social movements, and of left party groups in Sergipe, highlighting that their consolidation in the political scenario of the State meant the consolidation of a new group of power in Sergipe s politics.

Papéis e funções dos profissionais dos serviços e política de saúde mental em Natal (RN)

A assistência psiquiátrica e as políticas de atenção à saúde mental passaram por diversas transformações, marcadas ora por avanços, ora por retrocessos centrados no estigma, desinteresse e preconceito que ainda permeiam a sociedade e o senso comum. Este estudo objetivou analisar o processo de reforma psiquiátrica e a política de saúde mental do Município de Natal/RN a partir dos papéis e funções dos profissionais de nível superior dos serviços substitutivos em saúde mental. Trata-se de uma pesquisa analítica, transversal, com dados quantitativos e qualitativos, realizada nos sete serviços substitutivos de saúde mental de Natal, entre os meses de março a agosto de 2013, após aprovação do estudo pelo Comitê de Ética em Pesquisa da Universidade Federal do Rio Grande do Norte, Parecer nº 217.808, CAAE: 10650612.8.1001.5537, em 01 de março de 2013. A amostra por conveniência compôs-se por 65 profissionais de nível superior das equipes de saúde mental. Utilizou-se um questionário com questões fechadas e semiabertas sobre o perfil socioeconômico, as políticas, as práticas e a formação em saúde mental. Tabularam-se e submeteram-se as respostas das questões fechadas do questionário no programa estatístico SPSS versão 20.0, analisando-os por meio de estatística descritiva, com a formulação de gráficos e tabelas. Para verificar o nível de significância, adotando-se p-valor<0,05, optou-se pela aplicação dos testes qui-quadrado e exato de Fisher. Submeteram-se os dados das questões semiabertas ao software ALCESTE e à luz da análise de conteúdo de Bardin. O perfil dos participantes caracterizou-se por maioria do sexo feminino (79%), faixa etária de 36 a 55 anos (52%), média de 42 anos, carga horária de 40 horas semanais (62%), tempo de conclusão da graduação de 6 a 15 anos (57%), trabalhavam na área de saúde mental há menos de 10 anos (72%) e na instituição pesquisada há 5 anos ou menos (52%). Da amostra estudada, 86% atendiam grupos de usuários, 97% realizavam atendimento individual, 94% observavam o comportamento do paciente, 92% realizavam atendimento familiar, utilizando, principalmente, a abordagem cognitiva (28%). Os dados qualitativos originaram cinco categorias: Formação acadêmica e atuação em saúde mental; Ausência de capacitação e supervisão em saúde mental; Dificuldades da prática profissional nos serviços substitutivos de saúde mental; Trabalho em equipe: entre acertos e conflitos; Política Nacional de Saúde Mental: uma realidade ainda distante. Detectou-se adequabilidade dos papéis e funções dos profissionais quanto ao tempo de trabalho na saúde mental e na instituição pesquisada; no atendimento e atividades individuais; na promoção de ações visando à autonomia do paciente; no atendimento em grupo de pacientes; e, em parte, à família/familiar dos portadores de transtorno mental, havendo inadequação quanto ao atendimento aos grupos de familiares (52.3%), à formação especializada em saúde mental (69.2%; p=0,02) e às dificuldades de trabalho nos serviços (87.7%). Evidenciou-se adequação nos papéis e nas funções d esenvolvidas pelos profissionais nos serviços substitutivos em saúde mental de Natal, embora convivendo em seu cotidiano com inúmeras dificuldades encontradas no desenvolvimento de suas práticas profissiona is frente às condições de trabalho

Dedução de Funções de Alívio para Priorização de Variantes de Chaveamento Adequadas à Eliminação de Sobrecargas

Eventually, violations of voltage limits at buses or admissible loadings of transmission lines and/or power transformers may occur by the power system operation. If violations are detected in the supervision process, corrective measures may be carried out in order to eliminate them or to reduce their intensity. Loading restriction is an extreme solution and should only be adopted as the last control action. Previous researches have shown that it is possible to control constraints in electrical systems by changing the network topology, using the technique named Corrective Switching, which requires no additional costs. In previous works, the proposed calculations for verifying the ability of a switching variant in eliminating an overload in a specific branch were based on network reduction or heuristic analysis. The purpose of this work is to develop analytical derivation of linear equations to estimate current changes in a specific branch (due to switching measures) by means of few calculations. For bus-bar coupling, derivations will be based on short-circuit theory and Relief Function methodology. For bus-bar splitting, a Relief Function will be derived based on a technique of equivalent circuit. Although systems of linear equations are used to substantiate deductions, its formal solution for each variant, in real time does not become necessary. A priority list of promising variants is then assigned for final check by an exact load flow calculation and a transient analysis using ATP Alternative Transient Program. At last, results obtained by simulation in networks with different features will be presented

Uma fundamentação para sinais e sistemas intervalares

In this work we use Interval Mathematics to establish interval counterparts for the main tools used in digital signal processing. More specifically, the approach developed here is oriented to signals, systems, sampling, quantization, coding and Fourier transforms. A detailed study for some interval arithmetics which handle with complex numbers is provided; they are: complex interval arithmetic (or rectangular), circular complex arithmetic, and interval arithmetic for polar sectors. This lead us to investigate some properties that are relevant for the development of a theory of interval digital signal processing. It is shown that the sets IR and R(C) endowed with any correct arithmetic is not an algebraic field, meaning that those sets do not behave like real and complex numbers. An alternative to the notion of interval complex width is also provided and the Kulisch- Miranker order is used in order to write complex numbers in the interval form enabling operations on endpoints. The use of interval signals and systems is possible thanks to the representation of complex values into floating point systems. That is, if a number x 2 R is not representable in a floating point system F then it is mapped to an interval [x;x], such that x is the largest number in F which is smaller than x and x is the smallest one in F which is greater than x. This interval representation is the starting point for definitions like interval signals and systems which take real or complex values. It provides the extension for notions like: causality, stability, time invariance, homogeneity, additivity and linearity to interval systems. The process of quantization is extended to its interval counterpart. Thereafter the interval versions for: quantization levels, quantization error and encoded signal are provided. It is shown that the interval levels of quantization represent complex quantization levels and the classical quantization error ranges over the interval quantization error. An estimation for the interval quantization error and an interval version for Z-transform (and hence Fourier transform) is provided. Finally, the results of an Matlab implementation is given

Análise de Agrupamentos Com Base na Teoria da Informação: Uma Abordagem Representativa

Currently, one of the biggest challenges for the field of data mining is to perform cluster analysis on complex data. Several techniques have been proposed but, in general, they can only achieve good results within specific areas providing no consensus of what would be the best way to group this kind of data. In general, these techniques fail due to non-realistic assumptions about the true probability distribution of the data. Based on this, this thesis proposes a new measure based on Cross Information Potential that uses representative points of the dataset and statistics extracted directly from data to measure the interaction between groups. The proposed approach allows us to use all advantages of this information-theoretic descriptor and solves the limitations imposed on it by its own nature. From this, two cost functions and three algorithms have been proposed to perform cluster analysis. As the use of Information Theory captures the relationship between different patterns, regardless of assumptions about the nature of this relationship, the proposed approach was able to achieve a better performance than the main algorithms in literature. These results apply to the context of synthetic data designed to test the algorithms in specific situations and to real data extracted from problems of different fields

Uma proposição para o cálculo de mapas de disparidade de imagens estéreo usando um interpolador neural baseado em funções de base radial

This study aims to seek a more viable alternative for the calculation of differences in images of stereo vision, using a factor that reduces heel the amount of points that are considered on the captured image, and a network neural-based radial basis functions to interpolate the results. The objective to be achieved is to produce an approximate picture of disparities using algorithms with low computational cost, unlike the classical algorithms

Identificação de uma planta de corrente de um motor de indução utilizando redes de base radial

The present work describes the use of a mathematical tool to solve problems arising from control theory, including the identification, analysis of the phase portrait and stability, as well as the temporal evolution of the plant s current induction motor. The system identification is an area of mathematical modeling that has as its objective the study of techniques which can determine a dynamic model in representing a real system. The tool used in the identification and analysis of nonlinear dynamical system is the Radial Basis Function (RBF). The process or plant that is used has a mathematical model unknown, but belongs to a particular class that contains an internal dynamics that can be modeled.Will be presented as contributions to the analysis of asymptotic stability of the RBF. The identification using radial basis function is demonstrated through computer simulations from a real data set obtained from the plant

Utilizando a televisão digital como um meio de comunicação para ambientes interativos reais

This Dissertation aims to provide a communication mechanism between Digital TV viewers and interaction devices, such as robots, for example, placed on the environment from which a TV program is being live broadcasted. Such communication mechanism has the objective to allow viewers controll the Interaction Devices through their TV devices, using the broadcast channel present in Interactive Digital TV systems, and receive data from the devices by the broadcast channel. This system was projected as a middlewaer system where the Interaction Devices in the TV program set are interconnected, creating a Interactive Device Network. With this approach, the system is capable of manage the devices on the network, controlling the flow of coming and leaving elements, in a transparent way for the viewers. The system yet allows the Interaction Devices communicate each other, with a integrated communication channel with no worries about the physical communication layer

Desenvolvimento de uma arquitetura em hardware prototipada em FPGA para aplicações genéricas utilizando redes neurais artificiais embarcadas

This work proposes hardware architecture, VHDL described, developed to embedded Artificial Neural Network (ANN), Multilayer Perceptron (MLP). The present work idealizes that, in this architecture, ANN applications could easily embed several different topologies of MLP network industrial field. The MLP topology in which the architecture can be configured is defined by a simple and specifically data input (instructions) that determines the layers and Perceptron quantity of the network. In order to set several MLP topologies, many components (datapath) and a controller were developed to execute these instructions. Thus, an user defines a group of previously known instructions which determine ANN characteristics. The system will guarantee the MLP execution through the neural processors (Perceptrons), the components of datapath and the controller that were developed. In other way, the biases and the weights must be static, the ANN that will be embedded must had been trained previously, in off-line way. The knowledge of system internal characteristics and the VHDL language by the user are not needed. The reconfigurable FPGA device was used to implement, simulate and test all the system, allowing application in several real daily problems