Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-02-22T12:19:46Z No. of bitstreams: 1 luizfernandonascimentovasconcellos.pdf: 592098 bytes, checksum: e48a1cd338b2f3a798491febc67e2897 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-02-26T14:00:18Z (GMT) No. of bitstreams: 1 luizfernandonascimentovasconcellos.pdf: 592098 bytes, checksum: e48a1cd338b2f3a798491febc67e2897 (MD5) / Made available in DSpace on 2016-02-26T14:00:18Z (GMT). No. of bitstreams: 1 luizfernandonascimentovasconcellos.pdf: 592098 bytes, checksum: e48a1cd338b2f3a798491febc67e2897 (MD5) Previous issue date: 2014-03-18 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho é voltado para professores e alunos do Ensino Médio. Tem como objetivo mostrar a utilização do Método da Eliminação de Gauss-Jordan para a resolução de sistemas de equações lineares, cálculo de matrizes inversas e cálculo de determinantes. A motivação para a escolha desse tema é que, cada vez mais, o estudo das matrizes, dos determinantes e, consequentemente, dos sistemas de equações lineares vem sendo deixado de lado no Ensino Médio. Inicialmente, é feito um pequeno apanhado sobre o que são matrizes equivalentes e operações elementares, além de se falar sobre cofator de um elemento de uma matriz e sobre matriz adjunta, necessária para o cálculo da inversa utilizando-se determinantes. Apresenta-se um pouco da história de Gauss e de Jordan e, logo em seguida, o método propriamente dito. Também é visto o que acontece com o método quando as matrizes não são invertíveis, os sistemas são possíveis e indeterminados ou os sistemas são impossíveis. Quanto aos determinantes, são apresentadas suas propriedades e mostrada a eficácia do método para determinantes de ordem n 3 e, além disso, é mostrada a aplicação dos determinantes no cálculo de inversas e na resolução de sistemas de equações pela Regra de Cramer. Finalmente, são apresentadas sugestões de exercícios com uma breve resolução. / This work is oriented to teachers and students in the high school. It aims to show the usage of Gauss-Jordan’s Elimination Method to solve systems of linear equations, calculation of inverse matrices and determinants. The motivation behind the selection of this topic is that, more and more, the study of matrices, determinants, and consequently, systems of linear equations has been ignored in the high school. Firstly, an abridgement is done on what equivalent matrices and elementary operations are. Secondly, it explains about the cofactor of an element of a matrix and about adjoint matrices, needed for the calculation of the inverse matrix using determinants. A little introduction of Gauss and Jordan’s histories is made, and then, the method itself. It is also shown what happens with the method when the matrices are not invertible, the systems are possible but undetermined, or, the systems are not possible. Concerning determinants, their properties are presented and the method’s efficacy for determinants of order n 3 is shown and furthermore, it is shown the application of the determinants in the calculation of inverse matrices and resolutions of systems using Cramer’s Rule. Finally, some suggestions for exercises are presented with brief resolutions.

Many problems in applied mathematics and physics are formulated most naturally in terms of matrices, and can be solved by computing functions of these matrices. For example, in quantum mechanics, the coherent dynamics of physical systems is described by the matrix exponential of their Hamiltonian. In state of the art experiments, one can now observe such unitary evolution of many-body systems, which is of fundamental interest in the study of many-body quantum phenomena. On the other hand the theoretical simulation of such non-equilibrium many-body dynamics is very challenging. In this thesis, we develop a symbolic approach to matrix functions and quantum dynamics based on a novel algebraic structure we identify for sets of walks on graphs. We begin by establishing the graph theoretic equivalent to the fundamental theorem of arithmetic: all the walks on any finite digraph uniquely factorise into products of prime elements. These are the simple paths and simple cycles, walks forbidden from visiting any vertex more than once. We give an algorithm that efficiently factorises individual walks and obtain a recursive formula to factorise sets of walks. This yields a universal continued fraction representation for the formal series of all walks on digraphs. It only involves simple paths and simple cycles and is thus called a path-sum. In the second part, we recast matrix functions into path-sums. We present explicit results for a matrix raised to a complex power, the matrix exponential, matrix inverse, and matrix logarithm. We introduce generalised matrix powers which extend desirable properties of the Drazin inverse to all powers of a matrix. In the third part, we derive an intermediary form of path-sum, called walk-sum, relying solely on physical considerations. Walk-sum describes the dynamics of a quantum system as resulting from the coherent superposition of its histories, a discrete analogue to the Feynman path-integrals. Using walk-sum we simulate the dynamics of quantum random walks and of Rydberg-excited Mott insulators. Using path-sum, we demonstrate many-body Anderson localisation in an interacting disordered spin system. We give two observable signatures of this phenomenon: localisation of the system magnetisation and of the linear magnetic response function. Lastly we return to the study of sets of walks. We show that one can construct as many representations of series of walks as there are ways to define a walk product such that the factorisation of a walk always exist and is unique. Illustrating this result we briefly present three further methods to evaluate functions of matrices. Regardless of the method used, we show that graphs are uniquely characterised, up to an isomorphism, by the prime walks they sustain.

Este trabalho apresenta uma nova metodologia para mapeamento no espaço de cor colorimétrico CIEXYZ, dos valores de triestímulo obtidos em um espaço de cor não colorimétrico definido pelas curvas de sensibilidade de um sensor eletrônico. A inovação do método proposto é realizar o mapeamento através de três redes neurais artificiais sendo que cada uma é especializada em mapear cores com um determinado triestímulo dominante. É feita a comparação dos resultados do mapeamento com vários trabalhos publicados sobre mapeamento de um espaço de cor em outro usando diversas técnicas. Os resultados mostram a eficiência do método proposto e permitem sua utilização em equipamentos para medir cores, incrementando sua precisão. / This work presents a new method for mapping a non colorimetric color space defined by the sensitivity curves of an electronic color sensor to the colorimetric color space CIEXYZ. The novelty of the proposed method is to perform the mapping by a set of three artificial neural networks, each one specialized in mapping colors with a specific dominant tristimulus. The results are compared with the ones obtained in published works about the mapping of color spaces, using several methods. The results of the method proposed in this work show that it is efficient and it can be used in equipments for measuring colors, improving its precision.

Este trabalho apresenta uma nova metodologia para mapeamento no espaço de cor colorimétrico CIEXYZ, dos valores de triestímulo obtidos em um espaço de cor não colorimétrico definido pelas curvas de sensibilidade de um sensor eletrônico. A inovação do método proposto é realizar o mapeamento através de três redes neurais artificiais sendo que cada uma é especializada em mapear cores com um determinado triestímulo dominante. É feita a comparação dos resultados do mapeamento com vários trabalhos publicados sobre mapeamento de um espaço de cor em outro usando diversas técnicas. Os resultados mostram a eficiência do método proposto e permitem sua utilização em equipamentos para medir cores, incrementando sua precisão. / This work presents a new method for mapping a non colorimetric color space defined by the sensitivity curves of an electronic color sensor to the colorimetric color space CIEXYZ. The novelty of the proposed method is to perform the mapping by a set of three artificial neural networks, each one specialized in mapping colors with a specific dominant tristimulus. The results are compared with the ones obtained in published works about the mapping of color spaces, using several methods. The results of the method proposed in this work show that it is efficient and it can be used in equipments for measuring colors, improving its precision.

The diploma thesis deals with the topic of free-form deformations. The main goal of this work were elaboration of theoretical knowledge about this issue and the programming of selected methods od free-form deformations. The first part describes the required spline theory, matrix calculus and free-form deformations. The resulting version shows three programs. The first program compares the selected free-form deformation methods to the example of the 4x4 control point grid. The second program serves as a generalization for the general case of grid of control points. The last program is based on direct manipulation of arbitrary surface point and following recomputation of the control points to obtain demanded shape.

The main objective of this thesis is the definition of tourism supply and demand of tourism to the region Bystřice Pernštejnem. The demand for the region is established on the basis of the survey. The first sub-goal is to evaluate the impact of tourism on the budget of municipalities. In this first part is carried out field research among the mayors of municipalities in the region on their perceptions of tourism. Evaluation of the impact of tourism is carried out on the town budget Bystřice Pernštejnem.First discussed are the revenues, expenditures, and finally the overall impact. Part of this section are evaluated impacts on employment and value of tourist activities found in the region. The second sub-goal is to assess the impact of subsidies on production in the region. This section compares the projects in the field of tourism and other projects on the basis of the calculated gross value added of these observed effects support. The last sub-goal is to determine the multiplier of tourism. Part of this section is a national regionalization symmetric input-output tables for the region SO ORP Bystřice Pernštejnem. Based on the tables are compiled using the technical coefficients matrix, Leontief inverse matrix and matrix Leontieofovi input multipliers calculated for each economic activity. Consequently, expenditure of tourists found the overall multiplier of tourism for the region Bystřice Pernštejnem spending tourists and the impact on production in the region.