https://repositorio.ufu.br/handle/123456789/24872 Wed, 15 Apr 2026 18:04:55 GMT 2026-04-15T18:04:55Z https://repositorio.ufu.br/handle/123456789/48333 Title: Existência e Unicidade de Medidas de Equilíbrio para o Fluxo Geométrico de Lorenz Abstract: This thesis addresses the problem of uniqueness of equilibrium states for the geometric Lorenz flow within the framework of thermodynamic formalism. The system is analyzed through its representation as a suspension flow over a two-dimensional Poincaré map P(x,y) = (L(x), g(x,y)), which is a partially hyperbolic extension of a one-dimensional Lorenz-like map L. While previous results by Bronzi and Oler [BO18] established generic uniqueness for the one-dimensional case, the transition to higher dimensions and continuous time remained a technical challenge due to transverse contraction and the flow's singularity. Our main result proves that, for the space of piecewise Hölder potentials, there exists an open and dense subset H for which the flow admits a unique equilibrium state. The proof is based on a hierarchical approach that begins with the geometric description of the attractor and the formalization of dimensional correspondences (Chapter 1). We then proceed to demonstrate generic uniqueness for the two-dimensional base map (Chapter 3) and the development of a shifted operator J which, through Abramov's formulas, allows for the transfer of openness and density properties from the base to the suspension flow (Chapter 4). This work unifies and extends existing literature, consolidating the genericity of uniqueness in singular-hyperbolic systems. Wed, 11 Feb 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/48333 2026-02-11T00:00:00Z https://repositorio.ufu.br/handle/123456789/47956 Title: Métodos Fuzzy aplicados ao estudo de problemas de programação linear Abstract: The objective of this work is to study Linear Programming Problems (LPP) and apply the algebra and the α-levels of fuzzy numbers in these problems with parameters and variables being real numbers or fuzzy numbers. The first problem studied is a voltage divider circuit that is modeled to determine the values of the centered resistors, so that the impedance of the voltage divider resistor is minimal. Three cases are analyzed for the LPP components: real numbers, type-1 fuzzy numbers and type-2 fuzzy sets. The first case was considered to validate the other two cases. Another analysis was carried out to evaluate the benefits and restrictions in the use of algebra and the α-levels of fuzzy numbers in an affine method of interior points, the Primal - Affine Algorithm (APA), in determining the optimal solution of a LPP with parameters and variables being real numbers. The modified algorithm, Primal – Affin Fuzzy Algorithm (APAF), used triangular fuzzy numbers for each LPP variable and the algebra and α-levels of these numbers. The results obtained by APAF are better with each iteration and APAF requires a smaller number of iterations to reach the optimal value compared to APA, considering the absolute error. This work also demonstrates that a type-2 fuzzy set is a useful and insightful way to model optimization problems under uncertainty.Toward this objective, a new representation of interval-valued fuzzy sets based on constraint functions, called generalized fuzzy intervals, is developed for the analysis of possibilistic optimization problems in which the parameters are generalizations of interval-valued fuzzy numbers. The aim of this study is to represent interval-valued fuzzy sets in a way that possibilistic optimization models solved with generalized fuzzy intervals result in increased information about the risk associated with proposed actions that might be taken based on a solution strategy. This methodology uses the penalty method to reduce a possibilistic LPP into a nonlinear optimization problem, whose results are compared with the resolution of the LPP by α-levels whose solutions are defuzzified via centroid and, possibility and necessity, taking as reference the solution of the deterministic LPP. An application of a supplemental diet is presented to an individual who has been diagnosed with nutritional deficiencies, with varying amounts of nutrients relative to their preferred foods, mathematically described by interval-valued fuzzy number. The results obtained in solving the possibilistic optimization problem using the penalty method allow the individual to determine the best diet to meet their daily nutrient needs at the lowest cost compared to the other methods presented. Wed, 10 Dec 2025 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/47956 2025-12-10T00:00:00Z https://repositorio.ufu.br/handle/123456789/36348 Title: Sobre elementos distinguidos em corpos finitos Abstract: In this thesis, we show some results about primitive normal elements and their generalizations. The thesis begins by studying the existence of primitive normal elements whose image by a rational function is primitive. The second result draws on a work of Cohen which studies consecutive primitive elements. In the thesis, we deal with arithmetic progressions, with a given common difference, such that all elements are primitive and one of them is normal. Next, we look for explicit formulas for the number of $k$-normal elements in extensions of finite fields. In particular, we find a formula that depends on the number of solutions of certain Diophantine equations. For k=0,1,2,3 we find combinatorial formulas that are easy to compute. We also study the existence of 2-normal primitive elements and finally we study r-primitive k-normal elements in general, and apply these results to the particular case where the field has characteristic 11, r=3 and k=3. Wed, 19 Oct 2022 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/36348 2022-10-19T00:00:00Z https://repositorio.ufu.br/handle/123456789/32716 Title: Modelagem da variabilidade em experimentos com misturas Abstract: In industrial experiments, controlling variability is of paramount importance to ensure product quality. Classical regression models are widely used in industry for mixture experiments; however, when the assumption of constant variance is not satisfied, the building of procedures that allow to minimize the variability becomes necessary and other methods of statistical modeling should be considered. The approach considered in this thesis uses the class of generalized linear models. This class is very general and quite flexible, generalizing some of the most important probability distributions and allowing to model variability through of the joint modeling for mean and dispersion (JMMD). The JMMD provides an efficient method for estimating the parameters of the joint models of mean and dispersion; however, the variable selection process is not clear and is based on subjective criteria for choosing the terms of the models. In this thesis the variable selection problem in JMMD is solved. A variable selection procedure, based on hypothesis testing and the goodness of fit of the model is proposed. Simulation methods are used to verify the efficiency of the procedure. The variable selection procedure is adapted for the case of experiments with mixtures and results in a very efficient method for obtaining the mean and variance models. The theory of optimal design of experiments is presented to the JMMD and applied to mixture experiments. The results obtained in this thesis through the application of JMMD in mixture experiments are very encouraging, indicating that the theory promises to be of great utility in modeling and conducting industrial experiments involving mixtures. Fri, 27 Aug 2021 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/32716 2021-08-27T00:00:00Z