https://repositorio.ufu.br/handle/123456789/5155 Tue, 21 Apr 2026 03:23:38 GMT 2026-04-21T03:23:38Z https://repositorio.ufu.br:443/retrieve/08c03a17-3f9a-4c1c-892c-fb3732cd3484/famat.jpg https://repositorio.ufu.br/handle/123456789/5155 https://repositorio.ufu.br/handle/123456789/48576 Title: A fatoração de xⁿ-1 em binômios e trinômios irredutíveis sobre os corpos com 2 e 4 elementos Abstract: Let q be a prime power and Fq the finite field with q elements. The factorization of polynomials over finite fields plays a fundamental role in several areas, such as error-correcting coding theory and cryptography. A particularly important polynomial is xⁿ-1, since, for example, each of its irreducible factors corresponds to a cyclic code. Under certain conditions, the polynomial xⁿ-1 factors exclusively into irreducible binomials and trinomials over Fq. In this case, we say that the pair (n, q) is 3-sparse. The aim of this work is to give a complete classification of the pairs (n, 2) and (n, 4) that are 3-sparse. Thu, 19 Feb 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/48576 2026-02-19T00:00:00Z https://repositorio.ufu.br/handle/123456789/48412 Title: Fibrado de memórias acadêmicas Fri, 20 Feb 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/48412 2026-02-20T00:00:00Z 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/123456789/48039 Title: A matemática do antigo Egito Abstract: This study analyzes the mathematics of Ancient Egypt, developed approximately between 3000 and 300 BC, emphasizing its numerical foundations, operational methods, and practical applications within its historical context. The Egyptian decimal and non-positional number system is examined, focusing on the use of hieroglyphic and later hieratic symbols employed to record quantities and solve administrative, economic, agricultural, and architectural problems. The main mathematical operations practiced by Egyptian scribes—addition, subtraction, multiplication, and division—are discussed, with particular emphasis on the predominant use of unit fractions, a distinctive feature of Egyptian arithmetic. The method of false position is also analyzed as a procedure for solving problems involving unknown quantities, revealing an efficient proportional reasoning despite the absence of formal algebraic notation. The study demonstrates that, although different from modern mathematical approaches, Egyptian methods exhibited a high degree of sophistication and were well suited to the practical demands of their time. Furthermore, the central role of mathematics in the development of agriculture, state administration, and monumental constructions is highlighted. Finally, the study discusses the pedagogical potential of Ancient Egyptian mathematics as a teaching resource in contemporary mathematics education, contributing to an understanding of mathematics as a historical, dynamic body of knowledge constructed by different civilizations throughout human history. Fri, 19 Dec 2025 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/48039 2025-12-19T00:00:00Z