DSpace Collection:
https://repositorio.ufu.br/handle/123456789/5473
2020-10-16T13:51:14ZÍndice polinomial numérico de um espaço de Banach
https://repositorio.ufu.br/handle/123456789/29718
Title: Índice polinomial numérico de um espaço de Banach
Abstract: This dissertation’s main purpose is to study of the polynomial numerical index of order k of
a Banach space. First, we will examine the polynomial numerical index for Banach spaces in
general. Next, we will calculate and estimate the polynomial numerical index of specific spaces.
We will begin working with the polynomial numerical index of continuos functions spaces and
essentially bounded measurable functions spaces. In sequence, we will study the polynomial
numerical index of order k of lush, CL and C-rich spaces. Finally, we will investigate the
polynomial numerical index of order k of sequences spaces.2020-07-24T00:00:00ZConjunto de bifurcação de funções algébricas no plano
https://repositorio.ufu.br/handle/123456789/29587
Title: Conjunto de bifurcação de funções algébricas no plano
Abstract: We present the characterization of the bifurcation set of algebraic functions defined in the
real and complex plane, obtained by Tibar e Zaharia in [16, Theorem 2.5] and by Parusiński
in [12, Theorem 1.4], respectively. We present two results obtained by D’Acunto e Grandjean
in [2, Theorem 3.4] and by Parusiński in [12, Lemma 1.2], that which allow us to know when a
semialgebraic or polynomial complex function a local topological fibration on a regular value.
The example of King, Tibar e Zaharia [16, Example 5.4] show that these last two results do
not provide a complete characterization of the bifurcation set.2020-07-21T00:00:00ZMáximo número de zeros de uma família de polinômios em um produto cartesiano finito
https://repositorio.ufu.br/handle/123456789/29293
Title: Máximo número de zeros de uma família de polinômios em um produto cartesiano finito
Abstract: In this work, we present an upper bound for the number of zeros of a family of polynomials in a finite cartesian product and additionally we show an example that takes that upper bound turning that upper bound in a maximum. These results have been proven using algebraic and combinatorial tools. The main elements used to prove this result are the Hilbert's base theorem, the Groebner's bases, the Hilber's function, the generalization of Macaulay's theorem and the generalization of Wei's theorem. This work was mainly based on the texts Ideals, Varieties and Algorithms (Cox D.) and Generalized Hamming weights for linear codes (Wei V.K.).2020-02-20T00:00:00ZAssociatividade nos produtos tensoriais projetivo e injetivo
https://repositorio.ufu.br/handle/123456789/28992
Title: Associatividade nos produtos tensoriais projetivo e injetivo
Abstract: Given the normed spaces X_1,...,X_n, real or complex, in this work we study some properties of the projective tensor product of X_1,...,X_n and of the injective tensor product of X_1,...,X_n. The main purposes are to state and to provide detailed proofs of the following results: (i) The projective tensor product is associative; (ii) If at least two of the normed spaces X_1,...,X_n are infinite dimensional, then the tensor product of X_1,...,X_n endowed with the projective norm is incomplete; (iii) The injective tensor product is associative. To prove these results, the algebraic tensor product is constructed, the projective
and injective norms are studied and linearization theorems for each of these cases are proved.2020-02-27T00:00:00Z