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Master's Dissertation
DOI
10.11606/D.55.2018.tde-24042018-155451
Document
Author
Full name
Adriana de Cassia Favoretti
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1995
Supervisor
Committee
Achcar, Jorge Alberto (President)
Diniz, Carlos Alberto Ribeiro
Paula, Gilberto Alvarenga
Title in Portuguese
MODELOS NÂO-LINEARES: UM ENFOQUE BAYESIANO.
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Dada uma função holomorfa f : Cn+1 → C com f(0) = 0 e, O é uma singularidade isolada, a hipersuperfície de nível f-1 (0) na vizinhança de O, Dε ∩ f-1 (0) é homeomorfo ao cone com base K = Sε ∩ f-1 (0). Logo o estudo de K é essencial para o entendimento de hipersuperfície de nível na vizinhança de zero, sob um ponto de vista topológica. A aplicação Φ = f / &Iota ; f Ι : Sε - K → S1, é a projeção de um fibrado localmente trivial denominado de Fibração de Milnor e a sua fibra F0= Φ-1 (1) tem o tipo de homotopia de um bouquet de esferas SnvSnv...vSn . Para um difeomorfismo específico h : F0 → F0, o polinômio característico Δ (t) de h* : Hn (F0) → Hn (F0 é um invariante de K, e se n ≠ 2 então K é homeomorfo a esfera de dimensão 2n -1 se, e somente se Δ (1) = ±1. Nesta dissertação, estudaremos K nos casos em que n=1 e nos casos em que f é da forma f(z1, z2,...,zn+1) = za11 + za22 + ...+ zan+1n+1 onde ai ' s são inteiros maiores que 1 (polinômio de Brieskorn). Também analizaremos Δ (t) e Δ (1) para o caso em que f seja polinômio de Brieskorn ou um polinômio f para a qual existam racionais positivos {w1, w2, ..., wn+1} tal que f(ec/w1z1, ec/w2,... ec/wn+1 zn+1) = ec/f(z1, z2,..., zn+1), para todo c ∈ C (polinômio quase-homogêneo).
Title in English
Not available
Keywords in English
Not available
Abstract in English
Given a holomorphic function f : Cn+1 → C, such that f(0) = 0 and 0 is an isolated singularity, the level hypersurface f-1 (O) near 0, Dε ∩ f-1 (0) is homeomorphic to the cone over K = Sε ∩ f-1(0). Thus, the study of K is essential to understand the level hypersurface near zero, from a topological point of view. The mapping Φ = f/ΙfΙ : Sε - K → S1 is the projection of a locally trivial bundle known as Milnor fibration and the fibre F0 = Φ -1(1) has the homotopy type of a wedge of spheres SnvSnv...vSn.For a specific diffeomorphism h : F0 → F0, the characteristic polynomial Δ(t) of h* : Hn(F0) is an invariant of K and if n ≠ 2 then K is homeomorphic to the (2n- 1) - sphere if, and only Δ(1) = ±1. Here we study K when n=l and when f is of the form f (z1, z2, ..., zn+1)= za11 + za22 + ... zan+1n+1, where the ai's are integers greater than 1 (Brieskorn polynomial). Also we analyse Δ(t) and Δ(1) when f is a Brieskorn polynomial or a polynomial f for which there are positive rational numbers {w1,w2,..., wn+1} such that f(ec/w1z1, ec/w2z2,...,ec/wn+1) = ecf(z1, z2,..., zn+1), for all c ∈ C (quasi-homogeneous polynomial).
 
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Publishing Date
2018-04-25
 
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