Teoria e aplicações das funções Wκ de Lambert-Kaniadakis, Wq de Lambert-Tsallis e as disentropias associadas

Abstract

In the first part of the present thesis, the Lambert-Kaniadakis W is introduced. Basically, the

W function solves the equation W(z)exp(W(z)) = z, where exp(z) is the -exponencial func- tion used by Kaniadakis in relativistic statistical mechanics. Following, the R function is in- troduced. Basically, the R function is a generalization of the W function that solves the equa- tion W(z)exp(W(z)) = z, where  is the -product operation. In the second part of this

thesis, the W and R functions are used to construct two -disentropies (D and D). The - disentropies and the q-disentropy (Dq), that uses the Lambert-Tsallis Wq function, are used in the calulation of the entanglement of pure bipartite states (Dq), image processing (D), non- linear maps (D and Dq) and random networks (D). At last, the transcendentality of the func- tions expq(z), lnq(z) and Wq(z) for q algebraic irrational are shown.