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

• Autor(a) principal: Silva, José Leonardo Esteves da
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/64982
• topic: Função Wq de Lambert-Tsallis; Função κ-exponencial; Caos; Números Transcendentais; Disentropia

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.