Contrasts in the basins of attraction of structurally identical iterative root finding methods

A numerical comparison is performed between three methods of third order with the same structure, namely BSC, Halley’s and Euler–Chebyshev’s methods. As the behavior of an iterative method applied to a nonlinear equation can be highly sensitive to the starting points, the numerical comparison is carried out, allowing for complex starting points and for complex roots, on the basins of attraction in the complex plane. Several examples of algebraic and transcendental equations are presented.

Applying complex network theory to the understanding of high-aspect-ratio carbon-filled composites

This work demonstrates that the theoretical framework of complex networks typically used to study systems such as social networks or the World Wide Web can be also applied to material science, allowing deeper understanding of fundamental physical relationships. In particular, through the application of the network theory to carbon nanotubes or vapour-grown carbon nanofiber composites, by mapping fillers to vertices and edges to the gap between fillers, the percolation threshold has been predicted and a formula that relates the composite conductance to the network disorder has been obtained. The theoretical arguments are validated by experimental results from the literature.

Tribunal Constitucional Internacional – auto de ciência

Resumo: a criação dum Tribunal Constitucional Internacional, no nosso entender, é uma exigência da própria Declaração Universal dos Direitos do Homem de 1948. Neste texto são apresentados uma série de argumentos velhos e novos para a importância da existência do Tribunal Constitucional Internacional a nível mundial. Trata-se dum Tribunal que é indispensável à defesa dos Direitos do Homem, contra qualquer tipo de ditadura ou fanatismo económico, social, político, cultural ou mental. § Abstract: the creation of an International Constitutional Court, in our view, is a requirement of own Universal Declaration of Human Rights of 1948. In this paper are given a lot of old and new arguments for the importance of the existence of the International Constitutional Court worldwide. It is of a Court that is indispensable to the defense of human rights, against all forms of dictatorship or economic fanaticism, social, political, cultural or mental.