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.

25 de Abril para sempre? "Fascismo" nunca mais?

Nem está garantido que o “25 de Abril seja para sempre”. O mais certo é que não esteja. Nem está assegurado, qual verdade ontológica, que não haverá mais “fascismo” ou um outro “Estado Novo de inspiração fascista”, como alguns preferem descrever o período histórico vivido em Portugal entre 1933 (com raízes em 1928 após eleição de Óscar Carmona) e o 25 de Abril de 1974. O mais certo é que surjam novos tipos de “fascismo”. § Abstract: Neither is guaranteed that the "April 25th is forever." Most likely it is not. Neither is assured, what ontological truth, there will be no more "fascism" or another "New State of fascist inspiration," as some prefer to describe the historical period lived in Portugal between 1933 (with roots in 1928 after Óscar Carmona Election) and April 25, 1974. most likely there are new types of "fascism."

Electromagnetic tracker feasibility in the design of a dental superstructure for edentulous patients

The success of the osseointegration concept and the Brånemark protocol is highly associated to the accuracy in the production of an implant-supported prosthesis. One of most critical steps for long-term success of these prosthesis is the accuracy obtained during the impression procedure, which is affected by factors such as the impression material, implant position, angulation and depth. This paper investigates the feasibility of 3D electromagnetic motion tracking systems as an acquisition method for modeling full-arch implant-supported prosthesis. To this extent, we propose an implant acquisition method at the patient mouth and a calibration procedure, based on a 3D electromagnetic tracker that obtains combined measurements of implant’s position and angulation, eliminating the use of any impression material. Three calibration algorithms (namely linear interpolation, higher-order polynomial and Hardy multiquadric) were tested to compensate for the electromagnetic tracker distortions introduced by the presence of nearby metals. Moreover, implants from different suppliers were also tested to study its impact on tracking accuracy. The calibration methodology and the algorithms employed proved to implement a suitable strategy for the evaluation of novel dental impression techniques. However, in the particular case of the evaluated electromagnetic tracking system, the order of magnitude of the obtained errors invalidates its use for the full-arch modeling of implant-supported prosthesis.