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.

The influence of the dispersion method on the electrical properties of vapor-grown carbon nanofiber/epoxy composites

The influence of the dispersion of vapor-grown carbon nanofibers (VGCNF) on the electrical properties of VGCNF/ Epoxy composites has been studied. A homogenous dispersion of the VGCNF does not imply better electrical properties. In fact, it is demonstrated that the most simple of the tested dispersion methods results in higher conductivity, since the presence of well-distributed nanofiber clusters appears to be a key factor for increasing composite conductivity.

Thoracic wall reconstruction using ultrasound images to model/bend the thoracic prosthesis for correction of pectus excavatum

Pectus excavatum is the most common congenital deformity of the anterior thoracic wall. The surgical correction of such deformity, using Nuss procedure, consists in the placement of a personalized convex prosthesis into sub-sternal position to correct the deformity. The aim of this work is the CT-scan substitution by ultrasound imaging for the pre-operative diagnosis and pre-modeling of the prosthesis, in order to avoid patient radiation exposure. To accomplish this, ultrasound images are acquired along an axial plane, followed by a rigid registration method to obtain the spatial transformation between subsequent images. These images are overlapped to reconstruct an axial plane equivalent to a CT-slice. A phantom was used to conduct preliminary experiments and the achieved results were compared with the corresponding CT-data, showing that the proposed methodology can be capable to create a valid approximation of the anterior thoracic wall, which can be used to model/bend the prosthesis