The attitude of spacecraft is represented by a 3x3 orthogonal matrix with unity determinant, which belongs to the three-dimensional special orthogonal group SO(3). The fact that all three-parameter representations of SO(3) are singular or discontinuous for certain attitudes has led to the use of higher-dimensional nonsingular parameterizations, especially the four-component quaternion. In attit...

Precession electron diffraction (PED) is a method that considerably reduces dynamical effects in electron diffraction data, potentially enabling more straightforward solution of structures using the transmission electron microscope. This study focuses upon the characterization of PED data in an effort to improve the understanding of how experimental parameters affect it in order to predict favo...

An interferogram of the wavefront deformation to a flat wave caused by an aircraft or spacecraft window contains all the error contribution effects of the window. The interferogram may be analyzed to determine the slope of this wavefront at a given point, which yields the angular deviation to a line of sight through the point. The interferogram as used in this study is a two-dimensional photo r...

This work was supported by FCT through the grant SFRH/BD/ 128657/2017 and projects PTDC/EMS-TEC/5422/2014_ADAPT PROSTHESIS, NORTE-01-0145-FEDER-000018 – HAMaBICo UID/ EEA/04436/2019.

Consider a density-dependent birth-death process X N on a finite state space of size N . Let PN be the law (on D.[0; T ]/ where T > 0 is arbitrary) of the density process XN =N and let 5N be the unique stationary distribution (on [0,1]) of X N =N , if it exists. Typically, these distributions converge weakly to a degenerate distribution as N ! 1, so the probability of sets not containing the de...