Os mártires ingleses de San Tomaso di Canterbury em Roma : troféus da Contra-reforma

O ciclo de martírio na Igreja Inglesa do Colégio S. Tomas o di Canterbury, Roma, datado de 1583, ilustrou a história do Catolicismo Inglês desde os mártires primitivos até aos mártires executados durante os reinados de Henrique VIII e Isabel I. A maior parte deste grupo de mártires era jesuítas que morreram durante a Missão Inglesa que começou com a viagem de Edmund Campion até à sua pátria em 1580. O martírio de Campioné bem conhecido, sendo o mais proeminente ciclo ilustrado nas paredes do colégio. Existiam, todavia, muitos mais ciclos, O facto mais extraordinário é que estes mártires ingleses contemporâneos, que não tiveram qualquer eco hagiográfico, foram colocados na tradição dos mártires cristãos primitivos. Além disso, estes mártires foram celebrados como os novos “troféus” da Contra-Reforma, através dos quais a Igreja Católica esperava restaurar a fé católica na Grã-Bretanha. O presente artigo introduz alguns destes jesuítas, as suas vidas e a razão para o seu martírio.

A Newton method for pose refinement of 3D models

Different optimization methods can be employed to optimize a numerical estimate for the match between an instantiated object model and an image. In order to take advantage of gradient-based optimization methods, perspective inversion must be used in this context. We show that convergence can be very fast by extrapolating to maximum goodness-of-fit with Newton's method. This approach is related to methods which either maximize a similar goodness-of-fit measure without use of gradient information, or else minimize distances between projected model lines and image features. Newton's method combines the accuracy of the former approach with the speed of convergence of the latter.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

Enhanced Templating in the Crystallisation of Poly(E-caprolactone) Using 1,3:2,4-di(4-Chlorobenzylidene) Sorbitol

We show that small quantities of 1,3:2,4-di(4-chlorobenzylidene) sorbitol dispersed in poly(epsilon-caprolactone) provide a very effective self-assembling nanoscale framework which, with a flow field, yields extremely high levels of polymer crystal orientation. During modest shear flow of the polymer melt, the additive forms highly extended nano-particles which adopt a preferred alignment with respect to the flow field. On cooling, polymer crystallisation is directed by these particles. This chloro substituted dibenzylidene sorbitol is considerably more effective at directing the crystal growth of poly(epsilon-caprolactone) than the unsubstituted compound.