Typology based method for choosing old masonry walls inspection procedures

The diagnosis of historic masonry walls is an intricate and complex field and has been an object of research for many years. This paper aims to propose practical methodologies for the diagnosis of historic masonry walls, specifically based on their typological characteristics. In order to develop such procedures, information relating to historic masonry typologies in Portugal, classified as rural, urban and military was gathered and techniques for the assessment of historic masonry were studied. All information was integrated to develop a pattern typology oriented methodology. Developed methodology was tested and validated in a small diagnosis campaign carried out in the Guimarães Castle. Methodology was proven to be advantageous and although the study is limited and focused on the Portuguese architectural specificities, it still holds global classifications, and therefore can be useful for any diagnosis procedure of a historic masonry wall.

An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.