On the connectivity of graph Lipscomb's space

A central role in topological dimension theory is played by Lipscomb's space $J_{A}$ since it is a universal space for metric spaces of weight $|A|\geq \aleph _{0}$. On the one hand, Lipscomb's space is the attractor of a possibly infinite iterated function system, i.e. it is a generalized Hutchinson-Barnsley fractal. As, on the other hand, some classical fractal sets are universal spaces, one can conclude that there exists a strong connection between topological dimension theory and fractal set theory. A generalization of Lipscomb's space, using graphs, has been recently introduced (see R. Miculescu, A. Mihail, Graph Lipscomb's space is a generalized Hutchinson-Barnsley fractal, Aequat. Math., \textbf{96} (2022), 1141-1157). It is denoted by J_{A}^{\G} and it is called graph Lipscomb's space associated with the graph \G on the set $A$. It turns out that it is a topological copy of a generalized Hutchinson-Barnsley fractal. This paper provides a characterization of those graphs \G for which J_{A}^{\G} is connected. In the particular case when $A$ is finite, some supplementary characterizations are presented.Comment: 13 page

TITANIUM FUNCTIONALIZING AND DERIVATIZING FOR IMPLANTABLE MATERIALS OSSEOINTEGRATION PROPERTIES ENHANCING

The article focuses on titanium functionalizing and derivatizing reactions for implantable materials osseointegration properties enhancing. Thus, the titanium dioxide was activated to the titanium hydroxide (functionalization), being further immobilized on the titanium surface by ethanolamine covalent reactions and (3-aminopropyl)triethoxysilane (APTS) for the osseointegration membranes reactive coating. The derivatizing was based on ether forming reactions between hydroxyl group from the titanium hydroxide surface and the ethanolamine hydroxyl groups and hydrolyzed APTS respectively. The obtained materials were characterized by scanning electron microscopy, FT-IR infrared spectroscopy, contact angle and X-Ray fluorescence

Rib biomechanical properties exhibit diagnostic potential for accurate ageing in forensic investigations

Age estimation remains one of the most challenging tasks in forensic practice when establishing a biological profile of unknown skeletonised remains. Morphological methods based on developmental markers of bones can provide accurate age estimates at a young age, but become highly unreliable for ages over 35 when all developmental markers disappear. This study explores the changes in the biomechanical properties of bone tissue and matrix, which continue to change with age even after skeletal maturity, and their potential value for age estimation. As a proof of concept we investigated the relationship of 28 variables at the macroscopic and microscopic level in rib autopsy samples from 24 individuals. Stepwise regression analysis produced a number of equations one of which with seven variables showed an R2=0.949; a mean residual error of 2.13 yrs ±0.4 (SD) and a maximum residual error value of 2.88 yrs. For forensic purposes, by using only bench top machines in tests which can be carried out within 36 hrs, a set of just 3 variables produced an equation with an R2=0.902 a mean residual error of 3.38 yrs ±2.6 (SD) and a maximum observed residual error 9.26yrs. This method outstrips all existing age-at-death methods based on ribs, thus providing a novel lab based accurate tool in the forensic investigation of human remains. The present application is optimised for fresh (uncompromised by taphonomic conditions) remains, but the potential of the principle and method is vast once the trends of the biomechanical variables are established for other environmental conditions and circumstances