Separability in Morse local‐to‐global groups

We show that in a Morse local‐to‐global group where stable subgroups are separable, the product of any stable subgroups is separable. As an application, we show that the product of stable subgroups in virtually special groups is separable

Titanium and Protein Adsorption: An Overview of Mechanisms and Effects of Surface Features

Titanium and its alloys, specially Ti6Al4V, are among the most employed materials in orthopedic and dental implants. Cells response and osseointegration of implant devices are strongly dependent on the body–biomaterial interface zone. This interface is mainly defined by proteins: They adsorb immediately after implantation from blood and biological fluids, forming a layer on implant surfaces. Therefore, it is of utmost importance to understand which features of biomaterials surfaces influence formation of the protein layer and how to guide it. In this paper, relevant literature of the last 15 years about protein adsorption on titanium-based materials is reviewed. How the surface characteristics affect protein adsorption is investigated, aiming to provide an as comprehensive a picture as possible of adsorption mechanisms and type of chemical bonding with the surface, as well as of the characterization techniques effectively applied to model and real implant surfaces. Surface free energy, charge, microroughness, and hydroxylation degree have been found to be the main surface parameters to affect the amount of adsorbed proteins. On the other hand, the conformation of adsorbed proteins is mainly dictated by the protein structure, surface topography at the nano-scale, and exposed functional groups. Protein adsorption on titanium surfaces still needs further clarification, in particular concerning adsorption from complex protein solutions. In addition, characterization techniques to investigate and compare the different aspects of protein adsorption on different surfaces (in terms of roughness and chemistry) shall be developed

Separability in Morse local-to-global groups

We show that in a Morse local-to-global group where stable subgroups are separable, the product of any stable subgroups is separable. As an application, we show that the product of stable subgroups in virtually special groups is separable.Comment: 10 page

Unbounded domains in hierarchically hyperbolic groups

We investigate unbounded domains in hierarchically hyperbolic groups and obtain constraints on the possible hierarchical structures. Using these insights, we characterise the structures of virtually abelian HHGs and show that the class of HHGs is not closed under finite extensions. This provides a strong answer to the question of whether being an HHG is invariant under quasiisometries. Along the way, we show that infinite torsion groups are not HHGs. By ruling out pathological behaviours, we are able to give simpler, direct proofs of the rank-rigidity and omnibus subgroup theorems for HHGs. This involves extending our techniques so that they apply to all subgroups of HHGs.Comment: 19 pages. v2: General improvements, including the addition of Corollary 4.1 and Remark 4.