Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture

By deploying dense subalgebras of $\ell^1(G)$ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the $\ell^1$-Bass Conjecture. We prove that hyperbolic groups relative to finitely many subgroups, each of which posses the polynomial conjugacy-bound property and nilpotent periodicity property, satisfy the $\ell^1$-Stronger-Bass Conjecture. Moreover, we determine the conjugacy-bound for relatively hyperbolic groups and compute the cyclic cohomology of the $\ell^1$-algebra of any discrete group.Comment: 32 pages, 2 figures; added an appendix also by C. Ogl

Optimized 3D-printing of Carbon Fiber-Reinforced Polyether-ether-ketone (CFR-PEEK) for Use in Overmolded Lattice Composite

Current orthopedic implants are overwhelmingly composed from metallic materials. These implants show superior mechanical properties, but this can additionally result in stress shielding due to a modulus mismatch between the bone tissue and implanted device. Polymeric implants reduce this stress shielding effect but have much lower mechanical properties, limiting their use. Polylactic acid (PLA) is a widely used biodegradable thermoplastic polymer, however, its use has been limited by the polymer’s mechanical properties and rapid loss of strength during degradation in vivo. Polyether-ether-ketone (PEEK) is another common biocompatible polymer , with chemical and mechanical properties which make it a popular alternative to metallic implants. The ability to 3D print carbon fiber-reinforced PEEK (CFR-PEEK) components with the relatively cheap fused filament fabrication (FFF) process furthers the favorability of this polymer. By incorporating the stronger CFR-PEEK as a reinforcing lattice structure, the properties of biodegradable polymer can be improved. The 3D-printed lattices have been extensively researched, but they have yet to be investigated as the reinforcing component of an overmolded composite. The purpose of this work is to develop a novel overmolded lattice (OML) composite. This was accomplished by first optimizing the print parameters to maximize interlayer adhesion (ILA) using a proposed redesigned tensile specimen. These results were then used to print CFR-PEEK gyroid and then injection overmolded with PLA and characterized via flexural testing. The results of the parameter optimization showed increases in ILA with increased print temperature, print speed, and reduced layer height. The flexural results of the OML showed specific flexural strength (SFS), specific flexural modulus (SFM), and specific energy absorption (SEA), compared to the PLA and the CFR-PEEK gyroid lattice. The overmolded composite was found to have properties comparable to CFR-PEEK and had a SFM (4.3GPa/g) which exceeded all other materials tested. This composite structure has the potential to be integrated in a number of applications to provide highly tailored reinforcement of a weaker polymer matrix