Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...

We investigate unbounded domains in hierarchically hyperbolic groups and obtain constraints on the possible hierarchical structures. Using these insights, we characterise structures of virtually abelian HHGs show that class is not closed under finite extensions. This provides a strong negative answer to question whether being an HHG invariant quasi-isometries. Along way, infinite torsion are HH...