Abstract We define a large class of abstract Coxeter groups that we call $\infty $–spanned, and for which the word growth rate geodesic appear to be Perron numbers. This contains fair amount acting on hyperbolic spaces, thus corroborating conjecture by Kellerhals Perren. also show this strictly dominates rate.

Lithium electrodeposition is important for lithium metal batteries and presently a safety reliability concern the lithium-ion technology. In literature, many models growth of dendrites can be found strong dependence on deposition rate expected. To elucidate process deposition, operando light microscopy at physical resolution limit was performed rates varying by more than three orders magnitude....

We study the countable set of rates growth a hyperbolic group with respect to all its finite generating sets. prove that is well-ordered, and every real number can be rate at most finitely many sets up automorphism group. ordinal least ${\omega _{0}}^{\omega _{0}}$ , in case limit (e.g. free surface groups) it . further generated subgroups their This proved well-ordered as well, isomorphism cla...