In this paper, we obtain some new Lyapunov-type inequalities for a class of even-order linear differential equations, the results are new and generalize and improve some early results in this field.
The authors derive a McShane identity for once-punctured super tori. Relying upon earlier work on super Teichmuller theory by the last two-named authors, they further develop the supergeometry of these surfaces and establish asymptotic growth rate of their length spectra.