Grassmann Convexity and Multiplicative Sturm Theory, Revisited

In this paper we settle a special case of the Grassmann convexity conjecture formulated earlier by B.and M.Shapiro. We present conjectural formula for maximal total number real zeros consecutive Wronskians an arbitrary fundamental solution to disconjugate linear ordinary differential equation with time. show that gives lower bound required equations order and, using our results on convexity, prove aforementioned is correct orders $4$ and $5$.