Takayuki Furuta "$A \geq B \geq {0}$ iff $\left( {B^r A^p B^r} \right)^{1/q} \geq B^{\left( {p + 2r} \right)/q} $ for $r \geq {0},p \geq{0},q \geq 1$ with $\left( {1 + 2r} \right)q \geq p + 2r$," Proceedings of the Japan Academy, Series A, Mathematical Sciences, Proc. Japan Acad. Ser. A Math. Sci. 63(1), 4-6, (1987)