Appendix 1 Proof of Lemma 3.1

If hhas the form (1), we have h = g f . Hence, we obtain h h = g2 f (1 f). Since 0 f <1 and f >0, we have h h <0. Now, from the other direction, suppose we know h h <0. To prove that hmust have the form (1), we first show that h(0)h() >0 ( 0), (2) namely, h() always keeps the same sign with h(0).