  The Boros-Moll polynomials $P_m(a)$ arise in the evaluation of a quartic
integral. It has been conjectured by Boros and Moll that these polynomials are
infinitely log-concave. In this paper, we show that $P_m(a)$ is 2-log-concave
for any $m\geq 2$. Let $d_i(m)$ be the coefficient of $a^i$ in $P_m(a)$. We
also show that the sequence $\{i
(i+1)(d_i^{\,2}(m)-d_{i-1}(m)d_{i+1}(m))\}_{1\leq i \leq m}$ is log-concave.
This leads another proof of Moll's minimum conjecture.
