  Using the quantum Monte Carlo method, we investigate the spin dynamics of
itinerant electrons in the one-dimensional Hubbard system. Based on the model
calculation, we have studied the spin-fluctuations in the quarter-filled
metallic Hubbard ring, which is aimed at the vanadium ring or chain defined
along corner-sharing tetrahedra of LiV$_2$O$_4$, and found the dramatic changes
of magnetic responses and spin-fluctuation characteristics with the
temperature. Such results can explain the central findings in the recent
neutron scattering experiment for LiV$_2$O$_4$.
