  We study equilibrium properties of Bose-Condensed gases in a one-dimensional
(1D) optical lattice at finite temperatures. We assume that an additional
harmonic confinement is highly anisotropic, in which the confinement in the
radial directions is much tighter than in the axial direction. We derive a
quasi-1D model of the Gross-Pitaeavkill equation and the Bogoliubov equations,
and numerically solve these equations to obtain the condensate fraction as a
function of the temperature.
