  We measure the frequency of the low m=0 quadrupolar excitation mode of weakly
interacting Bose-Einstein condensates in the transition region from the 3D to
the 1D mean-field regime. Various effects shifting the frequency of the mode
are discussed. In particular we take the dynamic coupling of the condensate
with the thermal component at finite temperature into account using a
time-dependent Hartree-Fock-Bogoliubov treatment developed in [S. Giorgini,
Phys. Rev. A 61, 063615 (2000)]. We show that the frequency rises in the
transition from 3D to 1D, in good agreement with the theoretical prediction [C.
Menotti and S. Stringari, Phys. Rev. A 66, 043610 (2002)].
