  We show that there exists critical trap aspect ratios for a trapped
Bose-Einstein condensate with dipole-dipole interactions. We discuss the role
of critical trap aspect ratios on both the critical angular velocity above
which a vortex is energetically favorable and the precession velocity of an
off-axis vortex in TF regime. We show that the stability diagram for a purely
dipolar gas depends crucially on the critical trap aspect ratios both for
positive and negative strength of dipolar interaction. We prove that the
critical points can be changed by an anharmonic potential.
