  The property of dark energy and the physical reason for acceleration of the
present universe are two of the most difficult problems in modern cosmology.
The dark energy contributes about two-thirds of the critical density of the
present universe from the observations of type-Ia supernova (SNe Ia) and
anisotropy of cosmic microwave background (CMB).The SN Ia observations also
suggest that the universe expanded from a deceleration to an acceleration phase
at some redshift, implying the existence of a nearly uniform component of dark
energy with negative pressure. We use the ``gold'' sample containing 157 SNe Ia
and two recent well-measured additions, SNe Ia 1994ae and 1998aq to explore the
properties of dark energy and the transition redshift. For a flat universe with
the cosmological constant, we measure $\Omega_{M}=0.28_{-0.05}^{+0.04}$, which
is consistent with Riess et al. The transition redshift is
$z_{T}=0.60_{-0.08}^{+0.06}$. We also discuss several dark energy models that
define the $w(z)$ of the parameterized equation of state of dark energy
including one parameter and two parameters ($w(z)$ being the ratio of the
pressure to energy density). Our calculations show that the accurately
calculated transition redshift varies from $z_{T}=0.29_{-0.06}^{+0.07}$ to
$z_{T}=0.60_{-0.08}^{+0.06}$ across these models. We also calculate the minimum
redshift $z_{c}$ at which the current observations need the universe to
accelerate.
