  We report the discovery of two field brown dwarfs, ULAS J0128-0041 and ULAS
J0321+0051, and the rediscovery of ULAS J0226+0051 (IfA 0230-Z1), in the Sloan
Digital Sky Survey (SDSS) southern equatorial stripe. They are found in the
course of our follow-up observation program of 1 um excess sources in the
United Kingdom Infrared Telescope Infrared Deep Sky Survey. The Gemini
Multi-Object Spectrographs spectra at red optical wavelengths (6500-10500 A)
are presented, which reveal that they are early-T dwarfs. The classification is
also supported by their optical to near-infrared colors. It is noted that ULAS
J0321+0051 is one of the faintest currently known T dwarfs. The estimated
distances to the three objects are 50-110 pc, thus they are among the most
distant field T dwarfs known. Dense temporal coverage of the target fields
achieved by the SDSS-II Supernova Survey allows us to perform a simple
time-series analysis, which leads to the finding of significant proper motions
of 150-290 mas/yr or the transverse velocities of 40-100 km/s for ULAS
J0128-0041 and ULAS J0226+0051. We also find that there are no detectable,
long-term (a-few-year) brightness variations above a few times 0.1 mag for the
two brown dwarfs.
