We conducted phase referencing VLBI observations of the Mira variable T~Lepus (T~Lep) using VERA, from 2003 to 2006. The distance to the source was determined from its annual parallax which was measured to be 3.06$pm$0.04 mas, corresponding to a dist
ance of 327$pm$4,pc. Our observations revealed the distribution and internal kinematics of H$_2$O masers in T~Lep, and we derived a source systemic motions of 14.60$pm$0.50 mas yr$^{-1}$ and $-$35.43$pm$0.79 mas yr$^{-1}$ in right ascension and declination, respectively. We also determined a LSR velocity of $V_mathrm{LSR}^{ast} = -$27.63 km s$^{-1}$. Comparison of our result with an image recently obtained from the VLTI infrared interferometer reveals a linear scale picture of the circumstellar structure of T~Lep. Analysis of the source systemic motion in the Galacto-centric coordinate frame indicates a large peculiar motion, which is consistent with the general characteristics of AGB stars. This source makes a contribution to the calibration of the period-luminosity relation of Galactic Mira variables. From the compilation of data for nearby Mira variables found in the literature, whose distances were derived from astrometric VLBI observations, we have calibrated the Galactic Mira period-luminosity relation to a high degree of accuracy.
We present a distance measurement for the semiregular variable S Crateris (S Crt) based on its annual parallax. With the unique dual beam system of the VLBI Exploration for Radio Astrometry (VERA) telescopes, we measured the absolute proper motion of
a water maser spot associated with S Crt, referred to the quasar J1147-0724 located at an angular separation of 1.23$^{circ}$. In observations spanning nearly two years, we have detected the maser spot at the LSR velocity of 34.7 km s$^{-1}$, for which we measured the annual parallax of 2.33$pm$0.13 mas corresponding to a distance of 430$^{+25}_{-23}$ pc. This measurement has an accuracy one order of magnitude better than the parallax measurements of HIPPARCOS. The angular distribution and three-dimensional velocity field of maser spots indicate a bipolar outflow with the flow axis along northeast-southwest direction. Using the distance and photospheric temperature, we estimate the stellar radius of S Crt and compare it with those of Mira variables.
