Parallax measurements of the mira-type star UX Cygni with phase-referencing VLBI

We have measured the annual parallax of the Mira-type variable star UX Cyg at omega = 0.54 +/- 0.06 max from phase-referencing VLBI observations of its circumstellar water masers with the VLBA. The corresponding distance is 1.85(-0.19)(+0.25) kpc. This is the mesurement of an annual parallax based on abservations of water masers. It is important to calibrate the period-luminosity relation of Mira variables because it is an important distance indicator in astronomy. We discuss the distance to the Large Megallanic Cloud. We obtained the three-dimensional position and velocity of UX Cyg in our galaxy: (R, theta, z) = (8.20 +/- 0.01 kpc, 12 degrees.4(-1.degrees 3)(+1.degrees 7), -0.30(-0.04)(+0.03) kpc), (VRVthetaVZ) = (-81.6(-15.3)(+14.0), 204.0(-3.4)(+3.6), -12.1(-10.3)(+10.2)) km s(-1). We also discuss the origin of UX Cyg.