A location verifier can be configured to receive a location report of a target mobile device, wherein the location report includes data characterizing a location for the target mobile device. The request is related to a purchase transaction. The estimating section detects the signal at the cut-off time so as to estimate the magnetic pole electric angle and the rotational speed in the low-speed period. The first and third lens groups are fixed, and the second lens group is movable to be selectively disposed in several discrete positions. Since this heat treatment is lower than the temperature which the gate wiring withstands and the gate wiring is protected with a protective film, the gate wiring retains its low resistance. Following multiplexing, a block encoder defines the frames and adds error detection or error correction information.