A piezoelectric resonator element includes: a resonating arm extending in a first direction and cantilever-supported; a base portion cantilever-supporting the resonating arm; and an excitation electrode allowing the resonating arm to perform flexural vibration in a second direction that is orthogonal to the first direction. In one aspect, the invention is an apparatus for removing a removable tooth positioning appliance from teeth of a patient comprising: a handle portion; a member extending from the handle portion and having a distal end; and an engagement block having a tapered edge for engaging an edge of the tooth positioning appliance, the engagement block protruding from the member at or near the distal end. A view of the data is created in the relevant databases, wherein the spatial data is converted to WKB and stored as a BLOB. The method includes receiving a user selection of at least one item of media content from the at least one recommended media content item. The effective load on the generator is reduced to approximately zero when the LP turbine spool exceeds the predetermined speed, permitting the generator to be electrically bound up to the predetermined speed and mechanically bound in excess of the predetermined speed.