Piezoelectric vibrating pieces are disclosed that have a base and a pair of vibrating arms extending from one end of the base in a designated direction. As a result, the discharge material is discharged from the nozzle hole onto the insulating substrate. Slide surfaces are provided which brake the downward material flow. Each clock inverter leg can further include an asymmetric variable delay circuit having an input coupled to an output of the first AOI circuit and an input coupled to a waitr_signal that can be used to delay and adjust breadth of non-overlap. Another embodiment is more tree centric, in that once a starting node is identified, all of its nodes are considered before progressing to another tree.