Abstract: An air pump device for a massage device includes a recognition device to acquire a type of the massage device via a wireless communication with an identification device of the massage device, and a controller to set an operation pattern based on the type of the massage device. The controller controls a pump connectable to an inflatable bladder of the massage device, based on the operation pattern.

Abstract: A license management method of performing license management using an execution unit that executes software and a software storage unit coupled to the execution unit includes the step of controlling execution of software that is stored in the software storage unit and on which a license is granted with a term being limited by the execution unit on the basis of term information that indicates the term by using a license management unit that controls execution of the software.

Abstract: A PLL circuit apparatus in accordance with the present invention includes a phase comparator, a delay circuit, a NOR circuit, and a loop filter. The phase comparator detects a phase difference between a reference clock signal and an internal clock signal. The delay circuit delays the reference clock signal by a delay time of an output of the phase comparator. The NOR circuit determines which pulse width is larger of a phase difference detecting signal from the phase comparator or of the delayed reference clock signal. The loop filter has its gain changed in response to an output of the NOR circuit. Thus, it is possible to shorten a synchronization pull-in time and accurately detect a deviation in synchronization. In addition, if a gain control signal is reset on the basis of logic states of a reference clock signal and an internal clock signal in accordance with rising edges and falling edges of the clock signals, it is possible to generate successive gain control signals.