Processes and apparatus are disclosed for recovery of purified products from a fluid mixture by means of integrated perm-selective separations with purified product recovery operations. The pulse width modulator reduces pop noise generated when power supply to a digital amplifier is started and interrupted. The trigger operation set includes a trigger, a connecting arm push plate, a trigger arm, a lift member, a connecting arm, a switch arm, a locking member, and a microswitch. The radio resource managing apparatus and method using the same are applied to IMT -Advanced system base station, thereby optimizing the efficiency of radio resources. A memory system includes a memory array and a memory controller configured to perform a rewrite process to change the memory array from an initial state to a target state in a manner that avoids violating a set of weight constraints at any time during the rewrite process.