A method of providing an automated auction for internalization for the purchase or sale of securities or derivatives in an exchange is disclosed. A brightness control circuit is coupled to the switching power converter to allow a duration of a conductive state of the power converter to exceed a duration of a conductive state of the LED string for maintaining a current magnitude in the LED string constant. A head driving power circuit incorporated in the printing apparatus compares a value obtained by dividing the reference voltage with a value obtained by dividing the output voltage from the power circuit and performs control so as to eliminate an error. Thus, the deformation forces generated upon compressing the hose are eliminated for the measurement of pressure. The image information processing unit may be connected via a network to one or more radiation image reading devices and one or more image output devices for outputting the second radiation images. The invention also provides DNA encoding such polypeptides, host cells augmented by such DNA, and methods for using the enzymes or host cells to provide useful and novel synthons.