Methods and apparatus to certify digital signatures are disclosed. If the gate lead wiring is disposed along the four edges of a chip, the area of the non-operative region increases. Then, the second portable electronic device transmits an approval of the request for payment to the first portable electronic device. The auxiliary electrode is formed partly in a peripheral region of the light emitting device. The transmitting device provides a source of light without interfering with the operation of the stethoscope and can be provided without retooling the stethoscope to accommodate a source of light. This invention further relates to methods for producing maize varieties derived from maize variety X08A141.