An improved multi-mode telephone for use in an improved satellite communication method and system. The device consists of a guide rail suspended by its ends on a mainframe which is mounted to a user’s torso. The hole extends through the handle so that a digit of the user’s hand, when grasping the handle, may be inserted through the hole. The saw is actuated to simultaneously remove material from both of the abutted ends. The flexible inner sleeve and the rigid shell can be used separately with the mobile device or can encase the mobile device as an integrated protective unit. The method comprises: calculating a stationary function of a predetermined cost functional selected such that the stationary function satisfies a mapping condition for mapping the predetermined input profile into the predetermined output profile, thereby providing a mapping function.