According to one embodiment, a phase estimating device includes a periodic signal obtaining unit that obtains a first periodic signal, and a wireless time synchronizing unit that synchronizes a reference time with that of a signal generating device by wirelessly communicating with the signal generating device that outputs a second periodic signal according to phase information. Also provided are other methods related to the active carbonate esters of water-soluble polymers, as well as corresponding compositions. The pair of half-domes are positioned together to form a cavity therein with a portion of the bladder trapped between the pair of half-domes adjacent to the bladder support ring, wherein the bladder is positioned within the cavity.