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The left-hand side of Eq. (21), represented by as a function of , showing the first three zeros, .
The wave number (dashed curve) and (solid curve) versus the inner ring radius for the mode. Here and .
The zeroth-order radial eigenstate for the azimuthal mode showing the (dashed) and (solid) modes.
Frequency versus inner ring radius for the and radial modes. Azimuthal modes are (dots), (dashed), and (solid) for the and ring.
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