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A circular cylindrical resonator with metallic walls is analyzed in the phasor domain. The resonator contains a wedge of double-negative (DNG) metamaterial that is anti-isorefractive to the double-positive (DPS) material filling the remaining volume of the resonator, and whose edge is located on the resonator axis. The resonance conditions are established. The problem of an electric line source parallel to the axis and located anywhere inside the DPS region is solved exactly. Numerical results are presented and discussed.