This is a numerical study of electromagnetic scattering by particles exhibiting negative absorption, i.e., with refractive index m = n(1 + kappai), where the time dependence is exp(+iomegat). The particle is a homogeneous circular cylinder. The stimulating incident plane wave travels perpendicularly to the cylinder axis. The scattering, amplification, and extinction cross sections as well as the differential scattering cross sections were evaluated for n = 1.50 over the nkappa = 0.001-1 range for the size parameter up to alpha = 50, where alpha = 2pia/lambda (a is the radius and lambda is the wavelength). In some cases results were obtained for much larger values of alpha. The most remarkable finding was the occurrence of sharp resonances. Not only does this provide for large amplification of the scattered radiation traveling outward as spherical waves (for 3-D objects) or as cylindrical waves (for 2-D objects), but, because of the occurrence of negative extinction cross sections, it may also result in amplification of the incident plane wave. The present formalism (Lorenz-Mie for spheres; Rayleigh for cylinders) implies a particular and highly contrived mechanism for pumping and stimulation. However, the formalism may be extended to other particular mechanisms.