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An improved nonlinear circuit model for IMPATT diodes is presented for which each element bears a simple relationship with the physical operating mechanisms inside the device. The model contains lumped nonlinear elements as well as lumped and distributed linear elements. In its most general form it incorporates various second-order effects heretofore neglected in other circuit models. These include the effects due to unequal hole and electron ionization rates, unequal hole and electron drift velocities, and carrier diffusion.
We present photometry of 12 recent supernovae (SNe) recovered in a {\it Hubble Space Telescope} Snapshot program, and tie the measurements to earlier ground-based observations, in order to study the late-time evolution of the SNe. Many of the ground-based measurements are previously unpublished, and were made primarily with a robotic telescope, the Katzman Automatic Imaging Telescope. Evidence for circumstellar interaction is common among the core-collapse SNe. Late-time decline rates for Type IIn SNe are found to span a wide range, perhaps due to differences in circumstellar interaction. An extreme case, SN IIn 1995N, declined by only 1.2 mag in $V$ over about 4 years following discovery. Template images of some SNe must therefore be obtained many years after the explosion, if contamination from the SN itself is to be minimized. Evidence is found against a previous hypothesis that the Type IIn SN 1997bs was actually a superoutburst of a luminous blue variable star. The peculiar SN Ic 1997ef, a "hypernova," declined very slowly at late times. The decline rate of the SN Ia 2000cx decreased at late times, but this is unlikely to have been caused by a light echo.