(Abridged) We present CARMA observations of the thermal dust emission from the circumstellar disks around the young stars RYTau and DGTau at wavelengths of 1.3mm and 2.8mm. The angular resolution of the maps is as high as 0.15arcsec, or 20AU at the distance of the Taurus cloud, which is a factor of 2 higher than has been achieved to date at these wavelengths. The unprecedented detail of the resulting disk images enables us to address three important questions related to the formation of planets. (1) What is the radial distribution of the circumstellar dust? (2) Does the dust emission show any indication of gaps that might signify the presence of (proto-)planets? (3) Do the dust properties depend on the orbital radius? We find that modeling the disk surface density in terms of either a classical power law or the similarity solution for viscous disk evolution, reproduces the observations well. The 1.3mm image from RYTau shows two peaks separated by 0.2arcsec with a decline in the dust emission toward the stellar position, which is significant at about 2-4sigma. For both RYTau and DGTau, the dust emission at radii larger than 15 AU displays no significant deviation from an unperturbed viscous disk model. In particular, no radial gaps in the dust distribution are detected. Under reasonable assumptions, we exclude the presence of planets more massive than 5 Jupiter masses orbiting either star at distances between about 10 and 60 AU. The radial variation of the dust opacity slope, beta, was investigated by comparing the 1.3mm and 2.8mm observations. We find mean values of beta of 0.5 and 0.7 for DGTau and RYTau respectively. Variations in beta are smaller than 0.7 between 20 and 70 AU. These results confirm that the circumstellar dust throughout these disks differs significantly from dust in the interstellar medium.
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