Gleason parts separated by smooth curves

Suppose Γ is a simple closed C² curve in the complex plane and let W₁, W₂ be the components of the complement of Γ. Let X be a compact plane set. Necessary and sufficient conditions are given that any two points x₁?X ∩ W₁, and x₂?X ∩ W₂ belong to different Gleason parts for the algebra R(X). We also give an answer to the question: How thin can a nontrivial part for R(X) be ?     

Ion beam exposure of resists

Problems caused by the statistical variation of the number of exposing ions in ionbeam lithography are discussed. Using Poisson statistics, the minimum dose required for exposure as a function of resist sensitivity and minimum feature size is calculated. It is found that, although ion-beam resists show a very high sensitivity of 10¹¹ to 10¹³,cm^–2, it would be possible to use still more sensitive resists and obtain submicron linewidth resolution.