Overlapping of the characteristic regions in the decay on heterogeneous centers with equal number density

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The situation of the decay of the metastable phase on the several types of heterogeneous centers is described analytically. The total number of heterogeneous centers is supposed to be equal for different types. This description decomposes the general situation into some characterisrtic cases. Every case can be described by some special method. The problem is to show that these characteristic cases cover all possible variants of the composition of the condensation system. This is done is this manuscript. In the first part we consider the general facts which allow to establish this overlapping in principle. In the second part we consider some real model systems and show this overlapping directly by explicit calculations. In the third part we consider the process of nucleation on ions and give the generalization for the centers with a rather arbitrary nature.