Let Κ be a unique factorization domain of characteristic p > 0, and let ƒ ∈ Κ[χ1,..., χn] be a polynomial not lying in Κ[wzór]. We prove that Κ[wzór] is the ring of constants of a Κ-derivation of Κ[χ1,..., χn] if and only if all the partial derivatives of ƒ are relatively prime. The proof is based on a generalization of Freudenburg's lemma to the case of polynomials over a unique factorization domain of arbitrary characteristic.
The laboratory method to investigate of layer process of coal coking by radioscopy is being devised by us. The lateral walls of the laboratory coking chamber and coke oven had the windows, which were carried out from transparent for X-ray beams material. Due to it was possible to record the coke-making process on radiographs. The application of contrasting of a coal charge with help contrasted element allowed to show the movement of mass in a coal load. This movement is a result of the interaction between zones, of which the plastic layer is composed. The coke oven was fitted out for measurements of the intra-layer pressure with help of the compensative technique, and measurement of the pressure on the side of swelling coal grains. The results of research will allow to understand the distinctions between processes of forming of a monolithic carbonizate from coals having the different caking. By this means an added criterion to assess coals for coking is founded.
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