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On Some Models of Indentation for Functionally-Graded Coatings

Authors: Vatulyan A. O., Plotnikov D. K., Poddubny A. A.

The paper presents approximate models of deformation for an inhomogeneous elastic strip. Approximate models reflect the distribution features of the inhomogeneous structure properties over the thickness. The models are based on hypotheses about the nature of the change in the components of the displacement field, which allows to consider arbitrary laws of heterogeneity: continuous, as well as discontinuous or having a strong gradient. Solutions of the contact problem for different inhomogeneity laws are constructed. Comparative analysis of the models is carried out.

Morphismes Based on Compatible Tolerances of Finite Automata

Authors: Mangusheva I. P.

It is suggested a method of a construction with the help of some triple of tolerances defined on the sets of states, input and output symbols of an finite definite automaton an another automaton which is connected with the original automaton by a certain morphism.
Considered construction generalizes the known method of finding of the homomorphic images of an automaton with the help of a triple of equivalences, which satisfies to the certain conditions.

Ordered automata and tolerant images of FDA

Authors: Mangusheva I. P.

Finite deterministic automaton (FDA) with partially ordered (an ordered automaton) sets of states, input and output symbols is described in the article. The mapping of FDA on an ordered automaton, which is named "p-morphism" is defined. It is shown that so called tolerant images, which are constructed with the help of compatible tolerances on the set of states of FDA, are particular case of ordered automata, which are connected with the original automaton by a p-morphism.