Binary correspondences and the inverse problem of chemical kinetics

Автор: Gutman Alexander E., Kononenko Larasa I.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.20, 2018 года.

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We show how binary correspondences can be used for simple formalization of the notion of problem, definition of the basic components of problems, their properties, and constructions. In particular, formalization of the following notions is presented: condition, data, unknowns, and solutions of a problem, solvability and unique solvability, inverse problem, composition and restriction of problems, isomorphism between problems. We also consider topological problems and the related notions of stability and correctness. A connection is indicated between the stability and continuity of a uniquely solvable topological problem. The definition of parametrized set is given. The notions are introduced of parametrized problem, the problem of reconstruction of an object by the values of parameters, as well as the notions of locally free set of parameters and stability with respect to a set of parameters. As an illustration, we consider a singularly perturbed system of ordinary differential equations which describe a process in chemical kinetics and burning...

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Binary correspondence, inverse problem, solvability, composition, stability, correctness, differential equation, chemical kinetics, linear independence

Короткий адрес: https://sciup.org/143168770

IDR: 143168770   |   DOI: 10.23671/VNC.2018.3.17981

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