@inproceedings { Gutman20161211,
  author = "Gutman A.E. and Kononenko L.I.",
  title = "Formalization of inverse problems and applications to systems of equations with parameters",
  booktitle = "Geometric Analysis and Control Theory. International conference (Novosibirsk, December, 8--12, 2016): Proceedings",
  address = "Novosibirsk",
  publisher = "Sobolev Institute of Mathematics SB RAS",
  year = "2016",
  pages = "40--42",
  annote = "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 (the condition of a problem, its data and unknowns, solvability and unique solvability of a problem, inverse problem, composition and restriction of problems, etc.). As an illustration, we consider a system of differential equations which describe a process in chemical kinetics, as well as the inverse problem."
}
@article { Gutman20161030,
  author = "Gutman A.E. and Kononenko L.I.",
  title = "Formalization of inverse problems and its applications",
  journal = "Sib. J. Pure. Appl. Math.",
  year = "2017",
  volume = "17",
  number = "4",
  pages = "49--56",
  doi = "10.17377/PAM.2017.17.5",
  language = "russian",
  annote = "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 (the condition of a problem, its data and unknowns, solvability and unique solvability of a problem, inverse problem, composition and restriction of problems, etc.). We also consider topological problems and the related notions of stability and correctness. Particular attention is paid to problems with parameters. As an illustration, we consider a system of differential equations which describes a process in chemical kinetics, as well as the inverse problem.",
  keywords = "inverse problem, binary correspondence, solvability, composition, stability, correctness, differential equation, chemical kinetics"
}
@inproceedings { Gutman20170817,
  author = "Gutman A.E. and Kononenko L.I.",
  title = "Binary correspondences and multidimensional problems of chemical kinetics",
  booktitle = "Mathematics in the Modern World. International conference dedicated to the 60th anniversary of the Sobolev Institute of Mathematics (Novosibirsk, August 14--19, 2017): Proceedings",
  address = "Novosibirsk",
  publisher = "Institute of Mathematics",
  year = "2017",
  pages = "205",
  language = "russian",
  annote = "It is shown that binary correspondences provide a simple and adequate formalization for the main components of problems (the condition of a problem, its data and unknowns), their basic properties and constructions (solvability and unique solvability of a problem, inverse problem, composition and restriction of problems), make it possible to formalize topological problems and related properties (stability, correctness), and also speak of parametrizations of problems and dependence of solutions on parameters. As an example, a singularly perturbed system is considered of ordinary differential equations which describes a process of chemical kinetics and burning."
}
@inproceedings { Gutman20170822,
  author = "Gutman A.E. and Kononenko L.I.",
  title = "Binary correspondences and problems of chemical kinetics with many-sheeted slow surface",
  booktitle = "Sobolev Readings. International School-Conference (Novosibirsk, August 20--23, 2017): Proceedings",
  address = "Novosibirsk",
  publisher = "Institute of Mathematics",
  year = "2017",
  pages = "122",
  annote = "It is shown that binary correspondences provide a simple and adequate formalization for components of problems, their properties and constructions, make it possible to formalize topological problems, their parametrizations, and dependence of solutions on parameters. As an example, a singularly perturbed system is considered of ordinary differential equations which describes a process of chemical kinetics with many-sheeted slow surface."
}
@inproceedings { Gutman20171115,
  author = "Gutman A.E. and Kononenko L.I.",
  howpublished = "Electronic",
  title = "Binary correspondences in problems of chemical kinetics",
  booktitle = "Lomonosov's Reading in Altai: Fundamental Problems of Science and Education, International conference (Barnaul, November 14--17, 2017): Collection of scientific articles",
  address = "Barnaul",
  publisher = "Altai State Univ.",
  year = "2017",
  issn = "2309-463X",
  pages = "424--430",
  language = "russian",
  annote = "Is it shown 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 (the condition of a problem, its data and unknowns, solvability and unique solvability of a problem, inverse problem, composition and restriction of problems, etc.). Topological problems are also considered as well as the related notions of stability and correctness. Particular attention is paid to problems with parameters. As an illustration, a system of differential equations is considered which describes a process in chemical kinetics, as well as the inverse problem."
}
@article { Gutman20171204,
  author = "Gutman A.E. and Kononenko L.I.",
  howpublished = "Electronic",
  title = "The inverse problem of chemical kinetics as a composition of binary correspondences",
  journal = "Sib. Electron. Math. Rep.",
  year = "2018",
  volume = "15",
  pages = "48--53",
  doi = "10.17377/semi.2018.15.006",
  language = "russian",
  annote = "Binary correspondences are employed for formalization of the notion of problem, definition of the basic components of problems, their properties, and constructions (the condition of a problem, its data and unknowns, solvability and unique solvability of a problem, inverse problem, and composition of problems). As an illustration, we consider a system of differential equations which describe a process in chemical kinetics. Within the study of the inverse problem, a criterion is established for linear independence of functions in terms of finite sets of their values.",
  keywords = "differential equation, chemical kinetics, inverse problem, linear independence, binary correspondence, solvability, composition"
}
@article { Gutman20180703,
  author = "Gutman A.E. and Kononenko L.I.",
  title = "Binary correspondences and the inverse problem of chemical kinetics",
  journal = "Vladikavk. Math. J.",
  year = "2018",
  volume = "20",
  number = "3",
  pages = "37--47",
  doi = "10.23671/VNC.2018.3.17981",
  annote = "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. Direct and inverse problems are stated for such a system. We extend the class of problems under study by considering polynomials of arbitrary degree as the right-hand sides of the differential equations. It is shown how the inverse problem of chemical kinetics can be corrected and made more practical by means of composition with a simple auxiliary problem which represents the relation between functions and finite sets of numerical characteristics being measured. For the corrected inverse problem, formulas for the solution are presented and the conditions of unique solvability are indicated. Within the study of solvability, a criterion is established for linear independence of functions in terms of finite sets of their values. With the help of the criterion, realizability is clarified of the condition for unique solvability of the inverse problem of chemical kinetics.",
  keywords = "binary correspondence, inverse problem, solvability, composition, stability, correctness, differential equation, chemical kinetics, linear independence"
}
@inproceedings { Gutman20181210,
  author = "Gutman A.E. and Kononenko L.I.",
  title = "Binary correspondences and the inverse problem of chemical kinetics",
  booktitle = "Sobolev Readings. International School-Conference dedicated to the 110th anniversary of the birthday of S.L.Sobolev (Novosibirsk, December 10--16, 2018): Proceedings",
  address = "Novosibirsk",
  publisher = "Institute of Mathematics",
  year = "2018",
  isbn = "978-5-86134-222-3",
  pages = "81",
  language = "russian",
  annote = "By treating the notion of problem as binary correspondence, we provide a simple and adequate formalization for the main components of problems, their basic properties, and constructions. In particular, we arrive at natural formal notions of inverse problem and composition of problems. As an illustration, the inverse problem is considered to a singularly perturbed system of ordinary differential equations which describe a process in chemical kinetics and burning. The inverse problem is corrected and made more practical by means of composition with a simple auxiliary problem which represents the relation between functions and finite sets of numers. For the corrected inverse problem, formulas for the solution are presented and the conditions of unique solvability are indicated."
}
@inproceedings { Gutman20190922,
  author = "Gutman A.E. and Kononenko L.I.",
  title = "Binary correspondences and an algorithm for solving an inverse problem of chemical kinetics",
  booktitle = "International conference on Geometric Analysis in honor of the 90th anniversary of academician Yu.G.Reshetnyak (Novosibirsk, September, 22--28, 2019): Proceedings",
  address = "Novosibirsk",
  publisher = "Sobolev Institute of Mathematics SB RAS",
  year = "2019",
  isbn = "978-5-4437-0949-9",
  pages = "67",
  annote = "Binary correspondences are used for formalization of problems, their basic components, properties, and constructions. A singularly perturbed system of ordinary differential equations is considered which describes a process in chemical kinetics. An iteration algorithm is proposed for finding an approximate solution to the inverse problem."
}
@inproceedings { Gutman20200914,
  author = "Gutman A.E. and Kononenko L.I.",
  title = "Binary correspondences and an algorithm for solving an inverse problem of chemical kinetics in a nondegenerate case",
  booktitle = "Geometry in the Large. Conference dedicated to the 90th birthday of Victor Toponogov (St. Petersburg, 2021): Abstracts",
  address = "St. Petersburg",
  publisher = "Euler International Mathematical Institute",
  year = "2021",
  pages = "12",
  annote = "Binary correspondences are used for formalization of problems, their basic components, properties, and constructions. A singularly perturbed system of ordinary differential equations is considered which describes a process in chemical kinetics in a nondegenerate case. An iteration algorithm is proposed for finding an approximate solution to the inverse problem."
}