Gutman A.E.
Problem formalism
10 publications, 2016–2021

Use of binary correspondences for formalization of the notion of problem and related notions

It is shown how binary correspondences can be used for formalization of the notion of problem, definition of the basic components of problems, their properties, and constructions.
The following notions are formalized: the condition of a problem, its data and unknowns, solvability and unique solvability of a problem, inverse problem, composition and restriction of problems.
In terms of correspondences, topological problems are described, as well as problems with parameters and the related notions of stability and correctness.
Binary correspondences are applied to the study of systems of differential equations which describe processes in chemical kinetics, as well as the inverse problems.
Within the clarification of the notion of inverse problem, a criterion is established for linear independence of functions in terms of finite sets of their values.

1.	Gutman A.E., Kononenko L.I. Formalization of inverse problems and applications to systems of equations with parameters // Report abstract. Geometric Analysis and Control Theory. International conference (Novosibirsk, December, 8–12, 2016): Proceedings. Novosibirsk: Sobolev Institute of Mathematics SB RAS, 2016. P. 40–42. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
2.	Gutman A.E., Kononenko L.I. Formalization of inverse problems and its applications [in Russian] // Sib. J. Pure. Appl. Math. 2017. V. 17, N 4. P. 49–56. Bibliographic record Record in BibTeX format Article (PDF) Information on ResearchGate DOI resolution Issue on the journal site Journal site
3.	Gutman A.E., Kononenko L.I. Binary correspondences and multidimensional problems of chemical kinetics [in Russian] // Report abstract. Mathematics in the Modern World. International conference dedicated to the 60th anniversary of the Sobolev Institute of Mathematics (Novosibirsk, August 14–19, 2017): Proceedings. Novosibirsk: Institute of Mathematics, 2017. P. 205. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
4.	Gutman A.E., Kononenko L.I. Binary correspondences and problems of chemical kinetics with many-sheeted slow surface // Report abstract. Sobolev Readings. International School-Conference (Novosibirsk, August 20–23, 2017): Proceedings. Novosibirsk: Institute of Mathematics, 2017. P. 122. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
5.	Gutman A.E., Kononenko L.I. Binary correspondences in problems of chemical kinetics [in Russian] // Report abstract. Lomonosov's Reading in Altai: Fundamental Problems of Science and Education, International conference (Barnaul, November 14–17, 2017): Collection of scientific articles. Barnaul: Altai State Univ., 2017. P. 424–430. Bibliographic record Record in BibTeX format Report abstract (PDF) Abstracts table of content (PDF) Participant certificate (PDF) Information on eLIBRARY Information on ResearchGate Abstracts on the site (Google Drive ISO) Abstracts table of content (Google Drive PDF) Conference site
6.	Gutman A.E., Kononenko L.I. The inverse problem of chemical kinetics as a composition of binary correspondences [in Russian] // Sib. Electron. Math. Rep. 2018. V. 15. P. 48–53. Bibliographic record Record in BibTeX format Article (PDF) Article on the journal site (PDF) Information on ResearchGate DOI resolution Volume on the journal site Journal site
7.	Gutman A.E., Kononenko L.I. Binary correspondences and the inverse problem of chemical kinetics // Vladikavk. Math. J. 2018. V. 20, issue 3. P. 37–47. Bibliographic record Record in BibTeX format Article (PDF) Prepublication version (PDF) Russian version (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate DOI resolution Journal site
8.	Gutman A.E., Kononenko L.I. Binary correspondences and the inverse problem of chemical kinetics [in Russian] // Report abstract. Sobolev Readings. International School-Conference dedicated to the 110th anniversary of the birthday of S.L.Sobolev (Novosibirsk, December 10–16, 2018): Proceedings. Novosibirsk: Institute of Mathematics, 2018. P. 81. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Invitation (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
9.	Gutman A.E., Kononenko L.I. Binary correspondences and an algorithm for solving an inverse problem of chemical kinetics // Report abstract. International conference on Geometric Analysis in honor of the 90th anniversary of academician Yu.G.Reshetnyak (Novosibirsk, September, 22–28, 2019): Proceedings. Novosibirsk: Sobolev Institute of Mathematics SB RAS, 2019. P. 67. Bibliographic record Record in BibTeX format Report abstract (PDF) Prepublication version (PDF) Abstracts (PDF) Conference program (PDF) Russian version (PDF) Information on ResearchGate Abstracts on the site Program on the conference site Conference site
10.	Gutman A.E., Kononenko L.I. Binary correspondences and an algorithm for solving an inverse problem of chemical kinetics in a nondegenerate case // Report abstract. Geometry in the Large. Conference dedicated to the 90th birthday of Victor Toponogov (St. Petersburg, 2021): Abstracts. St. Petersburg: Euler International Mathematical Institute, 2021. P. 12. Bibliographic record Record in BibTeX format Report abstract (PDF) Prepublication version (PDF) Abstracts (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site Conference site

List in BibTeX format

The papers are presented here for academic purposes and are not intended for mass dissemination or copying.

Last updated
February 8, 2022

Gutman A.E.Problem formalism10 publications, 2016–2021

Gutman A.E.
Problem formalism
10 publications, 2016–2021