{"id":12978,"date":"2022-07-01T12:28:01","date_gmt":"2022-07-01T09:28:01","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=12978"},"modified":"2023-02-01T23:11:30","modified_gmt":"2023-02-01T21:11:30","slug":"arhitektonika-rozrahunkovyh-matematychnyh-modelej-v-umovah-nevyznachenosti","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=12978","title":{"rendered":"\u0410\u0440\u0445\u0456\u0442\u0435\u043a\u0442\u043e\u043d\u0456\u043a\u0430 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u043e\u0432\u0438\u0445 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0438\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0432 \u0443\u043c\u043e\u0432\u0430\u0445 \u043d\u0435\u0432\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u043e\u0441\u0442\u0456"},"content":{"rendered":"

<\/p>\n

\u0410\u0420\u0425\u0406\u0422\u0415\u041a\u0422\u041e\u041d\u0406\u041a\u0410 \u0420\u041e\u0417\u0420\u0410\u0425\u0423\u041d\u041a\u041e\u0412\u0418\u0425 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u041d\u0418\u0425 \u041c\u041e\u0414\u0415\u041b\u0415\u0419 \u0412 \u0423\u041c\u041e\u0412\u0410\u0425 \u041d\u0415\u0412\u0418\u0417\u041d\u0410\u0427\u0415\u041d\u041e\u0421\u0422\u0406<\/p>\n

ARCHITECTONICS OF CALCULATED MATHEMATICAL MODELS UNDER UNCERTAINTY<\/p>\n

\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438:\u00a0<\/strong>135<\/strong>–<\/strong>137<\/strong>. \u041d\u043e\u043c\u0435\u0440: \u21163, 2022 (309)\u00a0<\/strong> \"\"<\/a>
\n\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u041b\u0415\u0412\u041a\u0406\u041d \u0414. \u0410.
\n\u0414\u0435\u0440\u0436\u0430\u0432\u043d\u0438\u0439 \u0431\u0456\u043e\u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\nhttps:\/\/orcid.org\/0000-0002-1980-4426<\/a>
\ne-mail: dimalevkin23@gmail.com<\/a>
\nDmytro LEVKIN
\nState Biotechnological University, Kharkiv, Ukraine
\nDOI:<\/strong>\u00a0https:\/\/www.doi.org\/10.31891\/2307-5732-2022-309-3-135-137<\/a><\/p>\n

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\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0430\u0440\u0445\u0456\u0442\u0435\u043a\u0442\u043e\u043d\u0456\u043a\u0430, \u043a\u0440\u0430\u0439\u043e\u0432\u0456 \u0437\u0430\u0434\u0430\u0447\u0456, \u043a\u043e\u0440\u0435\u043a\u0442\u043d\u0456\u0441\u0442\u044c, \u0434\u0438\u0444\u0435\u0440\u0435\u043d\u0446\u0456\u0430\u043b\u044c\u043d\u0456 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u00a0\u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

This article concerns the improvement of calculated mathematical models of technological, biotechnological, and economic systems. It is necessary to increase the number of considered parameters to increase the accuracy of calculating the parameters of complex systems during mathematical modeling. This leads to the need to solve nonlocal boundary value problems with non-stationary differential equations, to prove the correctness of which it is impossible to apply the traditional theory of existence and unity of solution. Note that after the architecture of boundary value problems assumes the existence of their solution, it is only necessary to prove its uniqueness. To prove the correctness of calculated mathematical models requires neither generalizing the parameters of the goal function and using approximate constraints, which, in turn, will reduce the boundary value problem to a standard form and its correctness will not be in doubt, nor propose a method to prove the correctness of boundary value certain differential equations, which will consider the specific features of the modeled processes. A separate technique must substantiate the correctness of boundary value problems depending on the type of differential equation that describes the physical and economic processes in the simulated systems.
\nThis article studied the conditions for the correctness of boundary value problems for differential equations with constant coefficients. It is proved that there is a corresponding boundary value problem for arbitrary homogeneous differential equations. It is defined the parabolic boundary value problems in terms that use constraints from above on the fundamental solution function. The conditions were obtained under which the parabolic boundary value problem exists and cannot exist, respectively. The obtained results will increase the accuracy of the main optimization task of improving the quality of simulated processes.
\nKeywords:<\/strong> architectonics, boundary value problems, correctness, differential equations.<\/p>\n

\u041b\u0456\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430<\/strong><\/p>\n

    \n
  1. \u0421\u0442\u043e\u044f\u043d \u042e.\u0413. \u041e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u044f \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0441 \u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0430\u043c\u0438 \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u043e\u043b\u0435\u0439 \/ \u042e.\u0413. \u0421\u0442\u043e\u044f\u043d, \u0412.\u041f. \u041f\u0443\u0442\u044f\u0442\u0438\u043d. \u2013 \u041a. : \u041d\u0430\u0443\u043a. \u0434\u0443\u043c\u043a\u0430, 1988. \u2013 \u0421. 44\u201348.<\/li>\n
  2. Asrorov F. Finding of bounded solutions to linear impulsive systems \/ F. Asrorov, V. Sobchuk, \u041e.\u00a0Kurylko \/\/ Eastern-European Journal of Enterprise Technologies. \u2013 \u2013 Vol. 6. No. 4 (102): Mathematics and Cybernetics – applied aspects. \u2013 P. 14\u201320. https:\/\/doi.org\/10.15587\/1729-4061.2019.178635<\/li>\n
  3. \u0417\u0430\u0439\u0446\u0435\u0432 \u0404.\u041f. \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0435 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u0434\u0432\u0456\u0447\u0456 \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0457 \u0437\u0430\u0434\u0430\u0447\u0456 \u0442\u0435\u043f\u043b\u043e\u043f\u0440\u043e\u0432\u0456\u0434\u043d\u043e\u0441\u0442\u0456 \u0442\u0440\u0430\u043d\u0441\u0432\u0435\u0440\u0441\u0430\u043b\u044c\u043d\u043e-\u0456\u0437\u043e\u0442\u0440\u043e\u043f\u043d\u043e\u0433\u043e \u0442\u0435\u0440\u043c\u043e\u0447\u0443\u0442\u043b\u0438\u0432\u043e\u0433\u043e \u0446\u0438\u043b\u0456\u043d\u0434\u0440\u0430 \u043f\u0456\u0434 \u0432\u043f\u043b\u0438\u0432\u043e\u043c \u0437\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0432\u0438\u0441\u043e\u043a\u043e\u0442\u0435\u043c\u043f\u0435\u0440\u0430\u0442\u0443\u0440\u043d\u043e\u0433\u043e \u0442\u0435\u043f\u043b\u043e\u043e\u0431\u043c\u0456\u043d\u0443 \/ \u0417\u0430\u0439\u0446\u0435\u0432\u0404.\u041f. \/\/ \u0412\u0447\u0435\u043d\u0456 \u0437\u0430\u043f\u0438\u0441\u043a\u0438 \u0422\u0430\u0432\u0440\u0456\u0439\u0441\u044c\u043a\u043e\u0433\u043e \u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0423\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443 \u0456\u043c\u0435\u043d\u0456 \u0412.\u0406. \u0412\u0435\u0440\u043d\u0430\u0434\u0441\u044c\u043a\u043e\u0433\u043e. \u0421\u0435\u0440\u0456\u044f: \u00ab\u0422\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u043d\u0430\u0443\u043a\u0438\u00bb. \u2013 \u041a\u0438\u0457\u0432, 2021. \u2013 \u0422. 32(71). \u2116 2. \u0427. \u2013 \u0421. 31\u201338. https:\/\/doi.org\/10.32838\/2663-5941\/2021.2-1\/07<\/li>\n
  4. Scoblo T.S. Features of the carbide phase degradation under heating and deformation \/ T.S. Scoblo, O.Y.\u00a0Klochko, V.N. Romanchenko, E.L. Belkin \/\/ Letters on Materials. \u2013 2021. \u2013 Vol. 11. No. 1. \u2013 P. 22\u201327. https:\/\/doi.org\/10.22226\/2410-3535-2021-1-22-27<\/li>\n
  5. Vojtov V.A. Criteria for evaluation of tribus system practices and its communication with tribological characteristics \/ A. Vojtov, A.SH. Bekirov, A.V. Voitov \/\/ Problems of Tribology. \u2013 2018. \u2013 Vol. 88. No. 2. \u2013 P. 35\u201342.<\/li>\n
  6. Tytarchuk I. Innovations financing in the agricultural sector. \/ I. Tytarchuk, Y. Nehoda, I. Shalyhina, N. Bazhanova, O. Horbachova, L. Rybina. \/\/ International Journal of Advanced Research in Engineering and Technology. \u2013 2020. \u2013 Vol. 11. Issue. 4. \u2013 Pp. 246\u2013255<\/li>\n
  7. Potyshniak O. Assessment of the effectiveness of the strategic management system of investment activities of companies \/ Potyshniak, L. Dobuliak, V. Filippov, Y. Malakhovskyi, O. Lozova \/\/ Academy of Strategic Management Journal. \u2013 2019. \u2013 Vol. 18. Issue. 4. \u2013 P. 1\u20135.<\/li>\n
  8. Fedicheva K. Controlling, monitoring and diagnostics in identifying effective management practices of agricultural enterprises<\/a>. \/ K. Fedicheva, O. Kochetkov, S. Honcharenko, R. Levkina, M. Bichevin. \/\/ Agricultural and Resource Economics. \u2013 2021. \u2013 Vol. 7. Issue. 2. \u2013 Pp. 200\u2013218. https:\/\/doi.org\/10.22004\/ag.econ.313636<\/a><\/li>\n
  9. \u041c\u0430\u043a\u0430\u0440\u043e\u0432 \u0410.\u0410. \u041c\u043d\u043e\u0433\u043e\u0442\u043e\u0447\u0435\u0447\u043d\u0430\u044f \u043a\u0440\u0430\u0435\u0432\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430 \u0434\u043b\u044f \u043f\u0441\u0435\u0432\u0434\u043e\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0432 \u043f\u043e\u043b\u0438\u0441\u043b\u043e\u0435 \/ \u0410.\u0410. \u041c\u0430\u043a\u0430\u0440\u043e\u0432, \u0414.\u0410. \u041b\u0435\u0432\u043a\u0438\u043d \/\/ \u0412i\u0441\u043d\u0438\u043a \u0425\u0430\u0440\u043ai\u0432\u0441\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446i\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043di\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443 i\u043c\u0435\u043di \u0412.\u041d.\u00a0\u041a\u0430\u0440\u0430\u0437i\u043d\u0430. \u0421\u0435\u0440i\u044f: \u00ab\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 i \u043c\u0435\u0445\u0430\u043di\u043a\u0430\u00bb. \u2013 \u0425. : \u0425\u041d\u0423 \u0456\u043c. \u0412.\u041d. \u041a\u0430\u0440\u0430\u0437\u0456\u043d\u0430, \u2013 \u2116 1120. \u0412\u0438\u043f. 69. \u2013 \u0421. 64\u201374. https:\/\/doi.org\/10.26565\/2221-5646-2014-1120-04<\/li>\n
  10. Skoblo T.S. Influence of Stresses on Structural Changes in Gray Cast Iron \/ T.S. Skoblo, O.I.Sidashenko, O.V. Saichuk, O.Y. Klochko, A. Levkin \/\/ Materials Science. \u2013 2020. \u2013 Vol. 56. Issue. 3. \u2013 P.\u00a0347\u2013358.<\/li>\n
  11. \u041c\u0435\u0433\u0435\u043b\u044c \u042e.\u0415. \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u043b\u0430\u0437\u0435\u0440\u043d\u043e\u0433\u043e \u043b\u0443\u0447\u0430 \u043d\u0430 \u043c\u043d\u043e\u0433\u043e\u0441\u043b\u043e\u0439\u043d\u044b\u0435 \u0431\u0438\u043e\u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044b \/ \u042e.\u0415. \u041c\u0435\u0433\u0435\u043b\u044c, \u0412.\u041f. \u041f\u0443\u0442\u044f\u0442\u0438\u043d, \u0414.\u0410. \u041b\u0435\u0432\u043a\u0438\u043d, \u0410.\u0412. \u041b\u0435\u0432\u043a\u0438\u043d \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443 \u00ab\u0425\u041f\u0406\u00bb. \u0417\u0431\u0456\u0440\u043d\u0438\u043a \u043d\u0430\u0443\u043a\u043e\u0432\u0438\u0445 \u043f\u0440\u0430\u0446\u044c. \u0421\u0435\u0440\u0456\u044f: \u00ab\u041c\u0435\u0445\u0430\u043d\u0456\u043a\u043e-\u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u0456 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0442\u0430 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u0438\u00bb. \u2013 \u0425. : \u041d\u0422\u0423 \u00ab\u0425\u041f\u0406\u00bb, 2017. \u2013 \u2116 20(1242). \u2013 \u0421. 60\u201364.<\/li>\n<\/ol>\n

    References<\/strong><\/p>\n

      \n
    1. Stojan Ju.G. Optimizacija tehnicheskih sistem s istochnikami fizicheskih polej \/ Ju.G. Stojan, V.P. Putjatin. \u2013 K. : Nauk. dumka, 1988. \u2013 S. 44\u201348.<\/li>\n
    2. Asrorov F. Finding of bounded solutions to linear impulsive systems \/ F. Asrorov, V. Sobchuk, O. Kurylko \/\/ Eastern-European Journal of Enterprise Technologies. \u2013 2019. \u2013 Vol. 6. No. 4 (102): Mathematics and Cybernetics – applied aspects. \u2013 P. 14\u201320. https:\/\/doi.org\/10.15587\/1729-4061.2019.178635<\/li>\n
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    4. Scoblo T.S. Features of the carbide phase degradation under heating and deformation \/ T.S. Scoblo, O.Y. Klochko, V.N. Romanchenko, E.L. Belkin \/\/ Letters on Materials. \u2013 2021. \u2013 Vol. 11. No. 1. \u2013 P. 22\u201327. https:\/\/doi.org\/10.22226\/2410-3535-2021-1-22-27<\/li>\n
    5. Vojtov V.A. Criteria for evaluation of tribus system practices and its communication with tribological characteristics \/ V.A. Vojtov, A.SH. Bekirov, A.V. Voitov \/\/ Problems of Tribology. \u2013 2018. \u2013 Vol. 88. No. 2. \u2013 P. 35\u201342.<\/li>\n
    6. Tytarchuk I. Innovations financing in the agricultural sector. \/ I. Tytarchuk, Y. Nehoda, I. Shalyhina, N. Bazhanova, O. Horbachova, L. Rybina. \/\/ International Journal of Advanced Research in Engineering and Technology. \u2013 2020. \u2013 Vol. 11. Issue. 4. \u2013 Pp. 246\u2013255.<\/li>\n
    7. Potyshniak O. Assessment of the effectiveness of the strategic management system of investment activities of companies \/ O. Potyshniak, L. Dobuliak, V. Filippov, Y. Malakhovskyi, O. Lozova \/\/ Academy of Strategic Management Journal. \u2013 2019. \u2013 Vol. 18. Issue. 4. \u2013 P. 1\u20135.<\/li>\n
    8. Fedicheva K. Controlling, monitoring and diagnostics in identifying effective management practices of agricultural enterprises<\/a>. \/ K. Fedicheva, O. Kochetkov, S. Honcharenko, R. Levkina, M. Bichevin. \/\/ Agricultural and Resource Economics. \u2013 2021. \u2013 Vol. 7. Issue. 2. \u2013 Pp. 200\u2013218. https:\/\/doi.org\/10.22004\/ag.econ.313636<\/a><\/li>\n
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    10. Skoblo T.S. Influence of Stresses on Structural Changes in Gray Cast Iron \/ T.S. Skoblo, O.I. Sidashenko, O.V. Saichuk, O.Y. Klochko, D.A. Levkin \/\/ Materials Science. \u2013 2020. \u2013 Vol. 56. Issue. 3. \u2013 P. 347\u2013358.<\/li>\n
    11. Megel’ Ju.E. Matematicheskoe modelirovanie i optimizacija parametrov dejstvija lazernogo lucha na mnogoslojnye biomaterialy \/ Ju.E. Megel’, V.P. Putjatin, D.A. Levkin, A.V. Levkin \/\/ V\u0456snik Nac\u0456onal’nogo tehn\u0456chnogo un\u0456versitetu \u00abHP\u0406\u00bb. Zb\u0456rnik naukovih prac’. Ser\u0456ja: \u00abMehan\u0456ko-tehnolog\u0456chn\u0456 sistemi ta kompleksi\u00bb. \u2013 H. : NTU \u00abHP\u0406\u00bb, 2017. \u2013 \u2116 20(1242). \u2013 S. 60\u201364.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[66],"tags":[],"_links":{"self":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/12978"}],"collection":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12978"}],"version-history":[{"count":6,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/12978\/revisions"}],"predecessor-version":[{"id":15730,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/12978\/revisions\/15730"}],"wp:attachment":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}