{"id":13394,"date":"2022-08-21T11:05:22","date_gmt":"2022-08-21T08:05:22","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=13394"},"modified":"2022-10-03T15:12:11","modified_gmt":"2022-10-03T12:12:11","slug":"rozrobka-matematychnyh-modelej-prykladnyh-zadach-geometrychnogo-proektuvannya-tehnichnyh-system","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=13394","title":{"rendered":"\u0420\u043e\u0437\u0440\u043e\u0431\u043a\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0438\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0435\u043a\u0442\u0443\u0432\u0430\u043d\u043d\u044f \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c"},"content":{"rendered":"

<\/p>\n

\u0420\u041e\u0417\u0420\u041e\u0411\u041a\u0410 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u041d\u0418\u0425 \u041c\u041e\u0414\u0415\u041b\u0415\u0419 \u041f\u0420\u0418\u041a\u041b\u0410\u0414\u041d\u0418\u0425 \u0417\u0410\u0414\u0410\u0427 \u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u041e\u0413\u041e \u041f\u0420\u041e\u0415\u041a\u0422\u0423\u0412\u0410\u041d\u041d\u042f \u0422\u0415\u0425\u041d\u0406\u0427\u041d\u0418\u0425 \u0421\u0418\u0421\u0422\u0415\u041c<\/p>\n

MATHEMATICAL MODELS\u2019 DEVELOPMENT OF APPLIED TASKS OF GEOMETRIC DESIGN OF TECHNICAL SYSTEMS<\/p>\n

\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438:\u00a0133-136. \u041d\u043e\u043c\u0435\u0440: \u21164, 2022 (311)\u00a0\u00a0 \"\"<\/a> <\/strong>
\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>
\n\u0416\u0415\u0420\u041d\u041e\u0412\u041d\u0418\u041a\u041e\u0412\u0410 \u041e. \u0410.
\n\u0425\u0430\u0440\u043a\u0456\u0432\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0413.\u0421. \u0421\u043a\u043e\u0432\u043e\u0440\u043e\u0434\u0438
\nhttps:\/\/orcid.org\/0000-0002-5383-4493<\/a>
\ne-mail: oazhernovnykova@gmail.com<\/a>
\nDmytro LEVKIN
\nState Biotechnological University, Kharkiv
\nOksana ZHERNOVNYKOVA
\nH.S. Skovoroda Kharkiv National Pedagogical University, Kharkiv
\nDOI:<\/strong>\u00a0https:\/\/www.doi.org\/10.31891\/2307-5732-2022-311-4-133-136<\/a><\/p>\n

\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u043c\u043e\u0432\u043e\u044e \u043e\u0440\u0438\u0433\u0456\u043d\u0430\u043b\u0443<\/strong><\/p>\n

\u0412 \u0441\u0442\u0430\u0442\u0442\u0456 \u0434\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u0456 \u043f\u0438\u0442\u0430\u043d\u043d\u044f \u0440\u043e\u0437\u0440\u043e\u0431\u043a\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0438\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432 \u0442\u0435\u0440\u043c\u0456\u0447\u043d\u043e\u0457 \u0434\u0456\u0457 \u043d\u0430 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0443 \u0441\u0438\u0441\u0442\u0435\u043c\u0443. \u0410\u0432\u0442\u043e\u0440\u0430\u043c\u0438 \u043f\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043f\u043e\u0448\u0443\u043a\u0443 \u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u0438\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432 \u0434\u0436\u0435\u0440\u0435\u043b \u0437\u0431\u0443\u0440\u0435\u043d\u043d\u044f \u0442\u0435\u043c\u043f\u0435\u0440\u0430\u0442\u0443\u0440\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f \u0443 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0456\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u0456 \u0437\u0430 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u043d\u0438\u043c\u0438 \u043e\u0431\u043c\u0435\u0436\u0435\u043d\u043d\u044f\u043c\u0438. \u0412\u0440\u0430\u0445\u0443\u0432\u0430\u0432\u0448\u0438 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0437\u0430\u0441\u043e\u0431\u0456\u0432, \u044f\u043a\u0456 \u0437\u0430\u0431\u0435\u0437\u043f\u0435\u0447\u0443\u044e\u0442\u044c \u043f\u0440\u043e\u0446\u0435\u0441 \u0442\u0435\u0440\u043c\u0456\u0447\u043d\u043e\u0457 \u0434\u0456\u0457 \u043d\u0430 \u043c\u0430\u0442\u0435\u0440\u0456\u0430\u043b, \u0442\u0430 \u043e\u0441\u043e\u0431\u043b\u0438\u0432\u043e\u0441\u0442\u0456 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0443, \u0437\u0430\u0434\u0430\u043d\u0456 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u043d\u0456 \u043e\u0431\u043c\u0435\u0436\u0435\u043d\u043d\u044f \u043d\u0430 \u0442\u0435\u043c\u043f\u0435\u0440\u0430\u0442\u0443\u0440\u043d\u0435 \u043f\u043e\u043b\u0435 \u0442\u0430 \u0439\u043e\u0433\u043e \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0438. \u041f\u0435\u0440\u0435\u0432\u0456\u0440\u043a\u0430 \u043e\u0431\u043c\u0435\u0436\u0435\u043d\u044c \u043d\u0430 \u0442\u0435\u043c\u043f\u0435\u0440\u0430\u0442\u0443\u0440\u043d\u0435 \u043f\u043e\u043b\u0435 \u0432\u0438\u043c\u0430\u0433\u0430\u0454 \u0437\u0434\u0456\u0439\u0441\u043d\u0435\u043d\u043d\u044f \u0431\u0430\u0433\u0430\u0442\u043e\u0440\u0430\u0437\u043e\u0432\u043e\u0433\u043e \u0439\u043e\u0433\u043e \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u0443, \u0449\u043e \u0437\u043c\u0435\u043d\u0448\u0443\u0454 \u0442\u0435\u0440\u043c\u0456\u0447\u043d\u0435 \u043f\u043e\u0448\u043a\u043e\u0434\u0436\u0435\u043d\u043d\u044f \u0447\u0430\u0441\u0442\u0438\u043d \u043c\u0430\u0442\u0435\u0440\u0456\u0430\u043b\u0443. \u0414\u043b\u044f \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0437\u0430\u0446\u0456\u0457 \u0444\u0443\u043d\u043a\u0446\u0456\u0457 \u043c\u0435\u0442\u0438 \u043c\u043e\u0436\u043b\u0438\u0432\u043e \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u0442\u0438 \u0441\u0456\u0442\u043a\u043e\u0432\u0456 \u043f\u0440\u043e\u0446\u0435\u0441\u043e\u0440\u0438, \u044f\u043a\u0456 \u0437\u0430\u0432\u0434\u044f\u043a\u0438 \u0437\u0430\u0441\u0442\u043e\u0441\u0443\u0432\u0430\u043d\u043d\u044e \u0441\u043f\u0435\u0446\u0456\u0430\u043b\u0456\u0437\u043e\u0432\u0430\u043d\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0445 \u0431\u043b\u043e\u043a\u0456\u0432 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u043d\u043e \u043c\u0438\u0442\u0442\u0454\u0432\u043e \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u0443\u044e\u0442\u044c \u0432\u0435\u043b\u0438\u0447\u0435\u0437\u043d\u0443 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u043a\u0440\u0430\u0439\u043e\u0432\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u043d\u0430 \u043a\u043e\u043c\u043f\u2019\u044e\u0442\u0435\u0440\u0430\u0445. \u0417\u0430\u0432\u0434\u044f\u043a\u0438 \u043f\u0435\u0440\u0435\u0431\u043e\u0440\u0443 \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u043a\u0456\u0432 \u043a\u0440\u0430\u0439\u043e\u0432\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u0446\u0435 \u0434\u043e\u0437\u0432\u043e\u043b\u0438\u0442\u044c \u0437\u043d\u0430\u0439\u0442\u0438 \u043e\u043f\u0442\u0438\u043c\u0430\u043b\u044c\u043d\u0456 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432, \u0430 \u043e\u0442\u0436\u0435, \u043f\u0456\u0434\u0432\u0438\u0449\u0438\u0442\u0438 \u0442\u043e\u0447\u043d\u0456\u0441\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u044c\u043e\u0432\u0430\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0443.
\n\u0414\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043d\u044f \u0446\u0456\u0454\u0457 \u0441\u0442\u0430\u0442\u0442\u0456 \u0432\u0456\u0434\u043d\u043e\u0441\u0438\u0442\u044c\u0441\u044f \u0434\u043e \u0440\u043e\u0437\u0434\u0456\u043b\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u043e\u0433\u043e \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u0442\u0430 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u0441\u0438\u0441\u0442\u0435\u043c \u0437 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0435\u043d\u0438\u043c\u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438. \u0414\u043b\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u043e\u0433\u043e \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u0437\u0430\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u044e\u0442\u044c \u043a\u0440\u0430\u0439\u043e\u0432\u0456 \u0437\u0430\u0434\u0430\u0447\u0456 \u0434\u0438\u0444\u0435\u0440\u0435\u043d\u0446\u0456\u0430\u043b\u044c\u043d\u0438\u0445 \u0440\u0456\u0432\u043d\u044f\u043d\u044c \u0437 \u0447\u0430\u0441\u0442\u0438\u043d\u043d\u0438\u043c\u0438 \u043f\u043e\u0445\u0456\u0434\u043d\u0438\u043c\u0438. \u0410\u0432\u0442\u043e\u0440\u0430\u043c\u0438 \u043d\u0430\u0432\u0435\u0434\u0435\u043d\u0456 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u0456 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0439\u043d\u0456 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0456 \u043c\u043e\u0434\u0435\u043b\u0456 \u043a\u043e\u043d\u0442\u0440\u043e\u043b\u044f \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443 \u0442\u0435\u043c\u043f\u0435\u0440\u0430\u0442\u0443\u0440\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f \u0442\u0430 \u0442\u0435\u0440\u043c\u043e\u043d\u0430\u043f\u0440\u0443\u0436\u0435\u043d\u044c \u0432 \u043c\u0430\u0442\u0435\u0440\u0456\u0430\u043b\u0456, \u043c\u0456\u043d\u0456\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u0439\u043e\u0433\u043e \u043f\u043e\u0448\u043a\u043e\u0434\u0436\u0435\u043d\u0438\u0445 \u0447\u0430\u0441\u0442\u0438\u043d. \u041e\u0441\u0442\u0430\u043d\u043d\u044f \u0437 \u043d\u0438\u0445 \u0437\u0430\u0441\u043d\u043e\u0432\u0430\u043d\u0430 \u043d\u0430 \u0434\u0438\u0444\u0435\u0440\u0435\u043d\u0446\u0456\u0430\u043b\u044c\u043d\u043e\u043c\u0443 \u043a\u0440\u0438\u0442\u0435\u0440\u0456\u0457 \u043e\u0446\u0456\u043d\u043a\u0438 \u0442\u0435\u043c\u043f\u0435\u0440\u0430\u0442\u0443\u0440\u0438 \u043e\u043f\u0440\u043e\u043c\u0456\u043d\u0435\u043d\u043d\u044f \u0456 \u043c\u043e\u0436\u0435 \u0431\u0443\u0442\u0438 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u043d\u0430 \u0434\u043b\u044f \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u0431\u0430\u0433\u0430\u0442\u044c\u043e\u0445 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0445, \u0431\u0456\u043e\u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u0438\u0445 \u0456 \u0435\u043a\u043e\u043d\u043e\u043c\u0456\u0447\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c. \u0414\u0435\u0442\u0430\u043b\u044c\u043d\u0438\u0439 \u0430\u043d\u0430\u043b\u0456\u0437 \u0441\u043f\u0435\u0446\u0438\u0444\u0456\u0447\u043d\u0438\u0445 \u043e\u0441\u043e\u0431\u043b\u0438\u0432\u043e\u0441\u0442\u0435\u0439 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u0438\u0445 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0439\u043d\u0438\u0445 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0438\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0434\u043e\u0437\u0432\u043e\u043b\u0438\u0442\u044c \u0437\u0431\u0456\u043b\u044c\u0448\u0438\u0442\u0438 \u0442\u043e\u0447\u043d\u0456\u0441\u0442\u044c \u0440\u043e\u0437\u0440\u043e\u0431\u043a\u0438 \u0447\u0438\u0441\u0435\u043b\u044c\u043d\u0438\u0445 \u043c\u0435\u0442\u043e\u0434\u0456\u0432 \u0456 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e-\u0430\u043f\u0430\u0440\u0430\u0442\u043d\u0438\u0445 \u0437\u0430\u0441\u043e\u0431\u0456\u0432 \u0434\u043b\u044f \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u0443 \u0456 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432 \u043c\u043e\u0434\u0435\u043b\u044c\u043e\u0432\u0430\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0456 \u043c\u043e\u0434\u0435\u043b\u0456, \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430, \u0441\u0456\u0442\u043a\u043e\u0432\u0456 \u043f\u0440\u043e\u0446\u0435\u0441\u043e\u0440\u0438, \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 examines the issues of developing mathematical models for optimizing the parameters of the thermal action on the technical systems. The authors set the task of determining the optimal parameters of sources of temperature field disturbance in the technical system under the appropriate restrictions. Considering the technical characteristics of the means that ensure the process of thermal action on the material, and the peculiarities of the technological process, appropriate restrictions on the temperature field and its components are set. Checking the limits of the temperature field requires multiple calculations, which reduce thermal damage to parts of the material. To automate the objective function, it is possible to use grid processors, which, due to the use of specialized functional blocks, solve a huge number of boundary problems with computers almost instantly. Because to the selection of solutions of boundary value problems, this will allow to find optimal values of technical parameters, and therefore to increase the accuracy of the simulated process.
\nThe research of this article refers to the section on mathematical modeling and optimization of systems with distributed parameters. For mathematical modeling of these systems, boundary value problems of differential equations with partial derivatives are used. The authors present applied optimization mathematical models for controlling the distribution of the temperature field and thermal stresses in the material, minimizing its damaged parts. The last them is based on the differential criterion for evaluating the temperature of irradiation and can be used to optimize many technical, biotechnological and economic systems. A detailed analysis of the specific features of applied optimization mathematical models will allow to increase the accuracy of the development of numerical methods and hardware and software tools for calculating and optimizing the parameters of simulated systems.
\nKeywords: mathematical models, technical system, grid processors, 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. Vojtov V.A. Assessment of the quality factor of tribosystems and relationship with tribological characteristics \/ A. Vojtov, A.V. Voitov \/\/ Problems of Tribology. \u2013 2020. \u2013 Vol. 25. No. 4\/98. \u2013 P. 20\u201326. https:\/\/doi.org\/10.31891\/2079-1372-2020-98-4-20-26<\/a><\/li>\n
  3. \u0410\u0443\u043b\u0456\u043d \u0412.\u0412. \u0422\u0435\u043e\u0440\u0435\u0442\u0438\u043a\u043e-\u0444\u0456\u0437\u0438\u0447\u043d\u0438\u0439 \u043f\u0456\u0434\u0445\u0456\u0434 \u0434\u043e \u0434\u0456\u0430\u0433\u043d\u043e\u0441\u0442\u0438\u0447\u043d\u043e\u0457 \u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u0457 \u043f\u0440\u043e \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0441\u0442\u0430\u043d \u0430\u0433\u0440\u0435\u0433\u0430\u0442\u0456\u0432 \u043c\u043e\u0431\u0456\u043b\u044c\u043d\u043e\u0457 \u0441\u0456\u043b\u044c\u0441\u044c\u043a\u043e\u0433\u043e\u0441\u043f\u043e\u0434\u0430\u0440\u0441\u044c\u043a\u043e\u0457 \u0442\u0435\u0445\u043d\u0456\u043a\u0438 \/ \u0412.\u0412. \u0410\u0443\u043b\u0456\u043d, \u0421.\u0412. \u041b\u0438\u0441\u0435\u043d\u043a\u043e, \u0414.\u0412. \u0413\u043e\u043b\u0443\u0431, \u0410.\u0412. \u0413\u0440\u0438\u043d\u044c\u043a\u0456\u0432, \u041e.\u0406. \u041c\u0430\u0440\u0442\u0438\u043d\u0435\u043d\u043a\u043e \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u0430\u0440\u043a\u0456\u0432\u0441\u044c\u043a\u043e\u0433\u043e \u043d\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 \u0441\u0456\u043b\u044c\u0441\u044c\u043a\u043e\u0433\u043e \u0433\u043e\u0441\u043f\u043e\u0434\u0430\u0440\u0441\u0442\u0432\u0430 \u0456\u043c\u0435\u043d\u0456 \u041f\u0435\u0442\u0440\u0430 \u0412\u0430\u0441\u0438\u043b\u0435\u043d\u043a\u0430. \u2013 \u0425\u0430\u0440\u043a\u0456\u0432 : \u0425\u041d\u0422\u0423\u0421\u0413, 2015. \u2013 \u0412\u0438\u043f. 158. \u2013 \u0421. 252\u2013262.<\/li>\n
  4. \u0410\u0443\u043b\u0456\u043d \u0412.\u0412. \u041c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u0456 \u0456 \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u043d\u0456 \u043e\u0441\u043d\u043e\u0432\u0438 \u0437\u0430\u0431\u0435\u0437\u043f\u0435\u0447\u0435\u043d\u043d\u044f \u0442\u0430 \u043f\u0456\u0434\u0432\u0438\u0449\u0435\u043d\u043d\u044f \u043d\u0430\u0434\u0456\u0439\u043d\u043e\u0441\u0442\u0456 \u0444\u0443\u043d\u043a\u0446\u0456\u043e\u043d\u0443\u0432\u0430\u043d\u043d\u044f \u0430\u0432\u0442\u043e\u043c\u043e\u0431\u0456\u043b\u044c\u043d\u0438\u0445 \u0442\u0440\u0430\u043d\u0441\u043f\u043e\u0440\u0442\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \/ \u0412.\u0412. \u0410\u0443\u043b\u0456\u043d, \u0414.\u0412. \u0413\u043e\u043b\u0443\u0431, \u0410.\u0412. \u0413\u0440\u0438\u043d\u044c\u043a\u0456\u0432, \u0421.\u0412. \u041b\u0438\u0441\u0435\u043d\u043a\u043e. \u2013 \u041a\u0440\u043e\u043f\u0438\u0432\u043d\u0438\u0446\u044c\u043a\u0438\u0439 : \u0422\u041e\u0412 \u00ab\u041a\u041e\u0414\u00bb, 2017. \u2013 369 \u0441.<\/li>\n
  5. Fardigola L.V. Transformation Operators in the Problems of Controllability for the Degenerate Wave Equation with Variable Coefficients \/ L.V. Fardigola. \/\/ Ukrainian Mathematical Journal. \u2013 2009. \u2013 Vol. 70. \u2116 8. \u2013 P. 1300\u20131318. https:\/\/doi.org\/10.1007\/s11253-018-1570-4<\/li>\n
  6. Tytarchuk I. Innovations financing in the agricultural sector \/ Tytarchuk, Y. Nehoda, I. Shalyhina, N. Bazhanova, O. Horbachova, L. Rubina \/\/ International Journal of Advanced Research in Engineering and Technology. \u2013 2020. \u2013 Vol. 11. Issue. 4. \u2013 P. 246\u2013255.<\/li>\n
  7. Levkina R. Management of innovative marketing techniques as an effective business tool \/ R. Levkina, A. Petrenko \/\/ Agricultural and Resource Economics: International Scientific E-Journal. \u2013 2019. \u2013 Vol. 5. No. 1. \u2013 P. 37\u2013<\/li>\n
  8. \u0417\u0430\u043c\u044f\u0442\u0456\u043d\u0430 \u041d.\u0412. \u041c\u0456\u0441\u0446\u0435 \u043a\u043e\u043d\u0442\u0440\u043e\u043b\u0456\u043d\u0433\u0443 \u0443 \u0441\u0438\u0441\u0442\u0435\u043c\u0456 \u0443\u043f\u0440\u0430\u0432\u043b\u0456\u043d\u043d\u044f \u0441\u0443\u0447\u0430\u0441\u043d\u0438\u043c \u043f\u0456\u0434\u043f\u0440\u0438\u0454\u043c\u0441\u0442\u0432\u043e\u043c \/ \u041d.\u0412. \u0417\u0430\u043c\u044f\u0442\u0456\u043d\u0430 \/\/ \u0415\u043a\u043e\u043d\u043e\u043c\u0456\u043a\u0430 \u0456 \u0441\u0443\u0441\u043f\u0456\u043b\u044c\u0441\u0442\u0432\u043e. \u2013 \u041c\u0443\u043a\u0430\u0447\u0456\u0432, \u2013 \u0412\u0438\u043f. 7. \u2013 \u0421. 324\u2013328.<\/li>\n
  9. \u0413\u0440\u0438\u043d\u0447\u0438\u0448\u0438\u043d \u042f.\u041c. \u0421\u0442\u0440\u0430\u0442\u0435\u0433\u0456\u0447\u043d\u0438\u0439 \u043f\u0456\u0434\u0445\u0456\u0434 \u0434\u043e \u0430\u043d\u0442\u0438\u043a\u0440\u0438\u0437\u043e\u0432\u043e\u0432\u043e\u0433\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u0456\u043d\u043d\u044f \u043f\u0456\u0434\u043f\u0440\u0438\u0454\u043c\u0441\u0442\u0432\u043e\u043c \/ \u042f.\u041c.\u00a0\u0413\u0440\u0438\u043d\u0447\u0438\u0448\u0438\u043d \/\/ \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: \u0415\u043a\u043e\u043d\u043e\u043c\u0456\u043a\u0430 \u0456 \u0443\u043f\u0440\u0430\u0432\u043b\u0456\u043d\u043d\u044f. \u2013 \u041a\u0438\u0457\u0432, 2021. \u2013 \u0422. 32(72). \u2116 1. \u2013 \u0421. 38\u201341. https:\/\/doi.org\/10.32838\/2523-4803\/71-1-6<\/li>\n
  10. \u041b\u0435\u0432\u043a\u0456\u043d \u0414.\u0410. \u0427\u0438\u0441\u0435\u043b\u044c\u043d\u0456 \u043c\u0435\u0442\u043e\u0434\u0438 \u0456 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0456 \u043c\u043e\u0434\u0435\u043b\u0456 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0456\u0432 \u0431\u0456\u043e\u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u0438\u0445 \u043f\u0440\u043e\u0446\u0435\u0441\u0456\u0432 \/ \u0414.\u0410. \u041b\u0435\u0432\u043a\u0456\u043d \/\/ \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: \u0422\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u043d\u0430\u0443\u043a\u0438. \u2013 \u041a\u0438\u0457\u0432, 2022. \u2013 \u0422. 33(72). \u2116 1. \u2013 \u0421. 128\u2013132. https:\/\/doi.org\/10.32838\/2663-5941\/2022.1\/21<\/a><\/li>\n
  11. Palii A.P. Assessment of cow lactation and milk parameters when applying various milking equipment<\/a> \/ A.P. Palii, Yu.M. Handola, I.O. Shevchenko, A.O. Stotskyi, O.G. Stotskyi, A.I. Sereda, D.A. Levkin, L.G. Ulko, O.I. Shkromada, A.P. Paliy \/\/ Ukrainian journal of Ecology. \u2013 Vol. 10. Issue. 4. \u2013 P. 195\u2013201. doi: 10_15421\/ 2020_188<\/li>\n
  12. Kravtsov A. Development of a rheological model of stress relaxation in the structure of an oil film on the friction surface with fullerene additives \/ Kravtsov, A. Suska, A. Biekirov, D. Levkin \/\/ Eastern-European Journal of Enterprise Technologies. \u2013 2021. \u2013 Vol. 3. No. 7 (111): Applied mechanics. \u2013 P. 93\u201399. https:\/\/doi.org\/10.15587\/1729-4061.2021.235468<\/a><\/li>\n<\/ol>\n

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

      \n
    1. Stoyan Yu.G. Optimizaciya tekhnicheskih sistem s istochnikami fizicheskih poley. \/ Yu.G. Stoyan, V.P. Putyatin. \u2013 Kyiv: Nauk. dumka, 1988. \u2013 Pp. 44\u201348.<\/li>\n
    2. Vojtov V.A. Assessment of the quality factor of tribosystems and relationship with tribological characteristics. \/ A. Vojtov, A.V. Voitov. \/\/ Problems of Tribology. \u2013 2020. \u2013 Vol. 25. No. 4\/98. \u2013 Pp. 20\u201326. https:\/\/doi.org\/10.31891\/2079-1372-2020-98-4-20-26<\/a><\/li>\n
    3. Aulin V.V. Teoretyko-fizychnyi pidkhid do diahnostychnoi informatsii pro tekhnichnyi stan agregativ mobilnoi silskogospodarskoi tekhniky. \/ V.V. Aulin, S.V. Lysenko, D.V. Holub, A.V. Hrynkiv, O.I. Martynenko. \/\/ Visnyk Kharkivskogo natsionalnogo tekhnichnogo universytetu silskogo gospodarstva imeni Petra Vasylenka. \u2013 Kharkiv: KhNTUSG, 2015. \u2013 Vyp. 158. \u2013 Pp. 252\u2013262.<\/li>\n
    4. Aulin V.V. Metodolohichni i teoretychni osnovy zabezpechennia ta pidvyshchennia nadiinosti funktsionuvannia avtomobilnykh transportnykh system. \/ V.V. Aulin, D.V. Holub, A.V. Hrynkiv, S.V. Lysenko. \u2013 Kropyvnytskyi: TOV \u00abKOD\u00bb, 2017. \u2013 369 p.<\/li>\n
    5. Fardigola L.V. Transformation Operators in the Problems of Controllability for the Degenerate Wave Equation with Variable Coefficients. \/ L.V. Fardigola. \/\/ Ukrainian Mathematical Journal. \u2013 2009. \u2013 Vol. 70. No. 8. \u2013 Pp. 1300\u20131318. https:\/\/doi.org\/10.1007\/s11253-018-1570-4<\/li>\n
    6. Tytarchuk I. Innovations financing in the agricultural sector. \/ Tytarchuk, Y. Negoda, 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. Levkina R. Management of innovative marketing techniques as an effective business tool. \/ R. Levkina, A. Petrenko. \/\/ Agricultural and Resource Economics: International Scientific E-Journal. \u2013 2019. \u2013 Vol. 5. No. 1. \u2013 Pp. 37\u2013<\/li>\n
    8. Zamiatina N.V. Mistse kontrolingu u systemi upravlinnia suchasnym pidpryiemstvom. \/ Zamiatina N.V. \/\/ Ekonomika i suspilstvo. \u2013 Mukachiv, 2016. \u2013 Vyp. 7. \u2013 Pp. 324\u2013328.<\/li>\n
    9. Grynchyshyn Ya.M. Stratehichnyi pidkhid do antykryzovovogo upravlinnia pidpryiemstvom. \/ Grynchyshyn Ya.M. \/\/ Vcheni zapysky Tavriiskogo Natsionalnogo Universytetu imeni V.I. Vernadskogo. Seriia: \u00abEkonomika i upravlinnia\u00bb. \u2013 Kyiv, 2021. \u2013 Vol.32(72). No.1. \u2013 Pp. 38\u201341. https:\/\/doi.org\/10.32838\/2523-4803\/71-1-6<\/a><\/li>\n
    10. Levkin D.A. Chyselni metody i matematychni modeli optymizatsii parametriv biotekhnolohichnykh protsesiv. \/ Levkin D.A. \/\/ Vcheni zapysky Tavriiskogo Natsionalnogo Universytetu imeni V.I. Vernadskoho. Seriia: \u00abTekhnichni nauky\u00bb. \u2013 Kyiv, 2022. \u2013 Vol. 33(72). No. 1. Ch. 1. \u2013 Pp. 128\u2013132. https:\/\/doi.org\/10.32838\/2663-5941\/2022.1\/21<\/a><\/li>\n
    11. Palii A.P. Assessment of cow lactation and milk parameters when applying various milking equipment<\/a>. \/ A.P. Palii, Yu. M. Handola, I.O. Shevchenko, A.O. Stotskyi, O.G. Stotskyi, A.I. Sereda, D.A. Levkin, L.G. Ulko, O.I. Shkromada, A.P. Paliy. \/\/ Ukrainian journal of Ecology. \u2013 Vol. 10. Issue. 4. \u2013 Pp. 195\u2013201. doi: 10_15421\/ 2020_188<\/li>\n
    12. Kravtsov A. Development of a rheological model of stress relaxation in the structure of an oil film on the friction surface with fullerene additives. \/ Kravtsov, A. Suska, A. Biekirov, D. Levkin. \/\/ Eastern-European Journal of Enterprise Technologies. \u2013 2021. \u2013 Vol. 3. No. 7 (111): Applied mechanics. \u2013 Pp. 93\u201399. https:\/\/doi.org\/10.15587\/1729-4061.2021.235468<\/a><\/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":[67],"tags":[],"_links":{"self":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/13394"}],"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=13394"}],"version-history":[{"count":6,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/13394\/revisions"}],"predecessor-version":[{"id":14154,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/13394\/revisions\/14154"}],"wp:attachment":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13394"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13394"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}