{"id":12102,"date":"2022-04-19T23:52:00","date_gmt":"2022-04-19T20:52:00","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=12102"},"modified":"2022-04-20T14:24:29","modified_gmt":"2022-04-20T11:24:29","slug":"teoretychni-osnovy-strukturyzacziyi-metodiv-spektralnogo-analizu-u-riznyh-teoretyko-chyslovyh-bazysah","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=12102","title":{"rendered":"\u0422\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u043d\u0456 \u043e\u0441\u043d\u043e\u0432\u0438 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0438\u0437\u0430\u0446\u0456\u0457 \u043c\u0435\u0442\u043e\u0434\u0456\u0432 \u0441\u043f\u0435\u043a\u0442\u0440\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443 \u0443 \u0440\u0456\u0437\u043d\u0438\u0445 \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u043a\u043e-\u0447\u0438\u0441\u043b\u043e\u0432\u0438\u0445 \u0431\u0430\u0437\u0438\u0441\u0430\u0445"},"content":{"rendered":"

<\/p>\n

\u0422\u0415\u041e\u0420\u0415\u0422\u0418\u0427\u041d\u0406 \u041e\u0421\u041d\u041e\u0412\u0418 \u0421\u0422\u0420\u0423\u041a\u0422\u0423\u0420\u0418\u0417\u0410\u0426\u0406\u0407 \u041c\u0415\u0422\u041e\u0414\u0406\u0412 \u0421\u041f\u0415\u041a\u0422\u0420\u0410\u041b\u042c\u041d\u041e\u0413\u041e \u0410\u041d\u0410\u041b\u0406\u0417\u0423 \u0423 \u0420\u0406\u0417\u041d\u0418\u0425 \u0422\u0415\u041e\u0420\u0415\u0422\u0418\u041a\u041e-\u0427\u0418\u0421\u041b\u041e\u0412\u0418\u0425 \u0411\u0410\u0417\u0418\u0421\u0410\u0425<\/p>\n

THEORETICAL FUNDAMENTALS OF STRUCTURING THE METHODS OF SPECTRAL ANALYSIS IN DIFFERENT NUMBER SYSTEMS<\/p>\n

\u00a0<\/strong>\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 168-174. \u041d\u043e\u043c\u0435\u0440: \u2116<\/strong>1<\/strong>, 202<\/strong>2<\/strong> (<\/strong>305<\/strong>)<\/strong> \"\"<\/a>
\n\u00a0<\/strong>\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u0412\u041e\u0417\u041d\u0410 \u041d. \u042f.
\nhttps:\/\/orcid.org\/0000-0002-8856-1720<\/a>
\ne-mail: nvozna@ukr.net<\/a>
\n\u041c\u0410\u041a\u041e\u0413\u0406\u041d \u0412. \u0411.
\ne-mail: vovamakogin@gmail.com<\/a>
\n\u0417\u0430\u0445\u0456\u0434\u043d\u043e\u0443\u043a\u0440\u0430\u0457\u043d\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442<\/p>\n

Vozna NATALIIA, Makogin VOLODYMYR
\nWest Ukrainian National University
\n\u00a0<\/strong>DOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2022-305-1-168-174<\/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

\u00a0<\/strong>\u0414\u0430\u043d\u0430 \u0440\u043e\u0431\u043e\u0442\u0430 \u043f\u0440\u0438\u0441\u0432\u044f\u0447\u0435\u043d\u0430 \u0432\u0438\u0440\u0456\u0448\u0435\u043d\u043d\u044e \u043d\u0430\u0443\u043a\u043e\u0432\u043e\u0457 \u0437\u0430\u0434\u0430\u0447\u0456 \u0440\u043e\u0437\u0432\u0438\u0442\u043a\u0443 \u0442\u0435\u043e\u0440\u0456\u0457 \u0442\u0430 \u043c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0456\u0457 \u0441\u043f\u0435\u043a\u0442\u0440\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443 \u0443 \u043f\u0440\u043e\u0446\u0435\u0441\u0430\u0445 \u0444\u043e\u0440\u043c\u0443\u0432\u0430\u043d\u043d\u044f, \u043f\u0435\u0440\u0435\u0442\u0432\u043e\u0440\u0435\u043d\u043d\u044f, \u043f\u0435\u0440\u0435\u0434\u0430\u0432\u0430\u043d\u043d\u044f, \u0446\u0438\u0444\u0440\u043e\u0432\u043e\u0433\u043e \u043e\u043f\u0440\u0430\u0446\u044e\u0432\u0430\u043d\u043d\u044f \u0442\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u044f \u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u0457 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0456 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0438\u0445 \u0437\u0430\u0441\u0430\u0434 \u0443 \u0440\u0456\u0437\u043d\u0438\u0445 \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u043a\u043e-\u0447\u0438\u0441\u043b\u043e\u0432\u0438\u0445 \u0431\u0430\u0437\u0438\u0441\u0430\u0445. \u041c\u043e\u0436\u043b\u0438\u0432\u0456\u0441\u0442\u044c \u0443\u0437\u0430\u0433\u0430\u043b\u044c\u043d\u0435\u043d\u043d\u044f \u0442\u0435\u043e\u0440\u0456\u0457 \u0442\u0430 \u043c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0456\u0457 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0438\u0437\u0430\u0446\u0456\u0457 \u043f\u043e\u043b\u0456\u0444\u0443\u043d\u043a\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0445 \u0434\u0430\u043d\u0438\u0445 \u0456 \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0443 \u0432\u0456\u0434 \u043e\u0434\u043d\u0438\u0445 \u0441\u043f\u0435\u043a\u0442\u0440\u0456\u0432 \u0434\u043e \u0456\u043d\u0448\u0438\u0445 \u0437\u0430\u0431\u0435\u0437\u043f\u0435\u0447\u0443\u0454 \u043e\u0441\u043d\u043e\u0432\u0443 \u0434\u043b\u044f \u0435\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443, \u043e\u0446\u0456\u043d\u044e\u0432\u0430\u043d\u043d\u044f \u0442\u0430 \u043e\u043f\u0440\u0430\u0446\u044e\u0432\u0430\u043d\u043d\u044f \u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u0457.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong>\u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0438\u0437\u0430\u0446\u0456\u044f, \u0441\u043f\u0435\u043a\u0442\u0440\u0430\u043b\u044c\u043d\u0438\u0439 \u0430\u043d\u0430\u043b\u0456\u0437, \u043f\u043e\u043b\u0456\u0444\u0443\u043d\u043a\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0456 \u0434\u0430\u043d\u0456.<\/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 paper deals with solving the scientific problem of developing the theory and methodology of spectral analysis of the processes of generation, conversion, transmission, digital processing and presentation of information based on mathematical principles in various number systems.
\nTheoretical foundations of data structuring in the processes of generation, conversion, transmission, digital processing and presentation of information based on mathematical principles of different code systems make the study of spectral analysis in this area a promising task, as almost all fields of modern civilization are closely connected with the informatization of society and the corresponding structuring of information flows. The possibility of generalizing the theory and methodology of structuring multifunctional data and the transition from one spectrum to another provides a basis for effective analysis, evaluation and processing of information. Spectral analysis is applied to algorithmic solutions when performing measurements, generating data codes in different code systems, number systems and conducting specialized transformations over information flows.
\nThe analysis of the existing experience of data structuring, methodology of structural organization of spectra and the creation of processors for computer systems using the Rademacher number system, which generates a binary number system, shows the tendency to increasing use of other number systems, including the unitary one, Haar, Chrestenson and Galois systems. The implementation of specialized, signal, switching and problem-oriented digital data processors is often carried out on the basis of the combined use of the above mentioned number systems.
\nIn this regard, a problem of in-depth study of the theory and methods of spectral analysis and the characteristics of the code systems of \u201cnon-Rademacher\u201d number systems and the limits of their use for the implementation of components of both specialized and universal processors arises.
\nKeywords:<\/strong> structuring, spectral analysis, \u00a0multifunctional data.<\/p>\n

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

    \n
  1. Carl Adam Petri<\/a>. Nets, time and space. Theoretical computer science, 153(12):3-48, 1996.<\/li>\n
  2. \u041b\u043e\u043a\u0430\u0437\u044e\u043a \u0412.\u041c. \u0406\u043d\u0442\u0435\u043b\u0435\u043a\u0442\u0443\u0430\u043b\u044c\u043d\u0435 \u0434\u0456\u0430\u0433\u043d\u043e\u0441\u0442\u0443\u0432\u0430\u043d\u043d\u044f \u043c\u0456\u043a\u0440\u043e\u043f\u0440\u043e\u0446\u0435\u0441\u043e\u0440\u043d\u0438\u0445 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u0457\u0432 \u0442\u0430 \u0441\u0438\u0441\u0442\u0435\u043c : \u043d\u0430\u0432\u0447. \u043f\u043e\u0441\u0456\u0431. \u0434\u043b\u044f \u0432\u0443\u0437\u0456\u0432 \/ \u0412.\u041c.\u00a0\u041b\u043e\u043a\u0430\u0437\u044e\u043a, \u041e.\u0412.\u00a0\u041f\u043e\u043c\u043e\u0440\u043e\u0432\u0430, \u0410.\u041e.\u00a0\u0414\u043e\u043c\u0456\u043d\u043e\u0432 \u2013 \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439 : \u0422\u0423\u041f, 2001. \u2013 286\u0441.<\/li>\n
  3. \u0417\u0430\u0439\u0446\u0435\u0432 \u0414.\u0410. \u0406\u043d\u0432\u0430\u0440\u0456\u0430\u043d\u0442\u0438 \u0447\u0430\u0441\u043e\u0432\u0438\u0445 \u043c\u0435\u0440\u0435\u0436 \u041f\u0435\u0442\u0440\u0456 \/ \u0414.\u0410.\u00a0\u0417\u0430\u0439\u0446\u0435\u0432 \/\/ \u041a\u0438\u0431\u0435\u0440\u043d\u0435\u0442\u0438\u043a\u0430 \u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u043d\u044b\u0439 \u0430\u043d\u0430\u043b\u0438\u0437. \u2011 2004. \u2011 \u2116 2. \u2011 \u0421. 92-106.<\/li>\n
  4. \u041d\u0456\u043a\u043e\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u042e.\u0412. \u0414\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 : \u043f\u0456\u0434\u0440\u0443\u0447\u043d\u0438\u043a \/ \u042e.\u0412.\u00a0\u041d\u0456\u043a\u043e\u043b\u044c\u0441\u044c\u043a\u0438\u0439, \u0412.\u0412.\u00a0\u041f\u0430\u0441\u0456\u0447\u043d\u0438\u043a, \u042e.\u041c.\u00a0\u0429\u0435\u0440\u0431\u0438\u043d\u0430. \u2013 \u041b\u044c\u0432\u0456\u0432 : “\u041c\u0430\u0433\u043d\u043e\u043b\u0456\u044f 2006”, 2007. \u2013 608\u0441.<\/li>\n
  5. Natalia Vozna Theory and methods of development of data flow models in distributed CS \/ N.\u00a0Vozna \/\/ Advanced computer system and network: design and application: Proceedings of the 4-th international conference ACSN-2009. – Lviv, 2009. \u2011 P. 304-307.<\/li>\n
  6. \u0412\u043e\u0437\u043d\u0430 \u041d.\u042f. \u0422\u0435\u043e\u0440\u0456\u044f \u0442\u0430 \u043c\u0435\u0442\u043e\u0434\u0438 \u043f\u043e\u0431\u0443\u0434\u043e\u0432\u0438 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0440\u0443\u0445\u0443 \u0434\u0430\u043d\u0438\u0445 \u0443 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0435\u043d\u0438\u0445 \u041a\u0421 \/ \u041d.\u042f. \u0412\u043e\u0437\u043d\u0430 \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u041d\u0423\u041b\u041f “\u041a\u043e\u043c\u043f\u2019\u044e\u0442\u0435\u0440\u043d\u0456 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0442\u0430 \u043c\u0435\u0440\u0435\u0436\u0456”, 2010. \u2011 \u2116688. \u2013 \u0421. 60-64.<\/li>\n
  7. \u0411\u043e\u0439\u0447\u0435\u043d\u043a\u043e \u041e.\u0412. \u0428\u0432\u0438\u0434\u043a\u043e\u0434\u0456\u044e\u0447\u0456 \u0431\u0430\u0433\u0430\u0442\u043e\u0434\u043e\u0434\u0430\u043d\u043a\u043e\u0432\u0456 \u0441\u0443\u043c\u0430\u0442\u043e\u0440\u0438 \u043a\u043e\u043c\u0431\u0456\u043d\u0430\u0446\u0456\u043d\u043e\u0433\u043e \u0442\u0438\u043f\u0443 \/ \u041e.\u0412.\u0411\u043e\u0439\u0447\u0435\u043d\u043a\u043e, \u042f.\u0406.\u0422\u043e\u0440\u043e\u0448\u0430\u043d\u043a\u043e \/\/ \u041c\u0456\u0436\u0432\u0443\u0437\u0456\u0432\u0441\u044c\u043a\u0438\u0439 \u0437\u0431\u0456\u0440\u043d\u0438\u043a “\u041a\u043e\u043c\u043f\u2019\u044e\u0442\u0435\u0440\u043d\u043e-\u0456\u043d\u0442\u0435\u0433\u0440\u043e\u0432\u0430\u043d\u0456 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0457: \u043e\u0441\u0432\u0456\u0442\u0430, \u043d\u0430\u0443\u043a\u0430, \u0432\u0438\u0440\u043e\u0431\u043d\u0438\u0446\u0442\u0432\u043e”, 2011. \u2013 \u2116 3. \u2013 C. 20-24.<\/li>\n
  8. \u041a\u0430\u0440\u0446\u0435\u0432 \u041c.\u0410. \u0410\u0440\u0438\u0444\u043c\u0435\u0442\u0438\u043a\u0430 \u0446\u0438\u0444\u0440\u043e\u0432\u044b\u0445 \u043c\u0430\u0448\u0438\u043d \/ \u041c.\u0410.\u041a\u0430\u0440\u0446\u0435\u0432<\/a> \u2013 \u041c. : \u041d\u0430\u0443\u043a\u0430, 1969. \u2013 576 c.<\/li>\n
  9. \u041c\u0430\u0439\u043e\u0440\u043e\u0432 \u0421.\u0410. \u041f\u0440\u0438\u043d\u0446\u0438\u043f\u044b \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u0438 \u0446\u0438\u0444\u0440\u043e\u0432\u044b\u0445 \u043c\u0430\u0448\u0438\u043d \/ \u0421.\u0410.\u00a0\u041c\u0430\u0439\u043e\u0440\u043e\u0432, \u0413.\u0418.\u00a0\u041d\u043e\u0432\u0438\u043a\u043e\u0432. \u2013 \u041b. : \u041c\u0430\u0448\u0438\u043d\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435, 1974. \u2013 432 \u0441.<\/li>\n
  10. \u0427\u0435\u0440\u043a\u0430\u0441\u044c\u043a\u0438\u0439 \u041c.\u0412. \u0410\u043d\u0430\u043b\u0456\u0437 \u0441\u043a\u043b\u0430\u0434\u043d\u043e\u0441\u0442\u0456 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u0457\u0432 \u043f\u043e\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u044f \/ \u041c.\u0412. \u0427\u0435\u0440\u043a\u0430\u0441\u044c\u043a\u0438\u0439, \u041c\u0443\u0440\u0430\u0434 \u0425\u0443\u0441\u0435\u0439\u043d \u0425\u0430\u043b\u0456\u043b \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u041d\u0423\u041b\u041f “\u041a\u043e\u043c\u043f\u2019\u044e\u0442\u0435\u0440\u043d\u0456 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u043f\u0440\u043e\u0435\u043a\u0442\u0443\u0432\u0430\u043d\u043d\u044f. \u0422\u0435\u043e\u0440\u0456\u044f \u0456 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0430”. \u2013 \u041b\u044c\u0432\u0456\u0432 : \u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u201c\u041b\u044c\u0432\u0456\u0432\u0441\u044c\u043a\u0430 \u043f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u043a\u0430\u201d, 2005. \u2013 \u2116 548. \u2013 \u0421. 15-21.<\/li>\n
  11. \u041c\u0435\u043b\u044c\u043d\u0438\u043a \u0420.\u0410. \u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438 \u0442\u0430 \u043c\u0435\u0442\u043e\u0434\u0438 \u043e\u043f\u0440\u0430\u0446\u044e\u0432\u0430\u043d\u043d\u044f \u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u044c : \u043d\u0430\u0432\u0447. \u043f\u043e\u0441\u0456\u0431\u043d\u0438\u043a \/ \u0420.\u0410. \u041c\u0435\u043b\u044c\u043d\u0438\u043a. \u2013 \u041b\u044c\u0432\u0456\u0432 : \u0412\u0438\u0434\u0430\u0432\u043d\u0438\u0446\u0442\u0432\u043e \u041b\u044c\u0432\u0456\u0432\u0441\u044c\u043a\u043e\u0457 \u043f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u043a\u0438, 2017. \u2013 220 \u0441.<\/li>\n
  12. James Martin<\/a>. Design and strategy for distributed data processing \/ Martin<\/a> \u2013 NJ: Prentice Hall PTR Upper Saddle River, 1990. \u2013 672 \u0440.<\/li>\n
  13. \u041f\u0456\u0442\u0443\u0445 \u0406. \u041f\u0440\u0438\u043d\u0446\u0438\u043f\u0438 \u043f\u043e\u0431\u0443\u0434\u043e\u0432\u0438 \u043a\u043e\u043c\u043f\u2019\u044e\u0442\u0435\u0440\u043d\u0438\u0445 \u043c\u0435\u0440\u0435\u0436 \u0437 \u0433\u043b\u0438\u0431\u043e\u043a\u0438\u043c \u0440\u043e\u0437\u043f\u0430\u0440\u0430\u043b\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f\u043c \u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u0439\u043d\u0438\u0445 \u043f\u043e\u0442\u043e\u043a\u0456\u0432 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0456 \u043c\u0430\u0442\u0440\u0438\u0447\u043d\u0438\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0440\u0443\u0445\u0443 \u0434\u0430\u043d\u0438\u0445 \/ \u0406.\u00a0\u041f\u0456\u0442\u0443\u0445, \u042f.\u00a0\u041d\u0438\u043a\u043e\u043b\u0430\u0439\u0447\u0443\u043a, \u041d.\u00a0\u0412\u043e\u0437\u043d\u0430 \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u041d\u0423\u041b\u041f “\u0420\u0430\u0434\u0456\u043e\u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u0456\u043a\u0430 \u0442\u0430 \u0442\u0435\u043b\u0435\u043a\u043e\u043c\u0443\u043d\u0456\u043a\u0430\u0446\u0456\u0457”. \u2013 \u041b\u044c\u0432\u0456\u0432, 2004. \u2011 \u2116 508. \u2011 \u0421. 263-268.<\/li>\n
  14. \u0413\u043b\u0443\u0445\u043e\u0432 \u0412.\u0421. \u041e\u0446\u0456\u043d\u043a\u0430 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u043d\u043e\u0457 \u0441\u043a\u043b\u0430\u0434\u043d\u043e\u0441\u0442\u0456 \u0431\u0430\u0433\u0430\u0442\u043e\u0441\u0435\u043a\u0446\u0456\u0439\u043d\u0438\u0445 \u043f\u043e\u043c\u043d\u043e\u0436\u0443\u0432\u0430\u0447\u0456\u0432 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0456\u0432 \u043f\u043e\u043b\u0456\u0432 \u0413\u0430\u043b\u0443\u0430 \/ \u0412.\u0421.\u00a0\u0413\u043b\u0443\u0445\u043e\u0432, \u0413.\u041c.\u00a0\u0422\u0440\u0456\u0449 \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443 “\u041b\u044c\u0432\u0456\u0432\u0441\u044c\u043a\u0430 \u043f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u043a\u0430” “\u041a\u043e\u043c\u043f\u044e\u0442\u0435\u0440\u043d\u0456 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0442\u0430 \u043c\u0435\u0440\u0435\u0436\u0456”. \u2013 \u041b\u044c\u0432\u0456\u0432, 2014. \u2013 \u0412\u0438\u043f. 806. \u2013 \u0421.27-33.<\/li>\n
  15. \u0412\u043e\u0437\u043d\u0430 \u041d.\u042f. \u041e\u0441\u043d\u043e\u0432\u0438 \u0442\u0435\u043e\u0440\u0456\u0457 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0438\u0437\u0430\u0446\u0456\u0457 \u043f\u043e\u043b\u0456\u0444\u0443\u043d\u043a\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0445 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0456\u0432 \u0441\u043a\u043b\u0430\u0434\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \/ \u041d.\u042f.\u00a0\u0412\u043e\u0437\u043d\u0430 \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443. \u2011 \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439, 2015. \u2013 \u2116 2 (223). \u2011 \u0421. 204-208.<\/li>\n
  16. \u0412\u043e\u0437\u043d\u0430 \u041d.\u042f. \u0424\u043e\u0440\u043c\u0430\u043b\u0456\u0437\u0430\u0446\u0456\u044f \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0440\u0443\u0445\u0443 \u0434\u0430\u043d\u0438\u0445 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0435\u043d\u0438\u0445 \u043a\u043e\u043c\u043f\u2019\u044e\u0442\u0435\u0440\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0442\u0430 \u043e\u0446\u0456\u043d\u044e\u0432\u0430\u043d\u043d\u044f \u0457\u0445 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u043d\u043e\u0457 \u0441\u043a\u043b\u0430\u0434\u043d\u043e\u0441\u0442\u0456 \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\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 \u0456\u043c. \u0406. \u041f\u0443\u043b\u044e\u044f, 2011. \u2011 \u2116 1. \u0422.16. \u2013 \u0421. 167-179.<\/li>\n
  17. \u041d\u0438\u043a\u043e\u043b\u0430\u0439\u0447\u0443\u043a \u042f.\u041c. \u0422\u0435\u043e\u0440\u0456\u044f \u0434\u0436\u0435\u0440\u0435\u043b \u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u0457 \/ \u042f.\u041c. \u041d\u0438\u043a\u043e\u043b\u0430\u0439\u0447\u0443\u043a. \u2013 \u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c : \u0422\u0437\u041e\u0412 “\u0422\u0435\u0440\u043d\u043e-\u0433\u0440\u0430\u0444”, 2010. \u2013 536\u00a0\u0441.<\/li>\n
  18. \u0428\u0438\u043b\u043e \u0412.\u041b. \u041f\u043e\u043f\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u0446\u0438\u0444\u0440\u043e\u0432\u0435 \u043c\u0438\u043a\u0440\u043e\u0441\u0445\u0435\u043c\u044b : \u0441\u043f\u0440\u0430\u0432\u043e\u0447\u043d\u0438\u043a. \u2013 2-\u0435 \u0438\u0437\u0434., \u0438\u0441\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0435 \/ \u0412.\u041b.\u00a0\u0428\u0438\u043b\u043e. \u2013 2-\u0435 \u0438\u0437\u0434., \u0438\u0441\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0435. \u2013 \u041c. : \u0420\u0430\u0434\u0438\u043e \u0438 \u0441\u0432\u044f\u0437\u044c, 1989. \u2013 352 \u0441.<\/li>\n
  19. \u041f\u0430\u0442. 115861 \u0423\u043a\u0440\u0430\u0457\u043d\u0430 \u041c\u041f\u041a (2006) G06F 7\/00 \u041e\u0434\u043d\u043e\u0440\u043e\u0437\u0440\u044f\u0434\u043d\u0438\u0439 \u043d\u0430\u043f\u0456\u0432\u0441\u0443\u043c\u0430\u0442\u043e\u0440 \/ \u0414\u0430\u0432\u043b\u0435\u0442\u043e\u0432\u0430 \u0410.\u042f., \u041d\u0438\u043a\u043e\u043b\u0430\u0439\u0447\u0443\u043a \u042f.\u041c. \u2013 \u2116 u201612463 ; \u0437\u0430\u044f\u0432\u043b.07.12.2016; \u043e\u043f\u0443\u0431\u043b.25.04.2017, \u0411\u044e\u043b. \u2116 8\/2017.<\/li>\n
  20. \u041f\u0430\u0442. 132520 \u0423\u043a\u0440\u0430\u0457\u043d\u0430 \u041c\u041f\u041a G06F 7\/52 (2006.01) \u041c\u0430\u0442\u0440\u0438\u0447\u043d\u0438\u0439 \u043f\u0435\u0440\u0435\u043c\u043d\u043e\u0436\u0443\u0432\u0430\u0447 \/ \u0414\u0430\u0432\u043b\u0435\u0442\u043e\u0432\u0430 \u0410.\u042f., \u0413\u0440\u0438\u0433\u0430 \u0412.\u041c., \u041d\u0438\u043a\u043e\u043b\u0430\u0439\u0447\u0443\u043a \u042f.\u041c. \u2013 \u2116 u20181030; \u0437\u0430\u044f\u0432\u043b. 17.10.2018014; \u043e\u043f\u0443\u0431\u043b.25.02.2019, \u0411\u044e\u043b. \u2116 4\/2019.<\/li>\n
  21. \u041f\u0430\u0442. 124563 \u0423\u043a\u0440\u0430\u0457\u043d\u0430 \u041c\u041f\u041a G06F 7\/00 (2018.01) \u041f\u043e\u0432\u043d\u0438\u0439 \u043e\u0434\u043d\u043e\u0440\u043e\u0437\u0440\u044f\u0434\u043d\u0438\u0439 \u0441\u0443\u043c\u0430\u0442\u043e\u0440 \/ \u041d\u0438\u043a\u043e\u043b\u0430\u0439\u0447\u0443\u043a \u042f.\u041c., \u0413\u0440\u0438\u0433\u0430 \u0412.\u041c., \u0412\u043e\u0437\u043d\u0430 \u041d.\u042f., \u0414\u0430\u0432\u043b\u0435\u0442\u043e\u0432\u0430 \u0410.\u042f. \u2013 \u2116\u00a0u\u00a02017\u00a011720 ; \u0437\u0430\u044f\u0432\u043b. 30.11.2017; \u043e\u043f\u0443\u0431\u043b.10.04.2018, \u0411\u044e\u043b. \u21167\/2018.<\/li>\n
  22. \u041f\u0430\u0442. 132145 \u0423\u043a\u0440\u0430\u0457\u043d\u0430 \u041c\u041f\u041a G06F 7\/00 (2018.01) G06F 7\/40 (2006.01) \u0420\u0456\u0437\u043d\u0438\u0446\u0435\u0432\u043e-\u043c\u043e\u0434\u0443\u043b\u044c\u043d\u0438\u0439 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0440 \/ \u0421\u0438\u0434\u043e\u0440\u00a0\u0410.\u0406., \u041d\u0438\u043a\u043e\u043b\u0430\u0439\u0447\u0443\u043a\u00a0\u042f.\u041c., \u0412\u043e\u0437\u043d\u0430\u00a0\u041d.\u042f. \u2013 \u2116\u00a0u\u00a02018\u00a009550 ; \u0437\u0430\u044f\u0432\u043b. 24.09.2018; \u043e\u043f\u0443\u0431\u043b. 11.02.2019, \u0411\u044e\u043b. \u21163\/2019.<\/li>\n<\/ol>\n

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