{"id":10291,"date":"2026-04-06T16:44:11","date_gmt":"2026-04-06T15:44:11","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=10291"},"modified":"2026-06-19T10:35:18","modified_gmt":"2026-06-19T09:35:18","slug":"25-6-8-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/","title":{"rendered":"25.6.8 En"},"content":{"rendered":"\n

Restoration of the order of fractional derivative in the problem of mathematical modelling of radon accumulation in the excess volume of the storage chamber based on the data of Petropavlovsk-Kamchatsky geodynamic polygon<\/strong><\/h1>\n\n\n\n

D.A. Tverdyi
<\/strong><\/p>\n\n\n\n

\n

<\/p>\n\n\n\n

\n
\n
PDF<\/a><\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n
\n
JATS XML<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n

<\/p>\n<\/div>\n\n\n\n

\n\n\n\n

Abstract<\/strong>. <\/em>The paper researches the issues related to the nonlinear transport of radon gas through the geosphere, in particular, when describing the variation of volumetric activity (RVA) in an accumulation chamber with recording sensors. RVA is considered to be an informative and operational precursor to earthquakes. Based on the assumption that the radon transport process takes place in a permeable geosphere, an ereditary RVA model based on the Riccati equation with fractional Gerasimov\u2013Kaputo derivative is used for modelling. The model has been previously validated at the geodynamic test site in PetropavlovskKamchatsky. In the study the identification of the order value of the fractional derivative, which is associated with such geo-environmental characteristics as porosity and permeability is of most interest. However, we do not have information about some parameters of the process under consideration to determine this value accurately enough. But we know additional information obtained from the experiment. This information can be used to reconstruct the values of interest. Which leads us to the inverse problems. To reconstruct the order of the fractional derivative, we solve the one-dimensional optimisation problem using the iterative Levenberg\u2013Marquardt method of Newtonian type. It is shown that this method can be used to reconstruct some parameters of such a dynamic system as radon transport through geo-environment. It is shown that the solution of the inverse problem by the Levenberg\u2013Marquardt method gives a more accurate result in a shorter time than the manual selection of parameter values and types of functions for the model equations.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Keywords<\/strong>:<\/em><\/strong> mathematical modelling, Gerasimov\u2013Kaputo fractional derivative, inverse problems, Levenberg\u2013Marquardt method, stress-strain state, geo-environment, volumetric radon activity, RVA, earthquake precursors<\/p>\n\n\n\n

<\/p>\n\n\n\n

For citation<\/strong>.<\/strong> Tverdyi D.A. Restoration of the order of fractional derivative in the problem of mathematical modelling of radon accumulation in the excess volume of the storage chamber based on the data of PetropavlovskKamchatsky geodynamic polygon. News of the Kabardino-Balkarian Scientific Center of RAS<\/em>. 2023. No. 6(116). Pp. 83\u201394. DOI: 10.35330\/1991-6639-2023-6-116-83-94<\/p>\n\n\n\n

<\/p>\n\n\n\n

R<\/strong>eferences<\/summary>\n
    \n
  1. Kabanihin S.I., Iskakov K.T. Optimizacionnye metody resheniya koefficientnyh obratnyh zadach<\/em> [Optimisation methods for solving coefficient inverse problems]. Novosibirsk: Novosibirskij gosudarstvennyj universitet, 2001. 315 p. (In Russian)<\/li>\n\n\n\n
  2. Rudakov V.P. Emanacionnyj monitoring geosred i processov<\/em> [Emanation monitoring of geo-mediations and processes]. Moscow: Nauchnyj mir, 2009. 175 p. (In Russian)<\/li>\n\n\n\n
  3. Firstov P.P., Makarov E.O., Gluhova I.P. et. al. Search for strong earthquake precursor anomalies from subsurface gas monitoring data at the Petropavlovsk-Kamchatsky geodynamic test site. Geosistemy perekhodnyh zon <\/em>[Geosystems of transition zones] 2018. Vol. 1. No 2. Pp. 16\u201332. DOI: 10.30730\/2541-8912.2018.2.1.016-032. (In Russian)<\/li>\n\n\n\n
  4. Cicerone R.D., Ebel J.E., Beitton J. A systematic compilation of earthquake precursors. Tectonophysics. <\/em>2009. Vol. 476. No. 3\u20134. Pp. 371\u2013396. DOI: 10.1016\/j.tecto.2009.06.008<\/li>\n\n\n\n
  5. Neri M., Giammanco S., Ferrera E. et al. Spatial distribution of soil radon as a tool to recognize active faulting on an active volcano: The example of Mt. Etna (Italy). Journal of environmental radioactivity. 2011. Vol. 102(9). Pp. 863\u2013870. DOI: 10.1016\/j.jenvrad.2011.05.002<\/li>\n\n\n\n
  6. Gill P.E., Murray W., Wright M.H. Practical Optimization. Philadelphia, USA: SIAM, 421 p.<\/li>\n\n\n\n
  7. Tverdyi D.A., Makarov E.O., Parovik R.I. Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber. Mathematics<\/em>. 2022. Vol. 11. No. 4:850. Pp. 1\u201320. DOI: 10.3390\/math11040850<\/li>\n\n\n\n
  8. Tverdyi D.A., Makarov E.O., Parovik R.I. Research of Stress-Strain State of GeoEnvironment by Emanation Methods on the Example of alpha(t)-Model of Radon Transport. Bulletin KRASEC. Physical and Mathematical Sciences.<\/em> 2023. Vol. 3. No. 44. Pp. 86\u2013104. DOI: 10.26117\/2079-6641-2023-44-3-86-104. (In Russian)<\/li>\n\n\n\n
  9. Ponamarev A.S. Fractionation in hydrotherm as a potential possibility of formation of earthquake precursors. Geohimiya [Geochemistry]. 1989. No 5. Pp. 714\u2013724. (In Russian)<\/li>\n\n\n\n
  10. Parovik R.I. Matematicheskoe modelirovanie neklassicheskoj teorii emanacionnogo metoda<\/em> [Mathematical modelling of the non-classical theory of the emanation method]. Petropavlovsk-Kamchatskij, KamGU im. Vitusa Beringa, 2014. 80 p. (In Russian)<\/li>\n\n\n\n
  11. Vasilyev A.V., Zhukovsky M.V. Determination of mechanisms and parameters which affect radon entry into a room. Journal of Environmental Radioactivity<\/em>. 2013. Vol. 124. Pp. 185\u2013190. DOI: 10.1016\/j.jenvrad.2013.04.014<\/li>\n\n\n\n
  12. Firstov P.P., Makarov E.O. Dinamika podpochvennogo radona na Kamchatke i sil’nye zemletryaseniya [Dynamics of subsurface radon in Kamchatka and strong earthquakes]. Petropavlovsk-Kamchatskij: KamGU im. Vitusa Beringa, 2018. 148 p. (In Russian)<\/li>\n\n\n\n
  13. King C.Y. Isotopic geochemical precursors of earthquakes and volcanic eruption. Advisory Group Meeting held. Vienna. International atomic energy agency. 1991. Pp. 22\u201336.<\/li>\n\n\n\n
  14. Uchaikin V.V. Fractional Derivatives for Physicists and Engineers. Vol. I. Background and Theory. Berlin, Springer. 2013. 373 p.<\/li>\n\n\n\n
  15. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Applications of Fractional Differential Equations. Amsterdam, Elsevier Science Limited. 2006. 204 p.<\/li>\n\n\n\n
  16. Nahushev A.M. Drobnoe ischislenie i ego primenenie [Fractional calculus and its applications]. Moscow: Fizmatlit, 2003. 272 p. (In Russian)<\/li>\n\n\n\n
  17. Pskhu A.V. Uravneniya v chastnyh proizvodnyh drobnogo poryadka [Equations in partial derivatives of fractional order]. Moscow: Nauka, 2005. 199 p. (In Russian)<\/li>\n\n\n\n
  18. Volterra V. Functional theory, integral and integro-differential equations. London: Blackie & Son Limited,1930. 226 p.<\/li>\n\n\n\n
  19. Gerasimov A.N. Generalization of linear deformation laws and their application to internal friction problems. Applied Mathematics and Mechanics. 1948. Vol. 12. Pp. 529\u2013539. <\/li>\n\n\n\n
  20. Caputo M. Elasticita e Dissipazione. Bologna, Zanichelli. 1969. 150 p.<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong><\/summary>\n
    \n

    Tverdyi Dmitrii Alexandrovich<\/strong>, Candidate of Physical and Mathematical Sciences, Researcher, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS;
    684034, Russia, Kamchatka, Elizovsky district, Paratunka village, 7 Miranaya street;
    tverdyi@ikir.ru, ORCID: https:\/\/orcid.org\/0000-0001-6983-5258<\/p>\n\n\n\n

    <\/p>\n\n\n\n


    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n<\/div>\n<\/details>\n\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    Restoration of the order of fractional derivative in the problem of mathematical modelling of radon accumulation in the excess volume of the storage chamber based on the data of Petropavlovsk-Kamchatsky geodynamic polygon D.A. Tverdyi Abstract. The paper researches the issues related to the nonlinear transport of radon gas through the geosphere, in particular, when describing […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-10291","page","type-page","status-publish","hentry"],"yoast_head":"\n25.6.8 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"25.6.8 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"Restoration of the order of fractional derivative in the problem of mathematical modelling of radon accumulation in the excess volume of the storage chamber based on the data of Petropavlovsk-Kamchatsky geodynamic polygon D.A. Tverdyi Abstract. The paper researches the issues related to the nonlinear transport of radon gas through the geosphere, in particular, when describing […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"article:modified_time\" content=\"2026-06-19T09:35:18+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u041f\u0440\u0438\u043c\u0435\u0440\u043d\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u0434\u043b\u044f \u0447\u0442\u0435\u043d\u0438\u044f\" \/>\n\t<meta name=\"twitter:data1\" content=\"5 \u043c\u0438\u043d\u0443\u0442\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-8-en\\\/\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-8-en\\\/\",\"name\":\"25.6.8 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#website\"},\"datePublished\":\"2026-04-06T15:44:11+00:00\",\"dateModified\":\"2026-06-19T09:35:18+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-8-en\\\/#breadcrumb\"},\"inLanguage\":\"ru-RU\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-8-en\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-8-en\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u0413\u043b\u0430\u0432\u043d\u0430\u044f \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430\",\"item\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"25.6.8 En\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#website\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/\",\"name\":\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\",\"description\":\"\u041d\u0430\u0443\u0447\u043d\u044b\u0439 \u0436\u0443\u0440\u043d\u0430\u043b\",\"publisher\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"ru-RU\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#organization\",\"name\":\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ru-RU\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/wp-content\\\/uploads\\\/2025\\\/07\\\/oblozhka-zhurnala-na-angl-scaled.jpg\",\"contentUrl\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/wp-content\\\/uploads\\\/2025\\\/07\\\/oblozhka-zhurnala-na-angl-scaled.jpg\",\"width\":1828,\"height\":2560,\"caption\":\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\"},\"image\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#\\\/schema\\\/logo\\\/image\\\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"25.6.8 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/","og_locale":"ru_RU","og_type":"article","og_title":"25.6.8 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","og_description":"Restoration of the order of fractional derivative in the problem of mathematical modelling of radon accumulation in the excess volume of the storage chamber based on the data of Petropavlovsk-Kamchatsky geodynamic polygon D.A. Tverdyi Abstract. The paper researches the issues related to the nonlinear transport of radon gas through the geosphere, in particular, when describing […]","og_url":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/","og_site_name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","article_modified_time":"2026-06-19T09:35:18+00:00","twitter_card":"summary_large_image","twitter_misc":{"\u041f\u0440\u0438\u043c\u0435\u0440\u043d\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u0434\u043b\u044f \u0447\u0442\u0435\u043d\u0438\u044f":"5 \u043c\u0438\u043d\u0443\u0442"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/","url":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/","name":"25.6.8 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","isPartOf":{"@id":"https:\/\/izvestiyakbncran.ru\/#website"},"datePublished":"2026-04-06T15:44:11+00:00","dateModified":"2026-06-19T09:35:18+00:00","breadcrumb":{"@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/#breadcrumb"},"inLanguage":"ru-RU","potentialAction":[{"@type":"ReadAction","target":["https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-8-en\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u0413\u043b\u0430\u0432\u043d\u0430\u044f \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430","item":"https:\/\/izvestiyakbncran.ru\/"},{"@type":"ListItem","position":2,"name":"25.6.8 En"}]},{"@type":"WebSite","@id":"https:\/\/izvestiyakbncran.ru\/#website","url":"https:\/\/izvestiyakbncran.ru\/","name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","description":"\u041d\u0430\u0443\u0447\u043d\u044b\u0439 \u0436\u0443\u0440\u043d\u0430\u043b","publisher":{"@id":"https:\/\/izvestiyakbncran.ru\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/izvestiyakbncran.ru\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"ru-RU"},{"@type":"Organization","@id":"https:\/\/izvestiyakbncran.ru\/#organization","name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","url":"https:\/\/izvestiyakbncran.ru\/","logo":{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/izvestiyakbncran.ru\/#\/schema\/logo\/image\/","url":"https:\/\/izvestiyakbncran.ru\/wp-content\/uploads\/2025\/07\/oblozhka-zhurnala-na-angl-scaled.jpg","contentUrl":"https:\/\/izvestiyakbncran.ru\/wp-content\/uploads\/2025\/07\/oblozhka-zhurnala-na-angl-scaled.jpg","width":1828,"height":2560,"caption":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb"},"image":{"@id":"https:\/\/izvestiyakbncran.ru\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages\/10291","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/comments?post=10291"}],"version-history":[{"count":16,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages\/10291\/revisions"}],"predecessor-version":[{"id":15144,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages\/10291\/revisions\/15144"}],"wp:attachment":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/media?parent=10291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}