{"id":15405,"date":"2026-06-24T13:06:09","date_gmt":"2026-06-24T12:06:09","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=15405"},"modified":"2026-06-30T09:59:38","modified_gmt":"2026-06-30T08:59:38","slug":"28-3-4-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/28-3-4-en\/","title":{"rendered":"28.3.4 En"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-lora-font-family\" style=\"font-size:22px\"><strong>Hourly load forecasting via PatchTST and Temporal Fusion Transformers: comparative system analysis with CatBoost and N-HiTS network models<\/strong><\/h2>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family has-extra-small-font-size wp-elements-b1ad7e20bf6ff992947224940214ab8e wp-block-paragraph\" style=\"margin-top:0;margin-bottom:0;padding-top:0;padding-bottom:0\"><strong>A.E. Dzgoev, E.V. Klimkin, V.V. Chernyauskas, A.V. Brailovsky, R.N. Rezenkov<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group is-vertical is-content-justification-left is-nowrap is-layout-flex wp-container-core-group-is-layout-20193d73 wp-block-group-is-layout-flex\" style=\"border-style:none;border-width:0px;margin-top:0;margin-bottom:0;padding-top:0;padding-bottom:0\">\n<p class=\"has-text-color has-link-color has-lora-font-family wp-elements-1934a6274ad67c2dd8d97ce7471e2bbb wp-block-paragraph\" style=\"color:#5b1919;font-size:12px;text-decoration:underline\"><\/p>\n\n\n\n<div class=\"wp-block-group is-horizontal is-layout-flex wp-container-core-group-is-layout-9076828a wp-block-group-is-layout-flex\" style=\"min-height:0px;margin-top:0;margin-bottom:0;padding-top:0;padding-bottom:0\">\n<div class=\"wp-block-buttons is-content-justification-left is-layout-flex wp-container-core-buttons-is-layout-856cf56e wp-block-buttons-is-layout-flex\" style=\"margin-top:0;margin-bottom:0;padding-top:0;padding-right:0;padding-bottom:0;padding-left:0\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-100 is-style-outline is-style-outline--1\"><a class=\"wp-block-button__link has-background-background-color has-text-color has-background has-link-color has-border-color has-custom-font-size wp-element-button\" href=\"http:\/\/izvestiyakbncran.ru\/wp-content\/uploads\/2026\/06\/4.-dzgoev-klimkin-chernyauskas.pdf\" style=\"border-color:#5b1919;border-style:solid;border-width:2px;border-radius:8px;color:#5b1919;padding-top:0.4rem;padding-right:var(--wp--preset--spacing--40);padding-bottom:0.4rem;padding-left:var(--wp--preset--spacing--40);font-size:12px\">PDF<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:0px;width:0px\" aria-hidden=\"true\" class=\"wp-block-spacer wp-container-content-273e683f\"><\/div>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-100 is-style-outline is-style-outline--2\"><a class=\"wp-block-button__link has-background-background-color has-text-color has-background has-link-color has-border-color has-text-align-center has-custom-font-size wp-element-button\" href=\"http:\/\/izvestiyakbncran.ru\/wp-content\/uploads\/2026\/06\/04-hourly.xml\" style=\"border-color:#5b1919;border-width:2px;border-top-left-radius:8px;border-top-right-radius:8px;border-bottom-left-radius:8px;border-bottom-right-radius:8px;color:#5b1919;padding-top:0.4rem;padding-right:var(--wp--preset--spacing--40);padding-bottom:0.4rem;padding-left:var(--wp--preset--spacing--40);font-size:12px\">JATS XML<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-lora-font-family has-extra-small-font-size wp-elements-41ee428b6a5740c7f514a7432ff786a3 wp-block-paragraph\" style=\"border-style:none;border-width:0px;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-left-radius:0px;border-bottom-right-radius:0px;color:#5b1919;margin-top:0;margin-right:0;margin-bottom:0;margin-left:0;padding-top:0;padding-right:0;padding-bottom:0;padding-left:0\"><\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" style=\"margin-top:var(--wp--preset--spacing--20);margin-bottom:var(--wp--preset--spacing--20)\"\/>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family has-extra-small-font-size wp-elements-fb05ab3ab79342ff04d276e5b85cd77a wp-block-paragraph\" style=\"line-height:1.4\"><em><strong><strong>Abstract<\/strong><\/strong>. <\/em>Under modern conditions of dynamic demand behavior and external factors, traditional statistical autoregressive modeling methods (ARIMA, SARIMAX) are increasingly outperformed by machine learning algorithms (Gradient Boosting) and modern deep learning architectures (Transformers).<br><strong>Aim<\/strong>. This study aims to address the problem of selecting the optimal model for next-day hourly electricity consumption forecasting under limited information constraints, utilizing advanced machine and deep learning methods such as CatBoost, Temporal Fusion Transformer (TFT), PatchTST, and N-HiTS.<br><strong>Materials and methods<\/strong>. The source code was developed in Python and is publicly available as an open-source repository on GitHub at https:\/\/github.com\/KEV0143\/Comparative-analysis-of-hourly-loadforecasting-using-PatchTST-TFT-NHiTS-and-CatBoost.<br><strong>Results<\/strong>. New highly accurate and robust mathematical models for electricity consumption forecasting were successfully developed for each of the evaluated methods. A key mathematical outcome of this study demonstrates that effective electricity consumption forecasting for corporate energy conservation can be formulated as a scientifically substantiated selection of the single optimal model. This approach is crucial for both the theoretical analysis of advanced machine learning algorithms and their practical deployment,<br>driven by the rapidly growing volume of data. Addressing this issue is highly significant for energy consumption optimization across individual enterprises and entire regions.<br><strong>Conclusion<\/strong>. The theoretical analysis and computational experiments utilizing empirical data from a Russian energy company provided valuable practical insights into the applicability of the CatBoost model for industrial energy consumption optimization. All conclusions presented in this paper are rigorously supported by statistical test results.<\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family has-extra-small-font-size wp-elements-df03325adc83c022634de6b79d43432f wp-block-paragraph\" style=\"line-height:1.4\"><\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family has-extra-small-font-size wp-elements-c1e7aa35147bac7ca698994bc0fbcadb wp-block-paragraph\" style=\"line-height:1.4\"><strong><em><strong>Keywords<\/strong><\/em><\/strong><em>:<\/em> systems analysis of models, mathematical statistics, short-term load forecasting, electricity consumption, comparative analysis, machine learning, deep learning, time series analysis, CatBoost, Temporal Fusion Transformer (TFT), PatchTST, N\u2011HiTS<\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family has-extra-small-font-size wp-elements-df03325adc83c022634de6b79d43432f wp-block-paragraph\" style=\"line-height:1.4\"><\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family wp-elements-ec6f78d38b4c72e34c77e21f62354138 wp-block-paragraph\" style=\"font-size:12px;line-height:1.4\"><strong><strong>For citation<\/strong>.<\/strong> Dzgoev A.E., Klimkin E.V., Chernyauskas V.V., Brailovsky A.V., Rezenkov R.N. Hourly load forecasting via PatchTST and Temporal Fusion Transformers: comparative system analysis with CatBoost and N-HiTS network models. News of the Kabardino-Balkarian Scientific Center of RAS. 2026. Vol. 28. No. 3. Pp. 49\u201370. DOI: 10.35330\/1991-6639-2026-28-3-49-70<\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family wp-elements-17c3333a0b1db39b7fa4a3e1a1572bc4 wp-block-paragraph\" style=\"font-size:12px;line-height:1.4\"><\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family wp-elements-e08383c0e8a3503e50e04a4ad8f28f20 wp-block-paragraph\" style=\"font-size:12px;line-height:1.4\">\u00a9&nbsp;&nbsp; Dzgoev A.E., Klimkin E.V., Chernyauskas V.V., Brailovsky A.V., Rezenkov R.N., 2026<\/p>\n\n\n\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-8e2b6fff wp-block-group-is-layout-flex\" style=\"margin-top:var(--wp--preset--spacing--20);padding-top:0;padding-bottom:0\">\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"80\" height=\"28\" src=\"https:\/\/izvestiyakbncran.ru\/wp-content\/uploads\/2026\/03\/image.png\" alt=\"\" class=\"wp-image-7229\"\/><\/figure>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family wp-elements-05a6ee62a5b706afe3764dcf35c80ac8 wp-block-paragraph\" style=\"margin-top:var(--wp--preset--spacing--20);margin-bottom:0;font-size:12px\">Content is available under license&nbsp;<a href=\"http:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\" rel=\"noreferrer noopener\">Creative Commons Attribution 4.0 License<\/a><\/p>\n<\/div>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color has-lora-font-family wp-elements-17c3333a0b1db39b7fa4a3e1a1572bc4 wp-block-paragraph\" style=\"font-size:12px;line-height:1.4\"><\/p>\n\n\n\n<details class=\"wp-block-details has-foreground-color has-text-color has-link-color has-lora-font-family has-extra-small-font-size wp-elements-3547fe42f6d4c2a63f1548be2399c5a3 is-layout-flow wp-container-core-details-is-layout-f488f964 wp-block-details-is-layout-flow\" style=\"font-style:normal;font-weight:700;line-height:1.5\"><summary><strong>R<\/strong>eferences<\/summary>\n<ol style=\"margin-top:0;margin-bottom:0\" class=\"wp-block-list\">\n<li style=\"font-style:normal;font-weight:400\">Karpenko S.M., Karpenko N.V., Ematin E.A., Marat Sh. Power consumption planning for an industrial enterprise under the conditions of the wholesale electricity market. Energy Safety and Energy Economy. 2024. No. 6. Pp. 35\u201340. EDN: CKFPVC. (In Russian)<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Karpenko S.M., Karpenko N.V., Ematin E.A., Jjunju D. Multiple factor analysis of the wholesale electricity market on the example of a specific pricing zone. Energy Safety and Energy Economy. 2024. No. 4. Pp. 37\u201342. EDN: QBTQHW. (In Russian)<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Byk F.L., Myshkina L.S. Economic efficiency of modern electric power industry. Energetik. No. 1. Pp. 17\u201321. EDN: OGTFOW. (In Russian)<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Hong T., Fan S. Probabilistic electric load forecasting: A Tutorial Review. International Journal of Forecasting. 2016. Vol. 32. No. 3. Pp. 914\u2013938. DOI: 10.1016\/j.ijforecast.2015.11.011<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Dudek G. Pattern-based local linear regression models for short-term load forecasting. Electric Power System Research. 2016. No. 130. Pp. 139\u2013147. DOI: 10.1016\/ j.epsr.2015.09.001<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Gochhait S., Sharma D.K. Regression model-based short-term load forecasting for load despatch centre. Journal of Applied Engineering and Technological Science. 2023. Vol. 4(2). Pp. 693\u2013710. DOI: 10.37385\/jaets.v4i2.1682<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Lee M.H.L., Ser Y.C., Selvachandran G., Pham T.H. A comparative study of forecasting electricity consumption using machine learning models. Mathematics. 2022. Vol. 10. Article 1329. DOI: 10.3390\/math10081329<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Dayarathna M., Wen Yo., Fan Rui. Data center energy consumption modeling: a survey. IEEE Communications Surveys &amp; Tutorials. 2016. Vol. 18. No. 1. DOI: 10.1109\/COMST.2015.2481183<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Mughees M., Li Y., Chen Y., Li Y.R. Short-term load forecasting for ai-data center. IEEE PES General Meeting 2025. Electrical Engineering and Systems Science. 2025. DOI: 10.48550\/arXiv.2503.07756<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Ye Z., Gao W., Hu Q. et al. Deep learning workload scheduling in GPU datacenters: A survey. ACM Computing Surveys. 2024. Vol. 56. No. 6. Pp. 1\u201338. DOI: 10.1145\/3638757<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Munkhammar J., Meer D., Wid\u00e9n J. Very short term load forecasting of residential electricity consumption using the Markov-chain mixture distribution (MCM) model. Applied Energy. 282(A):116180. DOI: 10.1016\/j.apenergy.2020.116180<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Hippert H.S., Pedreira C.E., Souza R.C. Neural networks for short-term load forecasting: a review and evaluation. IEEE Transactions on Power Systems. Vol. 16. No. 1. Pp. 44\u201355. DOI: 10.1109\/59.910780<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Sailor D.J., Munoz J.R. Sensitivity of electricity and natural gas consumption to climate in the U.S.A. Methodology and results for eight states. Energy. 1997. Vol. 22. No. 10. Pp. 987\u2013998. DOI: 10.1016\/S0360-5442(97)00034-0<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Hong T., Pinson P., Fan S. et al. Probabilistic energy forecasting: global energy forecasting competition 2014 and beyond. International Journal of Forecasting. 2016. Vol. 32. No. 3. Pp. 896\u2013913. DOI: 10.1016\/j.ijforecast.2016.02.001<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Wang A., Yu Q., Wang J. et al. Electric load forecasting based on deep ensemble learning. Applied Sciences. 2023. Vol. 13. No. 17. P. 9706. DOI: 10.3390\/app13179706<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Lim B., Ar\u0131k \u00d6.S., Loeff N., Pfister T. Temporal fusion transformer for interpretable multi-horizon time series forecasting. International Journal of Forecasting. 2021. Vol. 37. No. 1. DOI: 10.1016\/j.ijforecast.2021.03.012<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Challu C., Olivares K.G., Oreshkin B.N. et al. N\u2011HiTS: Neural hierarchical interpolation for time series forecasting. Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 37. No. 6. Pp. 6989\u20136997. DOI: 10.48550\/arXiv.2201.12886<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Ahmad H., Mortazavi S.K., Bahnasawi M.E. et al. Enhanced time series forecasting: integrating PatchTST with BERT Layers. Conference: 5th International Conference on Applied<br>Mathematics &amp; Computer Science (ICAMCS 2025). At: Venice, Italy, September 27\u201329, 2025. DOI: 10.1109\/ICAMCS62774.2024.00014<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Dorogush A.V., Ershov V., Gulin A. Catboost: gradient boosting with categorical features support. DOI: 10.48550\/arXiv.1810.11363.2018<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Lim B., Ar\u0131k S.\u00d6., Loeff N., Pfister T. Temporal fusion transformer for interpretable multi-horizon time series forecasting. International Journal of Forecasting. Vol. 37. No. 4. Pp. 1748\u20131764. DOI: 10.1016\/j.ijforecast.2021.03.012<\/li>\n\n\n\n<li style=\"font-style:normal;font-weight:400\">Nie Y., Nguyen N.H., Sinthong P., Kalagnanam J. A time series is worth 64 words: long-term forecasting with transformers (PatchTST). Proceedings of the International Conference on Learning Representations. International Conference on Learning Representations ICLR 2023. https:\/\/arxiv.org\/pdf\/2211.14730.pdf<\/li>\n<\/ol>\n<\/details>\n\n\n\n<details class=\"wp-block-details has-foreground-color has-text-color has-link-color has-lora-font-family has-extra-small-font-size wp-elements-99a0186dd970610af34b47d195e7b183 is-layout-flow wp-container-core-details-is-layout-9ff6af70 wp-block-details-is-layout-flow\" style=\"font-style:normal;font-weight:700;line-height:1.5\"><summary><strong>Information about the authors<\/strong><\/summary>\n<div class=\"wp-block-group is-vertical is-layout-flex wp-container-core-group-is-layout-1c18c512 wp-block-group-is-layout-flex\" style=\"min-height:0px;margin-top:0;margin-bottom:0;padding-top:var(--wp--preset--spacing--20);padding-right:var(--wp--preset--spacing--40);padding-bottom:var(--wp--preset--spacing--20);padding-left:var(--wp--preset--spacing--40)\">\n<p class=\"wp-block-paragraph\" style=\"font-style:normal;font-weight:400\"><strong>Alan E. Dzgoev<\/strong>, Candidate of Technical Sciences, Associate Professor, Associate Professor at the Department of Digital Transformation, Institute of Information Technologies, MIREA \u2013 Russian Technological University;<br>78, Vernadsky prospekt, Moscow, 119454, Russia;<br>dzgoev@mirea.ru, ORCID: https:\/\/orcid.org\/0000-0002-1314-6151, SPIN-code: 8092-8784<br><strong>Egor V. Klimkin<\/strong>, Undergraduate Student, Department of Applied Mathematics, Institute of Information Technologies, MIREA \u2013 Russian Technological University;<br>78, Vernadsky prospekt, Moscow, 119454, Russia.;<br>KlimkinEVK@yandex.ru, ORCID: https:\/\/orcid.org\/0009-0001-3876-3041<br><strong>Vladislav V. Chernyauskas<\/strong>, Senior Lecturer, Department of Digital Transformation, Institute of Information Technologies, MIREA \u2013 Russian Technological University;<br>78, Vernadsky prospekt, Moscow, 119454, Russia;<br>chernyauskas-vladislav@yandex.ru, ORCID: https:\/\/orcid.org\/0009-0002-8438-3418, SPIN-code: 5867-6366<br><strong>Andrey V. Brailovsky<\/strong>, Assistant Professor, Department of Digital Transformation, Institute of Information Technologies, MIREA \u2013 Russian Technological University;<br>78, Vernadsky prospekt, Moscow, 119454, Russia;<br>brajlovskij@mirea.ru, ORCID: https:\/\/orcid.org\/0009-0006-1794-7825, SPIN-code: 5900-1835<br><strong>Roman N. Rezenkov<\/strong>, Candidate of Technical Sciences, Associate Professor, Associate Professor at the Digital Transformation Department, Institute of Information Technologies, MIREA \u2013 Russian Technological University;<br>78, Vernadsky prospekt, Moscow, 119454, Russia;<br>rezenkov@mirea.ru, ORCID: https:\/\/orcid.org\/0009-0005-5542-2125<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"font-style:normal;font-weight:400\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"font-style:normal;font-weight:400\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"font-style:normal;font-weight:400\"><\/p>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details has-foreground-color has-text-color has-link-color has-lora-font-family wp-elements-452cbc12bbc5feb9a1402dce7d5f0f2f is-layout-flow wp-block-details-is-layout-flow\" style=\"font-size:14px\"><summary><strong>Funding<\/strong><\/summary>\n<p class=\"wp-block-paragraph\" style=\"margin-top:var(--wp--preset--spacing--20);margin-bottom:var(--wp--preset--spacing--20)\">The study was performed without external funding.<\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hourly load forecasting via PatchTST and Temporal Fusion Transformers: comparative system analysis with CatBoost and N-HiTS network models A.E. Dzgoev, E.V. Klimkin, V.V. Chernyauskas, A.V. Brailovsky, R.N. Rezenkov Abstract. Under modern conditions of dynamic demand behavior and external factors, traditional statistical autoregressive modeling methods (ARIMA, SARIMAX) are increasingly outperformed by machine learning algorithms (Gradient Boosting) [&hellip;]<\/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-15405","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>28.3.4 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\/28-3-4-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"28.3.4 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=\"Hourly load forecasting via PatchTST and Temporal Fusion Transformers: comparative system analysis with CatBoost and N-HiTS network models A.E. Dzgoev, E.V. Klimkin, V.V. Chernyauskas, A.V. Brailovsky, R.N. Rezenkov Abstract. 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