<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">blackmet</journal-id><journal-title-group><journal-title xml:lang="ru">Известия высших учебных заведений. Черная Металлургия</journal-title><trans-title-group xml:lang="en"><trans-title>Izvestiya. Ferrous Metallurgy</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0368-0797</issn><issn pub-type="epub">2410-2091</issn><publisher><publisher-name>National University of Science and Technology "MISIS"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17073/0368-0797-2022-4-232-239</article-id><article-id custom-type="elpub" pub-id-type="custom">blackmet-2293</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МЕТАЛЛУРГИЧЕСКИЕ ТЕХНОЛОГИИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>METALLURGICAL TECHNOLOGIES</subject></subj-group></article-categories><title-group><article-title>Исследование закономерностей процессов  в искровом промежутке при контактной стыковой сварке железнодорожных рельсов</article-title><trans-title-group xml:lang="en"><trans-title>Investigation of processes in spark gap  during contact butt welding of railway rails</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Шевченко</surname><given-names>Р. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Shevchenko</surname><given-names>R. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Роман Алексеевич Шевченко, ассистент кафедры материаловедения, литейного и сварочного производства</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Roman A. Shevchenko, Assistant of the Chair “Materials, Foundry and Welding Production”</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">shefn1200@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4403-9006</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Юрьев</surname><given-names>А. Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Yur’ev</surname><given-names>A. B.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексей Борисович Юрьев, д.т.н., ректор</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Aleksei B. Yur’ev, Dr. Sci. (Eng.), Rector</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p><p> </p></bio><email xlink:type="simple">rector@sibsiu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7391-6816</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Козырев</surname><given-names>Н. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Kozyrev</surname><given-names>N. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Николай Анатольевич Козырев, д.т.н., профессор, проректор по научной и инновационной деятельности</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Nikolai A. Kozyrev, Dr. Sci. (Eng.), Prof., Vice-Rector for Research and Innovation, </p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">kozyrev_na@mtsp.sibsiu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7305-6692</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Михно</surname><given-names>А. Р.</given-names></name><name name-style="western" xml:lang="en"><surname>Mikhno</surname><given-names>A. R.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексей Романович Михно, аспирант кафедры материаловедения, литейного и сварочного производства</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Aleksei R. Mikhno, MA Student of the Chair “Materials, Foundry and Welding Production”</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">mikno-mm131@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Сибирский государственный индустриальный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Siberian State Industrial University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>05</day><month>05</month><year>2022</year></pub-date><volume>65</volume><issue>4</issue><fpage>232</fpage><lpage>239</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Шевченко Р.А., Юрьев А.Б., Козырев Н.А., Михно А.Р., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Шевченко Р.А., Юрьев А.Б., Козырев Н.А., Михно А.Р.</copyright-holder><copyright-holder xml:lang="en">Shevchenko R.A., Yur’ev A.B., Kozyrev N.A., Mikhno A.R.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://fermet.misis.ru/jour/article/view/2293">https://fermet.misis.ru/jour/article/view/2293</self-uri><abstract><p>Современное оборудование для контактной стыковой сварки железнодорожных рельсов имеет огромное количество технологических параметров (входных факторов), влияющих на качество получаемого сварного соединения. Такое количество параметров не позволяет в полной мере подобрать оптимальные режимы сварки. Изучение процессов, протекающих в искровом промежутке (образование микроконтактов, увеличение или уменьшение их площади поперечного сечения, взрыв образовавшихся микроконтактов), позволит определить количество и равномерность вложенного тепла при сварке рельсов. Полученные знания сократят количество влияющих факторов на качество сварного стыка. С использованием большого количества статистических данных исследованы процессы, протекающие в искровом промежутке при контактной стыковой сварке железнодорожных рельсов типа Р65 категории ДТ350 на рельсосварочной машине К1000. При изучении влияния характера перемещения подвижной плиты сварочной машины во время оплавления на силу сварочного тока, определено, что зависимости между данными величинами нет. Предположительно, распределение силы сварочного тока имеет случайный характер, изменяющегося в результате процессов образования, существования и взрыва большого количества мельчайших электрических контактов. Исходя из анализа распределения частот определено, что распределение сопротивления искрового промежутка не соответствует нормальному закону распределения. При увеличении выборки отклонение от него усиливается, визуально гистограмма описывает гамма-распределение. С помощью закона гамма-распределения смоделирована сила сварочного тока при контактной стыковой сварке оплавлением. Результаты исследований планируется применять для моделирования тепловых процессов и формирования структуры металла шва и зон термического влияния сварного соединения железнодорожных рельсов.</p></abstract><trans-abstract xml:lang="en"><p>Modern equipment for contact butt welding of railway rails has a huge number of technological parameters (input factors) that affect the quality of the resulting welded joint. These parameters do not allow the optimal welding modes to be fully selected. The study of the processes occurring in the spark gap (formation of microcontacts, increase or decrease in their cross-sectional area, explosion of the resulting microcontacts) will make it possible to determine the amount and uniformity of the invested heat during rail welding. The acquired knowledge will reduce the number of influencing factors on quality of the welded joint. Using a large amount of statistical data, the authors have investigated the processes occurring in the spark gap during contact butt welding of railway rails of R65 type of DT350 category on K1000 rail welding machine. When studying the influence of movable plate movement of the welding machine during reflow on the strength of welding current, it was determined that there is no dependence between these values. The random nature of distribution of the welding current values is assumed, changing as a result of the processes of formation, existence and explosion of a large number of tiny electrical contacts. Based on the analysis of frequency distribution, it is certain that distribution of the spark gap resistance does not correspond to the normal distribution law. As the sample increases, the deviation from it increases; visually the histogram describes the gamma distribution. With the help of the gamma distribution law, the welding current forces during contact butt welding were modeled by reflow. The research results are planned to be used to simulate thermal processes and formation of the structure of weld metal and the zones of thermal influence of railway rails welded joint. </p></trans-abstract><kwd-group xml:lang="ru"><kwd>контактная стыковая сварка</kwd><kwd>рельсовая сталь</kwd><kwd>искровой промежуток</kwd><kwd>сила тока</kwd><kwd>электрическое сопротивление</kwd><kwd>гамма-распределение</kwd></kwd-group><kwd-group xml:lang="en"><kwd>contact butt welding</kwd><kwd>rail steel</kwd><kwd>spark gap</kwd><kwd>current strength</kwd><kwd>electrical resistance</kwd><kwd>gamma distribution</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено при финансовой поддержке РФФИ и Кемеровской области – Кузбасса в рамках научного проекта № 20-48-420003 «Развитие физико-химических и технологических основ создания принципиально нового способа сварки дифференцированно термоупрочненных железнодорожных рельсов».</funding-statement><funding-statement xml:lang="en">The research was supported by the RFBR and the Kemerovo region – Kuzbass within the framework of the scientific project  no. 20-48-420003 “Development of physico-chemical and technological foundations for creating a fundamentally new method of welding differentially heat-strengthened railway rails”.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Клименко Л.B. Бесстыковой путь прогрессивная конструкция железнодорожного пути // Приложение к журналу «Мир транспорта» МКЖТ МПС РФ. 2004. № 1. С. 88–93.</mixed-citation><mixed-citation xml:lang="en">Klimenko L.V. Continuous welded rail: Progressive design of a railway track. Prilozhenie k zhurnalu “Mir transporta” MKZhT MPS RF. 2004, no. 1, pp. 88–93. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Кучук-Яценко С.И., Богорский М.В., Горонков Н.Д. Контактная стыковая сварка рельсов повышенной прочности // Автоматическая сварка. 1994. № 3 (492). С. 34–40.</mixed-citation><mixed-citation xml:lang="en">Kuchuk-Yatsenko S.I., Bogorskii M.V., Goronkov N.D. Contact butt welding of high-strength rails. Avtomaticheskaya svarka. 1994, no.  3 (492), pp. 34–40. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Шур Е.А. Перспективные требования Российских железных дорог к рельсам // Железнодорожный транспорт. 2008. № 2. С. 41–45.</mixed-citation><mixed-citation xml:lang="en">Shur E.A. Perspective requirements of Russian railways to rails. Zheleznodorozhnyi transport. 2008, no. 2, pp. 41–45. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Шур Е.А. Влияние структуры на эксплуатационную стойкость рельсов. В кн.: Влияние свойств металлической матрицы на эксплуатационную стойкость рельсов. Екатеринбург: УИМ, 2006. С. 37–63.</mixed-citation><mixed-citation xml:lang="en">Shur E.A. Influence of the structure on rails operational stability. In: Influence of Metal Matrix Properties on Rails Operational Stability. Yekaterinburg: UIM, 2006, pp. 37–63. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Козырев Н.А., Шевченко Р.А., Усольцев А.А., Прудников А.Н., Бащенко Л.П. Разработка и моделирование технологического процесса сварки дифференцированно термоупрочненных железнодорожных рельсов. Моделирование процессов, протекающих при сварке и локальной термической обработке // Известия вузов. Черная металлургия. 2020. Т. 63. № 2. С. 93–101. https://doi.org/10.17073/0368-0797-2020-2-93-101</mixed-citation><mixed-citation xml:lang="en">Kozyrev N.A., Shevchenko R.A., Usol’tsev A.A., Prudnikov A.N., Bashchenko L.P. Welding of differentially heat-strengthened rails. Modeling of processes during welding and local thermal processing. Izvestiya. Ferrous Metallurgy. 2020, vol. 63, no. 2, pp. 93–101. (In Russ.). https://doi.org/10.17073/0368-0797-2020-2-93-101</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Козырев Н.А., Шевченко Р.А., Усольцев А.А., Прудников А.Н., Бащенко Л.П. Разработка и моделирование технологического процесса сварки дифференцированно термоупрочненных железнодорожных рельсов. Промышленное опробование // Известия вузов. Черная металлургия. 2020. Т. 63. № 5. С. 305–312. https://doi.org/10.17073/0368-0797-2020-5-305-312</mixed-citation><mixed-citation xml:lang="en">Kozyrev N.A., Shevchenko R.A., Usol’tsev A.A., Prudnikov A.N., Bashchenko L.P. Welding of differentially heat-strengthened rails. Industrial testing. Izvestiya. Ferrous Metallurgy. 2020, vol. 63, no.  5, pp. 305–312. (In Russ.). https://doi.org/10.17073/0368-0797-2020-5-305-312</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Солодовников С.А. и др. Оборудование для контактной сварки рельсов и его эксплуатация. Киев: Изд-во «Наукова думка», 1974. 184 с.</mixed-citation><mixed-citation xml:lang="en">Solodovnikov S.A., etc. Equipment for Contact Welding of Rails and its Operation. Kiev: Naukova dumka, 1974, 184 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Schmid-Fetzer R., Andersson D., Chevalier P.Y., etc. Assessment techniques, database design and software facilities for thermodynamics and diffusion // Computer Coupling of Phase Diagrams and Thermochemistry. 2007. Vol. 31. No. 1. P. 38–52. https://doi.org/10.1016/j.calphad.2006.02.007</mixed-citation><mixed-citation xml:lang="en">Schmid-Fetzer R., Andersson D., Chevalier P.Y., etc. Assessment techniques, database design and software facilities for thermodynamics and diffusion. Computer Coupling of Phase Diagrams and Thermochemistry. 2007, vol. 31, no. 1, pp. 38–52. https://doi.org/10.1016/j.calphad.2006.02.007</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Dahl B., Mogard B., Gretoft B., Ulander B. Repair of rails on-site by welding // Svetsaren. 1995. Vol. 50. No. 2. P. 10–14.</mixed-citation><mixed-citation xml:lang="en">Dahl B., Mogard B., Gretoft B., Ulander B. Repair of rails on-site by welding. Svetsaren. 1995, vol. 50, no. 2, pp. 10–14.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Kavunichenko A.V., Shvets V.I., Antipin E.V. Peculiarities of flash-butt welding of rail frogs with rail ends // The Paton Welding Journal. 2018. No. 4. P. 14–18. https://doi.org/10.15407/tpwj2018.04.03</mixed-citation><mixed-citation xml:lang="en">Kavunichenko A.V., Shvets V.I., Antipin E.V. Peculiarities of flash-butt welding of rail frogs with rail ends. The Paton Welding Journal. 2018, no. 4, pp. 14–18. https://doi.org/10.15407/tpwj2018.04.03</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Duvel J., Mutton P. Rail requirements for 40 tonne axle loads. In: Int. Heavy Haul Association Conf. 2005. P. 719–729.</mixed-citation><mixed-citation xml:lang="en">Duvel J., Mutton P. Rail requirements for 40 tonne axle loads. In: Int. Heavy Haul Association Conf. 2005, pp. 719–729.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Saita K., Ueda M., Miyazaki T. Developing technologies to improve the reliability of flash-butt welds. In: Int. Heavy Haul Association Conf. Grabe P.J., Frohling R.D. eds. Cape Town, South Africa, 2017. P. 208–215.</mixed-citation><mixed-citation xml:lang="en">Saita K., Ueda M., Miyazaki T. Developing technologies to improve the reliability of flash-butt welds. In: Int. Heavy Haul Association Conf. Grabe P.J., Frohling R.D. eds. Cape Town, South Africa, 2017, pp. 208–215.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Farhangi H., Mousavizadeh S.M. Horizontal split-web fractures of flash butt welded rails. In: Proceedings of the 8th Int. Fracture Conf. 2007. P. 509–517.</mixed-citation><mixed-citation xml:lang="en">Farhangi H., Mousavizadeh S.M. Horizontal split-web fractures of flash butt welded rails. In: Proceedings of the 8th Int. Fracture Conf. 2007, pp. 509–517.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Porcaro R.R., Araújo F.C., Godefroid L.B., Faria G.L., Silva L.L. Simulation of flash-butt welding process of a railway steel. Part 2: Dilatometric and numerical analysis // Soldagem &amp; Inspeção. 2020. No. 25. Article 2533. https://doi.org/10.1590/0104-9224/SI25.33</mixed-citation><mixed-citation xml:lang="en">Porcaro R.R., Araújo F.C., Godefroid L.B., Faria G.L., Silva L.L. Simulation of flash-butt welding process of a railway steel. Part 2: Dilatometric and numerical analysis. Soldagem &amp; Inspeção. 2020, no.  25, article 2533. (In Port.). https://doi.org/10.1590/0104-9224/SI25.33</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Pernach M. Application of the mixed-mode model for numerical simulation of pearlitic transformation // Journal of Materials Engineering and Performance. 2019. No. 28. P. 3136–3148. https://doi.org/10.1007/s11665-019-04069-0</mixed-citation><mixed-citation xml:lang="en">Pernach M. Application of the mixed-mode model for numerical simulation of pearlitic transformation. Journal of Materials Engineering and Performance. 2019, no. 28, pp. 3136–3148. https://doi.org/10.1007/s11665-019-04069-0</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Milenin A., Pernach M., Rauch R., Kuziak R., Zygmunt T., Pietrzyk M. Modelling and optimization of the manufacturing chain for rails // Procedia Engineering. 2017. No. 207. P. 2011–2016. https://doi.org/10.1016/j.proeng.2017.10.1112</mixed-citation><mixed-citation xml:lang="en">Milenin A., Pernach M., Rauch R., Kuziak R., Zygmunt T., Pietr­zyk  M. Modelling and optimization of the manufacturing chain for rails. Procedia Engineering. 2017, no. 207, pp. 2011–2016. https://doi.org/10.1016/j.proeng.2017.10.1112</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Faria G.L., Godefroid L.B., Cândido L.C., Porcaro R.R. Microstructural characterization and kinetic study about phase transformations in standard and premium rail steels. In: Congresso Anual da ABM, Rio de Janeiro-RJ. Anais. Rio de Janeiro: ABM, 2016. https://doi.org/10.5151/1516-392X-27668</mixed-citation><mixed-citation xml:lang="en">Faria G.L., Godefroid L.B., Cândido L.C., Porcaro R.R. Microstructural characterization and kinetic study about phase transformations in standard and premium rail steels. In: Congresso Anual da ABM, Rio de Janeiro-RJ. Anais. Rio de Janeiro: ABM, 2016. (In Port.). https://doi.org/10.5151/1516-392X-27668</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Tawfik D., Mutton P.J., Chiu W.K. Experimental and numerical investigations: Alleviating tensile residual stresses in flash-butt welds by localized rapid post-weld heat treatment // Journal of Materials Processing Technology. 2008. Vol. 196. No. 1-3. P. 279–291. https://doi.org/10.1016/j.jmatprotec.2007.05.055</mixed-citation><mixed-citation xml:lang="en">Tawfik D., Mutton P.J., Chiu W.K. Experimental and numerical investigations: Alleviating tensile residual stresses in flash-butt welds by localized rapid post-weld heat treatment. Journal of Materials Processing Technology. 2008, vol. 196, no. 1-3, pp. 279–291. https://doi.org/10.1016/j.jmatprotec.2007.05.055</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Гладков Э.А. Управление процессами и оборудованием при сварке. М.: ИЦ «Академия», 2006. 432 с.</mixed-citation><mixed-citation xml:lang="en">Gladkov E.A. Control of Processes and Equipment in Welding. Moscow: Akademiya, 2006, 432 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Джонсон Н.Л., Коц С., Балакришнан Н. Одномерные непрерывные распределения. М.: БИНОМ, Лаборатория знаний, 2010. 703 с.</mixed-citation><mixed-citation xml:lang="en">Johnson N.L., Kotz S., Balakrishnan N. Continuous Univariate Distributions. New York: John Wiley &amp; Sons, Inc., 1994. (Russ. ed.: Johnson  N.L., Kotz S., Balakrishnan N. Odnomernye nepreryvnye raspredeleniya. Moscow: BINOM, Laboratoriya znanii, 2010, 703 p.).</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
