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  <front>
    <journal-meta>
      <journal-id journal-id-type="issn">2411-3336</journal-id>
      <journal-id journal-id-type="eissn">2541-9404</journal-id>
      <journal-title-group>
        <journal-title xml:lang="ru">Записки Горного института</journal-title>
        <journal-title xml:lang="en">Journal of Mining Institute</journal-title>
      </journal-title-group>
      <publisher>
        <publisher-name xml:lang="ru">Санкт-Петербургский горный университет императрицы Екатерины ΙΙ</publisher-name>
        <publisher-name xml:lang="en">Empress Catherine II Saint Petersburg Mining University</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-14746</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/14746</article-id>
      <article-categories>
        <subj-group subj-group-type="section-heading" xml:lang="ru">
          <subject>Статьи</subject>
        </subj-group>
        <subj-group subj-group-type="section-heading" xml:lang="en">
          <subject>Articles</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Construction of solutions of integral equations in the form of degree series</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Построение решений интегральных уравнений в виде степенных рядов</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="eastern">
            <surname>Sergeev</surname>
            <given-names>N. P.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Сергеев</surname>
              <given-names>Н. П.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Sergeev</surname>
              <given-names>N. P.</given-names>
            </name>
          </name-alternatives>
          <email>pmi@spmi.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru"> (Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en"> (Russia)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="1956-03-13">
        <day>13</day>
        <month>03</month>
        <year>1956</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>1956</year>
      </pub-date>
      <volume>33</volume>
      <issue>3</issue>
      <fpage>154</fpage>
      <lpage>160</lpage>
      <history>
        <date date-type="received" iso-8601-date="1955-04-20">
          <day>20</day>
          <month>04</month>
          <year>1955</year>
        </date>
        <date date-type="accepted" iso-8601-date="1955-11-02">
          <day>02</day>
          <month>11</month>
          <year>1955</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="1956-03-13">
          <day>13</day>
          <month>03</month>
          <year>1956</year>
        </date>
      </history>
      <permissions>
        <copyright-statement xml:lang="ru">© 1956 Н. П. Сергеев</copyright-statement>
        <copyright-statement xml:lang="en">© 1956 N. P. Sergeev</copyright-statement>
        <copyright-year>1956</copyright-year>
        <copyright-holder xml:lang="ru">Н. П. Сергеев</copyright-holder>
        <copyright-holder xml:lang="en">N. P. Sergeev</copyright-holder>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="ru">
          <license-p>Эта статья доступна по лицензии Creative Commons Attribution 4.0 International (CC BY 4.0)</license-p>
        </license>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="en">
          <license-p>This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0)</license-p>
        </license>
      </permissions>
      <self-uri xlink:type="simple" xlink:href="https://pmi.spmi.ru/pmi/article/view/14746">https://pmi.spmi.ru/pmi/article/view/14746</self-uri>
      <abstract xml:lang="ru">
        <p>1.Уравнение Фредгольма Решение уравнения Фредгольма II рода с непрерывным ядром может быть сведено к решению двух функциональных дифференциальных уравнений с условиями Коши. Это обстоятельство наводит на мысль о построении решений интегральных уравнений в виде степенных рядов. Рассмотрим уравнение Фредгольма (см. статью). 2. Уравнение Вольтерра В этом параграфе указанные выше соображения к уравнению Вольтерра. Рассмотрим мы применим уравнение (см. статью).</p>
      </abstract>
      <abstract xml:lang="en">
        <p>1. Fredholm equation. The solution of the Fredholm equation of genus II with a continuous kernel can be reduced to the solution of two functional differential equations with Cauchy conditions. This fact suggests the idea of constructing solutions of integral equations in the form of degree series. Let us consider the Fredholm equation (see Ref.) 2. Volterra equation. In this paragraph, the above considerations to the Volterra equation. We will consider applying the equation (see article).</p>
      </abstract>
      <kwd-group xml:lang="ru">
        <title>Ключевые слова</title>
        <kwd>-</kwd>
      </kwd-group>
      <kwd-group xml:lang="en">
        <title>Keywords</title>
        <kwd>-</kwd>
      </kwd-group>
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        <label>1</label>
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