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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">cndcgs</journal-id>
      <journal-title-group>
        <journal-title>Challenges to national defence in contemporary geopolitical situation</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2538-8959</issn>
      <issn pub-type="ppub">2669-2023</issn>
      <publisher>
        <publisher-name>LKA</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="publisher-id">161_JEKL</article-id>
      <article-id pub-id-type="doi">10.47459/cndcgs.2026.161</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Article</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Lanchester Law Model with Fractional Distribution of Fire and Variable Performance Against Multiple Opponents</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>JEKL</surname>
            <given-names>Jan</given-names>
          </name>
          <email xlink:href="mailto:jan.jekl2@unob.cz">jan.jekl2@unob.cz</email>
          <xref ref-type="aff" rid="j_cndcgs_aff_000"/>
          <xref ref-type="corresp" rid="cor1">∗</xref>
        </contrib>
        <aff id="j_cndcgs_aff_000">Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Czech Republic</aff>
        <contrib contrib-type="author">
          <name>
            <surname>RŮŽIČKA</surname>
            <given-names>Vojtěch</given-names>
          </name>
          <xref ref-type="aff" rid="j_cndcgs_aff_001"/>
        </contrib>
        <aff id="j_cndcgs_aff_001">Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Czech Republic</aff>
        <contrib contrib-type="author">
          <name>
            <surname>FEDORKOVÁ</surname>
            <given-names>Lucie</given-names>
          </name>
          <xref ref-type="aff" rid="j_cndcgs_aff_002"/>
        </contrib>
        <aff id="j_cndcgs_aff_002">Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Czech Republic</aff>
      </contrib-group>
      <author-notes>
        <corresp id="cor1"><label>∗</label>Corresponding author.</corresp>
      </author-notes>
      <volume>2026</volume>
      <issue>1</issue>
      <fpage>1369</fpage>
      <lpage>1377</lpage>
      <pub-date pub-type="epub">
        <day>31</day>
        <month>08</month>
        <year>2026</year>
      </pub-date>
      <permissions>
        <license license-type="open-access">
          <license-p>Creative Commons Attribution International License (CC BY)</license-p>
        </license>
      </permissions>
      <abstract>
        <p>Lanchester’s law serves as a deterministic mathematical model of a battle between two or more opponents. We build a new model that incorporates both variable offense and variable defense, as well as the commander’s ability to focus fire on a selected enemy. We show that in a situation where an army fights two allies, the correct strategy of focusing on the weaker enemy leads to an eventual win, whereas the incorrect decision to split the fire equally leads to the army’s annihilation.</p>
      </abstract>
      <kwd-group>
        <label>Keywords</label>
        <kwd>Lanchester law</kwd>
        <kwd>differential equations</kwd>
        <kwd>battle simulation</kwd>
        <kwd>command and control</kwd>
        <kwd>military model</kwd>
      </kwd-group>
    </article-meta>
  </front>
</article>
