<?xml version="1.0" encoding="utf-8"?>
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  <doc>
    <id>24297</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>447</pageFirst>
    <pageLast>459</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>12</volume>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-08-09</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Minimal polynomial descriptions of polyhedra and special semialgebraic sets</title>
    <abstract language="eng">We show that a d-dimensional polyhedron S in Rd can be represented by d-polynomial inequalities, that is, S = fx 2 Rd : p0(x)  0; : : : ; pd(x) 0g, where p0; : : : ; pd1 are appropriate polynomials. Furthermore, if an elementary closed semialgebraic set S is given by&#13;
polynomials q1; : : : ; qk and for each x 2 S at most s of these polynomials vanish in x, then S can be represented by s + 1 polynomials (and by s polynomials)</abstract>
    <parentTitle language="eng">Advances in geometry</parentTitle>
    <identifier type="doi">10.1515/advgeom-2011-059</identifier>
    <identifier type="url">https://www.degruyter.com/view/j/advg.2012.12.issue-3/advgeom-2011-059/advgeom-2011-059.xml</identifier>
    <identifier type="issn">1615-715X</identifier>
    <identifier type="issn">1615-7168</identifier>
    <enrichment key="BTU">nicht an der BTU erstellt / not created at BTU</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <author>
      <firstName>Gennadiy</firstName>
      <lastName>Averkov</lastName>
    </author>
    <submitter>
      <firstName>Angelika</firstName>
      <lastName>Breu</lastName>
    </submitter>
    <author>
      <firstName>Ludwig</firstName>
      <lastName>Bröcker</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hörmander–Łojasiewicz’s Inequality</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedron</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polynomial</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polytope</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>semialge-braic set</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stability index</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Theorem of Bröcker and Scheiderer</value>
    </subject>
    <collection role="institutes" number="1302">FG Algorithmische Mathematik</collection>
  </doc>
</export-example>
