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<export-example>
  <doc>
    <id>83</id>
    <completedYear>2005</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-10-31</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Quantization for Dyadic Homogeneous Cantor Distributions</title>
    <abstract language="eng">For a large class of dyadic homogeneous Cantor distributions in \mathbb{R}, which are not necessarily self-similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non-existence of the quantization coefficient. The class contains all self-similar dyadic Cantor distributions, with contraction factor less than or equal to \frac{1}{3}. For these distributions we calculate the quantization errors explicitly.</abstract>
    <identifier type="urn">urn:nbn:de:bvb:739-opus-3845</identifier>
    <identifier type="opus3-id">384</identifier>
    <note>Die Endfassung des Artikels kann beim Verfasser angefordert werden. Kontaktinformation: opus@uni-passau.de</note>
    <enrichment key="SourceTitle">This is a preprint of an article accepted for publication in Mathematische Nachrichten, Print ISSN:0025-584X, Online ISSN:1522-2616, Copyright © by Wiley http://www3.interscience.wiley.com/journal/60500208/home. The digital object identifier (DOI) of the definitive article is 10.1002/mana.200510680.</enrichment>
    <licence>Standardbedingung laut Einverständniserklärung</licence>
    <author>Wolfgang Kreitmeier</author>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Maßtheorie</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Fraktale Dimension</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Iteriertes Funktionensystem</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Cantor-Menge</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Dimension</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Maß</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quantization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>homogeneous Cantor measures</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quantization dimension</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quantization coefficient</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="28A80">Fractals [See also 37Fxx]</collection>
    <collection role="open_access" number="">open_access</collection>
    <collection role="institutes" number="">Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik</collection>
    <thesisPublisher>Universität Passau</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-uni-passau/files/83/dyadic_cantor.pdf</file>
  </doc>
  <doc>
    <id>119</id>
    <completedYear>2009</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-02-10</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hausdorff measure of uniform self-similar fractals</title>
    <abstract language="eng">Let &lt;i&gt;d&lt;/i&gt; &amp;#8805; 1 be an integer and &lt;i&gt;E&lt;/i&gt; a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on R&lt;sup&gt;d&lt;/sup&gt;. Denote by &lt;i&gt;D&lt;/i&gt; the Hausdorff dimension, by &lt;i&gt;H&lt;/i&gt;&lt;sup&gt;D&lt;/sup&gt;&lt;i&gt;(E)&lt;/i&gt; the Hausdorff measure and by diam &lt;i&gt;(E)&lt;/i&gt; the diameter of &lt;i&gt;E&lt;/i&gt;. If the UIFS is parametrised by its contracting factor &lt;i&gt;c&lt;/i&gt;, while the set &amp;omega; of fixed points of the UIFS does not depend on &lt;i&gt;c&lt;/i&gt;, we will show the existence of a positive constant depending only on &amp;omega;, such that the Hausdorff dimension is smaller than one and &lt;i&gt;H&lt;/i&gt;&lt;sup&gt;D&lt;/sup&gt; = &lt;i&gt;(E)&lt;/i&gt; &lt;sup&gt;D&lt;/sup&gt; if &lt;i&gt;c&lt;/i&gt; is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover we present a parametrised UIFS where &amp;omega; depends on &lt;i&gt;c&lt;/i&gt; and &lt;i&gt;H&lt;/i&gt;&lt;sup&gt;D&lt;/sup&gt; &lt; diam&lt;i&gt;(E)&lt;/i&gt;&lt;sup&gt;D&lt;/sup&gt;, if &lt;i&gt;c&lt;/i&gt; is small enough.</abstract>
    <identifier type="urn">urn:nbn:de:bvb:739-opus-17948</identifier>
    <identifier type="opus3-id">1794</identifier>
    <note>This is a preprint of an article accepted for publication in Analysis in Theory and Applications ISSN: 1672-4070 (print version) ISSN: 1573-8175 (electronic version) Copyright (c) by Springer. The original publication is available at www.springerlink.com</note>
    <enrichment key="SourceTitle">Analysis in Theory and Applications ISSN: 1672-4070 (print version) ISSN: 1573-8175 (electronic version)</enrichment>
    <licence>Standardbedingung laut Einverständniserklärung</licence>
    <author>Wolfgang Kreitmeier</author>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Maßtheorie</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Iteriertes Funktionensystem</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Dimension</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Maß</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Self-similar set</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hausdorff measure</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="28A78">Hausdorff and packing measures</collection>
    <collection role="msc" number="28A80">Fractals [See also 37Fxx]</collection>
    <collection role="open_access" number="">open_access</collection>
    <collection role="institutes" number="">Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik</collection>
    <thesisPublisher>Universität Passau</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-uni-passau/files/119/haus_meas_v3.pdf</file>
  </doc>
  <doc>
    <id>74</id>
    <completedYear>2006</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>doctoralthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-07-09</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>2007-06-04</thesisDateAccepted>
    <title language="deu">Optimale Quantisierung verallgemeinerter Cantor-Verteilungen</title>
    <abstract language="deu">Für verallgemeinerte Cantor-Verteilungen, die im Eindimensionalen mittels klassischer Wischkonstruktion bzw. in höheren Dimensionen über iterierte Funktionensysteme definiert werden, wird das Problem der optimalen Quantisierung unter bestimmten Voraussetzungen vollständig gelöst. Es werden die optimalen Codebücher bestimmt und Formeln für den optimalen Quantisierungsfehler bewiesen. Im eindimensionalen Fall wird eine Existenzcharakterisierung der Quantisierungsdimension gegeben und unter bestimmten Voraussetzungen die Nichtexistenz des Quantisierungskoeffizienten gezeigt. Auch in höheren Dimensionen wird für die betrachteten Verteilungen bewiesen, dass der Quantisierungskoeffizient, bei existenter Quantisierungsdimension, nicht existiert. Die gewonnenen Resultate werden auf die Gleichverteilungen von modifizierten klassischen fraktalen Mengen, wie das Sierpinski-Dreieck, die Cantormenge und den Cantor-Staub angewandt.</abstract>
    <identifier type="urn">urn:nbn:de:bvb:739-opus-913</identifier>
    <identifier type="opus3-id">91</identifier>
    <licence>Standardbedingung laut Einverständniserklärung</licence>
    <author>Wolfgang Kreitmeier</author>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Maßtheorie</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Fraktale Dimension</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Iteriertes Funktionensystem</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Sierpinski-Menge</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Cantor-Menge</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Dimension</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Maß</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Optimale Quantisierung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>homogene Cantormaße</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Quantisierungsdimension</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Quantisierungskoeffizient</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Sierpinski-Dreieck</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal Quantization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>homogeneous Cantor measures</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quantization dimension</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quantization coefficient</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Sierpinski Gasket</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="28A78">Hausdorff and packing measures</collection>
    <collection role="msc" number="28A80">Fractals [See also 37Fxx]</collection>
    <collection role="msc" number="62H30">Classification and discrimination; cluster analysis [See also 68T10]</collection>
    <collection role="open_access" number="">open_access</collection>
    <collection role="institutes" number="">Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik</collection>
    <thesisPublisher>Universität Passau</thesisPublisher>
    <thesisGrantor>Universität Passau</thesisGrantor>
    <file>https://opus4.kobv.de/opus4-uni-passau/files/74/Kreitmeier_Wolfgang.pdf</file>
  </doc>
  <doc>
    <id>86</id>
    <completedYear>2007</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-01-02</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Asymptotic order of quantization for Cantor distributions in terms of Euler characteristic, Hausdorff and Packing measure</title>
    <abstract language="eng">For homogeneous one-dimensional Cantor sets, which are not necessarily self-similar, we show under some restrictions that the Euler exponent equals the quantization dimension of the uniform distribution on these Cantor sets. Moreover for a special sub-class of these sets we present a linkage between the Hausdorff and the Packing measure of these sets and the high-rate asymptotics of the quantization error.</abstract>
    <identifier type="urn">urn:nbn:de:bvb:739-opus-7374</identifier>
    <identifier type="opus3-id">737</identifier>
    <note>Die Endfassung des Artikels kann beim Verfasser angefordert werden. Kontaktinformation: opus@uni-passau.de</note>
    <enrichment key="SourceTitle">This is a preprint of an article accepted for publication in Journal of Mathematical Analysis and Applications, ISSN: 0022-247X. Copyright (c) by Elsevier. URL: http://www.elsevier.com/. The digital object identifier (DOI) of the definitive article is 10.1016/j.jmaa.2007.12.052</enrichment>
    <licence>Standardbedingung laut Einverständniserklärung</licence>
    <author>Wolfgang Kreitmeier</author>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Maßtheorie</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Fraktale Dimension</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Iteriertes Funktionensystem</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Cantor-Menge</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Dimension</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Hausdorff-Maß</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Homogeneous Cantor set</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Euler characteristic</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Euler exponent</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quantization dimension</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quantization coefficient</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hausdorff dimension</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="28A78">Hausdorff and packing measures</collection>
    <collection role="msc" number="28A80">Fractals [See also 37Fxx]</collection>
    <collection role="open_access" number="">open_access</collection>
    <collection role="institutes" number="">Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik</collection>
    <thesisPublisher>Universität Passau</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-uni-passau/files/86/kreitmeier_eul_quant.pdf</file>
  </doc>
</export-example>
