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Title:          Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant
Subject:        Calculus of Variations and Partial Differential Equations, https://doi.org/10.1007/s00526-022-02426-x
Keywords:       31B05; 31B20; 35J25
Author:         Josep M. Gallegos 
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Jhove (Rel. 1.22.1, 2019-04-17)
 Date: 2023-10-07 02:26:14 CEST
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     Item: 
      Title: Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant
      Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@6121c9d6
      Children: 
       Item: 
        Title: Abstract
        Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@87f383f
       Item: 
        Title: 1 Introduction
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        Children: 
         Item: 
          Title: 1.1 Further questions
          Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@eafc191
         Item: 
          Title: 1.2 Outline of the paper
          Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@612fc6eb
       Item: 
        Title: 2 Lipschitz domains with small constant and some properties of elliptic PDEs
        Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@1060b431
        Children: 
         Item: 
          Title: 2.1 Divergence form elliptic PDEs with Lipschitz coefficients
          Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@612679d6
         Item: 
          Title: 2.2 Modifying the domain and A(x)
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       Item: 
        Title: 3 Frequency function for solutions of elliptic PDEs in divergence form
        Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@e720b71
        Children: 
         Item: 
          Title: 3.1 Frequency function centered at arbitrary points
          Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@1b26f7b2
         Item: 
          Title: 3.2 Auxiliar lemmas on the behavior of H(r) and N(r)
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       Item: 
        Title: 4 Behavior of the frequency function on cubes near the boundary
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        Children: 
         Item: 
          Title: 4.1 Whitney cube structure on Omega
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         Item: 
          Title: 4.2 Lemma on the behavior of the frequency in the Whitney tree
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       Item: 
        Title: 5 Balls without zeros near the boundary
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       Item: 
        Title: 6 Proof of Theorems 1.1 and 1.5
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        Children: 
         Item: 
          Title: 6.1 Modified frequency function
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         Item: 
          Title: 6.2 Proof of Theorem 1.1
          Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@66d1af89
         Item: 
          Title: 6.3 Planar case of Theorem 1.1
          Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@8646db9
         Item: 
          Title: 6.4 Estimates on the measure of nodal sets in the interior of the domain
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         Item: 
          Title: 6.5 Proof of Theorem 1.5
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         Item: 
          Title: 6.6 (d-1)-dimensional Hausdorff measure of Dirichlet eigenfunctions
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       Item: 
        Title: 7 Proof of Corollary 1.6
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       Item: 
        Title: 8 Proof of Corollary 1.8
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       Item: 
        Title: 9 Example of domain with set of zero density of harmonic measure with small codimension
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       Item: 
        Title: 10 Equality between S(u) and S'(u) in the Dini smooth case
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       Item: 
        Title: Acknowledgements
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       Item: 
        Title: Appendix A. Existence of non-tangential limits for nabla u
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       Item: 
        Title: References
        Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@3ecd23d9
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    Title: Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant
    Author: Josep M. Gallegos 
    Subject: Calculus of Variations and Partial Differential Equations, https://doi.org/10.1007/s00526-022-02426-x
    Keywords: 31B05; 31B20; 35J25
    Creator: Springer
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         <crossmark:CrossMarkDomains>
            <rdf:Seq>
               <rdf:li>springer.com</rdf:li>
               <rdf:li>springerlink.com</rdf:li>
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         <prism:doi>10.1007/s00526-022-02426-x</prism:doi>
         <prism:issn>1432-0835</prism:issn>
         <prism:volume>62</prism:volume>
         <prism:number>4</prism:number>
         <prism:startingPage>1</prism:startingPage>
         <prism:endingPage>52</prism:endingPage>
         <prism:aggregationType>journal</prism:aggregationType>
         <prism:publicationName>Calculus of Variations and Partial Differential Equations</prism:publicationName>
         <prism:copyright>The Author(s)</prism:copyright>
         <pdfx:CrossmarkMajorVersionDate>2010-04-23</pdfx:CrossmarkMajorVersionDate>
         <pdfx:CrossmarkDomainExclusive>true</pdfx:CrossmarkDomainExclusive>
         <pdfx:doi>10.1007/s00526-022-02426-x</pdfx:doi>
         <pdfx:robots>noindex</pdfx:robots>
         <pdfx:CrossMarkDomains>
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               <rdf:li>springer.com</rdf:li>
               <rdf:li>springerlink.com</rdf:li>
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         </pdfx:CrossMarkDomains>
         <jav:journal_article_version>VoR</jav:journal_article_version>
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               <rdf:li rdf:parseType="Resource">
                  <stEvt:action>converted</stEvt:action>
                  <stEvt:instanceID>uuid:0dedb043-6f59-4f4c-a55e-64f32cc439fc</stEvt:instanceID>
                  <stEvt:parameters>converted to PDF/A-2b</stEvt:parameters>
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                  <stEvt:parameters>converted to PDF/A-2b</stEvt:parameters>
                  <stEvt:softwareAgent>pdfToolbox</stEvt:softwareAgent>
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                  <pdfaSchema:schema>Adobe Document Info PDF eXtension Schema</pdfaSchema:schema>
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                           <pdfaProperty:description>Mirrors crossmark:MajorVersionDate</pdfaProperty:description>
                           <pdfaProperty:name>CrossmarkMajorVersionDate</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Mirrors crossmark:CrossmarkDomainExclusive</pdfaProperty:description>
                           <pdfaProperty:name>CrossmarkDomainExclusive</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Mirrors crossmark:DOI</pdfaProperty:description>
                           <pdfaProperty:name>doi</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Mirrors crossmark:CrosMarkDomains</pdfaProperty:description>
                           <pdfaProperty:name>CrossMarkDomains</pdfaProperty:name>
                           <pdfaProperty:valueType>seq Text</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>A name object indicating whether the document has been modified to include trapping information</pdfaProperty:description>
                           <pdfaProperty:name>robots</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
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                           <pdfaProperty:description>ID of PDF/X standard</pdfaProperty:description>
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                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                           <pdfaProperty:description>Conformance level of PDF/X standard</pdfaProperty:description>
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                           <pdfaProperty:description>Company creating the PDF</pdfaProperty:description>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Date when document was last modified</pdfaProperty:description>
                           <pdfaProperty:name>SourceModified</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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               <rdf:li rdf:parseType="Resource">
                  <pdfaSchema:namespaceURI>http://crossref.org/crossmark/1.0/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>crossmark</pdfaSchema:prefix>
                  <pdfaSchema:schema>Crossmark Schema</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Usual same as prism:doi</pdfaProperty:description>
                           <pdfaProperty:name>DOI</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
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                           <pdfaProperty:description>The date when a publication was publishe.</pdfaProperty:description>
                           <pdfaProperty:name>MajorVersionDate</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
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                           <pdfaProperty:description>CrossmarkDomainExclusive</pdfaProperty:description>
                           <pdfaProperty:name>CrossmarkDomainExclusive</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>CrossMarkDomains</pdfaProperty:description>
                           <pdfaProperty:name>CrossMarkDomains</pdfaProperty:name>
                           <pdfaProperty:valueType>seq Text</pdfaProperty:valueType>
                        </rdf:li>
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                  </pdfaSchema:property>
               </rdf:li>
               <rdf:li rdf:parseType="Resource">
                  <pdfaSchema:namespaceURI>http://prismstandard.org/namespaces/basic/2.0/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>prism</pdfaSchema:prefix>
                  <pdfaSchema:schema>Prism Schema</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>This element provides the url for an article or unit of content. The attribute platform is optionally allowed for situations in which multiple URLs must be specified. PRISM recommends that a subset of the PCV platform values, namely “mobile” and “web”, be used in conjunction with this element. NOTE: PRISM recommends against the use of the #other value allowed in the PRISM Platform controlled vocabulary. In lieu of using #other please reach out to the PRISM group at prism-wg@yahoogroups.com to request addition of your term to the Platform Controlled Vocabulary.</pdfaProperty:description>
                           <pdfaProperty:name>url</pdfaProperty:name>
                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>The Digital Object Identifier for the article. The DOI may also be used as the dc:identifier. If used as a dc:identifier, the URI form should be captured, and the bare identifier should also be captured using prism:doi. If an alternate unique identifier is used as the required dc:identifier, then the DOI should be specified as a bare identifier within prism:doi only. If the URL associated with a DOI is to be specified, then prism:url may be used in conjunction with prism:doi in order to provide the service endpoint (i.e. the URL). </pdfaProperty:description>
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                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>ISSN for an electronic version of the issue in which the resource occurs. Permits publishers to include a second ISSN, identifying an electronic version of the issue in which the resource occurs (therefore e(lectronic)Issn. If used, prism:eIssn MUST contain the ISSN of the electronic version.</pdfaProperty:description>
                           <pdfaProperty:name>issn</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Volume number</pdfaProperty:description>
                           <pdfaProperty:name>volume</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Issue number</pdfaProperty:description>
                           <pdfaProperty:name>number</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Starting page</pdfaProperty:description>
                           <pdfaProperty:name>startingPage</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Ending page</pdfaProperty:description>
                           <pdfaProperty:name>endingPage</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>The aggregation type specifies the unit of aggregation for a content collection. Comment PRISM recommends that the PRISM Aggregation Type Controlled Vocabulary be used to provide values for this element. Note: PRISM recommends against the use of the #other value currently allowed in this controlled vocabulary. In lieu of using #other please reach out to the PRISM group at info@prismstandard.org to request addition of your term to the Aggregation Type Controlled Vocabulary. </pdfaProperty:description>
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                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Title of the magazine, or other publication, in which a resource was/will be published. Typically this will be used to provide the name of the magazine an article appeared in as metadata for the article, along with information such as the article title, the publisher, volume, number, and cover date. Note: Publication name can be used to differentiate between a print magazine and the online version if the names are different such as “magazine” and “magazine.com.”</pdfaProperty:description>
                           <pdfaProperty:name>publicationName</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Copyright</pdfaProperty:description>
                           <pdfaProperty:name>copyright</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                     </rdf:Seq>
                  </pdfaSchema:property>
               </rdf:li>
               <rdf:li rdf:parseType="Resource">
                  <pdfaSchema:namespaceURI>http://ns.adobe.com/pdf/1.3/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>pdf</pdfaSchema:prefix>
                  <pdfaSchema:schema>Adobe PDF Schema</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>A name object indicating whether the document has been modified to include trapping information</pdfaProperty:description>
                           <pdfaProperty:name>Trapped</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                     </rdf:Seq>
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               </rdf:li>
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                  <pdfaSchema:namespaceURI>http://ns.adobe.com/xap/1.0/mm/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>xmpMM</pdfaSchema:prefix>
                  <pdfaSchema:schema>XMP Media Management Schema</pdfaSchema:schema>
                  <pdfaSchema:property>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>UUID based identifier for specific incarnation of a document</pdfaProperty:description>
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                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>The common identifier for all versions and renditions of a document.</pdfaProperty:description>
                           <pdfaProperty:name>DocumentID</pdfaProperty:name>
                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
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                           <pdfaProperty:description>The common identifier for all versions and renditions of a document.</pdfaProperty:description>
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                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
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                           <pdfaProperty:description>A reference to the original document from which this one is derived. It is a minimal reference; missing components can be assumed to be unchanged. For example, a new version might only need to specify the instance ID and version number of the previous version, or a rendition might only need to specify the instance ID and rendition class of the original.</pdfaProperty:description>
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                           <pdfaProperty:valueType>ResourceRef</pdfaProperty:valueType>
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                  <pdfaSchema:valueType>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaType:description>Identifies a portion of a document. This can be a position at which the document has been changed since the most recent event history (stEvt:changed). For a resource within an xmpMM:Ingredients list, the ResourceRef uses this type to identify both the portion of the containing document that refers to the resource, and the portion of the referenced resource that is referenced.</pdfaType:description>
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               <rdf:li rdf:parseType="Resource">
                  <pdfaSchema:namespaceURI>http://www.aiim.org/pdfa/ns/id/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>pdfaid</pdfaSchema:prefix>
                  <pdfaSchema:schema>PDF/A ID Schema</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Part of PDF/A standard</pdfaProperty:description>
                           <pdfaProperty:name>part</pdfaProperty:name>
                           <pdfaProperty:valueType>Integer</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Amendment of PDF/A standard</pdfaProperty:description>
                           <pdfaProperty:name>amd</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Conformance level of PDF/A standard</pdfaProperty:description>
                           <pdfaProperty:name>conformance</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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               <rdf:li rdf:parseType="Resource">
                  <pdfaSchema:schema>Springer Nature ORCID Schema</pdfaSchema:schema>
                  <pdfaSchema:namespaceURI>http://springernature.com/ns/xmpExtensions/2.0/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>sn</pdfaSchema:prefix>
                  <pdfaSchema:property>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:name>authorInfo</pdfaProperty:name>
                           <pdfaProperty:valueType>Bag AuthorInformation</pdfaProperty:valueType>
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Author information: contains the name of each author and his/her ORCiD (ORCiD: Open Researcher and Contributor ID). An ORCiD is a persistent identifier (a non-proprietary alphanumeric code) to uniquely identify scientific and other academic authors.</pdfaProperty:description>
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                           <pdfaType:prefix>author</pdfaType:prefix>
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                                 <rdf:li rdf:parseType="Resource">
                                    <pdfaField:name>name</pdfaField:name>
                                    <pdfaField:valueType>Text</pdfaField:valueType>
                                    <pdfaField:description>Gives the name of an author.</pdfaField:description>
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                                 <rdf:li rdf:parseType="Resource">
                                    <pdfaField:name>orcid</pdfaField:name>
                                    <pdfaField:valueType>URI</pdfaField:valueType>
                                    <pdfaField:description>Gives the ORCID of an author.</pdfaField:description>
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                  <pdfaSchema:prefix>xmpTPg</pdfaSchema:prefix>
                  <pdfaSchema:schema>XMP Paged-Text</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>XMP08 Spec: An ordered array of plate names that are needed to print the document (including any in contained documents).</pdfaProperty:description>
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                           <pdfaProperty:description>A structure containing the characteristics of a font used in a document</pdfaProperty:description>
                           <pdfaProperty:name>Fonts</pdfaProperty:name>
                           <pdfaProperty:valueType>Bag Font</pdfaProperty:valueType>
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                  <pdfaSchema:valueType>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaType:description>A structure containing the characteristics of a font used in a document.</pdfaType:description>
                           <pdfaType:namespaceURI>http://ns.adobe.com/xap/1.0/sType/Font#</pdfaType:namespaceURI>
                           <pdfaType:prefix>stFnt</pdfaType:prefix>
                           <pdfaType:type>Font</pdfaType:type>
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                  <pdfaSchema:namespaceURI>http://www.niso.org/schemas/jav/1.0/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>jav</pdfaSchema:prefix>
                  <pdfaSchema:schema>NISO</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Values for Journal Article Version are one of the following:&#xA;AO = Author’s Original&#xA;SMUR = Submitted Manuscript Under Review&#xA;AM = Accepted Manuscript&#xA;P = Proof&#xA;VoR = Version of Record&#xA;CVoR = Corrected Version of Record&#xA;EVoR = Enhanced Version of Record</pdfaProperty:description>
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                           <pdfaProperty:valueType>Closed Choice of Text</pdfaProperty:valueType>
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