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Title:           A stochastic population model with hierarchic size-structure
Subject:         Journal of Applied Mathematics and Computing, https://doi.org/10.1007/s12190-024-02187-0
Keywords:        Hierarchically size-structured population; Individual based stochastic model; Quasi-stationary distribution
Author:          Carles Barril 
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      Title: A stochastic population model with hierarchic size-structure
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       Item: 
        Title: Abstract
        Destination: abscnt.2
       Item: 
        Title: 1 Introduction
        Destination: section.1
       Item: 
        Title: 2 Stochasticity and population size
        Destination: section.2
        Children: 
         Item: 
          Title: 2.1 Existence and characterisation of stationary birth rates
          Destination: subsection.2.1
       Item: 
        Title: 3 Formal comparison between the deterministic and the stochastic models
        Destination: section.3
       Item: 
        Title: 4 Numerical comparison between the deterministic and stochastic models
        Destination: section.4
       Item: 
        Title: 5 Conclusions
        Destination: section.5
       Item: 
        Title: Appendix A. Derivation of equation (15)
        Destination: section.1
       Item: 
        Title: Appendix B. Explicit computation of barB with g(z)=g0/(1+z) and A=1
        Destination: section.2
        Children: 
         Item: 
          Title: Appendix C. Auxiliary propositions
          Destination: section.3
       Item: 
        Title: Acknowledgements
        Destination: equation.3.1
       Item: 
        Title: References
        Destination: myseccnt.1
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    Author: Carles Barril 
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>The date when a publication was publishe.</pdfaProperty:description>
                           <pdfaProperty:name>MajorVersionDate</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>CrossmarkDomainExclusive</pdfaProperty:description>
                           <pdfaProperty:name>CrossmarkDomainExclusive</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>CrossMarkDomains</pdfaProperty:description>
                           <pdfaProperty:name>CrossMarkDomains</pdfaProperty:name>
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                  <pdfaSchema:schema>Prism Schema</pdfaSchema:schema>
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                           <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>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>The Digital Object Identifier for the article.&#xA;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>
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                        <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>
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                        <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>
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                        <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>
                           <pdfaProperty:name>aggregationType</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                        <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>
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                        <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>
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                  <pdfaSchema:prefix>pdf</pdfaSchema:prefix>
                  <pdfaSchema:schema>Adobe PDF Schema</pdfaSchema:schema>
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                           <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>
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                  <pdfaSchema:schema>XMP Media Management Schema</pdfaSchema:schema>
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                           <pdfaProperty:description>UUID based identifier for specific incarnation of a document</pdfaProperty:description>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <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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                           <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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                  <pdfaSchema:prefix>pdfaid</pdfaSchema:prefix>
                  <pdfaSchema:schema>PDF/A ID Schema</pdfaSchema:schema>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Part of PDF/A standard</pdfaProperty:description>
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                           <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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                                    <pdfaField:name>name</pdfaField:name>
                                    <pdfaField:valueType>Text</pdfaField:valueType>
                                    <pdfaField:description>Gives the name of an author.</pdfaField:description>
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                                    <pdfaField:valueType>URI</pdfaField:valueType>
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                     <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>
                           <pdfaProperty:name>PlateNames</pdfaProperty:name>
                           <pdfaProperty:valueType>Seq Text</pdfaProperty:valueType>
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                  <pdfaSchema:schema>NISO</pdfaSchema:schema>
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                     <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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   Type: CRC32
  Checksum: 6af65088ce736cbcc8b4fb7c4da6258c
   Type: MD5
  Checksum: 6b19f4acc3f6c7051ba4cb93ac3e119bf67b075c
   Type: SHA-1
  Checksum: 551f3b6aafc290a81639ed1119de64446cf07807eccd5cbb47d8f01c68eadc27
   Type: SHA-256