<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332020000200355</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v27i2.34109</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A stochastic model for germination]]></article-title>
<article-title xml:lang="es"><![CDATA[Un modelo estocástico de germinación]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Villa-Morales]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de Aguascalientes  Departamento de Matemáticas y Física]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<volume>27</volume>
<numero>2</numero>
<fpage>355</fpage>
<lpage>365</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332020000200355&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332020000200355&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332020000200355&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Assuming that the germination process of a seed passes through several stages (or states), including a state of non-germination, we model this phenomenon by means of a continuous-time Markov chain. The distribution of the germination time and the average of the first germination is obtained. In particular, when the duration of the process at each stage is on average the same we see that the proposed model adjusts rather well some experimental data.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Asumiendo que el proceso de germinación de una semilla pasa por varias etapas (o estados), incluyendo un estado de no germinación, se modela éste fenómeno por medio de una cadena de Markov a tiempo continuo. Se obtienen la distribución del tiempo de germinación y la media del tiempo de la primera germinación. En particular, cuando la duración del proceso de germinación es en promedio el mismo en cada etapa vemos que el modelo propuesto se ajusta bastante bien a datos experimentales.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[seed germination]]></kwd>
<kwd lng="en"><![CDATA[first germination time]]></kwd>
<kwd lng="en"><![CDATA[continuous-time Markov chains.]]></kwd>
<kwd lng="es"><![CDATA[germinación de semillas]]></kwd>
<kwd lng="es"><![CDATA[tiempo de la primera germinación]]></kwd>
<kwd lng="es"><![CDATA[cadenas de Markov a tiempo continuo.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[G,J]]></surname>
<given-names><![CDATA[Barry]]></given-names>
</name>
<name>
<surname><![CDATA[R,J]]></surname>
<given-names><![CDATA[Cawood]]></given-names>
</name>
<name>
<surname><![CDATA[R,G]]></surname>
<given-names><![CDATA[Flood.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Curve fitting of germination data using the Richards function]]></article-title>
<source><![CDATA[Plant, Cell and Environment]]></source>
<year>1988</year>
<volume>11</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>183-8</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Bould]]></given-names>
</name>
<name>
<surname><![CDATA[B,K]]></surname>
<given-names><![CDATA[Abrol.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A model for seed germination curves]]></article-title>
<source><![CDATA[Seed Sci and Tech]]></source>
<year>1981</year>
<volume>9</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>601-11</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[H]]></surname>
<given-names><![CDATA[Challa.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Prediction of production: requisite of an integrated approach]]></article-title>
<source><![CDATA[Acta Hortic.]]></source>
<year>1988</year>
<volume>229</volume>
<page-range>133-41</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A,A]]></surname>
<given-names><![CDATA[Goloff Jr]]></given-names>
</name>
<name>
<surname><![CDATA[F,A]]></surname>
<given-names><![CDATA[Bazzaz.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A germination model for natural seed population]]></article-title>
<source><![CDATA[J. Theor. Biol]]></source>
<year>1975</year>
<volume>52</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>259-83</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[M,K]]></surname>
<given-names><![CDATA[Gupta]]></given-names>
</name>
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[Chandra]]></given-names>
</name>
<name>
<surname><![CDATA[D,V,K]]></surname>
<given-names><![CDATA[Samuel]]></given-names>
</name>
<name>
<surname><![CDATA[B]]></surname>
<given-names><![CDATA[Singh]]></given-names>
</name>
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Singh]]></given-names>
</name>
<name>
<surname><![CDATA[M,K]]></surname>
<given-names><![CDATA[Garg.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modeling of tomato seedling growth in greenhouse]]></article-title>
<source><![CDATA[Agric. Res.]]></source>
<year>2012</year>
<volume>1</volume>
<page-range>362-9</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Hara.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Estimating the temperature dependence of germination time by assuming multiple rate-determining steps]]></article-title>
<source><![CDATA[Plant. Prod. Sci.]]></source>
<year>2005</year>
<volume>8</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>361-7</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[H,O]]></surname>
<given-names><![CDATA[Harley.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The modified Gauss-Newton method for the fitting of nonlinear regresion function by least squares]]></article-title>
<source><![CDATA[Technometric]]></source>
<year>1961</year>
<volume>3</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>269-80</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hoel]]></surname>
<given-names><![CDATA[P,G]]></given-names>
</name>
<name>
<surname><![CDATA[Port]]></surname>
<given-names><![CDATA[S,C]]></given-names>
</name>
<name>
<surname><![CDATA[Stone.]]></surname>
<given-names><![CDATA[C,J]]></given-names>
</name>
</person-group>
<source><![CDATA[Introduction to Stochastic Processes]]></source>
<year>1972</year>
<publisher-loc><![CDATA[Boston ]]></publisher-loc>
<publisher-name><![CDATA[Houghton Mifflin]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[F,H]]></surname>
<given-names><![CDATA[Hsu]]></given-names>
</name>
<name>
<surname><![CDATA[C,J]]></surname>
<given-names><![CDATA[Nelson]]></given-names>
</name>
<name>
<surname><![CDATA[W,S]]></surname>
<given-names><![CDATA[Chow.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A mathematical model to utilize the logistic function in germination and seedling growth]]></article-title>
<source><![CDATA[J. Expl. Bot.]]></source>
<year>1984</year>
<volume>351</volume>
<numero>11</numero>
<issue>11</issue>
<page-range>1629-40</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J,G,M]]></surname>
<given-names><![CDATA[Janssen.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A method of recording germination curves]]></article-title>
<source><![CDATA[Ann. Bot.]]></source>
<year>1973</year>
<volume>37</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>705-8</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J,R]]></surname>
<given-names><![CDATA[Norris.]]></given-names>
</name>
</person-group>
<source><![CDATA[Markov Chains]]></source>
<year>1997</year>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J,H,M]]></surname>
<given-names><![CDATA[Thornley.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Germination of seeds and spores]]></article-title>
<source><![CDATA[Annals of Botany]]></source>
<year>1977</year>
<volume>41</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1363-5</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[M]]></surname>
<given-names><![CDATA[Torres]]></given-names>
</name>
<name>
<surname><![CDATA[G]]></surname>
<given-names><![CDATA[Frutos.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Logistic function analysis of germination behaviour of age fennel seeds]]></article-title>
<source><![CDATA[Enviromental and Experimental Botany]]></source>
<year>1990</year>
<volume>30</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>383-90</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Tseng]]></given-names>
</name>
<name>
<surname><![CDATA[J,P]]></surname>
<given-names><![CDATA[Hsu.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A stochastic analysis of seed germination]]></article-title>
<source><![CDATA[Botanic Bulletin of the Academia Sinica]]></source>
<year>1989</year>
<volume>30</volume>
<page-range>201-5</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
