<?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>0185-1101</journal-id>
<journal-title><![CDATA[Revista mexicana de astronomía y astrofísica]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. astron. astrofis]]></abbrev-journal-title>
<issn>0185-1101</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Astronomía]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0185-11012022000200321</article-id>
<article-id pub-id-type="doi">10.22201/ia.01851101p.2022.58.02.13</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Ann and Analytical Solutions to Relativistic Isothermal Gas Spheres]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Nouh]]></surname>
<given-names><![CDATA[Mohamed I.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Azzam]]></surname>
<given-names><![CDATA[Yosry A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Abdel-Salam]]></surname>
<given-names><![CDATA[Emad A-B]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Elnagahy]]></surname>
<given-names><![CDATA[Farag I.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Kamel]]></surname>
<given-names><![CDATA[Tarek M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,National Research Institute of Astronomy and Geophysics Astronomy Department ]]></institution>
<addr-line><![CDATA[Cairo ]]></addr-line>
<country>Egypt</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,New Valley University Faculty of Science Department of Mathematics]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Egypt</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<volume>58</volume>
<numero>2</numero>
<fpage>321</fpage>
<lpage>332</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-11012022000200321&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-11012022000200321&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-11012022000200321&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT Relativistic isothermal gas spheres are a powerful tool to model many astronomical objects, like compact stars and clusters of galaxies. In the present paper, we introduce an artificial neural network (ANN) algorithm and Taylor series to model the relativistic gas spheres using Tolman-Oppenheimer-Volkoff differential equations (TOV). Comparing the analytical solutions with the numerical ones revealed good agreement with maximum relative errors of 10&#8722;3. The ANN algorithm implements a three-layer feed-forward neural network built using a back-propagation learning technique that is based on the gradient descent rule. We analyzed the massradius relations and the density profiles of the relativistic isothermal gas spheres against different relativistic parameters and compared the ANN solutions with the analytical ones. The comparison between the two solutions reflects the efficiency of using the ANN to solve TOV equations.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Las esferas isotérmicas relativistas son una herramienta poderosa para modelar objetos astronómicos, tales como estrellas compactas y cúmulos de galaxias. En este trabajo presentamos un algoritmo basado en una red neuronal artificial (ANN) y series de Taylor para modelar esferas de gas relativistas usando las ecuaciones diferenciales de Tolman-Oppenheimer-Volkoff (TOV). La comparación de las soluciones analíticas con las numéricas muestra una buena concordancia, con errores relativos máximos de 10&#8722;3. El algoritmo ANN implementa una red neuronal de tres niveles con pro-alimentación, construida usando una técnica de aprendizaje con retro-propagación basada en la regla del gradiente descendente. Analizamos las relaciones masa-radio y los perfiles de densidad de las esferas relativistas isotérmicas y comparamos las soluciones ANN con las analíticas. Esta comparación muestra la eficiencia de ANN para resolver las ecuacines TOV.]]></p></abstract>
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