<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Nesrine Kamouche</style></author><author><style face="normal" font="default" size="100%">Abdallah Benaissa</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Asymptotic expansion of double Laplace-type integrals: The case of non-stationary minimum points</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the American Mathematical Society</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><volume><style face="normal" font="default" size="100%">144</style></volume><pages><style face="normal" font="default" size="100%">3741-3756</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">In this paper, we show that the asymptotic expansion of a double Laplace-type integral with a non-stationary minimum point, located on the boundary of the domain of integration, is governed by the order of contact between the boundary curve and the level curve of the phase through the minimum point. This achievement will enable us to construct complete asymptotic expansions in more general settings. Especially, the problem will be completely solved if the phase and the boundary curve of the domain of integration are analytic near the minimum point.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Karima Chatouh</style></author><author><style face="normal" font="default" size="100%">kenza Guenda</style></author><author><style face="normal" font="default" size="100%">T. A Gulliver</style></author><author><style face="normal" font="default" size="100%">Lemnouar Noui</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Simplex and MacDonald codes over Rq</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Applied Mathematics and Computing</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><volume><style face="normal" font="default" size="100%">55</style></volume><pages><style face="normal" font="default" size="100%">455–478</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">{ In this paper, we introduce the homogeneous weight and homogeneous Gray map over the ring&amp;nbsp;Rq=F2[u1,u2,…,uq]/⟨u2i=0</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Karima Chatouh</style></author><author><style face="normal" font="default" size="100%">kenza Guenda</style></author><author><style face="normal" font="default" size="100%">T Aaron Gulliver</style></author><author><style face="normal" font="default" size="100%">Lemnouar Noui</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On some classes of linear codes over Z2Z4 and their covering radii</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Applied Mathematics and Computing</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><volume><style face="normal" font="default" size="100%">53</style></volume><pages><style face="normal" font="default" size="100%">201–222</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">In this paper, we define the simplex and MacDonald codes of types&amp;nbsp;αα&amp;nbsp;and&amp;nbsp;β&amp;nbsp;over&amp;nbsp;Z2Z4. We also examine the covering radii of these codes. Further, we study the binary images of these codes and prove that the binary image of the simplex codes of type&amp;nbsp;αα&amp;nbsp;meets the Gilbert bound.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Karima Chatouh</style></author><author><style face="normal" font="default" size="100%">kenza Guenda</style></author><author><style face="normal" font="default" size="100%">T. A Gulliver</style></author><author><style face="normal" font="default" size="100%">Lemnouar Noui</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Simplex and MacDonald codes over R&lt;sub&gt;q&lt;/sub&gt;</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Applied Mathematics and Computing</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><volume><style face="normal" font="default" size="100%">55</style></volume><pages><style face="normal" font="default" size="100%">455–478</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	In this paper, we introduce the homogeneous weight and homogeneous Gray map over the ring&amp;nbsp;R&lt;sub&gt;q&lt;/sub&gt;=F&lt;sub&gt;2&lt;/sub&gt;[u&lt;sub&gt;1&lt;/sub&gt;,u&lt;sub&gt;2&lt;/sub&gt;,…,u&lt;sub&gt;q&lt;/sub&gt;]/⟨u&lt;sup&gt;2&lt;/sup&gt;&lt;sub&gt;i&lt;/sub&gt;=0,u&lt;sub&gt;i&lt;/sub&gt;u&lt;sub&gt;j&lt;/sub&gt;=u&lt;sub&gt;j&lt;/sub&gt;u&lt;sub&gt;i&lt;/sub&gt;⟩&amp;nbsp;for&amp;nbsp;q≥1q≥1. We also consider the construction of simplex and MacDonald codes of types&amp;nbsp;α&amp;nbsp;and&amp;nbsp;β&amp;nbsp;over this ring and their covering radius.
&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Karima Chatouh</style></author><author><style face="normal" font="default" size="100%">kenza Guenda</style></author><author><style face="normal" font="default" size="100%">T Aaron Gulliver</style></author><author><style face="normal" font="default" size="100%">Lemnouar Noui</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On some classes of linear codes over Z&lt;sub&gt;2&lt;/sub&gt;Z&lt;sub&gt;4&lt;/sub&gt; and their covering radii</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Applied Mathematics and Computing</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><volume><style face="normal" font="default" size="100%">53</style></volume><pages><style face="normal" font="default" size="100%">201–222</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	In this paper, we define the simplex and MacDonald codes of types&amp;nbsp;αα&amp;nbsp;and&amp;nbsp;β&amp;nbsp;over&amp;nbsp;Z&lt;sub&gt;2&lt;/sub&gt;Z&lt;sub&gt;4&lt;/sub&gt;. We also examine the covering radii of these codes. Further, we study the binary images of these codes and prove that the binary image of the simplex codes of type&amp;nbsp;αα&amp;nbsp;meets the Gilbert bound.
&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Nesrine Kamouche</style></author><author><style face="normal" font="default" size="100%">Abdallah Benaissa</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Asymptotic expansion of double Laplace-type integrals: The case of non-stationary minimum points</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the American Mathematical Society</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><volume><style face="normal" font="default" size="100%">144</style></volume><pages><style face="normal" font="default" size="100%">3741-3756</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	In this paper, we show that the asymptotic expansion of a double Laplace-type integral with a non-stationary minimum point, located on the boundary of the domain of integration, is governed by the order of contact between the boundary curve and the level curve of the phase through the minimum point. This achievement will enable us to construct complete asymptotic expansions in more general settings. Especially, the problem will be completely solved if the phase and the boundary curve of the domain of integration are analytic near the minimum point.
&lt;/p&gt;
</style></abstract></record></records></xml>