<?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%">Benaissa, Abdallah</style></author><author><style face="normal" font="default" size="100%">Benlahcene, Moussa</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematica SlovacaMathematica Slovaca</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">3</style></number><volume><style face="normal" font="default" size="100%">67</style></volume><pages><style face="normal" font="default" size="100%">737–750</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 consider the problem of the asymptotic expansion of double Laplace-type integrals, in the case when the set&amp;nbsp;γ&amp;nbsp;of points where the phase achieves its absolute minimum is a simple curve. It will be shown that the asymptotic behaviour of such integrals is governed by the order of degeneracy of normal derivatives of the phase with respect to the curve&amp;nbsp;γ. Complete asymptotic expansions will be constructed if that order is constant along&amp;nbsp;γ, and the first two coefficients will be explicitly computed. If not, a uniform asymptotic expansion method, involving special functions, is suggested.</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%">Kamouche, Nesrine</style></author><author><style face="normal" font="default" size="100%">Benaissa, Abdallah</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 SocietyProceedings of the American Mathematical Society</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></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>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Benaissa, Abdallah</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC EXPANSION OF DOUBLE OSCILLATORY INTEGRALS: CONTRIBUTION OF NON STATIONARY CRITICAL POINTS OF THE SECOND KIND</style></title><secondary-title><style face="normal" font="default" size="100%">International Conference on Pure and Applied Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><pages><style face="normal" font="default" size="100%">49</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></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%">Benaissa, Abdallah</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the exit problem of dynamic systems perturbed by a white noise</style></title><secondary-title><style face="normal" font="default" size="100%">AIP Conference ProceedingsAIP Conference Proceedings</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">1</style></number><volume><style face="normal" font="default" size="100%">1660</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&amp;nbsp; In this paper we are concerned with the exit time problem of a dynamic system perturbed by a&amp;nbsp;white noise,&amp;nbsp;in the case where the noiseless dynamics has a global&amp;nbsp;attractor&amp;nbsp;in a given domain. By the use of a singular&amp;nbsp;perturbation technique&amp;nbsp;and recent results on the asymptotic expansion of a class of Laplace-type integrals, new results concerning the problem under investigation will be presented. &amp;nbsp;</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%">Benaissa, Abdallah</style></author><author><style face="normal" font="default" size="100%">Roger, Claude</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Développement asymptotique d'intégrales oscillantes doubles…</style></title><secondary-title><style face="normal" font="default" size="100%">Comptes Rendus de l'Académie des Sciences-Series I-MathematicsComptes Rendus de l'Académie des Sciences-Series I-Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2001</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2001</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">1</style></number><volume><style face="normal" font="default" size="100%">333</style></volume><pages><style face="normal" font="default" size="100%">17-22</style></pages><isbn><style face="normal" font="default" size="100%">0764-4442</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language></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%">Melkemi, Lamine</style></author><author><style face="normal" font="default" size="100%">Benaissa, Abdallah</style></author><author><style face="normal" font="default" size="100%">Benacer, Rachid</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Factorisation QR des matrices de Tchebychev–Vandermonde confluentes</style></title><secondary-title><style face="normal" font="default" size="100%">Comptes Rendus de l'Académie des Sciences-Series I-MathematicsComptes Rendus de l'Académie des Sciences-Series I-Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2000</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2000</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">2</style></number><volume><style face="normal" font="default" size="100%">330</style></volume><pages><style face="normal" font="default" size="100%">147-152</style></pages><isbn><style face="normal" font="default" size="100%">0764-4442</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language></record></records></xml>