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<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'>The department
of Mathematics and Statistics invites you to a seminar by </span>Prof. Irina
Markina (<st1:place w:st="on"><st1:City w:st="on">University of Bergen</st1:City>,
 <st1:country-region w:st="on">Norway</st1:country-region></st1:place>):</font><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=2
color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'>---------------------------------------------------------------------------------------</span></font><font
size=2 color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;
font-family:Arial;color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'>Title:&nbsp; </span>Optimal
control versus sub-Riemannian geometry: physical and mechanical applications</font><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'><o:p></o:p></span></font></p>

<p class=section1><font size=3 face="Times New Roman"><span lang=EN-IE
style='font-size:12.0pt'>Abstract:&nbsp; </span>In this communication we
present a formulation of optimal control systems for problems with
non-holonomic constraints in a geometric way introducing the notion of the
sub-Riemannian geometry. We give some examples of sub-Riemannian manifolds
related to the Lie groups and principal bundles that appear in physics and
mechanics. We discuss advantages of the geometric methods and open problems. </font><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'>---------------------------------------------------------------------------------------</span></font><font
size=2 color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;
font-family:Arial;color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=2
color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;font-family:
Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'>The seminar
will take place on <b><span style='font-weight:bold'>Wednesday 18<sup>th</sup>
November, at 2pm</span></b>, in A2-002.</span></font><font size=2 color=navy
face=Arial><span lang=EN-IE style='font-size:10.0pt;font-family:Arial;
color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=2
color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;font-family:
Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'>If you have
any questions regarding this seminar, please direct them to Sarah Mitchell (061
202259, <a href="mailto:sarah.mitchell@ul.ie"
title="blocked::mailto:sarah.mitchell@ul.ie"><font size=2 color=navy
face=Arial title="blocked::mailto:sarah.mitchell@ul.ie"><span
title="blocked::mailto:sarah.mitchell@ul.ie"><span style='font-size:10.0pt;
font-family:Arial;color:navy'>sarah.mitchell@ul.ie</span></span></font></a>).&nbsp;
A full list of Seminars for this semester can be found at: </span></font><font
size=2 color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;
font-family:Arial;color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=2
color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;font-family:
Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'><a
href="http://www.staff.ul.ie/mitchells/MACSI_seminars.html"
title="blocked::http://www.staff.ul.ie/mitchells/MACSI_seminars.html"><font
size=2 color=navy face=Arial
title="blocked::http://www.staff.ul.ie/mitchells/MACSI_seminars.html"><span
title="blocked::http://www.staff.ul.ie/mitchells/MACSI_seminars.html"><span
style='font-size:10.0pt;font-family:Arial;color:navy'>http://www.staff.ul.ie/mitchells/MACSI_seminars.html</span></span></font></a></span></font><font
size=2 color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;
font-family:Arial;color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=2
color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;font-family:
Arial;color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'>----------------------------------------------------------------------------</span></font><font
size=2 color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;
font-family:Arial;color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'>Supported by
Science Foundation Ireland Mathematics Initiative funding, MACSI - the
Mathematics Applications Consortium for Science and Industry (<a
href="www.macsi.ie" title="blocked::www.macsi.ie"><font size=2 color=navy
face=Arial title="blocked::www.macsi.ie"><span title="blocked::www.macsi.ie"><span
title="blocked::www.macsi.ie"><span style='font-size:10.0pt;font-family:Arial;
color:navy;text-decoration:none'>www.macsi.ie</span></span></span></font></a>),
centred at the University of Limerick, is dedicated to the mathematical
modelling and solution of problems which arise in science, engineering and
industry in Ireland</span></font><font size=2 color=navy face=Arial><span
lang=EN-IE style='font-size:10.0pt;font-family:Arial;color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'>----------------------------------------------</span></font><font
size=2 color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;
font-family:Arial;color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span lang=EN-IE style='font-size:12.0pt'><img border=0
width=142 height=142 id="_x0000_i1025" src="cid:image001.jpg@01CA675A.F9383B50"></span></font><font
size=2 color=navy face=Arial><span lang=EN-IE style='font-size:10.0pt;
font-family:Arial;color:navy'><o:p></o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=2
color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'><o:p>&nbsp;</o:p></span></font></p>

<p class=section1 style='margin:0cm;margin-bottom:.0001pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'><o:p>&nbsp;</o:p></span></font></p>

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