<html><body><div style="font-family: arial, helvetica, sans-serif; font-size: 12pt; color: #330066"><div>Hi Jasper,<br></div><div><br data-mce-bogus="1"></div><div>Thanks for your answer. This is a good news ! However, at lunch time I thought about it a bit more and figured out that one has to take into account the fact that a permanent magnet is anisotropic and therefore we should use a permeability tensor instead of a scalar constant ... this will make the formulation much more complicated !<br data-mce-bogus="1"></div><div><br data-mce-bogus="1"></div><div>Cheers,<br data-mce-bogus="1"></div><div><br data-mce-bogus="1"></div><div> Gilles<br data-mce-bogus="1"></div><div><br></div><hr id="zwchr" data-marker="__DIVIDER__"><div data-marker="__HEADERS__"><blockquote style="border-left:2px solid #1010FF;margin-left:5px;padding-left:5px;color:#000;font-weight:normal;font-style:normal;text-decoration:none;font-family:Helvetica,Arial,sans-serif;font-size:12pt;"><b>De: </b>"Jasper" <funkybob@gmail.com><br><b>À: </b>"Gilles Quéméner" <quemener@lpccaen.in2p3.fr><br><b>Cc: </b>"getdp" <getdp@onelab.info><br><b>Envoyé: </b>Mercredi 9 Août 2017 16:37:12<br><b>Objet: </b>Re: [Getdp] Permanent magnet in GetDP<br></blockquote></div><div data-marker="__QUOTED_TEXT__"><blockquote style="border-left:2px solid #1010FF;margin-left:5px;padding-left:5px;color:#000;font-weight:normal;font-style:normal;text-decoration:none;font-family:Helvetica,Arial,sans-serif;font-size:12pt;"><div dir="ltr">Hi Gilles,<br><div>Your suggestion is typically the way I've done it in the past, specify by HcB and mu_r. From my understanding, in a NdFeB magnet at low temperatures this linear relation should be valid and the results have appear plausible so far :-)</div><div>Keep in mind that once the relatively small difference between e.g. N40 and N42 starts to matter in your simulation you should really consult your magnet supplier as the magnets typically have tolerances and are also not completely homogenous etc...</div><br><div>Best regards,</div><br><div>Jasper</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Aug 9, 2017 at 11:55 AM, gilles quemener <span dir="ltr"><<a href="mailto:quemener@lpccaen.in2p3.fr" target="_blank">quemener@lpccaen.in2p3.fr</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div style="font-family:arial,helvetica,sans-serif;font-size:12pt;color:#330066"><div>Hi,<br></div><br><div>Following my previous message, I digged more into the .pro files of GetDP demos magnet.xxx<br></div><div>and it seems that one could perhaps use both Hc and µ_r to distinguish between NdFeB magnets grades.<br></div><div>In GetDP demos, the permanent magnets material could be defined as in MaterialDatabase.pro w/<br></div><div>the following lines :<br></div><div><br> // NdFeB magnet N45<br> Materials() += Str[ "NdFeB_Grade_N45" ];<br> NdFeB_mur = 1.172; // Br = 1370 mT, Hcb = 930000 A/m and µ_r = Br / Hcb / µ_o<br> NdFeB_sigma = 2e5;<br> NdFeB_hc = 930000;<br><br></div><div>where µ_r and Hcb values have been taken from the ttypical table below.<br></div><div><div>Could anyone confirm or infirm this approach ?</div><br></div><div><table cellspacing="0" border="1"><colgroup width="93" span="9"></colgroup> <colgroup width="147"></colgroup> <colgroup width="102"></colgroup><tbody><tr><td height="19" align="left"><br></td><td align="right">Remanence</td><td align="right"><br></td><td align="right">coercivity</td><td align="right"><br></td><td align="right">coercivity</td><td align="right"><br></td><td align="right">product</td><td align="right"><br></td><td align="left"><br></td><td align="left"><br></td></tr><tr><td height="19" align="left"><br></td><td align="right">Br</td><td align="right"><br></td><td align="right">Hcb</td><td align="right"><br></td><td align="right">Hcj</td><td align="right"><br></td><td align="right">B H max</td><td align="right"><br></td><td align="right">µ = Br / Hcb</td><td align="right">µ_r= µ / µo</td></tr><tr><td height="19" align="left"><br></td><td align="right">mT</td><td align="right"><br></td><td align="right">kA/m</td><td align="right"><br></td><td align="right">kA/m</td><td align="right"><br></td><td align="right">kJ/m3</td><td align="right"><br></td><td align="left"> T/A/m<br></td><td align="left"><br></td></tr><tr><td height="19" align="left"><br></td><td align="right">min</td><td align="right">typ</td><td align="right">min</td><td align="right">typ</td><td align="right">min</td><td align="right">min</td><td align="right">typ</td><td align="right">°C</td><td align="left"><br></td><td align="left"><br></td></tr><tr><td height="19" align="left">N-35</td><td align="right">1170</td><td align="right">1120</td><td align="right">870</td><td align="right">920</td><td align="right">955</td><td align="right">263</td><td align="right">279</td><td align="right">80</td><td align="right">1.217391E-06</td><td align="right">0.969</td></tr><tr><td height="19" align="left">N-38</td><td align="right">1220</td><td align="right">1260</td><td align="right">870</td><td align="right">920</td><td align="right">955</td><td align="right">279</td><td align="right">303</td><td align="right">80</td><td align="right">1.369565E-06</td><td align="right">1.090</td></tr><tr><td height="19" align="left">N-40</td><td align="right">1260</td><td align="right">1300</td><td align="right">870</td><td align="right">920</td><td align="right">955</td><td align="right">303</td><td align="right">318</td><td align="right">80</td><td align="right">1.413043E-06</td><td align="right">1.124</td></tr><tr><td height="19" align="left">N-42</td><td align="right">1300</td><td align="right">1330</td><td align="right">870</td><td align="right">920</td><td align="right">955</td><td align="right">318</td><td align="right">334</td><td align="right">80</td><td align="right">1.445652E-06</td><td align="right">1.150</td></tr><tr><td height="19" align="left">N-45</td><td align="right">1330</td><td align="right">1370</td><td align="right">900</td><td align="right">930</td><td align="right">955</td><td align="right">334</td><td align="right">358</td><td align="right">80</td><td align="right">1.473118E-06</td><td align="right">1.172</td></tr><tr><td height="19" align="left">N-48</td><td align="right">1370</td><td align="right">1410</td><td align="right">900</td><td align="right">930</td><td align="right">875</td><td align="right">358</td><td align="right">382</td><td align="right">80</td><td align="right">1.516129E-06</td><td align="right">1.206</td></tr><tr><td height="19" align="left">N-50</td><td align="right">1410</td><td align="right">1440</td><td align="right">830</td><td align="right">850</td><td align="right">875</td><td align="right">382</td><td align="right">398</td><td align="right">80</td><td align="right">1.694118E-06</td><td align="right">1.348</td></tr><tr><td height="19" align="left">N-52</td><td align="right">1430</td><td align="right">1480</td><td align="right">820</td><td align="right">840</td><td align="right">875</td><td align="right">398</td><td align="right">422</td><td align="right">80</td><td align="right">1.761905E-06</td><td align="right">1.402</td></tr><tr><td height="19" align="left">N-33M</td><td align="right">1140</td><td align="right">1170</td><td align="right">830</td><td align="right">859</td><td align="right">1114</td><td align="right">239</td><td align="right">263</td><td align="right">100</td><td align="right">1.362049E-06</td><td align="right">1.084</td></tr><tr><td height="19" align="left">N-35M</td><td align="right">1170</td><td align="right">1220</td><td align="right">870</td><td align="right">891</td><td align="right">1114</td><td align="right">263</td><td align="right">279</td><td align="right">100</td><td align="right">1.369248E-06</td><td align="right">1.090</td></tr><tr><td height="19" align="left">N-38M</td><td align="right">1220</td><td align="right">1260</td><td align="right">900</td><td align="right">915</td><td align="right">1114</td><td align="right">279</td><td align="right">303</td><td align="right">100</td><td align="right">1.377049E-06</td><td align="right">1.096</td></tr><tr><td height="19" align="left">N-40M</td><td align="right">1260</td><td align="right">1300</td><td align="right">930</td><td align="right">915</td><td align="right">1114</td><td align="right">303</td><td align="right">318</td><td align="right">100</td><td align="right">1.420765E-06</td><td align="right">1.131</td></tr><tr><td height="19" align="left">N-42M</td><td align="right">1300</td><td align="right">1330</td><td align="right">950</td><td align="right">915</td><td align="right">1114</td><td align="right">318</td><td align="right">334</td><td align="right">100</td><td align="right">1.453552E-06</td><td align="right">1.157</td></tr><tr><td height="19" align="left">N-45M</td><td align="right">1330</td><td align="right">1370</td><td align="right">980</td><td align="right">915</td><td align="right">1114</td><td align="right">334</td><td align="right">358</td><td align="right">100</td><td align="right">1.497268E-06</td><td align="right">1.191</td></tr><tr><td height="19" align="left">N-48M</td><td align="right">1370</td><td align="right">1410</td><td align="right">1010</td><td align="right">980</td><td align="right">1114</td><td align="right">358</td><td align="right">382</td><td align="right">90</td><td align="right">1.438776E-06</td><td align="right">1.145</td></tr><tr><td height="19" align="left">N-50M</td><td align="right">1410</td><td align="right">1440</td><td align="right">1030</td><td align="right">980</td><td align="right">1114</td><td align="right">382</td><td align="right">398</td><td align="right">90</td><td align="right">1.469388E-06</td><td align="right">1.169</td></tr><tr><td height="19" align="left">N-30H</td><td align="right">1080</td><td align="right">1140</td><td align="right">810</td><td align="right">810</td><td align="right">1353</td><td align="right">223</td><td align="right">239</td><td align="right">120</td><td align="right">1.407407E-06</td><td align="right">1.120</td></tr><tr><td height="19" align="left">N-33H</td><td align="right">1140</td><td align="right">1170</td><td align="right">830</td><td align="right">830</td><td align="right">1353</td><td align="right">239</td><td align="right">263</td><td align="right">120</td><td align="right">1.409639E-06</td><td align="right">1.122</td></tr><tr><td height="19" align="left">N-35H</td><td align="right">1170</td><td align="right">1220</td><td align="right">870</td><td align="right">870</td><td align="right">1353</td><td align="right">263</td><td align="right">279</td><td align="right">120</td><td align="right">1.402299E-06</td><td align="right">1.116</td></tr><tr><td height="19" align="left">N-38H</td><td align="right">1220</td><td align="right">1260</td><td align="right">900</td><td align="right">900</td><td align="right">1353</td><td align="right">279</td><td align="right">303</td><td align="right">120</td><td align="right">1.400000E-06</td><td align="right">1.114</td></tr><tr><td height="19" align="left">N-40H</td><td align="right">1260</td><td align="right">1300</td><td align="right">930</td><td align="right">930</td><td align="right">1353</td><td align="right">303</td><td align="right">318</td><td align="right">120</td><td align="right">1.397849E-06</td><td align="right">1.112</td></tr><tr><td height="19" align="left">N-42H</td><td align="right">1300</td><td align="right">1330</td><td align="right">950</td><td align="right">950</td><td align="right">1353</td><td align="right">318</td><td align="right">334</td><td align="right">120</td><td align="right">1.400000E-06</td><td align="right">1.114</td></tr><tr><td height="19" align="left">N-44H</td><td align="right">1330</td><td align="right">1360</td><td align="right">970</td><td align="right">970</td><td align="right">1353</td><td align="right">334</td><td align="right">350</td><td align="right">120</td><td align="right">1.402062E-06</td><td align="right">1.116</td></tr><tr><td height="19" align="left">N-46H</td><td align="right">1360</td><td align="right">1380</td><td align="right">980</td><td align="right">980</td><td align="right">1353</td><td align="right">350</td><td align="right">366</td><td align="right">120</td><td align="right">1.408163E-06</td><td align="right">1.121</td></tr><tr><td height="19" align="left">N-48H</td><td align="right">1380</td><td align="right">1410</td><td align="right">1010</td><td align="right">1060</td><td align="right">1353</td><td align="right">366</td><td align="right">382</td><td align="right">120</td><td align="right">1.330189E-06</td><td align="right">1.059</td></tr><tr><td height="19" align="left">N-30SH</td><td align="right">1080</td><td align="right">1140</td><td align="right">810</td><td align="right">860</td><td align="right">1592</td><td align="right">223</td><td align="right">239</td><td align="right">150</td><td align="right">1.325581E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-33SH</td><td align="right">1140</td><td align="right">1170</td><td align="right">830</td><td align="right">880</td><td align="right">1592</td><td align="right">239</td><td align="right">263</td><td align="right">150</td><td align="right">1.329545E-06</td><td align="right">1.058</td></tr><tr><td height="19" align="left">N-35SH</td><td align="right">1170</td><td align="right">1220</td><td align="right">870</td><td align="right">920</td><td align="right">1592</td><td align="right">263</td><td align="right">279</td><td align="right">150</td><td align="right">1.326087E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-38SH</td><td align="right">1220</td><td align="right">1260</td><td align="right">900</td><td align="right">950</td><td align="right">1592</td><td align="right">279</td><td align="right">303</td><td align="right">150</td><td align="right">1.326316E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-40SH</td><td align="right">1260</td><td align="right">1300</td><td align="right">930</td><td align="right">980</td><td align="right">1592</td><td align="right">303</td><td align="right">318</td><td align="right">150</td><td align="right">1.326531E-06</td><td align="right">1.056</td></tr><tr><td height="19" align="left">N-42SH</td><td align="right">1300</td><td align="right">1330</td><td align="right">950</td><td align="right">1000</td><td align="right">1592</td><td align="right">318</td><td align="right">334</td><td align="right">150</td><td align="right">1.330000E-06</td><td align="right">1.058</td></tr><tr><td height="19" align="left">N-44SH</td><td align="right">1330</td><td align="right">1360</td><td align="right">970</td><td align="right">1020</td><td align="right">1592</td><td align="right">334</td><td align="right">350</td><td align="right">150</td><td align="right">1.333333E-06</td><td align="right">1.061</td></tr><tr><td height="19" align="left">N-28UH</td><td align="right">1040</td><td align="right">1080</td><td align="right">770</td><td align="right">810</td><td align="right">1989</td><td align="right">199</td><td align="right">223</td><td align="right">180</td><td align="right">1.333333E-06</td><td align="right">1.061</td></tr><tr><td height="19" align="left">N-30UH</td><td align="right">1080</td><td align="right">1140</td><td align="right">810</td><td align="right">860</td><td align="right">1989</td><td align="right">223</td><td align="right">239</td><td align="right">180</td><td align="right">1.325581E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-33UH</td><td align="right">1140</td><td align="right">1170</td><td align="right">830</td><td align="right">880</td><td align="right">1989</td><td align="right">239</td><td align="right">263</td><td align="right">180</td><td align="right">1.329545E-06</td><td align="right">1.058</td></tr><tr><td height="19" align="left">N-35UH</td><td align="right">1170</td><td align="right">1220</td><td align="right">870</td><td align="right">920</td><td align="right">1989</td><td align="right">263</td><td align="right">279</td><td align="right">180</td><td align="right">1.326087E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-38UH</td><td align="right">1220</td><td align="right">1260</td><td align="right">900</td><td align="right">950</td><td align="right">1989</td><td align="right">279</td><td align="right">303</td><td align="right">180</td><td align="right">1.326316E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-40UH</td><td align="right">1250</td><td align="right">1280</td><td align="right">900</td><td align="right">950</td><td align="right">1989</td><td align="right">302</td><td align="right">326</td><td align="right">180</td><td align="right">1.347368E-06</td><td align="right">1.072</td></tr><tr><td height="19" align="left">N-28EH</td><td align="right">1040</td><td align="right">1080</td><td align="right">770</td><td align="right">810</td><td align="right">2387</td><td align="right">199</td><td align="right">223</td><td align="right">200</td><td align="right">1.333333E-06</td><td align="right">1.061</td></tr><tr><td height="19" align="left">N-30EH</td><td align="right">1080</td><td align="right">1140</td><td align="right">810</td><td align="right">860</td><td align="right">2387</td><td align="right">223</td><td align="right">239</td><td align="right">200</td><td align="right">1.325581E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-33EH</td><td align="right">1140</td><td align="right">1170</td><td align="right">830</td><td align="right">880</td><td align="right">2387</td><td align="right">239</td><td align="right">263</td><td align="right">200</td><td align="right">1.329545E-06</td><td align="right">1.058</td></tr><tr><td height="19" align="left">N-35EH</td><td align="right">1170</td><td align="right">1220</td><td align="right">870</td><td align="right">920</td><td align="right">2387</td><td align="right">263</td><td align="right">279</td><td align="right">200</td><td align="right">1.326087E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-38EH</td><td align="right">1220</td><td align="right">1260</td><td align="right">900</td><td align="right">950</td><td align="right">2387</td><td align="right">279</td><td align="right">303</td><td align="right">200</td><td align="right">1.326316E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-25AH</td><td align="right">970</td><td align="right">1020</td><td align="right">730</td><td align="right">770</td><td align="right">2787</td><td align="right">180</td><td align="right">200</td><td align="right">220</td><td align="right">1.324675E-06</td><td align="right">1.054</td></tr><tr><td height="19" align="left">N-28AH</td><td align="right">1040</td><td align="right">1080</td><td align="right">770</td><td align="right">810</td><td align="right">2787</td><td align="right">203</td><td align="right">218</td><td align="right">220</td><td align="right">1.333333E-06</td><td align="right">1.061</td></tr><tr><td height="19" align="left">N-30AH</td><td align="right">1080</td><td align="right">1140</td><td align="right">810</td><td align="right">860</td><td align="right">2787</td><td align="right">220</td><td align="right">250</td><td align="right">220</td><td align="right">1.325581E-06</td><td align="right">1.055</td></tr><tr><td height="19" align="left">N-25BH</td><td align="right">950</td><td align="right">1000</td><td align="right">710</td><td align="right">750</td><td align="right">3000</td><td align="right">170</td><td align="right">190</td><td align="right">230</td><td align="right">1.333333E-06</td><td align="right">1.061</td></tr><tr><td height="19" align="left">Data upto temperature column from :</td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td></tr><tr><td height="19" align="left"><a href="http://www.goudsmitmagnets.com/magnets-assemblies/permanent-magnets/neodymium-magnets-ndfeb/neodymium-magnets-ndfeb" target="_blank">http://www.goudsmitmagnets.com/magnets-assemblies/permanent-magnets/neodymium-magnets-ndfeb/neodymium-magnets-ndfeb</a><br data-mce-bogus="1"></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td><td align="left"><br></td></tr></tbody></table><div style="clear:both"><br></div></div><div>Cheers,<br></div><br><div><div><div> <span style="color:#003366"> Gilles <br></span></div></div><div><table style="width:747px;table-layout:fixed;height:141px" cellpadding="3" border="0"><tbody><tr><td style="width:280px"><br></td><td><br></td></tr></tbody></table><br><table style="width:792px;table-layout:fixed;height:145px" cellpadding="0" border="0"><tbody><tr><td style="width:200px;text-align:left"></td><td><span style="color:#000080;font-size:10pt"></span><span style="color:#000080;font-size:10pt"></span></td></tr></tbody></table></div></div><br><hr id="m_-4741375849683933128zwchr"><div><blockquote style="border-left:2px solid #1010ff;margin-left:5px;padding-left:5px;color:#000;font-weight:normal;font-style:normal;text-decoration:none;font-family:Helvetica,Arial,sans-serif;font-size:12pt"><b>De: </b>"Gilles Quéméner" <<a href="mailto:quemener@lpccaen.in2p3.fr" target="_blank">quemener@lpccaen.in2p3.fr</a>><br><b>À: </b>"getdp" <<a href="mailto:getdp@onelab.info" target="_blank">getdp@onelab.info</a>><br><b>Envoyé: </b>Mercredi 9 Août 2017 10:21:31<br><b>Objet: </b>Permanent magnet in GetDP<br></blockquote></div><div><div class="h5"><div><blockquote style="border-left:2px solid #1010ff;margin-left:5px;padding-left:5px;color:#000;font-weight:normal;font-style:normal;text-decoration:none;font-family:Helvetica,Arial,sans-serif;font-size:12pt"><div style="font-family:arial,helvetica,sans-serif;font-size:12pt;color:#330066"><div>Hi,<br></div><br><div>When simulating permanent NdFeB magnets in a homemade BEM program, I use a permeability of 1.05 and a remanent magnetization/field<br></div><div>depending on the magnet grade as given for instance in the following table :<br></div><br><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">Minimum Values</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">Grade Br Hc (Hcb) Hci (Hcj) BHmax</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif"> (T) (kA/m) (kA/m) (kJ/m³)</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N27 1.030 796 955 199</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N30 1.080 796 955 223</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N33 1.130 836 955 247</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N35 1.170 867 955 263</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N38 1.210 899 955 287</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N40 1.240 923 955 302</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N42 1.280 923 955 318</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N45 1.320 875 955 342</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N48 1.380 836 875 366</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N50 1.400 796 875 382</span><br><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">N52 1.430 796 875 398</span><br></div><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif"><br></span></div><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">Looking closer to the magnet.xxx files in the GetDP demos folder, I cannot figure out how the <br></span></div><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">remanent magnetization is taken into account as only Hc seems to be used in the material definition.<br></span></div><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">I would think that both Hc and Br should be used.<br></span></div><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">How would one distinguish between N40 and N42 grades which have the same Hc values ? How the fact </span></div><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">that an N50 magnet has a larger remanent field than an N40 one is accounted for in GetDP when </span></div><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">Hc(N50) is smaller than Hc(N40) and equal to Hc(N27) ?<br></span></div><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif"><br></span></div><div><span style="font-family:"courier new",courier,monaco,monospace,sans-serif">Thanks a lot for any hints,<br></span></div><br><div><div><div> <span style="color:#003366"> Gilles <br></span></div></div><div><table style="width:747px;table-layout:fixed;height:141px" cellpadding="3" border="0"><tbody><tr><td style="width:280px"><br></td><td><br></td></tr></tbody></table><br><table style="width:792px;table-layout:fixed;height:145px" cellpadding="0" border="0"><tbody><tr><td style="width:200px;text-align:left"></td><td><span style="color:#000080;font-size:10pt"></span><span style="color:#000080;font-size:10pt"></span></td></tr></tbody></table></div></div></div><br></blockquote></div></div></div></div></div><br>_______________________________________________<br>
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