https://katlas.org/index.php?action=history&feed=atom&title=Burau%27s_Theorem
Burau's Theorem - Revision history
2026-05-15T13:00:03Z
Revision history for this page on the wiki
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https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1720992&oldid=prev
Drorbn at 19:07, 20 October 2013
2013-10-20T19:07:54Z
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Drorbn
https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1689578&oldid=prev
IvaH at 15:20, 29 November 2007
2007-11-29T15:20:02Z
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> K = Mirror[Knot[11, NonAlternating, 52]]]) // DrawMorseLink</div></td>
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IvaH
https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1689576&oldid=prev
IvaH at 15:12, 29 November 2007
2007-11-29T15:12:08Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:12, 29 November 2007</td>
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IvaH
https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1689575&oldid=prev
IvaH at 15:00, 29 November 2007
2007-11-29T15:00:36Z
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> K = Mirror[Knot[11, NonAlternating, 52]]]) // DrawMorseLink</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> K = Mirror[Knot[11, NonAlternating, 52]]]) // DrawMorseLink</div></td>
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IvaH
https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1689519&oldid=prev
IvaH at 23:50, 18 November 2007
2007-11-18T23:50:42Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:50, 18 November 2007</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> K = Mirror[Knot[11, NonAlternating, 52]]]) // DrawMorseLink</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>out= <nowiki>-Graphics-</nowiki>}}</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><!--END--> </div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><!--END--> </div></td>
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IvaH
https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1689518&oldid=prev
IvaH at 23:44, 18 November 2007
2007-11-18T23:44:00Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:44, 18 November 2007</td>
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<td colspan="2" class="diff-lineno">Line 21:</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> K = Mirror[Knot[11, NonAlternating, 52]]]) // DrawMorseLink</div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> K = Mirror[Knot[11, NonAlternating, 52]]]) // DrawMorseLink</div></td>
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<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></nowiki> |</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></nowiki> |</div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>img= Burau'<del style="font-weight: bold; text-decoration: none;">s Theorem_Out_3</del>.gif |</div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>img= Burau'<ins style="font-weight: bold; text-decoration: none;">s_Theorem_Out_3</ins>.gif |</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>out= <nowiki>-Graphics-</nowiki>}}</div></td>
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IvaH
https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1689516&oldid=prev
IvaH at 23:32, 18 November 2007
2007-11-18T23:32:42Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:32, 18 November 2007</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><!--Robot Land, no human edits to "END"--></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Graphics|</div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Graphics|</div></td>
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<td class="diff-marker" data-marker="−"></td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>n = <del style="font-weight: bold; text-decoration: none;">2</del> |</div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>n = <ins style="font-weight: bold; text-decoration: none;">3</ins> |</div></td>
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<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>in = <nowiki>(cc = CableComponent[BR[6, {1, 2, 3, 4, 5}], </div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>in = <nowiki>(cc = CableComponent[BR[6, {1, 2, 3, 4, 5}], </div></td>
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<tr>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> K = Mirror[Knot[11, NonAlternating, 52]]]) // DrawMorseLink</div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> K = Mirror[Knot[11, NonAlternating, 52]]]) // DrawMorseLink</div></td>
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<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></nowiki> |</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></nowiki> |</div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>img= <del style="font-weight: bold; text-decoration: none;">User_IvaH_Examples2_Out_2</del>.gif |</div></td>
<td class="diff-marker" data-marker="+"></td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>img= <ins style="font-weight: bold; text-decoration: none;">Burau's Theorem_Out_3</ins>.gif |</div></td>
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<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>out= <nowiki>-Graphics-</nowiki>}}</div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>out= <nowiki>-Graphics-</nowiki>}}</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><!--END--> </div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><!--Robot Land, no human edits to "END"--></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{InOut|</div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{InOut|</div></td>
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<td class="diff-marker" data-marker="−"></td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>n = <del style="font-weight: bold; text-decoration: none;">3</del> |</div></td>
<td class="diff-marker" data-marker="+"></td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>n = <ins style="font-weight: bold; text-decoration: none;">4</ins> |</div></td>
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<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>in = <nowiki>Alexander[#][t] & /@ {cc, K}</nowiki> |</div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>in = <nowiki>Alexander[#][t] & /@ {cc, K}</nowiki> |</div></td>
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<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>out= <nowiki> -18 6 14 6 12 18</div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>out= <nowiki> -18 6 14 6 12 18</div></td>
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IvaH
https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1689515&oldid=prev
IvaH at 23:31, 18 November 2007
2007-11-18T23:31:48Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:31, 18 November 2007</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><!--$$Import["http://katlas.org/wiki/CableComponent.m&action=raw"];$$--></div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><!--$$Import["http://katlas.org/wiki/CableComponent.m&action=raw"];$$--></div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><!--Robot Land, no human edits to "END"--></div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{In|</div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>n = 2 |</div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>in = <nowiki>Import["http://katlas.org/wiki/CableComponent.m&action=raw"];</nowiki>}}</div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><!--END--></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><!--$$(cc = CableComponent[BR[6, {1, 2, 3, 4, 5}], </div></td>
<td class="diff-marker"></td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><!--$$(cc = CableComponent[BR[6, {1, 2, 3, 4, 5}], </div></td>
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IvaH
https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1689511&oldid=prev
IvaH at 22:59, 18 November 2007
2007-11-18T22:59:47Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{In|n=2|in=**** Enter the same definition for <code>CableComponent</code> as in [[Cabling]] **** }}</div></td>
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IvaH
https://katlas.org/index.php?title=Burau%27s_Theorem&diff=1689493&oldid=prev
Drorbn at 18:53, 25 October 2007
2007-10-25T18:53:45Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:53, 25 October 2007</td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><br /></td>
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Drorbn