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Polyproline helix - Revision history
2026-09-05T12:23:26Z
Revision history for this page on the wiki
MediaWiki 1.47.0-wmf.7
https://en.formulasearchengine.com/w/index.php?title=Polyproline_helix&diff=13879&oldid=prev
en>Amkilpatrick: Disambiguated: cis → Cis–trans isomerism
2013-08-16T06:48:31Z
<p>Disambiguated: <a href="/w/index.php?title=Cis&action=edit&redlink=1" class="new" title="Cis (page does not exist)">cis</a> → <a href="/w/index.php?title=Cis%E2%80%93trans_isomerism&action=edit&redlink=1" class="new" title="Cis–trans isomerism (page does not exist)">Cis–trans isomerism</a></p>
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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 08:48, 16 August 2013</td>
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<tr><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><del style="font-weight: bold; text-decoration: none;">The writer </del>is <del style="font-weight: bold; text-decoration: none;">known by the name </del>of <del style="font-weight: bold; text-decoration: none;">Numbers Wunder</del>. <del style="font-weight: bold; text-decoration: none;">Years ago he moved to North Dakota and his family members enjoys it</del>. <del style="font-weight: bold; text-decoration: none;">One </del>of <del style="font-weight: bold; text-decoration: none;">the issues she loves most is to study comics and she</del>'<del style="font-weight: bold; text-decoration: none;">ll </del>be <del style="font-weight: bold; text-decoration: none;">starting something else alongside with it</del>. <del style="font-weight: bold; text-decoration: none;">My working day job </del>is a <del style="font-weight: bold; text-decoration: none;">librarian.</del><<del style="font-weight: bold; text-decoration: none;">br</del>><<del style="font-weight: bold; text-decoration: none;">br</del>><del style="font-weight: bold; text-decoration: none;">my homepage: [http</del>://<del style="font-weight: bold; text-decoration: none;">www</del>.<del style="font-weight: bold; text-decoration: none;">shipzula</del>.<del style="font-weight: bold; text-decoration: none;">com</del>/<del style="font-weight: bold; text-decoration: none;">blogs</del>/<del style="font-weight: bold; text-decoration: none;">post</del>/<del style="font-weight: bold; text-decoration: none;">16377 at home std test</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><ins style="font-weight: bold; text-decoration: none;">In [[mathematics]], the '''Margulis lemma''' (named after [[Grigory Margulis]]) </ins>is <ins style="font-weight: bold; text-decoration: none;">a result about [[discrete subgroup]]s of isometries </ins>of <ins style="font-weight: bold; text-decoration: none;">a [[symmetric space]] (e</ins>.<ins style="font-weight: bold; text-decoration: none;">g</ins>. <ins style="font-weight: bold; text-decoration: none;">the [[hyperbolic space|hyperbolic n-space]]), or more generally a space </ins>of <ins style="font-weight: bold; text-decoration: none;">[[non-positive curvature]]. </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">Theorem: Let '''S''</ins>' be <ins style="font-weight: bold; text-decoration: none;">a [[Riemannian symmetric space]] of non-compact type</ins>. <ins style="font-weight: bold; text-decoration: none;">There </ins>is a <ins style="font-weight: bold; text-decoration: none;">positive constant </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">:</ins><<ins style="font-weight: bold; text-decoration: none;">math</ins>><ins style="font-weight: bold; text-decoration: none;">\epsilon=\epsilon(S)>0</ins><<ins style="font-weight: bold; text-decoration: none;">/math</ins>> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">with the following property. Let F be subset of isometries of '''S'''. Suppose there is a point x in '''S''' such that </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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>:<ins style="font-weight: bold; text-decoration: none;"><math>d(f \cdot x,x)<\epsilon<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">for all f in F. Assume further that the subgroup <math>\Gamma<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> generated by F is discrete in Isom('''S''')</ins>. <ins style="font-weight: bold; text-decoration: none;">Then <math>\Gamma</math> is virtually nilpotent</ins>. <ins style="font-weight: bold; text-decoration: none;">More precisely, there exists a subgroup <math>\Gamma_0</math> in <math>\Gamma<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> which is [[Nilpotent group|nilpotent]] of nilpotency class at most r and of [[Index of a subgroup|index]] at most N in <math>\Gamma<</ins>/<ins style="font-weight: bold; text-decoration: none;">math>, where r and N are constants depending on '''S''' only.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">The constant <math>\epsilon(S)<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> is often referred as the ''Margulis constant''.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">==References==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">{{refbegin}}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">*Werner Ballman, Mikhael Gromov, Victor Schroeder, ''Manifolds of Non-positive Curvature'', Birkhauser, Boston (1985) p.&nbsp;107</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">{{refend}}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">[[Category:Hyperbolic geometry]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">[[Category:Differential geometry]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">[[Category:Lemmas]</ins>]</div></td></tr>
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en>Amkilpatrick
https://en.formulasearchengine.com/w/index.php?title=Polyproline_helix&diff=248592&oldid=prev
en>SchreiberBike: Repairing links to disambiguation pages - You can help! - Trans
2012-05-05T22:02:09Z
<p>Repairing links to disambiguation pages - <a href="/w/index.php?title=WP:DPL&action=edit&redlink=1" class="new" title="WP:DPL (page does not exist)">You can help!</a> - <a href="/w/index.php?title=Trans&action=edit&redlink=1" class="new" title="Trans (page does not exist)">Trans</a></p>
<p><b>New page</b></p><div>The writer is known by the name of Numbers Wunder. Years ago he moved to North Dakota and his family members enjoys it. One of the issues she loves most is to study comics and she'll be starting something else alongside with it. My working day job is a librarian.<br><br>my homepage: [http://www.shipzula.com/blogs/post/16377 at home std test]</div>
en>SchreiberBike