https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Steane_code 2026-05-24T10:25:46Z Revision history for this page on the wiki MediaWiki 1.43.0-wmf.28 https://en.formulasearchengine.com/index.php?title=Steane_code&diff=14294&oldid=prev 2012-10-19T05:42:47Z

<p><a href="/index.php?title=En:WP:CLEANER&amp;action=edit&amp;redlink=1" class="new" title="En:WP:CLEANER (page does not exist)">WPCleaner</a> v1.19 - fix link to <a href="/index.php?title=Standard_form&amp;action=edit&amp;redlink=1" class="new" title="Standard form (page does not exist)">standard form</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <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 07:42, 19 October 2012</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <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;">Hello</del>. <del style="font-weight: bold; text-decoration: none;">Let me introduce the author</del>. <del style="font-weight: bold; text-decoration: none;">Her name </del>is <del style="font-weight: bold; text-decoration: none;">Refugia Shryock. </del>[<del style="font-weight: bold; text-decoration: none;">http://Www.anylabtestnow.com/franchises/hialeah-33012/ California</del>] <del style="font-weight: bold; text-decoration: none;"> home </del>[<del style="font-weight: bold; text-decoration: none;">http://exchange.craftemergency.org/thankyous/can-men-be-sexually-harassed-ladies std testing at home</del>] <del style="font-weight: bold; text-decoration: none;"> home std test test </del>is <del style="font-weight: bold; text-decoration: none;">exactly where her </del>[<del style="font-weight: bold; text-decoration: none;">http://premium.asslikethat.com/user/CSalerno at home std testing</del>] is <del style="font-weight: bold; text-decoration: none;">but she needs to transfer because of her family</del>. <del style="font-weight: bold; text-decoration: none;">Since she was 18 she'</del>s <del style="font-weight: bold; text-decoration: none;">been operating as </del>a <del style="font-weight: bold; text-decoration: none;">receptionist but her marketing never comes. 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text-decoration: none;">com/user/RWhiteman http</del>:<del style="font-weight: bold; text-decoration: none;">//www.hotporn123.com/</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;">{{Unreferenced|date=December 2009}}</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;">[[File:Apollonian circles</ins>.<ins style="font-weight: bold; text-decoration: none;">svg|thumb|The [[Apollonian circles]], two orthogonal families of circles</ins>.<ins style="font-weight: bold; text-decoration: none;">]]</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;">A '''family of curves''' </ins>is <ins style="font-weight: bold; text-decoration: none;">a [</ins>[<ins style="font-weight: bold; text-decoration: none;">Set (mathematics)|set]</ins>] <ins style="font-weight: bold; text-decoration: none;">of [</ins>[<ins style="font-weight: bold; text-decoration: none;">curve]</ins>]<ins style="font-weight: bold; text-decoration: none;">s, each of which </ins>is <ins style="font-weight: bold; text-decoration: none;">given by a [[function (mathematics)|function]] or </ins>[<ins style="font-weight: bold; text-decoration: none;">[parametric equation|parametrization]</ins>] <ins style="font-weight: bold; text-decoration: none;">in which one or more of the parameters </ins>is <ins style="font-weight: bold; text-decoration: none;">variable</ins>. <ins style="font-weight: bold; text-decoration: none;">In general, the parameter(</ins>s<ins style="font-weight: bold; text-decoration: none;">) influence the shape of the curve in a way that is more complicated than </ins>a <ins style="font-weight: bold; text-decoration: none;">simple [</ins>[<ins style="font-weight: bold; text-decoration: none;">linear transformation]]</ins>. <ins style="font-weight: bold; text-decoration: none;">Sets of curves given by an implicit relation may also represent families of curves</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;">Families of curves appear frequently in solutions of [[differential equation]]s; when an additive [[constant </ins>of <ins style="font-weight: bold; text-decoration: none;">integration]</ins>] is <ins style="font-weight: bold; text-decoration: none;">introduced, it will usually be manipulated algebraically until </ins>it <ins style="font-weight: bold; text-decoration: none;">no longer represents </ins>a <ins style="font-weight: bold; text-decoration: none;">simple linear transformation</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;">Families of curves may also arise in other areas. For example, all non-degenerate [[conic sections]] can be represented using a single polar equation with one parameter, the eccentricity of the curve: </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>&lt;<ins style="font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="font-weight: bold; text-decoration: none;">r(\theta) = {e \over 1+e \cos \theta}</ins>&lt;<ins style="font-weight: bold; text-decoration: none;">/math</ins>&gt;</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;">as the value of e changes, the appearance of the curve varies in a relatively complicated way.</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;">== Applications ==</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;">Families of curves may arise in various topics in geometry, including the [[envelope (mathematics)|envelope]] of a set of curves and the [</ins>[<ins style="font-weight: bold; text-decoration: none;">caustic (optics)|caustic]] of a given curve</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;">== Generalizations ==</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;">In [[algebraic geometry]], an algebraic generalization is given by the notion of a [[linear system of divisors]]</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;">{{DEFAULTSORT:Family Of Curves}}</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</ins>:<ins style="font-weight: bold; text-decoration: none;">Algebraic geometry]</ins>]</div></td></tr> </table>

en>Niceguyedc https://en.formulasearchengine.com/index.php?title=Steane_code&diff=249315&oldid=prev 2012-08-29T07:10:27Z

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en>David Eppstein