https://en.formulasearchengine.com/index.php?title=Ventricular_hypertrophy&feed=atom&action=history
Ventricular hypertrophy - Revision history
2024-03-28T15:56:24Z
Revision history for this page on the wiki
MediaWiki 1.42.0-wmf.5
https://en.formulasearchengine.com/index.php?title=Ventricular_hypertrophy&diff=319476&oldid=prev
en>Paine Ellsworth: /* Mechanics of cardiac growth */ rm deprecated "coauthors" parameter - see Help:CS1 errors#deprecated params
2014-11-05T02:19:35Z
<p><span dir="auto"><span class="autocomment">Mechanics of cardiac growth: </span> rm deprecated "coauthors" parameter - see <a href="/index.php?title=Help:CS1_errors&action=edit&redlink=1" class="new" title="Help:CS1 errors (page does not exist)">Help:CS1 errors#deprecated params</a></span></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 03:19, 5 November 2014</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;">In [[mathematics]], an '''''LF</del>'<del style="font-weight: bold; text-decoration: none;">'-space''' is a [[topological vector space]] ''V'' that is a locally convex [[inductive limit]] of a countable inductive system <math>(V_n, i_{nm})</math> of [[Fréchet space]]</del>s<del style="font-weight: bold; text-decoration: none;">. This means that ''V'' is a [[direct limit]] of the system <math>(V_n</del>, <del style="font-weight: bold; text-decoration: none;">i_{nm})</math> in the category of [[locally convex]] topological vector spaces </del>and <del style="font-weight: bold; text-decoration: none;">each <math>V_n</math> is a Fréchet space.</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;">Ship</ins>'s <ins style="font-weight: bold; text-decoration: none;">Officer Bedell from Vanderhoof</ins>, <ins style="font-weight: bold; text-decoration: none;">has hobbies </ins>and <ins style="font-weight: bold; text-decoration: none;">interests for instance beach</ins>, <ins style="font-weight: bold; text-decoration: none;">[http:</ins>//<ins style="font-weight: bold; text-decoration: none;">vibeliving.com</ins>.<ins style="font-weight: bold; text-decoration: none;">au</ins>/<ins style="font-weight: bold; text-decoration: none;">?option</ins>=<ins style="font-weight: bold; text-decoration: none;">com_k2&view</ins>=<ins style="font-weight: bold; text-decoration: none;">itemlist&task</ins>=<ins style="font-weight: bold; text-decoration: none;">user&id</ins>=<ins style="font-weight: bold; text-decoration: none;">53146 commercial Property singapore</ins>] <ins style="font-weight: bold; text-decoration: none;">developers in singapore </ins>and <ins style="font-weight: bold; text-decoration: none;">architecture</ins>. <ins style="font-weight: bold; text-decoration: none;">Have been these days going to </ins> <ins style="font-weight: bold; text-decoration: none;">Al-Khutm </ins>and <ins style="font-weight: bold; text-decoration: none;">Al</ins>-<ins style="font-weight: bold; text-decoration: none;">Ayn</ins>.</div></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> </div></td><td colspan="2" class="diff-side-added"></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;">Original definition was also assuming that ''V'' is a strict locally convex inductive limit</del>, <del style="font-weight: bold; text-decoration: none;">which means that the topology induced on <math>V_n<</del>/<del style="font-weight: bold; text-decoration: none;">math> by <math>V_{n+1}<</del>/<del style="font-weight: bold; text-decoration: none;">math> is identical to the original topology on <math>V_n</math></del>.</div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">The topology on ''V'' can be described by specifying that an absolutely convex subset ''U'' is a neighborhood of 0 if and only if <math>U \cap V_n </math> is an absolutely convex neighborhood of 0 in <math>V_n<</del>/<del style="font-weight: bold; text-decoration: none;">math> for every n.</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">Properties</del>==</div></td><td colspan="2" class="diff-side-added"></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;">An LF space is [[complete</del>]<del style="font-weight: bold; text-decoration: none;">], [[barrelled space|barrelled]] and [[bornological space|bornological]] (and thus [[ultrabornological space|ultrabornological]]).</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">==Examples==</del></div></td><td colspan="2" class="diff-side-added"></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;">A typical example of an ''LF''-space is, <math>C^\infty_c(\mathbb{R}^n)</math>, the space of all infinitely differentiable functions on <math>\mathbb{R}^n</math> with compact support. The LF-space structure is obtained by considering a sequence of compact sets <math>K_1 \subset K_2 \subset \ldots \subset K_i \subset \ldots \subset \mathbb{R}^n</math> with <math>\bigcup_i K_i = \mathbb{R}^n</math> </del>and <del style="font-weight: bold; text-decoration: none;">for all i, <math>K_i</math> is a subset of the interior of <math>K_{i+1}</math>. Such a sequence could be the balls of radius ''i'' centered at the origin</del>. <del style="font-weight: bold; text-decoration: none;">The space <math>C_c^\infty(K_i)</math> of infinitely differentiable functions on <math>\mathbb{R}^n</math>with compact support contained in <math>K_i</math> has a natural [[Fréchet space]] structure </del>and <del style="font-weight: bold; text-decoration: none;"> <math>C^\infty_c(\mathbb{R}^n)</math> inherits its ''LF''-space structure as described above. The ''LF''</del>-<del style="font-weight: bold; text-decoration: none;">space topology does not depend on the particular sequence of compact sets <math>K_i</math></del>.</div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">With this ''LF''-space structure, <math>C^\infty_c(\mathbb{R}^n)</math> is known as the space of test functions, of fundamental importance in the [[distribution (mathematics)|theory of distributions]].</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">==References==</del></div></td><td colspan="2" class="diff-side-added"></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;">*{{citation|first=François|last=Treves|authorlink=François Treves|title=Topological Vector Spaces, Distributions and Kernels|publisher=Academic Press|year=1967|pages=p. 126 ff}}.</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">{{Functional Analysis}}</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">[[Category:Topological vector spaces]]</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
</table>
en>Paine Ellsworth
https://en.formulasearchengine.com/index.php?title=Ventricular_hypertrophy&diff=10371&oldid=prev
en>Monkbot: /* Physiology */Fix CS1 deprecated date parameter errors
2014-01-31T13:56:31Z
<p><span dir="auto"><span class="autocomment">Physiology: </span>Fix <a href="/index.php?title=Help:CS1_errors&action=edit&redlink=1" class="new" title="Help:CS1 errors (page does not exist)">CS1 deprecated date parameter errors</a></span></p>
<p><b>New page</b></p><div>In [[mathematics]], an '''''LF''-space''' is a [[topological vector space]] ''V'' that is a locally convex [[inductive limit]] of a countable inductive system <math>(V_n, i_{nm})</math> of [[Fréchet space]]s. This means that ''V'' is a [[direct limit]] of the system <math>(V_n, i_{nm})</math> in the category of [[locally convex]] topological vector spaces and each <math>V_n</math> is a Fréchet space.<br />
<br />
Original definition was also assuming that ''V'' is a strict locally convex inductive limit, which means that the topology induced on <math>V_n</math> by <math>V_{n+1}</math> is identical to the original topology on <math>V_n</math>.<br />
<br />
The topology on ''V'' can be described by specifying that an absolutely convex subset ''U'' is a neighborhood of 0 if and only if <math>U \cap V_n </math> is an absolutely convex neighborhood of 0 in <math>V_n</math> for every n.<br />
<br />
==Properties==<br />
An LF space is [[complete]], [[barrelled space|barrelled]] and [[bornological space|bornological]] (and thus [[ultrabornological space|ultrabornological]]).<br />
<br />
==Examples==<br />
A typical example of an ''LF''-space is, <math>C^\infty_c(\mathbb{R}^n)</math>, the space of all infinitely differentiable functions on <math>\mathbb{R}^n</math> with compact support. The LF-space structure is obtained by considering a sequence of compact sets <math>K_1 \subset K_2 \subset \ldots \subset K_i \subset \ldots \subset \mathbb{R}^n</math> with <math>\bigcup_i K_i = \mathbb{R}^n</math> and for all i, <math>K_i</math> is a subset of the interior of <math>K_{i+1}</math>. Such a sequence could be the balls of radius ''i'' centered at the origin. The space <math>C_c^\infty(K_i)</math> of infinitely differentiable functions on <math>\mathbb{R}^n</math>with compact support contained in <math>K_i</math> has a natural [[Fréchet space]] structure and <math>C^\infty_c(\mathbb{R}^n)</math> inherits its ''LF''-space structure as described above. The ''LF''-space topology does not depend on the particular sequence of compact sets <math>K_i</math>.<br />
<br />
With this ''LF''-space structure, <math>C^\infty_c(\mathbb{R}^n)</math> is known as the space of test functions, of fundamental importance in the [[distribution (mathematics)|theory of distributions]].<br />
<br />
==References==<br />
*{{citation|first=François|last=Treves|authorlink=François Treves|title=Topological Vector Spaces, Distributions and Kernels|publisher=Academic Press|year=1967|pages=p. 126 ff}}.<br />
<br />
{{Functional Analysis}}<br />
<br />
[[Category:Topological vector spaces]]</div>
en>Monkbot