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Mozyraska-Torres logarithm is negative on (0,1) - Revision history
2024-03-29T12:01:30Z
Revision history for this page on the wiki
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http://timescalewiki.org/index.php?title=Mozyraska-Torres_logarithm_is_negative_on_(0,1)&diff=2209&oldid=prev
Tom at 15:13, 21 January 2023
2023-01-21T15:13:53Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:13, 21 January 2023</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm is increasing|next=Mozyrska-Torres logarithm is positive on (1,infinity)}}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm is increasing|next=Mozyrska-Torres logarithm is positive on (1,infinity)}}</div></td></tr>
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Tom
http://timescalewiki.org/index.php?title=Mozyraska-Torres_logarithm_is_negative_on_(0,1)&diff=1719&oldid=prev
Tom at 15:27, 21 October 2017
2017-10-21T15:27:56Z
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==References==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==References==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>{{PaperReference|The Natural Logarithm on Time Scales|<del class="diffchange diffchange-inline">2009</del>|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm is increasing|next=Mozyrska-Torres logarithm is positive on (1,infinity)}}</div></td><td class='diff-marker'>+</td><td style="color:black; 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>{{PaperReference|The Natural Logarithm on Time Scales|<ins class="diffchange diffchange-inline">2008</ins>|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm is increasing|next=Mozyrska-Torres logarithm is positive on (1,infinity)}}</div></td></tr>
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Tom
http://timescalewiki.org/index.php?title=Mozyraska-Torres_logarithm_is_negative_on_(0,1)&diff=1713&oldid=prev
Tom at 15:22, 21 October 2017
2017-10-21T15:22:31Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:22, 21 October 2017</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Theorem==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Theorem==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>Let $\mathbb{T}$ be a [[time scale]]. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$, where $L_{\<del class="diffchange diffchange-inline">mathb</del>{T}}$ denotes the [[Mozyrska-Torres logarithm]].  </div></td><td class='diff-marker'>+</td><td style="color:black; 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>Let $\mathbb{T}$ be a [[time scale]]. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$, where $L_{\<ins class="diffchange diffchange-inline">mathbb</ins>{T}}$ denotes the [[Mozyrska-Torres logarithm]].  </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Proof==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Proof==</div></td></tr>
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Tom
http://timescalewiki.org/index.php?title=Mozyraska-Torres_logarithm_is_negative_on_(0,1)&diff=1712&oldid=prev
Tom at 15:22, 21 October 2017
2017-10-21T15:22:21Z
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Theorem==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Theorem==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>Let $\mathbb{T}$ be a [[time scale]]. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$.  </div></td><td class='diff-marker'>+</td><td style="color:black; 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>Let $\mathbb{T}$ be a [[time scale]]. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$<ins class="diffchange diffchange-inline">, where $L_{\mathb{T}}$ denotes the [[Mozyrska-Torres logarithm]]</ins>.  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Proof==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Proof==</div></td></tr>
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Tom
http://timescalewiki.org/index.php?title=Mozyraska-Torres_logarithm_is_negative_on_(0,1)&diff=1711&oldid=prev
Tom at 15:22, 21 October 2017
2017-10-21T15:22:03Z
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==References==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==References==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>{{PaperReference|The Natural Logarithm on Time Scales|2009|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm is increasing|next=<del class="diffchange diffchange-inline">Mozyraska</del>-Torres logarithm is positive on (1,infinity)}}</div></td><td class='diff-marker'>+</td><td style="color:black; 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>{{PaperReference|The Natural Logarithm on Time Scales|2009|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm is increasing|next=<ins class="diffchange diffchange-inline">Mozyrska</ins>-Torres logarithm is positive on (1,infinity)}}</div></td></tr>
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Tom
http://timescalewiki.org/index.php?title=Mozyraska-Torres_logarithm_is_negative_on_(0,1)&diff=1707&oldid=prev
Tom: Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$. ==Proof== ==References== {{PaperReference|The Natural Loga..."
2017-10-21T15:20:06Z
<p>Created page with "==Theorem== Let $\mathbb{T}$ be a <a href="/index.php/Time_scale" title="Time scale">time scale</a>. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$. ==Proof== ==References== {{PaperReference|The Natural Loga..."</p>
<p><b>New page</b></p><div>==Theorem==<br />
Let $\mathbb{T}$ be a [[time scale]]. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$. <br />
<br />
==Proof==<br />
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==References==<br />
{{PaperReference|The Natural Logarithm on Time Scales|2009|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm is increasing|next=Mozyraska-Torres logarithm is positive on (1,infinity)}}</div>
Tom