Format Recommendations

Equations

Simplest Form

Example extracted from Wiki chapter titled: Dyson (1893)

$[\frac{π}{G M}] Φ_{T R}$

$=$

$- \frac{2 K (k)}{R_{1}},$

Raw text used to generate this simple equation:

<!-- (BEGIN) Raw Text Providing a Template for Mathematical Expression in its Simplest Form-->
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>\biggl[ \frac{\pi}{GM}\biggr] \Phi_\mathrm{TR}</math>
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>- \frac{2K(k)}{R_1}    \, ,</math>
  </td>
</tr>
</table>
<!-- (END) Raw Text Providing a Template for Mathematical Expression in its Simplest Form-->

With Title and References

Example extracted from Wiki chapter titled: Ostriker (1964)

Scalar Gravitational Potential
$Φ (\vec{x})$	$\equiv$	$- G ∭ \frac{ρ ({\vec{x}}^{^{'}})}{\| {\vec{x}}^{^{'}} - \vec{x} \|} d^{3} x^{'} .$
[BT87], p. 31, Eq. (2-3) [EFE], §10, p. 17, Eq. (11) [T78], §4.2, p. 77, Eq. (12)

Raw text used to generate this expression ensemble:

<!-- (BEGIN) Raw Text Providing a Template for Mathematical Expression with Title and References-->
<div align="center" id="GravitationalPotential">
<table border="0" cellpadding="5" align="center">
<tr>
  <td align="center" colspan="3">
<font color="#770000">'''Scalar Gravitational Potential'''</font>
  </td>
</tr>
<tr>
  <td align="right">
<math>\Phi(\vec{x})</math>
  </td>
  <td align="center">
<math>\equiv</math>
  </td>
  <td align="left">
<math> -G \iiint \frac{\rho(\vec{x}^{~'})}{|\vec{x}^{~'} - \vec{x}|} d^3x^' \, .</math>
  </td>
</tr>
<tr>
  <td align="center" colspan="3">
[<b>[[Appendix/References#BT87|<font color="red">BT87</font>]]</b>], p. 31, Eq. (2-3)<br />
[<b>[[Appendix/References#EFE|<font color="red">EFE</font>]]</b>], §10, p. 17, Eq. (11)<br />
[<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>], §4.2, p. 77, Eq. (12)
  </td>
</tr>
</table>
</div>
<!-- (END) Raw Text Providing a Template for Mathematical Expression with Title and References-->

Multiple Lines

Example extracted from Wiki chapter titled: Dyson (1893)

$[\frac{π}{G M}] Φ_{T R}$	$=$	$- \frac{2}{R_{1}} [(1 + k_{1}) K (k_{1})]$
	$=$	$- \frac{2 K (μ)}{R_{1}} [1 + \frac{R_{1} - R}{R_{1} + R}]$
	$=$	$- \frac{4 K (μ)}{R_{1} + R} .$

Raw text used to generate this multi-line expression:

<!-- (BEGIN) Raw Text Providing a Template for Multiline Mathematical Expression -->
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>\biggl[ \frac{\pi}{GM}\biggr] \Phi_\mathrm{TR}</math>
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>- \frac{2}{R_1} \biggl[(1+k_1)K(k_1) \biggr] </math>
  </td>
</tr>

<tr>
  <td align="right">
 
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>-  \frac{2K(\mu)}{R_1} \biggl[1+\frac{R_1-R}{R_1+R}  \biggr] </math>
  </td>
</tr>

<tr>
  <td align="right">
 
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>-  \frac{4K(\mu)}{R_1+R} \, .</math>
  </td>
</tr>
</table>
<!-- (END) Raw Text Providing a Template for Multiline Mathematical Expression -->

Darkgreen Quotation Inset

Example extracted from Wiki chapter titled: Onset of Bar-mode Instability …

"… the onset of instability is not very sensitive to the compressibility or angular momentum distribution of the polytrope when the models are parameterized by T/|W| — [in particular, the m = 2 barmode becomes unstable at T/|W| ∼ 0.26 - 0.28. ] The polytrope eigenfunctions are … qualitatively different from the Maclaurin eigenfunctions in one respect: they develop strong spiral arms. The spiral arms are stronger for more compressible polytropes and for polytropes whose angular momentum distributions deviate significantly from those of the Maclaurin spheroids."

— Drawn from Toman, Imamura, Pickett & Durisen (1998), ApJ, 497, 370

Raw text used to generate this example quotation inset:

<!-- (BEGIN) Raw Text Providing a Template for Darkgreen Quotation Inset-->
<table border="0" cellpadding="3" align="center" width="80%">
<tr><td align="left">
<font color="darkgreen">
"… the onset of instability is not very sensitive to the compressibility or angular momentum distribution of the polytrope when the models are parameterized by T/|W|</font> — [in particular, the m = 2 barmode becomes unstable at T/|W| ∼ 0.26 - 0.28. ] <font color="darkgreen">The polytrope eigenfunctions are … qualitatively different from the Maclaurin eigenfunctions in one respect: they develop strong spiral arms. The spiral arms are stronger for more compressible polytropes and for polytropes whose angular momentum distributions deviate significantly from those of the Maclaurin spheroids."
</font>
</td></tr>
<tr><td align="right">
— Drawn from [https://ui.adsabs.harvard.edu/abs/1998ApJ...497..370T/abstract Toman, Imamura, Pickett & Durisen (1998)], ApJ, 497, 370 
</td></tr></table>
<!-- (END) Raw Text Providing a Template for Darkgreen Quotation Inset-->

Pink Comment Balloon

Example extracted from Wiki chapter titled: Maclaurin Spheroids

Comment by J. E. Tohline: In Tassoul (1978), the leading coefficient in the expression for the pressure — and, hence, the central pressure — is too large by a factor of 2.

We know from our separate discussion of supplemental, barotropic equations of state that, for a uniform-density,

n = 0

polytropic configuration, the pressure is related to the enthalpy via the expression,

P = H ρ

. Hence, we conclude that,

$P (ϖ, z)$	$=$	$π G ρ^{2} a_{1}^{2} A_{3} (1 - e^{2}) [1 - (\frac{ϖ}{a_{1}})^{2} - (\frac{z}{a_{3}})^{2}]$
[T78], §4.5, p. 86, Eq. (51) [ST83], §7.3, p. 172, Eqs. (7.3.16) & (7.3.17)

Raw text used to generate this illustration of the pink comment balloon:

<!-- (BEGIN) raw text illustrating pink comment balloon -->
[[File:CommentButton02.png|right|100px|Comment by J. E. Tohline:  In Tassoul (1978), the leading coefficient in the expression for the pressure — and, hence, the central pressure — is too large by a factor of 2.]]We know from our [[SR#Barotropic_Structure|separate discussion of supplemental, barotropic equations of state]] that, for a uniform-density, <math>~n = 0</math> polytropic configuration, the pressure is related to the enthalpy via the expression, <math>~P = H\rho</math>.  Hence, we conclude that,
<table align="center" border="0" cellpadding="5">
<tr>
  <td align="right">
<math>
P(\varpi,z)
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
\pi G \rho^2 a_1^2 A_3 (1-e^2)\biggl[1 - \biggl( \frac{\varpi}{a_1} \biggr)^2 - \biggl( \frac{z}{a_3} \biggr)^2  
\biggr] 
</math>
  </td>
</tr>
<tr>
  <td align="center" colspan="3">
[<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>], §4.5, p. 86, Eq. (51)<br />
[<b>[[Appendix/References#ST83|<font color="red">ST83</font>]]</b>], §7.3, p. 172, Eqs. (7.3.16) & (7.3.17)
  </td>
</tr>
</table>
<!-- (END) raw text illustrating pink comment balloon -->

Wikitable Overflow

Example extracted from Wiki chapter titled: Toroidal Configurations and Related Coordinate Systems

Example 2
$ϖ_{t}$	$r_{t}$		$Z_{0}$		$a$		$K$
$\frac{3}{4}$	$\frac{1}{4}$		$\frac{3}{4}$		$\frac{1}{3}$		$(\frac{5}{12})^{2}$
Torus Intersection Points
$ξ_{1}$	$β$	$ℓ$	Intersection #1 (superior sign)			Intersection #2 (inferior sign)
$ξ_{1}$	$β$	$ℓ$	$ξ_{2}$	$ϖ_{i}$	$z_{i}$	$ξ_{2}$	$ϖ_{i}$	$z_{i}$
$1.1927843$	$+ 0.138485$	$1.000000$	$0.885198$	$0.704606$	$0.245844$	Degenerate Coordinate Values
$1.176$	$+ 0.116568$	$0.981258$	$0.922142$	$0.812595$	$0.242037$	$0.841611$	$0.616896$	$0.211621$
$1.160$	$+ 0.092267$	$0.962725$	$0.933386$	$0.864726$	$0.222121$	$0.824945$	$0.584858$	$0.187691$
$1.144$	$+ 0.063705$	$0.943871$	$0.940238$	$0.908969$	$0.192948$	$0.813713$	$0.560766$	$0.163372$
$1.127$	$+ 0.027202$	$0.924221$	$0.944608$	$0.949856$	$0.150191$	$0.806047$	$0.539788$	$0.135318$
$1.111$	$- 0.015045$	$0.907444$	$0.946487$	$0.980806$	$0.096065$	$0.802617$	$0.523232$	$0.105244$
$1.094$	$- 0.071947$	$0.894425$	$0.945995$	$0.999208$	$0.019887$	$0.803522$	$0.509118$	$0.066901$
$1.078$	$- 0.142539$	$0.892548$	$0.942353$	$0.989322$	$- 0.072283$	$0.810056$	$0.500846$	$0.020554$
$1.061$	$- 0.247448$	$0.916366$	$0.932024$	$0.916375$	$- 0.186599$	$0.827074$	$0.505248$	$- 0.050956$
$1.0449467$	$- 0.398902$	$1.000000$	$0.885198$	$0.632605$	$- 0.220722$	Degenerate Coordinate Values

In order to see how this overflow command works, place your mouse cursor anywhere inside the displayed table, then scroll down/up. Here is the raw text illustrating how to handle "Wikitable Overflow":

<!-- (BEGIN) Raw Text Providing Example of Wikitable Overflow -->
<div id="Example2" style="width: 85%; height: 15em; overflow: auto;">
<table align="center" border="1" cellpadding="5">
<tr><th align="center" colspan="10">Example 2</th></tr>
<tr>
  <td align="center" colspan="2" width="25%"><math>~\varpi_t</math></td>
  <td align="center" colspan="2" width="25%"><math>~r_t</math></td>
  <td align="center" colspan="2" width="25%"><math>~Z_0</math></td>
  <td align="center" colspan="2"><math>~a</math></td>
  <td align="center" colspan="2"><math>~\Kappa</math></td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~\tfrac{3}{4}</math></td>
  <td align="center" colspan="2"><math>~\tfrac{1}{4}</math></td>
  <td align="center" colspan="2"><math>~\tfrac{3}{4}</math></td>
  <td align="center" colspan="2"><math>~\tfrac{1}{3}</math></td>
  <td align="center" colspan="2"><math>~(\tfrac{5}{12})^2</math></td>
</tr>
<tr>
  <th colspan="10" align="center">Torus Intersection Points</th>
</tr>
<tr>
  <td align="center" colspan="2" rowspan="2"><math>~\xi_1</math></td>
  <td align="center" colspan="1" rowspan="2"><math>~\beta</math></td>
  <td align="center" colspan="1" rowspan="2"><math>~\ell</math></td>
  <td align="center" colspan="3" bgcolor="yellow">Intersection #1 (''superior'' sign)</td>
  <td align="center" colspan="3" bgcolor="yellow">Intersection #2 (''inferior'' sign)</td>
</tr>
<tr>
  <td align="center"><math>~\xi_2</math>
  <td align="center"><math>~\varpi_i</math>
  <td align="center"><math>~z_i</math>
  <td align="center"><math>~\xi_2</math>
  <td align="center"><math>~\varpi_i</math>
  <td align="center"><math>~z_i</math>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.1927843</math></td>
  <td align="center" colspan="1"><math>~+0.138485</math></td>
  <td align="center" colspan="1"><math>~1.000000</math></td>
  <td align="center" colspan="1"><math>~0.885198</math></td>
  <td align="center" colspan="1"><math>~0.704606</math></td>
  <td align="center" colspan="1"><math>~0.245844</math></td>
  <td align="center" colspan="3">Degenerate Coordinate Values</td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.176</math></td>
  <td align="center" colspan="1"><math>~+0.116568</math></td>
  <td align="center" colspan="1"><math>~0.981258</math></td>
  <td align="center" colspan="1"><math>~0.922142</math></td>
  <td align="center" colspan="1"><math>~0.812595</math></td>
  <td align="center" colspan="1"><math>~0.242037</math></td>
  <td align="center" colspan="1"><math>~0.841611</math></td>
  <td align="center" colspan="1"><math>~0.616896</math></td>
  <td align="center" colspan="1"><math>~0.211621</math></td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.160</math></td>
  <td align="center" colspan="1"><math>~+0.092267</math></td>
  <td align="center" colspan="1"><math>~0.962725</math></td>
  <td align="center" colspan="1"><math>~0.933386</math></td>
  <td align="center" colspan="1"><math>~0.864726</math></td>
  <td align="center" colspan="1"><math>~0.222121</math></td>
  <td align="center" colspan="1"><math>~0.824945</math></td>
  <td align="center" colspan="1"><math>~0.584858</math></td>
  <td align="center" colspan="1"><math>~0.187691</math></td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.144</math></td>
  <td align="center" colspan="1"><math>~+0.063705</math></td>
  <td align="center" colspan="1"><math>~0.943871</math></td>
  <td align="center" colspan="1"><math>~0.940238</math></td>
  <td align="center" colspan="1"><math>~0.908969</math></td>
  <td align="center" colspan="1"><math>~0.192948</math></td>
  <td align="center" colspan="1"><math>~0.813713</math></td>
  <td align="center" colspan="1"><math>~0.560766</math></td>
  <td align="center" colspan="1"><math>~0.163372</math></td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.127</math></td>
  <td align="center" colspan="1"><math>~+0.027202</math></td>
  <td align="center" colspan="1"><math>~0.924221</math></td>
  <td align="center" colspan="1"><math>~0.944608</math></td>
  <td align="center" colspan="1"><math>~0.949856</math></td>
  <td align="center" colspan="1"><math>~0.150191</math></td>
  <td align="center" colspan="1"><math>~0.806047</math></td>
  <td align="center" colspan="1"><math>~0.539788</math></td>
  <td align="center" colspan="1"><math>~0.135318</math></td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.111</math></td>
  <td align="center" colspan="1"><math>~-0.015045</math></td>
  <td align="center" colspan="1"><math>~0.907444</math></td>
  <td align="center" colspan="1"><math>~0.946487</math></td>
  <td align="center" colspan="1"><math>~0.980806</math></td>
  <td align="center" colspan="1"><math>~0.096065</math></td>
  <td align="center" colspan="1"><math>~0.802617</math></td>
  <td align="center" colspan="1"><math>~0.523232</math></td>
  <td align="center" colspan="1"><math>~0.105244</math></td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.094</math></td>
  <td align="center" colspan="1"><math>~-0.071947</math></td>
  <td align="center" colspan="1"><math>~0.894425</math></td>
  <td align="center" colspan="1"><math>~0.945995</math></td>
  <td align="center" colspan="1"><math>~0.999208</math></td>
  <td align="center" colspan="1"><math>~0.019887</math></td>
  <td align="center" colspan="1"><math>~0.803522</math></td>
  <td align="center" colspan="1"><math>~0.509118</math></td>
  <td align="center" colspan="1"><math>~0.066901</math></td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.078</math></td>
  <td align="center" colspan="1"><math>~-0.142539</math></td>
  <td align="center" colspan="1"><math>~0.892548</math></td>
  <td align="center" colspan="1"><math>~0.942353</math></td>
  <td align="center" colspan="1"><math>~0.989322</math></td>
  <td align="center" colspan="1"><math>~-0.072283</math></td>
  <td align="center" colspan="1"><math>~0.810056</math></td>
  <td align="center" colspan="1"><math>~0.500846</math></td>
  <td align="center" colspan="1"><math>~0.020554</math></td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.061</math></td>
  <td align="center" colspan="1"><math>~-0.247448</math></td>
  <td align="center" colspan="1"><math>~0.916366</math></td>
  <td align="center" colspan="1"><math>~0.932024</math></td>
  <td align="center" colspan="1"><math>~0.916375</math></td>
  <td align="center" colspan="1"><math>~-0.186599</math></td>
  <td align="center" colspan="1"><math>~0.827074</math></td>
  <td align="center" colspan="1"><math>~0.505248</math></td>
  <td align="center" colspan="1"><math>~-0.050956</math></td>
</tr>
<tr>
  <td align="center" colspan="2"><math>~1.0449467</math></td>
  <td align="center" colspan="1"><math>~-0.398902</math></td>
  <td align="center" colspan="1"><math>~1.000000</math></td>
  <td align="center" colspan="1"><math>~0.885198</math></td>
  <td align="center" colspan="1"><math>~0.632605</math></td>
  <td align="center" colspan="1"><math>~-0.220722</math></td>
  <td align="center" colspan="3">Degenerate Coordinate Values</td>
</tr>
</table>
</div>
<!-- (END) Raw Text Providing Example of Wikitable Overflow -->

Permissions

Here is an example layout that we have adopted to provide a record of Permissions that have been granted to us by other authors and/or publishers to reproduce figures (and/or digitally clipped images of other material) from previously published (usually journal) articles.

🔵

Wiki chapter titled: Dyson (1893)

Author(s):	F. W. (Frank Watson) Dyson
Title:	II. The Potential of an Anchor Ring
Reference:	F. W. Dyson (1893, Philosophical Transactions of the Royal Society of London. A., 184, 43 - 95)
DOI:	https://doi.org/10.1098/rsta.1893.0002
(Scanned Images) Copyright:	© 2017, Royal Society
Publisher:	Royal Society Publishing
(Apparently) Relevant Permission:	"You do not need to seek permissions for re-use of material over 70 years old for up to 5 articles or figures — re-use is only subject to acknowledgement."
Information Entry:	2021/09/15

Here is the raw text that has been typed into our MediaWiki editor in order to generate this example Permissions layout. Generally speaking the statements of permission that we have received from various authors/publishers have been grouped in our Permissions Appendix, but this raw text can be cut (from here) and pasted into any other MediaWiki-formatted chapter to serve as a template of this adopted Permissions format.

<!-- (BEGIN) Raw Text Providing a Template for Recorded Permissions -->
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2"> 
Wiki chapter titled: &nbsp; [[Apps/DysonPotential#Evaluation|Dyson (1893)]]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%"> </td>
  <td align="left" colspan="2"> 
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">F. W. (Frank Watson) Dyson</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''II.   The Potential of an Anchor Ring''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893, Philosophical Transactions of the Royal Society of London. A., 184, 43 - 95)]</td>
</tr>
<tr>
  <td align="right">DOI:</td>
  <td align="left">[https://doi.org/10.1098/rsta.1893.0002 https://doi.org/10.1098/rsta.1893.0002]</td>
</tr>
<tr>
  <td align="right">(Scanned Images) Copyright:</td>
  <td align="left">&copy; 2017, Royal Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Royal Society Publishing</td>
</tr>
<tr>
  <td align="right">(Apparently)<br />Relevant Permission:</td>
  <td align="left">"[https://royalsociety.org/journals/permissions/ You do not need to seek permissions for re-use of material over 70 years old for up to 5 articles or figures &#8212; re-use is only subject to acknowledgement.]"</td>
</tr>
<tr>
  <td align="right">Information Entry:</td>
  <td align="left">2021/09/15</td>
</tr>
</table>
  </td>
</tr>
</table>
<!-- (END) Raw Text Providing a Template for Recorded Permissions -->

Appendix/FormatRecommendations

Contents

Format Recommendations

Equations

Simplest Form

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Multiple Lines

Darkgreen Quotation Inset

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Wikitable Overflow

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See Also

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Appendix/FormatRecommendations

Format Recommendations

Equations

Simplest Form

With Title and References

Multiple Lines

Darkgreen Quotation Inset

Pink Comment Balloon

Wikitable Overflow

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