Index: sansmodels/src/sans/models/media/model_functions.html
===================================================================
--- sansmodels/src/sans/models/media/model_functions.html	(revision 940aca737db034347a7b2bcbe30f143b76e47cbc)
+++ sansmodels/src/sans/models/media/model_functions.html	(revision e040559221c7f4660f0a3dfc4e9a805d2c6aefe2)
@@ -444,5 +444,7 @@
 {margin-bottom:0in;}
 -->
-</style><title></title></head>
+</style><title></title>
+
+</head>
 <body lang="EN-US" link="blue" vlink="purple">
 <div class="WordSection1">
@@ -453,5 +455,5 @@
 <li class="MsoNormal" style="line-height: 115%;"><a href="#Introduction"><b>Introduction</b></a>
 </li>
-<li class="MsoNormal" style="line-height: 115%;"><a href="#Shapes"><b>Shapes</b></a>: <a href="#SphereModel">SphereModel</a>, <a href="#BinaryHSModel">BinaryHSModel</a>, <a href="#FuzzySphereModel">FuzzySphereModel</a>, <a href="#CoreShellModel">CoreShellModel</a>,&nbsp;<a href="#Core2ndMomentModel">Core2ndMomentModel</a>, <a href="#CoreMultiShellModel">CoreMultiShellModel</a>, <a href="#VesicleModel">VesicleModel</a>, <a href="#MultiShellModel">MultiShellModel</a>, &nbsp;<a href="#OnionExpShellModel">OnionExpShellModel</a>, <a href="#SphericalSLDModel">SphericalSLDModel</a>, <a href="#LinearPearlsModel">LinearPearlsModel</a>, <a href="#PearlNecklaceModel">PearlNecklaceModel</a> , <a href="#CylinderModel">CylinderModel</a>, <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>,
+<li class="MsoNormal" style="line-height: 115%;"><a href="#Shapes"><b>Shapes</b></a>: <a href="#SphereModel">SphereModel</a>, <a href="#BinaryHSModel">BinaryHSModel</a>, <a href="#FuzzySphereModel">FuzzySphereModel</a>, <a href="#RaspBerryModel">RaspBerryModel</a>, <a href="#CoreShellModel">CoreShellModel</a>,&nbsp;<a href="#Core2ndMomentModel">Core2ndMomentModel</a>, <a href="#CoreMultiShellModel">CoreMultiShellModel</a>, <a href="#VesicleModel">VesicleModel</a>, <a href="#MultiShellModel">MultiShellModel</a>, &nbsp;<a href="#OnionExpShellModel">OnionExpShellModel</a>, <a href="#SphericalSLDModel">SphericalSLDModel</a>, <a href="#LinearPearlsModel">LinearPearlsModel</a>, <a href="#PearlNecklaceModel">PearlNecklaceModel</a> , <a href="#CylinderModel">CylinderModel</a>, <a href="#CoreShellCylinderModel">CoreShellCylinderModel</a>,
 <a href="#CoreShellBicelleModel">CoreShellBicelleModel</a>,<a href="#HollowCylinderModel">HollowCylinderModel</a>,
 <a href="#FlexibleCylinderModel">FlexibleCylinderModel</a>,
@@ -531,9 +533,9 @@
 particle:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image001.PNG" ></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image001.PNG"></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">with</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 8pt;"><img src="image002.PNG" ></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 8pt;"><img src="image002.PNG"></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">where <i>P</i><sub>0</sub><i>(<b>q</b>)</i>
@@ -550,5 +552,5 @@
 particle
 volume fraction:<span style="position: relative; top: 5pt;">
-<img src="image003.PNG" ></span>.</p>
+<img src="image003.PNG"></span>.</p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">Our so-called 1D scattering intensity
@@ -588,5 +590,5 @@
 way (Guinier, 1955):</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image004.PNG" ></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image004.PNG"></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
@@ -726,5 +728,5 @@
 calculation is an exact multi-component solution:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 5pt;"><img src="image006.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 5pt;"><img src="image006.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
@@ -740,5 +742,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 24pt;"><img src="image007.PNG" ></span>.</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 24pt;"><img src="image007.PNG"></span>.</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
@@ -746,5 +748,5 @@
 <p class="MsoNormal">The 2D scattering intensity is the
 same as 1D, regardless of
-the orientation of the <i>q</i> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG" ></span><span style="font-size: 14pt;">.</span></p>
+the orientation of the <i>q</i> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG"></span><span style="font-size: 14pt;">.</span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
@@ -904,5 +906,5 @@
 calculated as:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image010.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image010.PNG"></span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">where the amplitude A(q) is given as
@@ -912,5 +914,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 18pt;"><img src="image011.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 18pt;"><img src="image011.PNG"></span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
@@ -947,5 +949,5 @@
 <p class="MsoNormal">For 2D data: The 2D scattering
 intensity is calculated in
-the same way as 1D, where the <i>q</i> vector is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG" ></span><span style="font-size: 14pt;">.</span></p>
+the same way as 1D, where the <i>q</i> vector is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG"></span><span style="font-size: 14pt;">.</span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">REFERENCE</p>
@@ -1049,6 +1051,170 @@
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
+<p class="MsoNormal">
+</p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.4.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></b><a name="RaspBerryModel"></a><b><span style="font-size: 14pt;">RaspBerryModel</span></b></p>
+&nbsp;<b> <br>
+</b>Calculates the form factor, P(q), for a "Raspberry-like"
+structure where there are smaller spheres at the surface of a larger
+sphere, such as the structure of a Pickering emulsion.&nbsp;
+<p class="MsoNormal">&nbsp;</p>
+<p class="MsoNormal" style="margin-left: 0.85in; text-indent: -0.35in;"><b>1.1.</b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;
+</span>Definition</b></p>
+<p class="MsoNormal">&nbsp;</p>
+The structure is:<br>
+<img src="raspberry_pic.jpg">
+<p class="MsoNormal"><br>
+Ro = the radius of the&nbsp;large sphere<br>
+Rp = the radius of the smaller sphere on the surface<br>
+delta = the fractional penetration depth<br>
+surface coverage = fractional coverage of the large sphere surface (0.9
+max)<br>
+<br>
+<br>
+The large and small spheres have their own SLD, as well as the solvent.
+The surface coverage term is a fractional coverage (maximum of
+approximately 0.9 for hexagonally packed spheres on a surface). Since
+not all of the small spheres are necessarily attached to the surface,
+the excess free (small) spheres scattering is also included in the
+calculation. The function calculated follows equations (8)-(12) of the
+reference below, and the equations are not reproduced here.<br>
+<br>
+The returned value is scaled to units of [cm-1]. No interparticle
+scattering is included in this model.<br>
+<br>
+</p>
+<p class="MsoNormal">For 2D data: The 2D scattering
+intensity is calculated in
+the same way as 1D, where the <i>q</i> vector is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG"></span><span style="font-size: 14pt;">.</span></p>
+<p class="MsoNormal">&nbsp;</p>
+&nbsp;&nbsp; REFERENCE<br>
+Kjersta Larson-Smith, Andrew Jackson, and Danilo C
+Pozzo, "Small angle scattering model for Pickering emulsions and
+raspberry particles." Journal of Colloid and Interface Science (2010)
+vol. 343 (1) pp. 36-41.<br>
+<p class="MsoNormal">&nbsp;</p>
+<p class="MsoNormal">TEST DATASET</p>
+<p class="MsoNormal">This example dataset is produced by
+running the RaspBerryModel, using 2000 data points, qmin = 0.0001 Å<sup>-1</sup>,&nbsp;
+qmax = 0.2 A<sup>-1</sup> and the default values, where
+Ssph/Lsph stands for Smaller/Large sphere and&nbsp;surfrac_Ssph for
+the surface fraction of the smaller spheres.</p>
+<p class="MsoNormal">&nbsp;</p>
+<div align="center">
+<table class="MsoNormalTable" style="border-collapse: collapse;" border="2" cellpadding="0" cellspacing="0">
+<tbody>
+<tr style="height: 18.8pt;">
+<td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">Parameter name</p>
+</td>
+<td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">Units</p>
+</td>
+<td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">Default value</p>
+</td>
+</tr>
+<tr>
+<td>&nbsp; delta_Ssph</td>
+<td></td>
+<td>&nbsp; 0</td>
+</tr>
+<tr>
+<td>&nbsp; radius_Lsph</td>
+<td>&nbsp; Å</td>
+<td>&nbsp; 5000</td>
+</tr>
+<tr>
+<td>&nbsp; radius_Ssph</td>
+<td>&nbsp; Å</td>
+<td>&nbsp; 100</td>
+</tr>
+<tr>
+<td>&nbsp; sld_Lsph</td>
+<td>&nbsp;&nbsp;Å<sup> -2</sup></td>
+<td>&nbsp; -4e-07</td>
+</tr>
+<tr style="height: 18.8pt;">
+<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">sld_Ssph</p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; vertical-align: top; width: 107pt; height: 18.8pt;">
+<p class="MsoBodyText">Å<sup> -2</sup></p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">3.5e-6</p>
+</td>
+</tr>
+<tr style="height: 18.8pt;">
+<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">sld_solv</p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">Å<sup> -2</sup></p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">6.3e-6</p>
+</td>
+</tr>
+<tr style="height: 18.8pt;">
+<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">surfrac_Ssph</p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText"><br>
+</p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">0.4</p>
+</td>
+</tr>
+<tr style="height: 18.8pt;">
+<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">volf_Lsph</p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">&nbsp;</p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">0.05</p>
+</td>
+</tr>
+<tr style="height: 18.8pt;">
+<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">volf_Lsph</p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText"><br>
+</p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">0.005</p>
+</td>
+</tr>
+<tr style="height: 18.8pt;">
+<td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">background</p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">cm<sup>-1</sup></p>
+</td>
+<td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 107pt; height: 18.8pt;" valign="top" width="143">
+<p class="MsoBodyText">0</p>
+</td>
+</tr>
+</tbody>
+</table>
+</div>
+<p class="MsoNormal">&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><img src="raspberry_plot.jpg"></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><b>Figure.
+1D plot using the values of /2000 data points.</b></p>
+<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"></p>
+<p class="MsoNormal">&nbsp;</p>
+<p class="MsoNormal"></p>
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="CoreShellModel"><b><span style="font-size: 14pt;">Core Shell
 (Sphere) Model</span></b></a></p>
@@ -1067,5 +1233,5 @@
 way (Guinier, 1955):</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image013.PNG" ></span>&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image013.PNG"></span>&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
@@ -1229,5 +1395,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.5.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.6.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="Core2ndMomentModel"><b><span style="font-size: 14pt;">Core2ndMomentModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -1399,5 +1565,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.6.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.7.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="CoreMultiShellModel"><b><span style="font-size: 14pt;">CoreMultiShell(Sphere)Model</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -1638,5 +1804,5 @@
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.7.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.8.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="VesicleModel"><b><span style="font-size: 14pt;">VesicleModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -1683,5 +1849,5 @@
 above, regardless of the orientation of the <i>q</i>
 vector&nbsp; which is
-defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG" ></span><span style="font-size: 14pt;">.</span></p>
+defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG"></span><span style="font-size: 14pt;">.</span></p>
 <p class="MsoNormal">For P*S: The outer most radius (=
 radius + thickness) is
@@ -1802,5 +1968,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.8.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.9.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="MultiShellModel"><b><span style="font-size: 14pt;">MultiShellModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -1819,5 +1985,5 @@
 <p class="MsoNormal">The 2D scattering intensity is the
 same as 1D, regardless of
-the orientation of the <i>q</i> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG" ></span><span style="font-size: 14pt;">.</span></p>
+the orientation of the <i>q</i> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG"></span><span style="font-size: 14pt;">.</span></p>
 <p class="MsoNormal">For P*S: The outer most radius (=
 core_radius +
@@ -1963,5 +2129,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.9.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.10.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="OnionExpShellModel"><b><span style="font-size: 14pt;">OnionExpShellModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;&nbsp;</p>
@@ -2222,5 +2388,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.10.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.11.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="SphericalSLDModel"><b><span style="font-size: 14pt;">SphericalSLDModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;&nbsp;</p>
@@ -2265,13 +2431,13 @@
 <p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image024.gif" height="41" width="200"></span></p>
 <p class="MsoNormal">so that</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image044.gif" ></span></p>
-<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image045.gif" ></span></p>
-<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image046.gif" ></span></p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image047.gif" ></span></p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image048.gif" ></span></p>
-<p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image027.gif" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image044.gif"></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image045.gif"></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image046.gif"></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image047.gif"></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image048.gif"></span></p>
+<p class="MsoNormal">&nbsp;</p>
+<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image027.gif"></span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
@@ -2285,5 +2451,5 @@
 <p class="MsoListParagraph" style="text-indent: -0.25in;">1)<span style="font-family: &quot;Times New Roman&quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span>Exp;&nbsp;&nbsp;&nbsp; </p>
-<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image049.gif" ></span></p>
+<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image049.gif"></span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoListParagraph" style="text-indent: -0.25in;">2)<span style="font-family: &quot;Times New Roman&quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
@@ -2291,5 +2457,5 @@
 <p class="MsoNormal" style="margin-left: 0.25in;">&nbsp;</p>
 <p class="MsoListParagraph">&nbsp;</p>
-<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image050.gif" ></span></p>
+<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image050.gif"></span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
@@ -2297,5 +2463,5 @@
 </span>Erf;</p>
 <p class="MsoNormal" style="margin-left: 0.25in;">&nbsp;</p>
-<p class="MsoListParagraph"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image051.gif" ></span></p>
+<p class="MsoListParagraph"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image051.gif"></span></p>
 <p class="MsoListParagraph">&nbsp;</p>
 <p class="MsoListParagraph">&nbsp;</p>
@@ -2321,5 +2487,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">In the equation, </p>
-<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image055.gif" ></span></p>
+<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image055.gif"></span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
@@ -2327,11 +2493,11 @@
 calculated by</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image037.gif" ></span></p>
+<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image037.gif"></span></p>
 <p class="MsoNormal">where </p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image038.gif" ></span></p>
+<p class="MsoNormal"><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;"><img src="image038.gif"></span></p>
 <p class="MsoNormal"><span style="font-family: Symbol;">&nbsp;</span></p>
 <p class="MsoNormal"><span style="font-family: Symbol;">&nbsp;</span></p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-family: Symbol;"><img id="Object 20" src="image056.gif" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="font-family: Symbol;"><img id="Object 20" src="image056.gif"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-family: Symbol;">&nbsp;</span></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -2340,5 +2506,5 @@
 above, regardless of the orientation of the <i>q</i>
 vector&nbsp; which is
-defined as<span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;; position: relative; top: 4.5pt;"><img src="image040.gif" ></span><span style="font-size: 14pt;">.</span></p>
+defined as<span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;; position: relative; top: 4.5pt;"><img src="image040.gif"></span><span style="font-size: 14pt;">.</span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">For P*S: The outer most radius is
@@ -2535,5 +2701,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.11.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.12.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><b><a name="LinearPearlsModel"><span style="font-size: 14pt;">LinearPearlsModel</span></a></b></p>
 <p class="MsoNormal"><a name="LinearPearlsModel">&nbsp;</a></p>
@@ -2676,5 +2842,5 @@
 <p class="MsoNormal"><a name="LinearPearlsModel">&nbsp;</a></p>
 <p class="MsoNormal"><a name="LinearPearlsModel">&nbsp;</a></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><a name="LinearPearlsModel"><b><span style="font-size: 14pt;">2.12.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><a name="LinearPearlsModel"><b><span style="font-size: 14pt;">2.13.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b></a><b><a name="PearlNecklaceModel"><span style="font-size: 14pt;">PearlNecklaceModel</span></a></b></p>
 <p class="MsoNormal"><a name="PearlNecklaceModel">&nbsp;</a></p>
@@ -2851,5 +3017,5 @@
 <p class="MsoNormal"><a name="PearlNecklaceModel">&nbsp;</a></p>
 <p class="MsoNormal"><a name="PearlNecklaceModel">&nbsp;</a></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><a name="PearlNecklaceModel"><b><span style="font-size: 14pt;">2.13.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><a name="PearlNecklaceModel"><b><span style="font-size: 14pt;">2.14.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b></a><a name="CylinderModel"><b><span style="font-size: 14pt;">Cylinder
 Model</span></b></a></p>
@@ -2869,7 +3035,7 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059.PNG" ></span>&nbsp;
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059.PNG"></span>&nbsp;
 </p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="image060.PNG" ></span>&nbsp;&nbsp;
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="image060.PNG"></span>&nbsp;&nbsp;
 </p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
@@ -3013,5 +3179,5 @@
 randomly oriented cylinders is then given by:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><a name="_Ref173306528"></a><a name="_Ref173306479"></a><span style="position: relative; top: 16pt;"><img src="image063.PNG" ></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="text-align: center;" align="center"><a name="_Ref173306528"></a><a name="_Ref173306479"></a><span style="position: relative; top: 16pt;"><img src="image063.PNG"></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </p>
 <p class="MsoNormal">&nbsp;</p>
@@ -3041,5 +3207,5 @@
 done by evaluating the following:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image064.PNG" ></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image064.PNG"></span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
@@ -3084,5 +3250,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.14.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.15.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="CoreShellCylinderModel"><b><span style="font-size: 14pt;">Core-Shell
 Cylinder Model</span></b></a></p>
@@ -3100,6 +3266,6 @@
 oriented core-shell cylinders is given by (Kline, 2006):</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image067.PNG" ></span>&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 32pt;"><img src="image068.PNG" ></span>&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image067.PNG"></span>&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 32pt;"><img src="image068.PNG"></span>&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
@@ -3338,5 +3504,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.15.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.16.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="CoreShellBicelleModel"><b><span style="font-size: 14pt;">Core-Shell (Cylinder) Bicelle Model</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -3515,5 +3681,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.16.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.17.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="HollowCylinderModel"><b><span style="font-size: 14pt;">HollowCylinderModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -3532,7 +3698,8 @@
 way (Guinier, 1955):</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><img src="image072.PNG" ></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><img src="image072.PNG"></p>
 <br>
 <nr>
+</nr>
 <p class="MsoNormal">where <i>scale</i> is a
 scale factor, <i>J<sub>1</sub></i>
@@ -3682,5 +3849,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.17.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.18.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="FlexibleCylinderModel"></a><b><span style="font-size: 14pt;">FlexibleCylinderModel</span></b></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -3845,5 +4012,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.18.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.19.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><b><span style="font-size: 14pt;">FlexCylEllipXMo<a name="FlexCylEllipXModel"></a>del</span></b></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -3939,5 +4106,5 @@
 <p class="MsoNormal">For 2D data: The 2D scattering
 intensity is calculated in
-the same way as 1D, where the <i>q</i> vector is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG" ></span><span style="font-size: 14pt;">.</span></p>
+the same way as 1D, where the <i>q</i> vector is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG"></span><span style="font-size: 14pt;">.</span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">REFERENCE</p>
@@ -4072,5 +4239,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.19.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.20.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="StackedDisksModel"><b><span style="font-size: 14pt;">StackedDisksModel
 </span></b></a></p>
@@ -4094,5 +4261,5 @@
 <p class="MsoNormal">The 2D scattering intensity is the
 same as 1D, regardless of
-the orientation of the <i>q</i> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG" ></span><span style="font-size: 14pt;">.</span></p>
+the orientation of the <i>q</i> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG"></span><span style="font-size: 14pt;">.</span></p>
 <p class="MsoNormal"><span style="font-size: 14pt;">&nbsp;</span></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -4108,8 +4275,8 @@
 <p class="MsoNormal">The scattering intensity I(q) is:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 9pt;"><img src="image081.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 9pt;"><img src="image081.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">where the contrast,</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image082.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image082.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
@@ -4121,12 +4288,13 @@
 disc, respectively.</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><img src="image083.PNG" ></p>
-<br><br>
-<p class="MsoNormal"></p><p class="MsoNormal">where d = thickness of the layer
+<p class="MsoNormal" style="text-align: center;" align="center"><img src="image083.PNG"></p>
+<br>
+<br>
+<p class="MsoNormal"></p>
+<p class="MsoNormal">where d = thickness of the layer
 (layer_thick), 2h= core
 thickness (core_thick),&nbsp; and R = radius of the disc (radius).</p>
-
-<p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="image084.PNG" ></span></p>
+<p class="MsoNormal">&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="image084.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
@@ -4314,5 +4482,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.20.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.21.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="ParallelepipedModel"><b><span style="font-size: 14pt;">ParallelepipedModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -4339,9 +4507,9 @@
 c=C/B&gt;1, the form factor,</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 48pt;"><img src="image088.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 48pt;"><img src="image088.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">The contrast is defined as</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image089.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image089.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
@@ -4509,5 +4677,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.21.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.22.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><b><span style="font-size: 14pt;"><a name="CSParallelepipedModel">CSParallelepipedModel</a></span></b></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -4542,5 +4710,5 @@
 <p class="MsoNormal">The volume of the solid is:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal"><span style="position: relative; top: 5pt;"><img src="image095.PNG" ></span></p>
+<p class="MsoNormal"><span style="position: relative; top: 5pt;"><img src="image095.PNG"></span></p>
 <p class="MsoNormal">meaning that there are "gaps" at the
 corners of
@@ -4818,5 +4986,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.22.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.23.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="EllipticalCylinderModel"><b><span style="font-size: 14pt;">Elliptical
 Cylinder Model</span></b></a></p>
@@ -4847,12 +5015,12 @@
 <p class="MsoNormal">The function calculated is:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image099.PNG" ></span>&nbsp;</p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image099.PNG"></span>&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">with the functions:</p>
 <br>
-<p class="MsoNormal" style="text-align: center;" align="center"><img src="image100.PNG" >
-</p><br>
-
+<p class="MsoNormal" style="text-align: center;" align="center"><img src="image100.PNG">
+</p>
+<br>
 <p class="MsoNormal">and the angle psi is defined as the
 orientation of the major
@@ -5050,5 +5218,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.23.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.24.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="BarBellModel"><b><span style="font-size: 14pt;">BarBell(/DumBell)Model</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -5090,9 +5258,9 @@
 calculated as:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image106.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image106.PNG"></span></p>
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">where the amplitude A(q) is given as:</p>
 <br>
-<p class="MsoNormal" style="text-align: center;" align="center"><img src="image107.PNG" ></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><img src="image107.PNG"></p>
 <br>
 <p class="MsoNormal">The &lt; &gt; brackets denote
@@ -5254,5 +5422,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.24.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.25.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="CappedCylinderModel"><b><span style="font-size: 14pt;">CappedCylinder(/ConvexLens)Model</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -5457,5 +5625,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.25.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.26.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="EllipsoidModel"><b><span style="font-size: 14pt;">Ellipsoid
 Model</span></b></a></p>
@@ -5475,11 +5643,11 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059.PNG" ></span>&nbsp;&nbsp;
+<p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059.PNG"></span>&nbsp;&nbsp;
 </p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image119.PNG" ></span>&nbsp;&nbsp;&nbsp;
+<p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image119.PNG"></span>&nbsp;&nbsp;&nbsp;
 </p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image120.PNG" ></span>&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image120.PNG"></span>&nbsp;&nbsp;&nbsp;&nbsp;
 </p>
 <p class="MsoNormal">&nbsp;</p>
@@ -5713,5 +5881,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.26.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.27.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="CoreShellEllipsoidModel"><b><span style="font-size: 14pt;">CoreShellEllipsoidModel
 </span></b></a></p>
@@ -5737,5 +5905,5 @@
 <p class="MsoNormal">The form factor calculated is:</p>
 <br>
-<p class="MsoNormal" style="text-align: center;" align="center"><img src="image126.PNG" ></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><img src="image126.PNG"></p>
 <br>
 <p class="MsoNormal">To provide easy access to the
@@ -5749,6 +5917,6 @@
 <p class="MsoNormal">The contrast is defined as SLD(core)
  SLD(shell) or
-SLD(shell  solvent). In the parameters, equat_core = equatorial core radius, 
-polar_core = polar core radius, equat_shell = r<sub>min</sub>
+SLD(shell  solvent). In the parameters, equat_core = equatorial core
+radius, polar_core = polar core radius, equat_shell = r<sub>min</sub>
 (or equatorial outer radius), and polar_shell = = r<sub>maj</sub>
 (or polar outer radius).</p>
@@ -5905,5 +6073,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.27.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="TriaxialEllipsoidModel"><b><span style="font-size: 14pt;">TriaxialEllipsoidModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -5928,5 +6096,5 @@
 <p class="MsoNormal">The form factor calculated is:</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 33pt;"><img src="image129.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 33pt;"><img src="image129.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">&nbsp;</p>
@@ -6102,5 +6270,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.28.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.29.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="LamellarModel"><b><span style="font-size: 14pt;">LamellarModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -6114,8 +6282,8 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">The scattering intensity I(q) is:</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image133.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image133.PNG"></span></p>
 <p class="MsoNormal">The form factor is,</p>
 <p class="MsoNormal">&nbsp;</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image134.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image134.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">where <span style="font-family: Symbol;">d</span> = bilayer
@@ -6226,5 +6394,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.29.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.30.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="LamellarFFHGModel"><b><span style="font-size: 14pt;">LamellarFFHGModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -6238,5 +6406,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">The scattering intensity I(q) is:</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image136.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image136.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
@@ -6379,5 +6547,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.30.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.31.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="LamellarPSModel"><b><span style="font-size: 14pt;">LamellarPSModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -6389,17 +6557,17 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">The scattering intensity I(q) is:</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image139.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image139.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">The form factor is</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image134.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image134.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">and the structure is </p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image140.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image140.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">where </p>
 <br>
-<p class="MsoNormal" style="text-align: center;" align="center"><img src="image141.PNG" ></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><img src="image141.PNG"></p>
 <br>
 <p class="MsoNormal">Here d= (repeat) spacing, <span style="font-family: Symbol;">d</span>
@@ -6543,5 +6711,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.31.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.32.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="LamellarPSHGModel"><b><span style="font-size: 14pt;">LamellarPSHGModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -6555,16 +6723,16 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal">The scattering intensity I(q) is:</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image139.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image139.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">The form factor is,</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image143.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image143.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">The structure factor is</p>
-<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image140.PNG" ></span></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image140.PNG"></span></p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal" style="text-align: center;" align="center">&nbsp;</p>
 <p class="MsoNormal">where </p>
 <br>
-<p class="MsoNormal" style="text-align: center;" align="center"><img src="image141.PNG" ></p>
+<p class="MsoNormal" style="text-align: center;" align="center"><img src="image141.PNG"></p>
 <br>
 <p class="MsoNormal">where <span style="font-family: Symbol;">d<sub>T</sub></span>
@@ -6746,5 +6914,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.32.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.33.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="LamellarPCrystalModel"><b><span style="font-size: 14pt;">LamellarPCrystalModel</span></b></a></p>
 <p class="MsoNormal">&nbsp;</p>
@@ -6919,5 +7087,5 @@
 <p class="MsoNormal"><b>&nbsp;</b></p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.33.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.34.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="SCCrystalModel"><b><span style="font-size: 14pt;">SC(Simple
 Cubic Para-)CrystalModel</span></b></a></p>
@@ -7137,5 +7305,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.34.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.35.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="FCCrystalModel"><b><span style="font-size: 14pt;">FC(Face
 Centered Cubic Para-)CrystalModel</span></b></a></p>
@@ -7361,5 +7529,5 @@
 <p class="MsoNormal">&nbsp;</p>
 <p class="MsoNormal"><b>&nbsp;</b></p>
-<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.35.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<p class="MsoNormal" style="margin-left: 0.55in; text-indent: -0.3in;"><b><span style="font-size: 14pt;">2.36.</span></b><b><span style="font-size: 7pt;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 </span></b><a name="BCCrystalModel"><b><span style="font-size: 14pt;">BC(Body
 Centered Cubic Para-)CrystalModel</span></b></a></p>
