Changeset 57eab9e in sasview for sansmodels/src/sans/models/media/model_functions.html
- Timestamp:
- May 2, 2012 6:44:03 PM (13 years ago)
- Branches:
- master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
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- 74d7b59
- Parents:
- dd4344a
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- 1 edited
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sansmodels/src/sans/models/media/model_functions.html
r6246e00 r57eab9e 444 444 {margin-bottom:0in;} 445 445 --> 446 </style><title></title> 447 448 </head> 446 </style><title></title></head> 449 447 <body lang="EN-US" link="blue" vlink="purple"> 450 448 <div class="WordSection1"> … … 533 531 particle:</p> 534 532 <p class="MsoNormal"> </p> 535 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image001. gif" height="43" width="192"></span> 533 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image001.PNG" ></span> 536 534 </p> 537 535 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 538 536 <p class="MsoNormal">with</p> 539 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 8pt;"><img src="image002. gif" height="29" width="159"></span> </p>537 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 8pt;"><img src="image002.PNG" ></span> </p> 540 538 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 541 539 <p class="MsoNormal">where <i>P</i><sub>0</sub><i>(<b>q</b>)</i> … … 552 550 particle 553 551 volume fraction:<span style="position: relative; top: 5pt;"> 554 <img src="image003. gif" height="21" width="92"></span>.</p>552 <img src="image003.PNG" ></span>.</p> 555 553 <p class="MsoNormal"> </p> 556 554 <p class="MsoNormal">Our so-called 1D scattering intensity … … 590 588 way (Guinier, 1955):</p> 591 589 <p class="MsoNormal"> </p> 592 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image004. gif" height="53" width="337"></span> 590 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image004.PNG" ></span> 593 591 </p> 594 592 <p class="MsoNormal" style="text-align: center;" align="center"> </p> … … 728 726 calculation is an exact multi-component solution:</p> 729 727 <p class="MsoNormal"> </p> 730 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 5pt;"><img src="image006. gif" height="25" width="479"></span></p>728 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 5pt;"><img src="image006.PNG" ></span></p> 731 729 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 732 730 <p class="MsoNormal" style="text-align: center;" align="center"> </p> … … 742 740 <p class="MsoNormal"> </p> 743 741 <p class="MsoNormal"> </p> 744 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 24pt;"><img src="image007. gif" height="98" width="248"></span>.</p>742 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 24pt;"><img src="image007.PNG" ></span>.</p> 745 743 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 746 744 <p class="MsoNormal" style="text-align: center;" align="center"> </p> … … 748 746 <p class="MsoNormal">The 2D scattering intensity is the 749 747 same as 1D, regardless of 750 the orientation of the <i>q</i> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008. gif" height="33" width="103"></span><span style="font-size: 14pt;">.</span></p>748 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> 751 749 <p class="MsoNormal"> </p> 752 750 <p class="MsoNormal"> </p> … … 906 904 calculated as:</p> 907 905 <p class="MsoNormal"> </p> 908 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image010. gif" height="41" width="233"></span></p>906 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image010.PNG" ></span></p> 909 907 <p class="MsoNormal"> </p> 910 908 <p class="MsoNormal">where the amplitude A(q) is given as … … 914 912 <p class="MsoNormal"> </p> 915 913 <p class="MsoNormal"> </p> 916 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 18pt;"><img src="image011. gif" height="56" width="315"></span></p>914 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 18pt;"><img src="image011.PNG" ></span></p> 917 915 <p class="MsoNormal"> </p> 918 916 <p class="MsoNormal"> </p> … … 949 947 <p class="MsoNormal">For 2D data: The 2D scattering 950 948 intensity is calculated in 951 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. gif" height="33" width="103"></span><span style="font-size: 14pt;">.</span></p>949 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> 952 950 <p class="MsoNormal"> </p> 953 951 <p class="MsoNormal">REFERENCE</p> … … 1069 1067 way (Guinier, 1955):</p> 1070 1068 <p class="MsoNormal"> </p> 1071 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image013. gif" height="55" width="642"></span> </p>1069 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image013.PNG" ></span> </p> 1072 1070 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 1073 1071 <p class="MsoNormal" style="text-align: center;" align="center"> </p> … … 1651 1649 way (Guinier, 1955):</p> 1652 1650 <p class="MsoNormal"> </p> 1653 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image017. gif" height="54" width="448"></span> </p>1651 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image017.PNG"></span> </p> 1654 1652 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 1655 1653 <p class="MsoNormal" style="text-align: center;" align="center"> </p> … … 1685 1683 above, regardless of the orientation of the <i>q</i> 1686 1684 vector which is 1687 defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008. gif" height="33" width="103"></span><span style="font-size: 14pt;">.</span></p>1685 defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG" ></span><span style="font-size: 14pt;">.</span></p> 1688 1686 <p class="MsoNormal">For P*S: The outer most radius (= 1689 1687 radius + thickness) is … … 1821 1819 <p class="MsoNormal">The 2D scattering intensity is the 1822 1820 same as 1D, regardless of 1823 the orientation of the <i>q</i> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008. gif" height="33" width="103"></span><span style="font-size: 14pt;">.</span></p>1821 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> 1824 1822 <p class="MsoNormal">For P*S: The outer most radius (= 1825 1823 core_radius + … … 2267 2265 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image024.gif" height="41" width="200"></span></p> 2268 2266 <p class="MsoNormal">so that</p> 2269 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image044.gif" height="87" width="519"></span></p>2270 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 2271 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image045.gif" height="54" width="315"></span></p>2272 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 2273 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image046.gif" height="50" width="312"></span></p>2274 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image047.gif" height="105" width="624"></span></p>2275 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image048.gif" height="46" width="440"></span></p>2276 <p class="MsoNormal"> </p> 2277 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image027.gif" height="89" width="466"></span></p>2267 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image044.gif" ></span></p> 2268 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 2269 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image045.gif" ></span></p> 2270 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 2271 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image046.gif" ></span></p> 2272 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image047.gif" ></span></p> 2273 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image048.gif" ></span></p> 2274 <p class="MsoNormal"> </p> 2275 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image027.gif" ></span></p> 2278 2276 <p class="MsoNormal"> </p> 2279 2277 <p class="MsoNormal"> </p> … … 2287 2285 <p class="MsoListParagraph" style="text-indent: -0.25in;">1)<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> 2288 2286 </span>Exp; </p> 2289 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image049.gif" height="98" width="379"></span></p>2287 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image049.gif" ></span></p> 2290 2288 <p class="MsoNormal"> </p> 2291 2289 <p class="MsoListParagraph" style="text-indent: -0.25in;">2)<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> … … 2293 2291 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 2294 2292 <p class="MsoListParagraph"> </p> 2295 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image050.gif" height="71" width="337"></span></p>2293 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image050.gif" ></span></p> 2296 2294 <p class="MsoNormal"> </p> 2297 2295 <p class="MsoNormal"> </p> … … 2299 2297 </span>Erf;</p> 2300 2298 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 2301 <p class="MsoListParagraph"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image051.gif" height="92" width="370"></span></p>2299 <p class="MsoListParagraph"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image051.gif" ></span></p> 2302 2300 <p class="MsoListParagraph"> </p> 2303 2301 <p class="MsoListParagraph"> </p> … … 2323 2321 <p class="MsoNormal"> </p> 2324 2322 <p class="MsoNormal">In the equation, </p> 2325 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image055.gif" height="99" width="237"></span></p>2323 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image055.gif" ></span></p> 2326 2324 <p class="MsoNormal"> </p> 2327 2325 <p class="MsoNormal"> </p> … … 2329 2327 calculated by</p> 2330 2328 <p class="MsoNormal"> </p> 2331 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image037.gif" height="21" width="143"></span></p>2329 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image037.gif" ></span></p> 2332 2330 <p class="MsoNormal">where </p> 2333 2331 <p class="MsoNormal"> </p> 2334 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image038.gif" height="21" width="144"></span></p>2332 <p class="MsoNormal"><span style="font-size: 12pt; font-family: "Times New Roman","serif";"><img src="image038.gif" ></span></p> 2335 2333 <p class="MsoNormal"><span style="font-family: Symbol;"> </span></p> 2336 2334 <p class="MsoNormal"><span style="font-family: Symbol;"> </span></p> 2337 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-family: Symbol;"><img id="Object 20" src="image056.gif" height="479" width="624"></span></p>2335 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-family: Symbol;"><img id="Object 20" src="image056.gif" ></span></p> 2338 2336 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-family: Symbol;"> </span></p> 2339 2337 <p class="MsoNormal"> </p> … … 2342 2340 above, regardless of the orientation of the <i>q</i> 2343 2341 vector which is 2344 defined as<span style="font-size: 12pt; font-family: "Times New Roman","serif"; position: relative; top: 4.5pt;"><img src="image040.gif" height="23" width="111"></span><span style="font-size: 14pt;">.</span></p>2342 defined as<span style="font-size: 12pt; font-family: "Times New Roman","serif"; position: relative; top: 4.5pt;"><img src="image040.gif" ></span><span style="font-size: 14pt;">.</span></p> 2345 2343 <p class="MsoNormal"> </p> 2346 2344 <p class="MsoNormal">For P*S: The outer most radius is … … 2871 2869 <p class="MsoNormal"> </p> 2872 2870 <p class="MsoNormal"> </p> 2873 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059. gif" height="41" width="184"></span> 2871 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059.PNG" ></span> 2874 2872 </p> 2875 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="image060. gif" height="45" width="373"></span> 2873 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="image060.PNG" ></span> 2876 2874 </p> 2877 2875 <p class="MsoNormal" style="text-align: center;" align="center"> </p> … … 3015 3013 randomly oriented cylinders is then given by:</p> 3016 3014 <p class="MsoNormal"> </p> 3017 <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. gif" height="56" width="253"></span> 3015 <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> 3018 3016 </p> 3019 3017 <p class="MsoNormal"> </p> … … 3043 3041 done by evaluating the following:</p> 3044 3042 <p class="MsoNormal"> </p> 3045 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image064. gif" height="51" width="244"></span> 3043 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image064.PNG" ></span> 3046 3044 </p> 3047 3045 <p class="MsoNormal" style="text-align: center;" align="center"> </p> … … 3102 3100 oriented core-shell cylinders is given by (Kline, 2006):</p> 3103 3101 <p class="MsoNormal"> </p> 3104 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image067. gif" height="45" width="184"></span> </p>3105 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 32pt;"><img src="image068. gif" height="93" width="476"></span> </p>3102 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image067.PNG" ></span> </p> 3103 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 32pt;"><img src="image068.PNG" ></span> </p> 3106 3104 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 3107 3105 <p class="MsoNormal" style="text-align: center;" align="center"> </p> … … 3534 3532 way (Guinier, 1955):</p> 3535 3533 <p class="MsoNormal"> </p> 3536 <p class="MsoNormal" style="text-align: center;" align="center">< span style="position: relative; top: 44pt;"><img src="image072.gif" height="176" width="514"></span> </p>3537 < p class="MsoNormal" style="text-align: center;" align="center"> </p>3538 < p class="MsoNormal" style="text-align: right;" align="right"> </p>3534 <p class="MsoNormal" style="text-align: center;" align="center"><img src="image072.PNG" ></p> 3535 <br> 3536 <nr> 3539 3537 <p class="MsoNormal">where <i>scale</i> is a 3540 3538 scale factor, <i>J<sub>1</sub></i> … … 3941 3939 <p class="MsoNormal">For 2D data: The 2D scattering 3942 3940 intensity is calculated in 3943 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. gif" height="33" width="103"></span><span style="font-size: 14pt;">.</span></p>3941 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> 3944 3942 <p class="MsoNormal"> </p> 3945 3943 <p class="MsoNormal">REFERENCE</p> … … 4096 4094 <p class="MsoNormal">The 2D scattering intensity is the 4097 4095 same as 1D, regardless of 4098 the orientation of the <i>q</i> vector which is defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008. gif" height="33" width="103"></span><span style="font-size: 14pt;">.</span></p>4096 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> 4099 4097 <p class="MsoNormal"><span style="font-size: 14pt;"> </span></p> 4100 4098 <p class="MsoNormal"> </p> … … 4110 4108 <p class="MsoNormal">The scattering intensity I(q) is:</p> 4111 4109 <p class="MsoNormal"> </p> 4112 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 9pt;"><img src="image081. gif" height="38" width="514"></span></p>4110 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 9pt;"><img src="image081.PNG" ></span></p> 4113 4111 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4114 4112 <p class="MsoNormal">where the contrast,</p> 4115 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image082. gif" height="24" width="115"></span></p>4113 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image082.PNG" ></span></p> 4116 4114 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4117 4115 <p class="MsoNormal"> </p> … … 4123 4121 disc, respectively.</p> 4124 4122 <p class="MsoNormal"> </p> 4125 <p class="MsoNormal"> </p> 4126 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 39pt;"><img src="image083.gif" height="113" width="424"></span></p> 4127 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4128 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4129 <p class="MsoNormal">where d = thickness of the layer 4123 <p class="MsoNormal" style="text-align: center;" align="center"><img src="image083.PNG" ></p> 4124 <br><br> 4125 <p class="MsoNormal"></p><p class="MsoNormal">where d = thickness of the layer 4130 4126 (layer_thick), 2h= core 4131 4127 thickness (core_thick), and R = radius of the disc (radius).</p> 4132 <p class="MsoNormal"> </p> 4133 <p class="MsoNormal"> </p> 4134 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="image084. gif" height="46" width="399"></span></p>4128 4129 <p class="MsoNormal"> </p> 4130 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 14pt;"><img src="image084.PNG" ></span></p> 4135 4131 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4136 4132 <p class="MsoNormal"> </p> … … 4343 4339 c=C/B>1, the form factor,</p> 4344 4340 <p class="MsoNormal"> </p> 4345 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 48pt;"><img src="image088. gif" height="145" width="360"></span></p>4341 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 48pt;"><img src="image088.PNG" ></span></p> 4346 4342 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4347 4343 <p class="MsoNormal">The contrast is defined as</p> 4348 4344 <p class="MsoNormal"> </p> 4349 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image089. gif" height="24" width="117"></span></p>4345 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image089.PNG" ></span></p> 4350 4346 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4351 4347 <p class="MsoNormal"> </p> … … 4546 4542 <p class="MsoNormal">The volume of the solid is:</p> 4547 4543 <p class="MsoNormal"> </p> 4548 <p class="MsoNormal"><span style="position: relative; top: 5pt;"><img src="image095. gif" height="23" width="180"></span></p>4544 <p class="MsoNormal"><span style="position: relative; top: 5pt;"><img src="image095.PNG" ></span></p> 4549 4545 <p class="MsoNormal">meaning that there are "gaps" at the 4550 4546 corners of … … 4851 4847 <p class="MsoNormal">The function calculated is:</p> 4852 4848 <p class="MsoNormal"> </p> 4853 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image099. gif" height="46" width="377"></span> </p>4849 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image099.PNG" ></span> </p> 4854 4850 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4855 4851 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4856 4852 <p class="MsoNormal">with the functions:</p> 4857 <p class="MsoNormal"> </p> 4858 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 39pt;"><img src="image100.gif" height="114" width="297"></span> 4859 (13)</p> 4860 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4861 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4862 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 4853 <br> 4854 <p class="MsoNormal" style="text-align: center;" align="center"><img src="image100.PNG" > 4855 </p><br> 4856 4863 4857 <p class="MsoNormal">and the angle psi is defined as the 4864 4858 orientation of the major … … 5096 5090 calculated as:</p> 5097 5091 <p class="MsoNormal"> </p> 5098 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image106. gif" height="41" width="285"></span></p>5092 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image106.PNG" ></span></p> 5099 5093 <p class="MsoNormal"> </p> 5100 5094 <p class="MsoNormal">where the amplitude A(q) is given as:</p> 5101 <p class="MsoNormal"> </p> 5102 <p class="MsoNormal"> </p> 5103 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 52pt;"><img src="image107.gif" height="144" width="288"></span></p> 5104 <p class="MsoNormal"> </p> 5105 <p class="MsoNormal"> </p> 5106 <p class="MsoNormal"></p> 5107 <p class="MsoNormal"></p> 5095 <br> 5096 <p class="MsoNormal" style="text-align: center;" align="center"><img src="image107.PNG" ></p> 5097 <br> 5108 5098 <p class="MsoNormal">The < > brackets denote 5109 5099 an average of the structure … … 5485 5475 <p class="MsoNormal"> </p> 5486 5476 <p class="MsoNormal"> </p> 5487 <p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059. gif" height="41" width="184"></span> 5477 <p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image059.PNG" ></span> 5488 5478 </p> 5489 5479 <p class="MsoNormal"> </p> 5490 <p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image119. gif" height="47" width="371"></span> 5480 <p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image119.PNG" ></span> 5491 5481 </p> 5492 5482 <p class="MsoNormal"> </p> 5493 <p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image120. gif" height="29" width="272"></span> 5483 <p class="MsoCaption" style="text-align: center;" align="center"><span style="position: relative; top: 6pt;"><img src="image120.PNG" ></span> 5494 5484 </p> 5495 5485 <p class="MsoNormal"> </p> … … 5746 5736 absolute scale. </p> 5747 5737 <p class="MsoNormal">The form factor calculated is:</p> 5748 <p class="MsoNormal"> </p> 5749 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 48pt;"><img src="image126.gif" height="137" width="334"></span></p> 5750 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 5751 <p class="MsoNormal"> </p> 5752 <p class="MsoNormal"> </p> 5738 <br> 5739 <p class="MsoNormal" style="text-align: center;" align="center"><img src="image126.PNG" ></p> 5740 <br> 5753 5741 <p class="MsoNormal">To provide easy access to the 5754 5742 orientation of the coreshell … … 5943 5931 <p class="MsoNormal">The form factor calculated is:</p> 5944 5932 <p class="MsoNormal"> </p> 5945 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 33pt;"><img src="image129. gif" height="97" width="472"></span></p>5933 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 33pt;"><img src="image129.PNG" ></span></p> 5946 5934 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 5947 5935 <p class="MsoNormal"> </p> … … 6129 6117 <p class="MsoNormal"> </p> 6130 6118 <p class="MsoNormal">The scattering intensity I(q) is:</p> 6131 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image133. gif" height="46" width="103"></span></p>6119 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image133.PNG" ></span></p> 6132 6120 <p class="MsoNormal">The form factor is,</p> 6133 6121 <p class="MsoNormal"> </p> 6134 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image134. gif" height="48" width="174"></span></p>6122 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image134.PNG" ></span></p> 6135 6123 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6136 6124 <p class="MsoNormal">where <span style="font-family: Symbol;">d</span> = bilayer … … 6253 6241 <p class="MsoNormal"> </p> 6254 6242 <p class="MsoNormal">The scattering intensity I(q) is:</p> 6255 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image136. gif" height="46" width="160"></span></p>6243 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image136.PNG" ></span></p> 6256 6244 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6257 6245 <p class="MsoNormal" style="text-align: center;" align="center"> </p> … … 6404 6392 <p class="MsoNormal"> </p> 6405 6393 <p class="MsoNormal">The scattering intensity I(q) is:</p> 6406 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image139. gif" height="46" width="133"></span></p>6394 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image139.PNG" ></span></p> 6407 6395 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6408 6396 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6409 6397 <p class="MsoNormal">The form factor is</p> 6410 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image134. gif" height="48" width="174"></span></p>6398 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image134.PNG" ></span></p> 6411 6399 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6412 6400 <p class="MsoNormal">and the structure is </p> 6413 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image140. gif" height="51" width="334"></span></p>6401 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image140.PNG" ></span></p> 6414 6402 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6415 6403 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6416 6404 <p class="MsoNormal">where </p> 6417 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 50pt;"><img src="image141.gif" height="133" width="252"></span></p> 6418 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6419 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6420 <p class="MsoNormal" style="text-align: center;" align="center"></p> 6421 <p class="MsoNormal" style="text-align: center;" align="center"></p> 6405 <br> 6406 <p class="MsoNormal" style="text-align: center;" align="center"><img src="image141.PNG" ></p> 6407 <br> 6422 6408 <p class="MsoNormal">Here d= (repeat) spacing, <span style="font-family: Symbol;">d</span> 6423 6409 = bilayer thickness, the contrast <span style="font-family: Symbol;">Dr</span> … … 6572 6558 <p class="MsoNormal"> </p> 6573 6559 <p class="MsoNormal">The scattering intensity I(q) is:</p> 6574 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image139. gif" height="46" width="133"></span></p>6560 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image139.PNG" ></span></p> 6575 6561 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6576 6562 <p class="MsoNormal">The form factor is,</p> 6577 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image143. gif" height="46" width="398"></span></p>6563 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image143.PNG" ></span></p> 6578 6564 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6579 6565 <p class="MsoNormal">The structure factor is</p> 6580 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image140. gif" height="51" width="334"></span></p>6566 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 16pt;"><img src="image140.PNG" ></span></p> 6581 6567 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6582 6568 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6583 6569 <p class="MsoNormal">where </p> 6584 <p class="MsoNormal" style="text-align: center;" align="center"><span style="position: relative; top: 50pt;"><img src="image141.gif" height="133" width="252"></span></p> 6585 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6586 <p class="MsoNormal" style="text-align: center;" align="center"> </p> 6587 <p class="MsoNormal"> </p> 6570 <br> 6571 <p class="MsoNormal" style="text-align: center;" align="center"><img src="image141.PNG" ></p> 6572 <br> 6588 6573 <p class="MsoNormal">where <span style="font-family: Symbol;">d<sub>T</sub></span> 6589 6574 = tail length (or t_length), <span style="font-family: Symbol;">d<sub>H</sub></span> … … 7615 7600 are included in the calculation. </p> 7616 7601 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 7617 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 27pt;"><img src="image172. gif"></span></p>7602 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 27pt;"><img src="image172.PNG"></span></p> 7618 7603 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 7619 7604 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> … … 7952 7937 by:</p> 7953 7938 <p class="MsoNormal"><span style="font-size: 14pt;"> </span></p> 7954 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="image178. gif"></span></p>7939 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="image178.PNG"></span></p> 7955 7940 <p class="MsoNormal"><span style="font-size: 14pt;"> </span></p> 7956 7941 <p class="MsoNormal" style="text-indent: 0.25in;">The … … 8040 8025 1). </p> 8041 8026 <p class="MsoNormal" style="text-indent: 0.25in;"> </p> 8042 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="image180. gif"></span></p>8027 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="image180.PNG"></span></p> 8043 8028 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 8044 8029 <p class="MsoNormal" style="margin-left: 0.25in;">The … … 8128 8113 model describes a power law 8129 8114 with background.</p> 8130 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="image182. gif"></span></p>8115 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="image182.PNG"></span></p> 8131 8116 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 8132 8117 <p class="MsoNormal" style="margin-left: 0.25in;">Note … … 8199 8184 model.</p> 8200 8185 <p class="MsoNormal" style="margin-left: 0.25in;"><b><span style="font-size: 14pt;"> </span></b></p> 8201 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 15pt;"><img src="image184. gif"></span></p>8186 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 15pt;"><img src="image184.PNG"></span></p> 8202 8187 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 8203 8188 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> … … 8292 8277 the 8293 8278 Texiera reference. The value returned is in cm<sup>-1</sup>.</p> 8294 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 85pt;"><img src="image186.gif"></span></p> 8295 <p class="MsoNormal" style="text-align: center;" align="center"></p> 8296 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 8297 <p class="MsoNormal"><b><span style="font-size: 14pt;"> </span></b></p> 8298 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8299 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8300 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8301 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8302 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8303 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 8279 <br> 8280 <p class="MsoNormal" style="text-align: center;" align="center"><img src="image186.PNG"></p> 8281 <br> 8304 8282 <p class="MsoNormal" style="margin-left: 0.25in;">The 8305 8283 scale … … 9064 9042 a polyelectrolyte solution with the RPA expression derived by Borue and 9065 9043 Erukhimovich. The value returned is in cm<sup>-1</sup>.</p> 9066 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9067 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 43pt;"><img src="image191.gif"></span></p> 9068 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 9069 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 9070 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9044 <br> 9045 <p class="MsoNormal" style="text-align: center;" align="center"><img src="image191.PNG"></p> 9046 <br> 9071 9047 <p class="MsoNormal" style="margin-left: 0.25in;">K 9072 9048 is a contrast factor of the … … 9221 9197 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9222 9198 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9223 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 7pt;"><img src="image192. gif"></span></p>9199 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 7pt;"><img src="image192.PNG"></span></p> 9224 9200 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 9225 9201 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;"> </span></b></p> … … 9352 9328 <p class="MsoNormal" style="margin-left: 0.25in;">For 9353 9329 2D plot, the wave transfer is 9354 defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008. gif"></span><span style="font-size: 14pt;">.</span></p>9330 defined as<span style="font-size: 14pt; position: relative; top: 8pt;"><img src="image008.PNG"></span><span style="font-size: 14pt;">.</span></p> 9355 9331 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><b><span style="font-size: 14pt;"> </span></b></p> 9356 9332 <div align="center"> … … 9438 9414 high q region we can fit the following model: </p> 9439 9415 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9440 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 6pt;"><img src="image197. gif"></span></p>9416 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 6pt;"><img src="image197.PNG"></span></p> 9441 9417 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 9442 9418 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> … … 9503 9479 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> 9504 9480 </p> 9505 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 6pt;"><img src="image198. gif"></span></p>9481 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 6pt;"><img src="image198.PNG"></span></p> 9506 9482 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> </p> 9507 9483 <p class="MsoNormal" style="margin-left: 0.25in;">with … … 9592 9568 describes a Lorentzian 9593 9569 shaped peak including a flat background,</p> 9594 <p class="MsoNormal" style="margin-left: 0.25in;"> 9595 </p> 9596 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 34pt;"><img src="image200.gif"></span></p> 9597 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"> </p> 9598 <p class="MsoNormal" style="margin-left: 0.25in;"></p> 9570 <br> 9571 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><img src="image200.PNG"></p> 9572 <br> 9599 9573 <p class="MsoNormal" style="margin-left: 0.25in;">with 9600 9574 the peak having height of I0 … … 9689 9663 value is scaled to units of [cm-1sr-1], absolute scale.</p> 9690 9664 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9691 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image202. gif"></span></p>9665 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image202.PNG"></span></p> 9692 9666 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9693 9667 <p class="MsoNormal" style="margin-left: 0.25in;">where 9694 9668 the 9695 9669 dimensionless chain dimension is:</p> 9696 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image203. gif"></span></p>9670 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="position: relative; top: 12pt;"><img src="image203.PNG"></span></p> 9697 9671 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 9698 9672 <p class="MsoNormal" style="margin-left: 0.25in;">and 9699 9673 the 9700 9674 polydispersion is</p> 9701 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image204. gif"></span>.</p>9675 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="position: relative; top: 15pt;"><img src="image204.PNG"></span>.</p> 9702 9676 <p class="MsoNormal" style="margin-left: 0.25in;">The 9703 9677 scattering … … 10674 10648 calculates:</p> 10675 10649 <p class="MsoNormal" style="margin-left: 0.25in;"> </p> 10676 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="image222. gif"></span></p>10650 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 5pt;"><img src="image222.PNG"></span></p> 10677 10651 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 10678 10652 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> … … 10895 10869 <p class="MsoNormal"> </p> 10896 10870 <p class="MsoNormal"> </p> 10897 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 15pt;"><img src="image223. gif"></span></p>10871 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 15pt;"><img src="image223.PNG"></span></p> 10898 10872 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 10899 10873 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> … … 11001 10975 <p class="MsoNormal"> </p> 11002 10976 <p class="MsoNormal"> </p> 11003 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 22pt;"><img src="image225. gif"></span></p>10977 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 22pt;"><img src="image225.PNG"></span></p> 11004 10978 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 11005 10979 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> … … 11249 11223 <p class="MsoNormal"> </p> 11250 11224 <p class="MsoNormal"> </p> 11251 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 22pt;"><img src="image228. gif"></span></p>11225 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 22pt;"><img src="image228.PNG"></span></p> 11252 11226 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 11253 11227 <p class="MsoNormal" style="text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> … … 11255 11229 <p class="MsoNormal"> </p> 11256 11230 <p class="MsoNormal"> </p> 11257 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 23pt;"><img src="image229. gif"></span></p>11231 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt; position: relative; top: 23pt;"><img src="image229.PNG"></span></p> 11258 11232 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p> 11259 11233 <p class="MsoNormal" style="margin-left: 0.25in; text-align: center;" align="center"><span style="font-size: 14pt;"> </span></p>
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