https://github.com/nikiforovavas/the_perturbations
Tip revision: 25262796111ac9f629734af8176d948bfe03521f authored by Vasilisa Nikiforova on 08 November 2017, 21:35:36 UTC
Rename folder
Rename folder
Tip revision: 2526279
Fifth part_html1.html
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8">
<title>Fifth part_html1.html</title>
<!-- Created by Maple 16.02, Mac OS X -->
</head>
<a name="MapleAutoBookmark1" />
<body bgcolor="FFFFFF">
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_1.gif" width="290" height="17" alt="" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_2.gif" width="14" height="14" alt="0" align="center" border="0"></td>
<td width='5%' align='center'>(1)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_3.gif" width="282" height="14" alt="fopen(`ItsM_ex_4.mw`, READ); 1; read `ItsM_ex_4.mw`; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_4.gif" width="276" height="14" alt="fopen(`ItsR_ex_4.mw`, READ); 1; read `ItsR_ex_4.mw`; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_5.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(2)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_6.gif" width="304" height="14" alt="fopen(`ItsMs0_ex_4.mw`, READ); 1; read `ItsMs0_ex_4.mw`; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_7.gif" width="14" height="14" alt="2" align="center" border="0"></td>
<td width='5%' align='center'>(3)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_8.gif" width="286" height="14" alt="fopen(`ItsRs_ex_4.mw`, READ); 1; read `ItsRs_ex_4.mw`; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_9.gif" width="14" height="14" alt="3" align="center" border="0"></td>
<td width='5%' align='center'>(4)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_10.gif" width="304" height="14" alt="fopen(`Equation3_5.mw`, READ); 1; read `Equation3_5.mw`; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_11.gif" width="14" height="14" alt="4" align="center" border="0"></td>
<td width='5%' align='center'>(5)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_12.gif" width="304" height="14" alt="fopen(`Equation5_5.mw`, READ); 1; read `Equation5_5.mw`; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_13.gif" width="14" height="14" alt="5" align="center" border="0"></td>
<td width='5%' align='center'>(6)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_14.gif" width="304" height="14" alt="fopen(`Equation6_5.mw`, READ); 1; read `Equation6_5.mw`; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_15.gif" width="14" height="14" alt="6" align="center" border="0"></td>
<td width='5%' align='center'>(7)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_16.gif" width="304" height="14" alt="fopen(`Equation8_5.mw`, READ); 1; read `Equation8_5.mw`; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_17.gif" width="14" height="14" alt="7" align="center" border="0"></td>
<td width='5%' align='center'>(8)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_18.gif" width="226" height="14" alt="" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_19.gif" width="576" height="14" alt="newser := proc (fe, x, p) local n, s, i, t; n := degree(fe, x); if `<`(n, p) then t := n else t := p end if; s := 0; for i from 0 to `+`(t, `-`(1)) do s := `+`(s, `*`(`^`(x, `+`(n, `-`(i))), `*`(coeff..." align="center" border="0"><br><img src="images/Fifth part_html_20.gif" width="576" height="17" alt="newser := proc (fe, x, p) local n, s, i, t; n := degree(fe, x); if `<`(n, p) then t := n else t := p end if; s := 0; for i from 0 to `+`(t, `-`(1)) do s := `+`(s, `*`(`^`(x, `+`(n, `-`(i))), `*`(coeff..." align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_21.gif" width="219" height="14" alt="" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_22.gif" width="347" height="30" alt="ItsM5 := normal(`/`(`*`(newser(numer(normal(ItsM_ex_4)), f, 10)), `*`(newser(denom(normal(ItsM_ex_4)), f, 10)))); -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_23.gif" width="338" height="30" alt="ItsR5 := normal(`/`(`*`(newser(numer(normal(ItsR_ex_4)), f, 10)), `*`(newser(denom(normal(ItsR_ex_4)), f, 10)))); -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_24.gif" width="360" height="30" alt="ItsMs5 := normal(`/`(`*`(newser(numer(normal(ItsMs0_ex_4)), f, 10)), `*`(newser(denom(normal(ItsMs0_ex_4)), f, 10)))); -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_25.gif" width="351" height="30" alt="ItsRs5 := normal(`/`(`*`(newser(numer(normal(ItsRs_ex_4)), f, 10)), `*`(newser(denom(normal(ItsRs_ex_4)), f, 10)))); -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_26.gif" width="219" height="18" alt="Eq3[1] := newser(normal(Eq3_5), f, 10); -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_27.gif" width="572" height="18" alt="Eq3[2] := newser(normal(`*`(denom(ItsMs5), `*`(subs(M__x = ItsMs5, collect(Eq3[1], M__x))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_28.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(9)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_29.gif" width="576" height="18" alt="Eq3[3] := newser(normal(`*`(denom(simplify(ItsRs5)), `*`(subs(R__x = simplify(ItsRs5), collect(Eq3[2], R__x))))), f, 10); -1; denom(%); 1" align="center" border="0"><br><img src="images/Fifth part_html_30.gif" width="576" height="18" alt="Eq3[3] := newser(normal(`*`(denom(simplify(ItsRs5)), `*`(subs(R__x = simplify(ItsRs5), collect(Eq3[2], R__x))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_31.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(10)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_32.gif" width="524" height="18" alt="Eq3[4] := newser(normal(`*`(denom(ItsM5), `*`(subs(M = ItsM5, collect(Eq3[3], M))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_33.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(11)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_34.gif" width="509" height="18" alt="Eq3[5] := newser(normal(`*`(denom(ItsR5), `*`(subs(R = ItsR5, collect(Eq3[4], R))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_35.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(12)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_36.gif" width="576" height="22" alt="Eq3_13 := algsubs(lambda = l, subs({P = psi, P__x = `+`(`ψ__x`, `*`(psi, `*`(lambda))), U = u, U__x = `+`(u__x, `-`(`*`(u, `*`(lambda)))), q = Q, q__x = `+`(Q__x, `-`(`*`(Q, `*`(lambda))))}, algsu..." align="center" border="0"><br><img src="images/Fifth part_html_37.gif" width="576" height="22" alt="Eq3_13 := algsubs(lambda = l, subs({P = psi, P__x = `+`(`ψ__x`, `*`(psi, `*`(lambda))), U = u, U__x = `+`(u__x, `-`(`*`(u, `*`(lambda)))), q = Q, q__x = `+`(Q__x, `-`(`*`(Q, `*`(lambda))))}, algsu..." align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_38.gif" width="199" height="14" alt="fk := `Eq3_13. mw`; 1; save Eq3_13, fk; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_39.gif" width="92" height="14" alt="`Eq3_13. mw`" align="center" border="0"></td>
<td width='5%' align='center'>(13)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_40.gif" width="219" height="18" alt="Eq5[1] := newser(normal(Eq5_5), f, 10); -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_41.gif" width="572" height="18" alt="Eq5[2] := newser(normal(`*`(denom(ItsMs5), `*`(subs(M__x = ItsMs5, collect(Eq5[1], M__x))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_42.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(14)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_43.gif" width="576" height="18" alt="Eq5[3] := newser(normal(`*`(denom(simplify(ItsRs5)), `*`(subs(R__x = simplify(ItsRs5), collect(Eq5[2], R__x))))), f, 10); -1; denom(%); 1" align="center" border="0"><br><img src="images/Fifth part_html_44.gif" width="576" height="18" alt="Eq5[3] := newser(normal(`*`(denom(simplify(ItsRs5)), `*`(subs(R__x = simplify(ItsRs5), collect(Eq5[2], R__x))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_45.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(15)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_46.gif" width="524" height="18" alt="Eq5[4] := newser(normal(`*`(denom(ItsM5), `*`(subs(M = ItsM5, collect(Eq5[3], M))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_47.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(16)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_48.gif" width="509" height="18" alt="Eq5[5] := newser(normal(`*`(denom(ItsR5), `*`(subs(R = ItsR5, collect(Eq5[4], R))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_49.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(17)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_50.gif" width="576" height="22" alt="Eq5_13 := algsubs(lambda = l, subs({P = psi, P__x = `+`(`ψ__x`, `*`(psi, `*`(lambda))), U = u, U__x = `+`(u__x, `-`(`*`(u, `*`(lambda)))), q = Q, q__x = `+`(Q__x, `-`(`*`(Q, `*`(lambda))))}, algsu..." align="center" border="0"><br><img src="images/Fifth part_html_51.gif" width="576" height="22" alt="Eq5_13 := algsubs(lambda = l, subs({P = psi, P__x = `+`(`ψ__x`, `*`(psi, `*`(lambda))), U = u, U__x = `+`(u__x, `-`(`*`(u, `*`(lambda)))), q = Q, q__x = `+`(Q__x, `-`(`*`(Q, `*`(lambda))))}, algsu..." align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_52.gif" width="199" height="14" alt="fk := `Eq5_13. mw`; 1; save Eq5_13, fk; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_53.gif" width="92" height="14" alt="`Eq5_13. mw`" align="center" border="0"></td>
<td width='5%' align='center'>(18)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_54.gif" width="219" height="18" alt="Eq6[1] := newser(normal(Eq6_5), f, 10); -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_55.gif" width="572" height="18" alt="Eq6[2] := newser(normal(`*`(denom(ItsMs5), `*`(subs(M__x = ItsMs5, collect(Eq6[1], M__x))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_56.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(19)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_57.gif" width="576" height="18" alt="Eq6[3] := newser(normal(`*`(denom(simplify(ItsRs5)), `*`(subs(R__x = simplify(ItsRs5), collect(Eq6[2], R__x))))), f, 10); -1; denom(%); 1" align="center" border="0"><br><img src="images/Fifth part_html_58.gif" width="576" height="18" alt="Eq6[3] := newser(normal(`*`(denom(simplify(ItsRs5)), `*`(subs(R__x = simplify(ItsRs5), collect(Eq6[2], R__x))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_59.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(20)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_60.gif" width="524" height="18" alt="Eq6[4] := newser(normal(`*`(denom(ItsM5), `*`(subs(M = ItsM5, collect(Eq6[3], M))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_61.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(21)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_62.gif" width="509" height="18" alt="Eq6[5] := newser(normal(`*`(denom(ItsR5), `*`(subs(R = ItsR5, collect(Eq6[4], R))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_63.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(22)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_64.gif" width="576" height="22" alt="Eq6_13 := algsubs(lambda = l, subs({P = psi, P__x = `+`(`ψ__x`, `*`(psi, `*`(lambda))), U = u, U__x = `+`(u__x, `-`(`*`(u, `*`(lambda)))), q = Q, q__x = `+`(Q__x, `-`(`*`(Q, `*`(lambda))))}, algsu..." align="center" border="0"><br><img src="images/Fifth part_html_65.gif" width="576" height="22" alt="Eq6_13 := algsubs(lambda = l, subs({P = psi, P__x = `+`(`ψ__x`, `*`(psi, `*`(lambda))), U = u, U__x = `+`(u__x, `-`(`*`(u, `*`(lambda)))), q = Q, q__x = `+`(Q__x, `-`(`*`(Q, `*`(lambda))))}, algsu..." align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_66.gif" width="199" height="14" alt="fk := `Eq6_13. mw`; 1; save Eq6_13, fk; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_67.gif" width="92" height="14" alt="`Eq6_13. mw`" align="center" border="0"></td>
<td width='5%' align='center'>(23)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><font color="#000000" size="3" face="Times New Roman"></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_68.gif" width="219" height="18" alt="Eq8[1] := newser(normal(Eq8_5), f, 10); -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_69.gif" width="572" height="18" alt="Eq8[2] := newser(normal(`*`(denom(ItsMs5), `*`(subs(M__x = ItsMs5, collect(Eq8[1], M__x))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_70.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(24)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_71.gif" width="576" height="18" alt="Eq8[3] := newser(normal(`*`(denom(simplify(ItsRs5)), `*`(subs(R__x = simplify(ItsRs5), collect(Eq8[2], R__x))))), f, 10); -1; denom(%); 1" align="center" border="0"><br><img src="images/Fifth part_html_72.gif" width="576" height="18" alt="Eq8[3] := newser(normal(`*`(denom(simplify(ItsRs5)), `*`(subs(R__x = simplify(ItsRs5), collect(Eq8[2], R__x))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_73.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(25)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_74.gif" width="524" height="18" alt="Eq8[4] := newser(normal(`*`(denom(ItsM5), `*`(subs(M = ItsM5, collect(Eq8[3], M))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_75.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(26)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_76.gif" width="509" height="18" alt="Eq8[5] := newser(normal(`*`(denom(ItsR5), `*`(subs(R = ItsR5, collect(Eq8[4], R))))), f, 10); -1; denom(%); 1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_77.gif" width="14" height="14" alt="1" align="center" border="0"></td>
<td width='5%' align='center'>(27)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_78.gif" width="576" height="22" alt="Eq8_13 := algsubs(lambda = l, subs({P = psi, P__x = `+`(`ψ__x`, `*`(psi, `*`(lambda))), U = u, U__x = `+`(u__x, `-`(`*`(u, `*`(lambda)))), q = Q, q__x = `+`(Q__x, `-`(`*`(Q, `*`(lambda))))}, algsu..." align="center" border="0"><br><img src="images/Fifth part_html_79.gif" width="576" height="22" alt="Eq8_13 := algsubs(lambda = l, subs({P = psi, P__x = `+`(`ψ__x`, `*`(psi, `*`(lambda))), U = u, U__x = `+`(u__x, `-`(`*`(u, `*`(lambda)))), q = Q, q__x = `+`(Q__x, `-`(`*`(Q, `*`(lambda))))}, algsu..." align="center" border="0"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"><img src="images/Fifth part_html_80.gif" width="199" height="14" alt="fk := `Eq8_13. mw`; 1; save Eq8_13, fk; -1" align="center" border="0"></td>
</tr>
</table> </p>
<p align="center"><table width='100%'>
<tr>
<td valign="top" align="center"><font color="#0000ff" size="3" face="Times New Roman"><img src="images/Fifth part_html_81.gif" width="92" height="14" alt="`Eq8_13. mw`" align="center" border="0"></td>
<td width='5%' align='center'>(28)</td>
</tr>
</table></font> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
<p align="left"><table>
<tr>
<td valign="top" align="center"><font color="#ff0000" size="3" face="Courier New"><strong>> </strong></font></td>
<td valign="top"></td>
</tr>
</table> </p>
</body>
</html>