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<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial>Hello Bernie,</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial>No, it is not iterative. It is closed form. The
step-wise procedure is an implementation of the Landen transformation to enable
calculation of elliptic sine from circular sine. That is all. If
Excel had a function call for elliptic sine, I would use that instead.
Once the elliptic sine is calculated the poles are obtained directly. Once
half the poles are obtained, then you just take the logarithms, set them
negative, and take the antilogs to find the other half.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial>The reason for the steps is that you must transform the k and
k' values using a simple formula until you obtain k = 0 and k' = 1. At
that point, sn = sin, so you can simply find the sines of the angles
(2n-1)*(pi/2)/4N and take those as the elliptic sines. Then, you go back
up the chain of k and k' values, calculating the elliptic sines from those below
(of which the first one, on the bottom of the table, is a circular sine).
When you get to the top of the table, you have an elliptic sine at
the desired modulus. This is then used to calculate the pole
directly.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial>To make this more plain, here is a table showing the
calculations in Excel.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial><SPAN class=661413100-10012021><FONT color=#0000ff size=2
face=Arial><IMG border=0 hspace=0 alt="" align=baseline
src="cid:661413100@10012021-3393"> <IMG border=0 hspace=0
alt="" align=baseline
src="cid:661413100@10012021-339A"></FONT></SPAN></FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial><SPAN
class=661413100-10012021></SPAN></FONT></SPAN> </DIV><SPAN
class=661413100-10012021><FONT color=#0000ff size=2><SPAN
class=661413100-10012021>
<DIV dir=ltr align=left>
<TABLE style="WIDTH: 818pt; BORDER-COLLAPSE: collapse" border=0 cellSpacing=0
cellPadding=0 width=1090 x:str>
<COLGROUP><FONT face=Arial>
<COL style="WIDTH: 75pt; mso-width-source: userset; mso-width-alt: 2844"
span=10 width=100>
<COL style="WIDTH: 68pt; mso-width-source: userset; mso-width-alt: 2560"
width=90></FONT>
<TBODY>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
height=21 width=100><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl35 width=100><FONT face=Arial>4N</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 width=100 x:num><FONT face=Arial>32</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 width=100 x:num><FONT face=Arial>1</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 width=100 x:num><FONT face=Arial>3</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 width=100 x:num><FONT face=Arial>5</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 width=100 x:num><FONT face=Arial>7</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 width=100 x:num><FONT face=Arial>9</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 width=100 x:num><FONT face=Arial>11</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 width=100 x:num><FONT face=Arial>13</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; WIDTH: 68pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 width=90 x:num><FONT face=Arial>15</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36 height=21><FONT face=Arial>i</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>k</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>k'</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>sn(π/64)</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>sn(3π/64)</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>sn(5π/64)</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>sn(7π/64)</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>sn(9π/64)</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>sn(11π/64)</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>sn(13π/64)</FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl36><FONT face=Arial>sn(15π/64)</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21 x:num><FONT face=Arial>0</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><FONT face=Arial>—</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl29 x:num="1E-4"><FONT color=#ff0000
face=Arial><STRONG>0.000100</STRONG></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl30 x:num="0.31954908778216407"
x:fmla="=(1+$B4)*D4/(1+$B4*D4^2)"><STRONG><FONT color=#3366ff
face=Arial>0.319549</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl30 x:num="0.75882300219892307"
x:fmla="=(1+$B4)*E4/(1+$B4*E4^2)"><STRONG><FONT color=#3366ff
face=Arial>0.758823</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl30 x:num="0.92963895262695051"
x:fmla="=(1+$B4)*F4/(1+$B4*F4^2)"><STRONG><FONT color=#3366ff
face=Arial>0.929639</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl30 x:num="0.98079395245268941"
x:fmla="=(1+$B4)*G4/(1+$B4*G4^2)"><STRONG><FONT color=#3366ff
face=Arial>0.980794</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl30 x:num="0.99485657133820127"
x:fmla="=(1+$B4)*H4/(1+$B4*H4^2)"><STRONG><FONT color=#3366ff
face=Arial>0.994857</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl30 x:num="0.99862970112246652"
x:fmla="=(1+$B4)*I4/(1+$B4*I4^2)"><STRONG><FONT color=#3366ff
face=Arial>0.998630</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl30 x:num="0.99963543572806379"
x:fmla="=(1+$B4)*J4/(1+$B4*J4^2)"><STRONG><FONT color=#3366ff
face=Arial>0.999635</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl30 x:num="0.99990304582766598"
x:fmla="=(1+$B4)*K4/(1+$B4*K4^2)"><STRONG><FONT color=#3366ff
face=Arial>0.999903</FONT></STRONG></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21 x:num><FONT face=Arial>1</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.99980001999800017" x:fmla="=(1-C3)/(1+C3)"><FONT
face=Arial>0.999800</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="1.9998000199982782E-2" x:fmla="=SQRT(1-B4^2)"><FONT
face=Arial>0.019998</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.16409222159323647"
x:fmla="=(1+$B5)*D5/(1+$B5*D5^2)"><FONT face=Arial>0.164092</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.45957748887243821"
x:fmla="=(1+$B5)*E5/(1+$B5*E5^2)"><FONT face=Arial>0.459577</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.67939430999979955"
x:fmla="=(1+$B5)*F5/(1+$B5*F5^2)"><FONT face=Arial>0.679394</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.82079804538860868"
x:fmla="=(1+$B5)*G5/(1+$B5*G5^2)"><FONT face=Arial>0.820798</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.9034429805416675"
x:fmla="=(1+$B5)*H5/(1+$B5*H5^2)"><FONT face=Arial>0.903443</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.94906239839059414"
x:fmla="=(1+$B5)*I5/(1+$B5*I5^2)"><FONT face=Arial>0.949062</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.97345209132416455"
x:fmla="=(1+$B5)*J5/(1+$B5*J5^2)"><FONT face=Arial>0.973452</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.98626912113215703"
x:fmla="=(1+$B5)*K5/(1+$B5*K5^2)"><FONT face=Arial>0.986269</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21 x:num><FONT face=Arial>2</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.96078815802371775" x:fmla="=(1-C4)/(1+C4)"><FONT
face=Arial>0.960788</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.27728345677553784" x:fmla="=SQRT(1-B5^2)"><FONT
face=Arial>0.277283</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="8.4257695419860446E-2"
x:fmla="=(1+$B6)*D6/(1+$B6*D6^2)"><FONT face=Arial>0.084258</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.24826384223891873"
x:fmla="=(1+$B6)*E6/(1+$B6*E6^2)"><FONT face=Arial>0.248264</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.39966617248610581"
x:fmla="=(1+$B6)*F6/(1+$B6*F6^2)"><FONT face=Arial>0.399666</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.5327627875975175"
x:fmla="=(1+$B6)*G6/(1+$B6*G6^2)"><FONT face=Arial>0.532763</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.64482349359736113"
x:fmla="=(1+$B6)*H6/(1+$B6*H6^2)"><FONT face=Arial>0.644823</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.73578453382704834"
x:fmla="=(1+$B6)*I6/(1+$B6*I6^2)"><FONT face=Arial>0.735785</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.80743701351050501"
x:fmla="=(1+$B6)*J6/(1+$B6*J6^2)"><FONT face=Arial>0.807437</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.86253585063777793"
x:fmla="=(1+$B6)*K6/(1+$B6*K6^2)"><FONT face=Arial>0.862536</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21 x:num><FONT face=Arial>3</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.56582314551300739" x:fmla="=(1-C5)/(1+C5)"><FONT
face=Arial>0.565823</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.82452663268190807" x:fmla="=SQRT(1-B6^2)"><FONT
face=Arial>0.824527</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="5.3898932282505044E-2"
x:fmla="=(1+$B7)*D7/(1+$B7*D7^2)"><FONT face=Arial>0.053899</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.16087342405339869"
x:fmla="=(1+$B7)*E7/(1+$B7*E7^2)"><FONT face=Arial>0.160873</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.2654175649715656"
x:fmla="=(1+$B7)*F7/(1+$B7*F7^2)"><FONT face=Arial>0.265418</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.36603901998352861"
x:fmla="=(1+$B7)*G7/(1+$B7*G7^2)"><FONT face=Arial>0.366039</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.46142187386290923"
x:fmla="=(1+$B7)*H7/(1+$B7*H7^2)"><FONT face=Arial>0.461422</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.55046926314605304"
x:fmla="=(1+$B7)*I7/(1+$B7*I7^2)"><FONT face=Arial>0.550469</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.63232407619966602"
x:fmla="=(1+$B7)*J7/(1+$B7*J7^2)"><FONT face=Arial>0.632324</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.7063682545863379"
x:fmla="=(1+$B7)*K7/(1+$B7*K7^2)"><FONT face=Arial>0.706368</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21 x:num><FONT face=Arial>4</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="9.6174736052035664E-2" x:fmla="=(1-C6)/(1+C6)"><FONT
face=Arial>0.096175</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.99536446598485784" x:fmla="=SQRT(1-B7^2)"><FONT
face=Arial>0.995364</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="4.9181457081762414E-2"
x:fmla="=(1+$B8)*D8/(1+$B8*D8^2)"><FONT face=Arial>0.049181</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.14706419000911147"
x:fmla="=(1+$B8)*E8/(1+$B8*E8^2)"><FONT face=Arial>0.147064</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.24351156938729249"
x:fmla="=(1+$B8)*F8/(1+$B8*F8^2)"><FONT face=Arial>0.243512</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.33758389401240496"
x:fmla="=(1+$B8)*G8/(1+$B8*G8^2)"><FONT face=Arial>0.337584</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.42836692199998322"
x:fmla="=(1+$B8)*H8/(1+$B8*H8^2)"><FONT face=Arial>0.428367</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.51498138851900621"
x:fmla="=(1+$B8)*I8/(1+$B8*I8^2)"><FONT face=Arial>0.514981</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.59659189985388728"
x:fmla="=(1+$B8)*J8/(1+$B8*J8^2)"><FONT face=Arial>0.596592</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.67241508194302824"
x:fmla="=(1+$B8)*K8/(1+$B8*K8^2)"><FONT face=Arial>0.672415</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21 x:num><FONT face=Arial>5</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="2.3231515315444832E-3" x:fmla="=(1-C7)/(1+C7)"><FONT
face=Arial>0.002323</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.99999730147983978" x:fmla="=SQRT(1-B8^2)"><FONT
face=Arial>0.999997</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="4.9067740373185675E-2"
x:fmla="=(1+$B9)*D9/(1+$B9*D9^2)"><FONT face=Arial>0.049068</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.14673066817083066"
x:fmla="=(1+$B9)*E9/(1+$B9*E9^2)"><FONT face=Arial>0.146731</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.24298048839154618"
x:fmla="=(1+$B9)*F9/(1+$B9*F9^2)"><FONT face=Arial>0.242980</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.33689025635558889"
x:fmla="=(1+$B9)*G9/(1+$B9*G9^2)"><FONT face=Arial>0.336890</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.42755556485782747"
x:fmla="=(1+$B9)*H9/(1+$B9*H9^2)"><FONT face=Arial>0.427556</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.51410325451718708"
x:fmla="=(1+$B9)*I9/(1+$B9*I9^2)"><FONT face=Arial>0.514103</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.59569982302833779"
x:fmla="=(1+$B9)*J9/(1+$B9*J9^2)"><FONT face=Arial>0.595700</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.67155945230844161"
x:fmla="=(1+$B9)*K9/(1+$B9*K9^2)"><FONT face=Arial>0.671559</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21 x:num><FONT face=Arial>6</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="1.3492619006131591E-6" x:fmla="=(1-C8)/(1+C8)"><FONT
face=Arial>0.000001</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.99999999999908973" x:fmla="=SQRT(1-B9^2)"><FONT
face=Arial>1.000000</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="4.9067674327440296E-2"
x:fmla="=(1+$B10)*D10/(1+$B10*D10^2)"><FONT face=Arial>0.049068</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.14673047445542708"
x:fmla="=(1+$B10)*E10/(1+$B10*E10^2)"><FONT face=Arial>0.146730</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.24298017990336795"
x:fmla="=(1+$B10)*F10/(1+$B10*F10^2)"><FONT face=Arial>0.242980</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.33688985339235594"
x:fmla="=(1+$B10)*G10/(1+$B10*G10^2)"><FONT face=Arial>0.336890</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.42755509343044112"
x:fmla="=(1+$B10)*H10/(1+$B10*H10^2)"><FONT face=Arial>0.427555</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.51410274419339386"
x:fmla="=(1+$B10)*I10/(1+$B10*I10^2)"><FONT face=Arial>0.514103</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.59569930449260833"
x:fmla="=(1+$B10)*J10/(1+$B10*J10^2)"><FONT face=Arial>0.595699</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.6715589548471862"
x:fmla="=(1+$B10)*K10/(1+$B10*K10^2)"><FONT
face=Arial>0.671559</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21 x:num><FONT face=Arial>7</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="4.5513592894529012E-13" x:fmla="=(1-C9)/(1+C9)"><FONT
face=Arial>0.000000</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num x:fmla="=SQRT(1-B10^2)"><FONT
face=Arial>1.000000</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="4.9067674327418015E-2"
x:fmla="=(1+$B11)*D11/(1+$B11*D11^2)"><FONT face=Arial>0.049068</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.14673047445536175"
x:fmla="=(1+$B11)*E11/(1+$B11*E11^2)"><FONT face=Arial>0.146730</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.24298017990326387"
x:fmla="=(1+$B11)*F11/(1+$B11*F11^2)"><FONT face=Arial>0.242980</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.33688985339222005"
x:fmla="=(1+$B11)*G11/(1+$B11*G11^2)"><FONT face=Arial>0.336890</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.42755509343028208"
x:fmla="=(1+$B11)*H11/(1+$B11*H11^2)"><FONT face=Arial>0.427555</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.51410274419322166"
x:fmla="=(1+$B11)*I11/(1+$B11*I11^2)"><FONT face=Arial>0.514103</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.59569930449243336"
x:fmla="=(1+$B11)*J11/(1+$B11*J11^2)"><FONT face=Arial>0.595699</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.67155895484701833"
x:fmla="=(1+$B11)*K11/(1+$B11*K11^2)"><FONT
face=Arial>0.671559</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21 x:num><FONT face=Arial>8</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num x:fmla="=(1-C10)/(1+C10)"><FONT
face=Arial>0.000000</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num x:fmla="=SQRT(1-B11^2)"><FONT
face=Arial>1.000000</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl31 x:num="4.9067674327418015E-2"
x:fmla="=SIN((PI()/2)*D1/$C$1)"><STRONG><FONT
face=Arial>0.049068</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl31 x:num="0.14673047445536175"
x:fmla="=SIN((PI()/2)*E1/$C$1)"><STRONG><FONT
face=Arial>0.146730</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl31 x:num="0.24298017990326387"
x:fmla="=SIN((PI()/2)*F1/$C$1)"><STRONG><FONT
face=Arial>0.242980</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl31 x:num="0.33688985339222005"
x:fmla="=SIN((PI()/2)*G1/$C$1)"><STRONG><FONT
face=Arial>0.336890</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl31 x:num="0.42755509343028208"
x:fmla="=SIN((PI()/2)*H1/$C$1)"><STRONG><FONT
face=Arial>0.427555</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl31 x:num="0.51410274419322166"
x:fmla="=SIN((PI()/2)*I1/$C$1)"><STRONG><FONT
face=Arial>0.514103</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl31 x:num="0.59569930449243336"
x:fmla="=SIN((PI()/2)*J1/$C$1)"><STRONG><FONT
face=Arial>0.595699</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl31 x:num="0.67155895484701833"
x:fmla="=SIN((PI()/2)*K1/$C$1)"><STRONG><FONT
face=Arial>0.671559</FONT></STRONG></TD></TR>
<TR style="HEIGHT: 16.5pt" height=22>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 16.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=22><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><STRONG><FONT face=Arial></FONT></STRONG></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: windowtext 1pt solid"
class=xl26><FONT face=Arial>omega</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl28><STRONG><FONT face=Arial>sn</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.31954908778216407" x:fmla="=D3"><FONT
face=Arial>0.319549</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.75882300219892307" x:fmla="=E3"><FONT
face=Arial>0.758823</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.92963895262695051" x:fmla="=F3"><FONT
face=Arial>0.929639</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.98079395245268941" x:fmla="=G3"><FONT
face=Arial>0.980794</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.99485657133820127" x:fmla="=H3"><FONT
face=Arial>0.994857</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.99862970112246652" x:fmla="=I3"><FONT
face=Arial>0.998630</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.99963543572806379" x:fmla="=J3"><FONT
face=Arial>0.999635</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.99990304582766598" x:fmla="=K3"><FONT
face=Arial>0.999903</FONT></TD></TR>
<TR style="HEIGHT: 16.5pt" height=22>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 16.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=22><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid"
class=xl27 x:num x:fmla="=SQRT(10000)"><FONT
face=Arial>100.000000</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl28><STRONG><FONT face=Arial>cn</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.94756972329089684" x:fmla="=SQRT(1-D13^2)"><FONT
face=Arial>0.947570</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.65129689952725334" x:fmla="=SQRT(1-E13^2)"><FONT
face=Arial>0.651297</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.36847173264535016" x:fmla="=SQRT(1-F13^2)"><FONT
face=Arial>0.368472</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.19504671961412631" x:fmla="=SQRT(1-G13^2)"><FONT
face=Arial>0.195047</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.10129364474239456" x:fmla="=SQRT(1-H13^2)"><FONT
face=Arial>0.101294</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="5.2332781657898175E-2" x:fmla="=SQRT(1-I13^2)"><FONT
face=Arial>0.052333</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="2.6999919199214208E-2" x:fmla="=SQRT(1-J13^2)"><FONT
face=Arial>0.027000</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="1.3924760125634435E-2" x:fmla="=SQRT(1-K13^2)"><FONT
face=Arial>0.013925</FONT></TD></TR>
<TR style="HEIGHT: 16.5pt" height=22>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 16.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=22><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl28><STRONG><FONT face=Arial>pole</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl32 x:num="296.53338392155041" x:fmla="=1/SQRT($C$3)*D14/D13"><FONT
face=Arial>296.533</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl32 x:num="85.829883601303621" x:fmla="=1/SQRT($C$3)*E14/E13"><FONT
face=Arial>85.830</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl32 x:num="39.63600402114519" x:fmla="=1/SQRT($C$3)*F14/F13"><FONT
face=Arial>39.636</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl32 x:num="19.886615239252791" x:fmla="=1/SQRT($C$3)*G14/G13"><FONT
face=Arial>19.887</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl32 x:num="10.181733494119909" x:fmla="=1/SQRT($C$3)*H14/H13"><FONT
face=Arial>10.182</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl32 x:num="5.2404591610960276" x:fmla="=1/SQRT($C$3)*I14/I13"><FONT
face=Arial>5.240</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl32 x:num="2.7009765994889299" x:fmla="=1/SQRT($C$3)*J14/J13"><FONT
face=Arial>2.701</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl32 x:num="1.3926110320134355" x:fmla="=1/SQRT($C$3)*K14/K13"><FONT
face=Arial>1.393</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: windowtext 1pt solid"
class=xl26><FONT face=Arial>f</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl28><STRONG><FONT face=Arial>log pole</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="2.4720735936084108" x:fmla="=LOG(D15)"><FONT
face=Arial>2.472074</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="1.9336385235543343" x:fmla="=LOG(E15)"><FONT
face=Arial>1.933639</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="1.5980898637990117" x:fmla="=LOG(F15)"><FONT
face=Arial>1.598090</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="1.2985608712086136" x:fmla="=LOG(G15)"><FONT
face=Arial>1.298561</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="1.0078217252344295" x:fmla="=LOG(H15)"><FONT
face=Arial>1.007822</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.71936934087571203" x:fmla="=LOG(I15)"><FONT
face=Arial>0.719369</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.43152082159698263" x:fmla="=LOG(J15)"><FONT
face=Arial>0.431521</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.14382983125574833" x:fmla="=LOG(K15)"><FONT
face=Arial>0.143830</FONT></TD></TR>
<TR style="HEIGHT: 16.5pt" height=22>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 16.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=22><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid"
class=xl27 x:num="628.31853071795865" x:fmla="=2*PI()*B14"><FONT
face=Arial>628.318531</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl28><STRONG><FONT face=Arial>−log pole</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="-2.4720735936084108" x:fmla="=-D16"><FONT
face=Arial>-2.472074</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="-1.9336385235543343" x:fmla="=-E16"><FONT
face=Arial>-1.933639</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="-1.5980898637990117" x:fmla="=-F16"><FONT
face=Arial>-1.598090</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="-1.2985608712086136" x:fmla="=-G16"><FONT
face=Arial>-1.298561</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="-1.0078217252344295" x:fmla="=-H16"><FONT
face=Arial>-1.007822</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="-0.71936934087571203" x:fmla="=-I16"><FONT
face=Arial>-0.719369</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="-0.43152082159698263" x:fmla="=-J16"><FONT
face=Arial>-0.431521</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="-0.14382983125574833" x:fmla="=-K16"><FONT
face=Arial>-0.143830</FONT></TD></TR>
<TR style="HEIGHT: 16.5pt" height=22>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 16.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=22><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl28><STRONG><FONT face=Arial>−pole</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="3.3723015829629339E-3" x:fmla="=10^D17"><FONT
face=Arial>0.003372</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="1.1650953700988256E-2" x:fmla="=10^E17"><FONT
face=Arial>0.011651</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="2.5229586702698769E-2" x:fmla="=10^F17"><FONT
face=Arial>0.025230</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="5.0285078077347715E-2" x:fmla="=10^G17"><FONT
face=Arial>0.050285</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="9.8215102622506628E-2" x:fmla="=10^H17"><FONT
face=Arial>0.098215</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.19082297357143277" x:fmla="=10^I17"><FONT
face=Arial>0.190823</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.37023645454359611" x:fmla="=10^J17"><FONT
face=Arial>0.370236</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25 x:num="0.71807559829121914" x:fmla="=10^K17"><FONT
face=Arial>0.718076</FONT></TD></TR>
<TR style="HEIGHT: 15.75pt" height=21>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; HEIGHT: 15.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl24 height=21><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=xl25><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: #ece9d8"
class=xl33><STRONG><FONT face=Arial>RC</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: #ece9d8"
class=xl37 x:num="0.47194753842881504" x:fmla="=D15/$B$17"><STRONG><FONT
face=Arial>0.471948</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: #ece9d8"
class=xl37 x:num="0.1366025024014948" x:fmla="=E15/$B$17"><STRONG><FONT
face=Arial>0.136603</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: #ece9d8"
class=xl37 x:num="6.3082659643754979E-2" x:fmla="=F15/$B$17"><STRONG><FONT
face=Arial>0.063083</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: #ece9d8"
class=xl37 x:num="3.1650531166936967E-2" x:fmla="=G15/$B$17"><STRONG><FONT
face=Arial>0.031651</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: #ece9d8"
class=xl37 x:num="1.6204732148334986E-2" x:fmla="=H15/$B$17"><STRONG><FONT
face=Arial>0.016205</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: #ece9d8"
class=xl37 x:num="8.3404497955963976E-3" x:fmla="=I15/$B$17"><STRONG><FONT
face=Arial>0.008340</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: #ece9d8"
class=xl37 x:num="4.298737769842016E-3" x:fmla="=J15/$B$17"><STRONG><FONT
face=Arial>0.004299</FONT></STRONG></TD>
<TD
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<DIV dir=ltr align=left><FONT face=Arial></FONT> </DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT face=Arial>So, you
see, there is no iteration. You simply have to transform k' until it
equals 1. I have determined that this always occurs within 8 steps, as
shown. Here it actually occurred in 6 steps, and the calculated sn values
were equal to the sine value until i = 4 to six decimal
places.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT face=Arial>The
calculation for "p" is closed-form, but there is no more convenient way to
calculate elliptic sines.</FONT></SPAN></DIV></SPAN></FONT></SPAN>
<DIV dir=ltr align=left><SPAN class=661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr lang=en-us class=OutlookMessageHeader align=left>
<HR tabIndex=-1>
<FONT size=2 face=Tahoma><B>From:</B> Bernard Arthur Hutchins, Jr
[mailto:bah13@cornell.edu] <BR><B>Sent:</B> Saturday, January 09, 2021 1:35
PM<BR><B>To:</B> synth-diy@synth-diy.org<BR><B>Cc:</B> David G
Dixon<BR><B>Subject:</B> [sdiy] 90-degree phase displacement network
calculations <BR></FONT><BR></DIV>
<DIV></DIV><SPAN
style="BACKGROUND-COLOR: #ffecb3; COLOR: #000000; FONT-SIZE: 12px"><SPAN
style="BACKGROUND-COLOR: #ffecb3; COLOR: #000000; FONT-SIZE: 12px"><SPAN
style="PADDING-BOTTOM: 3px; LINE-HEIGHT: 1.6; BACKGROUND-COLOR: #ffecb3; FONT-STYLE: normal; PADDING-LEFT: 3px; PADDING-RIGHT: 3px; COLOR: #000000; FONT-SIZE: 12px; FONT-WEIGHT: normal; PADDING-TOP: 3px">[<STRONG>CAUTION:</STRONG>
Non-UBC Email]</SPAN></SPAN></SPAN>
<DIV>
<P style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt" class=MsoNormal><FONT
color=#ff0000 face="Arial, sans-serif"><SPAN
style="BACKGROUND-COLOR: rgb(250,250,250)"></SPAN></FONT> </P>
<P
style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt; FONT-FAMILY: Calibri, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 11pt"
class=MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt">Thanks again David
–<O:P> </O:P></SPAN></P>
<P
style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt; FONT-FAMILY: Calibri, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 11pt"
class=MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt"><O:P></O:P></SPAN></P>
<P
style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt; FONT-FAMILY: Calibri, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 11pt"
class=MsoNormal><SPAN style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt">I
see. Your function is NOT closed form – it is iterative; self-terminating at 8
“for loops” – absolutely NOTHING wrong with that.<SPAN
style="mso-spacerun: yes"> </SPAN><O:P> </O:P></SPAN></P>
<P
style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt; FONT-FAMILY: Calibri, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 11pt"
class=MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt"><O:P></O:P></SPAN></P>
<P
style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt; FONT-FAMILY: Calibri, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 11pt"
class=MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt">In equiripple designs
we have the powerful “alternation theorem” to tell us WHEN we have “found” an
acceptable ER solution (at least - close enough). <SPAN
style="mso-spacerun: yes"> </SPAN>At the same time, the mathematicians
assure us (prove!) that we will never find closed form!<SPAN
style="mso-spacerun: yes"> </SPAN>(Don’t you hate it when you are shown
that they are right?)<O:P> </O:P></SPAN></P>
<P
style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt; FONT-FAMILY: Calibri, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 11pt"
class=MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt"><O:P></O:P></SPAN></P>
<P
style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt; FONT-FAMILY: Calibri, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 11pt"
class=MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt">What happens (if you
know) if you terminate after just a couple of iterations?<SPAN
style="mso-spacerun: yes"> That is: </SPAN>How does convergence
progress?<O:P> </O:P></SPAN></P>
<P
style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt; FONT-FAMILY: Calibri, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 11pt"
class=MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt"><O:P></O:P></SPAN></P>
<P
style="LINE-HEIGHT: 107%; MARGIN: 0in 0in 8pt; FONT-FAMILY: Calibri, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 11pt"
class=MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt">-Bernie<O:P> </O:P></SPAN></P><BR></DIV></BODY></HTML>