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<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial>OK, I made a mistake. The Jacobi elliptic sine values
one ends up with using the Landen transformation do not have the same argument
as the sines at the bottom of the table. If they did, there would be no
need for the transformation. Whereas the sines are evaluated at fractions
of their quarter-period pi/2, the elliptic sines sn are also evaluated at those
same fractions of their quarter-periods K. However, K is not equal to
pi/2. Since we don't actually know K a priori (or at all, unless
the elliptic sines are inverted), the Landen transformation is
needed.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial>What this means is that the poles are calculated using the
elliptic sines and cosines evaluated at fractions (2n-1)/N of their
quarter-periods K. Unlike circular functions, each elliptic function has a
different quarter-period depending on its modulus k. I believe this
process is referred to in the math-world as "mapping."</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial>Needless to say, the mathematics of this is well beyond my
knowledge -- I'm a guy who uses math, not one who understands it. (In
other words, I'm an engineer.)</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial>So, Bernie, if you want to insist on this being an iterative
process, I guess you can. However, if you actually knew the quarter-period
of sn for a given k, then sn could be calculated with an approximation, which is
actually sn(u,m) = tanh u + 0.25k' (sinh u cosh u - u)/cosh*2 u. The
problem here is that we don't actually know u, so we can't calculate sn.
The Landen transformation gives us both sn and the argument at which to
calculate it (but not explicitly so).</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial>In any case, I can now design best-case phase displacement
networks for any bandwidth in about 15 seconds, so suck it,
Jacobi!</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=053452005-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
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<HR tabIndex=-1>
</DIV>
<DIV dir=ltr align=left><FONT size=2 face=Tahoma><B>From:</B> Bernard Arthur
Hutchins, Jr [mailto:bah13@cornell.edu] <BR><B>Sent:</B> Saturday, January 09,
2021 8:45 PM<BR><B>To:</B> synth-diy@synth-diy.org; David G Dixon; Brian
Willoughby<BR><B>Subject:</B> Re: [sdiy] 90-degree phase displacement network
calculations <BR></FONT><BR></DIV>
<DIV></DIV><SPAN
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Non-UBC Email]</SPAN></SPAN></SPAN>
<DIV
style="FONT-FAMILY: Arial, Helvetica, sans-serif; COLOR: rgb(0,0,0); FONT-SIZE: 10pt"><SPAN
style="FONT-SIZE: 12pt">David - what you show as the Landen transform (in the
box) is EXACTLY called iteration............</SPAN>! - Bernie</DIV>
<DIV id=appendonsend></DIV>
<HR style="WIDTH: 98%; DISPLAY: inline-block" tabIndex=-1>
<DIV dir=ltr id=divRplyFwdMsg><FONT style="FONT-SIZE: 11pt" color=#000000
face="Calibri, sans-serif"><B>From:</B> David G Dixon
<dixon@mail.ubc.ca><BR><B>Sent:</B> Saturday, January 9, 2021 8:16
PM<BR><B>To:</B> Bernard Arthur Hutchins, Jr <bah13@cornell.edu>;
synth-diy@synth-diy.org <synth-diy@synth-diy.org><BR><B>Subject:</B> RE:
[sdiy] 90-degree phase displacement network calculations </FONT>
<DIV> </DIV></DIV>
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<DIV dir=ltr align=left><SPAN class=x_661413100-10012021><FONT color=#0000ff
size=2 face=Arial>Hello Bernie,</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=x_661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=x_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=x_661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=x_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=x_661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=x_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=x_661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=x_661413100-10012021><FONT color=#0000ff
size=2 face=Arial><SPAN class=x_661413100-10012021><FONT color=#0000ff size=2
face=Arial><IMG border=0 hspace=0 alt="" align=baseline
src="cid:053452005@10012021-2367"
data-outlook-trace="F:1|T:1"> <IMG border=0 hspace=0 alt=""
align=baseline src="cid:053452005@10012021-236E"
data-outlook-trace="F:1|T:1"></FONT></SPAN></FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=x_661413100-10012021><FONT color=#0000ff
size=2 face=Arial><SPAN
class=x_661413100-10012021></SPAN></FONT></SPAN> </DIV><SPAN
class=x_661413100-10012021><FONT color=#0000ff size=2><SPAN
class=x_661413100-10012021>
<DIV dir=ltr align=left>
<TABLE style="WIDTH: 818pt; BORDER-COLLAPSE: collapse" border=0 cellSpacing=0
cellPadding=0 width=1090>
<COLGROUP><FONT face=Arial>
<COL style="WIDTH: 75pt" span=10 width=100>
<COL style="WIDTH: 68pt" width=90></FONT></COLGROUP>
<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=x_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=x_xl24 width=100><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=x_xl24 width=100><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=x_xl24 width=100><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=x_xl24 width=100><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=x_xl24 width=100><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=x_xl24 width=100><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=x_xl24 width=100><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=x_xl24 width=100><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=x_xl24 width=90><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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_xl24 height=21><FONT face=Arial>0</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl25><FONT face=Arial>—</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl29><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=x_xl30><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=x_xl30><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=x_xl30><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=x_xl30><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=x_xl30><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=x_xl30><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=x_xl30><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=x_xl30><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=x_xl24 height=21><FONT face=Arial>1</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl25><FONT face=Arial>0.999800</FONT></TD>
<TD
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class=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl24 height=21><FONT face=Arial>2</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl25><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=x_xl25><FONT face=Arial>0.277283</FONT></TD>
<TD
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class=x_xl25><FONT face=Arial>0.084258</FONT></TD>
<TD
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class=x_xl25><FONT face=Arial>0.248264</FONT></TD>
<TD
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class=x_xl25><FONT face=Arial>0.399666</FONT></TD>
<TD
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class=x_xl25><FONT face=Arial>0.532763</FONT></TD>
<TD
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class=x_xl25><FONT face=Arial>0.644823</FONT></TD>
<TD
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class=x_xl25><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=x_xl25><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=x_xl25><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=x_xl24 height=21><FONT face=Arial>3</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
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<TD
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class=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl24 height=21><FONT face=Arial>4</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl24 height=21><FONT face=Arial>5</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl24 height=21><FONT face=Arial>6</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl24 height=21><FONT face=Arial>7</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl24 height=21><FONT face=Arial>8</FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl25><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=x_xl25><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=x_xl31><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=x_xl31><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=x_xl31><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=x_xl31><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=x_xl31><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=x_xl31><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=x_xl31><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=x_xl31><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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_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=x_xl27><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=x_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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_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=x_xl24><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_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=x_xl32><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=x_xl32><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=x_xl32><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=x_xl32><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=x_xl32><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=x_xl32><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=x_xl32><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=x_xl32><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=x_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=x_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=x_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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_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=x_xl27><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=x_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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_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=x_xl25><FONT face=Arial></FONT></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_xl25><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=x_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=x_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=x_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=x_xl37><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=x_xl37><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=x_xl37><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=x_xl37><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=x_xl37><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=x_xl37><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=x_xl37><STRONG><FONT face=Arial>0.004299</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: windowtext 1pt solid"
class=x_xl38><STRONG><FONT face=Arial>0.002216</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=x_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=x_xl25><STRONG><FONT face=Arial></FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl34><FONT face=Arial> </FONT></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl39><STRONG><FONT face=Arial>0.000005</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl39><STRONG><FONT face=Arial>0.000019</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl39><STRONG><FONT face=Arial>0.000040</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl39><STRONG><FONT face=Arial>0.000080</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl39><STRONG><FONT face=Arial>0.000156</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl39><STRONG><FONT face=Arial>0.000304</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: #ece9d8"
class=x_xl39><STRONG><FONT face=Arial>0.000589</FONT></STRONG></TD>
<TD
style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid"
class=x_xl40><STRONG><FONT
face=Arial>0.001143</FONT></STRONG></TD></TR></TBODY></TABLE></DIV>
<DIV dir=ltr align=left><FONT face=Arial></FONT> </DIV>
<DIV dir=ltr align=left><SPAN class=x_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=x_661413100-10012021><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=x_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=x_661413100-10012021><FONT color=#0000ff
size=2 face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr lang=en-us class=x_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=x_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=x_MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt">Thanks again David
– </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=x_MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt"></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=x_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> </SPAN> </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=x_MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt"></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=x_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> </SPAN>At the same
time, the mathematicians assure us (prove!) that we will never find closed
form!<SPAN> </SPAN>(Don’t you hate it when you are shown that they are
right?) </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=x_MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt"></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=x_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> That
is: </SPAN>How does convergence progress? </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=x_MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt"></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=x_MsoNormal><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; FONT-SIZE: 12pt">-Bernie </SPAN></P><BR></DIV></DIV></BODY></HTML>