f >-·--·~·-~~----~-~----~-.-~-·-----' ~--·-·-·-
·----···-· ----
.·
CAliFORNIA STATE UNIVERSITY, NORTHRIDGE
DIG I 1ri\L
:t:;\J~..fl:i.Ol'~l'fiEI~1T
II
CC~PUT2~
A~ALYSIS
A graduate project subTitted in partial
satisfaction of ~he re~ireGents for the
degree of Master of Scie~ce in
Erlgin.e€r·irtg
Steven LuJwig Barrows
The graduate project of Steven Ludwig Barrows is approved:
Committee Chairman
California State University, Northridge
August , 1975
j_j_
Table of Contents
iv
• ABSTRACT
Analysis of Cathode Ray Tube Displays
1
SIDEWINDER Missile
8
Bibliography
19
.A.ppendix A
20
Appendix B
24
Appendix C
26
Appendix D
32
Illustrations
L~1e
Pattern on the Cathode Ray Tube
SIDE"NINDER Target Tracking Discr·iption
9
SIDEWINDER Missile Test Bench
10
Spiral Form
lJ
Matrix Form of the Initial EQuations
1.4'
15
· Program Block Diagram
1
4
Curve Fitting
28
Computational Method
29
Computational Results
31
iii
I
iI
~---- -------·--·~--····-~ ···~-----··---
•
·• - • -
_.
'
ABSTRACT
Digital Environment
Computer Analysis
(DEGA)
by
Steven Ludwig Barrows
Masters of Science in Engineering
August~
19'7 5
This report contains discriptions of two projects completed at the Pacific Missile Test Center, Point Mugu,
California.
The first deals with factors which affect the
probability of identification of objects on Cathode Ray
:Tube (CRT) displays.
The second was the establishment of
the amplitude phase relationship for gyro head to body
coupling in the SIDEWINDER missilee
iv
r- - -------- --- ------- -------
Analysis
~f
Cathode Ray Tube Displays
Cathode ray tube (CRT) displays have become an integral part of cockpit hardware.
reconnaissance operations.
They are used heavily in
A camera mounted on the under-
: body of the aircraft picks up visual images which are displayed on a CRT monitor.
This·allows aircraft personnel
. to view enemy weapons from the air.
This system has great
capabilities over simple viewing from a window
magnifieations are possible..
sine~
large
The greatest advantage,
• though, is that the system enable_s the viewer to perceive
·"invisible" light since cameras are not as limited as the
· human eye and electronic processing produces a visible
image on a CRT display.
The range of the spectrum of
major interest now is tne infrared.
The process of viewing an
imag~
on a CRT display
introduces new fields of investigation.
display image, the resolution of
~he
The size of the
display image and the
contrast of the image with its background are factors
i
which influence the accuracy with which objects can be
recognized.
This project intends to make usable
• tative information available.
The ability to identify an
object on a screen from a range of objects was
interest.
quanti~
~f
special
That is, not merely the location of an object
but also its propei identification was required.
1
' Investigation -----_.
~--~~--~----~~-~---~----
Forty reports on the capabilities of CRT displays
were investigated.
These reports were the results of ex-
periments done with untrained personnel.
In these exper-
iments the subjects were instructed to view a screen and
identify objects.
For example, one group of experiments
involved the recognition of military targets.
The subject
was given a pictorial list of targets such as tanks, guns
and supply trucks.
He then viewed a CRT screen which had
a terrain displayed on it.
Within this terrain was one
or more of the given figures.
The subject was then scored
on his ability to correctly identify the object.
Table one contains a listing of the
iables used in the tests.
~ndependent
var-
Each of these variables was a
factor which was believed to affect the probability that
a subject would correctly identify an object displayed on
a CRT screen.
the reader.
ture.
Display lines inay be a term unfamiliar to
A CRT display does not show a continuous pic-
Actually the image is made up of a series of lines,
A beam of electrons is swept across the face of the dis• play (See Diagram one).
In general the more lines involved
the better is the quality of the picture.
Each report selected was searched for each of the
variables listed in Table one.
In every report some of
these variables were constant.
Often a variable was not
even listed in a report.
In that case the author of the
3
Table bne
List of Independent Variables
nur:-~ber
1.
The
of different types of symbols displayed·.
2.
The type of symbol displayed (numeric, military, etc.).
J.
The size of the s_y'1!1bol on the display screen.
4.
The size of the display screen •.
t'..
.J•
The number of lines on th.e display screen •
6.
The number of lines in :the symbol.
_.
[_IN E PATTE. RN ON
-r \--\E._
CATHODE RAY TUBE
ELECTR0JN G-Ul'.J
/
·/:·
- ------- -
--
L:-
1
---
I
SCREEN__/
..
Diagram One
'
'
-
.•'•
.
.
•
~\~
I
- ------ ----5
to the value of that variable in the report.
Once the data
were collected they were placed on a TYMSHARE data file.
The TYMSHARE data file allows extensiva lists to be
made up and stored on a main library disk.
Once a data
file is complete the TYMSHARE system has a large number
.
. of analysis routines which can be easily run to investigate relations between data vectors.
Since a reduction of
the data collected was the intent of this project, collection of the data on computer files was thought advan• tageous.
Once this data file was complete a print out of
it was produced (See Appendix A).
. iables are listed as vectors..
The independent var-
The last column contains
the accuracy vector which was the one kno'Arn dependent
vector.
Table two is included in Appendix A to explain
the abbreviations of vector names used within the program.
Analysis
The analysis was done to establish a rating of the
relative effectiveness of each independent variable in
the prediction of the accuracy of recognition.
In order
to proceed with this it was necessary to remove a bias
from the accuracy vector.
Clearly. as the number of
symbols decreases there exists a good chance of merely
guessing the outcome.
The probability of guessing an
outcome is the inverse of the number of symbols.
This
6
.
bias was removed by·the use of ad' statistic.
The value
: of the accuracy was taken as the mean of a biased population while the inverse of the number of symbols was taken
as the mean of the bias.
The means of the two distribu-
tions in terms of a standard deviation were subtracted.
This yielded a d' statistic which was a good unbiased
estimator of the accuracy.
From these calcuations a new
vector was formed entitled ZSCOR and the analysis was
continued.
The method used
linear correlation.
~o
evaluate the data was a simple
Correlation methods test an assump-
. tion that a dependent variable is a function of a number
of independent variables.
If the assumption is correct a
corrclatior. analysis will produce a number (correlation
coefficient) which has a
magni~ude
close to one.
If the
assumption was false the correlation coeficient will have
a magnitude close to zero.
used in this report.
Only simple correlation was
Simple correlation is performed on
the assumption tl1.at the dependent variable is directly
:related to only ..J:ne independent variable.
This is scored
the same way except that when the coefficient is positive,
the dependent variable tends to increase as the independent variable increases, whereas, it will decrease if the
coefficient is negative.
Of course
~here
is an infinite
number of ways in which a dependent varia.ble can be related to an independent variable.
~·--
1
1,)------------
Appendix B contains the results of a simple corre-·
: lation.
This is an output from a program available on the
TYMSHARE system.
·collected.
This program was run using the data
The line of interest is the bottom line which
:lists the correlation coefficients associated with each
'independent variable and the dependent variable ZSCOR •.
These data are interpited as explained; that is, CONT
has a higher correlation than WLIN and, therefore, it is
viewed as a greater determiner of the outcome.
Thus, the
variables have been quantitatively ranked as to significance.
The data were very extensive so thera is strong
reason to assume that these results are reliable.
Con-
· firmation of this prediction would be a good basis for
further experimentation.
SlDEWINDER Missile
The purpose of this project is twofold.
The first
area of concern is to perform laboratory measurements of
. seeker gyro transient precession rate in relation to gyro
:head angle.
The second is to establish the amplitude phass
relationship from the data derived for gyro head to body
coupling in the SIDEWINDER missile.
!J.'he SIDEVHNDER missile tracks a target by following
'the infrared light given out by its jet exhaust.
The
guidance section consists of a photocell that is sensitive
to infrared light.
A servo system keeps the missile body
aligned with the gyro seeker by activating small jets which
reorient the missile body (See Diagram two).
The missile
ignites when it is within a specified distance from the
·target*
·1aborator_x
The missile guidance unit was strapped to a rotating
platter.
The platter was placed on a bench along with a
signa]. source.
This approach allows tracking of a signal
'source at different angles (See Diagram three).
The plat-
ter was placed in its
"zero~
tracking the target.
Then the platter was rotated.
the seeker still
tr~cking,
position until the seeker was
the source was shut off.
With
By
rotating both the platter and the guidance system body,
all points of the target plane were reached.
8
5 f D E WTNL5l~l~:--rA R;Gl~T~~":TF{ACK~T1~J&~"~~~~·-~.-~~""-~··
DISCR\ PT\ON
BODY
./
,--A.RGET
F I I""-'
r::>....::.T -,Ir\ t.:,
I ..-
<' c
.- \.. . . -
'-' .... C l-.... C::
R H <",-'c C:....:;
.,... c li
THG':Tl\R&S=.T
THEN THE f::OD'/ REf\LI (_3-~.!S
Diagram Two
10
.. SEE'...-r- 8
.
\)
?4=--]~.
\ ""-·::or /
L/1-··---·--·- Al
--------------1
fs,s1 QJ:lAr-~.L-_ /8F.]\\CH ~i''HSS!L.E .
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1
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1
Diagram Three
' .·.
,, .
1
• •
:· •
.. -... ~: _~~
\...J"
.' ' .
·~ ~
I ,I ..
t
•
.· ,
t
t1
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)
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:il
which when electronically processed produce orthogonal
voltage references for the seeker position relative to the
guidance unit body.
In this way the seeker position can
be easily monitored.
:was
suspect~
Since the linearity of these voltages
calibration data were taken at intervals
throughout the target plane.
Reduction of these data
·showed the two signals to be approximately linear,
A
total of nine runs·were made •. Included is a graph of
these data.
The arrows indicate progression with
time~
The next step was to attempt a. curve fit on the data
·(See Appendix C).
There was reason to believe from primary
·data analysis that the data approximately follow a spiral.
A general form is given in Diagram four.
Therefore, the
spiral is a function of the four variables which are
constraints of velocity, angle, and final position.
Gener-
ated values for x(t), y(t) were calculated by the use of
z transforms.
Since there are four variables there will
be sixteen partial differential equations (second order).
· Therefore matrix solution was used in evaluation of incremental adjustments to the
variable~.
The equations involved are discribed in Diagram
five ("S" is explained in Appendix C).
These equations have the formt
AX=Y
Inversion creates the solutiont
~- --~~--~-~--~~~~----~---~----- ~~-
-s pi ·r~aJ-
---
~~--~3-~-~
-
~~~-~~~--~··~- -~-~-~~~~~--~-~~-~--~-
F;Y"n/
Diagram Four
1. 4-
fv'\ATRlX
~OR~·t OF THE
IN l Tl AL EQl)A.T\O~~S
n
_ otS
-
--
d. Y.ii
~q;.
'j
Diagram Five
-
15
t~··-------.------------------·
!
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·-----·
-
.
------- ··----
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---
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-------
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7
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COHPt'TE
FO!?At
lv1A7t-?~
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)/0
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Diagram Six
16
---------------
<>-------------------~---.
!which is the method
~mployed
by the computer program.
Program
Diagram six is a block diagram of the program.
The
function of each block is described as followsa
Subroutine
Track T
Given a value of t, searches a
t ( j) file for t ( j)
<t <t ( j+I)
then returns j.
Value Generation
Generates values of the function
through Inter-
for values of t lying between
polation
experimental data points.
Assignment of
Constraints
Index Monitor
Sets up a file for the derivation
of the partial derivatives.
Deletes computation of duplicate
derivatives.
Compute
Controls the calculation from
S,x(t) ,y(t)
Subroutine
GYSSQD
Form l\'Iatrix
and Solve
Controls the z transforms and
calculates
s.
Performs the inversion of the
p~rtial
derivative matrix.
Decision process for "Is S small
He turn
Yes
mathematical models of S,x(t),y(t).
No
enough"
17
Increment
_.
Constraints
Output t,x(t),
Adds calculated increment to
previous guess for a.
Forms output file.
y(t) ,xt,Yt
Given the experimental values and some guesses for
the constraints this program calculates the "best fit"
parameters for a spiral.
The program and a sample output
are included in Appendix D.
Ontnut
_........_
T~e
first line of output contains the values of the
constraints which produced the lowest mean squared
deviation along with a print out of that deviation.
first column of data is the ref ererwe time c
The
The second and
fourth columns are interpolated values of the normalized
input values.
The third and fifth columns are the computed
values from the z transform using the constraints given
above.
Table three contains a listing of results.
Table Three
.·
Tabulated Results
Lamda
Phi
X(final)
.121
-3.42
-3.23
.. 45
.075
-3.00
' -4.02
-2.39
.029
-3.71
-2.77
-1.02
.113
-3.06
-4.27
-3.63
.089
-3.12
-4.14
-2.24
.020
-3.52
-2.20
-0.39
.077
-3.06
-2.29
-5.02
.065
-3.00
-2.86
-1.57
.148
-3.00
-· 3. 00
~1.60
-3.08
-3.50
-2.28
Y(final)
Average•
.100
.·
Cress, Di:::·h:sen, and Graha--~, FO?'I'I=U,~'i Fom_~ w:i_t!"l '.'[/;_ :cT;C~ 8x:d
1:/_\-J:'FI'/, j\Ir::w Jersey:
Prcr:tice-~all, Inc. 19-iO.
Hoe1, Introduction to ~athematica1 Statistics,
John Wiley and Sans, Inc. 1970.
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California.
F'ou~.",
( 19 ?O) ,
20
.·
Anpendix A
CRT Data Files
This is a complete listing of the data collected on CRT
displays.
Included is a table of the abbreviations used.
T I TLEi:- CF:TIIi4T ----'"
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Table Two
List of Program Vectors Used
The number of different symbols used.
'NYSM
ALPHA
. GEOM
The types of symbols were-alpha or numeric •.
'!'he types of s;)'Thbols were geometric •
MILT
The types of symbols were military.
SYMSIZ
'l'he size of the s:;,rmbols (degrees).
SYMI.IN
The number of lines per symbol.
BW
The band width of the display.
DSIZE
The size of the display (inches) •
.DLINE
The number of lines on the display.
ACCU
The accuracy of identification.
24
_.
Ap-:;endix B
Correlation
This is the result of a correlation performed on the
collected data.
system.
This program was run on the
~PYiv:SHARE
25 "-:
j
···I
I
I'
j
':F·:::: ;F-:,···:·,
PLEA~E LOG
PF:O.J CODE:
l
I
i
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TYMSHARE
IN:
CAP2534~:tt;
Cll 1/17/75
13:20
- S:TATF'AK
1>LDAD F.'EDUC
j
iI
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2>REPLACE NSYM=LOG(NSYM)
. I!
l
j
3>REM_NAME NSYM AS LSYM
f
'i
!
;
;
4>COPPE!_ATIOri
CORRELATION MATRIX
LSYM
ALPHA
HLIN
Ht'1I t-1
GEOM
cm·n
fiCCU
: S:COF"
I
lI
l
l
LS:'·•'t-1
1.0000
I
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ALPHA
. '31 o·::: 1 . oooo
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~-1
GE01·1
-.0'333 -.4286 1.0000
I,JL In
-.5326 -.6480
.4020 1.0000
Hr·1 It·~
-.3212 -.1416 -.2450
.3634 1.0000
l.o.H·l I fi
-.2909 -.1592
.0169
.5119
.8258 1.0000
.3291 -.1686
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-
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Appendix C
Theory of Curve Fitting
This is a complete discussion of the second derivative
method of curve fitting.
>)...-.----------- - - -
Theory of Curve Fitting
A curve of one constant has the forma
x=y=a(t)
The intent is to find a value of "a" such that the com: puted values of x,y agree as closely as possible to the
experimental values.
To accomplish this a sum is form-
ed (see diagram seven).
Clearly smaller values of "S"
represent closer fits and S/(number of values minus one)
equals the experimental variance "s2".
to minimize "S".
be chosen.
In this example the
The objective is
con~traint
"a" must
The technique is to alter the value of "a"
until a "best fit" is found.
A simple computational model
for derivine; "a." is shown in diagram eight.
Consider "S" as a function of Ha", S(a) then S(a)
vs. "a" is some graph whose absolute minimum of S(a)
occurs at the desired value of "a" (see diagram seven,
bottom).
To arrive at good guesses at this constraint
consider the graph of the yartial derivative of S(a) with
respect to
"a"~
guess for "a".
Evaluate this :partial at some initial
A line with slope equal to the second par-
tial derivative of S(a) can be evaluated at this guess
(see diagram eight, bottom).
This line can be used as an
approximation to the curve and the value of the constraint
"a" when this line intersects the horizontal axis is the
new guess for "a".
27 -
28
WHERE
x't" ;
Y-c_ A ec £X PERl /vtEJ.JTA L. VALUeS
;cc.-t) > y c..-c)
A 12c co.utovT£0 .
____ . tlA L U.C..S___
a
Diagram Seven
- r·
--- L.()i'·Yf3t]TA\\CY1V7-\C--~~~r~RDD----·---~------~-~----------~--­
~G
t-
00 P)
J-------.
h.
x <.:f) -=- a l-t)
\f ct) = ~l-t)
s
NO
=0?
YeS
LT P..Y-NEYJ. "a".
~-~·-•w•---·-·----------~------------~
F-----~~--~----------------~~
a..
Diagram Eight ·
)0
_,_,!
The reasoning b·ehind this technique is that "S" is at
• its minimum value when its partial derivative with respect
to "a" equals zero.
The following is an explanation as to
how the previously discussed method arrives at this value
of "a".
Consider the general equation for a linea
y=mx+b
A transformation of axis yields the equationa
y=m(x-ao)
Assuming that the line drawn in diagram eight, bottom is
a close approximation to the actual curve, it must intersect the horizontal axis at the desired value of "a".
Thus a new, better guess has been arrived at (see diagram
· nine).
. ~·· ...
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A NEtU 13£ST GUESC>.
Diagrm Nine
_:zs
_. ____
.
-
.·
A. .Imendix D
SIDEWINDER Program
This program performs a spiral curve fit using a set of
input data.
--- -
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.
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FOR~t.n ( 11111
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T ltH ( I -f l l == Tl
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______ AVFC 21 =YFO
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--------------~-------,------------
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AL A'-\ 01\ {3 l =XL Mhl + 0 l M\
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... ·~·
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- - - - - - !\P.f-1 U 3 l,;PII I iJ:!:ClC:Hl
C
THIS IS f!H'JGRM-1 SHUTTLE
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5
IF {J.Et).K) GC T'1 107
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F(I;~J,t<,Ll=S
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(·)~JT I 'ILE
________NlMAX~~~AX+~--------------------------------·----~-------------------------------DL"''2=2
.*GLAr~
----------~PHL=2.*02HL----~-----------------------------------------------~---------
OXF2=2.*i1XF
·---"---OVF2 ==2 .~DYF____________·
PlF( l)=(F{3,Z,2r2l-F( 1,2;2,2) )/0Ln2
---:---'Plf:{ 2J ::0 .__ _ _ _ _ _ _ _ _
. ---·- •._
P 1 F ( 4} =( F- ( 2 t 2 1 2 1 3) -F ( 2 1 2, 2, l) I fDVF 2
_;p_1f( 31.=0. - - 02 F ( 1' 4) = ( F ( 3, 2 '2, 3 )+_F \ l I 2 f 2 J 1)- F ( 3 '2 J 2, 1) -r: ( 1 '2 J 2 I 3) } I ( OL ~12 >:'8 't'F 2)
.. --~-rzr: < 4, 1 l = 0 ZF < 1, 4 t _____________ __.:._ ___ _:____ ;.. ______________ _
P 2 F (_ l , 1 ) == ( F ( 3 , 2 , ~ , 2 ) + F ( 1 r 2 , 2 , 2 } - ~ • * F { 2 1 2 , 2 1 2 } l I ( 0 l I' ~I ** 2 )
_ __..P2F ( 4, :'-l = ( F! 2, 2 t 2, 3) +_': { 2, 2 t 2 t l.l-:2 ._::<FJ 2 s2J_2c,?,ll/ (QV_F**._2..._}_ _ _ _,c_._ _ _ _ __
0 E: L ::J = " ;z;: : 1 , l ) * P 2 '- ( 4 , t,.) -· P 2 i= ! t., , ·t} *" 2
_:Z.lL_frJ~·~&r _< lH r E 15.3 l ______ .. ____ __.:._ ____-___ _
A(lr 1)-=D2F(4,4l/•J:O:LO
_____ A( 1, 4 l :=- 0 2 F( 1 ,t+ l /f'E;;lD
*
_ ... ·_. _ _. _
.....
,-
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A(4,l}=A{l,4)
___!. (it, 4 )__:=_~ 2F:U t 1)_/'1 EJ...D
h ( 4, 2) =0.
· ___ .1\(1,2)=0~-------------J\( 1,3) =0.
.
o= LY F =- ( :. ( 4, 1 )
-·- ________ ,.(t,,J)::Q._
------- - · - - - - - - - - - · - - - - - - - - - - -
---------------------
1 F ( 1 ) + H 4 , 2) * P 1 F ( 2 ) +:. ( 4, 3) *? 1 F ( J} + ~d 4, 4} *? 1 F ( 4 ))
-~--·_____ DELl A'.(=~ ( .'1 ( 1, }.)~ D l FJ ll.+ AU ,z.L-:-.!?
{_2} ~ ·~_(_lr.U :>_1?_1 U3l..:':.l\JJ, 4_l;:_:~t_U...4_}_,lc__ _ _ __
YF 'J= Y F ( + C C l Y F ·
... _ - - - - .. XLf-,'1~= )L.'YC+OELLM' _ - - - - - ! F ( S. (T. H ( l ) ) G'l TO 2 Z9 ·
... --~---- H { 1) = S.. _ ---------...,.--..:....-~
:::< P
t.:
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H(2)=Xl:\~ 1 0
_ _ _ H ( 5 L=_Y_fO _ _ _ _ _ _ _ _ _ _ _ _ __
22 9
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CONTINLE
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