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h
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r
s
i
n
t
h
i
s
f
i
e
l
d.
V
a
l
i
d
a
t
i
o
n
o
f
a
h
y
b
r
i
d
a
l
go
r
i
t
h
m
fo
r
s
t
a
t
e
e
s
t
i
m
a
t
i
o
n
i
s
a
c
hi
e
v
e
d
w
i
t
h
s
a
t
i
s
f
a
c
t
o
r
y
pe
r
f
o
r
m
a
n
c
e
r
a
t
e
s
[7].
R
e
a
l
po
w
e
r
s
y
s
t
e
m
l
o
a
d
m
o
de
l
s
a
re
n
o
nl
i
n
e
a
r
a
n
d
l
i
n
e
a
r
i
n
p
ha
s
e
a
n
d
a
m
pl
i
t
ude
,
r
e
s
pe
c
t
i
v
e
l
y
[8].
N
o
n
l
i
n
e
a
r
l
o
a
ds
e
n
c
o
un
t
e
r
p
r
o
b
l
e
m
s
w
i
t
h
a
l
go
ri
t
hm
c
o
n
v
e
r
ge
n
c
e
s
pe
e
d;
t
h
e
r
e
f
o
r
e
,
h
y
b
r
i
d
a
l
go
ri
t
hm
s
a
r
e
us
e
d
t
o
e
s
t
i
m
a
t
e
p
h
a
s
e
a
n
d
a
m
pl
i
t
ude
v
a
l
ue
s
i
n
s
i
de
e
a
c
h
l
o
a
d
t
o
a
vo
i
d
s
u
c
h
pr
o
b
l
e
m
s
[9].
I
n
[10],
F
A
C
T
S
de
v
i
c
e
s
w
e
r
e
ut
i
l
i
s
e
d
t
o
i
m
p
r
o
v
e
pow
e
r
s
y
s
t
e
m
o
pe
r
a
t
i
o
n
c
o
n
t
r
o
l
,
a
n
d
P
M
U
w
a
s
us
e
d
a
s
a
m
o
n
i
t
o
r
t
o
i
m
p
r
o
v
e
t
h
e
c
a
pa
b
i
l
i
t
y
of
s
t
a
t
e
e
s
t
i
m
a
t
i
o
n
s
y
s
t
e
m
s
a
n
d
f
ul
l
o
b
s
e
r
v
a
b
l
e
s
y
s
t
e
m
s
.
T
h
e
s
t
a
b
i
l
i
t
y
o
f
a
pow
e
r
s
y
s
t
e
m
i
s
a
c
r
uc
i
a
l
a
r
e
a
o
f
r
e
s
e
a
r
c
h
t
o
de
s
c
r
i
b
e
t
h
e
ha
rm
o
n
i
c
s
p
r
o
b
l
e
m
,
a
n
d
m
a
n
y
s
t
udi
e
s
e
m
pl
o
y
F
A
CT
de
v
i
c
e
s
,
s
uc
h
a
s
D
S
T
A
T
CO
M
,
a
s
s
h
o
w
n
i
n
[11
,
1
2].
S
t
a
t
e
e
s
t
i
m
a
t
i
o
n
i
s
e
xt
r
e
m
e
l
y
i
m
po
r
t
a
nt
i
n
a
pow
e
r
di
s
t
ri
b
ut
i
o
n
s
y
s
t
e
m
fo
r
de
t
e
r
m
i
n
i
ng
t
h
e
v
a
r
i
a
b
l
e
s
t
a
t
e
i
n
a
s
y
s
t
e
m
n
e
t
w
o
r
k,
a
s
s
h
o
w
n
i
n
[
13].
T
h
e
m
a
i
n
pu
rpo
s
e
of
m
o
n
i
t
o
r
i
n
g
a
s
y
s
t
e
m
i
s
t
o
ob
s
e
r
ve
a
n
d
pr
o
t
e
c
t
a
f
ul
l
s
y
s
t
e
m
.
H
ow
e
ve
r
,
s
uc
h
a
s
y
s
t
e
m
c
a
nn
o
t
m
o
n
i
t
o
r
ha
rm
o
n
i
c
s
w
i
t
h
a
t
r
a
d
i
t
i
o
n
a
l
m
e
t
e
r;
t
hus
,
a
s
t
a
t
e
e
s
t
i
m
a
t
i
o
n
m
e
t
h
o
d
i
s
c
r
uc
i
a
l
f
o
r
pow
e
r
s
y
s
t
e
m
s
.
M
o
r
e
ove
r
,
e
v
o
l
ut
i
o
n
a
r
y
a
l
go
r
i
t
h
m
s
a
r
e
a
l
s
o
i
n
t
r
o
duc
e
d,
w
h
i
c
h
c
a
n
de
s
c
r
i
b
e
m
o
ni
t
o
ri
n
g
s
y
s
t
e
m
s
t
a
t
e
v
a
ri
a
b
l
e
s
i
n
a
po
w
e
r
n
e
t
w
o
r
k
(c
urr
e
nt
a
n
d
v
o
l
t
a
ge
)
[1
4].
T
o
po
l
o
g
y
e
v
a
l
ua
t
i
o
n
n
e
t
w
o
r
ks
w
e
r
e
i
n
v
e
s
t
i
ga
t
e
d
i
n
[1
5],
w
h
i
c
h
a
r
e
de
f
i
n
e
d
a
s
s
t
ra
t
e
gi
c
s
i
t
e
s
f
o
r
m
e
t
e
r
c
o
nn
e
c
t
i
o
n
s
,
a
n
d
m
e
a
s
u
r
e
d
v
a
l
ue
s
us
e
d
t
o
c
a
l
c
ul
a
t
e
t
h
e
r
e
s
t
o
f
t
h
e
v
a
r
i
a
b
l
e
s
t
a
t
e
(X
s
e
r
i
e
s
a
nd
Y
s
h
u
nt
)
.
I
n
[16
,
17]
,
t
h
e
t
o
po
l
o
g
y
a
ppr
o
a
c
h
w
a
s
i
n
t
r
o
duc
e
d
a
n
d
us
e
d
t
o
a
c
h
i
e
v
e
h
a
rm
o
ni
c
s
t
a
t
e
e
s
t
i
m
a
t
i
o
n
(
H
S
E
),
w
h
i
c
h
i
s
c
o
n
duc
t
e
d
by
a
s
s
um
i
n
g
t
ha
t
t
h
e
c
urr
e
n
t
m
e
a
s
u
r
e
d
by
a
pow
e
r
qua
l
i
t
y
m
e
t
e
r
i
s
c
o
nn
e
c
t
e
d
t
o
a
b
us
a
n
d
c
a
n
c
ha
n
ge
t
h
e
P
Q
m
e
t
e
r
l
o
c
a
t
i
o
n
de
pe
n
di
n
g
o
n
t
h
e
n
u
m
b
e
r
of
s
e
c
t
i
o
n
s
l
i
n
ke
d
t
o
t
h
e
c
o
r
r
e
s
po
n
di
n
g
b
us
.
H
ow
e
ve
r
,
t
h
e
a
s
s
um
p
t
i
o
n
s
i
n
t
h
i
s
a
pp
r
o
a
c
h
a
r
e
n
o
t
p
r
a
g
m
a
t
i
c
ow
i
n
g
t
o
t
h
e
l
i
m
i
t
e
d
n
um
b
e
r
o
f
c
h
a
nn
e
l
s
f
o
r
m
o
s
t
pow
e
r
qua
l
i
t
y
m
e
t
e
r
s
.
T
h
us
,
a
m
e
n
d
m
e
nt
s
a
r
e
m
a
de
t
o
p
e
r
m
i
t
t
h
e
us
e
o
f
t
h
e
t
o
po
l
o
g
y
a
pp
r
o
a
c
h
t
o
o
b
t
a
i
n
o
pt
i
m
um
l
o
c
a
t
i
o
n
s
f
o
r
i
n
s
t
a
l
l
i
n
g
pow
e
r
qua
l
i
t
y
m
e
t
e
r
s
.
Co
n
t
i
n
ge
n
t
o
n
s
y
s
t
e
m
a
v
a
i
l
a
b
i
l
i
t
y
,
w
h
e
n
a
s
e
t
n
u
m
b
e
r
o
f
c
h
a
nn
e
l
s
a
r
e
c
o
n
s
i
de
r
e
d
f
o
r
pow
e
r
qua
l
i
t
y
m
e
t
e
r
s
,
a
f
e
w
a
s
s
oc
i
a
t
i
o
n
o
pt
i
o
n
s
b
e
c
o
m
e
a
c
c
e
s
s
i
b
l
e
a
t
a
n
e
s
t
a
b
l
i
s
h
e
d
s
i
t
e
.
I
n
t
hi
s
w
a
y
,
t
h
e
s
y
s
t
e
m
w
o
ul
d
c
h
a
r
a
c
t
e
r
i
s
e
h
o
w
t
h
e
m
e
t
e
r
s
s
h
o
ul
d
b
e
a
s
s
o
c
i
a
t
e
d
w
i
t
h
a
po
w
e
r
a
rr
a
nge
m
e
nt
ra
t
h
e
r
t
ha
n
t
h
e
i
r
n
u
m
b
e
r
a
n
d
e
s
t
a
b
l
i
s
hm
e
nt
de
s
t
i
n
a
t
i
o
n
[18
].
F
i
na
l
l
y
,
t
w
o
m
e
t
h
o
ds
a
r
e
us
e
d
i
n
t
hi
s
s
t
udy
(i
.
e
.
di
s
c
r
e
t
e
fo
uri
e
r
t
r
a
n
s
f
o
r
m
D
F
T
a
nd
pa
rt
i
c
l
e
s
w
a
rm
o
pt
i
m
i
s
a
t
i
o
n
P
S
O
)
a
n
d
c
o
m
pa
r
e
d
w
i
t
h
t
h
e
p
r
o
po
s
e
d
n
ov
e
l
P
S
O
-
RL
S
m
e
t
h
o
d.
M
A
T
L
A
B
i
s
e
m
pl
oy
e
d
t
o
a
c
hi
e
v
e
t
h
e
ob
j
e
c
t
i
ve
of
t
h
e
s
t
udy
,
a
nd
t
h
e
c
o
m
put
a
t
i
o
na
l
m
e
t
h
o
d
i
s
t
e
s
t
e
d
o
n
a
n
I
E
E
E
14
-
b
us
s
t
a
n
d
a
r
d
s
y
s
t
e
m
.
T
h
e
r
e
s
ul
t
s
s
h
o
w
t
h
a
t
t
h
e
P
S
O
-
R
L
S
m
e
t
h
o
d
i
s
s
a
t
i
s
f
a
c
t
o
r
y
,
f
a
s
t
a
nd
m
o
r
e
a
c
c
ura
t
e
t
h
a
n
t
h
e
o
t
h
e
r
t
w
o
m
e
t
h
o
ds
.
T
h
i
s
p
r
o
c
e
dur
e
c
a
n
upg
ra
de
t
h
e
n
u
m
b
e
r
o
f
e
s
t
i
m
a
t
i
o
n
s
a
nd
l
i
m
i
t
e
s
t
i
m
a
t
i
o
n
m
i
s
t
a
ke
s
s
i
m
ul
t
a
n
e
o
us
l
y
.
B
a
s
e
d
o
n
t
h
e
a
b
ov
e
i
n
f
o
r
m
a
t
i
o
n
,
t
h
e
m
a
i
n
c
o
nt
r
i
b
ut
i
o
n
s
o
f
t
h
i
s
s
t
udy
a
r
e
a
s
f
o
l
l
ow
s
:
a)
A
ppl
i
c
a
t
i
o
n
o
f
c
o
m
put
a
t
i
o
na
l
m
e
t
h
o
ds
,
s
uc
h
a
s
t
h
e
h
y
b
r
i
d
a
l
go
ri
t
hm
(P
S
O
-
R
L
S
),
fo
r
s
t
a
t
e
e
s
t
i
m
a
t
i
o
n;
a
l
l
f
unda
m
e
nt
a
l
,
i
nt
e
r
-
a
nd
s
ub
h
a
rm
o
ni
c
s
o
f
p
ow
e
r
s
y
s
t
e
m
s
i
gna
l
s
c
o
nt
a
i
n
v
a
r
i
o
us
n
o
i
s
e
s
o
ur
c
e
s
.
b)
E
v
a
l
ua
t
i
o
n
o
f
t
w
o
i
m
po
rt
a
nt
p
a
ra
m
e
t
e
r
s
o
f
t
h
e
p
r
o
po
s
e
d
P
S
O
-
R
L
S
a
l
go
ri
t
hm
,
t
ha
t
i
s
,
t
h
e
pe
r
f
o
r
m
a
n
c
e
a
n
d
b
e
s
t
ha
rm
o
n
i
c
s
t
a
t
e
e
s
t
i
m
a
t
o
r;
t
h
e
p
r
o
p
o
s
e
d
a
l
go
r
i
t
hm
i
s
t
h
e
n
c
o
m
pa
r
e
d
w
i
t
h
c
o
m
m
o
n
D
F
T
a
nd
P
S
O
a
l
go
r
i
t
h
m
s
.
c)
E
v
a
l
ua
t
i
o
n
o
f
t
h
e
t
hr
e
e
a
l
go
r
i
t
h
m
s
’
pe
r
f
o
r
m
a
n
c
e
i
n
e
s
t
i
m
a
t
i
n
g
t
h
e
ha
rm
o
n
i
c
p
a
r
a
m
e
t
e
r
s
o
f
s
t
a
n
d
a
r
d
s
y
s
t
e
m
da
t
a
p
r
e
c
i
s
e
l
y
f
o
r
f
i
n
d
i
n
g
t
h
e
b
e
s
t
a
nd
m
o
s
t
a
p
p
r
o
pri
a
t
e
m
e
t
h
o
d
f
o
r
ha
rm
o
n
i
c
e
s
t
i
m
a
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In
S
e
c
t
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2,
t
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de
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t
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ha
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a
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n
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t
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m
a
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d.
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p
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t
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c
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6
,
a
n
d
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us
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p
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o
v
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d
i
n
S
e
c
t
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n
7
.
2.
P
O
WER
S
Y
S
TE
M
H
A
R
M
O
N
I
C
S
In
po
w
e
r
s
y
s
t
e
m
n
e
t
w
o
r
ks
,
t
h
e
h
a
rm
o
n
i
c
s
p
r
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b
l
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m
i
s
a
r
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s
e
a
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h
h
o
t
s
po
t
f
o
r
po
w
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r
s
y
s
t
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m
s
c
h
o
l
a
r
s
;
T
h
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r
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f
o
r
e
,
h
a
rm
o
ni
c
s
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n
a
l
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pe
c
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y
,
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o
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t
ra
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o
r
m
,
p
l
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s
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ngi
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f
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t
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E
pi
s
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o
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;
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h
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t
a
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d
(2
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a
n
d
(3)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
In
do
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ppl
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3
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w
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[20
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21]
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h
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us
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d
t
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xp
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s
s
x
(
t
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.
3.
S
TA
TE
ES
TI
M
A
TI
O
N
F
O
R
M
U
LA
TI
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N
T
h
e
f
o
l
l
ow
i
n
g
m
a
t
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e
m
a
t
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c
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l
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t
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o
n
s
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o
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s
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d
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o
r
[1
3
,
22]
.
=
ℎ
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2
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3
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(6)
w
h
e
r
e
i
s
t
h
e
ith
e
rr
o
r
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nt
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x
i
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i
s
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l
a
c
k
b
us
a
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e
i
n
t
h
i
s
c
a
s
e
).
4.
M
A
TH
EM
A
TI
C
A
L
B
A
C
K
G
R
O
U
N
D
4.
1
.
D
F
T
F
o
ur
i
e
r
a
na
l
y
s
i
s
c
o
n
s
i
s
t
s
o
f
v
a
r
i
o
us
t
y
pe
s
of
s
i
gn
a
l
p
r
o
c
e
s
s
i
n
g,
s
uc
h
a
s
f
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r
t
r
a
n
s
f
o
r
m
a
t
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o
n
a
n
d
D
F
T
,
w
h
i
c
h
i
s
a
t
y
pe
of
di
s
c
r
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t
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t
r
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m
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t
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v
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s
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f
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e
of
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s
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s
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pa
ra
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d
b
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s
a
m
pl
e
t
i
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e
s
.
L
e
t
f
(
t
)
be
a
c
o
n
t
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n
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us
s
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na
l
(d
a
t
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s
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r
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e
).
L
e
t
N
b
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f
[
0
]
,
f
[
1
]
,
f
[
2
]
…
.
.
,
f
[
k
]
,
…
.
f
[
N
-
1]
(
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s
a
F
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T
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s
f
o
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m
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s
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na
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,
w
hi
c
h
c
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w
r
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t
t
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n
a
s
:
(
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(
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−
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(7)
We
c
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s
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t
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a
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f
[
k
]
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s
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dri
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[
k
]
.
A
t
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(8)
t
h
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,
(
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[
]
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(9)
O
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f
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t
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a
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y
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ds
a
r
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c
r
uc
i
a
l
[
23
-
25]
.
4.
2
.
P
ar
ti
c
l
e
s
w
ar
m
o
p
ti
m
i
z
at
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t
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ati
o
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P
S
O
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l
s
s
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c
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a
m
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s
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.
In
t
h
e
h
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nt
s
pa
c
e
i
n
s
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a
s
pe
c
i
f
i
e
d
t
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m
e
i
nt
e
r
i
m
,
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
In
do
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s
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a
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o
l
.
22
,
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.
1
,
A
p
r
i
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20
21
:
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9
4
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m
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