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s
y
s
t
e
m
v
i
a
v
a
r
i
a
t
i
o
n
a
l
i
t
e
ra
t
i
o
n
m
e
t
h
o
d
w
i
t
h
t
h
e
de
s
c
r
i
pt
i
o
n
o
f
pa
r
t
i
a
l
de
ri
v
a
t
i
v
e
s
us
i
ng
c
a
pu
t
o
[11].
S
o
l
ve
t
h
e
Z
a
k
ha
r
o
v
-
K
uz
n
e
t
s
o
v
s
y
s
t
e
m
us
i
n
g
t
h
e
H
o
m
o
t
o
p
y
a
na
l
y
s
i
s
m
e
t
h
o
d
[12]
.
F
i
n
d
t
h
e
a
pp
r
o
xi
m
a
t
e
a
na
l
y
t
i
c
a
l
s
o
l
ut
i
o
n
o
f
Z
a
kh
a
r
o
v
-
K
uz
n
e
t
s
o
v
s
y
s
t
e
m
us
i
n
g
t
h
e
f
r
a
c
t
i
o
n
a
l
i
t
e
r
a
t
i
o
n
m
e
t
h
o
d
[13].
I
n
o
r
de
r
t
o
de
a
l
w
i
t
h
n
o
rm
a
l
a
n
d
p
a
r
t
i
a
l
l
i
n
e
a
r
a
n
d
n
o
n
-
l
i
n
e
a
r
di
f
fe
r
e
nt
i
a
l
e
qua
t
i
o
n
s
w
e
h
a
v
e
us
e
d
t
h
e
n
e
w
i
t
e
r
a
t
i
v
e
m
e
t
h
o
d
(N
IM
)
b
e
c
a
us
e
of
i
t
s
f
l
e
xi
b
i
l
i
t
y
a
n
d
a
b
i
l
i
t
y
t
o
s
o
l
ve
n
o
n
-
l
i
n
e
a
r
di
f
f
e
r
e
n
t
i
a
l
e
qua
t
i
o
n
s
w
i
t
h
hi
g
h
qu
a
l
i
t
y
a
n
d
s
m
o
o
t
h
l
y
a
n
d
h
e
r
e
l
i
e
s
i
t
s
s
t
r
o
n
g
c
ha
ra
c
t
e
ri
s
t
i
c
.
It
h
a
s
a
l
s
o
be
e
n
us
e
d
i
n
t
h
e
a
na
l
y
t
i
c
a
l
p
r
o
c
e
s
s
i
n
g
o
f
f
r
a
c
t
i
o
n
a
l
pa
r
t
i
a
l
di
f
f
e
r
e
n
t
i
a
l
e
qua
t
i
o
n
s
i
n
ge
n
e
r
a
l
p
h
y
s
i
c
s
a
n
d
f
l
ui
d
m
e
c
h
a
ni
c
s
[14].
T
h
e
n
e
w
i
t
e
r
a
t
i
v
e
m
e
t
h
o
d
w
a
s
pro
pos
e
d
by
D
a
f
t
a
r
da
r
-
G
e
j
j
i
a
n
d
J
a
f
a
r
i
i
n
o
r
de
r
t
o
ov
e
r
c
o
m
e
t
h
e
pr
o
b
l
e
m
of
s
o
l
v
i
n
g
pa
r
t
i
a
l
a
n
d
o
r
d
i
n
a
r
y
n
o
n
l
i
ne
a
r
di
f
f
e
r
e
n
t
i
a
l
e
qua
t
i
o
n
s
,
s
y
s
t
e
m
s
of
di
f
fe
r
e
n
t
i
a
l
a
n
d
a
l
ge
b
r
a
i
c
e
qua
t
i
o
n
s
[15
-
18]
.
O
n
e
o
f
t
h
e
m
o
s
t
pr
o
m
i
n
e
nt
p
r
o
b
l
e
m
s
w
e
f
a
c
e
i
n
m
a
t
h
e
m
a
t
i
c
a
l
s
c
i
e
n
c
e
s
,
e
s
pe
c
i
a
l
l
y
i
n
n
u
m
e
r
i
c
a
l
a
na
l
y
s
i
s
,
i
s
s
o
l
v
i
n
g
n
o
n
-
l
i
n
e
a
r
e
qua
t
i
o
n
s
.
T
h
e
n
e
w
i
t
e
r
a
t
i
v
e
m
e
t
h
o
d
i
s
o
n
e
of
t
h
e
b
e
s
t
m
o
de
rn
m
e
t
h
o
ds
fo
r
s
o
l
v
i
n
g
n
o
n
-
l
i
n
e
a
r
e
qua
t
i
o
n
s
i
n
a
d
di
t
i
o
n
t
o
t
h
e
H
o
m
o
t
o
p
y
pe
r
t
u
r
b
a
t
i
o
n
m
e
t
h
o
d,
a
n
d
de
c
o
m
po
s
i
t
i
o
n
m
e
t
h
o
d
a
n
d
o
t
h
e
r
s
[19
-
21
].
M
o
r
e
ov
e
r
,
G
r
o
s
a
n
a
nd
A
b
ra
ha
m
[6]
,
a
l
s
o
de
b
a
t
e
t
h
e
a
pp
l
i
c
a
b
i
l
i
t
y
of
t
h
e
i
t
e
ra
t
i
v
e
m
e
t
h
o
ds
f
o
r
s
o
l
v
i
n
g
n
o
nl
i
n
e
a
r
s
y
s
t
e
m
s
i
n
v
a
r
i
o
us
s
c
i
e
n
c
e
s
l
i
ke
:
n
e
u
r
o
ph
y
s
i
o
l
o
g
y
,
t
h
e
k
i
n
e
m
a
t
i
c
s
s
y
n
t
h
e
s
i
s
p
r
o
b
l
e
m
,
t
h
e
b
urn
i
n
g
p
r
o
b
l
e
m
,
a
n
d
t
h
e
e
c
o
n
o
m
i
c
s
m
o
de
l
i
n
g
p
r
o
b
l
e
m
[22
-
24
].
O
n
e
o
f
t
h
e
b
e
s
t
i
m
p
r
o
v
e
m
e
n
t
s
f
r
o
m
na
t
u
r
e
i
s
P
S
O
,
w
h
i
c
h
w
a
s
de
v
e
l
o
p
e
d
by
J
a
m
e
s
K
e
nn
e
dy
a
n
d
R
us
s
e
l
l
E
b
e
rh
a
rt
i
n
19
95
[1
,
2].
P
S
O
h
a
s
r
e
c
e
n
t
l
y
e
m
e
r
ge
d
a
s
a
n
a
l
go
r
i
t
hm
i
n
s
o
l
v
i
n
g
m
u
l
t
i
pl
e
i
m
p
r
o
v
e
m
e
n
t
p
r
o
b
l
e
m
s
a
n
d
i
n
v
a
r
i
o
us
s
c
i
e
n
c
e
a
n
d
e
n
gi
n
e
e
r
i
n
g
.
[25
-
27]
.
T
h
e
p
a
r
t
i
c
l
e
s
w
a
rm
o
pt
i
m
i
z
a
t
i
o
n
a
l
go
r
i
t
hm
i
s
a
po
pul
a
t
i
o
n
-
b
a
s
e
d
r
a
ndo
m
s
e
a
r
c
h
a
l
go
ri
t
hm
t
ha
t
i
s
a
go
o
d
s
o
l
ut
i
o
n
t
o
t
h
e
pr
o
b
l
e
m
of
n
o
n
l
i
n
e
a
r
o
pt
i
m
i
z
a
t
i
o
n
,
t
h
e
b
a
s
i
s
of
t
h
e
P
S
O
a
l
go
r
i
t
hm
i
s
i
n
s
pi
r
e
d
by
t
h
e
s
o
c
i
a
l
b
e
h
a
v
i
o
r
of
a
n
i
m
a
l
s
s
uc
h
a
s
t
h
e
f
l
ow
of
f
i
s
h
,
t
h
e
e
duc
a
t
i
o
n
o
f
b
i
r
ds
,
e
t
c
.
A
s
e
ve
r
y
o
n
e
kn
o
w
s
,
w
h
e
n
a
g
r
o
up
o
f
b
i
r
ds
o
r
f
i
s
h
w
a
n
t
t
o
f
i
n
d
f
oo
d,
t
h
e
y
s
e
a
r
c
h
i
n
a
n
a
r
e
a
t
o
f
i
n
d
t
h
e
b
e
s
t
pl
a
c
e
t
o
e
a
t
.
T
h
e
n
a
t
u
r
e
o
f
s
o
c
i
a
l
b
e
h
a
v
i
o
r
e
na
b
l
e
s
a
n
y
m
e
m
b
e
r
of
t
hi
s
s
qua
d
r
o
n
t
o
f
i
n
d
a
w
a
y
t
ha
t
i
s
de
s
i
r
a
b
l
e
(t
h
e
b
e
s
t
w
a
y
)
t
h
e
n
t
h
e
p
r
o
c
e
s
s
of
fo
l
l
ow
i
n
g
t
h
e
m
e
m
b
e
r
s
o
f
t
h
e
s
qua
d
r
o
n
b
e
gi
n
s
t
o
f
o
l
l
ow
t
h
e
o
pt
i
m
a
l
pa
t
h
de
pe
n
di
n
g
o
n
t
h
e
l
o
c
a
t
i
o
n
o
f
t
h
e
p
a
rt
i
c
l
e
a
nd
i
t
s
s
pe
e
d
a
s
t
h
e
s
qua
d
r
o
n
s
c
o
m
m
u
ni
c
a
t
e
t
h
i
s
i
n
f
o
r
m
a
t
i
o
n
t
o
e
a
c
h
o
t
h
e
r
w
h
i
l
e
a
dj
us
t
i
n
g
i
t
s
l
o
c
a
t
i
o
n
a
n
d
s
pe
e
d
D
y
n
a
m
i
c
a
l
l
y
e
x
pl
o
i
t
e
d
b
e
s
t
F
o
r
e
a
c
h
s
i
t
e
pa
rt
i
c
l
e
s
t
h
e
n
t
h
e
n
e
x
t
s
t
e
p
be
gi
n
s
a
t
r
a
n
s
i
t
i
o
n
t
o
t
h
e
r
e
s
t
of
t
h
e
m
e
m
b
e
r
s
of
t
h
e
s
qua
d
r
o
n
t
o
t
h
e
i
de
a
l
l
o
c
a
t
i
o
n,
T
h
e
P
S
O
m
e
t
h
o
d
ha
s
b
e
c
o
m
i
n
g
k
n
o
w
n
a
n
d
w
i
de
l
y
us
e
d
b
e
c
a
us
e
of
i
t
s
f
e
a
t
ur
e
s
,
i
n
c
l
ud
i
n
g
e
a
s
e
a
nd
s
i
m
pl
i
c
i
t
y
i
n
i
m
pl
e
m
e
nt
a
t
i
o
n,
i
t
s
a
b
i
l
i
t
y
t
o
r
e
a
c
h
c
o
n
v
e
r
ge
n
c
e
qui
c
kl
y
t
o
a
n
o
pt
i
m
a
l
s
o
l
ut
i
o
n,
T
h
e
us
e
of
r
udi
m
e
n
t
a
r
y
m
a
t
h
e
m
a
t
i
c
a
l
o
pe
r
a
t
o
r
s
[28
,
2
9].
T
h
e
P
S
O
a
l
go
ri
t
hm
a
l
s
o
f
e
a
t
u
r
e
s
t
h
e
f
o
l
l
o
w
i
n
g:
T
h
e
ps
o
a
l
go
r
i
t
hm
do
e
s
n
o
t
c
o
n
t
a
i
n
de
r
i
v
a
t
i
v
e
s
,
t
h
e
r
e
a
r
e
a
f
i
n
i
t
e
num
b
e
r
o
f
pa
ra
m
e
t
e
r
s
a
n
d
t
h
e
i
r
i
m
p
a
c
t
i
s
s
m
a
l
l
c
o
m
pa
r
e
d
t
o
o
t
h
e
r
o
pt
i
m
i
z
a
t
i
o
n
t
e
c
hn
i
que
s
,
y
o
u
d
o
n
o
t
n
e
e
d
a
l
o
n
g
pe
ri
o
d
o
f
t
i
m
e
i
n
o
r
de
r
t
o
gua
r
a
nt
e
e
t
h
e
c
l
o
s
e
n
e
s
s
a
nd
o
pt
i
m
a
l
v
a
l
ue
o
f
t
h
e
p
r
o
b
l
e
m
,
It
'
s
e
a
s
y
i
n
t
h
e
o
r
y
[30,
31]
,
W
o
r
k
t
o
r
e
duc
e
t
h
e
e
rr
o
r
i
n
t
h
e
n
u
m
e
ri
c
a
l
m
e
t
h
o
d
us
e
d
a
n
d
t
h
e
p
r
o
po
s
e
d
s
t
ra
t
e
g
y
a
n
d
t
h
us
t
o
r
e
a
c
h
t
h
e
s
l
i
g
h
t
e
s
t
e
rr
o
r
w
e
c
a
n
ge
t
a
n
a
pp
r
o
xi
m
a
t
e
a
n
d
a
n
a
l
y
t
i
c
a
l
s
o
l
ut
i
o
n
c
l
o
s
e
r
t
o
t
h
e
a
c
c
ur
a
t
e
s
o
l
ut
i
o
n
o
f
t
h
e
Z
a
k
ha
r
o
v
-
K
uz
n
e
t
s
o
v
s
y
s
t
e
m
.
In
t
h
i
s
a
rt
i
c
l
e
i
t
i
s
t
i
dy
a
s
fo
l
l
ow
s
:
1.
I
n
t
h
e
f
i
r
s
t
p
a
ra
g
r
a
p
h
t
h
e
m
a
t
h
e
m
a
t
i
c
a
l
m
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2.
I
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t
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s
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c
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d
pa
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of
t
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c
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d
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3.
In
t
h
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hi
r
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pa
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w
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t
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d
m
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d
of
(N
IM
-
P
S
O
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5.
I
n
t
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f
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f
t
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pa
r
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a
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d
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s
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t
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y
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ff
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-
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s
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m
.
2.
TH
E
N
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ER
I
C
A
L
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D
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x
t
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l
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qua
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[8]
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(
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our
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l
as
m
a
P
hy
s
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c
s
,
v
o
l
.
62
,
no
.
3
,
pp
.
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-
3
17
,
1999
.
[
10]
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.
C
.
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s
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v
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l
.
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no
.
11
-
12
,
pp
.
2523
-
2
5
27
,
20
09
.
[
11]
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Y
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o
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l
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.
2
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p.
10
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,
20
09
.
[
12]
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nd
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.
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.
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e
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ou
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l
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i
ne
ar
and
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o
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c
a
l
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l
g
e
br
a
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v
o
l
.
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,
n
o
.
01
,
p
p.
7
-
13
,
2014
.
[
13]
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.
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a
m
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nd
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.
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ka
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l
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1
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2
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pp
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28
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33
,
2
013
.
[
14]
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1
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13
.
[
15]
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pp
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l
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pp
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753
-
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06
.
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16]
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d
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om
p
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e
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o
l
.
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,
no
.
3
,
pp.
16
38
-
1645
,
202
0.
[
17]
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.
B
ha
l
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a
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f
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da
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-
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e
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j
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e
w
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d
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v
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l
.
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p
p.
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008
.
[
18]
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.
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da
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ha
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r
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n
al
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s
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s
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o
l
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no
.
2
,
pp
.
193
-
2
02
,
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08
.
[
19]
F
.
A
l
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,
e
t
a
l
.
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e
w
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m
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l
y
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o
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ne
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r
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o
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l
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D
i
s
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r
e
t
e
D
y
nam
i
c
s
i
n
N
at
ur
e
and
Soc
i
e
t
y
,
p
p.
1
-
12
,
2018
.
[
20]
S
.
F
.
A
l
-
A
z
z
w
M
M
A
z
z
“
C
s
S
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r
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l
e
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ndr
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a
E
ng
i
ne
e
r
i
ng
J
our
nal
,
v
o
l
.
5
7,
no
.
4,
p
p.
34
9
3
-
3500,
D
e
c
2018
.
[
21]
X
.
W
a
ng
,
e
t
a
l
.
“
C
v
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t
v
t
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s
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s
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om
put
e
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s
&
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a
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at
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c
s
w
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h
A
p
pl
i
c
a
t
i
ons
,
v
o
l
.
6
6,
no
.
7,
p
p.
13
22
-
1328
,
201
3
.
[
22]
R
.
B
e
hl
,
e
t
a
l
.
,
“
N
e
w
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t
e
r
a
t
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v
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e
t
ho
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o
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l
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o
nl
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a
r
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s
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ne
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nd
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e
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r
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l
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nkno
w
ns
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a
t
he
m
at
i
c
s
,
v
o
l
.
6
,
no
.
1
2,
p
.
2
9
6
,
2018
.
[
23]
M
.
N
.
A
l
a
m
,
“
P
a
r
t
i
c
l
e
S
w
a
r
m
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pt
i
m
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z
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t
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o
n:
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nd
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t
s
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,
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r
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i
nt
s
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o
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pe
n
A
c
c
e
s
s
A
r
t
i
c
l
e
,
201
6.
[
24]
R
.
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bo
us
l
e
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m
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n
a
n
d
O
.
R
a
w
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s
hde
h,
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l
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r
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c
v
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hi
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l
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l
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nd
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ne
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g
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e
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r
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o
n,
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E
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t
e
l
l
i
ge
nt
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r
an
s
por
t
Sy
s
t
e
m
s
,
v
o
l
.
10
,
no
.
2
,
pp
.
65
-
72
,
20
16
.
[
25]
S
.
T
a
l
ukde
r
,
“
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a
t
h
e
m
a
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i
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a
l
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o
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l
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a
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at
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c
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l
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o
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m
u
l
a
t
i
on
,
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he
s
i
s
,
201
0
.
[
26]
S
.
F
.
A
l
-
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M
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z
z
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g
s
L
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k
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om
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om
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t
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c
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ont
r
o
l
,
v
o
l
.
17,
n
o
.
4,
p
p.
19
31
-
1940
,
A
ug
2019
.
[
27]
C
.
M
i
s
h
r
a
,
e
t
a
l
.
,
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l
.
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,
no
.
2,
pp.
55
5
-
562,
2
016
.
[
28]
Z
.
N
.
J
.
Al
-
ka
t
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n
d
M
.
R
.
J
.
M
.
Al
-
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z
z
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p y
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s
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i
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r
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t
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our
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ur
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S
c
i
e
nc
e
,
v
o
l
.
24,
no
.
3
,
pp.
1
11
-
117
,
M
a
y
2019
.
[
29]
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.
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l
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l
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a
nd
S
.
F
.
A
L
-
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o
l
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l
.
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,
n
o
.
2
,
pp.
99
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-
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,
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pr
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0.
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30]
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our
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om
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t
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e
nc
e
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v
o
l
.
19
,
no
.
1
,
pp.
37
9
-
386,
J
ul
20
20
.
[
31]
A
.
S
.
A
l
-
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n
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