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atel
y
f
o
r
lar
g
e
ti
m
e
d
o
m
ai
n
.
T
h
e
r
est
o
f
th
i
s
p
ap
er
is
ar
r
an
g
ed
as
f
o
llo
w
s
.
W
e
w
r
ite
t
h
e
m
at
h
e
m
a
tical
m
o
d
el
f
o
r
th
e
v
an
d
er
P
o
l
eq
u
atio
n
i
n
se
ctio
n
2
.
So
lv
in
g
m
et
h
o
d
s
ar
e
p
r
esen
ted
in
se
ctio
n
3
.
R
es
u
lts
a
n
d
d
is
cu
s
s
i
o
n
ar
e
p
r
o
v
id
ed
in
s
ec
tio
n
4
.
W
e
co
n
clu
d
e
th
e
p
a
p
er
in
s
ec
tio
n
5.
2.
M
AT
H
E
M
AT
I
CAL M
O
DE
L
T
h
e
v
an
d
er
P
o
l e
q
u
ati
o
n
is
:
2
(
)
2
−
(
1
−
(
)
2
)
(
)
+
(
)
=
0
,
(
1
)
w
it
h
i
n
itial c
o
n
d
itio
n
:
(
0
)
=
0
,
′
(
0
)
=
0
,
(
2
)
w
h
er
e
is
a
p
o
s
itiv
e
p
ar
a
m
eter
in
d
icatin
g
t
h
e
s
tr
en
g
t
h
s
o
f
th
e
d
am
p
i
n
g
a
n
d
th
e
n
o
n
li
n
ea
r
it
y
o
f
th
e
p
r
o
b
lem
,
is
th
e
t
i
m
e
v
ar
iab
le,
an
d
(
)
is
th
e
u
n
k
n
o
w
n
f
u
n
ctio
n
.
T
h
e
g
i
v
e
n
d
o
m
ai
n
is
0
≤
≤
,
w
h
er
e
0
an
d
ar
e
th
e
in
itial
an
d
t
h
e
f
i
n
al
o
f
t
h
e
ti
m
e
d
o
m
ai
n
,
r
esp
ec
tiv
el
y
.
Her
e
′
(
)
=
/
.
T
h
e
v
an
d
er
P
o
l
as
s
h
o
w
n
i
n
(
1
)
d
escr
ib
es
s
elf
-
ex
ci
ted
o
s
cillati
o
n
s
in
a
tr
io
d
e
el
ec
tr
ical
cir
cu
it.
I
t
w
a
s
f
o
r
m
u
lated
b
y
B
alth
asar
v
an
d
er
Po
l,
a
Du
tc
h
p
h
y
s
ici
s
t,
i
n
ar
o
u
n
d
1
9
2
0
[
29
]
f
o
r
th
e
elec
tr
ical
cir
cu
i
t p
r
o
b
lem
,
as
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
I
n
th
is
p
ap
er
,
w
e
li
m
it
o
u
r
r
esear
ch
i
n
t
h
e
co
m
p
u
tatio
n
a
l
m
e
th
o
d
f
o
r
s
o
l
v
in
g
t
h
e
v
a
n
d
er
P
o
l
eq
u
a
tio
n
.
R
ea
d
er
s
in
ter
ested
i
n
t
h
e
m
o
d
ell
in
g
o
f
t
h
e
v
a
n
d
er
P
o
l e
q
u
atio
n
ca
n
co
n
s
u
lt t
h
e
liter
at
u
r
e
[
29
]
-
[
3
3
]
an
d
r
ef
er
en
ce
s
t
h
er
ein
.
Fig
u
r
e
1
.
I
llu
s
tr
atio
n
o
f
th
e
ele
ctr
ical
cir
cu
it o
f
v
an
d
er
P
o
l [
2
9
]
T
h
e
v
an
d
er
P
o
l
as
s
h
o
w
n
in
(
1
)
ca
n
b
e
w
r
itte
n
eq
u
i
v
ale
n
tl
y
i
n
to
t
h
e
f
o
llo
w
i
n
g
s
y
s
te
m
o
f
t
w
o
f
ir
s
t
o
r
d
er
d
if
f
er
en
tial e
q
u
atio
n
s
:
=
,
(
3
)
=
−
+
(
1
−
2
)
.
(
4
)
T
h
e
r
e
f
o
r
e
,
th
e
s
o
lu
t
i
o
n
t
o
th
e
v
a
n
d
e
r
Po
l
as
s
h
o
w
n
in
(
1
)
is
th
e
s
o
lu
ti
o
n
t
o
th
e
s
y
s
t
em
o
f
as
s
h
o
w
n
in
(
3
)
an
d
(
4
)
.
T
o
o
b
t
a
i
n
t
h
e
s
o
lu
ti
o
n
t
o
th
e
v
an
d
e
r
Po
l
s
h
o
w
n
in
(
1
)
,
w
e
s
h
a
ll
s
o
lv
e
th
e
s
y
s
t
em
o
f
a
s
s
h
o
w
n
i
n
(
3
)
an
d
(
4
)
.
3.
SO
L
VI
NG
M
E
T
H
O
DS
T
h
is
s
ec
tio
n
is
d
ev
o
ted
to
p
r
esen
t
t
w
o
s
o
l
v
in
g
m
et
h
o
d
s
f
o
r
th
e
co
n
s
id
er
ed
v
a
n
d
er
P
o
l
p
r
o
b
lem
.
W
e
r
ec
all
an
ex
is
t
in
g
iter
ati
v
e
m
e
th
o
d
.
W
e
also
p
r
o
v
id
e
th
e
p
r
o
p
o
s
ed
n
u
m
er
ical
-
a
n
al
y
tical
ite
r
ativ
e
m
et
h
o
d
.
Ou
r
p
r
o
p
o
s
ed
m
et
h
o
d
tak
es
t
h
e
s
tr
en
g
t
h
a
n
d
av
o
id
s
th
e
w
ea
k
n
es
s
o
f
th
e
e
x
is
tin
g
iter
ati
v
e
m
eth
o
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
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KOM
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K
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o
m
m
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p
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t E
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C
o
n
tr
o
l
,
Vo
l.
19
,
No
.
4
,
A
u
g
u
s
t 2
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2
1
:
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it
er
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An
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liter
at
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t
h
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s
u
cc
es
s
i
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e
ap
p
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x
im
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tio
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m
et
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d
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s
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s
s
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ap
p
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x
im
a
tio
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m
eth
o
d
f
o
r
s
o
l
v
in
g
t
h
e
v
a
n
d
er
P
o
l
eq
u
atio
n
is
d
escr
ib
ed
as
f
o
llo
w
s
.
T
o
b
e
g
in
,
let
u
s
co
n
s
id
er
th
e
g
e
n
er
al
f
ir
s
t o
r
d
er
o
r
d
in
ar
y
d
if
f
er
e
n
tial e
q
u
atio
n
:
(
)
=
(
,
(
)
)
,
(
5
)
w
it
h
i
n
itial c
o
n
d
itio
n
:
(
0
)
=
0
,
(
6
)
w
h
er
e
th
e
g
i
v
en
d
o
m
ai
n
is
0
≤
≤
.
Her
e
0
is
th
e
in
i
tial p
o
in
t o
f
t
h
e
d
o
m
a
in
,
is
th
e
f
in
a
l p
o
in
t o
f
t
h
e
d
o
m
ai
n
.
P
icar
d
’
s
s
u
cc
es
s
iv
e
a
p
p
r
o
x
im
a
tio
n
m
et
h
o
d
f
o
r
s
o
lv
i
n
g
p
r
o
b
le
m
(
5
)
-
(
6
)
is
:
(
)
=
0
+
∫
(
,
−
1
(
)
)
0
,
(
7
)
w
h
er
e
=
1
,
2
,
3
,
…
an
d
th
e
e
x
ac
t so
l
u
tio
n
(
)
to
p
r
o
b
lem
(
5
)
-
(
6
)
is
g
i
v
e
n
b
y
t
h
e
li
m
it
:
l
im
→
∞
(
)
=
(
)
.
(
8
)
Fo
llo
w
i
n
g
P
icar
d
’
s
s
u
cc
es
s
i
v
e
ap
p
r
o
x
i
m
atio
n
m
et
h
o
d
f
o
r
s
o
lv
i
n
g
p
r
o
b
le
m
(
5
)
-
(
6
)
,
w
e
d
ev
elo
p
a
s
u
cc
e
s
s
i
v
e
ap
p
r
o
x
i
m
atio
n
m
et
h
o
d
f
o
r
s
o
lv
i
n
g
th
e
v
a
n
d
er
P
o
l
as s
h
o
w
n
i
n
(
1
)
w
i
th
i
n
it
ial
c
o
n
d
itio
n
(
2
)
.
I
n
th
i
s
ca
s
e,
w
e
s
h
all
s
o
lv
e
t
h
e
eq
u
i
v
a
len
t
f
o
r
m
(
3
)
-
(
4
)
w
it
h
in
itial c
o
n
d
itio
n
(
2
)
.
T
ak
in
g
th
e
i
n
itial
izatio
n
:
0
(
)
=
0
,
0
(
)
=
0
,
(
9
)
an
d
ac
co
r
d
in
g
to
P
icar
d
’
s
s
u
c
ce
s
s
i
v
e
ap
p
r
o
x
i
m
atio
n
m
et
h
o
d
,
w
e
h
a
v
e
th
e
s
u
cc
e
s
s
i
v
e
ap
p
r
o
x
i
m
atio
n
m
et
h
o
d
f
o
r
p
r
o
b
lem
(
3
)
-
(
4
)
w
it
h
in
i
tial
co
n
d
itio
n
(
2
)
as
s
h
o
w
n
i
n
(
1
0
)
an
d
(
1
1
)
:
(
)
=
0
+
∫
−
1
(
)
,
0
(
1
0
)
(
)
=
0
+
∫
[
−
−
1
(
)
+
(
1
−
−
1
(
)
2
)
−
1
(
)
]
.
0
(
1
1
)
T
h
e
s
u
cc
ess
i
v
e
ap
p
r
o
x
i
m
atio
n
m
e
th
o
d
is
ab
le
to
s
o
lv
e
th
e
v
an
d
er
Po
l
eq
u
atio
n
ac
cu
r
atel
y
o
n
l
y
f
o
r
a
s
h
o
r
t
ti
m
e
af
ter
t
h
e
i
n
itiali
s
ati
o
n
,
u
n
less
w
e
ta
k
e
a
v
er
y
lar
g
e
n
u
m
b
er
o
f
s
u
cc
es
s
iv
e
i
ter
atio
n
s
.
Ho
w
e
v
er
,
tak
i
n
g
a
v
er
y
lar
g
e
n
u
m
b
er
o
f
s
u
cc
e
s
s
i
v
e
iter
atio
n
s
is
v
er
y
ted
io
u
s
an
d
i
m
p
r
ac
tical.
T
o
d
ea
l
w
i
th
th
i
s
p
r
o
b
lem
,
w
e
p
r
o
p
o
s
e
a
n
u
m
er
ical
-
a
n
al
y
tica
l
m
et
h
o
d
th
at
w
e
w
r
ite
i
n
w
h
at
f
o
llo
w
s
.
3
.
2
.
P
r
o
po
s
ed
nu
m
er
ica
l
-
a
n
a
ly
t
ica
l it
er
a
t
iv
e
m
et
ho
d
W
e
d
ev
elo
p
a
n
u
m
er
ical
-
an
a
l
y
tical
iter
ativ
e
m
et
h
o
d
f
o
r
s
o
lv
i
n
g
t
h
e
v
an
d
er
P
o
l
eq
u
atio
n
.
W
ith
in
itia
l
co
n
d
itio
n
(
2
)
an
d
f
o
r
as sh
o
w
n
in
(
3
)
an
d
(
4
)
,
let
u
s
tak
e
th
e
f
o
llo
w
i
n
g
co
r
r
ec
tio
n
f
u
n
ctio
n
al
s
:
+
1
(
)
=
(
)
+
∫
1
(
)
[
(
)
−
̅
(
)
]
,
0
(
1
2
)
+
1
(
)
=
(
)
+
∫
2
(
)
[
(
)
+
̅
(
)
−
(
1
−
̅
2
(
)
)
̅
(
)
]
,
0
(
1
3
)
w
h
er
e
1
(
)
an
d
2
(
)
ar
e
L
ag
r
a
n
g
e
m
u
ltip
lier
s
to
b
e
d
eter
m
in
ed
o
p
ti
m
all
y
v
ia
th
e
v
ar
iatio
n
al
t
h
eo
r
y
.
Her
e
=
0
,
1
,
2
…
.
A
ll
v
ar
iab
les
h
a
v
i
n
g
b
ar
n
o
t
atio
n
s
ar
e
r
estricte
d
v
ar
iab
les.
T
ak
in
g
t
h
e
v
ar
iatio
n
s
o
f
a
s
s
h
o
w
n
in
(
1
2
)
an
d
(
1
3
)
,
w
e
o
b
tain
:
+
1
(
)
=
(
)
+
∫
1
(
)
[
(
)
]
,
0
(
1
4
)
+
1
(
)
=
(
)
+
∫
2
(
)
[
(
)
]
.
0
(
1
5
)
R
e
w
r
iti
n
g
s
h
o
w
n
in
(
1
4
)
an
d
(
1
5
)
,
w
e
h
a
v
e
:
+
1
(
)
=
[
(
1
+
1
(
)
)
(
)
]
−
∫
′
1
(
)
(
)
,
0
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
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m
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C
o
n
tr
o
l
A
n
u
merica
l
-
a
n
a
lytica
l itera
tive
meth
o
d
fo
r
s
o
lvin
g
a
n
elec
t
r
ica
l o
s
cilla
to
r
eq
u
a
tio
n
(
S
u
d
i
Mu
n
g
ka
s
i
)
1221
+
1
(
)
=
[
(
1
+
2
(
)
)
(
)
]
−
∫
′
2
(
)
(
)
.
0
(
1
7
)
W
e
o
b
tain
s
tatio
n
ar
y
co
n
d
it
io
n
s
b
ased
o
n
s
h
o
w
n
i
n
(
1
6
)
an
d
(
1
7
)
as
s
h
o
w
n
i
n
(
1
8
)
an
d
(
1
9
)
:
1
+
1
(
)
=
0
,
′
1
(
)
=
0
,
(
1
8
)
1
+
2
(
)
=
0
,
′
2
(
)
=
0
.
(
1
9
)
T
h
e
s
o
lu
tio
n
s
to
s
ta
tio
n
ar
y
co
n
d
itio
n
s
(
1
8
)
an
d
(
1
9
)
ar
e
(
2
0
)
:
1
=
2
=
−
1
.
(
2
0
)
T
h
er
ef
o
r
e,
th
e
iter
ati
v
e
f
o
r
m
u
l
as
b
ased
o
n
th
e
tak
e
n
co
r
r
ec
tio
n
f
u
n
ctio
n
als
f
o
r
s
o
l
v
i
n
g
t
h
e
v
an
d
er
P
o
l
eq
u
atio
n
ar
e
:
+
1
(
)
=
(
)
−
∫
[
(
)
−
(
)
]
,
0
(
2
1
)
+
1
(
)
=
(
)
−
∫
[
(
)
+
(
)
−
(
1
−
2
(
)
)
(
)
]
.
0
(
2
2
)
Kn
o
w
i
n
g
th
e
p
r
o
p
er
ties
o
f
th
e
s
tan
d
ar
d
iter
ati
v
e
m
et
h
o
d
,
w
e
s
h
al
l
ta
k
e
ad
v
a
n
ta
g
e
o
f
t
h
e
s
tr
en
g
t
h
a
n
d
av
o
id
th
e
w
ea
k
n
e
s
s
o
f
th
e
iter
ativ
e
m
et
h
o
d
b
y
i
m
p
l
e
m
en
tin
g
it in
to
s
m
all
s
izes o
f
t
h
e
ti
m
e
in
ter
v
a
ls
.
T
o
d
o
s
o
,
th
e
o
r
ig
i
n
all
y
-
g
i
v
en
lar
g
e
s
iz
e
o
f
th
e
ti
m
e
d
o
m
ai
n
is
s
u
b
d
iv
id
ed
in
to
s
m
all
s
ize
s
o
f
ti
m
e
in
ter
v
al
s
,
an
d
w
e
i
m
p
le
m
en
t
t
h
e
iter
ativ
e
m
et
h
o
d
(
2
1
)
-
(
2
1
)
in
to
ea
ch
o
f
th
e
m
.
C
o
n
s
id
er
in
g
t
h
e
o
r
ig
in
all
y
-
g
iv
en
lar
g
e
s
ize
o
f
ti
m
e
d
o
m
ai
n
0
≤
≤
,
w
e
tak
e
d
is
cr
ete
p
o
i
n
ts
0
,
1
,
2
,
…
,
.
T
h
ese
d
is
cr
ete
p
o
in
ts
ca
n
b
e
eith
er
eq
u
id
is
ta
n
t
o
r
n
o
n
-
eq
u
id
i
s
tan
t.
Fo
r
s
i
m
p
lici
t
y
i
n
th
i
s
p
ap
er
,
w
e
ass
u
m
e
th
at
w
e
ta
k
e
+
1
eq
u
id
is
ta
n
t
d
is
cr
ete
p
o
in
ts
0
,
1
,
2
,
…
,
,
w
h
er
e
∆
=
−
−
1
f
o
r
all
an
d
=
.
I
n
th
is
w
a
y
,
w
e
h
a
v
e
s
m
all
s
a
m
e
-
s
iz
e
s
u
b
i
n
ter
v
al
s
o
f
t
i
m
e
d
o
m
a
in
=
[
−
1
,
]
w
h
er
e
=
1
,
2
,
3
,
.
.
.
,
.
Su
p
p
o
s
e
th
at
w
e
w
a
n
t
to
h
av
e
iter
atio
n
s
i
n
th
e
n
u
m
er
ical
-
a
n
a
l
y
tical
m
eth
o
d
f
o
r
ea
ch
s
u
b
i
n
te
r
v
al.
W
e
d
en
o
te
,
(
)
th
e
ap
p
r
o
x
im
ate
s
o
lu
tio
n
o
f
(
)
at
th
e
th
iter
atio
n
o
n
t
h
e
th
s
u
b
i
n
ter
v
al.
No
tatio
n
,
(
)
is
m
ea
n
t a
n
alo
g
o
u
s
l
y
.
T
h
er
ef
o
r
e,
th
e
n
u
m
er
ical
-
a
n
al
y
tical
m
et
h
o
d
f
o
r
s
o
lv
i
n
g
th
e
v
an
d
er
P
o
l
eq
u
atio
n
w
o
r
k
s
as
f
o
llo
w
s
.
Fo
r
=
1
,
2
,
3
,
.
.
.
,
an
d
f
o
r
=
1
,
2
,
3
,
.
.
.
,
,
w
e
iter
ate
:
,
(
)
=
−
1
,
(
)
−
∫
[
−
1
,
(
)
−
−
1
,
(
)
]
,
−
1
(
2
3
)
,
(
)
=
−
1
,
(
)
−
∫
[
−
1
,
(
)
+
−
1
,
(
)
−
(
1
−
−
1
,
2
(
)
)
−
1
,
(
)
]
.
0
(
2
4
)
Her
e
f
o
r
th
e
in
i
tialis
a
tio
n
o
f
t
h
e
n
u
m
er
ical
-
an
a
l
y
t
ical
m
et
h
o
d
o
n
ea
ch
s
u
b
in
ter
v
al,
if
=
1
w
e
ta
k
e
:
0
,
(
)
=
0
,
0
,
(
)
=
0
,
(
2
5
)
o
th
er
w
is
e
(
if
≥
2
)
w
e
ta
k
e
:
0
,
(
)
=
,
−
1
(
−
1
)
,
0
,
(
)
=
,
−
1
(
−
1
)
.
(
2
6
)
C
o
m
p
u
tatio
n
al
te
s
ts
w
i
ll s
h
o
w
th
at
o
u
r
p
r
o
p
o
s
ed
m
et
h
o
d
is
ac
cu
r
ate
o
n
lar
g
e
s
izes o
f
ti
m
e
d
o
m
ai
n
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
is
s
ec
tio
n
,
w
e
p
r
esen
t
o
u
r
r
esear
ch
r
e
s
u
l
ts
a
n
d
d
is
c
u
s
s
io
n
ab
o
u
t
t
h
e
m
.
First,
w
e
e
x
p
lain
th
e
n
u
m
er
ical
i
m
p
le
m
en
tatio
n
o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
.
T
h
en
,
t
w
o
test
ca
s
es
ar
e
co
n
s
id
er
ed
.
T
h
e
f
ir
s
t
te
s
t
ca
s
e
ta
k
e
s
=
5
,
0
=
0
,
=
3
,
=
0
.
1
,
0
=
1
,
an
d
0
=
0
.
T
h
e
s
ec
o
n
d
test
ca
s
e
ta
k
es
th
e
s
a
m
e
p
ar
a
m
eter
v
al
u
es
as
in
th
e
f
ir
s
t
o
n
e,
ex
ce
p
t
=
0
.
5
an
d
0
=
2
.
I
n
th
is
s
ec
tio
n
,
w
e
u
s
e
t
w
o
ab
b
r
ev
iatio
n
s
,
n
a
m
el
y
,
s
u
cc
es
s
iv
e
ap
p
r
o
x
im
a
tio
n
m
e
th
o
d
(
SAM
)
an
d
n
u
m
er
ical
-
a
n
al
y
tical
m
eth
o
d
(
NA
M
)
.
S
A
M
s
ta
n
d
s
f
o
r
th
e
s
u
cc
e
s
s
i
v
e
ap
p
r
o
x
im
a
tio
n
m
eth
o
d
,
w
h
ic
h
is
th
e
s
ta
n
d
ar
d
m
eth
o
d
.
N
A
M
s
tan
d
s
f
o
r
th
e
n
u
m
er
ical
-
a
n
al
y
tical
m
et
h
o
d
,
w
h
ich
is
th
e
o
n
e
t
h
at
w
e
p
r
o
p
o
s
e
.
4
.
1
.
Nu
m
er
ica
l i
m
p
le
m
ent
a
t
io
n o
f
t
he
pro
po
s
ed
m
et
ho
d
I
n
th
e
n
u
m
er
ical
i
m
p
le
m
en
tat
io
n
,
th
e
a
n
al
y
tical
iter
ati
v
e
m
eth
o
d
m
u
s
t
b
e
w
r
itte
n
in
th
e
s
i
m
p
le
s
t
p
o
s
s
ib
le
f
o
r
m
.
T
h
is
is
in
o
r
d
er
th
at
th
e
co
m
p
u
tatio
n
is
ef
f
icie
n
t.
T
o
s
im
p
li
f
y
t
h
e
n
u
m
er
ical
i
m
p
le
m
e
n
tat
io
n
,
let
u
s
r
ec
o
n
s
id
er
th
e
iter
ati
v
e
m
et
h
o
d
(
2
1
)
-
(
2
2
)
,
w
h
ic
h
ca
n
b
e
wr
itten
as s
h
o
w
n
in
(
2
7
)
an
d
(
2
8
)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
19
,
No
.
4
,
A
u
g
u
s
t 2
0
2
1
:
1
2
1
8
-
1
2
2
5
1222
+
1
(
)
=
(
)
−
∫
[
(
)
]
+
∫
(
)
0
,
0
(
2
7
)
+
1
(
)
=
(
)
−
∫
[
(
)
]
+
∫
[
−
(
)
+
(
1
−
2
(
)
)
(
)
]
0
.
0
(
2
8
)
T
h
en
,
w
e
r
e
w
r
ite
as s
h
o
w
n
in
(
2
7
)
an
d
(
2
8
)
as
:
+
1
(
)
=
0
(
)
+
∫
(
)
0
,
(
2
9
)
+
1
(
)
=
0
(
)
+
∫
[
−
(
)
+
(
1
−
2
(
)
)
(
)
]
.
0
(
3
0
)
T
h
is
is
i
n
ter
est
in
g
,
b
ec
au
s
e
t
h
e
iter
ativ
e
m
et
h
o
d
(
2
1
)
-
(
2
2
)
h
as
b
ec
o
m
e
as
s
h
o
w
n
in
(
2
9
)
an
d
(
3
0
)
,
w
h
ic
h
ar
e
ac
tu
all
y
an
o
t
h
er
as s
h
o
w
n
i
n
(
1
0
)
an
d
(
1
1
)
w
it
h
d
if
f
er
e
n
t in
d
ices.
T
h
er
ef
o
r
e,
th
e
n
u
m
er
ical
i
m
p
le
m
en
ta
tio
n
o
f
t
h
e
p
r
o
p
o
s
e
d
m
et
h
o
d
f
o
r
s
o
lv
i
n
g
th
e
v
a
n
d
er
P
o
l
eq
u
atio
n
w
o
r
k
s
as f
o
llo
w
s
.
Fo
r
=
1
,
2
,
3
,
.
.
.
,
an
d
f
o
r
=
1
,
2
,
3
,
.
.
.
,
,
w
e
iter
ate
:
,
(
)
=
0
,
(
)
+
∫
−
1
,
(
)
0
,
(
3
1
)
,
(
)
=
0
,
(
)
+
∫
[
−
−
1
,
(
)
+
(
1
−
−
1
,
2
(
)
)
−
1
,
(
)
]
.
0
(
3
2
)
Her
e
f
o
r
th
e
in
i
tialis
a
tio
n
o
f
t
h
e
n
u
m
er
ical
-
an
a
l
y
t
ical
m
et
h
o
d
o
n
ea
ch
s
u
b
in
ter
v
al,
if
=
1
w
e
ta
k
e
:
0
,
(
)
=
0
,
0
,
(
)
=
0
,
(
3
3
)
o
th
er
w
is
e
(
if
≥
2
)
w
e
ta
k
e
:
0
,
(
)
=
,
−
1
(
−
1
)
,
0
,
(
)
=
,
−
1
(
−
1
)
.
(
3
4
)
4
.
2
.
Resul
t
s
a
nd
dis
cu
s
s
io
n f
o
r
t
he
ex
is
t
ing
m
et
ho
d
W
e
o
b
tain
th
at
S
A
M
s
o
lu
tio
n
is
ac
cu
r
ate
o
n
l
y
f
o
r
s
m
all
s
ize
s
o
f
th
e
ti
m
e
d
o
m
ai
n
f
o
r
b
o
th
test
ca
s
es,
as
s
h
o
w
n
in
Fi
g
u
r
e
s
2
an
d
3
w
it
h
=
5
.
I
n
Fig
u
r
e
2
,
w
e
o
b
s
er
v
e
th
at
S
A
M
s
o
lu
t
io
n
i
s
i
n
ac
cu
r
ate
f
o
r
clo
s
e
to
th
e
f
in
al
p
o
in
t
o
f
ti
m
e.
T
h
i
s
p
h
en
o
m
e
n
o
n
i
s
ev
e
n
w
o
r
s
e
w
h
en
th
e
v
al
u
e
s
o
f
th
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o
rt
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ircu
it
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li
m
it
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ti
o
n
,
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ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
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ter
En
g
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n
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g
,
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l.
8
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o
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1
,
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p
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2
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e
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.
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0
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8
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o
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1
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jec
e
.
v
8
i1
.
p
p
5
0
5
-
5
1
2
.
[
3
]
I.
P
a
rk
h
o
m
e
y
,
J.
Bo
ik
o
,
N.
T
so
p
a
,
I.
Zen
iv
a
n
d
O.
Ero
m
e
n
k
o
,
“
As
se
ss
m
e
n
t
o
f
q
u
a
li
ty
in
d
ica
to
rs
o
f
th
e
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u
to
m
a
ti
c
c
o
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tro
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sy
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m
in
f
lu
e
n
c
e
o
f
a
c
c
id
e
n
t
in
terf
e
re
n
c
e
,
”
T
EL
KOM
NIKA
T
e
lec
o
mm
u
n
ica
ti
o
n
C
o
mp
u
ti
n
g
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e
c
tro
n
ics
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n
d
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n
tro
l
,
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l.
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8
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o
.
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p
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0
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9
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2
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n
ik
a
.
v
1
8
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.
1
5
6
0
1
.
[
4
]
S
.
D.
P
u
tra,
M
.
Yu
d
h
i
p
ra
w
ira,
S
.
S
u
ti
k
n
o
,
Y.
Ku
rn
iaw
a
n
a
n
d
A
.
S
.
A
h
m
a
d
,
“
P
o
w
e
r
a
n
a
l
y
sis
a
tt
a
c
k
a
g
a
in
st
e
n
c
ry
p
ti
o
n
d
e
v
ice
s:
A
c
o
m
p
re
h
e
n
siv
e
a
n
a
ly
sis
o
f
A
ES
,
DES
,
a
n
d
BC3
,
”
T
EL
KOM
NIKA
T
e
lec
o
mm
u
n
ica
ti
o
n
Co
mp
u
ti
n
g
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e
c
tro
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ics
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n
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o
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tro
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v
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l.
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7
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o
.
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p
.
1
2
8
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2
8
9
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u
n
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0
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9
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0
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2
9
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8
/
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ik
a
.
v
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7
i3
.
9
3
8
4
.
[
5
]
T
jen
d
ro
a
n
d
S
.
M
u
n
g
k
a
si,
“
F
o
r
m
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l
e
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p
a
n
sio
n
m
e
th
o
d
f
o
r
so
lv
in
g
a
n
e
lec
tri
c
a
l
c
ircu
it
m
o
d
e
l,
”
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EL
KOM
NIKA
T
e
lec
o
mm
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n
ica
ti
o
n
Co
mp
u
ti
n
g
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e
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tro
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ics
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n
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o
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tro
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,
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l.
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7
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o
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1
3
3
8
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1
3
4
3
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0
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9
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0
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8
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ik
a
.
v
1
7
i3
.
1
0
3
1
8
.
[
6
]
A
.
A
.
A
h
m
a
d
,
“
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u
sin
g
a
n
e
w
it
e
ra
ti
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m
e
th
o
d
to
th
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g
e
n
e
ra
li
z
e
d
sy
ste
m
Zak
h
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ro
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-
Ku
z
n
e
tso
v
a
n
d
e
stim
a
te
th
e
b
e
s
t
p
a
ra
m
e
ters
v
ia
a
p
p
li
e
d
th
e
p
s
o
a
lg
o
rit
h
m
,
”
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d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
Co
mp
u
ter
S
c
ien
c
e
,
v
o
l.
1
9
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n
o
.
2
,
p
p
.
1
0
5
5
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1
0
6
1
,
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g
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2
0
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0
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0
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1
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9
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1
9
.
i2
.
p
p
1
0
5
5
-
1
0
6
1
.
[
7
]
F
.
Ish
a
k
a
n
d
N.
Ch
a
i
n
i,
“
Nu
m
e
rica
l
c
o
m
p
u
tatio
n
f
o
r
so
lv
in
g
f
u
z
z
y
d
iff
e
re
n
ti
a
l
e
q
u
a
ti
o
n
s,”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
Co
mp
u
ter
S
c
ien
c
e
,
v
o
l.
1
6
,
n
o
.
2
,
p
p
.
1
0
2
6
-
1
0
3
3
,
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.
2
0
1
9
,
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o
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0
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1
6
.
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.
p
p
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0
2
6
-
1
0
3
3
.
[
8
]
M
.
M
o
h
a
g
h
e
g
h
i
a
n
d
K
.
S
a
leh
i,
“
Im
p
ro
v
in
g
g
ra
p
h
-
b
a
se
d
m
e
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h
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d
s
f
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o
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p
u
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g
q
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a
li
tativ
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p
ro
p
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e
s
o
f
m
a
rk
o
v
d
e
c
isio
n
p
ro
c
e
ss
e
s,”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
C
o
mp
u
ter
S
c
ien
c
e
,
v
o
l.
1
7
,
n
o
.
3
,
pp.
1
5
7
1
-
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5
7
7
,
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a
r.
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0
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0
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0
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1
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7
.
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.
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p
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1
-
1
5
7
7
.
[
9
]
R.
H.
A
.
Ra
h
im
,
A
.
Ba
h
a
ru
m
a
n
d
H.
Hijaz
i,
“
Ev
a
lu
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ti
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ti
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li
n
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r
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lg
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ra
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sin
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g
a
m
i
f
ica
ti
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n
,
”
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d
o
n
e
si
a
n
J
o
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n
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l
o
f
E
lec
trica
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E
n
g
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l
.
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7
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2
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0
0
4
.
[
1
0
]
S
.
A
li
p
o
u
r
a
n
d
F
.
M
irza
e
e
,
“
An
it
e
ra
ti
v
e
a
lg
o
rit
h
m
f
o
r
so
lv
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g
tw
o
d
im
e
n
sio
n
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l
n
o
n
li
n
e
a
r
sto
c
h
a
stic
in
teg
ra
l
e
q
u
a
ti
o
n
s:
A
c
o
m
b
in
e
d
su
c
c
e
ss
iv
e
a
p
p
ro
x
im
a
ti
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n
s
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e
th
o
d
w
it
h
b
il
in
e
a
r
sp
li
n
e
i
n
terp
o
latio
n
,
”
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p
li
e
d
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a
th
e
ma
ti
c
s
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n
d
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m
p
u
t
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ti
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n
,
v
o
l.
3
7
1
,
p
p
.
1
2
4
9
4
7
,
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p
r.
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0
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o
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:
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6
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.
a
m
c
.
2
0
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9
.
1
2
4
9
4
7
.
[
1
1
]
X
.
Ch
e
n
,
H.
G
u
a
n
d
X.
W
a
n
g
,
“
Ex
isten
c
e
a
n
d
u
n
i
q
u
e
n
e
ss
f
o
r
f
u
z
z
y
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iff
e
re
n
ti
a
l
e
q
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a
ti
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n
w
it
h
Hi
lf
e
r
-
Ka
tu
g
a
m
p
o
la
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ra
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n
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l
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e
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ti
v
e
,
”
A
d
v
a
n
c
e
s
i
n
Diff
e
re
n
c
e
Eq
u
a
ti
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n
s
,
v
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l
.
2
0
2
0
,
pp
.
24
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,
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a
y
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6
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[
1
2
]
Y.
G
.
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a
n
g
,
H.
D.
Kw
o
n
a
n
d
J.
L
e
e
,
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e
e
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b
a
c
k
c
o
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tro
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r
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lem
o
f
a
n
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d
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m
ic m
o
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e
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se
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o
n
t
h
e
Ha
m
il
to
n
-
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c
o
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ll
m
a
n
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q
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a
ti
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n
,
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a
th
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ti
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a
l
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o
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e
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n
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n
g
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o
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n
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0
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9
3
4
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2
0
1
2
1
.
[
1
3
]
M
.
M
.
K
h
a
p
a
e
v
,
M
.
Y.
Ku
p
r
iy
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n
o
v
,
S
.
V
.
Ba
k
u
rsk
i
y
,
N.
V
.
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n
o
v
a
n
d
I.
I.
S
o
lo
v
iev
,
“
M
o
d
e
li
n
g
su
p
e
rc
o
n
d
u
c
t
o
r
SFN
-
stru
c
tu
re
s
u
si
n
g
th
e
f
in
it
e
e
lem
e
n
t
m
e
th
o
d
,
”
Diff
e
re
n
ti
a
l
Eq
u
a
ti
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n
s
,
v
o
l
.
5
6
,
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o
.
7
,
p
p
.
9
5
9
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9
6
7
,
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g
.
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,
d
o
i:
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3
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0
0
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2
2
6
6
1
2
0
0
7
0
1
4
9
.
[
1
4
]
C.
L
i
a
n
d
Z
.
Ch
e
n
,
“
A
f
a
st
v
ib
ra
ti
o
n
-
lev
e
l
a
d
ju
stm
e
n
t
m
e
th
o
d
f
o
r
lo
w
-
f
re
q
u
e
n
c
y
v
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ra
ti
o
n
c
a
li
b
ra
ti
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b
a
se
d
o
n
m
o
d
if
ied
f
il
tere
d
-
x
le
a
st
m
e
a
n
sq
u
a
re
a
lg
o
rit
h
m
,
”
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e
a
su
re
me
n
t
a
n
d
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n
tro
l
,
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l.
5
3
,
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o
.
5
,
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p
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3
2
8
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3
3
8
,
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n
.
2
0
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0
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o
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0
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1
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0
2
0
2
9
4
0
1
9
8
8
1
7
2
7
.
[
1
5
]
S
.
L
i,
W
.
S
u
n
a
n
d
Q.
L
.
L
i,
“
Util
it
y
m
a
x
i
m
iz
a
ti
o
n
f
o
r
b
a
n
d
w
id
th
a
ll
o
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a
ti
o
n
i
n
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e
e
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-
to
-
p
e
e
r
f
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-
sh
a
rin
g
n
e
tw
o
rk
s,”
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o
u
rn
a
l
o
f
In
d
u
stri
a
l
a
n
d
M
a
n
a
g
e
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n
t
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a
ti
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n
,
v
o
l.
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6
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n
o
.
1
,
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o
.
3
,
p
p
.
1
0
9
9
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1
1
7
,
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a
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,
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o
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0
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3
9
3
4
/
ji
m
o
.
2
0
1
8
1
9
4
.
[
1
6
]
W
.
S
u
n
,
C.
L
iu
,
M
.
Qia
n
a
n
d
S
.
Xu
,
“
S
im
u
lt
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n
e
o
u
s
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irele
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fo
rm
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ti
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n
a
n
d
p
o
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e
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tran
sf
e
r
f
o
r
m
a
ss
iv
e
M
IM
O
n
e
tw
o
rk
s,”
IET
Co
mm
u
n
ica
ti
o
n
s
,
v
o
l.
1
4
,
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o
.
5
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p
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8
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o
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0
4
9
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e
t
-
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o
m
.
2
0
1
9
.
0
0
4
6
.
[
1
7
]
S
.
M
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[
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K.
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B
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M
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rc
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m
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it
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sm
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m
m
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tro
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,
a
s
w
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m
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li
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g
a
n
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latio
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f
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r
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tri
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g
in
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ro
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lem
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rre
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h
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ta
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h
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rm
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c
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d
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m
ic
Aff
a
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rs i
n
t
h
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F
a
c
u
lt
y
.
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