I
n
d
on
e
s
i
an
Jo
u
r
n
al
o
f
El
e
c
t
r
i
c
al
En
gi
n
e
e
r
i
n
g
an
d
C
o
m
p
u
te
r
S
c
i
e
n
c
e
V
o
l
.
21
,
N
o
.
3
,
M
a
r
c
h
2021
,
pp.
14
44
~
14
5
4
IS
S
N
:
25
02
-
4752
,
D
O
I
:
10.
1
1591
/
i
j
e
e
c
s
.
v
21
.i
3
.
pp
144
4
-
145
4
1444
Jou
r
n
al
h
o
m
e
pa
ge
:
ht
t
p:
/
/
i
j
e
e
c
s
.
i
a
e
s
c
or
e
.
c
om
Ha
a
r
w
a
v
e
l
e
t
m
e
t
h
o
d
f
o
r
so
l
v
i
n
g
c
o
u
p
l
e
d
s
y
st
e
m
o
f
f
r
a
c
t
i
o
n
a
l
o
r
d
e
r
p
a
r
t
i
a
l
d
i
f
f
e
r
e
n
t
i
a
l
e
q
u
a
t
i
o
n
s
A
b
b
as
A
L
-
S
h
i
m
m
ar
y
1
,
S
aje
d
a
K
ar
e
e
m
R
ad
h
i
2
,
A
m
i
n
a
K
as
s
i
m
H
u
s
s
ai
n
3
1
D
e
pa
r
t
m
e
n
t
o
f
E
l
e
c
t
r
i
c
a
l
E
ng
i
ne
e
r
i
ng
,
F
a
c
ul
t
y
of
E
ng
i
ne
e
r
i
ng
,
U
n
i
v
e
r
s
i
t
y
of
A
l
-
M
us
t
a
ns
i
r
i
y
a
h,
B
a
g
hda
d
,
I
r
a
q
2
D
e
pa
r
t
m
e
n
t
o
f
R
e
m
o
t
e
S
e
n
s
i
ng
,
C
o
l
l
e
g
e
o
f
R
e
m
o
t
e
S
e
n
s
i
ng
&
G
e
o
ph
y
s
i
c
s
,
AL
-
K
a
r
kh
U
ni
v
e
r
s
i
t
y
,
B
a
g
hda
d
,
I
r
a
q
3
D
e
pa
r
t
m
e
n
t
o
f
M
e
t
e
r
i
a
l
E
ng
i
ne
e
r
i
ng
,
F
a
c
ul
t
y
o
f
E
ng
i
ne
e
r
i
ng
,
U
n
i
v
e
r
s
i
t
y
o
f
A
l
-
M
us
t
a
n
s
i
r
i
y
a
h,
B
a
g
hda
d
,
I
r
a
q
A
r
ti
c
l
e
I
n
fo
A
B
S
TR
A
C
T
Ar
t
i
c
l
e
h
i
s
t
or
y
:
R
e
c
e
i
v
e
d
J
un
5
,
2020
R
e
v
i
s
e
d
S
e
p
18
,
202
0
A
c
c
e
pt
e
d
N
o
v
30
,
2020
T
hi
s
pa
pe
r
d
e
a
l
w
i
t
h
t
he
num
e
r
i
c
a
l
m
e
t
ho
d,
ba
s
e
d
o
n
t
he
o
pe
r
a
t
i
o
na
l
m
a
t
r
i
c
e
s
o
f
t
he
H
a
a
r
w
a
v
e
l
e
t
o
r
t
ho
no
r
m
a
l
f
unc
t
i
o
ns
a
ppr
o
a
c
h
t
o
a
ppr
o
xi
m
a
t
e
s
o
l
ut
i
o
ns
t
o
a
c
l
a
s
s
o
f
c
o
u
pl
e
d
s
y
s
t
e
m
s
o
f
t
i
m
e
-
f
r
a
c
t
i
o
na
l
o
r
de
r
p
a
r
t
i
a
l
d
i
f
f
e
r
e
n
t
i
a
l
e
qua
t
i
o
ns
(
F
P
D
E
s
.
)
.
B
y
i
nt
r
o
duc
i
ng
t
h
e
f
r
a
c
t
i
o
na
l
d
e
r
i
v
a
t
i
v
e
o
f
t
he
C
a
pu
t
o
s
e
ns
e
,
t
o
a
v
o
i
d
t
he
t
e
d
i
o
us
c
a
l
c
ul
a
t
i
o
ns
a
nd
t
o
pr
o
m
o
t
e
t
he
s
t
udy
of
w
a
v
e
l
e
t
s
t
o
be
g
i
nne
r
s
,
w
e
u
s
e
t
he
i
nt
e
g
r
a
t
i
o
n
pr
o
pe
r
t
y
o
f
t
hi
s
m
e
t
ho
d
w
i
t
h
t
he
a
i
d
o
f
t
he
a
f
o
r
e
s
a
i
d
o
r
t
ho
g
o
na
l
m
a
t
r
i
c
e
s
w
hi
c
h
c
o
nv
e
r
t
t
h
e
c
o
upl
e
d
s
y
s
t
e
m
unde
r
s
o
m
e
c
o
ns
i
de
r
a
t
i
o
n
i
n
t
o
a
n
e
a
s
i
l
y
a
l
g
e
br
a
i
c
s
y
s
t
e
m
o
f
L
y
a
puno
v
o
r
S
y
l
v
e
s
t
e
r
e
qua
t
i
o
n
t
y
pe
.
T
he
a
dv
a
nt
a
g
e
o
f
t
he
p
r
e
s
e
n
t
m
e
t
ho
d,
i
nc
l
u
di
ng
t
he
s
i
m
pl
e
c
om
put
a
t
i
o
n,
c
o
m
put
e
r
-
o
r
i
e
nt
e
d,
w
h
i
c
h
r
e
qu
i
r
e
s
l
e
s
s
s
p
a
c
e
t
o
s
t
o
r
e
,
t
i
m
e
-
e
f
f
i
c
i
e
nt
,
a
nd
i
t
c
a
n
be
a
ppl
i
e
d
f
o
r
s
o
l
v
i
ng
i
nt
e
g
e
r
(
f
r
a
c
t
i
o
na
l
)
o
r
de
r
pa
r
t
i
a
l
di
f
f
e
r
e
n
t
i
a
l
e
qu
a
t
i
o
ns
.
S
o
m
e
s
pe
c
i
f
i
c
a
nd
i
l
l
us
t
r
a
t
i
ng
e
x
a
m
pl
e
s
ha
v
e
be
e
n
g
i
v
e
n;
f
i
g
ur
e
s
a
r
e
us
e
d
t
o
s
ho
w
t
he
e
f
f
i
c
i
e
nc
y
,
a
s
w
e
l
l
a
s
t
h
e
a
c
c
ur
a
c
y
o
f
t
he
,
a
c
hi
e
v
e
d
a
pp
r
o
xi
m
a
t
e
d
r
e
s
ul
t
s
.
A
l
l
num
e
r
i
c
a
l
c
a
l
c
ul
a
t
i
o
ns
i
n
t
hi
s
p
a
pe
r
ha
v
e
be
e
n
c
a
r
r
i
e
d
o
u
t
w
i
t
h
M
A
T
L
A
B
.
Ke
y
w
or
d
s
:
F
r
a
c
t
i
o
na
l
o
r
de
r
pa
rt
i
a
l
D
i
f
fe
r
e
n
t
i
a
l
e
qu
a
t
i
o
n
s
H
a
a
r
w
a
v
e
l
e
t
T
hi
s
i
s
an
ope
n
ac
c
e
s
s
ar
t
i
c
l
e
u
nde
r
t
he
C
C
B
Y
-
SA
l
i
c
e
ns
e
.
Cor
r
e
s
pon
di
n
g
Au
t
h
or
:
A
bb
a
s
F
a
d
h
i
l
A
l
-
S
h
i
m
m
a
r
y
D
e
pa
rt
m
e
n
t
o
f
E
l
e
c
t
ri
c
a
l
E
ngi
n
e
e
ri
n
g
Al
-
M
us
t
a
n
s
i
r
i
y
a
h
U
n
i
v
e
r
s
i
t
y
,
S
e
c
.
322,
S
t
.
30
,
B
a
g
hda
d
,
I
r
a
q
E
m
a
i
l
:
a
b
b
s
.
f
a
dh
i
l
62
@
gm
a
i
l
.
c
o
m
1.
I
N
TR
O
D
U
C
TI
O
N
T
h
e
s
ub
j
e
c
t
of
f
r
a
c
t
i
o
na
l
c
a
l
c
ul
us
i
s
a
b
r
a
n
c
h
o
f
a
ppl
i
e
d
m
a
t
h
e
m
a
t
i
c
s
w
h
i
c
h
de
a
l
w
i
t
h
de
ri
v
a
t
i
v
e
s
a
n
d
i
n
t
e
g
ra
l
s
o
f
a
n
y
a
r
b
i
t
r
a
r
y
o
r
de
r
s
.
I
n
t
hi
s
s
t
udy
,
w
e
i
n
t
r
o
d
uc
e
f
r
a
c
t
i
o
na
l
o
r
de
r
p
a
r
t
i
a
l
di
f
f
e
r
e
n
t
i
a
l
e
qu
a
t
i
o
n
s
(F
P
D
E
s
)
w
h
i
c
h
r
e
p
r
e
s
e
nt
a
n
e
f
f
e
c
t
i
v
e
t
oo
l
t
o
de
s
c
r
i
b
e
s
e
ve
ra
l
c
e
r
t
a
i
n
r
e
a
l
p
h
y
s
i
c
a
l
p
h
e
n
o
m
e
n
a
.
M
o
s
t
o
f
t
h
e
e
n
gi
n
e
e
r
i
n
g
a
nd
p
h
y
s
i
c
a
l
pr
o
c
e
s
s
e
s
a
r
e
n
a
t
u
ra
l
l
y
l
e
d
t
o
(F
P
D
E
s
),
s
uc
h
a
s
da
m
p
i
n
g
l
a
w
s
,
dy
n
a
m
i
c
a
l
p
r
o
c
e
s
s
e
s
i
n
f
l
ui
d
,
a
nd
po
r
o
us
s
t
r
uc
t
u
r
e
[1
, 2
]
.
F
P
D
E
s
a
ppe
a
r
a
l
s
o
i
n
t
he
c
o
n
t
r
o
l
t
h
e
o
r
y
of
d
y
n
a
m
i
c
a
l
s
y
s
t
e
m
s
,
w
h
e
n
t
h
e
c
o
n
t
r
o
l
l
e
d
s
y
s
t
e
m
i
s
de
l
i
n
e
a
t
e
d,
m
o
s
t
s
t
udi
e
s
s
h
o
w
t
h
a
t
,
t
h
e
f
r
a
c
t
i
o
n
a
l
-
o
r
de
r
c
o
n
t
r
o
l
l
e
r
c
a
n
p
r
o
v
i
de
be
t
t
e
r
pe
r
f
o
r
m
a
n
c
e
t
h
a
n
t
h
e
c
o
n
t
r
o
l
l
e
r
w
i
t
h
a
n
i
nt
e
ge
r
o
r
de
r
.
A
l
s
o
,
m
o
s
t
c
o
upl
e
d
s
y
s
t
e
m
s
of
F
P
D
E
s
c
a
n
b
e
fo
un
d
i
n
b
i
o
m
e
c
h
a
ni
c
s
,
a
s
t
h
e
m
o
de
l
i
n
g
p
h
e
n
o
m
e
na
o
f
e
l
e
c
t
r
i
c
a
l
a
c
t
i
v
i
t
y
i
n
t
h
e
h
e
a
r
t
[3
-
5
]
.
F
u
rt
h
e
r
m
o
r
e
,
i
t
a
ppe
a
r
s
i
n
s
o
l
i
d
-
s
t
a
t
e
p
h
y
s
i
c
s
a
n
d
m
e
c
h
a
ni
c
s
,
a
s
t
h
e
c
o
upl
e
d
s
y
s
t
e
m
i
s
de
s
c
r
i
b
e
d
by
t
h
e
d
y
n
a
m
i
c
s
of
m
ul
t
i
-
de
f
o
r
m
a
b
l
e
bo
di
e
s
c
o
upl
e
d
w
i
t
h
s
t
a
nda
r
d
l
i
g
h
t
f
ra
c
t
i
o
na
l
o
r
de
r
d
i
s
c
r
e
t
e
c
o
n
t
i
nuum
l
a
y
e
r
s
[6
-
9
]
.
A
nd
s
i
n
c
e
m
o
s
t
o
f
F
P
D
E
s
do
n
o
t
h
a
v
e
e
xa
c
t
a
na
l
y
t
i
c
s
o
l
ut
i
o
n
s
,
s
o
t
h
e
b
r
a
n
c
h
de
a
l
i
ng
w
i
t
h
a
n
a
pp
r
o
xi
m
a
t
e
n
u
m
e
ri
c
a
l
s
o
l
ut
i
o
n
o
f
t
h
i
s
t
y
p
e
of
di
ffe
r
e
n
t
i
a
l
e
qua
t
i
o
n
s
h
a
s
a
t
t
ra
c
t
e
d
t
h
e
a
t
t
e
nt
i
o
n
o
f
m
a
n
y
r
e
s
e
a
r
c
h
e
r
s
i
n
r
e
c
e
n
t
y
e
a
r
s
.
S
o
m
e
o
f
t
h
e
s
e
m
e
t
h
o
ds
a
r
e
;
A
do
m
a
i
n
de
c
o
m
po
s
i
t
i
o
n
m
e
t
h
o
d
(A
D
M
)
[
10].
T
h
e
ge
n
e
ra
l
i
z
e
d
di
f
f
e
r
e
n
t
i
a
l
s
t
ra
n
s
f
o
r
m
m
e
t
h
o
d
(G
D
T
M
)
[11].
V
a
ri
a
t
i
o
n
i
t
e
r
a
t
i
o
n
m
e
t
h
o
d
(V
IM
)
[12].
W
a
v
e
l
e
t
m
e
t
h
o
d
(W
M
)
[13].
G
e
n
e
r
a
l
i
z
e
d
b
l
o
c
k
pul
s
e
o
pe
r
a
t
i
o
n
a
l
m
a
t
ri
x
m
e
t
h
o
d
(G
B
P
M
)
[14]
.
T
h
e
h
o
m
o
t
o
py
pe
r
t
u
r
b
a
t
i
o
n
m
e
t
h
o
d
(H
P
M
)
a
nd
S
t
e
h
f
e
s
t
'
s
Evaluation Warning : The document was created with Spire.PDF for Python.
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
IS
S
N
:
2502
-
4752
H
aar
w
av
e
l
e
t
m
e
t
hod
f
or
s
ol
v
i
n
g
c
oup
l
e
d
s
y
s
t
e
m
of
f
r
ac
t
i
o
na
l
or
d
e
r
…
(
A
bbas
F
adh
i
l
A
l
S
hi
m
m
ar
y
)
1445
n
u
m
e
r
i
c
a
l
a
l
go
r
i
t
hm
f
o
r
t
h
e
c
a
l
c
ul
a
t
i
o
n
o
f
i
n
v
e
r
s
e
(L
T
)
[15
]
,
e
t
c
.
I
n
t
h
i
s
s
t
udy
,
w
e
fo
c
us
o
n
t
h
e
n
um
e
r
i
c
a
l
m
e
t
h
o
d
o
f
s
o
l
v
i
n
g
a
c
o
upl
e
d
s
y
s
t
e
m
of
t
h
e
f
r
a
c
t
i
o
na
l
p
a
r
t
i
a
l
di
f
f
e
r
e
n
t
i
a
l
e
qua
t
i
o
n
b
a
s
e
d
o
n
t
h
e
o
pe
r
a
t
i
o
n
a
l
m
a
t
r
i
c
e
s
o
f
H
a
a
r
w
a
v
e
l
e
t
o
r
t
h
o
n
o
r
m
a
l
f
un
c
t
i
o
n
s
.
T
h
e
m
a
i
n
a
i
m
o
f
t
hi
s
s
t
u
dy
i
s
t
o
ob
t
a
i
n
f
a
s
t
a
nd
e
f
fe
c
t
i
ve
a
l
go
r
i
t
hm
s
t
ha
t
a
r
e
s
u
i
t
a
b
l
e
f
o
r
di
gi
t
a
l
c
o
m
put
e
r
s
.
T
h
e
r
e
s
t
of
t
h
i
s
pa
pe
r
i
s
o
r
ga
ni
z
e
d
a
s
f
o
l
l
ow
s
:
In
S
e
c
t
i
o
n
2,
w
e
r
e
c
a
l
l
s
o
m
e
n
e
c
e
s
s
a
r
y
de
f
i
n
i
t
i
o
n
s
of
t
h
e
f
r
a
c
t
i
o
na
l
c
a
l
c
ul
us
t
h
e
o
r
y
t
o
m
a
ke
t
h
i
s
a
rt
i
c
l
e
s
e
l
f
-
c
o
n
t
a
i
n
e
d
.
T
h
e
H
a
rr
w
a
v
e
l
e
t
c
o
n
c
e
pt
ha
s
b
e
e
n
pr
e
s
e
nt
e
d
i
n
S
e
c
t
i
o
n
3.
S
e
c
t
i
o
n
4
i
s
de
v
o
t
e
d
t
o
t
h
e
o
pe
r
a
t
i
o
n
a
l
m
a
t
r
i
c
e
s
of
t
h
e
H
a
a
r
w
a
ve
l
e
t
,
i
l
l
us
t
ra
t
i
n
g
e
xa
m
pl
e
s
o
f
t
h
e
a
ppl
i
e
d
m
e
t
h
o
d
i
s
i
nt
r
o
duc
e
d
i
n
S
e
c
t
i
o
n
5
.
F
i
n
a
l
l
y
,
c
o
n
c
l
us
i
o
n
a
n
d
f
ut
u
r
e
s
t
u
di
e
s
a
r
e
i
n
t
r
o
duc
e
d
i
n
S
e
c
t
i
o
n
6
.
2.
P
R
ELI
M
I
N
A
R
I
ES
T
h
i
s
s
e
c
t
i
o
n
i
s
de
vo
t
e
d
t
o
s
o
m
e
f
un
da
m
e
n
t
a
l
a
nd
n
e
c
e
s
s
a
r
y
de
f
i
n
i
t
i
o
n
s
o
f
t
h
e
t
h
e
o
r
y
of
f
r
a
c
t
i
o
na
l
c
a
l
c
ul
us
,
w
h
i
c
h
a
r
e
r
e
qu
i
r
e
d
f
o
r
b
ui
l
d
i
n
g
up
o
ur
o
ut
c
o
m
e
s
[16,
17].
D
e
f
i
n
i
t
i
o
n
1
:
A
r
e
a
l
f
un
c
t
i
o
n
R
t
x
t
x
u
,
),
,
(
,
0
t
i
s
s
a
i
d
t
o
b
e
i
n
t
h
e
s
p
a
c
e
R
,
C
,
i
f
t
h
e
r
e
e
xi
s
t
a
r
e
a
l
n
u
m
b
e
r
>
p
,
s
uc
h
t
ha
t
)
,
(
)
,
(
1
t
x
u
t
t
x
u
p
,
w
h
e
r
e
))
,
0
[
(
)
,
(
1
R
C
t
x
u
,
a
n
d
i
t
i
s
s
a
i
d
t
o
b
e
i
n
s
pa
c
e
n
C
i
f
a
nd
o
nl
y
i
f
C
n
n
t
t
x
u
)
,
(
{
0}
N
,
n
.
D
e
f
i
n
i
t
i
o
n
2
:
T
h
e
(l
e
f
t
s
i
de
d)
R
i
e
m
a
nn
-
L
i
o
uv
i
l
l
e
f
r
a
c
t
i
o
na
l
i
n
t
e
g
r
a
l
o
pe
ra
t
o
r
)
(
j
o
f
o
r
de
r
0
>
,
o
f
a
f
un
c
t
i
o
n
1
)
,
(
,
C
t
x
u
,
w
i
t
h
r
e
s
pe
c
t
t
o
t
i
s
de
f
i
n
e
d
a
s
:
).
,
(
)
,
(
,
0
,
)
,
(
)
(
)
(
1
)
,
(
0
0
1
t
x
u
t
x
u
j
t
d
x
u
t
t
x
u
j
t
t
t
>
(1)
D
e
f
i
n
i
t
i
o
n
3
:
T
h
e
(l
e
f
t
s
i
de
d)
f
r
a
c
t
i
o
n
a
l
de
r
i
v
a
t
i
v
e
o
pe
r
a
t
o
r
t
c
D
o
f
o
r
de
r
0
,
o
f
a
f
un
c
t
i
o
n
1
)
,
(
,
C
t
x
u
,
w
i
t
h
r
e
s
pe
c
t
t
o
"
t
"
i
n
t
h
e
Ca
pu
t
o
s
e
n
s
e
i
s
de
f
i
n
e
d
a
s
,
s
e
e
[18
]
:
.
,
<
<
n
t
x
u
n
t
n
t
n
n-
d
n
t
t
x
u
n
t
x
u
D
n
n
t
c
)
,
(
0
,
1
0
,
1
)
(
)
,
(
)
(
1
)
,
(
(2)
W
h
e
r
e
n
n
<
1
,
n
,
n
an
d
i
s
t
h
e
gr
e
a
t
e
s
t
po
s
i
t
i
v
e
i
n
t
e
ge
r
f
un
c
t
i
o
n
.
T
h
e
f
r
a
c
t
i
o
na
l
de
r
i
v
a
t
i
v
e
of
o
r
de
r
i
n
t
h
e
s
e
n
s
e
o
f
Ca
put
o
i
s
a
l
s
o
de
f
i
n
e
d
a
s
.
)
,
(
)
,
(
t
x
u
D
j
t
x
u
D
r
t
r
t
c
,
w
h
e
r
e
r
t
D
i
s
t
h
e
us
u
a
l
di
f
f
e
r
e
n
t
i
a
l
o
pe
r
a
t
o
r
o
f
o
r
de
r
r.
T
h
e
r
e
l
a
t
i
o
n
b
e
t
w
e
e
n
Ca
put
o
d
i
f
f
e
r
e
n
t
i
a
l
o
pe
r
a
t
o
r
a
n
d
R
i
e
m
a
nn
–
L
i
o
uv
i
l
l
e
i
nt
e
g
r
a
l
o
pe
r
a
t
o
r
i
s
gi
v
e
n
by
t
h
e
e
xp
r
e
s
s
i
o
n
:
),
,
(
)
,
(
t
x
u
t
x
u
j
D
t
t
(3)
.
0
!
)
0
,
(
)
,
(
)
,
(
1
0
,
>
t
k
t
t
x
u
t
x
u
t
x
u
D
j
k
n
k
k
k
t
t
(4)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
,
V
o
l
.
21
,
N
o
.
3
,
M
a
r
c
h
2
021
:
1
4
4
4
-
1
4
5
4
1446
3.
H
A
A
R
WA
V
E
LETS
A
w
a
ve
l
e
t
i
s
a
m
a
t
h
e
m
a
t
i
c
a
l
f
u
n
c
t
i
o
n
us
e
d
i
n
s
i
g
na
l
p
r
o
c
e
s
s
i
n
g
a
nd
i
m
a
ge
c
o
m
p
r
e
s
s
i
o
n
,
i
n
t
h
e
f
i
r
s
t
a
ppl
i
e
d
i
n
ge
o
ph
y
s
i
c
s
t
o
ge
t
pi
c
t
ur
e
s
o
f
l
a
y
e
r
s
i
n
s
ub
s
urf
a
c
e
r
o
c
k,
w
h
i
c
h
a
r
e
us
e
d
i
n
o
i
l
a
n
d
m
i
n
e
ra
l
e
xpl
o
r
a
t
i
o
n.
O
n
e
o
f
t
h
e
po
pul
a
r
f
a
m
i
l
i
e
s
o
f
w
a
ve
l
e
t
s
i
s
t
he
H
a
a
r
w
a
v
e
l
e
t
,
i
t
i
s
t
h
e
o
l
de
s
t
w
a
v
e
l
e
t
,
i
t
w
a
s
i
n
t
r
o
duc
e
d
by
t
h
e
H
un
ga
r
i
a
n
m
a
t
h
e
m
a
t
i
c
i
a
n
A
l
f
r
e
d
H
a
a
r
i
n
1
909,
a
n
d
t
h
e
w
a
v
e
l
e
t
s
t
h
e
o
r
y
s
t
a
r
t
e
d
m
uc
h
i
n
t
h
e
1980s
.
I
t
i
s
a
po
pul
a
r
t
o
pi
c
i
n
d
i
v
e
r
s
e
f
i
e
l
ds
of
e
n
gi
n
e
e
r
i
n
g
a
n
d
s
c
i
e
n
c
e
,
t
h
e
H
a
a
r
w
a
v
e
l
e
t
i
s
a
l
s
o
c
o
n
s
i
de
r
e
d
t
h
e
f
i
r
s
t
k
n
o
w
n
s
i
m
pl
e
s
t
w
a
v
e
l
e
t
b
e
c
a
us
e
i
t
w
a
s
c
o
n
s
i
s
t
i
n
g
o
f
a
pi
e
c
e
w
i
s
e
c
o
n
s
t
a
nt
f
u
n
c
t
i
o
n,
t
h
a
t
t
a
ke
o
n
l
y
t
h
e
t
hr
e
e
v
a
l
ue
s
0,
1
a
n
d
-
1
.
I
n
t
h
e
l
a
s
t
t
w
o
de
c
a
de
s
,
t
h
e
s
ub
j
e
c
t
of
w
a
v
e
l
e
t
s
t
h
e
o
r
y
h
a
s
b
e
e
n
p
l
a
y
i
n
g
a
n
i
m
po
rt
a
nt
r
o
l
e
i
n
m
a
n
y
c
o
m
put
i
n
g
m
a
t
h
e
m
a
t
i
c
a
l
s
c
i
e
nt
i
s
t
s
,
e
s
pe
c
i
a
l
l
y
i
n
t
i
m
e
-
f
r
e
que
n
c
y
a
na
l
y
s
i
s
,
s
i
gn
a
l
a
na
l
y
s
i
s
,
a
n
d
n
u
m
e
r
i
c
a
l
a
na
l
y
s
i
s
,
w
a
v
e
l
e
t
t
e
c
h
n
i
que
e
na
b
l
e
s
us
t
o
de
c
om
po
s
e
d
di
ff
e
r
e
n
t
c
o
m
pl
i
c
a
t
e
d
f
un
c
t
i
o
n
s
i
n
t
o
a
s
um
m
a
t
i
o
n
o
f
b
a
s
i
c
f
un
c
t
i
o
n
s
,
a
s
w
e
l
l
a
s
e
a
c
h
b
a
s
i
c
f
un
c
t
i
o
n
c
a
n
b
e
ge
n
e
ra
t
e
d
f
r
o
m
di
l
a
t
i
o
n
a
nd
t
r
a
n
s
l
a
t
i
o
n
o
f
a
m
o
t
h
e
r
w
a
v
e
l
e
t
f
un
c
t
i
o
n.
Co
n
s
e
que
n
t
l
y
,
t
h
e
w
a
v
e
l
e
t
a
n
a
l
y
s
i
s
of
f
un
c
t
i
o
n
s
i
s
m
o
r
e
a
c
c
ura
t
e
l
y
de
s
c
r
i
b
e
d
a
n
d
f
a
s
t
e
r
t
ha
n
F
o
ur
i
e
r
a
na
l
y
s
i
s
.
M
a
n
y
s
t
udi
e
s
a
r
e
fo
c
us
i
n
g
o
n
t
h
e
m
e
t
h
o
d
o
f
o
r
t
h
o
go
na
l
po
l
y
n
o
m
i
a
l
a
n
d
f
un
c
t
i
o
n
s
,
t
o
o
b
t
a
i
n
a
n
e
ff
e
c
t
i
v
e
a
l
go
r
i
t
h
m
t
ha
t
c
a
n
b
e
s
u
i
t
a
b
l
e
fo
r
a
di
g
i
t
a
l
c
o
m
pu
t
e
r.
S
uc
h
a
s
a
n
u
m
e
ri
c
a
l
m
e
t
h
o
d
w
i
t
h
o
m
i
t
t
i
n
g
di
s
c
r
e
t
i
z
a
t
i
o
n
[19]
,
H
a
a
r
w
a
v
e
l
e
t
f
un
c
t
i
o
n
s
[2
0
-
24]
,
e
t
c
.
In
t
h
i
s
w
o
r
k,
w
e
foc
us
o
n
t
h
e
H
a
a
r
w
a
v
e
l
e
t
m
e
t
h
o
d
b
a
s
e
d
o
n
t
h
e
o
r
t
h
o
go
n
a
l
m
a
t
ri
x
i
n
c
l
udi
ng
t
h
e
i
n
t
e
g
r
a
t
i
o
n
of
o
r
t
h
o
n
o
rm
a
l
f
un
c
t
i
o
n
s
,
w
i
t
h
o
ut
us
i
ng
H
a
a
r
w
a
v
e
l
e
t
-
b
a
s
e
d
o
n
b
l
o
c
k
pul
s
e
f
un
c
t
i
o
n
s
t
h
a
t
di
f
f
e
r
f
r
o
m
i
t
,
a
r
e
ut
i
l
i
z
e
d
t
o
r
e
duc
e
t
h
e
f
r
a
c
t
i
o
na
l
pa
rt
i
a
l
d
i
f
fe
re
n
t
i
a
l
e
qu
a
t
i
o
n
i
nt
o
a
n
e
a
s
i
l
y
a
l
ge
b
r
a
i
c
m
a
t
ri
x
e
qua
t
i
o
n
o
n
e
of
L
y
a
pun
o
v
o
r
S
y
l
ve
s
t
e
r
t
y
pe
,
w
h
i
c
h
c
a
n
b
e
s
o
l
ve
d
by
c
o
m
pu
t
e
r
o
r
i
e
n
t
e
d
m
e
t
h
o
ds
,
t
h
e
c
a
l
c
ul
a
t
i
o
n
s
a
r
e
do
n
e
by
us
i
n
g
M
a
t
h
l
a
b
s
of
t
w
a
r
e
w
i
t
h
c
e
rt
a
i
n
c
o
m
m
a
nds
o
r
s
pe
c
i
a
l
t
o
o
l
bo
x.
M
o
r
e
ov
e
r
,
i
t
i
s
a
n
e
f
fe
c
t
i
ve
t
o
o
l
i
n
t
h
e
c
o
m
put
a
t
i
o
na
l
s
c
i
e
n
c
e
s
,
e
s
pe
c
i
a
l
l
y
i
n
t
h
e
s
ub
j
e
c
t
of
s
i
gna
l
a
na
l
y
s
i
s
,
da
t
a
c
o
m
pr
e
s
s
i
o
n,
a
n
d
m
a
n
y
o
t
h
e
r
s
,
a
n
d
b
e
c
a
us
e
i
t
s
fe
a
t
u
r
e
s
,
s
uc
h
a
s
hi
g
h
e
n
e
r
gy
pa
c
ki
n
g
,
f
l
e
xi
b
l
e
,
t
h
e
n
o
n
-
s
t
a
b
i
l
i
t
y
of
n
u
m
e
r
i
c
a
l
s
o
l
ut
i
o
n
s
do
e
s
n
o
t
o
c
c
ur
i
n
t
h
i
s
m
e
t
h
o
d,
e
f
fe
c
t
i
v
e
fo
r
t
r
e
a
t
i
n
g
s
i
n
gu
l
a
ri
t
i
e
s
,
m
o
r
e
o
ve
r
s
m
a
l
l
c
o
m
put
a
t
i
o
n
a
l
c
o
s
t
a
n
d
i
t
ha
s
p
r
o
pe
rt
i
e
s
t
ha
t
h
e
l
p
s
pe
e
d
c
a
l
c
ul
a
t
i
o
n
s
,
a
f
t
e
r
t
hi
s
i
nt
r
o
duc
t
i
o
n.
L
e
t
us
b
e
gi
n
w
i
t
h
t
h
e
de
f
i
n
i
t
i
o
n
o
f
t
h
e
o
r
t
h
o
n
o
r
m
a
l
s
e
t
o
f
H
a
a
r
f
un
c
t
i
o
n
s
,
s
e
e
[25],
w
h
i
c
h
i
s
a
f
a
m
i
l
y
of
s
w
i
t
c
h
e
d
r
e
c
t
a
n
gl
e
w
a
ve
fo
r
m
w
i
t
h
a
m
pl
i
t
ude
d
i
f
fe
r
o
n
e
t
o
a
n
o
t
h
e
r
,
i
t
c
o
n
t
a
i
n
s
j
us
t
o
n
e
w
a
v
e
l
e
t
duri
n
g
t
h
e
i
nt
e
r
e
s
t
u
ni
t
s
ub
i
n
t
e
r
v
a
l
o
f
t
i
m
e
[0,
1),
r
e
m
a
i
n
z
e
r
o
e
l
s
e
w
h
e
r
e
,
a
n
d
o
rt
ho
n
o
r
m
a
l
,
t
h
e
i
t
h
u
ni
f
o
r
m
H
a
a
r
w
a
v
e
l
e
t
)
(
t
h
ij
i
s
de
f
i
n
e
a
s
:
.
0
1
0
1
1
)
(
00
o
t
h
e
r
w
i
s
e
t<
m
t
h
,
,
,
(5)
.
0
),
2
2
5
0
2
),
2
5
0
2
1
2
1
)
(
2
2
o
t
he
r
w
i
z
e
k
,
.
k-
t
.
k-
,
k-
t
m
t
h
j
j
j
j
j
j
ij
,
[
,
[
,
(6)
W
h
e
r
e
t
h
e
di
l
a
t
i
o
n
pa
ra
m
e
t
e
r
J
j
,
,
2
,
1
,
0
,
1
2
j
m
,
a
n
d
J
i
s
t
h
e
m
a
x
i
m
u
m
l
e
v
e
l
of
r
e
s
o
l
ut
i
o
n,
t
h
e
p
a
r
a
m
e
t
e
r
1
,
,
2
,
1
m
k
r
e
p
r
e
s
e
nt
s
t
h
e
t
r
a
n
s
l
a
t
i
o
n
o
f
t
he
w
a
ve
l
e
t
,
t
h
e
i
nt
e
ge
r
s
j
k
,
r
e
p
r
e
s
e
n
t
t
h
e
de
c
o
m
pos
i
t
i
o
n
o
f
t
h
e
i
nde
x
i
,
1
2
k
i
j
,
t
h
e
m
a
xi
m
u
m
v
a
l
ue
o
f
i
i
s
1
2
2
J
M
i
,
t
h
e
r
e
a
r
e
t
w
o
f
un
c
t
i
o
n
s
p
l
a
y
a
pri
m
a
r
y
r
o
l
e
i
n
w
a
v
e
l
e
t
a
n
a
l
y
s
i
s
,
t
h
e
f
u
n
c
t
i
o
n
)
(
00
t
h
,
w
hi
c
h
i
s
c
a
l
l
e
d
a
H
a
a
r
f
at
h
e
r
f
un
c
t
i
on
a
n
d
t
h
e
f
un
c
t
i
o
n
)
(
10
t
h
,
w
h
i
c
h
i
s
c
a
l
l
e
d
a
H
a
a
r
m
ot
he
r
f
unc
t
i
o
n
t
ha
t
ge
n
e
r
a
t
e
s
w
h
o
l
e
o
t
h
e
r
da
ug
ht
e
r
a
n
d
g
r
a
ndda
u
g
h
t
e
r
f
un
c
t
i
o
n
s
o
n
u
n
i
t
i
nt
e
r
v
a
l
[0
,
1)
,
t
h
e
r
e
a
r
e
t
w
o
b
a
s
i
c
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
o
c
c
ur
s
i
n
H
a
a
r
f
un
c
t
i
o
n
s
r
e
p
r
e
s
e
nt
by
t
ra
n
s
l
a
t
i
o
n
(s
hi
f
t
i
n
g)
a
nd
d
i
l
a
t
i
o
n
,
w
hi
l
e
t
h
e
r
e
s
t
o
f
f
un
c
t
i
o
n
s
c
a
n
b
e
ge
n
e
r
a
t
e
d
f
r
o
m
)
(
10
t
h
us
i
n
g
t
h
e
s
e
t
w
o
o
p
e
r
a
t
i
o
n
s
a
n
d
k
n
o
w
l
e
dge
by
t
h
e
f
o
l
l
ow
i
n
g
re
l
a
t
i
o
n
s
h
i
p
:
),
2
2
(
)
(
1
j
j
j
ij
k
t
h
t
h
1
2
k
i
j
,
.
0
j
(7)
E
a
c
h
H
a
a
r
w
a
v
e
l
e
t
c
o
n
s
i
s
t
s
o
f
a
c
o
upl
e
of
c
o
n
s
t
a
n
t
s
t
e
ps
w
i
t
h
a
n
o
ppo
s
i
t
e
s
i
gn
du
r
i
ng
i
t
s
s
ub
i
n
t
e
r
v
a
l
a
n
d
s
a
t
i
s
f
i
e
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
IS
S
N
:
2502
-
4752
H
aar
w
av
e
l
e
t
m
e
t
hod
f
or
s
ol
v
i
n
g
c
oup
l
e
d
s
y
s
t
e
m
of
f
r
ac
t
i
o
na
l
or
d
e
r
…
(
A
bbas
F
adh
i
l
A
l
S
hi
m
m
ar
y
)
1447
.
,
2
)
(
)
(
1
0
r
i
r
i
dt
t
h
t
h
j
rj
ij
,
0
,
(8)
T
h
i
s
r
e
l
a
t
i
o
n
s
h
i
p
s
h
o
w
s
t
h
a
t
H
a
a
r
w
a
v
e
l
e
t
s
a
r
e
o
r
t
h
o
n
o
rm
a
l
t
h
e
r
e
f
o
r
e
,
i
t
f
o
r
m
s
a
n
o
r
t
h
o
n
o
rm
a
l
b
a
s
i
s
,
a
n
d
i
n
t
h
i
s
c
a
s
e
,
w
e
h
a
v
e
a
n
e
xpl
i
c
i
t
f
o
r
m
ul
a
f
o
r
t
h
e
u
n
i
que
c
oe
ff
i
c
i
e
n
t
s
i
n
t
h
e
l
i
n
e
a
r
c
o
m
b
i
n
a
t
i
o
n.
W
i
t
h
t
h
e
di
l
a
t
i
o
n
a
nd
t
r
a
n
s
l
a
t
i
o
n
p
r
o
c
e
s
s
,
o
n
e
c
a
n
e
a
s
i
l
y
ob
t
a
i
n
b
a
s
i
s
f
un
c
t
i
o
n
s
o
f
t
w
o
di
m
e
n
s
i
o
n
s
,
a
s
s
h
o
w
n
i
n
F
i
gu
r
e
1
.
F
i
gu
r
e
1
.
T
h
e
f
i
r
s
t
1x4
b
a
s
i
s
f
o
r
H
a
a
r
w
a
v
e
l
e
t
o
r
t
h
o
go
na
l
f
unc
t
i
o
n
s
w
i
t
h
m=
8
In
t
hi
s
c
a
s
e
,
t
h
e
H
a
a
r
o
rt
h
o
n
o
r
m
a
l
m
a
t
ri
x
f
o
r
r
e
s
o
l
ut
i
o
n
up
t
o
2
l
e
v
e
l
s
i
s
gi
v
e
n
by
:
,
2
1
2
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
1
2
1
2
1
2
1
2
1
2
1
0
0
0
0
0
0
0
0
2
1
2
1
2
1
2
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
33
32
31
30
21
20
10
00
8
8
0
0
0
0
0
0
0
0
t
h
t
h
t
h
t
h
t
h
t
h
t
h
t
h
t
H
(9)
W
h
e
r
e
T
0
0
0
2
1
0
2
1
8
1
8
1
)
16
1
(
H
8
,
T
0
0
0
2
1
-
0
2
1
8
1
8
1
)
16
3
(
H
8
,
.
2
1
8
1
)
16
15
(
T
2
1
-
0
0
0
0
8
1
H
8
4.
TH
E
O
P
ER
A
TI
O
N
A
L
M
A
TR
I
C
ES
O
F
H
A
A
R
WA
V
EL
ET
In
t
hi
s
s
e
c
t
i
o
n
,
w
e
i
n
t
r
o
duc
e
t
h
e
o
pe
r
a
t
i
o
n
a
l
m
a
t
ri
c
e
s
o
f
t
h
e
H
a
a
r
w
a
v
e
l
e
t
.
T
h
e
m
a
i
n
i
de
a
o
f
a
n
o
pe
r
a
t
i
o
n
a
l
m
a
t
r
i
x
i
s
u
t
i
l
i
z
e
d
t
o
r
e
duc
e
t
h
e
i
nt
e
ge
r
(f
r
a
c
t
i
o
n
a
l
)
o
r
d
i
na
r
y
(pa
rt
i
a
l
)
di
f
f
e
r
e
n
t
i
a
l
e
qua
t
i
o
n
i
nt
o
a
n
a
l
ge
b
r
a
i
c
s
i
m
p
l
e
m
a
t
r
i
x
e
qua
t
i
o
n
o
f
L
y
a
pun
o
v
(
S
y
l
v
e
s
t
e
r
)
t
y
pe
,
w
h
i
c
h
c
a
n
b
e
s
o
l
v
e
d
e
a
s
i
l
y
by
a
c
o
m
put
e
r
-
o
r
i
e
nt
e
d
m
e
t
h
o
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
,
V
o
l
.
21
,
N
o
.
3
,
M
a
r
c
h
2
021
:
1
4
4
4
-
1
4
5
4
1448
4.
1
.
F
u
n
c
ti
o
n
ap
p
r
o
x
i
m
ati
o
n
N
ow
,
s
i
m
i
l
a
r
a
s
o
n
e
-
di
m
e
n
s
i
o
na
l
f
u
n
c
t
i
o
n,
a
n
y
t
w
o
-
di
m
e
n
s
i
o
n
a
l
f
un
c
t
i
o
n
)
,
(
t
x
u
))
1
,
0
[
)
1
,
0
([
2
L
w
h
i
c
h
i
s
a
p
i
e
c
e
w
i
s
e
c
o
n
s
t
a
n
t
o
r
a
pp
r
o
xi
m
a
t
e
l
y
pi
e
c
e
w
i
s
e
c
on
s
t
a
n
t
du
ri
n
g
e
a
c
h
s
ub
i
nt
e
r
v
a
l
a
n
d
s
qua
r
e
i
nt
e
g
r
a
b
l
e
i
n
t
h
e
i
n
t
e
r
v
a
l
s
1
<
0
x
a
n
d
1
<
0
t
a
l
s
o
c
a
n
b
e
de
c
o
m
po
s
e
d
i
n
t
o
a
n
i
n
f
i
ni
t
e
H
a
a
r
s
e
r
i
e
s
a
s
s
e
e
[26]
:
,
)
(
)
(
)
,
(
1
1
,
i
j
j
i
j
i
t
h
x
h
c
t
x
u
(10)
W
h
e
r
e
j
i
c
,
i
s
M
M
2
2
c
oe
ff
i
c
i
e
n
t
m
a
t
r
i
x,
w
h
i
c
h
c
a
n
b
e
de
t
e
rm
i
n
e
d
f
r
o
m
t
h
e
i
nn
e
r
p
r
o
duc
t
:
.
)
(
)
,
(
)
(
)
,
(
,
)
(
),
,
(
),
(
1
0
1
0
,
dt
t
h
t
x
u
dx
x
h
t
x
u
t
h
t
x
u
x
h
c
j
i
j
i
j
i
2j
2
(11)
A
n
d
c
a
l
l
e
d
t
h
e
w
a
v
e
l
e
t
c
o
e
ff
i
c
i
e
n
t
s
.
L
e
t
T
m
m
x
h
x
h
x
h
x
H
)]
(
,
),
(
),
(
[
)
(
1
1
0
a
nd
T
m
m
t
h
t
h
t
h
t
H
)]
(
,
),
(
),
(
[
)
(
1
1
0
,
h
e
r
e
m
H
i
s
c
a
l
l
e
d
t
h
e
H
a
a
r
w
a
v
e
l
e
t
m
a
t
ri
x
o
f
o
r
de
r
m
,
w
h
e
r
e
j
m
2
a
s
p
r
e
v
i
o
us
l
y
m
e
n
t
i
o
n
e
d
,
a
nd
T
de
n
o
t
e
s
t
h
e
t
ra
n
s
po
s
e
of
t
h
e
m
a
t
r
i
x,
h
e
n
c
e
t
h
e
a
pp
r
o
xi
m
a
t
e
d
s
u
m
o
f
m
t
e
rm
s
o
f
t
h
e
f
i
ni
t
e
s
e
r
i
e
s
o
f
(10)
c
a
n
b
e
w
r
i
t
t
e
n
i
n
m
a
t
ri
x
f
o
r
m
a
s
:
.
)
(
)
(
)
,
(
1
0
1
0
,
m
i
m
j
j
i
j
i
t
h
x
h
c
t
x
u
(12)
N
ow
,
t
o
de
t
e
r
m
i
n
e
t
h
e
c
o
e
ff
i
c
i
e
n
t
s
j
i
c
,
,
w
e
w
i
l
l
a
ppl
y
t
h
e
w
a
ve
l
e
t
c
o
l
l
oc
a
t
i
o
n
m
e
t
h
o
d,
t
h
e
s
e
s
h
o
w
n
i
n
t
h
e
f
o
l
l
ow
i
n
g
:
M
t
x
2
/
)
5
.
0
(
,
.
2
,
,
2
,
1
M
(13)
W
r
i
t
e
(12)
i
n
d
i
s
c
r
e
t
e
f
o
r
m
by
us
i
n
g
(13
),
w
e
ob
t
a
i
n
t
h
e
m
a
t
r
i
x
e
qu
a
t
i
o
n
:
),
(
)
(
)
,
(
t
CH
x
H
t
x
U
m
T
m
(14)
W
h
e
r
e
m
m
j
i
t
x
u
U
)]
,
(
[
,
m
m
j
i
c
C
]
[
,
a
nd
m
H
i
s
c
a
l
l
e
d
H
a
a
r
w
a
v
e
l
e
t
m
a
t
r
i
x
o
f
o
r
de
r
m
,
i
.
e
:
,
1
,
1
2
,
1
1
,
1
0
,
1
1
,
1
2
,
1
1
,
1
0
,
1
1
,
0
2
,
0
1
,
0
0
,
0
1
1
0
m
m
m
m
m
m
m
m
m
h
h
h
h
h
h
h
h
h
h
h
h
h
h
h
H
(15)
H
e
r
e
1
2
1
0
,
,
,
,
h
m
h
h
h
a
r
e
t
h
e
di
s
c
r
e
t
e
fo
r
m
s
o
f
t
h
e
H
a
a
r
w
a
v
e
l
e
t
b
a
s
i
s
.
S
i
n
c
e
t
h
e
H
a
a
r
w
a
v
e
l
e
t
m
a
t
r
i
x
i
s
o
r
t
h
o
go
n
a
l
a
s
m
e
nt
i
o
n
e
d
e
a
r
l
i
e
r
(i
.
e
.
T
m
m
H
H
1
),
a
c
c
o
r
di
n
g
l
y
t
h
e
w
a
v
e
l
e
t
c
oe
ff
i
c
i
e
n
t
s
c
a
n
b
e
c
a
l
c
ul
a
t
e
d
f
r
o
m
(
14)
by
:
.
T
m
m
m
m
UH
H
C
(16)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
IS
S
N
:
2502
-
4752
H
aar
w
av
e
l
e
t
m
e
t
hod
f
or
s
ol
v
i
n
g
c
oup
l
e
d
s
y
s
t
e
m
of
f
r
ac
t
i
o
na
l
or
d
e
r
…
(
A
bbas
F
adh
i
l
A
l
S
hi
m
m
ar
y
)
1449
4.
2
.
H
aa
r
w
av
e
l
e
t
o
f
I
n
te
g
e
r
O
r
d
e
r
T
o
a
ppl
y
t
h
e
H
a
a
r
w
a
v
e
l
e
t
m
e
t
h
o
d
f
o
r
s
o
l
v
i
n
g
a
n
y
i
nt
e
ge
r
o
r
de
r
p
a
r
t
i
a
l
di
f
f
e
r
e
n
t
i
a
l
e
qu
a
t
i
o
n
s
o
n
e
n
e
e
ds
t
h
e
i
n
t
e
g
ra
l
s
b
e
l
ow
a
s
p
r
e
s
e
n
t
e
d
i
n
[
23]
:
t
t
h
0
0
,
m
1
d
)
(
,
1
0
<
t
(17)
F
o
r
1
,
,
2
,
1
m
i
,
c
a
n
b
e
de
s
c
r
i
b
e
d
a
s
b
e
l
ow
:
t
j
j
j
j
j
j
j
i
k
t
k
t
k
k
t
k
k
t
h
0
2
,
2
1
2
5
.
0
,
2
1
,
2
5
.
0
2
,
2
)
(
.
o
t
h
e
r
w
i
s
e
,
0
<
<
m
2
d
(18)
A
n
d
t
h
e
m
a
t
ri
x
f
o
r
m
o
f
i
nt
e
g
r
a
t
i
o
n
o
f
H
a
a
r
w
a
v
e
l
e
t
i
s
:
.
3
2
1
),
(
)
(
0
1
,...
,
,
n
t
H
p
d
H
p
m
n
m
t
m
n
m
(19)
S
i
m
i
l
a
rl
y
,
fo
r
i
n
t
e
g
r
a
t
i
o
n
t
h
e
t
ra
n
s
po
s
e
H
a
a
r
w
a
v
e
l
e
t
:
.
)
)
(
)
(
1
0
T
m
T
m
t
T
m
p
t
H
d
H
(
(20)
W
h
e
r
e
t
h
e
m
m
m
a
t
ri
x
1
m
p
i
s
c
a
l
l
e
d
t
h
e
H
a
a
r
w
a
v
e
l
e
t
o
p
e
r
a
t
i
o
na
l
m
a
t
r
i
x
o
f
o
n
e
-
t
i
m
e
i
n
t
e
g
ra
t
i
o
n
of
m
a
t
r
i
x
)
(
t
H
m
,
C
h
e
n
a
n
d
H
s
a
i
o
i
n
[2
3],
s
h
o
w
e
d
t
h
a
t
t
h
e
m
a
t
r
i
x
1
m
p
c
a
n
b
e
c
a
l
c
ul
a
t
e
d
f
r
o
m
t
h
e
pa
rt
i
t
i
o
n
fo
ur
s
ub
m
a
t
r
i
c
e
s
:
.
2
2
1
1
2
2
1
1
2
0
-
m
m
m
m
H
H
P
m
m
p
(21)
W
h
e
r
e
0
i
s
t
h
e
z
e
r
o
m
a
t
ri
x
o
f
o
r
de
r
2
2
m
m
.
4.
3
.
H
aa
r
Wav
e
l
e
t
o
f
F
r
a
c
ti
o
n
al
O
r
d
e
r
N
ow
,
l
i
ke
w
h
a
t
w
e
h
a
v
e
do
n
e
w
i
t
h
t
h
e
i
nt
e
ge
r
o
r
de
r
,
w
e
w
i
l
l
l
i
ke
w
i
s
e
t
o
d
e
r
i
v
e
t
h
e
H
a
a
r
w
a
v
e
l
e
t
o
pe
r
a
t
i
o
n
a
l
m
a
t
ri
x
o
f
f
r
a
c
t
i
o
n
a
l
o
r
de
r
i
nt
e
gra
t
i
o
n
m
p
,
R
.
F
o
r
t
h
i
s
pu
r
po
s
e
,
w
e
w
i
l
l
r
e
c
a
l
l
t
h
e
R
i
e
m
a
nn
-
L
i
o
uv
i
l
l
e
f
r
a
c
t
i
o
na
l
i
nt
e
gra
l
o
pe
r
a
t
o
r
)
(
j
us
i
n
g
de
f
i
ni
t
i
o
n
(2)
:
)
(
)
(
t
H
p
t
H
j
m
m
m
,
)]
(
,
),
(
),
(
[
1
1
0
T
m
m
m
m
t
h
p
t
h
p
t
h
p
(22)
W
h
e
r
e
,
.
),
1
0
[
,
)
1
(
)
(
0
e
l
s
e
w
h
e
r
e
,
t
m
t
t
h
p
m
0
(23)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
,
V
o
l
.
21
,
N
o
.
3
,
M
a
r
c
h
2
021
:
1
4
4
4
-
1
4
5
4
1450
F
o
r
1
,
,
2
,
1
m
i
.
1
)
2
(
)
2
5
.
0
(
2
)
2
1
(
,
)
2
5
.
0
(
2
)
2
1
(
,
)
2
1
(
,
0
)
1
(
2
)
(
2
<
t
2
k
,
2
k
<
t
2
0.5
-
k
,
2
0.5
-
k
<
t
2
1
-
k
,
2
1
-
k
<
t
0
,
j
j
j
j
j
j
j
j
j
j
j
j
j
i
m
k
t
k
t
k
t
k
t
k
t
k
t
m
t
h
p
(24)
L
e
t
m
m
D
de
n
o
t
e
t
o
t
h
e
H
a
rr
w
a
v
e
l
e
t
o
pe
r
a
t
i
o
na
l
m
m
m
a
t
ri
x
f
r
a
c
t
i
o
na
l
di
f
f
e
r
e
n
t
i
a
t
i
o
n
o
f
o
r
de
r
,
s
i
n
c
e
I
p
D
m
m
m
m
,
t
h
e
n
w
e
c
a
n
c
a
l
c
u
l
a
t
e
m
m
D
by
i
n
v
e
r
t
i
n
g
m
m
p
.
M
o
r
e
o
ve
r
,
t
h
e
H
a
a
r
w
a
v
e
l
e
t
f
r
a
c
t
i
o
na
l
p
a
r
t
i
a
l
de
r
i
v
a
t
i
v
e
s
of
o
r
de
r
de
f
i
n
e
by
:
]
)
(
[
)
(
)
,
(
t
t
H
C
x
H
t
U
t
t
x
u
m
T
m
),
(
)
(
t
H
CP
x
H
m
m
T
m
(25)
A
n
d
)
(
)
(
)
,
(
t
CH
x
x
H
x
U
x
t
x
u
m
T
m
).
(
]
)[
(
t
CH
P
x
H
m
T
m
T
m
(26)
A
s
w
e
l
l
a
s
,
H
a
a
r
w
a
v
e
l
e
t
f
r
a
c
t
i
o
na
l
i
nt
e
g
r
a
t
i
o
n
o
f
o
r
de
r
w
i
t
h
r
e
s
pe
c
t
t
o
t
a
n
d
x
r
e
s
pe
c
t
i
v
e
l
y
gi
v
e
n
by
:
(
)
(
)
(
)
(
(
)
TT
t
t
m
m
m
t
m
j
U
j
H
x
CH
t
H
x
Cj
H
t
,
m
m
T
m
H
Cp
H
(27)
)
(
(
))
(
(
))
(
)
(
(
t
H
C
x
H
j
t
CH
x
H
j
U
j
m
T
m
x
m
T
m
x
x
.
)
(
m
T
m
T
m
CH
p
H
(28)
4.
4
.
Th
e
M
e
th
o
d
o
l
o
gy
o
f
H
ar
r
w
av
e
l
e
t
In
t
hi
s
s
e
c
t
i
o
n,
w
e
a
ppl
y
t
h
e
H
a
a
r
w
a
v
e
l
e
t
o
r
t
h
o
n
o
rm
a
l
m
a
t
ri
x
m
e
t
h
o
d
f
o
r
a
pp
r
o
xi
m
a
t
e
s
o
l
ut
i
o
n
s
o
f
c
o
upl
e
d
s
y
s
t
e
m
of
f
r
a
c
t
i
o
n
a
l
pa
rt
i
a
l
di
f
f
e
r
e
n
t
i
a
l
e
qua
t
i
o
n
s
.
A
l
l
c
o
m
put
a
t
i
o
n
s
a
nd
pl
o
t
s
ha
v
e
be
e
n
do
n
e
i
n
t
h
e
h
e
l
p
o
f
M
A
T
L
A
B
.
C
o
n
s
i
de
r
t
h
e
c
o
upl
e
d
s
y
s
t
e
m
fo
r
t
i
m
e
de
pe
n
de
nt
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
of
o
r
de
r
s
a
nd
r
e
s
pe
c
t
i
v
e
l
y
of
t
h
e
ki
nd
:
.
,
,
1
0
)
,
(
)
,
,
,
,
(
)
,
(
),
,
(
)
,
,
,
,
(
)
,
(
2
1
t
x
f
u
v
u
v
u
g
t
x
v
D
t
x
f
u
v
u
v
u
f
t
x
u
D
xx
t
x
t
xx
t
x
t
(29)
W
i
t
h
i
n
i
t
i
a
l
a
nd
b
o
un
da
r
y
c
o
n
di
t
i
o
n
s
:
)
,.
..
(
)
,
0
(
),
(
)
,
0
(
),
(
)
0
,
(
),
(
)
0
,
(
),
(
)
,
0
(
),
(
)
,
0
(
t
t
v
t
t
u
x
x
v
x
x
u
t
t
v
t
t
u
x
x
(30)
W
h
e
r
e
),
(
),
(
),
(
),
(
),
,
(
),
,
(
2
1
x
x
t
t
t
x
f
t
x
f
)
(
t
a
n
d
)
(
t
a
r
e
k
n
o
w
n
c
o
n
t
i
n
uo
us
f
un
c
t
i
o
n
s
,
a
n
d
1
,
0
<
t
x
.
O
u
r
m
e
t
h
o
d
c
a
n
b
e
s
um
m
a
ri
z
e
d
a
s
t
h
e
s
t
e
p
b
y
s
t
e
p
p
r
o
c
e
dur
e
b
e
l
ow
:
S
t
e
p1:
S
a
m
pl
i
n
g
t
h
e
c
o
n
t
i
nuo
us
f
un
c
t
i
o
n
s
)
,
(
t
x
u
a
n
d
)
,
(
t
x
v
i
nt
o
di
s
c
r
e
t
e
m
a
t
ri
c
e
s
fo
r
m
]
[
,
j
i
u
U
a
n
d
w
h
e
r
e
m
2
/
1
of
x
a
nd
t
.
S
t
e
p
2:
T
ra
n
s
f
e
r
t
h
e
m
a
t
ri
c
e
s
i
n
t
o
H
a
a
r
do
m
a
i
n
b
y
us
i
n
g
H
a
a
r
w
a
v
e
l
e
t
t
ra
n
s
f
o
r
m
.
]
[
,
j
i
v
V
Evaluation Warning : The document was created with Spire.PDF for Python.
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
IS
S
N
:
2502
-
4752
H
aar
w
av
e
l
e
t
m
e
t
hod
f
or
s
ol
v
i
n
g
c
oup
l
e
d
s
y
s
t
e
m
of
f
r
ac
t
i
o
na
l
or
d
e
r
…
(
A
bbas
F
adh
i
l
A
l
S
hi
m
m
ar
y
)
1451
).
(
)
(
),
(
)
(
t
BH
x
H
V
t
AH
x
H
U
T
T
(31)
W
h
e
r
e
]
[
]
[
,
,
j
i
j
i
b
B
a
A
,
a
r
e
t
h
e
H
a
a
r
c
o
e
ff
i
c
i
e
n
t
m
a
t
ri
c
e
s
a
n
d
H
i
s
t
h
e
H
a
a
r
w
a
v
e
l
e
t
m
a
t
ri
x.
S
t
e
p
3:
W
r
i
t
e
a
l
l
i
n
t
e
ge
r
a
n
d
f
ra
c
t
i
o
na
l
pa
rt
i
a
l
d
i
f
fe
r
e
nt
i
a
t
i
o
n
s
i
n
H
a
a
r
w
a
v
e
l
e
t
t
ra
n
s
f
o
r
m
.
S
t
e
p
4:
Ca
l
c
ul
a
t
e
t
h
e
w
a
ve
l
e
t
w
e
i
gh
t
i
n
g
c
o
e
f
f
i
c
i
e
n
t
s
A
a
n
d
B
a
f
t
e
r
pl
ugg
i
n
g
(s
t
e
p
3),
w
i
t
h
i
ni
t
i
a
l
a
n
d
bo
un
da
r
y
c
o
n
di
t
i
o
n
s
(
30)
i
n
(29)
:
).
(
)
(
)}
(
]
,
,
)
(
,
,
)[
(
{
)
0
,
(
)
(
)
(
),
(
)
(
)}
(
]
,
,
)
(
,
,
)[
(
{
)
0
,
(
)
(
)
(
2
1
1
1
1
1
t
H
F
x
H
t
H
BP
A
P
B
A
x
H
f
x
u
t
H
AP
x
H
t
H
F
x
H
t
H
BP
A
P
B
A
x
H
f
x
u
t
H
AP
x
H
T
m
T
m
T
m
T
T
m
T
m
T
m
T
(32)
T
h
i
s
s
y
s
t
e
m
of
m
a
t
r
i
c
e
s
in
(32)
ha
s
u
n
k
n
o
w
n
H
a
a
r
c
o
e
ff
i
c
i
e
n
t
s
A
a
n
d
B
.
W
e
s
o
l
ve
t
h
e
s
y
s
t
e
m
s
i
m
ul
t
a
n
e
o
us
l
y
f
o
r
u
n
k
n
o
w
n
w
i
t
h
t
h
e
h
e
l
p
o
f
us
i
ng
s
o
l
ut
i
o
n
of
L
y
a
pun
o
v
e
qua
t
i
o
n
t
y
pe
.
S
t
e
p
5:
F
i
n
a
l
y
,
H
a
a
r
n
u
m
e
ri
c
a
l
s
o
l
ut
i
o
n
s
f
o
r
)
,
(
t
x
u
a
n
d
)
,
(
t
x
v
c
a
n
b
e
c
o
n
s
t
r
uc
t
e
d
f
r
o
m
s
ub
i
s
t
i
t
ut
e
v
a
l
ue
s
of
H
a
a
r
c
o
e
ff
i
c
i
e
n
t
i
n
(
31).
5.
N
U
M
ER
I
C
A
L
TES
T
P
R
O
BLEM
S
T
h
i
s
s
e
c
t
i
o
n
c
o
n
c
e
rni
n
g
t
o
t
h
e
num
e
r
i
c
a
l
t
e
s
t
p
r
o
b
l
e
m
s
a
nd
t
h
e
i
r
v
i
s
ua
l
i
z
a
t
i
o
n
s
.
P
r
o
b
l
e
m
1.
Co
n
s
i
de
r
t
h
e
c
o
upl
e
d
F
P
D
E
s
[
26]
:
,
0
,
0
u
v
v
v
D
u
v
u
u
D
x
t
x
t
.
1
,
0
(33)
S
ub
j
e
c
t
t
o
i
ni
t
i
a
l
c
o
n
d
i
t
i
o
n
s
.
.
c
o
s
h
)
0
,
(
,
s
i
n
h
)
0
,
(
x
x
v
x
x
u
(34)
T
h
e
e
xa
c
t
s
o
l
ut
i
o
n
f
o
r
1
,
i
s
)
c
o
s
h
(
)
,
(
)
s
i
n
h
(
)
,
(
t
x
t
x
v
t
x
t
x
u
,
,
by
f
o
l
l
ow
i
n
g
t
h
e
m
e
t
h
o
d
i
l
l
us
t
ra
t
e
d
i
n
S
e
c
t
i
o
n
5.
(S
t
e
p
1
-
S
t
e
p
4),
t
h
e
a
b
ov
e
s
y
s
t
e
m
of
l
i
n
e
a
r
t
i
m
e
F
P
D
E
s
.
In
(3
3)
a
n
d
(34
)
Co
rr
e
s
po
n
di
n
g
t
o
(31)
a
nd
(3
2),
w
h
e
n
75
.
0
,
8
m
w
i
t
h
s
ub
s
t
i
t
ut
i
n
g
i
n
i
t
i
a
l
c
o
n
d
i
t
i
o
n
(34)
l
e
a
d
t
o
t
h
e
c
o
upl
e
d
s
y
s
t
e
m
:
,
0
)
(
)
(
)
(
)
(
)
(
)
)(
(
)
s
i
n
h
(
)
(
)
(
1
8
75
.
8
t
AH
x
H
t
BH
x
H
t
BH
P
x
H
x
t
H
AP
x
H
T
T
T
T
T
.
0
)
(
)
(
)
(
)
(
)
(
)
)(
(
)
c
o
s
h
(
)
(
)
(
1
75
.
8
t
AH
x
H
t
BH
x
H
t
AH
P
x
H
x
t
H
BP
x
H
T
T
T
m
T
T
(35)
T
h
e
s
y
s
t
e
m
of
(35)
h
a
s
u
n
k
n
o
w
n
H
a
a
r
c
o
e
ff
i
c
i
e
n
t
s
A
a
n
d
B
.
W
e
s
o
l
ve
t
h
i
s
s
y
s
t
e
m
s
i
m
ul
t
a
n
e
o
us
l
y
fo
r
u
n
k
n
o
w
n
s
.
F
i
n
e
l
y
,
s
ub
s
t
i
t
ut
e
v
a
l
ue
s
of
H
a
a
r
c
o
e
ff
i
c
i
e
n
t
s
i
n
(
31).
H
a
a
r
s
o
l
ut
i
o
n
s
o
f
c
o
upl
e
d
t
i
m
e
-
(F
P
D
E
s
.
)
s
y
s
t
e
m
a
r
e
a
t
t
a
i
n
e
d;
s
e
e
F
i
gu
r
e
2.
T
h
e
o
b
t
a
i
n
e
d
H
a
a
r
s
o
l
ut
i
o
n
s
a
r
e
c
o
m
pa
r
e
d
w
i
t
h
e
xa
c
t
s
o
l
ut
i
o
n
s
a
t
v
a
l
ue
s
)
75
.
0
(
a
n
d
)
75
.
0
(
a
r
e
s
h
o
w
n
i
n
T
a
b
l
e
1
a
n
d
T
a
b
l
e
2.
T
a
b
l
e
1
.
Co
m
p
a
r
s
i
o
n
b
e
t
w
e
e
n
e
xa
c
t
a
n
d
n
u
m
e
r
i
c
a
l
h
a
a
r
s
o
l
ut
i
o
n
o
f
)
,
(
t
x
u
of
p
r
o
b
l
e
m
1
t
x
0
.
0
6
2
5
0
.
1
8
7
5
0
.
3
1
2
5
0
.
4
3
7
5
0
.
5
6
2
5
0
.
6
8
7
5
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
0
.
0
6
2
5
0
.
0
0
0
0
0
.
0
3
1
2
0
.
1
2
5
3
0
.
1
5
6
5
0
.
2
5
2
6
0
.
2
8
3
8
0
.
3
8
3
9
0
.
4
1
5
1
0
.
5
2
1
1
0
.
5
5
2
3
0
.
6
6
6
5
0
.
6
9
7
7
0
.
1
8
7
5
-
0
.
1
2
5
3
-
0
.
0
9
4
1
0
.
0
0
0
0
0
.
0
3
1
2
0
.
1
2
5
3
0
.
1
5
6
5
0
.
2
5
2
6
0
.
2
8
3
8
0
.
3
8
3
9
0
.
4
1
5
1
0
.
5
2
1
1
0
.
5
5
2
3
0
.
3
1
2
5
-
0
.
2
5
2
6
-
0
.
2
2
1
4
-
0
.
1
2
5
3
-
0
.
0
9
4
1
0
.
0
0
0
0
0
.
0
3
1
2
0
.
1
2
5
3
0
.
1
5
6
5
0
.
2
5
2
6
0
.
2
8
3
8
0
.
3
8
3
9
0
.
4
1
5
1
0
.
4
3
7
5
-
0
.
3
8
3
9
-
0
.
3
5
2
7
-
0
.
2
5
2
6
-
0
.
2
2
1
4
-
0
.
1
253
-
0
.
0
9
4
1
0
.
0
0
0
0
0
.
0
3
1
2
0
.
1
2
5
3
0
.
1
5
6
5
0
.
2
5
2
6
0
.
2
8
3
8
0
.
5
6
2
5
-
0
.
5
2
1
1
-
0
.
4
8
9
9
-
0
.
3
8
3
9
-
0
.
3
5
2
7
-
0
.
2
5
2
6
-
0
.
2
2
1
4
-
0
.
1
2
5
3
-
0
.
0
9
4
1
0
.
0
0
0
0
0
.
0
3
1
2
0
.
1
2
5
3
0
.
1
5
6
5
0
.
6
8
7
5
-
0
.
6
6
6
5
-
0
.
6
3
5
3
-
0
.
5
2
1
1
-
0
.
4
8
9
9
-
0
.
3
8
3
9
-
0
.
3
5
2
7
-
0
.
2
5
2
6
-
0
.
2
2
1
4
-
0
.
1
2
5
3
-
0
.
0
9
4
1
0
.
0
0
0
0
0
.
0
3
1
2
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
,
V
o
l
.
21
,
N
o
.
3
,
M
a
r
c
h
2
021
:
1
4
4
4
-
1
4
5
4
1452
T
a
b
l
e
2
.
Co
m
p
a
r
s
i
o
n
b
e
t
w
e
e
n
e
xa
c
t
a
n
d
n
u
m
e
r
i
c
a
l
h
a
a
r
s
o
l
ut
i
o
n
o
f
)
,
(
t
x
v
of
p
r
o
b
l
e
m
1
t
x
0
.
0
6
2
5
0
.
1
8
7
5
0
.
3
1
2
5
0
.
4
3
7
5
0
.
5
6
2
5
0
.
6
8
7
5
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
0
.
0
6
2
5
1
.
0
0
0
0
1
.
0
3
1
2
1
.
0
0
7
8
1
.
0
3
9
0
1
.
0
3
1
4
1
.
0
6
2
6
1
.
0
7
1
1
1
.
1
0
2
3
1
.
1
2
7
6
1
.
1
5
8
8
1
.
2
0
1
8
1
.
2
3
3
0
0
.
1
8
7
5
1
.
0
0
7
8
1
.
0
3
9
0
1
.
0
0
0
0
1
.
0
3
1
2
1
.
0
0
7
8
1
.
0
3
9
0
1
.
0
3
1
4
1
.
0
6
2
6
1
.
0
7
1
1
1
.
1
0
2
3
1
.
1
2
7
6
1
.
1
5
8
8
0
.
3
1
2
5
1
.
0
3
1
4
1
.
0
6
2
6
1
.
0
0
7
8
1
.
0
3
9
0
1
.
0
0
0
0
1
.
0
3
1
2
1
.
0
0
7
8
1
.
0
3
9
0
1
.
0
3
1
4
1
.
0
6
2
6
1
.
0
7
1
1
1
.
1
0
2
3
0
.
4
3
7
5
1
.
0
7
1
1
1
.
1
0
2
3
1
.
0
3
1
4
1
.
0
6
2
6
1
.
0
0
7
8
1
.
0
3
9
0
1
.
0
0
0
0
1
.
0
3
1
2
1
.
0
0
7
8
1
.
0
3
9
0
1
.
0
3
1
4
1
.
0
6
2
6
0
.
5
6
2
5
1
.
1
2
7
6
1
.
1
5
8
8
1
.
0
7
1
1
1
.
1
0
2
3
1
.
0
3
1
4
1
.
0
6
2
6
1
.
0
0
7
8
1
.
0
3
9
0
1
.
0
0
0
0
1
.
0
3
1
2
1
.
0
0
7
8
1
.
0
3
9
0
0
.
6
8
7
5
1
.
2
0
1
8
1
.
2
3
3
0
1
.
1
2
7
6
1
.
1
5
8
8
1
.
0
7
1
1
1
.
1
0
2
3
1
.
0
3
1
4
1
.
0
6
2
6
1.
0078
1
.
0
3
9
0
1
.
0
0
0
0
1
.
0
3
1
2
F
i
gu
r
e
2
.
E
xa
c
t
a
nd
H
a
a
r
n
u
m
e
r
i
c
a
l
s
o
l
ut
i
o
n
s
)
,
(
t
x
u
a
nd
)
,
(
t
x
v
of
pr
o
b
l
e
m
1
P
r
o
b
l
e
m
2.
Co
n
s
i
de
r
t
h
e
c
o
upl
e
d
F
P
D
E
s
.
[26]
:
.
0
2
,
0
2
u
v
v
D
v
u
u
D
x
t
x
t
(36)
S
ub
j
e
c
t
t
o
i
ni
t
i
a
l
c
o
n
d
i
t
i
o
n
s
:
.
c
o
s
)
0
,
(
,
s
i
n
)
0
,
(
x
x
v
x
x
u
(37)
T
h
e
e
xa
c
t
s
o
l
ut
i
o
n
f
o
r
1
i
s
,
)
c
o
s
(
)
,
(
)
s
i
n
(
)
,
(
t
x
t
x
v
t
x
t
x
u
,
,
By
fo
l
l
ow
i
n
g
t
h
e
m
e
t
h
o
d
i
l
l
us
t
ra
t
e
d
i
n
S
e
c
t
i
o
n
5.
(S
t
e
p
1
-
S
t
e
p
4),
t
h
e
a
b
ov
e
s
y
s
t
e
m
of
l
i
n
e
a
r
t
i
m
e
F
P
D
E
s
.
In
(3
6)
a
n
d
(37
)
Co
rr
e
s
po
n
di
n
g
t
o
(31)
,
w
h
e
n
75
.
0
,
8
m
w
i
t
h
s
ub
s
t
i
t
ut
i
ng
i
ni
t
i
a
l
c
o
ndi
t
i
o
n
(51
)
l
e
a
d
t
o
t
h
e
c
o
upl
e
d
s
y
s
t
e
m
:
,
0
)
(
)
(
2
)
(
)
)(
(
)
s
i
n
(
)
(
)
(
1
8
75
.
8
t
BH
x
H
t
AH
P
x
H
x
t
H
AP
x
H
T
T
T
T
.
0
)
(
)
(
2
)
(
)
)(
(
)
c
o
s
(
)
(
)
(
1
75
.
8
t
AH
x
H
t
BH
P
x
H
x
t
H
BP
x
H
T
T
m
T
T
(38)
T
h
e
s
y
s
t
e
m
of
(38)
h
a
s
u
n
k
n
o
w
n
H
a
a
r
c
o
e
ff
i
c
i
e
n
t
s
A
a
n
d
B
.
W
e
s
o
l
ve
t
h
i
s
s
y
s
t
e
m
s
i
m
ul
t
a
n
e
o
us
l
y
fo
r
u
n
k
n
o
w
n
.
F
i
n
e
l
y
,
s
ub
s
t
i
t
ut
e
v
a
l
ue
s
of
H
a
a
r
c
o
e
ff
i
c
i
e
n
t
s
i
n
(3
1).
H
a
a
r
s
o
l
ut
i
o
n
s
o
f
c
o
upl
e
d
t
i
m
e
-
(F
P
D
E
s
.
)
s
y
s
t
e
m
a
r
e
a
t
t
a
i
n
e
d;
s
e
e
F
i
gu
r
e
3.
T
h
e
o
b
t
a
i
n
e
d
H
a
a
r
s
o
l
ut
i
o
n
s
a
r
e
c
o
m
pa
r
e
d
w
i
t
h
e
xa
c
t
s
o
l
ut
i
o
n
s
a
t
v
a
l
ue
s
)
75
.
0
(
a
n
d
(
75
.
0
)
a
r
e
s
h
o
w
n
i
n
T
a
b
l
e
3
a
n
d
T
a
b
l
e
4.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
IS
S
N
:
2502
-
4752
H
aar
w
av
e
l
e
t
m
e
t
hod
f
or
s
ol
v
i
n
g
c
oup
l
e
d
s
y
s
t
e
m
of
f
r
ac
t
i
o
na
l
or
d
e
r
…
(
A
bbas
F
adh
i
l
A
l
S
hi
m
m
ar
y
)
1453
T
a
b
l
e
3
.
Co
m
p
a
r
s
i
o
n
b
e
t
w
e
e
n
e
xa
c
t
a
n
d
n
u
m
e
r
i
c
a
l
h
a
a
r
s
o
l
ut
i
o
n
o
f
)
,
(
t
x
u
of
p
r
o
b
l
e
m
2
t
x
0
.
0
6
2
5
0
.
1
8
7
5
0
.
3
1
2
5
0
.
4
3
7
5
0
.
5
6
2
5
0
.
6
8
7
5
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
0
.
0
6
2
5
0
.
1
2
4
7
0
.
1
5
5
9
0
.
2
4
7
4
0
.
2
7
8
6
0
.
3
6
6
3
0
.
3
9
7
5
0
.
4
7
9
4
0
.
5
1
0
6
0
.
5
8
5
1
0
.
6
1
6
3
0
.
6
8
1
6
0
.
7
1
2
8
0
.
1
8
7
5
0
.
2
4
7
4
0
.
2
7
8
6
0
.
3
6
6
3
0
.
3
9
7
5
0
.
4
7
9
4
0
.
5
1
0
6
0
.
5
8
5
1
0
.
6
1
6
3
0
.
6
8
1
6
0
.
7
1
2
8
0
.
7
6
7
5
0
.
7
9
8
7
0
.
3
1
2
5
0
.
3
6
6
3
0
.
3
9
7
5
0
.
4
7
9
4
0
.
5
1
0
6
0
.
5
8
5
1
0
.
6
1
6
3
0
.
6
8
1
6
0
.
7
1
2
8
0
.
7
6
7
5
0
.
7
9
8
7
0
.
8
4
1
5
0
.
8
7
2
7
0
.
4
3
7
5
0
.
4
7
9
4
0
.
5
1
0
6
0
.
5
8
5
1
0
.
6
1
6
3
0
.
6
8
1
6
0
.
7
1
2
8
0
.
7
6
7
5
0
.
7
9
8
7
0
.
8
4
1
5
0
.
8
7
2
7
0
.
9
0
2
3
0
.
9
3
3
5
0
.
5
6
2
5
0
.
5
8
5
1
0
.
6
1
6
3
0
.
6
8
1
6
0
.
7
1
2
8
0
.
7
6
7
5
0
.
7
9
8
7
0
.
8
4
1
5
0
.
8
7
2
7
0
.
9
0
2
3
0
.
9
3
3
5
0
.
9
4
9
0
0
.
9
8
0
2
0
.
6
8
7
5
0
.
6
8
1
6
0
.
7
1
2
8
0
.
7
6
7
5
0
.
7
9
8
7
0
.
8
4
1
5
0
.
8
7
2
7
0
.
9
0
2
3
0
.
9
3
3
5
0
.
9
4
9
0
0
.
9
8
0
2
0
.
9
8
0
9
1
.
0
1
2
1
T
a
b
l
e
4
.
Co
m
p
a
r
s
i
o
n
b
e
t
w
e
e
n
e
xa
c
t
a
n
d
n
u
m
e
r
i
c
a
l
h
a
a
r
s
o
l
ut
i
o
n
o
f
)
,
(
t
x
v
of
p
r
o
b
l
e
m
2
t
x
0
.
0
6
2
5
0
.
1
8
7
5
0
.
3
1
2
5
0
.
4
375
0
.
5
6
2
5
0
.
6
8
7
5
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
E
x
a
c
t
A
p
p
r
.
0
.
0
6
2
5
0
.
9
9
2
2
1
.
0
2
3
4
0
.
9
6
8
9
1
.
0
0
0
1
0
.
9
3
0
5
0
.
9
6
1
7
0
.
8
7
7
6
0
.
9
0
8
8
0
.
8
1
1
0
0
.
8
4
2
2
0
.
7
3
1
7
0
.
7
6
2
9
0
.
1
8
7
5
0
.
9
6
8
9
1
.
0
0
0
1
0
.
9
3
0
5
0
.
9
6
1
7
0
.
8
7
7
6
0
.
9
0
8
8
0
.
8
1
1
0
0
.
8
4
2
2
0
.
7
3
1
7
0
.
7
6
2
9
0
.
6
4
1
0
0
.
6
7
2
2
0
.
3
1
2
5
0
.
9
3
0
5
0
.
9
6
1
7
0
.
8
7
7
6
0
.
9
0
8
8
0
.
8
1
1
0
0
.
8
4
2
2
0
.
7
3
1
7
0
.
7
6
2
9
0
.
6
4
1
0
0
.
6
7
2
2
0
.
5
4
0
3
0
.
5
7
1
5
0
.
4
3
7
5
0
.
8
7
7
6
0
.
9
0
8
8
0
.
8
1
1
0
0
.
8
4
2
2
0
.
7
3
1
7
0
.
7
6
2
9
0
.
6
4
1
0
0
.
6
7
2
2
0
.
5
4
0
3
0
.
5
7
1
5
0
.
4
3
1
2
0
.
4
6
2
4
0
.
5
6
2
5
0
.
8
1
1
0
0
.
8
4
2
2
0
.
7
3
1
7
0
.
7
6
2
9
0
.
6
4
1
0
0
.
6
7
2
2
0.
5403
0
.
5
7
1
5
0
.
4
3
1
2
0
.
4
6
2
4
0
.
3
1
5
3
0
.
3
4
6
5
0
.
6
8
7
5
0
.
7
3
1
7
0
.
7
6
2
9
0
.
6
4
1
0
0
.
6
7
2
2
0
.
5
4
0
3
0
.
5
7
1
5
0
.
4
3
1
2
0
.
4
6
2
4
0
.
3
1
5
3
0
.
3
4
6
5
0
.
1
9
4
5
0
.
2
2
5
7
F
i
gu
r
e
3
.
E
xa
c
t
a
nd
H
a
a
r
n
u
m
e
r
i
c
a
l
s
o
l
ut
i
o
n
s
)
,
(
t
x
u
a
nd
)
,
(
t
x
v
of
pr
o
b
l
e
m
2
6.
C
O
N
C
LU
S
I
O
N
In
t
h
i
s
pa
pe
r
,
w
e
a
ppl
i
e
d
t
h
e
H
a
a
r
o
pe
ra
t
i
o
n
a
l
m
a
t
ri
x
m
e
t
h
o
d
o
f
f
r
a
c
t
i
o
na
l
o
r
de
r
a
n
d
i
nt
e
gra
t
e
d
w
i
t
h
di
s
c
r
e
t
i
z
a
t
i
o
n
i
n
Ca
p
ut
o
'
s
s
e
n
s
e
t
o
t
i
m
e
a
n
d
s
p
a
t
i
a
l
de
r
i
v
a
t
i
v
e
s
.
T
h
e
m
a
i
n
a
i
m
o
f
t
h
e
p
r
o
po
s
e
d
m
e
t
h
o
d
i
s
a
ppl
i
e
d
t
o
a
s
y
s
t
e
m
of
c
o
upl
e
d
f
r
a
c
t
i
o
n
a
l
p
a
r
t
i
a
l
di
f
f
e
r
e
n
t
i
a
l
e
qua
t
i
o
n
s
,
t
hi
s
a
p
p
r
o
a
c
h
i
s
us
e
d
t
o
t
ra
n
s
f
o
r
m
t
h
e
s
y
s
t
e
m
i
n
t
o
a
n
e
a
s
i
l
y
a
l
ge
b
r
a
i
c
s
y
s
t
e
m
of
L
y
a
pun
o
v
o
r
S
y
l
ve
s
t
e
r
e
qua
t
i
o
n
t
y
pe
,
a
n
d
t
h
e
r
e
s
ul
t
s
a
r
e
c
o
m
pa
r
e
d
w
i
t
h
t
h
e
e
xa
c
t
s
o
l
ut
i
o
n.
T
h
e
a
pp
r
o
xi
m
a
t
e
n
u
m
e
r
i
c
a
l
s
o
l
ut
i
o
n
v
i
a
t
h
e
H
a
a
r
w
a
ve
l
e
t
m
e
t
h
o
d
i
s
m
o
r
e
e
l
e
ga
n
t
i
n
t
h
e
o
r
y
,
m
o
r
e
c
o
n
v
e
n
i
e
n
t
i
n
n
u
m
e
ri
c
c
o
m
put
a
t
i
o
n
s
,
a
n
d
m
uc
h
f
a
s
t
e
r
i
n
t
h
e
da
t
a
p
r
o
c
e
s
s
i
n
g.
A
C
K
N
O
WL
ED
G
E
M
EN
TS
T
h
e
a
ut
h
o
r
w
o
ul
d
l
i
ke
t
o
t
ha
n
k
A
l
-
M
us
t
a
n
s
i
ri
y
a
h
U
n
i
v
e
r
s
i
t
y
(
w
w
w
.
u
o
m
us
t
a
n
s
i
r
o
y
a
h
.
e
du.
i
q
)
B
a
gh
d
a
d
-
I
ra
q
f
o
r
i
t
s
s
uppo
rt
i
n
t
h
e
p
r
e
s
e
n
t
w
o
r
k.
R
EF
ER
EN
C
ES
[
1]
K
.
S
.
M
i
l
l
e
r
a
nd
B
.
R
o
s
s
,
"
A
n
i
nt
r
o
duc
t
i
o
n
t
o
f
r
a
c
t
i
o
na
l
c
a
l
c
u
l
us
a
nd
f
r
a
c
t
i
o
na
l
d
i
f
f
e
r
e
n
t
i
a
l
e
q
ua
t
i
o
n,
"
J
ohn
W
i
l
e
y
,
1993
.
[
2]
I
.
P
o
dl
ubny
,
"
F
r
a
c
t
i
o
na
l
D
i
f
f
e
r
e
nt
i
a
l
E
qua
t
i
o
ns
,
"
19
8
A
c
a
de
m
i
c
P
r
e
s
s
San
D
i
e
go
,
C
al
i
f
or
n
i
a
,
U
S
A
,
199
9.
[
3]
J
.
s
un
dne
s
,
G
.
T
.
L
i
ne
s
a
nd
A
.
T
v
e
i
t
o
,
"
M
ul
t
i
g
r
i
d
bl
o
c
k
c
o
ndi
t
i
o
ni
ng
f
o
r
a
c
o
upl
e
d
s
y
s
t
e
m
of
pa
r
t
i
a
l
di
f
f
e
r
e
nt
i
a
l
e
qua
t
i
o
ns
m
o
de
l
i
ng
t
he
e
l
e
c
t
r
i
c
a
l
a
c
t
i
v
i
t
y
i
n
t
he
he
a
r
t
,
"
C
om
p
ut
e
r
M
e
t
hods
i
n
b
i
om
e
-
c
h
ani
c
s
a
nd
bi
om
e
di
c
a
l
e
ngi
ne
e
r
i
ng
,
v
o
l
.
5,
no
.
6
,
pp.
3
97
-
409
,
2002
.
Evaluation Warning : The document was created with Spire.PDF for Python.