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n
t
i
n
uo
us
o
pe
r
a
ti
o
n
f
o
r
a
s
pe
c
i
f
i
c
pe
r
i
o
d
o
f
t
i
m
e
a
n
d
t
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e
r
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a
r
e
ot
h
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r
f
a
c
t
or
s
th
a
t
t
h
e
s
pe
c
i
a
li
s
t
c
o
n
s
i
de
r
s
a
ppr
o
pr
i
a
t
e
[
20]
–
[
24]
.
T
hi
s
pa
pe
r
s
t
ud
i
e
s
t
h
e
pr
o
bl
e
m
o
f
o
pt
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m
a
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n
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a
bil
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y
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m
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t
he
m
a
t
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c
a
l
pr
o
bl
e
m
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v
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n
t
h
o
ugh
pr
o
bl
e
m
s
r
o
ot
s
b
e
l
o
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g
to
n
e
t
wor
k.
T
h
i
s
p
a
pe
r
de
a
l
s
w
i
t
h
t
h
e
pr
o
bl
e
m
o
f
o
pt
i
m
i
z
a
t
i
o
n
o
f
t
he
de
vi
c
e
R
OSS
[
25]
–
[
28]
.
T
h
e
s
y
s
t
e
m
c
o
ns
i
s
t
s
o
f
s
u
b
s
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t
e
m
s
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r
c
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m
po
n
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n
t
s
w
h
e
r
e
t
h
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e
li
a
bil
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t
y
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qui
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m
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t
s
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b
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y
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t
e
m
s
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r
c
o
m
po
n
e
n
t
s
a
r
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de
t
e
r
mi
ne
d
b
a
s
e
d
o
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t
h
e
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m
po
r
t
a
n
c
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f
r
e
l
i
a
bil
i
t
y
o
r
t
h
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l
o
c
a
t
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o
n
o
f
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c
o
m
po
n
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n
t
i
n
t
h
e
s
y
s
t
e
m
.
T
h
e
m
o
d
e
l
f
o
r
a
c
o
m
po
n
e
n
t
’
s
r
e
li
a
bil
i
t
y
a
ll
o
c
a
t
i
o
n
i
s
ba
s
e
d
o
n
t
he
c
o
s
t
o
f
i
nc
r
e
a
s
i
n
g
r
e
li
a
bil
i
t
y
t
h
a
t
’
s
o
wn
.
T
h
e
c
o
s
t
l
i
e
s
t
e
l
e
m
e
n
t
s
w
il
l
b
e
(
t
h
e
c
o
s
t
e
x
pr
e
s
s
i
ng
by
we
i
g
h
t
,
c
o
s
t,
s
i
z
e
,
o
r
a
ny
o
t
h
e
r
a
m
o
u
n
t
)
i
n
c
r
e
a
s
e
s
i
n
r
e
l
i
a
bil
i
t
y
.
B
y
us
in
g
t
h
e
s
e
a
l
go
r
i
t
hm
s
,
i
t
i
s
po
s
s
i
bl
e
t
o
a
s
s
i
g
n
r
e
li
a
bil
i
t
y
t
o
s
o
m
e
o
r
a
l
l
o
f
t
h
e
c
o
m
po
n
e
n
t
s
o
f
a
ny
s
y
s
t
e
m
,
w
he
t
h
e
r
t
h
a
t
s
y
s
t
e
m
i
s
c
o
m
p
l
e
x
o
r
n
o
t
[
29]
–
[
33]
.
P
a
r
a
m
e
t
e
r
s
a
r
e
po
s
s
i
bl
e
t
o
b
e
c
h
a
n
ge
t
h
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o
f
t
h
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pr
o
po
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e
d
c
o
s
t
f
u
n
c
t
i
o
n
a
c
c
o
r
d
i
n
g
t
o
b
us
i
ne
s
s
r
e
qu
i
r
e
m
e
n
t
s
o
r
t
h
e
a
c
t
ua
l
n
e
e
d
f
o
r
t
h
e
s
y
s
t
e
m
t
o
f
u
n
c
t
i
o
n
we
ll
,
w
hi
c
h
w
il
l
h
a
v
e
e
n
g
i
ne
e
r
s
e
x
a
mi
ne
a
ll
o
c
a
t
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o
n
s
c
e
n
a
r
i
o
s
f
o
r
r
e
l
i
a
bil
i
t
y
in
a
l
l
r
e
s
pe
c
t
s
b
e
f
o
r
e
m
a
k
i
ng
de
c
i
s
i
o
ns
.
T
h
e
l
o
ga
r
i
t
hmi
c
c
o
s
t
f
un
c
t
i
o
n
i
s
i
nc
r
e
a
s
i
ng
a
n
d
c
o
n
ve
x
.
Al
s
o
,
th
e
r
e
s
u
l
t
s
o
b
t
a
i
n
e
d
a
f
t
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r
s
o
l
vi
ng
t
h
e
o
pt
i
mi
z
a
t
i
o
n
pr
o
bl
e
m
u
s
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ng
t
h
e
J
a
y
a
a
l
go
r
i
t
hm
[
34]
–
[
68]
c
o
n
t
r
i
b
ut
e
d
to
i
mpr
o
vi
n
g
t
h
e
o
p
t
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m
i
z
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t
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o
n
o
f
t
h
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s
y
s
t
e
m
r
e
li
a
bil
i
t
y
w
i
t
h
a
ppr
o
pr
i
a
t
e
c
o
s
t
s
[
33]
,
[
69
]
–
[
80]
.
2.
RE
S
E
AR
CH
M
E
T
HO
D
2.
1
.
Op
t
im
iz
at
ion
f
or
R
OS
S
of
a
s
p
ac
e
c
r
a
f
t
C
o
n
s
i
de
r
a
R
OSS
o
f
a
s
pa
c
e
c
r
a
f
t
c
o
n
s
i
s
t
i
n
g
o
f
e
l
e
m
e
n
t
s
c
o
n
ne
c
t
e
d
r
e
l
i
a
bil
i
t
y
[
15]
,
[
81
]
–
[
84]
,
t
h
e
f
o
l
l
o
w
i
n
g
n
o
t
e
s
a
r
e
us
e
d:
-
0
≤
R
i
≤
1
i
s
t
h
e
e
l
e
m
e
n
t
r
e
l
i
a
bil
i
t
y
i
-
C
i
(
Q
i
)
i
s
t
h
e
c
o
s
t
o
f
t
h
e
e
l
e
m
e
n
t
i
-
(
1
,
…
,
)
=
∑
(
)
=
1
t
h
e
s
y
s
t
e
m
’
s
tot
a
l
c
o
s
t,
wh
e
r
e
a
i
>
0
-
Q
i
:
is
unr
e
li
abil
it
y
-
Q
s
:
is
t
h
e
u
n
r
e
l
i
a
b
i
li
t
y
o
f
t
h
e
s
y
s
t
e
m
-
Q
G
:
i
s
t
h
e
un
r
e
li
a
bil
i
t
y
go
a
l
o
f
t
h
e
s
y
s
t
e
m
T
h
e
m
a
i
n
go
a
l
o
f
t
h
e
pr
o
bl
e
m
i
s
to
a
l
l
o
c
a
t
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e
l
i
a
bil
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t
y
t
o
s
o
m
e
o
r
a
l
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c
o
m
po
n
e
n
t
s
o
f
t
h
e
s
y
s
t
e
m
t
o
r
e
duc
e
c
o
s
t
s
to
t
h
e
l
e
a
s
t
po
s
s
i
bl
e
.
T
h
e
pr
o
bl
e
m
P
w
i
ll
b
e
f
o
r
m
u
l
a
t
e
d
a
s
t
h
e
o
bj
e
c
t
i
v
e
f
u
n
c
t
i
o
n
(
c
o
s
t
f
u
n
c
t
i
o
n
)
a
n
d
t
h
e
c
o
n
s
t
r
a
i
n
t
s
a
s
t
h
e
o
p
t
i
mi
z
a
t
i
o
n
pr
o
bl
e
m
i
n
n
o
nli
ne
a
r
pr
o
gr
a
m
m
i
ng
a
s
(
1)
:
:
(
1
,
…
,
)
=
∑
(
)
,
=
1
>
0
(
1)
(
1
−
)
≥
(
1
−
)
0
≤
≤
1
,
=
1
,
2
,
…
,
wh
e
r
e
+
=
1
,
a
s
s
u
m
i
ng
C
i
(
Q
i
)
t
h
e
c
o
s
t
f
u
n
c
t
i
o
n
be
po
s
i
t
i
v
e
a
n
d
d
i
f
f
e
r
e
n
t
i
a
bl
e
[
21]
:
[
⇒
≥
0
]
.
T
h
e
c
o
s
t
c
o
n
v
e
xi
t
y
o
f
E
uc
l
i
de
a
n
f
u
n
c
t
i
o
n
i
s
to
m
i
nim
i
z
e
t
h
e
c
o
s
t
f
u
n
c
t
i
o
n
.
T
hi
s
i
s
t
h
e
s
a
m
e
a
s
t
h
e
d
e
r
i
v
a
t
i
v
e
i
s
m
o
n
o
to
ni
c
a
ll
y
i
nc
r
e
a
s
i
ng,
i
,
e
.
,
2
2
≥
0
.
T
h
e
pur
po
s
e
o
f
t
h
e
pr
e
vi
o
us
p
l
a
n
i
s
t
o
a
c
hi
e
v
e
a
n
a
ll
-
o
u
t
f
r
a
m
e
wo
r
k
c
o
s
t
b
a
s
e
[
4]
,
s
ubj
e
c
t
to
R
G
,
t
h
e
l
o
we
r
s
y
s
t
e
m
r
e
li
a
bil
i
t
y
li
mi
t
.
2.
2
.
M
od
e
l
of
l
ogar
it
h
m
ic
f
u
n
c
t
ion
L
e
t
0
<
Q
i
<
1
a
n
d
,
c
o
n
s
t
a
n
t
,
i
=
1
,
2
,
.
.
.
,
n
.
,
t
h
e
c
o
s
t
f
unc
t
i
o
n
h
a
s
b
e
e
n
pr
o
p
o
s
e
d
i
n
a
n
u
m
be
r
o
f
r
e
f
e
r
e
n
c
e
s
.
T
h
e
m
o
s
t
i
m
po
r
t
a
n
t
o
f
w
hi
c
h
a
r
e
i
n
t
h
e
f
o
r
m
f
o
r
m
u
l
a
g
i
ve
t
h
e
f
o
l
l
o
w
i
ng
c
o
s
t
un
r
e
li
a
bil
i
t
y
c
ur
v
e
a
s
(
2)
.
=
(
1
1
−
(
1
−
)
)
,
>
0
(
2)
C
o
n
s
e
que
n
t
l
y
,
e
a
c
h
C
i
(
Q
i
)
i
t
i
s
a
m
o
n
oto
ny
i
nc
r
e
a
s
i
n
g
a
n
d
c
o
nv
e
x
f
u
nc
t
i
o
n
i
n.
T
he
c
o
s
t
o
f
t
h
e
e
n
t
i
r
e
(
1
,
…
,
)
=
∑
(
)
=
1
h
a
s
s
im
il
a
r
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
[
3]
.
2.
3
.
Jaya
a
l
gor
it
h
m
J
a
y
a
a
l
go
r
i
t
hm
c
a
n
s
o
l
v
e
o
pt
i
m
i
z
a
t
i
o
n
pr
o
bl
e
m
s
a
n
d
i
t
i
s
o
n
e
o
f
t
h
e
m
e
t
h
o
ds
us
e
d
to
s
o
l
vi
ng
li
ne
a
r
a
n
d
n
o
nl
i
ne
a
r
pr
o
bl
e
m
s
(
w
i
t
h
c
o
ns
t
r
a
i
n
t
o
r
un
c
o
n
s
t
r
a
i
n
t
)
,
a
n
d
t
hi
s
a
l
go
r
i
t
hm
h
a
s
b
e
e
n
a
pp
li
e
d
i
n
m
a
ny
o
f
t
he
m
o
s
t
d
i
f
f
i
c
u
l
t
o
p
t
i
mi
z
a
t
i
o
n
pr
o
bl
e
m
s
[
29]
,
[
74
]
.
A
n
im
po
r
t
a
n
t
di
f
f
e
r
e
n
c
e
b
e
t
we
e
n
J
a
y
a
a
n
d
th
e
o
t
h
e
r
a
l
go
r
i
t
hm
i
n
o
pt
i
m
i
z
a
t
i
o
n
i
s
t
h
a
t
pa
r
a
m
e
t
e
r
s
o
f
J
a
y
a
do
e
s
n
o
t
r
e
qui
r
e
t
uni
n
g
(
a
pr
o
c
e
s
s
r
e
qu
i
r
e
d
i
n
ot
h
e
r
a
l
go
r
i
t
hm
s
t
o
a
v
o
i
d
u
n
wa
n
t
e
d
c
o
n
ve
r
ge
nc
e
)
.
An
o
t
h
e
r
d
i
f
f
e
r
e
n
c
e
i
s
J
a
y
a
's
e
f
f
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c
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e
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y
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n
a
l
wa
y
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c
h
o
o
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g
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s
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l
ut
i
o
n
.
Ne
x
t
i
s
t
h
e
s
t
e
ps
o
f
J
a
y
a
a
l
go
r
i
t
hm
a
n
d
F
i
g
ur
e
1
s
h
o
ws
i
n
f
l
o
wc
h
a
r
t
f
o
r
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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8
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[3
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.
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Ru
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ar
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[4
2
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.
,
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[4
3
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.
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.
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H
u
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,
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mmed
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4
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.
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[4
5
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A
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In
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.
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A
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[4
6
]
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ar,
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d
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S.
D
as
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d
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.
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21.
[4
7
]
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.
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.
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d
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d
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.
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.
[4
8
]
R.
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.
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,
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A
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.
M.
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en
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.
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d
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s
.
J.
E
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.
[4
9
]
S.
S.
Sad
i
q
,
A
.
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A
b
d
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l
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ee
z,
an
d
H
.
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d
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.
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.
[5
0
]
S.
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H
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ai
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d
A
.
H
.
Ch
o
w
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y
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mi
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,
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In
t
.
J.
E
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.
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[6
5
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M.
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J
arrah
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.
J.
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[6
6
]
Al
-
K
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o
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mi
,
R.
S
y
ah
,
M.
K
.
M
.
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as
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[6
7
]
A
.
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.
Fo
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S.
R.
Ri
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an
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D
.
C.
R.
N
o
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ari
,
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(Tel
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4
.
[6
8
]
V
.
Sri
s
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C.
J
i
t
t
aw
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n
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k
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v
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[6
9
]
S.
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.
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n
g
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,
R.
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as
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M.
A
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an
ab
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,
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[7
0
]
W
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.
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,
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-
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[7
1
]
J
.
R.
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d
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t
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[7
2
]
B.
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a,
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.
J
a
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San
k
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a
n
d
V
.
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a,
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.
[7
3
]
B.
Q
as
E
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,
M.
A
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s
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,
P.
J
.
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a
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d
A
.
A
.
A
l
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i
n
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9
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d
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)
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,
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–
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.
[7
4
]
M.
A
l
s
aj
ri
,
M.
A
.
I
s
m
ai
l
,
an
d
S.
A
b
d
u
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-
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i
,
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Re
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n
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p
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[7
5
]
A
.
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an
d
M.
A
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me
d
,
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Fu
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In
t
.
J.
In
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.
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.
, v
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l
.
1
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,
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o
.
1
,
p
p
.
8
1
–
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0
,
2
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2
0
.
[7
6
]
M.
A
.
Bah
ari
,
Z
.
A
.
Bah
aru
d
i
n
,
T
.
Su
t
i
k
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o
,
A
.
I
.
A
.
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m
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,
M.
A
.
M.
H
a
n
afi
a
h
,
an
d
M.
I
b
rah
i
m
,
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A
n
an
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s
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s
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m
an
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a
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arame
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ro
k
e
,
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In
d
o
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e
s
ian
Jo
u
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n
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E
l
ect
r
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g
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d
Co
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ce
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.
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3
.
i
3
.
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4
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1
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4
5
7
.
[7
7
]
V
.
H
.
A
h
g
aj
an
,
Y
.
G
.
Ras
h
i
d
,
an
d
F.
M.
T
u
ai
m
ah
,
“
A
rt
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fi
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al
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ee
co
l
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m
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s
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c
h
as
t
i
c
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n
d
p
o
w
e
r
,
”
In
t
er
n
a
t
i
o
n
a
l
Jo
u
r
n
a
l
o
f
P
o
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er
E
l
ect
r
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i
c
s
a
n
d
D
r
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ve
S
ys
t
em
s
,
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o
l
.
1
2
,
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o
.
3
.
p
p
.
1
8
9
0
–
1
8
9
9
,
2
0
2
1
,
d
o
i
:
1
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