I
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rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
2
0
1
7
,
p
p
.
18
5
~
1
9
2
I
SS
N:
2252
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8814
185
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er
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s
[
1
]
.
I
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y
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1
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T
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[
2
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[
2
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3
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[
5
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T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8814
IJ
AA
S
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
201
7
:
1
8
5
–
1
9
2
186
w
o
r
k
s
o
f
an
I
talia
n
m
a
th
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m
ati
cian
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Vito
Vo
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in
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last
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[
7
,
8
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T
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2
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u
e
n
c
y
d
o
m
a
in
i
s
in
v
esti
g
ated
in
[
1
0
]
.
A
n
o
n
-
lin
ea
r
a
n
al
y
tic
an
d
n
u
m
er
ical
s
t
u
d
y
o
f
in
te
g
r
al
-
d
i
f
f
er
en
tial
eq
u
atio
n
f
o
r
Vo
lter
r
a
s
er
ies
is
d
is
cu
s
s
ed
in
[
1
1
]
w
h
ile
[
1
2
]
p
r
esen
t
s
th
e
s
e
lectio
n
o
f
g
en
er
al
o
r
th
o
g
o
n
al
b
ases
f
o
r
s
ec
o
n
d
-
o
r
d
er
Vo
lter
r
a
f
ilter
.
I
n
t
h
is
p
ap
er
,
s
ec
tio
n
2
p
r
ese
n
ts
Vo
lter
r
a
s
er
ie
s
a
n
d
in
s
ec
t
i
o
n
3
,
th
e
w
a
y
s
o
f
ca
lc
u
lati
n
g
t
h
e
k
er
n
el
s
o
r
f
ac
to
r
s
o
f
Vo
lter
r
a
s
er
ies
ar
e
illu
s
tr
ated
.
Sectio
n
3
-
1
d
is
cu
s
s
es
t
h
e
o
r
th
o
g
o
n
al
f
u
n
cti
o
n
an
d
s
ec
tio
n
3
-
2
ex
p
r
ess
es
t
h
e
ex
p
a
n
s
io
n
o
f
k
e
r
n
els
w
it
h
o
r
th
o
g
o
n
a
l
f
u
n
c
tio
n
s
.
Hea
t
ex
ch
a
n
g
er
s
y
s
te
m
i
s
d
escr
ib
ed
in
s
ec
tio
n
4
an
d
th
e
r
esu
lt
s
o
f
t
h
e
s
i
m
u
lat
io
n
ar
e
p
r
o
v
id
ed
in
s
ec
tio
n
5
.
2.
VO
L
T
E
RRA
SE
R
I
E
S
Vo
lter
r
a
s
er
ies
is
o
n
e
o
f
th
e
m
et
h
o
d
s
f
o
r
id
en
tif
icat
io
n
o
f
n
o
n
-
li
n
ea
r
s
y
s
te
m
s
as
a
b
lack
-
b
o
x
.
T
h
e
m
ai
n
ad
v
an
tag
e
o
f
th
i
s
s
er
ies
i
s
its
g
e
n
er
alit
y
w
h
ic
h
to
o
m
a
n
y
n
u
m
b
er
s
o
f
n
o
n
-
l
in
ea
r
s
y
s
te
m
s
ca
n
b
e
m
o
d
eled
b
y
t
h
at
[
1
3
]
.
Vo
lter
r
a
s
er
ies
p
r
o
v
id
es
a
m
o
d
el
f
o
r
b
eh
a
v
io
r
o
f
a
n
o
n
-
l
in
ea
r
s
y
s
te
m
lik
e
T
a
y
lo
r
s
er
ies,
b
u
t
th
er
e
is
a
d
if
f
er
en
ce
b
et
w
ee
n
th
e
s
e
t
w
o
s
er
ie
s
.
T
h
e
r
esu
lted
m
o
d
e
l
b
y
T
a
y
lo
r
s
er
ies
i
s
ex
tr
e
m
el
y
d
ep
en
d
ed
o
n
th
e
in
p
u
t
i
n
a
ce
r
tai
n
ti
m
e
w
h
ile
i
n
t
h
e
Vo
lter
r
a
s
er
ies
t
h
e
o
u
tp
u
t
o
f
n
o
n
-
lin
ea
r
s
y
s
te
m
is
d
ep
e
n
d
ed
o
n
th
e
i
n
p
u
t
in
al
l
in
s
ta
n
t
s
o
f
ti
m
e
[
6
]
.
C
o
n
v
o
lu
tio
n
i
n
teg
r
al
i
s
u
s
ed
f
o
r
m
o
d
elin
g
a
lin
ea
r
s
y
s
te
m
b
et
w
e
en
in
p
u
t
an
d
o
u
tp
u
t,
w
h
ile
Vo
lter
r
a
s
er
ies
is
u
s
ed
to
id
en
tify
a
n
d
m
o
d
el
th
e
n
o
n
-
lin
ea
r
s
y
s
te
m
w
h
ic
h
is
a
g
en
er
aliza
tio
n
to
th
e
co
n
v
o
lu
tio
n
i
n
te
g
r
al
[
2
]
.
Mo
d
el
r
esp
o
n
s
e
is
eq
u
al
to
[
1
4
]
:
...
3
2
1
0
y
y
y
y
y
(
1
)
No
m
e
n
c
l
a
tu
r
e
Co
n
sta
n
t
:
y
Ou
tp
u
t
:
u
in
p
u
t
:
N
S
e
t
o
f
n
a
tu
ra
l
n
u
m
b
e
rs
:
Orth
o
g
o
n
a
l
f
u
n
c
ti
o
n
:
l
L
a
g
u
e
rre
o
rth
o
g
o
n
a
l
f
u
n
c
ti
o
n
:
P
L
e
g
e
n
d
re
p
o
ly
n
o
m
ial
Va
r
ia
b
les
:
M
m
e
m
o
r
y
o
f
th
e
s
y
ste
m
:
L
d
e
g
re
e
o
f
s
y
st
e
m
:
a
P
o
le
o
rth
o
g
o
n
a
l
f
u
n
c
ti
o
n
:
p
Ex
p
a
n
sio
n
o
f
o
rt
h
o
g
o
n
a
l
f
u
n
c
ti
o
n
s
:
h
Ke
rn
e
l
o
f
Vo
lt
e
rra
:
n
S
a
m
p
le
:
t
ti
m
e
(se
c
)
:
,
Co
e
ff
icie
n
t
:
e
e
rro
r
:
U
Da
ta M
a
tri
x
:
P
a
ra
m
e
ter v
e
c
to
r
Ind
ice
s
:
,
,
j
i
k
De
g
re
e
w
h
er
e
y
0
is
a
co
n
s
ta
n
t
v
al
u
e
(
f
o
r
ex
a
m
p
le
th
e
av
er
a
g
e
o
f
th
e
s
ig
n
al)
an
d
th
e
f
ir
s
t
ter
m
is
ca
lcu
lated
b
y
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
AA
S
I
SS
N:
2252
-
8814
I
d
en
tifi
ca
tio
n
o
f
a
N
o
n
-
Lin
ea
r
S
ystem
u
s
in
g
V
o
lter
r
a
S
eries
Mo
d
el
…
(
V
a
h
id
Mo
s
s
a
d
eg
h
)
187
0
1
1
1
1
1
)
(
).
(
)
(
m
m
n
u
m
h
n
y
(
2
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An
d
h
i
g
h
o
r
d
er
ter
m
s
ar
e
ca
lc
u
lated
b
y
th
e
f
o
llo
w
i
n
g
eq
u
ati
o
n
s
:
0
0
2
1
2
1
2
2
1
2
)
(
).
(
).
,
(
)
(
m
m
m
n
u
m
n
u
m
m
h
n
y
(
3
)
)
(
).
(
).
(
.
)
,
,
(
)
(
3
2
1
0
0
0
3
2
1
2
3
1
2
3
m
n
u
m
n
u
m
n
u
m
m
m
h
n
y
m
m
m
(
4
)
No
w
,
t
h
e
Vo
lter
r
a
s
er
ies eq
u
at
io
n
is
ch
a
n
g
ed
in
to
eq
u
atio
n
(
5
)
b
y
s
u
b
s
tit
u
ti
n
g
y
i
s
i
n
eq
u
at
i
o
n
(
1
)
:
0
0
2
1
2
1
2
0
1
1
1
0
1
2
1
...
)
(
).
(
).
,
(
)
(
)
(
)
(
m
m
m
m
n
u
m
n
u
m
m
h
m
n
u
m
h
y
n
y
(
5
)
h
n
i
s
r
an
k
n
k
er
n
el
o
f
Vo
lter
r
a.
I
n
f
ac
t,
h
1
(
t)
s
h
o
w
s
i
m
p
u
ls
e
f
u
n
c
tio
n
o
f
li
n
ea
r
s
y
s
te
m
a
n
d
h
1
(
t)
i
s
i
m
p
u
l
s
e
f
u
n
ctio
n
o
f
a
o
n
e
-
d
i
m
en
s
io
n
al
n
o
n
-
li
n
ea
r
s
y
s
te
m
.
I
n
p
r
ac
tice,
s
o
m
e
li
m
ita
tio
n
s
h
a
v
e
to
b
e
c
o
n
s
id
er
ed
s
u
c
h
as
to
o
m
a
n
y
n
u
m
b
er
o
f
u
n
k
n
o
w
n
s
,
li
m
i
ted
n
u
m
b
er
o
f
in
p
u
t
a
n
d
o
u
tp
u
t
d
ata
an
d
th
e
f
ac
t
th
at
r
eg
r
e
s
s
io
n
m
atr
i
x
is
n
o
t
p
r
o
p
er
.
T
h
ese
d
ef
icie
n
cies
ca
u
s
e
th
e
i
n
d
e
f
in
it
e
s
er
ies
o
f
eq
u
atio
n
(
5
)
to
ch
an
g
e
in
to
a
li
m
i
ted
s
er
ies o
f
eq
u
atio
n
(
6
)
w
h
ich
m
ea
n
s
li
m
ited
d
eg
r
ee
an
d
m
e
m
o
r
y
:
1
0
1
0
2
1
2
1
2
1
0
1
1
1
0
1
2
1
)
(
).
(
).
,
(
)
(
)
(
)
(
M
m
M
m
M
m
m
n
u
m
n
u
m
m
h
m
n
u
m
h
y
n
y
(
6
)
M
is
m
e
m
o
r
y
o
f
th
e
s
y
s
te
m
a
n
d
L
is
d
e
g
r
ee
o
f
s
y
s
te
m
.
P
r
o
p
er
s
elec
tio
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o
f
th
e
s
e
p
ar
a
m
et
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s
is
v
er
y
ef
f
ec
tiv
e
in
s
p
ee
d
an
d
ac
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r
ac
y
o
f
t
h
e
id
en
ti
f
ica
tio
n
.
I
n
eq
u
atio
n
(
6
)
th
er
e
is
al
w
a
y
s
)
1
(
0
M
an
d
n
u
m
b
er
o
f
p
ar
a
m
eter
s
i
s
eq
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al
to
[
1
5
]
:
1
2
)
1
(
M
M
M
(
7
)
I
n
o
r
d
er
t
o
m
o
d
el
th
e
s
y
s
te
m
b
ased
o
n
Vo
lter
r
a
s
er
ies,
k
er
n
els
h
av
e
to
f
u
l
f
ill
t
h
e
f
o
llo
w
in
g
f
ea
t
u
r
es [
1
6
]
:
Fo
r
a
ca
u
s
al
m
o
d
el:
)
,
.
.
.
,
1
(
0
0
)
,
.
.
.
,
,
(
)
,
.
.
.
,
1
(
0
0
)
,
.
.
.
,
,
(
2
1
2
1
n
i
k
k
k
k
H
n
i
g
i
if
n
n
i
if
n
n
(
8
)
Fo
r
a
s
tab
le
m
o
d
el:
0
0
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2
1
0
0
0
2
1
1
1
)
,
.
.
.
,
,
(
...
)
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.
,
,
(
...
n
k
k
n
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t
n
n
n
n
k
k
k
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g
(
9
)
W
h
er
e
g
n
is
th
e
n
-
d
i
m
e
n
s
io
n
al
co
n
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u
o
u
s
i
m
p
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ls
e
r
esp
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an
d
H
n
n
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d
i
m
en
s
io
n
a
l
d
is
cr
ete
i
m
p
u
l
s
e
r
esp
o
n
s
e.
Deta
iled
in
f
o
r
m
at
io
n
ab
o
u
t V
o
lter
r
a
s
er
ies an
d
its
ch
ar
ac
ter
is
tic
s
is
g
iv
e
n
i
n
[
1
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
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8814
IJ
AA
S
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
201
7
:
1
8
5
–
1
9
2
188
3.
CALCU
L
A
T
I
N
G
T
H
E
K
E
R
NE
L
S O
F
VO
L
T
E
RRA
SE
RIE
S
On
e
o
f
t
h
e
p
r
o
b
lem
s
o
f
s
y
s
te
m
id
en
ti
f
ica
tio
n
w
it
h
Vo
lter
r
a
s
er
ies
is
t
h
e
esti
m
atio
n
o
f
k
e
r
n
els
b
y
a
p
air
o
f
in
p
u
t
a
n
d
o
u
tp
u
t
w
h
ic
h
h
a
v
e
n
o
is
e.
C
alcu
la
tio
n
o
f
Vo
lter
r
a
s
er
ies
f
ac
to
r
s
(
k
er
n
el
s
)
i
s
t
h
e
m
ain
is
s
u
e
i
n
s
o
lv
i
n
g
th
e
eq
u
atio
n
an
d
id
en
tify
i
n
g
th
e
s
y
s
te
m
s
u
s
i
n
g
th
i
s
s
er
ies.
T
h
er
e
ar
e
m
a
n
y
m
e
th
o
d
s
f
o
r
t
h
is
p
u
r
p
o
s
e
s
u
c
h
as
r
ec
u
r
s
iv
e
al
g
o
r
ith
m
[
1
4
]
,
Gau
s
s
ian
i
n
p
u
t
m
et
h
o
d
[
1
4
]
,
Gr
a
d
ien
t
-
b
ased
s
ea
r
c
h
[
1
7
]
,
cr
o
s
s
-
co
r
r
elatio
n
m
et
h
o
d
[
1
8
]
,
m
et
h
o
d
o
f
Hilb
e
r
t
s
p
ac
e
r
e
p
r
o
d
u
cin
g
k
er
n
el
[
1
9
]
,
an
d
etc.
I
n
ad
d
itio
n
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IJ
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8814
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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2
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8814
IJ
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Vo
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id
er
ed
r
an
k
o
f
m
o
d
el
is
m
o
r
e
th
a
n
ac
t
u
al
r
an
k
o
f
s
y
s
te
m
3
.
Sy
s
te
m
is
id
e
n
ti
f
ied
in
clo
s
e
d
-
lo
o
p
o
p
er
atio
n
.
Fo
r
co
m
p
en
s
atin
g
th
is
p
r
o
b
le
m
in
leas
t
s
q
u
ar
e
m
et
h
o
d
,
in
v
er
s
i
n
g
U
T
U
i
s
n
o
t
all
o
w
ed
a
n
d
alter
n
ati
v
el
y
o
t
h
er
tech
n
iq
u
es
ar
e
em
p
lo
y
ed
.
I
n
th
i
s
p
ap
er
S
VD
is
ch
o
s
e
n
f
o
r
th
is
p
u
r
p
o
s
e
.
B
esid
e
s
,
eq
u
atio
n
(
2
2
)
is
a
cr
iter
io
n
f
o
r
f
ea
s
ib
ili
t
y
as
s
es
s
m
en
t
o
f
m
o
d
el
u
n
d
er
th
e
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a
m
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o
f
r
e
s
id
u
al
o
f
n
o
r
m
alize
d
o
u
tp
u
t
er
r
o
r
[
28
]:
M
n
M
n
db
n
y
n
J
1
2
1
2
)
(
)
(
l
o
g
10
(
22
)
w
h
er
e
)
(
n
is
th
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er
r
o
r
b
etw
ee
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al
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d
esti
m
ated
o
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tp
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t,
)
(
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al
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e
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ac
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al
o
u
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t
at
in
s
ta
n
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n
.
I
f
id
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icatio
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ata.
4.
H
E
AT
E
XCH
AN
G
E
R
SYS
T
E
M
C
ase
s
t
u
d
y
o
f
t
h
is
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esear
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a
n
o
n
-
li
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r
h
ea
t
ex
c
h
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g
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s
y
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te
m
.
Hea
t
ex
c
h
an
g
er
s
ar
e
u
s
ed
in
cr
ea
s
i
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g
l
y
in
m
o
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t
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t
h
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i
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d
u
s
tr
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p
r
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ce
s
s
es
a
s
a
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i
m
p
o
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tan
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p
ar
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en
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g
y
r
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g
en
er
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s
y
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te
m
s
s
u
c
h
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,
r
ef
r
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g
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,
e
x
o
th
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m
ic
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d
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d
o
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ic
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ac
tio
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if
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k
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eg
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h
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er
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t
u
d
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h
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ap
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w
h
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in
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i
l
r
e
f
in
er
ie
s
an
d
ch
e
m
ical
p
r
o
ce
s
s
es
[
2
9
]
.
A
s
s
h
o
w
n
in
F
ig
u
r
e
1
,
w
ater
is
h
ea
ted
b
y
p
r
ess
u
r
iz
ed
an
d
s
atu
r
ated
s
tea
m
w
it
h
a
co
p
p
er
tu
b
e.
I
n
th
e
m
e
n
ti
o
n
ed
s
y
s
te
m
,
in
p
u
t
v
ar
iab
les
ar
e
th
e
v
al
u
e
o
f
f
l
u
id
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m
p
er
at
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d
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t
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ar
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h
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te
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p
er
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e
o
f
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t
f
lu
id
.
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n
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er
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tify
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h
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n
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er
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tu
d
y
s
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te
m
,
i
n
p
u
t
a
n
d
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u
tp
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t
d
ata
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ee
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ed
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h
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ar
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ea
s
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r
ed
b
y
a
r
ese
a
r
ch
ce
n
ter
in
r
ea
l
co
n
d
itio
n
[
3
0
]
.
A
cc
o
r
d
in
g
to
th
is
d
ata,
w
h
ich
i
s
co
m
p
o
s
ed
o
f
4
0
0
0
s
am
p
les
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i
n
p
u
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d
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t
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th
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a
m
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li
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ti
m
e
o
f
1
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id
en
tif
icatio
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m
ed
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t
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t
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t
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s
t
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r
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s
s
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ata
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r
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m
e
n
t,
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o
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s
tea
m
an
d
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n
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u
t
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l
u
id
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co
n
s
id
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co
n
s
tan
t
a
n
d
n
o
m
i
n
al.
Fig
u
r
e
1
s
h
o
w
s
t
h
e
h
ea
t e
x
c
h
a
n
g
er
o
f
s
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r
ated
f
l
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id
s
tea
m
.
Fig
u
r
e
1
.
Hea
t
E
x
ch
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n
g
er
o
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S
atu
r
ated
Flu
id
Stea
m
5.
SI
M
UL
AT
I
O
N
As
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e
n
tio
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in
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3
-
1
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ir
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(
d
eg
r
ee
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te
m
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s
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(
m
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m
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te
m
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a
n
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a
(
p
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th
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w
h
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b
y
t
h
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m
s
q
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ar
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m
o
f
er
r
o
r
s
is
ca
lcu
lated
f
r
o
m
eq
u
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(
1
6
)
.
I
n
th
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p
ap
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r
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P
SO
alg
o
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ith
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f
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el
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.
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n
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te
m
ar
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ca
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[2
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h
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T
ru
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g
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sin
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o
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ls.
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ter
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.
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DA
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Y,
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ta
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.
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