I
nte
rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
3
,
No
.
3
,
Sep
tem
b
er
201
4
,
p
p
.
14
1
~
1
50
I
SS
N:
2252
-
8814
141
J
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In
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[
1
]
.
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telier
[
2
]
p
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a
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tr
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L
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4
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T
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Kib
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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.
3
,
No
.
3
,
Sep
tem
b
er
2
0
1
4
:
14
1
–
1
50
142
len
s
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s
Vile
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y
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e
f
u
n
ctio
n
)
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i
x
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e
r
e
i
x
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co
o
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d
in
ates
in
th
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r
–
d
i
m
en
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io
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m
a
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f
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h
t
h
e
m
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ic
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o
f
th
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m
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if
o
ld
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h
e
f
ield
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s
g
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y
Se
n
a
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Du
n
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th
e
co
m
b
i
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ca
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ten
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o
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e
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k
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j
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ij
ij
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g
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g
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,
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,
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1
(
1
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2
3
ij
R
an
d
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lar
(
i
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r
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its
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8
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C
)
.
R
ec
en
t
l
y
,
co
n
s
id
er
ab
le
in
ter
e
s
t
h
a
v
e
b
ee
n
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in
ce
d
i
n
th
e
o
r
ies
o
f
m
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r
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th
a
n
f
o
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r
d
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m
en
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io
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s
,
i
n
w
h
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h
th
e
ex
tr
a
d
i
m
en
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io
n
s
ar
e
co
m
p
ac
ted
to
s
m
all
s
ize
i
n
t
h
e
co
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r
s
e
o
f
ev
o
l
u
tio
n
o
f
t
h
e
u
n
i
v
er
s
e
[
1
1
]
.
T
h
e
co
s
m
o
lo
g
ical
s
tu
d
y
in
h
i
g
h
er
d
im
e
n
s
io
n
al
s
p
ac
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ti
m
e
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n
ec
es
s
itated
,
ev
e
n
m
ad
e
u
r
g
e
n
t,
b
y
th
e
g
r
o
w
in
g
b
elief
t
h
at
t
h
e
n
a
tu
r
e
o
f
s
p
a
ce
ti
m
e
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n
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h
e
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iv
er
s
e
ar
e
h
ig
h
er
t
h
a
n
f
o
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r
.
C
h
atter
j
ee
[
1
2
]
s
tu
d
ied
m
a
s
s
i
v
e
s
tr
in
g
s
i
n
h
i
g
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d
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m
e
n
s
io
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al
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o
m
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g
e
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eo
u
s
s
p
ac
e
ti
m
e.
K
r
o
r
i
et
al.
[
1
3
]
d
is
cu
s
s
ed
B
ian
ch
i
t
y
p
e
-
1
h
ig
h
er
d
i
m
en
s
io
n
al
co
s
m
o
lo
g
ies
an
d
co
n
clu
d
ed
t
h
at,
p
h
y
s
icall
y
,
s
tr
in
g
s
w
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ll
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e
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ik
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g
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m
etr
ic
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tr
in
g
,
an
d
m
atter
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d
s
tr
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co
ex
is
t
t
h
r
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u
g
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t
t
h
e
ev
o
lu
tio
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o
f
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h
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n
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e.
T
h
ey
m
e
n
tio
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ed
t
h
at
co
s
m
ic
s
tr
in
g
s
w
i
th
s
o
m
e
s
p
ec
if
ic
o
r
ien
tatio
n
d
o
n
o
t
o
c
cu
r
in
B
ian
c
h
i
t
y
p
e
-
V
co
s
m
o
l
o
g
y
.
R
a
h
a
m
an
et
al.
[
1
4
]
d
is
c
u
s
s
ed
s
o
m
e
s
tr
i
n
g
co
s
m
o
lo
g
ical
m
o
d
els
i
n
a
h
i
g
h
er
d
i
m
e
n
s
io
n
al
s
p
h
er
icall
y
s
y
m
m
etr
ic
s
p
ac
e
ti
m
e
b
ased
o
n
L
y
r
a
‟
s
g
eo
m
e
tr
y
.
Ven
k
ates
w
ar
l
u
[
1
5
]
co
n
s
tr
u
ct
ed
h
ig
h
er
d
i
m
en
s
io
n
al
s
tr
in
g
co
s
m
o
lo
g
ical
m
o
d
els
in
s
ca
le
co
v
ar
ian
t
t
h
eo
r
y
o
f
g
r
av
ita
tio
n
.
R
ec
en
tl
y
Mo
h
a
n
t
y
et
al.
[
1
6
]
an
d
Mo
h
a
n
t
y
an
d
Ma
h
an
ta
[
1
7
]
co
n
s
tr
u
c
ted
v
ar
io
u
s
h
ig
h
er
d
i
m
en
s
io
n
al
s
tr
i
n
g
co
s
m
o
lo
g
i
ca
l
m
o
d
els
a
n
d
s
t
u
d
ied
th
eir
g
eo
m
etr
ical
a
n
d
p
h
y
s
ica
l
b
eh
av
io
r
s
.
Du
n
n
[
1
8
]
,
Half
o
r
d
[
1
9
]
,
Sin
g
h
[
2
0
]
,
R
ed
d
y
[
2
1
]
,
[
2
2
]
,
R
o
y
a
n
d
C
h
att
er
j
ee
[
2
3
]
,
[
2
4
]
,
R
ed
d
y
an
d
Ven
k
ates
w
ar
l
u
[
2
5
]
,
an
d
Mu
k
h
er
j
ee
[
2
6
]
,
[
2
7
]
ar
e
s
o
m
e
o
f
th
e
a
u
t
h
o
r
s
w
h
o
h
a
v
e
s
t
u
d
ied
v
ar
io
u
s
asp
ec
t
s
o
f
th
is
s
ca
lar
-
ten
s
o
r
th
eo
r
y
o
f
g
r
a
v
itatio
n
.
Ver
y
r
ec
en
tl
y
Ve
n
k
ates
w
ar
lu
,
Sati
s
h
an
d
P
av
an
Ku
m
ar
[
2
8
]
h
av
e
s
tu
d
ied
th
e
B
ian
ch
i
T
y
p
e
–
I
co
s
m
ic
s
tr
in
g
s
i
n
t
h
is
th
eo
r
y
.
I
n
t
h
is
p
ap
er
,
w
e
m
ad
e
a
n
at
te
m
p
t to
s
o
lv
e
th
e
f
iv
e
d
i
m
e
n
s
io
n
al
s
p
h
er
icall
y
s
y
m
m
etr
ic
s
p
ac
e
-
ti
m
e
i
n
th
e
co
n
tex
t
o
f
co
s
m
ic
s
tr
i
n
g
s
in
a
n
e
w
s
ca
lar
-
ten
s
o
r
th
eo
r
y
o
f
g
r
av
ita
tio
n
p
r
o
p
o
s
ed
b
y
S
en
a
n
d
Du
n
n
[
1
0
]
.
E
x
ac
t so
lu
tio
n
s
o
f
th
e
f
ield
eq
u
atio
n
s
ar
e
o
b
tain
ed
v
iz.
p
o
w
e
r
la
w
t
y
p
e
as
s
u
m
p
tio
n
.
2
.
M
E
T
RIC AN
D
F
I
E
L
D
E
Q
UA
T
I
O
N
S
W
e
co
n
s
id
er
th
e
lin
e
ele
m
e
n
t f
o
r
th
e
f
iv
e
-
d
i
m
e
n
s
io
n
a
l K
alu
z
a
-
k
lien
m
o
d
el
is
:
2
)
(
2
2
2
2
2
2
)
(
2
2
s
i
n
dy
e
d
r
d
r
dr
e
dt
ds
t
B
t
A
(
2
)
W
h
er
e
A
an
d
B
ar
e
f
u
n
ctio
n
s
o
f
co
s
m
ic
ti
m
e
t
o
n
l
y
.
T
h
e
f
i
f
t
h
co
o
r
d
in
ate
y
is
al
s
o
ass
u
m
ed
to
b
e
s
p
ac
e
lik
e
co
o
r
d
in
ate.
T
h
e
en
er
g
y
m
o
m
e
n
t
u
m
ten
s
o
r
f
o
r
a
clo
u
d
o
f
m
as
s
i
v
e
s
tr
i
n
g
s
th
at
ca
n
b
e
w
r
itte
n
as
:
j
i
j
i
ij
x
x
u
u
.
(
3
)
Her
e
is
th
e
r
est
e
n
er
g
y
d
en
s
it
y
o
f
t
h
e
clo
u
d
o
f
s
tr
i
n
g
s
w
i
th
p
ar
ticles
attac
h
ed
to
t
h
e
m
,
is
th
e
ten
s
io
n
d
en
s
it
y
o
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tr
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s
an
d
p
,
p
b
ein
g
th
e
en
er
g
y
d
e
n
s
it
y
o
f
th
e
p
ar
ticles.
Fro
m
all
th
e
th
r
ee
en
er
g
y
co
n
d
itio
n
s
(
w
ea
k
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s
tr
o
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a
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d
d
o
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t)
f
o
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o
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el,
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ca
n
f
in
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t
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at
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d
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p
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IJ
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n
fla
tio
n
a
r
y
K
a
lu
z
a
-
K
lien
C
o
s
mic
S
tr
in
g
in
S
ca
la
r
-
Ten
s
o
r
T
h
eo
r
y
o
f G
r
a
vita
tio
n
(
J.
S
a
tis
h
)
143
an
d
th
e
s
i
g
n
o
f
is
u
n
r
es
tr
icte
d
.
On
e
ca
n
n
o
te
t
h
at
th
e
f
ield
eq
u
atio
n
s
w
i
th
λ
<
0
ca
n
b
e
in
ter
p
r
eted
as
th
e
p
r
esen
ce
o
f
a
n
is
o
tr
o
p
ic
f
l
u
id
w
it
h
p
r
es
s
u
r
e
d
i
f
f
er
e
n
t
f
r
o
m
z
er
o
alo
n
g
t
h
e
d
ir
ec
tio
n
o
f
t
h
e
s
tr
in
g
.
T
h
e
v
elo
cit
y
i
u
d
escr
ib
es
th
e
f
i
v
e
–
v
elo
cit
y
w
h
ic
h
h
a
s
co
m
p
o
n
e
n
t
s
(
1
,
0
,
0
,
0
,
0
)
f
o
r
a
clo
u
d
o
f
p
ar
ticles
an
d
i
x
r
ep
r
esen
ts
th
e
d
ir
ec
tio
n
o
f
s
tr
i
n
g
w
h
ic
h
w
ill
s
atis
f
y
:
1
i
i
i
i
x
x
u
u
an
d
0
i
i
x
u
(
4
)
T
h
e
d
ir
ec
tio
n
o
f
th
e
s
tr
i
n
g
s
i
s
tak
en
to
b
e
alo
n
g
X
4
–
a
x
i
s
s
o
th
at
w
e
h
a
v
e
X
i
=
(
0
,
0
,
0
,
0
,
e
-
B
)
.
No
w
t
h
e
f
ield
eq
u
atio
n
s
f
o
r
th
e
m
etr
ic
(
2
)
ar
e
g
iv
e
n
b
y
:
2
2
2
2
2
1
4
1
2
4
3
B
A
B
B
A
A
(
5
)
2
2
2
2
2
3
2
3
A
A
(
6
)
2
2
2
2
4
3
4
3
B
A
A
(
7
)
W
h
er
e
th
e
o
v
er
h
ea
d
d
o
t d
en
o
tes o
r
d
in
ar
y
d
if
f
er
en
tia
tio
n
w
i
th
r
esp
ec
t to
t
.
3.
SO
L
U
T
I
O
NS
T
O
T
H
E
F
I
E
L
D
E
Q
UA
T
I
O
N
S
T
h
e
f
ield
E
q
u
atio
n
(
5
)
–
(
7
)
ar
e
a
s
y
s
te
m
o
f
t
h
r
ee
eq
u
atio
n
s
with
f
i
v
e
u
n
k
n
o
w
n
p
ar
a
m
eter
s
A
,
B
,
,
ρ
an
d
λ.
W
e
n
ee
d
tw
o
ad
d
itio
n
al
co
n
d
itio
n
s
to
g
et
a
d
eter
m
i
n
is
t
ic
s
o
lu
tio
n
o
f
th
e
ab
o
v
e
s
y
s
te
m
o
f
eq
u
atio
n
s
.
T
h
u
s
w
e
p
r
esen
t
th
e
s
o
l
u
tio
n
s
o
f
t
h
e
f
ield
eq
u
atio
n
s
i
n
th
e
f
o
llo
w
in
g
p
h
y
s
ical
l
y
m
ea
n
in
g
f
u
l
ca
s
es
.
T
o
g
et
a
r
ea
lis
tic
s
o
l
u
tio
n
h
er
e
w
e
a
s
s
u
m
e
th
a
t
:
mn
A
t
e
an
d
n
B
t
e
(
8
)
W
h
er
e
m
an
d
n
ar
e
ar
b
itra
r
y
c
o
n
s
ta
n
ts
.
T
h
en
f
r
o
m
E
q
u
ati
o
n
(
5
)
w
e
o
b
tain
:
k
t
0
(
9
)
W
h
er
e
0
is
an
ar
b
itra
r
y
co
n
s
ta
n
t a
n
d
2
1
2
2
2
)
1
2
(
2
)
1
2
3
(
m
n
m
m
n
k
.
T
h
u
s
th
e
f
i
v
e
d
i
m
e
n
s
io
n
al
Kal
u
za
-
k
lie
n
s
p
ac
e
-
ti
m
e
is
:
2
2
2
2
2
2
2
2
2
s
i
n
dy
t
d
r
d
r
dr
t
dt
ds
n
mn
.
(
1
0
)
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8814
IJ
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No
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A:
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Nu
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n
.
6
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1
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
5
2
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8814
IJ
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