I
nte
rna
t
io
na
l
J
o
urna
l o
f
I
nfo
r
m
a
t
ics a
nd
Co
mm
u
n
ica
t
io
n T
ec
hn
o
lo
g
y
(
I
J
-
I
CT
)
Vo
l.
4
,
No
.
3
,
Dec
em
b
er
201
5
,
p
p
.
1
1
7
~1
2
3
I
SS
N:
2252
-
8776
117
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
J
I
C
T
T
w
o
Ter
m
Ap
pro
x
i
m
a
tion
f
o
r
N
ea
r
F
ield
Ana
ly
sis
o
f
Wire
S
ca
tt
ere
rs
Va
ibh
a
v
S
Ya
v
a
lk
a
r
*
,
C
ha
nd
a
n Sin
g
h
D
Ra
w
a
t
*
*
,
S S
K
a
k
a
t
k
a
r*
*
*
a
nd
K
P
Ra
y
*
*
*
*
M
.
E.
S
tu
d
e
n
t,
V
.
E.
S
.
In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
,
Ch
e
m
b
u
r,
M
u
m
b
a
i
*
*
De
p
a
rt
m
e
n
t
o
f
El
e
c
tro
n
ics
a
n
d
T
e
lec
o
m
m
u
n
ica
ti
o
n
En
g
i
n
e
e
rin
g
,
V
.
E.
S
.
In
stit
u
te o
f
T
e
c
h
n
o
lo
g
y
,
Ch
e
m
b
u
r,
M
u
m
b
a
i
*
*
*
S
o
c
iet
y
f
o
r
A
p
p
l
ied
M
icro
w
a
v
e
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
a
n
d
R
e
se
a
rc
h
(S
A
M
EE
R),
IIT
C
a
m
p
u
s,
Hill
S
i
d
e
,
P
o
w
a
i,
Mu
m
b
a
i
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Au
g
29
,
2
0
1
5
R
ev
i
s
ed
No
v
1
0
,
2
0
1
5
A
cc
ep
ted
No
v
1
6
,
2
0
1
5
T
h
is
p
a
p
e
r
p
re
se
n
ts
a
n
a
n
a
l
y
sis
o
f
n
e
a
r
f
ield
o
f
w
ir
e
s
c
a
tt
e
re
r
s
.
In
th
is
p
a
p
e
r,
th
e
e
x
a
c
t
d
istri
b
u
ti
o
n
o
n
w
ire
sc
a
tt
e
re
rs
is
a
p
p
ro
x
im
a
t
e
d
u
sin
g
a
m
o
r
e
a
c
c
u
ra
te
t
w
o
ter
m
a
p
p
ro
x
ima
ti
o
n
f
o
r
th
e
e
a
se
o
f
c
lo
se
d
f
o
r
m
a
n
a
l
y
sis
.
It
h
a
s
b
e
e
n
sh
o
w
n
th
a
t
th
e
re
su
l
ts
o
b
ta
in
e
d
u
sin
g
t
h
e
tw
o
term
a
p
p
ro
x
i
m
a
ti
o
n
a
re
v
e
r
y
c
lo
se
to
th
e
c
o
sin
u
so
i
d
a
l
d
i
strib
u
ti
o
n
f
o
r
th
e
e
lem
e
n
t
len
g
th
u
p
to
0
.
7
w
it
h
les
s
th
a
n
5
%
e
rro
r
in
th
e
f
i
e
ld
e
v
a
lu
a
ted
f
ro
m
th
is
a
p
p
ro
x
im
a
ti
o
n
.
T
h
is
a
n
a
ly
sis
f
o
r
m
u
latio
n
is
u
se
f
u
l
in
e
stim
a
ti
n
g
f
ield
s
f
o
r
m
w
ire
sc
a
tt
e
re
rs,
m
u
tu
a
l
c
o
u
p
li
n
g
in
a
n
a
rra
y
o
f
sc
a
tt
e
re
rs
o
r
a
n
a
ly
sis o
f
Ya
g
i
-
Ud
a
a
n
ten
n
a
s
.
K
ey
w
o
r
d
:
C
lo
s
ed
f
o
r
m
Nea
r
f
ield
T
w
o
t
er
m
a
p
p
r
o
x
i
m
atio
n
W
ir
e
s
ca
tter
er
Co
p
y
rig
h
t
©
2
0
1
5
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Vaib
h
av
S.
Yav
al
k
ar
,
M
.
E.
S
tu
d
e
n
t,
V.E
.
S
.
In
sti
tu
te
o
f
T
e
c
h
n
o
lo
g
y
,
Ch
e
m
b
u
r,
M
u
m
b
a
i.
E
m
ail:
v
aib
h
a
v
y
a
v
al
k
ar
@
y
a
h
o
o
.
in
1.
I
NT
RO
D
UCT
I
O
N
W
ir
e
s
ca
tter
er
is
t
y
p
ical
l
y
a
s
i
m
p
le
m
e
tal
r
o
d
ac
ti
n
g
as
a
p
ass
i
v
e
r
ad
iato
r
.
Scatter
er
o
r
p
ar
asit
ic
ele
m
e
n
t
i
s
a
co
n
d
u
cti
v
e
ele
m
en
t
i
n
a
r
ad
io
a
n
ten
n
a
w
h
ic
h
is
n
o
t
elec
tr
icall
y
co
n
n
ec
ted
t
o
an
y
t
h
i
n
g
else.
I
n
ca
s
e
o
f
Ya
g
i
-
u
d
a
an
te
n
n
a
[
1
]
,
th
er
e
is
o
n
e
d
r
iv
e
n
ele
m
e
n
t
a
n
d
o
th
er
s
ar
e
s
ca
tter
er
s
(
eith
er
d
ir
ec
to
r
s
o
r
r
ef
lecto
r
s
)
.
W
ir
e
s
ca
tter
er
s
ar
e
also
u
s
ed
in
ap
p
licatio
n
s
li
k
e
w
ir
e
g
r
id
p
o
lar
izer
s
[2
]
,
f
r
eq
u
en
c
y
s
elec
ti
v
e
s
u
r
f
ac
es,
c
h
a
f
f
,
e
tc.
An
al
y
s
is
o
f
w
ir
e
s
ca
tter
er
s
i
s
also
e
s
s
e
n
tial
i
n
est
i
m
a
tin
g
t
h
e
e
f
f
ec
t
o
n
an
d
d
eg
r
ad
atio
n
in
p
atter
n
d
u
e
to
w
ir
e
s
ca
tter
es
s
u
ch
a
s
ad
j
ac
en
t
m
etal
lic
s
tr
u
ct
u
r
es,
s
u
p
p
o
r
t
r
o
d
s
,
in
ter
f
er
en
c
e
o
r
p
ick
u
p
d
u
e
to
P
C
B
tr
ac
es
etc.
I
n
ca
s
e
o
f
s
c
atter
er
s
u
s
ed
i
n
a
n
ar
r
a
y
,
t
h
e
f
ield
s
ar
e
o
f
te
n
m
ea
s
u
r
ed
at
v
er
y
clo
s
e
d
i
s
tan
ce
w
h
er
e
th
e
n
ea
r
f
ield
cr
iter
ia
ar
e
u
s
e
f
u
l
f
o
r
t
h
e
an
al
y
s
is
.
Mu
t
u
al
co
u
p
li
n
g
b
et
w
ee
n
s
c
atter
er
s
n
ee
d
s
to
b
e
s
tu
d
ied
ac
cu
r
atel
y
i
n
ca
s
e
o
f
a
r
r
ay
o
f
s
ca
tter
er
s
o
r
m
u
ltip
le
s
ca
tter
er
s
in
clo
s
e
p
r
o
x
i
m
it
y
.
T
h
e
cu
r
r
en
t
d
i
s
tr
ib
u
tio
n
o
n
d
ip
o
les
is
o
f
te
n
ap
p
r
o
x
i
m
ated
w
ith
p
iece
w
is
e
s
i
n
u
s
o
i
d
al
(
P
W
S)
d
is
tr
ib
u
tio
n
w
h
ic
h
i
s
o
f
t
h
e
f
o
r
m
,
(
|
|
)
-
,
w
h
er
e
2
is
th
e
len
g
t
h
o
f
t
h
e
s
ca
tter
er
a
n
d
is
th
e
w
a
v
e
n
u
m
b
er
[
3,
4
]
.
Scatter
er
s
ar
e
al
s
o
o
f
te
n
an
al
y
s
ed
u
s
i
n
g
P
W
S
d
is
tr
ib
u
tio
n
s
i
m
ilar
to
d
ip
o
les
,
b
u
t
a
s
th
e
len
g
th
o
f
th
e
s
ca
tter
er
d
ev
iate
s
f
r
o
m
h
al
f
a
w
av
ele
n
g
t
h
,
th
e
P
W
S
d
o
es
n
o
t
h
o
ld
tr
u
e.
Her
e
C
o
s
in
e
d
is
tr
ib
u
tio
n
s
i
m
ilar
to
w
a
v
e
g
u
id
e
f
ed
s
lo
t
ap
er
tu
r
e
d
is
tr
ib
u
tio
n
i
s
m
o
r
e
a
p
p
r
o
p
r
iate
an
d
s
h
o
u
ld
b
e
u
s
ed
f
o
r
m
o
r
e
ac
cu
r
ate
an
n
al
y
s
is
.
Ho
w
ev
er
,
n
ea
r
f
ield
s
f
r
o
m
co
s
in
e
d
is
tr
ib
u
tio
n
o
f
t
h
e
f
o
r
m
co
s
(
π/2
l
z
)
ca
n
n
o
t
b
e
an
al
y
ze
d
in
clo
s
ed
f
o
r
m
.
I
t
is
th
is
c
h
an
g
e
f
r
o
m
f
r
ee
s
p
ac
e
w
a
v
en
u
m
b
er
to
th
at
w
h
er
e
k
is
n
o
t
i
n
v
o
lv
ed
th
a
t
ca
u
s
es
tr
o
u
b
le
in
ca
lcu
lati
n
g
t
h
e
clo
s
ed
f
o
r
m
e
x
p
r
ess
io
n
i
n
C
o
s
in
e
d
i
s
tr
ib
u
ti
o
n
[
5
].
T
h
er
ef
o
r
e,
h
er
e
th
e
n
ea
r
f
ield
a
n
al
y
s
is
is
d
o
n
e
n
u
m
er
icall
y
u
s
i
n
g
t
w
o
t
er
m
ap
p
r
o
x
i
m
atio
n
d
is
tr
ib
u
tio
n
s
i
n
ce
it
is
v
er
y
clo
s
e
to
th
e
co
s
in
e
d
is
tr
ib
u
t
io
n
an
d
it
ca
n
also
b
e
an
a
l
y
ze
d
in
clo
s
ed
f
o
r
m
[
6
,
7]
.
T
h
is
p
ap
er
h
ig
h
lig
h
t
s
t
h
e
ap
p
licab
ilit
y
o
f
t
w
o
ter
m
ap
p
r
o
x
im
a
tio
n
to
w
ir
e
s
ca
tter
er
s
o
f
d
if
f
er
e
n
t
le
n
g
th
s
.
T
h
e
m
ax
i
m
u
m
le
n
g
th
o
f
s
ca
tter
er
f
o
r
w
h
ic
h
n
ea
r
f
ield
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8776
I
J
I
C
T
Vo
l.
4
,
No
.
3
,
Dec
em
b
er
201
5
:
1
1
7
–
12
3
118
m
a
y
b
e
ev
al
u
ated
i
n
clo
s
ed
f
o
r
m
u
s
i
n
g
th
e
p
r
o
p
o
s
ed
t
w
o
ter
m
ap
p
r
o
x
i
m
a
tio
n
w
i
th
a
n
er
r
o
r
o
f
less
th
a
n
5
%
is
also
f
o
u
n
d
o
u
t.
T
h
e
an
al
y
s
is
m
eth
o
d
o
lo
g
y
is
p
r
ese
n
ted
in
Sec
tio
n
2
an
d
r
esu
lt
s
ar
e
d
is
cu
s
s
e
d
in
Sectio
n
3
.
2.
M
E
T
H
O
D
O
L
O
G
Y
Fig
u
r
e
1
s
h
o
w
s
t
h
e
g
eo
m
etr
y
o
f
t
h
e
w
ir
e
s
ca
tter
er
w
i
th
th
e
co
-
o
r
d
in
ate
s
y
s
te
m
.
T
h
e
s
ca
tter
er
is
ass
u
m
ed
to
b
e
o
f
len
g
th
2
,
d
ia
m
eter
d
an
d
p
lace
d
alo
n
g
z
-
ax
is
in
th
e
y
z
p
lan
e.
T
h
e
d
iam
et
er
o
f
th
e
s
ca
tter
er
is
m
u
c
h
les
s
t
h
an
t
h
e
le
n
g
th
o
f
th
e
s
ca
tter
er
.
T
h
e
s
ca
tter
er
ca
n
b
e
r
ep
lace
d
b
y
an
eq
u
i
v
alen
t
li
n
ea
r
elec
tr
ic
cu
r
r
en
t
s
o
u
r
ce
alo
n
g
th
e
ax
i
s
o
f
t
h
e
s
ca
t
ter
er
o
r
th
e
z
-
a
x
is
i
n
t
h
is
ca
s
e.
T
h
e
s
ca
tter
er
h
a
s
a
f
ield
p
atter
n
w
it
h
az
i
m
u
th
a
l
s
y
m
m
etr
y
s
i
m
ilar
to
a
d
ip
o
le.
T
h
u
s
,
th
e
f
ield
p
o
in
t
ca
n
b
e
co
n
v
e
n
ien
tl
y
lo
ca
t
ed
in
th
e
y
z
p
lan
e
(
)
,
w
it
h
o
u
t
lo
s
s
o
f
g
en
er
alit
y
.
T
h
e
ce
n
tr
e
o
f
t
h
e
s
ca
tter
er
is
at
o
r
ig
i
n
O
(
0
,
0
,
0
)
an
d
th
e
o
b
s
er
v
atio
n
p
o
in
t
P
is
at
(
0
,
y
0
,
z
0
)
.
P
=
(
y
0
,
,
z
0
)
in
c
y
li
n
d
r
ical
co
o
r
d
in
ates
an
d
P
=
(
R
0
,
,
)
in
s
p
h
er
ical
c
o
o
r
d
in
ates.
T
h
e
ce
n
tr
e
to
th
e
f
ield
d
is
ta
n
c
e
is
R
0
.
is
an
y
p
o
in
t
o
n
t
h
e
s
c
atter
er
alo
n
g
z
ax
i
s
.
R
is
t
h
e
d
i
s
tan
ce
b
et
w
ee
n
an
d
th
e
o
b
s
er
v
atio
n
p
o
in
t P
.
T
h
e
to
tal
f
ield
at
o
b
s
er
v
atio
n
p
o
in
t P
is
,
E
t
= E
z
̅
+ E
̅
(
1
)
T
h
e
elec
tr
ic
cu
r
r
en
t o
n
th
e
s
ca
tter
er
is
ass
u
m
ed
co
s
i
n
u
s
o
id
al
o
r
J
=
c
o
s
(
)
̅
.
Fo
llo
w
i
n
g
th
e
p
r
o
ce
d
u
r
e
in
[
3
,
8
],
∫
.
/
(
2
)
∫
(
3
)
w
h
er
e
,
,
is
t
h
e
f
r
ee
s
p
ac
e
w
a
v
elen
g
t
h
,
η
=
1
2
0
π
is
th
e
f
r
ee
s
p
ac
e
i
m
p
ed
an
ce
,
(
)
is
th
e
f
r
ee
s
p
ac
e
Gr
ee
n
’
s
f
u
n
c
tio
n
an
d
√
(
)
.
2
.
1
.
T
w
o
T
er
m
A
pp
ro
x
i
m
a
t
io
n
A
t
w
o
ter
m
ap
p
r
o
x
i
m
ati
o
n
i
s
s
i
m
ilar
to
th
at
i
n
[
6
]
is
u
s
ed
f
o
r
s
ca
tter
er
elec
tr
ic
cu
r
r
en
t d
is
tr
i
b
u
tio
n
(
)
.
/
*
,
(
|
|
)
-
(
|
|
)
,
(
|
|
)
-
+
(
4
)
Her
e
w
e
ap
p
r
o
x
i
m
ate
t
h
e
cu
r
r
en
t to
a
co
s
in
u
s
o
id
an
d
th
e
co
n
s
ta
n
t
s
,
ar
e
ev
alu
ated
s
u
b
j
ec
t to
Fig
u
r
e
1
.
Geo
m
e
tr
y
o
f
t
h
e
P
r
o
b
le
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
I
C
T
I
SS
N:
2
2
5
2
-
8776
Tw
o
Ter
m
A
p
p
r
o
xima
tio
n
f
o
r
N
ea
r
F
ield
A
n
a
lysi
s
…
(
V
a
ib
h
a
v
S
Ya
va
lk
a
r
)
119
0
.
0
0
0
.
1
0
0
.
2
0
0
.
3
0
0
.
4
0
0
.
5
0
0
.
6
0
0
.
7
0
0
.
8
0
0
.
9
0
1
.
0
0
0
0
.
2
0
.
4
0
.
6
0
.
8
1
D
i
st
r
i
b
u
t
i
o
n
J
P
o
si
t
i
o
n
a
l
o
n
g
sca
t
t
e
r
e
r
l
e
n
g
t
h
z
/
l
C
o
s
0
.
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
.
0
0
0
.
2
0
.
4
0
.
6
0
.
8
1
D
i
st
r
i
b
u
t
i
o
n
J
P
o
si
t
i
o
n
a
l
o
n
g
sca
t
t
e
r
e
r
l
e
n
g
t
h
z
/
l
C
o
s
Tw
o
Te
r
m
(
)
an
d
T
h
en
,
(
)
(
5
)
(
)
(
)
(
6
)
(
b
)
T
h
e
s
ca
tter
er
d
is
tr
ib
u
tio
n
u
s
i
n
g
co
s
in
e
a
n
d
t
w
o
ter
m
ap
p
r
o
x
im
atio
n
d
i
s
tr
ib
u
tio
n
is
g
iv
e
n
i
n
f
ig
u
r
e
2
f
o
r
s
ca
tter
er
len
g
th
2l
=
0
.
6
λ
an
d
2l
=
0
.
7
5
λ
.
I
t c
an
b
e
s
ee
n
f
r
o
m
g
r
ap
h
t
h
at
t
h
e
t
w
o
d
is
tr
ib
u
tio
n
s
ar
e
clo
s
e
to
ea
ch
o
th
er
.
2
.
2
.
Nea
r
F
ield o
f
Sca
t
t
er
er
s
us
ing
T
w
o
T
er
m
Appro
x
i
m
a
t
io
n
Usi
n
g
t
h
e
t
w
o
ter
m
ap
p
r
o
x
im
atio
n
eq
u
atio
n
(
4
)
f
o
r
s
ca
t
ter
er
elec
tr
ic
cu
r
r
en
t
d
i
s
tr
ib
u
tio
n
J
in
eq
u
atio
n
s
(
2
, 3
)
,
th
e
eq
u
atio
n
s
f
o
r
an
d
ca
n
b
e
w
r
itte
n
as
,
∫
(
)
2
(
)
(
)
,
(
)
-
3
(
7
)
Fig
u
r
e
2
.
Dis
tr
ib
u
tio
n
f
o
r
C
o
s
i
n
u
s
o
id
al
an
d
t
w
o
ter
m
ap
p
r
o
x
im
atio
n
f
o
r
s
ca
tter
er
len
g
t
h
s
(
a)
0
.
6
λ
an
d
(
b
)
0
.
7
5
λ
(
b
)
(
b
)
(
a)
(
a)
(
b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8776
I
J
I
C
T
Vo
l.
4
,
No
.
3
,
Dec
em
b
er
201
5
:
1
1
7
–
12
3
120
(
)
0
.
/
1
(
)
(
8
)
W
h
er
e,
(
)
*
,
(
|
|
)
-
(
|
|
)
,
(
|
|
)
-
+
Fig
u
r
e
3
.
C
o
r
r
ec
tio
n
f
ac
to
r
f
o
r
t
w
o
ter
m
ap
p
r
o
x
i
m
atio
n
T
h
e
f
ield
s
g
i
v
e
n
ab
o
v
e
ca
n
b
e
f
u
r
t
h
er
co
r
r
ec
ted
f
o
r
th
e
d
if
f
er
en
ce
in
t
h
e
t
w
o
d
is
tr
ib
u
t
io
n
s
b
y
u
s
in
g
a
m
u
ltip
licati
v
e
ci
n
s
ta
n
t γ
[
8
].
*
(
)
,
(
)
-
(
)
+
(9
)
T
h
e
co
r
r
ec
tio
n
f
ac
to
r
f
o
r
t
w
o
ter
m
ap
p
r
o
x
i
m
atio
n
t
h
at
is
t
h
e
r
atio
o
f
th
e
f
ir
s
t
m
o
m
e
n
t
s
o
f
t
h
e
t
w
o
d
is
tr
ib
u
tio
n
s
is
p
lo
tted
in
f
i
g
u
r
e
3.
T
h
e
v
alu
e
o
f
co
r
r
ec
tio
n
f
ac
to
r
is
n
ea
r
l
y
eq
u
al
to
o
n
e
f
o
r
s
ca
tter
er
s
len
g
t
h
u
p
to
0
.
5
,
h
o
w
e
v
er
,
it
in
cr
ea
s
es
f
r
o
m
u
n
it
y
ab
o
v
e
0
.
5
.
3.
RE
SU
L
T
S
A
ND
D
I
SCU
SI
O
N
T
h
e
p
er
ce
n
tag
e
er
r
o
r
v
ar
iatio
n
i
n
elec
tr
ic
f
ield
w
i
th
d
is
ta
n
c
e
R
0
/
is
p
lo
tted
in
f
ig
u
r
e
4
to
F
ig
u
r
e
8
.
Her
e
th
e
p
er
ce
n
ta
g
e
er
r
o
r
v
ar
iatio
n
is
th
e
er
r
o
r
b
et
w
ee
n
t
w
o
ter
m
d
is
tr
ib
u
tio
n
a
n
d
co
s
in
u
s
o
id
al
d
is
tr
ib
u
tio
n
.
I
t
is
ca
lc
u
lated
b
y
tak
i
n
g
t
h
e
p
e
r
ce
n
tag
e
o
f
t
h
e
d
i
f
f
er
en
ce
b
et
w
ee
n
t
h
e
t
w
o
ter
m
a
n
d
t
h
e
c
o
s
in
e
d
is
tr
ib
u
tio
n
s
w
it
h
r
e
f
er
en
ce
to
co
s
i
n
e
d
is
tr
i
b
u
tio
n
.
Fro
m
f
i
g
u
r
e
4
,
w
e
ca
n
s
a
y
t
h
at
f
o
r
s
ca
tter
er
len
g
t
h
o
f
2l
=0
.
3
,
th
e
er
r
o
r
r
e
m
ain
s
le
s
s
th
a
n
1
%
o
v
er
t
h
e
en
tire
a
n
g
u
lar
r
an
g
e
0
0
≤
θ
≤
9
0
0
in
n
ea
r
f
ield
a
n
d
i
n
t
h
e
f
ar
f
ield
t
h
e
er
r
o
r
b
ec
o
m
e
s
n
e
g
li
g
ib
le
i.e
.
al
m
o
s
t
eq
u
al
to
ze
r
o
an
d
it r
em
ai
n
s
c
o
n
s
ta
n
t.
Fo
r
s
ca
tter
er
len
g
th
2l
=
0
.
6
5
λ
,
th
e
p
er
ce
n
tag
e
er
r
o
r
in
m
a
g
n
i
tu
d
e
o
f
E
-
f
ield
is
p
lo
tted
in
f
i
g
u
r
e
5
.
Her
e
th
e
er
r
o
r
in
n
ea
r
f
ield
i
s
m
o
r
e
a
s
co
m
p
ar
ed
to
er
r
o
r
in
th
e
p
r
ev
io
u
s
r
e
s
u
lt
o
f
f
i
g
u
r
e
4
.
I
n
t
h
is
g
r
ap
h
,
t
h
e
er
r
o
r
in
E
-
f
ield
m
a
g
n
it
u
d
e
is
l
ess
t
h
an
2
% o
v
er
t
h
e
en
tire
a
n
g
u
lar
r
an
g
e.
Si
m
i
lar
l
y
,
r
e
s
u
l
ts
ar
e
p
lo
tted
f
o
r
s
ca
t
ter
er
len
g
t
h
s
o
f
0
.
7
λ
,
0
.
8
λ
an
d
1
λ
in
f
ig
u
r
es
6
,
7
an
d
8
r
esp
ec
tiv
el
y
.
I
n
f
ig
u
r
e
6
,
f
o
r
2l
=
0
.
7
λ
,
th
e
er
r
o
r
in
cr
ea
s
es
u
p
to
4
%
i
n
n
ea
r
f
ield
an
d
t
h
e
er
r
o
r
r
e
m
ai
n
s
co
n
s
ta
n
t
a
n
d
le
s
s
th
an
1
.
5
%
i
n
t
h
e
f
ar
f
ield
.
I
n
f
i
g
u
r
e
7
a
n
d
8
,
t
h
e
len
g
t
h
o
f
s
ca
tter
er
is
m
o
r
e
t
h
an
0
.
7
λ
,
it
c
a
n
b
e
s
ee
n
th
a
t
t
h
e
er
r
o
r
in
cr
ea
s
es c
o
n
s
id
er
ab
l
y
in
th
e
n
ea
r
f
ield
an
d
b
ec
o
m
es
m
u
ch
m
o
r
e
th
a
n
5
%
.
I
n
f
ig
u
r
e
9
,
th
e
r
ela
tiv
e
er
r
o
r
in
n
ea
r
E
-
f
ield
m
a
g
n
it
u
d
e
i
s
p
l
o
tted
o
v
er
0
0
≤
θ
≤
9
0
0
f
o
r
2l
=
0
.
7
λ
an
d
R
0
=0
.
5
λ
,
R
0
=0
.
6
5
λ
,
R
0
=0
.
7
λ
,
R
0
=1
λ
.
Her
e
t
h
e
er
r
o
r
is
m
o
r
e
f
o
r
w
id
er
an
g
le
s
as
co
m
p
ar
ed
to
θ
=
0
0
.
Fo
r
w
id
er
an
g
le
s
(
e.
g
.
,
θ
=
9
0
0
)
,
th
e
er
r
o
r
ca
n
b
e
s
ee
n
to
in
cr
ea
s
e
w
i
th
d
is
tan
ce
i
n
th
e
n
ea
r
f
ield
,
b
u
t
r
e
m
ain
s
co
n
s
ta
n
t
i
n
th
e
f
ar
f
ield
as see
n
f
r
o
m
f
i
g
u
r
e
b
elo
w
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
I
C
T
I
SS
N:
2
2
5
2
-
8776
Tw
o
Ter
m
A
p
p
r
o
xima
tio
n
f
o
r
N
ea
r
F
ield
A
n
a
lysi
s
…
(
V
a
ib
h
a
v
S
Ya
va
lk
a
r
)
121
Fig
u
r
e
4
.
Var
iatio
n
o
f
p
er
ce
n
tag
e
er
r
o
r
in
m
ag
n
it
u
d
e
o
f
elec
tr
ic
f
ield
ca
l
cu
lated
f
r
o
m
T
w
o
T
er
m
A
p
p
r
o
x
i
m
atio
n
w
it
h
d
is
tan
ce
R
0
/
λ
f
o
r
s
lo
t
len
g
th
2
l =
0
.
3
λ
at
v
ar
io
u
s
a
n
g
les
.
Fig
u
r
e
5
.
Var
iatio
n
o
f
p
er
ce
n
tag
e
er
r
o
r
in
m
a
g
n
itu
d
e
o
f
elec
tr
ic
f
ield
ca
lcu
lated
f
r
o
m
T
w
o
T
er
m
A
p
p
r
o
x
i
m
atio
n
w
i
t
h
d
is
tan
ce
R
0
/
f
o
r
s
lo
t
len
g
th
2
l
=
0
.
6
5
at
v
ar
io
u
s
an
g
les
.
Fig
u
r
e
6
.
Var
iatio
n
o
f
p
er
ce
n
tag
e
er
r
o
r
in
m
a
g
n
it
u
d
e
o
f
ele
ctr
ic
f
ield
ca
lcu
la
t
ed
f
r
o
m
T
w
o
T
er
m
A
p
p
r
o
x
i
m
atio
n
w
it
h
d
is
tan
ce
R
0
/
f
o
r
s
lo
t
len
g
th
2
l
=
0
.
7
at
v
ar
io
u
s
a
n
g
les
.
Fig
u
r
e
7
.
Var
iatio
n
o
f
p
er
ce
n
t
ag
e
er
r
o
r
in
m
a
g
n
it
u
d
e
o
f
ele
ctr
ic
f
ie
ld
ca
lcu
late
d
f
r
o
m
T
w
o
T
er
m
A
p
p
r
o
x
i
m
atio
n
w
i
th
d
i
s
tan
ce
R
0
/
f
o
r
s
lo
t
len
g
t
h
2
l
=
0
.
8
at
v
ar
io
u
s
a
n
g
le
s
.
Fig
u
r
e
8
.
Var
iatio
n
o
f
p
er
ce
n
t
ag
e
er
r
o
r
in
m
a
g
n
itu
d
e
o
f
ele
ctr
ic
f
ield
ca
lc
u
late
d
f
r
o
m
T
w
o
T
er
m
A
p
p
r
o
x
i
m
atio
n
w
it
h
d
is
ta
n
ce
R
0
/
f
o
r
s
lo
t le
n
g
t
h
2
l
=
1
at
v
ar
io
u
s
an
g
le
s
.
Fig
u
r
e
9
.
Var
iatio
n
o
f
p
er
ce
n
t
ag
e
er
r
o
r
in
m
a
g
n
it
u
d
e
o
f
elec
tr
ic
f
ield
ca
lc
u
late
d
f
r
o
m
T
w
o
T
er
m
A
p
p
r
o
x
i
m
atio
n
w
it
h
t
h
eta
(
)
f
o
r
s
ca
tter
er
len
g
th
2
l
=
0
.
7
an
d
R
0
=
0
.
7
,
0
.
6
5
,
0
.
3
an
d
1
.
T
h
e
co
r
r
ec
tio
n
f
ac
to
r
is
tak
en
in
to
ac
co
u
n
t
w
h
ile
p
lo
tti
n
g
th
e
r
esu
lt
s
.
T
h
e
n
u
m
er
ical
r
esu
lt
s
ar
e
ev
alu
a
ted
b
y
d
i
v
id
in
g
th
e
s
ca
tter
er
in
to
ce
lls
an
d
e
m
p
lo
y
in
g
th
r
ee
p
o
in
t
Ga
u
s
s
ian
q
u
ad
r
a
tu
r
e
m
et
h
o
d
o
v
er
ea
ch
ce
ll.
I
t
is
s
ee
n
t
h
at
t
h
e
er
r
o
r
r
em
ai
n
s
les
s
th
a
n
1
%
o
v
er
th
e
en
tire
a
n
g
u
lar
r
an
g
e
0
0
≤
θ
≤
9
0
0
,
f
o
r
s
ca
tter
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8776
I
J
I
C
T
Vo
l.
4
,
No
.
3
,
Dec
em
b
er
201
5
:
1
1
7
–
12
3
122
len
g
th
2l
≤
0
.
5
λ
.
T
h
e
er
r
o
r
in
cr
ea
s
es
f
o
r
s
ca
tter
er
le
n
g
t
h
2l
>
0
.
5
λ
w
h
er
e
t
h
e
ap
p
r
o
x
i
m
a
te
a
p
er
tu
r
e
d
is
tr
ib
u
tio
n
d
if
f
er
s
m
o
r
e
s
i
g
n
i
f
ica
n
tl
y
f
r
o
m
co
s
i
n
u
s
o
id
al
o
n
e.
T
h
e
ex
p
r
ess
io
n
s
d
er
iv
ed
i
n
th
i
s
p
ap
er
ar
e
u
s
e
f
u
l i
n
ca
lcu
la
tin
g
t
h
e
clo
s
ed
f
o
r
m
ex
p
r
es
s
io
n
s
u
s
i
n
g
t
w
o
ter
m
ap
p
r
o
x
i
m
at
io
n
d
is
tr
ib
u
ti
o
n
f
o
r
n
ea
r
f
ield
o
f
w
ir
e
s
c
atter
er
s
.
C
lo
s
ed
f
o
r
m
e
x
p
r
es
s
io
n
s
f
o
r
s
lo
t
s
ar
e
d
er
iv
ed
in
[
7
]
.
Si
m
ilar
tec
h
n
i
q
u
e
is
u
s
ed
to
f
i
n
d
th
e
clo
s
e
d
f
o
r
m
ex
p
r
ess
io
n
s
f
o
r
d
ip
o
le
s
ca
tter
er
s
.
I
n
t
h
is
p
ap
er
,
r
esu
lts
ar
e
ca
lcu
lated
u
s
in
g
th
e
t
w
o
ter
m
ap
p
r
o
x
i
m
at
io
n
an
d
o
v
er
d
i
f
f
er
e
n
t
len
g
t
h
s
o
f
s
ca
tter
er
s
(
u
p
to
len
g
th
1
λ
)
.
T
h
is
ap
p
r
o
x
i
m
atio
n
ca
n
b
e
u
s
ed
ac
cu
r
atel
y
u
p
to
0
.
7
λ
len
g
t
h
s
ca
tter
er
s
.
4.
CO
NCLU
SI
O
N
T
h
e
t
w
o
ter
m
ap
p
r
o
x
i
m
a
tio
n
h
as
b
ee
n
ap
p
lied
to
co
s
in
u
s
o
i
d
al
elec
tr
ic
cu
r
r
en
t
o
n
a
w
ir
e
s
ca
tter
er
.
I
t
h
as
b
ee
n
s
h
o
w
n
th
a
t
t
h
e
t
wo
ter
m
ap
p
r
o
x
i
m
atio
n
w
it
h
co
r
r
ec
tio
n
f
ac
to
r
i
s
v
er
y
clo
s
e
to
co
s
i
n
u
s
o
id
al
d
is
tr
ib
u
tio
n
as
co
m
p
ar
ed
.
T
h
e
n
ea
r
f
ield
s
f
r
o
m
t
h
is
ap
p
r
o
x
i
m
ate
d
is
tr
ib
u
tio
n
h
a
v
e
b
ee
n
co
m
p
ar
ed
w
it
h
th
e
ex
ac
t
f
ield
s
f
o
r
v
ar
io
u
s
le
n
g
t
h
s
o
f
s
ca
tter
er
s
.
I
t
h
a
s
b
ee
n
s
h
o
w
n
t
h
at
f
o
r
s
ca
tter
er
s
w
it
h
le
n
g
th
s
2l
≤
0
.
7
λ
,
th
e
t
w
o
ter
m
ap
p
r
o
x
i
m
at
io
n
d
ev
el
o
p
ed
is
v
e
r
y
clo
s
e
to
th
e
co
s
in
u
s
o
id
al
d
is
tr
ib
u
tio
n
w
i
th
les
s
t
h
an
5
%
er
r
o
r
.
T
h
e
ap
p
r
o
x
im
a
tio
n
y
ield
s
b
etter
t
h
an
1
%
er
r
o
r
f
o
r
s
ca
tter
er
s
u
p
to
len
g
t
h
s
≤
0
.
5
λ
.
Fo
r
s
ca
tt
er
er
s
h
av
i
n
g
le
n
g
t
h
s
lo
n
g
er
th
a
n
0
.
7
λ
,
f
ield
s
d
er
iv
e
d
u
s
in
g
th
is
t
w
o
ter
m
ap
p
r
o
x
im
atio
n
d
is
tr
ib
u
t
io
n
d
o
n
o
t
g
i
v
e
s
atis
f
ac
to
r
y
r
esu
l
ts
an
d
a
b
etter
ap
p
r
o
x
i
m
atio
n
is
n
ee
d
ed
.
T
h
e
ab
o
v
e
f
o
r
m
u
lati
o
n
is
v
er
y
u
s
ef
u
l
in
e
s
ti
m
ati
n
g
t
h
e
n
ea
r
f
ield
s
o
f
s
ca
tter
er
n
u
m
er
icall
y
a
n
d
ca
n
b
e
u
s
ed
to
ev
alu
ate
t
h
e
clo
s
e
d
f
o
r
m
ex
p
r
ess
io
n
s
f
o
r
n
ea
r
f
ield
w
it
h
t
w
o
ter
m
ap
p
r
o
x
im
a
tio
n
.
RE
F
E
R
E
NC
E
S
[1
]
Ba
lan
is,
C.
A
.
,
“
A
n
ten
n
a
T
h
e
o
ry
-
A
n
a
l
y
si
s an
d
De
sig
n
”
,
Ch
.
3
&
C
h
.
1
1
,
J
o
h
n
W
il
e
y
&
S
o
n
s,
In
c
.
,
1
9
8
2
.
[2
]
D.G
o
ld
ste
in
,
“
P
o
lariz
e
d
L
ig
h
t”,
2
nd
e
d
.
,
CRC
P
re
ss
,
Ne
w
Yo
rk
,
2
0
0
3
.
[3
]
S
c
h
e
lk
u
n
o
f
f
,
S
.
A
.
,
El
e
c
tro
ma
g
n
e
ti
c
W
a
v
e
s
,
3
6
9
–
3
7
1
,
D.
V
a
n
No
st
ra
n
d
Co
.
,
I
n
c
.
,
Ne
w
Yo
rk
,
1
9
5
7
.
[4
]
Rich
m
o
n
d
,
J.
a
n
d
N.
G
e
a
r
y
,
,
“
M
u
tu
a
l
im
p
e
d
a
n
c
e
b
e
tw
e
e
n
c
o
p
lan
a
r
-
sk
e
w
d
ip
o
les
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
A
n
ten
n
a
s
a
n
d
Pro
p
a
g
a
t
io
n
,
V
o
l.
1
8
,
4
1
4
–
4
1
6
,
M
a
y
1
9
7
0
.
[5
]
Jo
h
a
n
n
e
s
A
.
G.
M
a
lh
e
rb
e
,
“
Co
rre
c
ti
o
n
to
T
h
e
De
sig
n
o
f
a
S
lo
t
A
rr
a
y
i
n
No
n
ra
d
iatin
g
Die
lec
tri
c
W
a
v
e
g
u
id
e
,
P
a
rt
I:
T
h
e
o
r
y
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
A
n
ten
n
a
s
a
n
d
P
r
o
p
a
g
a
ti
o
n
,
V
o
l.
ap
-
3
3
,
N
o
.
1
1
,
N
o
v
e
m
b
e
r
1
9
8
5
.
[6
]
T
a
i,
C.
T
.
,
“
A
n
e
w
in
terp
re
tatio
n
o
f
th
e
in
teg
ra
l
e
q
u
a
ti
o
n
f
o
rm
u
lati
o
n
o
f
c
y
li
n
d
rica
l
a
n
ten
n
a
s,”
IRE
T
ra
n
sa
c
ti
o
n
s
o
n
An
ten
n
a
s
a
n
d
Pro
p
a
g
a
t
io
n
,
1
2
5
–
1
2
7
,
1
9
5
5
.
[7
]
S
.
S
.
Ka
k
a
tk
a
r
a
n
d
K.
P
.
Ra
y
,
“N
e
a
r
f
ield
o
f
slo
t
ra
d
iato
rs
”
,
Pro
g
re
ss
In
El
e
c
tro
ma
g
n
e
ti
c
s
Res
e
a
rc
h
M
,
Vo
l.
7
,
4
1
–
5
5
,
2
0
0
9
.
[8
]
Re
n
g
a
ra
jan
,
S
.
R.
,
“
Ef
f
ici
e
n
t
a
n
d
a
c
c
u
ra
te
e
v
a
lu
a
ti
o
n
o
f
e
x
tern
a
l
m
u
tu
a
l
c
o
u
p
li
n
g
b
e
tw
e
e
n
c
o
m
p
o
u
n
d
b
ro
a
d
w
a
ll
slo
ts,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
A
n
t
e
n
n
a
s
a
n
d
Pro
p
a
g
a
ti
o
n
,
Vo
l.
4
0
,
No
.
6
,
7
3
4
–
7
3
7
,
Ju
n
e
1
9
9
2
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
Va
ib
h
a
v
S
Ya
v
a
l
k
a
r
o
b
tain
e
d
B.
E.
d
e
g
re
e
in
E
lec
tro
n
ics
a
n
d
T
e
lec
o
m
m
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
f
ro
m
Un
iv
e
rsi
t
y
o
f
M
u
m
b
a
i
in
2
0
1
1
.
H
e
is
c
u
rre
n
tl
y
p
e
rsu
in
g
M
.
E.
d
e
g
re
e
f
ro
m
V
.
E.
S
.
In
stit
u
te o
f
T
e
c
h
n
o
lo
g
y
,
Ch
e
m
b
u
r
,
M
u
m
b
a
i
.
Em
a
il
:
v
a
ib
h
a
v
y
a
v
a
lk
a
r@
y
a
h
o
o
.
i
n
Ch
a
n
d
a
n
S
i
n
g
h
D
R
a
w
a
t
c
u
rre
n
tl
y
p
u
rsu
in
g
P
h
.
D
f
ro
m
N
a
t
io
n
a
l
In
sti
tu
te
o
f
T
e
c
h
n
o
lo
g
y
,
Ro
u
rk
e
la.
He
is
w
o
rk
in
g
a
s
a
n
A
ss
o
c
iate
P
ro
f
e
ss
o
r
in
El
e
c
tro
n
ics
a
n
d
T
e
lec
o
m
m
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
De
p
a
rtm
e
n
t,
V
.
E.
S
.
In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
,
M
u
m
b
a
i,
In
d
ia.
He
h
a
s
2
0
Ye
a
rs
tea
c
h
in
g
e
x
p
e
rien
c
e
.
His a
re
a
s o
f
e
x
p
e
rti
se
a
re
sig
n
a
l
a
n
d
sy
ste
m
,
ima
g
e
p
ro
c
e
ss
in
g
.
Em
a
il
:
c
h
a
n
d
a
n
sra
wa
t@g
m
a
il
.
c
o
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
I
C
T
I
SS
N:
2
2
5
2
-
8776
Tw
o
Ter
m
A
p
p
r
o
xima
tio
n
f
o
r
N
ea
r
F
ield
A
n
a
lysi
s
…
(
V
a
ib
h
a
v
S
Ya
va
lk
a
r
)
123
S
S
K
a
k
a
t
k
a
r
o
b
tain
e
d
M
.
T
e
c
h
d
e
g
re
e
in
M
icro
w
a
v
e
En
g
in
e
e
r
in
g
f
ro
m
In
d
ian
In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
,
Kh
a
ra
g
p
u
r
in
1
9
9
1
.
He
jo
in
e
d
S
A
M
EE
R,
M
u
m
b
a
i
in
th
e
sa
m
e
y
e
a
r
a
n
d
h
a
s
b
e
e
n
w
o
rk
in
g
o
n
th
e
d
e
sig
n
o
f
d
iffere
n
t
ty
p
e
s
o
f
a
n
ten
n
a
s
f
o
r
ra
d
a
r
a
n
d
o
t
h
e
r
a
p
p
l
ica
ti
o
n
s,
m
icro
w
a
v
e
c
ircu
it
s
a
n
d
EM
I
/E
M
C.
His
in
tere
sts
in
c
lu
d
e
e
lec
tro
m
a
g
n
e
ti
c
th
e
o
ry
a
n
d
a
n
ten
n
a
a
n
a
ly
sis a
n
d
d
e
sig
n
.
Em
a
il
:
ss
k
a
k
a
t@red
iffma
il
.
c
o
m
K
P
Ra
y
o
b
tain
e
d
M
.
T
e
c
h
d
e
g
r
e
e
in
M
icro
w
a
v
e
El
e
c
tro
n
ics
f
ro
m
Un
iv
e
rsit
y
o
f
D
e
lh
i,
S
o
u
th
Ca
m
p
u
s,
in
1
9
8
5
.
He
jo
in
e
d
S
A
M
EE
R
(T
IF
R),
M
u
m
b
a
i
in
th
e
sa
m
e
y
e
a
r
a
n
d
h
a
s b
e
e
n
w
o
rk
in
g
o
n
th
e
d
e
sig
n
o
f
d
if
f
e
re
n
t
t
y
p
e
s
o
f
a
n
ten
n
a
e
lem
e
n
ts
a
n
d
a
rra
y
s,
h
ig
h
p
o
w
e
r
g
e
n
e
ra
ti
o
n
o
f
RF
a
n
d
M
icr
o
w
a
v
e
s an
d
o
th
e
r
m
icro
w
a
v
e
c
o
m
p
o
n
e
n
ts
a
n
d
sy
ste
m
s.
H
e
h
a
s su
c
c
e
ss
f
u
ll
y
c
o
m
p
lete
d
o
v
e
r
2
0
G
o
v
t.
a
n
d
In
d
u
stry
sp
o
n
so
re
d
p
r
o
jec
ts.
Cu
rre
n
tl
y
,
h
e
is
h
e
a
d
in
g
th
e
RF
a
n
d
M
icro
w
a
v
e
S
y
st
e
m
(RF
M
S
)
Div
isio
n
in
S
A
M
EE
R.
He
r
e
c
e
iv
e
d
h
is
P
h
.
D.
d
e
g
re
e
f
ro
m
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
De
p
a
rtme
n
t,
I.
I.
T
.
,
Bo
m
b
a
y
,
in
1
9
9
9
.
His
th
e
sis
w
o
rk
w
a
s
o
n
"
Bro
a
d
b
a
n
d
,
Co
m
p
a
c
t
a
n
d
Du
a
l
F
re
q
u
e
n
c
y
M
icro
strip
A
n
ten
n
a
s"
.
He
h
a
s
b
e
e
n
a
v
isit
in
g
/g
u
e
st
fa
c
u
lt
y
in
IIT
,
Bo
m
b
a
y
a
n
d
Bo
m
b
a
y
Un
iv
e
rsity
f
o
r
p
o
st
g
ra
d
u
a
te
c
o
u
rse
s.
He
h
a
s
p
u
b
li
s
h
e
d
m
o
re
th
a
n
1
9
0
re
se
a
rc
h
p
a
p
e
rs
i
n
n
a
ti
o
n
a
l/
i
n
tern
a
ti
o
n
a
l
j
o
u
r
n
a
ls
a
n
d
c
o
n
f
e
re
n
c
e
s
a
n
d
c
o
-
a
u
th
o
re
d
a
b
o
o
k
e
n
ti
tl
e
d
,
"
Bro
a
d
b
a
n
d
M
icro
strip
A
n
ten
n
a
s"
f
o
r
A
rtec
h
Ho
u
se
,
USA
in
2
0
0
3
.
He
h
a
s
b
e
e
n
a
re
v
ie
w
e
r
o
f
IET
(F
o
r
m
e
rl
y
IEE
)
,
In
tern
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
a
n
ten
n
a
s
a
n
d
P
ro
p
a
g
a
ti
o
n
(USA
),
P
IER
S
(USA
),
In
tern
a
ti
o
n
a
l
Jo
u
rn
a
l
o
f
e
lec
tro
n
ics
(USA
).
He
is
a
se
n
io
r
m
e
m
b
e
r
o
f
IEE
E
(USA
),
a
f
e
ll
o
w
IE
T
E
a
n
d
li
fe
m
e
m
b
e
r
o
f
In
stru
m
e
n
t
so
c
iet
y
o
f
In
d
ia
a
n
d
S
E
M
CEI.
He
h
a
s
f
il
e
d
f
i
v
e
n
a
ti
o
n
a
l
p
a
ten
ts.
Em
a
il
:
k
p
ra
y
@re
d
iffm
a
il
.
c
o
m
Evaluation Warning : The document was created with Spire.PDF for Python.