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.
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n
o
u
r
ap
p
r
o
ac
h
a
s
y
s
te
m
a
tic
m
a
th
e
m
atica
l
m
et
h
o
d
to
ca
lcu
late
ab
o
v
e
p
ar
am
et
er
s
.
T
h
e
s
w
i
tch
i
n
g
ac
ti
v
it
y
p
la
y
s
a
m
aj
o
r
r
o
le
in
d
y
n
a
m
ic
p
o
wer
co
n
s
u
m
p
tio
n
.
Hen
ce
i
t
is
i
m
p
o
r
ta
n
t
to
d
eter
m
in
e
α
T
w
h
ile
g
o
in
g
f
o
r
lo
w
p
o
w
er
d
es
ig
n
.
A
l
s
o
s
w
itc
h
i
n
g
ta
k
es
p
lace
at
a
ll
n
o
d
es
o
f
t
h
e
cir
c
u
it,
m
ak
in
g
it
d
i
f
f
icu
l
t
to
ca
lc
u
lat
e
all
s
w
itc
h
i
n
g
ac
ti
v
ities
s
i
m
u
lta
n
eo
u
s
l
y
.
S
w
itc
h
i
n
g
ac
ti
v
it
y
i
s
r
esp
o
n
s
ib
le
f
o
r
b
u
s
p
o
w
er
co
n
s
u
m
p
tio
n
at
th
e
n
o
d
es.
D
y
n
a
m
ic
P
o
w
er
co
n
s
u
m
p
tio
n
is
n
o
t
o
n
l
y
li
m
ited
t
o
d
esig
n
in
g
p
ar
t
i
n
VL
SI,
b
u
t
also
i
n
test
i
n
g
p
ar
t
it
is
o
f
g
r
ea
t
co
n
ce
r
n
.
A
co
n
s
id
er
ab
le
a
m
o
u
n
t
o
f
p
o
w
er
is
co
n
s
u
m
ed
w
h
ile
test
i
n
g
d
i
g
ital
cir
cu
i
ts
.
He
n
ce
lo
w
p
o
w
er
tes
tin
g
i
s
d
esire
d
s
o
lu
tio
n
.
T
h
e
d
i
f
f
er
e
n
t
s
o
lu
tio
n
s
to
r
ed
u
ce
p
o
w
er
co
n
s
u
m
p
tio
n
w
h
ile
test
i
n
g
o
f
a
d
ig
ital
cir
c
u
it
ar
e
lo
w
s
w
it
ch
in
g
test
p
atter
n
g
e
n
er
ato
r
s
.
T
h
e
lo
w
tr
an
s
itio
n
ac
tiv
it
y
is
p
r
ef
er
r
ed
in
m
e
m
o
r
y
test
i
n
g
,
d
esig
n
i
n
g
o
f
lo
w
s
w
i
tch
i
n
g
ad
d
r
ess
g
en
er
ato
r
s
,
n
e
u
r
al
n
et
w
o
r
k
s
[
7
]
.
T
h
e
r
em
ai
n
d
er
o
f
th
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
I
n
Sectio
n
1
.
1
an
d
1
.
2
w
e
d
e
s
cr
ib
e
th
e
d
ef
in
i
tio
n
s
an
d
ex
p
lai
n
t
h
e
tes
t
p
atter
n
g
e
n
er
ato
r
s
.
I
n
Sectio
n
2
,
w
e
d
i
s
cu
s
s
th
e
d
esi
g
n
m
e
th
o
d
o
lo
g
y
a
n
d
t
h
e
alg
o
r
ith
m
a
n
d
t
h
eir
r
esp
ec
ti
v
e
p
r
o
o
f
s
to
ca
lcu
late
s
w
itc
h
i
n
g
ac
ti
v
it
y
.
I
n
Sec
tio
n
3
e
x
p
l
ain
s
th
e
r
esu
lts
a
n
d
d
is
cu
s
s
io
n
o
n
tr
a
n
s
it
io
n
d
e
n
s
it
ies
o
f
p
atter
n
g
e
n
er
ato
r
an
d
tes
tin
g
t
i
m
e
r
ed
u
ctio
n
o
f
o
u
r
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
Fin
all
y
,
t
h
e
p
ap
er
is
co
n
clu
d
ed
w
ith
co
n
clu
s
io
n
i
n
Sectio
n
4
.
1
.
1
.
Def
ini
t
io
ns
So
m
e
o
f
t
h
e
d
ef
i
n
itio
n
s
r
elate
d
to
th
e
to
p
ic
ar
e
as f
o
llo
w
s
:
a.
Sig
n
al
P
r
o
b
ab
ilit
y
(
P
x
)
-
I
t
is
d
e
f
i
n
ed
as
th
e
l
ik
el
ih
o
o
d
th
at
a
s
ig
n
a
l
w
ill
h
a
v
e
th
e
lo
g
ic
v
a
lu
e
o
f
„
1
‟
.
A
Z
er
o
P
r
o
b
ab
ilit
y
(
)
m
ea
n
s
t
h
at
t
h
e
s
ig
n
a
l is al
w
a
y
s
lo
w
.
b.
T
r
an
s
itio
n
P
r
o
b
ab
ilit
y
-
I
t
i
s
d
ef
in
ed
as
t
h
e
p
r
o
b
ab
ilit
y
t
h
at
a
s
ig
n
a
l
v
a
lu
e
e
x
p
er
ien
ce
s
a
tr
a
n
s
itio
n
f
r
o
m
0
to
1
,
o
r
1
to
0
.
c.
T
o
g
g
le
d
en
s
it
y
-
I
t i
s
t
h
e
n
u
m
b
e
r
o
f
s
w
itch
e
s
p
er
u
n
i
t ti
m
e;
th
e
u
n
it i
s
g
e
n
er
all
y
o
n
e
clo
ck
c
y
cle.
d.
S
w
itch
i
n
g
A
cti
v
it
y
/
A
cti
v
it
y
f
ac
to
r
(
α
T
)
-
I
t is d
ef
i
n
ed
as th
e
m
ea
s
u
r
e
m
e
n
t o
f
ch
a
n
g
e
i
n
v
al
u
es o
f
a
s
ig
n
al.
e.
Sig
n
al
i
n
ac
ti
v
it
y
α
)
-
I
t is d
e
f
in
ed
as th
e
p
r
o
b
ab
ilit
y
t
h
at
t
h
e
s
i
g
n
al
v
al
u
e
r
e
m
ain
s
in
t
h
e
s
a
m
e
s
tate
f.
T
r
an
s
iti
o
n
Den
s
it
y
/Si
g
n
al
ac
ti
v
it
y
/No
d
e
T
r
an
s
itio
n
f
ac
to
r
(
T
D)
-
I
t
is
d
ef
i
n
ed
as
th
e
a
v
er
ag
e
s
w
itch
in
g
r
ate
at
a
cir
cu
it n
o
d
e.
T
D=
T
o
tal
n
o
o
f
b
it tr
an
s
itio
n
s
/T
o
tal
n
o
o
f
b
its
(
4
)
1
.
2
.
T
est
pa
t
t
er
n g
ener
a
t
o
rs
P
s
eu
d
o
r
an
d
o
m
b
i
n
ar
y
s
eq
u
e
n
ce
s
(
P
R
B
Ss
)
ar
e
also
k
n
o
w
n
as
p
s
eu
d
o
n
o
is
e
(
P
N)
s
eq
u
e
n
ce
s
w
h
ic
h
ar
e
ea
s
il
y
g
e
n
er
ated
b
y
r
ec
u
r
s
iv
e
p
r
o
ce
d
u
r
es,
s
u
ch
as
L
in
ea
r
Feed
b
ac
k
Sh
if
t
R
e
g
i
s
ter
(
L
FS
R
)
.
I
n
a
P
N,
th
e
n
u
m
b
er
o
f
s
ta
g
es
g
i
v
es t
h
e
s
eq
u
en
ce
le
n
g
th
(
2
n
-
1
)
w
h
ile
th
e
clo
ck
f
r
eq
u
e
n
c
y
d
ec
id
es t
h
e
b
i
t r
ate.
P
R
B
Ss
h
av
e
an
ad
v
an
ta
g
eo
u
s
f
ea
t
u
r
e
f
r
o
m
th
e
co
m
p
u
tat
io
n
al
v
ie
w
p
o
i
n
t,
an
d
th
e
y
te
n
d
to
h
a
v
e
u
s
e
f
u
l
s
t
r
u
ctu
r
al
p
r
o
p
er
ties
.
T
h
ese
s
tr
u
ct
u
r
al
p
r
o
p
er
ties
,
b
i
n
ar
y
s
eq
u
e
n
ce
s
h
a
v
e
m
a
n
y
ap
p
licatio
n
s
;
f
o
r
e
x
a
m
p
le,
Dir
ec
t
Seq
u
e
n
ce
Sp
r
e
ad
Sp
ec
tr
u
m
(
D
SS
S),
P
N
g
e
n
er
at
io
n
,
B
u
ilt
-
i
n
Sel
f
T
est (
B
I
ST
)
,
Dec
r
y
p
tio
n
–
E
n
cr
y
p
t
io
n
S
y
s
te
m
(
DE
S)
a
n
d
E
r
r
o
r
d
etec
tio
n
[
8
]
E
r
r
o
r
C
o
r
r
ec
tio
n
an
d
Dete
ctio
n
co
d
es
[
9
]
an
d
o
th
er
ap
p
licatio
n
s
in
c
l
u
d
e
Dig
ital
Si
g
n
al
P
r
o
ce
s
s
in
g
,
W
ir
eless
C
o
m
m
u
n
icatio
n
s
,
Data
I
n
te
g
r
it
y
c
h
ec
k
s
u
m
s
,
Dat
a
C
o
m
p
r
ess
io
n
,
Scr
a
m
b
ler
/d
escr
a
m
b
ler
,
Op
ti
m
ized
C
o
u
n
ter
s
[
1
0
]
-
[
1
2
]
.
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p
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Tes
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(
S
a
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ir
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s
s
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in
)
2065
T
h
e
ab
o
v
e
m
en
tio
n
ed
ap
p
lic
atio
n
s
u
s
e
th
e
b
asic
h
ar
d
w
a
r
e
o
f
L
in
ea
r
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ac
k
S
h
i
f
t
R
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ter
s
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FS
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ate
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s
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d
o
R
an
d
o
m
B
in
ar
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Seq
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e
n
ce
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P
R
B
S).
L
FS
R
co
n
s
i
s
ts
o
f
t
w
o
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ar
ts
:
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s
h
i
f
t
r
e
g
is
ter
an
d
a
f
ee
d
b
ac
k
f
u
n
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n
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a
s
s
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o
w
n
i
n
Fi
g
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r
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h
e
s
h
if
t
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eg
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ter
i
s
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ch
ai
n
s
eq
u
en
ce
o
f
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-
b
it
s
o
f
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-
t
y
p
e
o
f
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F
lo
p
s
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FF
s
)
.
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ac
h
t
i
m
e
a
n
e
w
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it is
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ir
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t b
it (
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th
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d
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h
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e
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le
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t
m
o
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s
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th
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i
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F
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h
e
o
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tp
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t
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h
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h
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a
s
h
i
f
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t
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g
t
h
o
f
t
h
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tp
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i
t
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ep
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ti
n
g
[
1
3
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,
[
1
4
]
.
T
h
e
L
i
n
ea
r
f
ee
d
b
ac
k
s
h
i
f
t
r
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g
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te
r
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m
a
k
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e
x
tr
e
m
e
l
y
g
o
o
d
P
N
s
eq
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en
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g
e
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ato
r
s
o
f
d
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m
ax
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l
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o
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ated
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h
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ad
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s
ee
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in
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all
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to
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atter
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t
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ig
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[
1
5
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.
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w
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ar
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h
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ca
n
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s
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eg
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r
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atter
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I
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ased
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late
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o
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4
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nd
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u
r
e
3
.
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w
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h
ar
t
2
.
1
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T
h
e
s
tu
d
y
p
ar
t
d
escr
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es
th
e
s
w
itc
h
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n
g
ac
tiv
i
t
y
(
S
A
)
eq
u
atio
n
s
f
o
r
d
if
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er
en
t
v
alu
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s
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SB
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d
MSB
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an
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g
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h
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atter
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h
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-
b
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r
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e
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atter
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t
h
f
o
r
m
o
f
m
atr
ix
[
A
]
,
w
h
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e
t
h
e
s
ize
o
f
m
atr
ix
[
A
]
i
s
r
x
c
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e
n
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m
b
er
o
f
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w
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d
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n
m
atr
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x
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A
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is
“
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d
“
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s
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itio
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er
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Fin
d
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d
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its
Size
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f
m
a
tr
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alcu
late
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r
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d
en
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it
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f
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ad
eq
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ate
S
A
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P
atter
n
No
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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&
C
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m
p
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g
I
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2
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8
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A
n
a
p
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to
Mea
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a
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s
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in
)
2067
b.
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h
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r
em
An
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it
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e
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atter
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i
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h
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m
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f
m
atr
ix
[
A
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w
h
er
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t
h
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ize
o
f
m
atr
ix
[
A
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s
r
x
c
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th
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m
b
er
o
f
r
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w
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d
C
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lu
m
i
n
m
atr
i
x
[
A
]
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d
“
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g
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atter
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atr
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ize
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atr
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A
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iv
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m
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f
m
atr
ix
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m
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n
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g
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it
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m
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
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0
8
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2068
3.
RE
SU
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AND
DI
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26
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27
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28
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T
r
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5
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P
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4
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n
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:0
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atin
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it
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T
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f
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al
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p
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m
p
le
m
e
n
ted
as
f
o
llo
w
in
g
e
q
u
atio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
a
p
p
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o
a
ch
to
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in
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Tes
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…
(
S
a
b
ir
Hu
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s
a
in
)
2069
SG[
0
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=
X[
0
]
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[
0
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1
]
=
X[
1
]
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[
1
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SG[
2
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=
X[
2
]
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[
2
]
…
SG[
n
-
1
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=
B
F[n
-
1
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C
[
n
-
1]
T
h
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f
iller
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c
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RE
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NC
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S
[1
]
A
h
m
a
d
,
A
,
A
l
-
M
u
sh
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f
i,
M
.
J.
a
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d
A
l
-
Bu
sa
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i,
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In
v
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o
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Co
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p
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ter
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a
n
d
El
e
c
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En
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,
2
0
0
8
,
v
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l.
34
,
pp.
2
7
0
-
280
.
[2
]
M
o
tam
a
rri
H
K,
a
n
d
L
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la
k
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m
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r
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1
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.
36
-
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[3
]
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b
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h
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ri
n
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rt
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G
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P
, “
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2
0
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1
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3
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[5
]
A.
Ka
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G.
S
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n
,
T
.
N.
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k
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d
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i
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sin
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”
,
3
r
d
IEE
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Co
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d
simu
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n
,
2
0
1
2
.
[6
]
Ba
lw
in
d
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r
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in
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h
,
A
ru
n
k
h
o
sla
,
S
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k
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lee
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Bin
d
ra
,
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ste
r(L
F
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f
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w
p
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r
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”
,
IEE
E
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n
ter
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a
t
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a
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v
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c
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c
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[7
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V
.
M
e
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.
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ti
,
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a
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sig
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g
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C
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in
a
,
2
0
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.
[9
]
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S
.
Re
d
d
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.
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u
m
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lath
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V
,
“
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n
e
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ig
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.
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Ad
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a
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s in
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C
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l
S
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ms
,
2
0
1
3
,
pp.
19
-
2
5
.
[1
0
]
Krish
n
a
,
S
a
il
a
ja
M
,
“
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o
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m
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sh
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g
isters
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o
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c
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g
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,
v
o
l
.
30
,
n
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.
1
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p
p
.
77
-
8
5
.
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2
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.
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3
]
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a
rh
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4
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C,
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n
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0
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4
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pp.
1
-
5.
[1
5
]
Du
rsu
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ra
n
,
M
u
sta
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a
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k
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,
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ss
e
in
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rim
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n
d
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ji
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G
,
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w
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A
c
ti
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lcu
latio
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f
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L
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d
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,
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,
2
0
1
0
.
[1
6
]
M
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m
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d
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b
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e
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i,
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d
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rg
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7
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8
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ter
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9
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6
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p
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7
7
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0
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m
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.
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.
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9
8
9
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ter
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8
.
[2
1
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.
H.
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rd
e
ll
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.
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M
c
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n
n
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y
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a
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il
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s
.
1
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8
7
.
[2
2
]
C.
V
.
Krish
n
a
,
A
.
Ja
s
a
n
d
N.
A
.
T
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b
a
,
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A
c
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iev
in
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o
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4
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.
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3
]
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.
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s,
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u
tze
r,
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it
e
,
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4
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.
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7
0
.
[2
5
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.
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j
m
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siti
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sity
,
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A
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sig
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,
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9
9
1
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.
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4
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-
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4
9
.
[2
6
]
A
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f
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M
o
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d
A
m
a
n
,
A
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sh
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.
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sh
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m
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d
a
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A
d
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o
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m
li
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latio
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ly
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tex
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o
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a
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d
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a
n
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o
u
rn
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l
o
f
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trica
l
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fo
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l
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5
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o
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4
,
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9
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9
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.
[2
7
]
Al
-
L
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wa
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A
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m
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,
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a
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-
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