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ad
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ec
tio
n
co
n
d
itio
n
o
n
a
clo
s
ed
cir
cle
p
ar
am
etr
ized
b
y
b
en
d
le
n
g
th
(
th
e
m
i
g
r
atio
n
f
l
y
w
a
y
)
th
at
b
eg
i
n
s
an
d
cl
o
s
es
at
t
h
e
ar
ea
w
h
er
e
f
o
w
l
s
b
r
ee
d
in
s
u
m
m
er
.
T
h
eir
m
o
d
elin
g
k
e
ep
s
t
h
e
w
i
n
g
ed
cr
ea
tu
r
es
to
g
et
h
er
a
s
a
r
u
n
,
t
h
e
p
o
s
itio
n
o
f
w
h
ich
is
ce
r
tain
l
y
d
ec
id
ed
an
d
k
n
o
w
n
f
o
r
all
f
u
t
u
r
e
ti
m
e.
B
i
r
th
s
h
ap
p
en
w
h
e
n
th
e
r
u
n
p
as
s
es
t
h
e
b
r
ee
d
in
g
ar
ea
an
d
ar
e
m
o
d
eled
u
tili
zi
n
g
th
o
u
g
h
ts
o
f
r
as
h
d
i
f
f
er
e
n
tial
c
o
n
d
itio
n
s
.
Sar
f
ar
az
[
14
]
clas
s
i
f
ied
t
h
e
p
ar
a
m
eter
s
p
ac
es
f
o
r
r
ea
ctio
n
-
d
i
f
f
u
s
io
n
f
r
a
m
e
w
o
r
k
s
o
f
t
w
o
ch
e
m
ical
s
p
ec
ies
o
n
s
tatio
n
ar
y
s
p
ac
es
i
n
ter
m
s
o
f
th
e
s
o
r
ts
a
n
d
s
o
lid
n
es
s
o
f
th
e
u
n
i
f
o
r
m
co
n
s
is
ten
t
s
tate
an
d
ir
r
itated
th
e
i
m
p
ac
t o
n
th
e
f
lo
w
o
f
t
h
e
r
e
-
ac
tio
n
-
d
i
f
f
u
s
io
n
f
r
a
m
e
w
o
r
k
.
C
h
u
n
w
e
i
[
1
5
]
d
ef
in
ed
a
p
o
s
tp
o
n
ed
r
ea
ctio
n
-
d
iff
u
s
io
n
d
e
m
o
n
s
tr
ate
t
h
at
d
ep
icts
co
m
p
etitio
n
b
et
w
ee
n
t
w
o
s
p
ec
ies
i
n
a
s
tr
ea
m
.
He
i
s
o
lates
ea
c
h
s
p
ec
ies
i
n
to
t
w
o
ch
a
m
p
er
s
,
p
eo
p
le
in
-
h
ab
iti
n
g
o
n
th
e
s
ea
b
ed
an
d
p
eo
p
le
f
lo
atin
g
w
i
th
in
t
h
e
s
t
r
ea
m
.
T
im
e
d
ela
y
s
ar
e
co
n
s
o
lid
a
ted
to
d
eg
r
ee
th
e
ti
m
e
len
g
th
s
f
r
o
m
b
ir
th
to
d
ev
elo
p
m
e
n
t
o
f
t
h
e
b
en
th
ic
p
o
p
u
lace
s
.
I
t
to
o
p
o
n
d
er
s
th
e
ele
m
en
t
s
o
f
t
h
e
n
o
n
-
s
p
atial
s
h
o
w
,
d
ec
id
e
th
e
p
r
ese
n
ce
a
n
d
w
o
r
ld
w
id
e
s
o
lid
n
ess
o
f
th
e
eq
u
ilib
r
i
u
m
,
a
n
d
g
iv
e
co
n
d
itio
n
s
b
e
n
ea
th
wh
ich
ar
r
an
g
e
m
en
t
s
m
er
g
e
to
t
h
e
b
ala
n
ce
.
A
t
t
h
at
p
o
in
t
h
e
ap
p
ea
r
s
t
h
at
t
h
e
p
r
ese
n
ce
o
f
tr
a
v
eli
n
g
w
av
e
ar
r
an
g
e
m
en
ts
ca
n
b
e
s
et
u
p
th
r
o
u
g
h
co
m
p
ac
t
f
u
n
d
a
m
e
n
tal
l
y
o
p
er
ato
r
s
.
A
t
last
,
h
e
d
efin
e
s
t
w
o
g
e
n
u
in
e
n
u
m
b
er
s
an
d
d
em
o
n
s
tr
ate
th
at
t
h
e
y
s
er
v
e
as t
h
e
lo
w
er
b
o
u
n
d
s
o
f
t
h
e
s
p
ee
d
s
o
f
tr
av
e
l
in
g
w
a
v
e
ar
r
an
g
e
m
e
n
ts
w
it
h
i
n
t
h
e
f
r
a
m
e
wo
r
k
.
R
atta
n
ak
u
l
[
1
6
]
b
u
ilt
an
ad
v
ec
tio
n
d
if
f
u
s
io
n
-
r
ea
ctio
n
m
o
d
el
d
em
o
n
s
tr
ate
f
o
r
th
e
a
n
g
l
e
p
o
p
u
lace
s
tr
u
ct
u
r
ed
to
tr
ac
k
t
h
e
p
o
p
u
la
ce
d
en
s
itie
s
o
f
b
o
th
t
h
e
lab
ele
d
an
g
le
a
n
d
t
h
e
ta
g
-
f
r
ee
a
n
g
le
,
in
w
h
ic
h
t
h
e
r
as
h
lab
el
in
g
h
o
n
e
is
j
o
in
ed
,
w
h
er
ea
s
n
o
n
s
to
p
lab
elin
g
is
ac
ce
p
t
ed
to
b
e
d
o
n
e
o
n
o
f
f
s
p
r
in
g
s
o
f
tr
ac
tab
le
lab
eled
an
g
le,
o
r
o
n
th
o
s
e
w
it
h
in
t
h
e
s
a
m
e
s
w
ar
m
as
t
h
e
tr
ac
ta
b
le
lab
eled
an
g
le.
Utilizi
n
g
th
e
tr
av
el
in
g
w
a
v
e
f
ac
ilit
ate,
th
e
y
i
n
f
er
e
x
p
lan
a
to
r
y
e
x
p
r
ess
io
n
f
o
r
th
e
ar
r
an
g
e
m
en
ts
to
t
h
e
s
h
o
w
f
r
a
m
e
w
o
r
k
.
A
l
s
o
,
th
e
y
i
n
f
er
r
ed
th
e
u
n
eq
u
iv
o
ca
l
e
x
p
r
ess
io
n
f
o
r
th
e
lev
el
o
f
lab
eled
an
g
le
w
h
ic
h
i
n
cr
e
m
e
n
ts
in
a
n
i
n
ter
m
itte
n
t
r
as
h
d
esi
g
n
.
So
lid
n
es
s
an
d
s
ta
g
e
p
lan
e
i
n
v
esti
g
a
tio
n
s
ar
e
m
o
r
eo
v
er
ca
r
r
ied
o
u
t
to
d
eter
m
i
n
e.
W
h
ile
V
en
k
atar
a
m
a
n
[
1
7
]
in
v
e
s
ti
g
ate
a
m
o
d
el
f
o
r
b
io
lo
g
ical
p
atter
n
f
o
r
m
a
tio
n
d
u
r
i
n
g
g
r
o
w
t
h
d
ev
elo
p
m
e
n
t.
T
h
e
p
atter
n
f
o
r
m
atio
n
p
h
en
o
m
e
n
o
n
i
s
d
escr
ib
ed
b
y
a
r
ea
ctio
n
-
d
i
f
f
u
s
io
n
s
y
s
te
m
o
n
a
ti
m
e
-
d
ep
en
d
en
t d
o
m
ai
n
.
B
o
o
n
r
an
g
s
i
m
a
n
et
al.
[
1
8
]
co
n
s
id
er
ed
an
ap
p
licatio
n
to
f
is
h
er
ies
an
d
ac
ce
p
ted
th
at
th
er
e
'
s
a
s
i
n
g
le
p
r
ey
p
o
p
u
lace
an
d
a
p
r
e
d
ato
r
p
o
p
u
lace
th
at
ca
n
b
e
is
o
lated
b
y
g
en
er
ati
o
n
ca
p
ac
it
y
in
to
a
y
o
u
t
h
f
u
l
a
n
d
a
d
ev
el
o
p
ar
r
an
g
e
,
w
ith
a
tim
e
d
e
lay
f
o
r
th
e
y
o
u
th
f
u
l
t
o
d
ev
e
lo
p
m
o
v
e.
T
h
ey
d
em
o
n
s
tr
at
ed
th
at
th
e
f
r
am
e
w
o
r
k
h
as
t
h
r
ee
n
o
n
n
eg
a
tiv
e
b
ala
n
ce
f
o
cu
s
e
s
,
s
p
ec
if
ica
ll
y
,
a
n
u
n
i
m
p
o
r
tan
t
p
o
in
t
w
it
h
all
p
o
p
u
lac
es
ze
r
o
,
a
p
r
ed
ato
r
-
f
r
ee
h
ar
m
o
n
y
p
o
in
t,
a
n
d
a
co
ex
is
te
n
ce
b
alan
ce
p
o
i
n
t
w
i
th
all
th
r
ee
p
o
p
u
lace
s
n
o
n
-
ze
r
o
.
I
t i
s
d
e
m
o
n
s
tr
ated
t
h
a
t
th
e
m
i
n
o
r
h
ar
m
o
n
y
p
o
in
t
is
c
o
n
tin
u
o
u
s
l
y
u
n
s
tead
y
,
t
h
at
th
e
p
r
ed
ato
r
-
f
r
ee
b
alan
ce
p
o
in
t
i
s
s
tead
y
o
n
th
e
o
f
f
ch
an
ce
t
h
at
a
n
d
as
it
w
er
e
i
n
th
e
e
v
e
n
t
t
h
at
t
h
e
e
x
is
te
n
ce
h
ar
m
o
n
y
p
o
in
t
d
o
es
n
o
t
e
x
is
t,
w
h
ic
h
t
h
e
e
x
i
s
te
n
ce
p
o
in
t
ca
n
eit
h
er
b
e
s
tead
y
f
o
r
all
ti
m
e
d
ela
y
s
o
r
e
n
d
ed
u
p
u
n
s
tead
y
i
n
t
h
e
ev
e
n
t
t
h
at
a
Ho
p
f
b
if
u
r
ca
tio
n
o
cc
u
r
s
at
a
b
asic
ti
m
e
d
ela
y
.
W
h
i
le
Z
h
an
g
[
1
9
]
ex
p
lo
r
ed
a
s
tag
e
-
s
tr
u
ctu
r
ed
p
o
s
tp
o
n
ed
r
ea
ctio
n
-
d
if
f
u
s
io
n
s
h
o
w
w
it
h
ad
v
ec
tio
n
t
h
at
d
ep
icts
co
m
p
etitio
n
b
et
w
ee
n
t
w
o
d
ev
e
l
o
p
s
p
ec
ies
in
w
ater
s
tr
ea
m
.
T
im
e
d
ela
y
s
ar
e
co
n
s
o
lid
ated
to
d
eg
r
ee
t
h
e
ti
m
e
le
n
g
t
h
s
f
r
o
m
b
ir
th
to
d
ev
e
lo
p
m
e
n
t
o
f
th
e
p
o
p
u
lace
s
.
T
h
e
y
ap
p
ea
r
th
at
t
h
er
e
ex
is
t
s
a
li
m
ited
p
o
s
iti
v
e
n
u
m
b
er
c
*
t
h
at
ca
n
b
e
c
h
ar
ac
ter
ized
as t
h
e
s
lo
w
est
s
p
r
ea
d
in
g
s
p
ee
d
o
f
tr
av
el
in
g
w
a
v
e
ar
r
an
g
e
m
en
t
s
i
n
ter
f
ac
in
g
t
w
o
m
o
n
o
-
cu
ltu
r
e
eq
u
ilib
r
ia
o
r
i
n
ter
f
ac
i
n
g
a
m
o
n
o
c
u
lt
u
r
e
w
it
h
t
h
e
co
ex
i
s
te
n
ce
h
ar
m
o
n
y
.
Mo
r
eo
v
er
,
C
an
g
ia
n
i
et
al.
[
20
]
illu
s
tr
ated
a
f
e
w
m
o
d
er
n
s
o
r
ts
o
f
w
a
v
e
p
r
o
life
r
atio
n
an
d
d
esig
n
ar
r
an
g
e
m
en
t
in
a
clas
s
ical
t
h
r
ee
s
p
ec
ies
c
y
clic
co
m
p
eti
tio
n
s
h
o
w
w
i
th
s
p
atial
d
is
s
e
m
in
a
tio
n
T
h
ese
u
n
u
s
e
d
d
esig
n
s
ar
e
ch
ar
ac
ter
ized
b
y
a
tall
n
o
r
m
alit
y
i
n
s
p
ac
e
b
u
t
ar
e
d
iv
er
s
e
f
r
o
m
d
esi
g
n
s
alr
ea
d
y
k
n
o
w
n
to
ex
i
s
t
i
n
r
ea
ctio
n
–
d
if
f
u
s
io
n
m
o
d
els
a
n
d
d
em
o
n
s
tr
ated
a
d
ep
en
d
ab
le
b
o
u
n
d
f
o
r
th
e
b
lu
n
d
er
o
f
t
h
e
n
u
m
er
ica
l
s
tr
ate
g
y
w
h
ic
h
p
er
m
it
u
s
to
ef
f
ec
ti
v
el
y
in
v
esti
g
a
te
t
h
e
d
y
n
a
m
ical
d
es
ig
n
s
i
n
b
o
th
t
w
o
a
n
d
th
r
ee
s
p
a
tial
m
ea
s
u
r
e
m
e
n
ts
.
A
t
la
s
t,
Mu
r
r
a
y
[
21
-
23
]
ex
a
m
i
n
ed
th
e
co
n
d
itio
n
f
o
r
th
e
lin
ea
r
s
tab
ilit
y
o
f
=
0
f
o
r
th
e
tak
in
g
af
ter
r
esp
o
n
s
e
d
is
s
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m
in
at
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n
d
e
m
o
n
s
tr
ate:
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(
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+
2
2
,
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≤
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(
2
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
2
6
0
-
6
2
6
7
6262
W
ith
th
e
f
o
llo
w
i
n
g
b
o
u
n
d
ar
y
an
d
in
itia
l c
o
n
d
itio
n
s
:
(
,
)
=
0
,
(
,
)
=
0
,
(
,
0
)
=
₀
(
)
,
w
h
er
e
d
en
o
tes
t
h
e
p
o
p
u
latio
n
d
en
s
it
y
o
f
a
s
p
ec
ie
s
,
(
)
is
t
h
e
s
p
ec
ies
d
y
n
a
m
ic
s
a
n
d
is
t
h
e
d
i
f
f
u
s
io
n
co
ef
f
icie
n
t
w
h
ic
h
m
ea
s
u
r
e
th
e
d
is
p
er
s
al
ef
f
icie
n
c
y
o
f
th
e
r
elev
an
t
s
p
ec
ie
s
,
is
th
e
len
g
t
h
o
f
th
e
d
o
m
ai
n
.
He
co
n
s
id
er
ed
th
e
d
i
f
f
er
en
t
b
o
u
n
d
ar
y
co
n
d
itio
n
s
w
h
ic
h
c
o
n
s
id
er
th
e
i
n
f
l
u
en
ce
o
f
t
h
e
r
eg
io
n
e
x
ter
io
r
to
th
e
r
ea
ctio
n
d
i
f
f
u
s
io
n
d
o
m
ai
n
.
He
s
h
o
w
ed
th
a
t
i
f
th
e
d
o
m
ai
n
s
iz
e
i
s
n
o
t
lar
g
e
e
n
o
u
g
h
,
t
h
en
(
2
)
ca
n
n
o
t
g
en
er
ate
s
p
atia
l p
atter
n
s
a
n
d
s
o
h
e
f
o
u
n
d
th
e
co
n
d
itio
n
o
n
s
u
ch
t
h
at
t
h
e
s
p
ec
ies
w
i
ll n
o
t b
ec
o
m
e
e
x
ti
n
ct
i
f
:
>
√
′
(
0
)
I
n
th
i
s
p
ap
er
,
an
ag
e
-
s
tr
u
ct
u
r
ed
m
o
d
el
is
u
s
ed
t
o
d
er
iv
e
a
d
elay
ad
v
ec
tio
n
r
ea
ctio
n
-
d
i
f
f
u
s
io
n
eq
u
atio
n
w
it
h
lin
ea
r
ad
v
ec
tio
n
ter
m
.
I
n
ad
d
itio
n
,
w
e
f
i
n
d
th
e
m
in
i
m
u
m
v
alu
e
o
f
th
at
p
r
ev
en
ts
e
x
ti
n
cti
o
n
o
f
th
e
s
p
ec
ie
s
u
n
d
er
th
e
e
f
f
ec
t o
f
ad
v
ec
t
io
n
t
er
m
f
o
r
th
e
r
ea
ctio
n
-
d
i
f
f
u
s
io
n
eq
u
atio
n
.
2.
A
DE
L
AY
ADV
E
C
T
I
O
N
R
E
AC
T
I
O
N
-
DIFF
U
SI
O
N
E
Q
UATI
O
N
W
I
T
H
L
I
NE
AR
ADVEC
T
I
O
N
T
E
RM
I
n
th
i
s
s
ec
tio
n
,
w
e
d
er
iv
e
a
d
ela
y
ad
v
ec
tio
n
r
ea
ctio
n
-
d
i
f
f
u
s
io
n
eq
u
atio
n
w
i
th
li
n
ea
r
ad
v
e
ctio
n
ter
m
f
r
o
m
a
n
ag
e
-
s
tr
u
ct
u
r
ed
m
o
d
el,
an
d
th
en
la
ter
o
n
,
w
e
s
t
u
d
y
an
d
an
al
y
ze
o
u
r
n
e
w
m
o
d
el
u
n
d
er
th
e
e
f
f
ec
t
o
f
th
e
ad
v
ec
tio
n
ter
m
.
De
f
i
n
e
(
,
)
to
b
e
th
e
in
te
n
s
i
t
y
o
f
m
at
u
r
e
ad
u
lts
,
w
it
h
ag
e
o
f
at
least
τ
.
T
h
en
it
ca
n
b
e
r
ep
r
esen
ted
as f
o
llo
w
s
:
(
,
)
=
∫
(
,
,
)
∞
,
(
3
)
w
h
er
e
(
,
,
)
is
th
e
in
ten
s
it
y
o
f
in
d
i
v
id
u
al
s
o
f
ag
e
at
p
o
in
t
,
tim
e
an
d
is
th
e
len
g
t
h
o
f
th
e
j
u
v
en
ile
p
er
io
d
.
N
o
w
,
let
s
atis
f
ie
s
th
e
f
o
llo
w
i
n
g
eq
u
a
tio
n
,
s
ee
Me
tz
[
2
4
]
an
d
Mc
Nair
[
2
5
]
:
+
=
+
2
2
−
,
0
<
<
,
(
4
)
an
d
th
at
t
h
e
m
a
tu
r
e
ev
o
l
v
e
ac
c
o
r
d
in
g
to
:
=
+
2
2
+
(
,
,
)
−
2
,
∈
(
−
∞
,
∞
)
,
>
0
(5
)
w
it
h
(
,
,
0
)
=
(
(
,
)
)
(6
)
th
e
ter
m
(
,
,
)
in
(
5
)
r
ep
r
esen
ts
ad
u
lt
r
ec
r
u
it
m
e
n
t,
s
i
n
ce
it
is
t
h
o
s
e
o
f
ag
e
(
m
at
u
r
atio
n
a
g
e)
an
d
(
)
in
(
6
)
r
ef
er
s
to
th
e
r
ar
e
o
f
th
e
b
ir
th
,
s
u
p
p
o
s
ed
to
d
ep
en
d
o
n
ly
o
n
t
h
e
n
u
m
b
er
o
f
m
at
u
r
es a
t
th
e
ti
m
e.
L
et
(
,
,
)
=
(
,
+
,
)
,
th
en
=
[
(
,
,
)
+
(
,
,
)
]
=
+
=
(
,
+
,
)
+
2
2
(
,
+
,
)
−
(
,
+
,
)
,
w
h
ic
h
i
m
p
lie
s
=
+
2
2
−
+
=
+
2
2
−
,
0
<
<
,
(7
)
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
s
ta
g
e
-
s
tr
u
ctu
r
ed
d
ela
ye
d
a
d
ve
ctio
n
r
ea
ctio
n
-
d
iffu
s
io
n
m
o
d
el
fo
r
s
in
g
le
s
p
ec
ies
(
R
a
ed
A
li A
lkh
a
s
a
w
n
eh
)
6263
No
w
,
w
e
ap
p
l
y
t
h
e
Fo
u
r
ier
tr
an
s
f
o
r
m
:
̂
(
,
,
)
=
∫
(
,
,
)
−
∞
−
∞
(8
)
T
o
(
8
)
g
iv
es:
̂
=
(
−
²
−
)
̂
(9
)
a
nd
̂
(
,
,
0
)
=
̂
(
,
,
0
)
=
ℱ
{
(
(
,
)
)
}
(
1
0
)
T
h
e
s
o
lu
tio
n
o
f
(
9
)
is
:
̂
(
,
,
)
=
ℱ
{
(
(
,
)
)
}
(
−
²
−
)
.
(
1
1
)
No
w
,
ℱ⁻
¹
(
(
−
²
−
)
)
=
1
2
(
−
²
−
)
=
−
√
4
−
(
+
)
²
/
(
4
)
.
B
y
u
s
i
n
g
co
n
v
o
lu
tio
n
th
eo
r
e
m
:
(
,
,
)
=
−
∫
1
√
4
∞
−
∞
−
(
+
−
)
2
4
(
(
,
)
)
,
T
h
er
ef
o
r
e
(
,
,
)
=
(
,
−
,
)
=
−
∫
1
√
4
∞
−
∞
−
(
+
−
)
2
4
(
(
,
−
)
)
.
(
1
2
)
I
f
(
)
=
,
th
en
th
e
b
ir
th
r
ate
is
s
y
m
m
etr
ic
to
th
e
n
u
m
b
er
o
f
th
e
m
atu
r
e
ad
u
lts
g
i
v
e
n
b
y
.
Mo
s
t
o
f
th
e
p
o
p
u
latio
n
s
,
s
u
ch
p
r
es
u
m
p
tio
n
is
v
alid
o
n
l
y
w
h
e
n
p
o
p
u
latio
n
n
u
m
b
er
s
ar
e
r
elativ
el
y
litt
le
o
r
w
h
en
t
h
er
e
is
ab
u
n
d
an
ce
o
f
n
o
u
r
i
s
h
m
e
n
t.
I
n
s
er
tin
g
(
1
2
)
w
it
h
(
)
=
in
to
(
4
)
y
ie
l
d
s
:
=
+
2
2
−
2
+
∝
−
∫
1
√
4
∞
−
∞
−
(
+
−
)
2
4
(
,
−
)
(
1
3
)
B
y
ap
p
l
y
i
n
g
t
h
e
f
o
llo
w
i
n
g
s
u
b
s
tit
u
tio
n
i
n
(
1
3
)
:
+
−
=
√
4
,
w
e
o
b
tain
:
−
∫
1
√
4
∞
−
∞
−
(
+
−
)
2
4
(
,
−
)
=
−
∫
1
√
∞
−
∞
−
2
(
+
−
√
4
,
−
)
.
(
1
4
)
T
h
is
f
o
r
m
o
f
th
e
in
te
g
r
al
allo
w
s
u
s
to
m
a
k
e
ap
p
r
o
x
i
m
a
tio
n
f
o
r
s
m
a
ll
v
a
lu
e
s
o
f
t
h
e
p
ar
a
m
e
ter
s
.
L
et
u
s
ap
p
r
o
x
im
a
te
(
1
4
)
f
o
r
s
m
al
l v
al
u
es o
f
t
h
e
i
m
m
atu
r
e
d
i
f
f
u
s
iv
i
t
y
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
2
6
0
-
6
2
6
7
6264
(
+
−
√
4
,
−
)
=
(
+
,
−
)
−
√
4
(
+
,
−
)
+
2
2
2
2
(
+
,
−
)
T
h
e
r
ef
o
r
e,
th
e
in
teg
r
al
ter
m
i
n
(
1
4
)
c
an
b
e
w
r
itte
n
as f
o
llo
w
s
:
−
∫
1
√
∞
−
∞
−
2
(
(
+
−
√
4
,
−
)
)
=
−
(
+
,
−
)
+
−
2
2
(
+
,
−
)
)
,
(
1
5
)
w
h
er
e
w
e
h
a
v
e
u
s
ed
th
e
f
o
llo
w
i
n
g
f
ac
t
:
∫
²
−
2
=
1
2
√
∞
−
∞
.
I
n
th
e
li
m
it
in
g
ca
s
e
→
0
(
i.e
.
,
im
m
at
u
r
es n
o
t d
i
f
f
u
s
in
g
at
all)
,
(
1
3
)
b
ec
o
m
es:
=
+
2
2
+
−
(
+
,
−
)
−
2
(
1
6
)
I
n
th
is
ca
s
e
=
0
,
th
e
ter
m
−
(
+
,
−
)
ca
n
b
e
u
n
d
er
s
to
o
d
ec
o
lo
g
icall
y
as
f
o
llo
w
s
:
Settin
g
=
0
m
ea
n
s
t
h
e
i
m
m
at
u
r
e
ar
e
n
o
t
d
if
f
u
s
i
n
g
.
T
h
e
y
ar
e,
h
o
w
e
v
er
,
s
till
s
u
b
j
ec
t
to
ad
v
ec
t
io
n
.
Du
r
i
n
g
th
e
p
er
io
d
o
f
i
m
m
atu
r
it
y
,
w
h
ich
is
o
f
d
u
r
atio
n
,
ea
ch
i
m
m
atu
r
e
w
ill
h
av
e
m
o
v
ed
a
d
is
t
an
ce
eq
u
al
to
.
I
t
f
o
llo
w
s
th
at
an
in
d
i
v
id
u
a
l
t
h
at
b
ec
o
m
es
m
at
u
r
e
at
lo
c
atio
n
x
m
u
s
t
h
a
v
e
b
ee
n
b
o
r
n
a
t
lo
ca
tio
n
+
(
s
in
ce
th
e
ad
v
ec
tio
n
is
f
r
o
m
r
i
g
h
t
to
lef
t)
.
T
h
e
ter
m
:
−
(
+
,
−
)
,
w
h
ic
h
is
th
e
r
ate
at
tim
e
,
p
o
s
itio
n
,
at
w
h
ic
h
i
n
d
iv
id
u
als
b
ec
o
m
e
m
atu
r
e,
is
g
iv
e
n
s
i
m
p
l
y
b
y
t
h
e
b
ir
th
r
ate
ti
m
e
u
n
i
t
s
ag
o
at
l
o
ca
tio
n
+
,
(
+
,
−
)
,
co
r
r
ec
ted
f
o
r
j
u
v
en
ile
m
o
r
tal
it
y
w
h
ic
h
e
x
p
lain
s
t
h
e
−
f
ac
to
r
.
I
f
th
e
s
p
ec
ies
i
s
clo
s
e
to
ex
ti
n
ctio
n
a
n
d
th
e
i
m
m
a
t
u
r
e
ar
e
n
o
t d
if
f
u
s
in
g
,
t
h
en
(
1
6
)
b
ec
o
m
es:
=
+
2
2
+
−
(
+
,
−
)
,
0
<
<
,
>
0
.
(
1
7
)
3.
E
F
F
E
C
T
O
F
AD
VE
C
T
I
O
N
T
E
RM
O
N
T
H
E
D
E
R
I
V
E
D
D
E
L
AY
AD
VE
C
T
I
O
N
RE
AC
T
I
O
N
-
DIFF
USI
O
N
E
Q
UA
T
I
O
N
Star
tin
g
b
y
s
tu
d
y
in
g
(
1
7
)
o
n
h
o
m
o
g
en
eo
u
s
Dir
ich
let
b
o
u
n
d
ar
y
co
n
d
itio
n
s
:
(
0
,
)
=
0
,
(
,
)
=
0
,
an
d
th
e
in
itia
l
co
n
d
itio
n
(
,
0
)
=
0
(
)
,
∈
[
−
,
0
]
w
i
th
0
(
0
)
>
0
.
As
a
s
tar
tin
g
p
o
in
t,
w
e
s
h
all
a
ls
o
co
n
s
id
er
t
h
e
ca
s
e
w
h
en
t
h
e
j
u
v
en
i
les
ar
e
n
o
t
s
u
b
j
ec
t
to
ad
v
ec
tio
n
,
in
t
h
is
ca
s
e,
th
e
ter
m
(
+
,
−
)
o
f
(
1
6
)
b
ec
o
m
e
s
:
−
(
,
−
)
.
Ho
w
e
v
er
,
th
e
ad
u
l
ts
w
ill
s
till
b
e
s
u
b
j
ec
t
to
ad
v
ec
tio
n
.
Seek
i
n
g
tr
ia
l so
lu
t
io
n
s
f
o
r
(
1
6
)
o
f
th
e
f
o
r
m
(
,
)
=
στ
(
)
,
y
ield
s
:
′′
(
)
+
′
−
−
−
)
(
)
=
0
(
1
8
)
T
h
e
ch
ar
ac
ter
is
tic
eq
u
atio
n
f
o
r
(
1
8
)
is
²
+
+
(
−
−
−
)
=
0
(
1
9
)
an
d
th
e
r
o
o
ts
ar
e
g
iv
e
n
b
y
:
₁
,
₂
=
1
2
(
−
±
(
√
2
−
4
(
−
−
−
)
)
T
h
u
s
,
w
e
h
a
v
e
t
w
o
ca
s
es
f
o
r
th
e
r
o
o
ts
:
I
f
₁
an
d
₂
ar
e
r
ea
l,
th
en
th
e
s
o
lu
t
i
o
n
f
o
r
s
atis
f
y
in
g
t
h
e
b
o
u
n
d
ar
y
co
n
d
itio
n
(
0
)
=
0
w
il
l b
e
in
th
e
f
o
r
m
(
)
=
(
₁
−
2
)
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
s
ta
g
e
-
s
tr
u
ctu
r
ed
d
ela
ye
d
a
d
ve
ctio
n
r
ea
ctio
n
-
d
iffu
s
io
n
m
o
d
el
fo
r
s
in
g
le
s
p
ec
ies
(
R
a
ed
A
li A
lkh
a
s
a
w
n
eh
)
6265
an
d
in
o
r
d
er
to
s
atis
f
y
(
)
=
0
,
w
e
w
i
l
l h
av
e
t
h
e
ze
r
o
s
o
lu
tio
n
.
I
f
M₁
an
d
M₂
ar
e
co
m
p
lex
,
t
h
en
th
e
s
o
lu
tio
n
f
o
r
(
)
s
atis
f
y
in
g
th
e
b
o
u
n
d
ar
y
co
n
d
itio
n
(
0
)
=
0
w
il
l b
e
o
f
th
e
f
o
r
m
(
)
=
(
−
2
)
(
√
4
(
−
−
−
)
−
²
2
)
.
(
2
0
)
I
n
o
r
d
er
to
b
e
ab
le
to
s
atis
f
y
(
)
=
0
,
w
e
n
ee
d
:
√
(
4
(
−
−
−
)
−
²
)
2
=
,
=
1
,
2
,
3
,
…
.
T
h
at
is
:
4
(
−
−
−
)
−
2
=
4
2
2
2
2
,
=
1
,
2
,
3
,
…
,
w
h
ic
h
g
i
v
es t
h
e
f
o
llo
w
in
g
eq
u
atio
n
to
b
e
s
o
lv
ed
f
o
r
:
=
−
−
−
²
4
−
²
²
²
(
2
1
)
T
h
e
s
o
lu
tio
n
(
,
)
o
f
th
e
li
n
ea
r
ized
(
1
7
)
is
o
f
th
e
f
o
llo
w
in
g
f
o
r
m
(
,
)
=
−
2
(
)
,
=
1
,
2
,
3
,
…
,
w
h
er
e
s
atis
f
ie
s
(
2
0
)
.
No
w
,
w
e
ar
e
g
o
i
n
g
to
f
in
d
th
e
s
o
l
u
tio
n
o
f
(
1
7
)
s
atis
f
y
i
n
g
t
h
e
i
n
itial
d
ata
b
y
s
u
m
m
i
n
g
o
v
er
to
o
b
tain
:
(
,
)
=
∑
∞
=
1
−
2
(
)
,
(
2
2
)
w
h
er
e
s
atis
f
ies
(
2
1
)
an
d
u
s
in
g
t
h
e
in
itia
l
co
n
d
itio
n
an
d
Fo
u
r
ier
co
ef
f
icie
n
t
s
,
th
en
t
h
e
v
alu
e
o
f
is
g
iv
e
n
b
y
:
{
}
=
2
∫
0
(
)
2
(
)
0
,
=
1
,
2
,
3
,
…
(
2
3
)
Su
b
s
ti
tu
t
in
g
t
h
is
v
alu
e
i
n
(
2
2
)
y
ield
s
t
h
e
f
i
n
al
s
o
lu
tio
n
o
f
t
h
e
lin
ea
r
ized
p
r
o
b
lem
:
(
,
)
=
∑
(
2
∫
0
(
)
2
(
)
×
0
∞
=
1
−
2
(
)
(
2
4
)
T
h
e
p
o
p
u
latio
n
w
ill
d
ec
a
y
to
ze
r
o
if
<
0
,
f
o
r
all
=
1
,
2
,
3
,
…
,
w
h
er
e
is
an
y
r
o
o
t
o
f
(
2
1
)
.
I
n
o
th
er
w
o
r
d
s
,
s
atis
f
ies:
=
−
−
−
2
2
2
−
²
4
I
n
o
r
d
er
t
o
d
etec
t
a
p
o
s
s
ib
le
ch
an
g
e
o
f
li
n
ea
r
s
tab
ilit
y
o
f
th
e
ze
r
o
s
o
lu
tio
n
o
f
(
1
7
)
w
e
s
et
=
,
w
h
ic
h
g
i
v
es
:
2
4
+
2
2
2
+
=
−
−
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
2
6
0
-
6
2
6
7
6266
an
d
th
e
co
m
p
le
x
co
n
j
u
g
a
te
o
f
ab
o
v
e
eq
u
atio
n
is
:
2
4
+
2
2
2
−
=
−
,
T
h
u
s
,
w
e
ar
e
eli
m
i
n
ati
n
g
−
f
r
o
m
th
e
last
t
w
o
eq
u
at
io
n
s
,
y
ield
s
:
²
=
²
−
2
−
[
2
4
+
2
2
2
]
²
.
T
o
f
in
d
th
e
co
n
d
itio
n
s
o
n
th
e
p
ar
am
eter
s
w
h
ich
e
n
s
u
r
e
t
h
a
t:
²
<
0
,
s
i
n
ce
th
is
m
ea
n
s
t
h
at
r
o
o
ts
o
f
(
2
1
)
o
f
th
e
f
o
r
m
=
,
w
i
th
r
ea
l
,
ca
n
n
o
t
ex
i
s
t.
No
te
th
at:
I
f
²
<
0
w
h
e
n
n
=1
th
e
n
au
to
m
atica
l
l
y
²
<
0
f
o
r
n
=2
,
3
,
4
,
…,
th
er
e
f
o
r
e
it
is
s
u
f
f
icie
n
t
to
s
et
=
1
.
W
h
en
=
1
,
²
<
0
an
d
if
th
e
f
o
llo
w
i
n
g
in
eq
u
ali
t
y
h
o
ld
s:
−
<
2
4
+
2
2
th
en
(
,
)
→
0
as
→
0
,
th
u
s
th
e
p
o
p
u
latio
n
w
il
l
b
ec
o
m
e
ex
ti
n
ct.
So
,
th
e
s
p
ec
ies
w
il
l
b
ec
o
m
e
ex
ti
n
ct
i
n
th
is
ca
s
e
if
:
(
ad
v
ec
tio
n
s
p
ee
d
)
is
lar
g
e
(
m
a
tu
r
e
d
if
f
u
s
io
n
)
is
eit
h
er
v
e
r
y
s
m
all
o
r
v
er
y
lar
g
e
(
len
g
t
h
o
f
d
o
m
ai
n
)
is
s
m
al
l
(
b
ir
th
r
ate)
is
to
o
s
m
al
l
(
j
u
v
en
ile
m
o
r
tal
it
y
)
i
s
lar
g
e
(
len
g
t
h
o
f
j
u
v
e
n
ile
p
er
io
d
)
is
lar
g
e.
A
l
s
o
,
if
t
h
e
f
o
llo
w
i
n
g
in
eq
u
ali
t
y
h
o
ld
s
:
−
>
2
4
+
2
2
,
th
en
=
−
−
−
2
2
2
−
²
4
w
it
h
=
1
h
as
a
r
ea
l
p
o
s
iti
v
e
r
o
o
t
.
T
h
is
ca
n
b
e
s
h
o
w
n
b
y
d
r
a
w
i
n
g
th
e
g
r
ap
h
s
o
f
2
4
+
2
2
+
an
d
−
−
ag
ain
s
t
,
w
h
er
e
w
e
ca
n
s
ee
th
at
t
h
e
t
w
o
f
u
n
ct
io
n
s
h
a
v
e
a
r
ea
l
p
o
s
itiv
e
r
o
o
t
σ
w
h
ich
m
ea
n
s
t
h
at
th
e
ze
r
o
s
o
lu
tio
n
o
f
(
1
7
)
is
u
n
s
tab
le.
So
,
w
e
ca
n
co
n
c
lu
d
e
t
h
at
th
e
p
o
p
u
latio
n
w
il
l s
u
r
v
i
v
e
in
th
is
ca
s
e
if
(
ad
v
ec
tio
n
s
p
ee
d
)
is
to
o
s
m
all
.
(
d
o
m
ai
n
)
is
to
o
lar
g
e
.
(
b
ir
th
r
ate)
is
to
o
lar
g
e.
4.
DIS
CU
SS
I
O
N
S
A
ND
CO
NC
L
US
I
O
N
W
e
h
av
e
d
er
iv
ed
a
d
elay
ad
v
ec
tio
n
r
ea
ctio
n
-
d
i
f
f
u
s
io
n
eq
u
a
tio
n
w
ith
li
n
ea
r
ad
v
ec
tio
n
ter
m
f
r
o
m
a
n
ag
e
-
s
tr
u
c
tu
r
ed
m
o
d
el
w
h
ich
i
s
g
iv
e
n
b
y
:
=
+
2
2
+
−
(
+
,
−
)
−
2
(
2
5
)
an
d
o
u
r
d
er
iv
ed
eq
u
atio
n
as
in
(
2
4
)
is
s
t
u
d
ied
w
h
e
n
t
h
e
s
p
ec
i
es is
clo
s
e
to
e
x
ti
n
ctio
n
a
n
d
th
e
i
m
m
at
u
r
e
ar
e
n
o
t
d
if
f
u
s
in
g
o
n
h
o
m
o
g
en
eo
u
s
Dir
ich
let
b
o
u
n
d
ar
y
co
n
d
itio
n
s
(
0
,
)
=
0
,
(
,
)
=
0
an
d
th
e
in
it
ial
co
n
d
itio
n
(
,
0
)
=
0
≥
0
f
o
r
∈
[
−
,
0
]
.
A
l
s
o
,
w
e
co
n
s
id
er
ed
th
e
ca
s
e
w
h
en
j
u
v
en
i
les
a
r
e
n
o
t
s
u
b
j
ec
t
to
ad
v
ec
tio
n
,
s
o
th
e
ter
m
(
+
,
−
)
in
(
2
4
)
b
ec
o
m
e
s
(
,
−
)
.
Ho
w
ev
er
,
th
e
a
d
u
lts
w
ill
s
till
b
e
s
u
b
j
ec
t
to
ad
v
ec
tio
n
.
T
h
e
co
n
d
itio
n
s
o
n
t
h
e
p
ar
a
m
eter
s
f
o
r
th
e
f
in
al
s
o
lu
tio
n
(
,
)
f
o
r
th
e
lin
e
ar
ized
(
2
5
)
th
at
p
r
ev
en
ts
ex
tin
ct
io
n
o
f
t
h
e
s
p
ec
ies
u
n
d
er
th
e
d
ef
ec
t
o
f
ad
v
ec
tio
n
f
o
r
th
e
r
ea
ctio
n
-
d
i
f
f
u
s
io
n
ar
e
f
o
u
n
d
s
,
w
h
er
e
th
e
co
n
c
lu
s
io
n
ca
n
b
e
s
u
m
m
ar
ized
as
f
o
llo
w
s
:
T
h
e
s
p
ec
ies
w
ill
b
ec
o
m
e
e
x
ti
n
ct
i
f
t
h
e
ad
v
ec
tio
n
s
p
ee
d
i
f
l
ar
g
e,
m
at
u
r
e
d
if
f
u
s
io
n
is
e
ith
er
v
er
y
s
m
al
l
o
r
v
er
y
lar
g
e,
le
n
g
th
o
f
d
o
m
ai
n
is
s
m
all,
j
u
v
en
i
le
m
o
r
talit
y
is
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[1
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Brit
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1
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[2
]
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e
w
is,
M
.
,
P
e
tro
v
sk
ii
,
S
.
,
P
o
tt
s,
J.,
“
Re
a
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ti
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D
if
f
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sio
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o
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e
ls:
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in
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le
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p
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ies
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h
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M
a
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ma
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Bi
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In
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69
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.
[3
]
A
ll
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n
,
L
.
,
“
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ies
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d
if
f
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sio
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m
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e
ls,”
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ll
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[4
]
A
iello
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.
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.
a
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d
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re
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m
a
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,
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I.
,
“
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ti
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sin
g
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ro
w
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tu
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.
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o
sc
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[5
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ish
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r,
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.
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“
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ics
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l
.
7
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p
.
3
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3
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9
,
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.
[6
]
Ko
lm
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g
o
ro
v
,
A
.
P
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tro
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sk
ii
,
I.
a
n
d
P
isc
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u
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o
v
,
N.,
“
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stu
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y
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f
th
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iffu
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q
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ti
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n
to
a
b
io
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ica
l
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ro
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lem
,”
In
V
.
M
.
T
ik
h
o
m
iro
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iv
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[7
]
F
ish
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A
.
,
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[8
]
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u
rn
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y
,
W
.
S.
C.
a
n
d
Nisb
e
t,
R.
M.,
“
F
lu
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ti
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icity
,
g
e
n
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ra
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f
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n
,
”
J
.
T
h
e
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re
ti
c
a
l
Po
p
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l.
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o
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,
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.
[9
]
A
b
lo
w
it
z
,
M
.
J.
a
n
d
Ze
p
p
e
tella,
A
.
,
“
Ex
p
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F
ish
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a
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sp
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ial
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a
v
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d
,”
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l
l.
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a
th
.
Bi
o
l.
,
v
o
l.
4
1
,
p
p
.
8
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5
-
8
4
0
,
1
9
7
9
.
[1
0
]
Al
-
O
m
a
ri
,
J.
F
.
M
.
a
n
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G
o
u
rley
S
.
A
.
,
“
A
n
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tu
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d
d
istr
ib
u
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m
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tu
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ti
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e
lay
,
”
Eu
ro
.
J
.
Ap
p
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M
a
th
.
,
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1
]
Al
-
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ri,
J.,
G
o
u
rley
,
S
.
,
“
D
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ics
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,”
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r A
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2
]
A
iello
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W
.
G
.
,
F
re
e
d
m
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n
,
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I.
a
n
d
W
u
,
J.
,
“
A
n
a
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y
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m
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h
sta
te
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d
e
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d
e
n
t
ti
m
e
d
e
la
y
,”
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IAM
J
.
A
p
p
l
.
M
a
th
.
,
v
o
l
.
5
2
,
p
p
.
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5
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9
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9
9
2
.
[1
3
]
G
o
u
rle
y
,
S
.
A
.
,
J
e
n
n
in
g
s
,
R.
a
n
d
L
iu
,
R.
,
“
A
n
A
d
v
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ti
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n
d
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g
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tru
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tu
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p
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ro
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o
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ig
ra
ti
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n
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In
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irec
t
T
ra
n
sm
issio
n
o
f
Av
i
a
n
In
f
lu
e
n
z
a
,”
S
IAM
J
.
A
p
p
l
.
M
a
t
h
.
,
v
o
l
.
7
5
,
n
o
.
4
,
p
p
.
1
6
2
0
-
1
6
4
7
,
2
0
0
5
.
[1
4
]
S
a
rf
a
r
a
z
W
,
M
a
d
z
v
a
m
u
se
A
.
,
“
Clas
sifi
c
a
ti
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n
o
f
p
a
ra
m
e
ter
sp
a
c
e
s
f
o
r
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re
a
c
ti
o
n
d
if
f
u
sio
n
m
o
d
e
l
o
n
sta
ti
o
n
a
ry
d
o
m
a
in
s
,
”
Ch
a
o
s
S
o
li
t
o
n
s F
r
a
c
ta
l
s,
v
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l.
1
0
3
,
p
p
.
3
3
-
5
1
,
2
0
0
7
.
[1
5
]
Ch
u
n
w
e
i
W
.
,
“
A
sta
g
e
-
stru
c
tu
re
d
d
e
lay
e
d
re
a
c
ti
o
n
-
d
if
f
u
sio
n
m
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l
f
o
r
A
sta
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stru
c
tu
re
d
d
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la
y
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d
re
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d
if
f
u
sio
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r
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o
m
p
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ti
ti
o
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b
e
tw
e
e
n
tw
o
sp
e
c
ies
,
”
El
e
c
tro
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ic
T
h
e
se
s
a
n
d
Diss
e
rtatio
n
s
,
Un
iv
e
rsity
o
f
L
o
u
isv
il
le,
2
0
1
3
.
[1
6
]
Ra
tt
a
n
a
k
u
l
,
C.
,
L
e
n
b
u
ry
,
Y.
a
n
d
S
u
k
sa
m
ra
n
,
J.,
“
A
n
a
l
y
sis
o
f
a
d
v
e
c
ti
o
n
-
d
if
f
u
sio
n
-
re
a
c
ti
o
n
m
o
d
e
l
f
o
r
f
ish
p
o
p
u
latio
n
m
o
v
e
m
e
n
t
w
it
h
im
p
u
lsiv
e
tag
g
i
n
g
:
sta
b
il
it
y
a
n
d
trav
e
li
n
g
w
a
v
e
so
lu
ti
o
n
,”
A
d
v
a
n
c
e
s
i
n
Diff
e
re
n
c
e
Eq
u
a
ti
o
n
s
,
v
o
l.
2
0
1
9
,
2
0
1
9
.
[1
7
]
V
e
n
k
a
tara
m
a
n
,
C.
,
“
Re
a
c
ti
o
n
-
d
if
f
u
sio
n
s
y
ste
m
o
n
e
v
o
lv
in
g
d
m
a
i
n
s
w
it
h
a
p
p
li
c
a
ti
o
n
s
to
th
e
th
e
o
r
y
o
f
b
io
lo
g
ica
l
p
a
tt
e
rn
f
o
rm
a
ti
o
n
,”
P
h
.
D
.
th
e
sis,
Un
iv
e
rsit
y
o
f
S
u
ss
e
x
,
2
0
1
1
.
[
1
8
]
B
o
o
n
r
a
n
g
s
i
m
a
n
,
S
.
,
B
u
n
w
o
n
,
K
.
a
n
d
E
l
v
i
n
,
J
.
,
“
A
b
i
f
u
r
c
a
t
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a
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m
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u
r
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n
d
m
a
t
u
r
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p
r
e
d
a
t
o
r
s
,”
M
a
t
h
.
C
o
m
p
u
t
e
r
s
S
i
m
u
l
.
,
v
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l
.
124
,
p
p
.
1
6
-
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9
,
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.
[1
9
]
Zh
a
n
g
,
L
.
a
n
d
Zh
a
o
,
H.
Y.,
“
T
ra
v
e
li
n
g
w
a
v
e
so
lu
ti
o
n
s
in
a
sta
g
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stru
c
tu
re
d
d
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lay
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re
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ti
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d
if
f
u
s
io
n
m
o
d
e
l
w
it
h
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d
v
e
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ti
o
n
,”
J
.
M
a
t
h
.
M
o
d
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ll
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g
A
n
a
l.
,
v
o
l.
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o
.
2
,
p
p
.
1
6
8
-
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8
7
,
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0
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5
.
[2
0
]
Ca
n
g
ian
i
,
A
.
,
G
e
o
rg
o
u
li
s
,
E.
,
M
o
ro
z
o
v
,
A
.
a
n
d
S
u
tt
o
n
O
.
,
“
Re
v
e
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li
n
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n
e
w
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y
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a
m
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a
l
p
a
tt
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in
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re
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d
if
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w
it
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y
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li
c
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p
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ti
ti
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v
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o
v
e
l
c
o
m
p
u
tatio
n
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l
f
ra
m
e
w
o
rk
,
”
P
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.
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.
[2
1
]
M
u
rra
y
,
J.
D.,
“
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a
ti
c
a
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Bio
lo
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2
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9
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.
[2
2
]
M
u
rra
y
,
J.
D.,
“
M
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io
lo
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,”
I.
An
in
tro
d
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c
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n
.
3
rd
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.
In
ter
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ry
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2
0
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2
.
[2
3
]
M
u
rra
y
,
J.
D.
,
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1
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.
[2
4
]
M
e
tz,
J.
A.
J
a
n
d
Die
k
m
a
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n
,
O
.
,
“
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.
[2
5
]
M
c
Na
ir,
J.,
N.,
a
n
d
G
o
u
ld
e
n
,
C.
E.
,
“
Th
e
d
y
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m
ics
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g
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stru
c
tu
re
d
p
o
p
u
latio
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s
w
it
h
a
g
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sta
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p
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rio
d
:
De
n
sity
-
in
d
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p
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d
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g
ro
w
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a
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d
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te
,”
T
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o
re
t.
Po
p
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l
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ti
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Bi
o
.
,
v
o
l
.
3
9
,
p
p
.
1
-
2
9
,
1
9
9
1
.
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