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Prio
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[
3
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4
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I
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r
n
is
h
s
ig
n
if
ican
t
d
e
s
cr
ip
tiv
e
n
ar
r
ativ
es,
th
e
y
f
r
e
q
u
en
tly
d
ep
en
d
o
n
p
r
e
-
d
ef
i
n
ed
ca
teg
o
r
ies
an
d
p
r
o
v
id
e
in
s
u
f
f
icien
t
u
n
d
er
s
tan
d
in
g
o
f
h
o
w
r
esear
ch
tr
ajec
to
r
ies
ar
e
f
o
r
m
u
lated
f
r
o
m
th
e
f
u
n
d
am
en
tal
is
s
u
es th
at
in
v
esti
g
atio
n
s
aim
to
r
eso
l
v
e.
A
m
o
r
e
m
ea
n
i
n
g
f
u
l
way
to
u
n
d
er
s
tan
d
g
r
ad
u
ate
r
esear
ch
is
to
l
o
o
k
at
h
o
w
s
tu
d
ies
a
r
e
f
r
a
m
ed
th
r
o
u
g
h
th
eir
ce
n
tr
al
r
esear
ch
p
r
o
b
lem
s
.
T
h
e
p
r
o
b
lem
s
tat
em
en
t,
in
p
ar
ticu
lar
,
ca
p
tu
r
es
wh
at
th
e
s
tu
d
y
is
tr
y
in
g
to
ad
d
r
ess
,
alo
n
g
with
i
ts
k
ey
v
ar
iab
les
an
d
d
ir
ec
tio
n
,
m
ak
in
g
it
a
s
tr
o
n
g
b
asis
f
o
r
c
lass
if
icatio
n
.
W
h
en
th
ese
ar
e
g
r
o
u
p
e
d
in
th
is
way
,
p
atter
n
s
ten
d
to
em
er
g
e
n
a
tu
r
ally
f
r
o
m
th
e
d
ata
r
ath
er
t
h
an
b
ein
g
im
p
o
s
ed
,
o
f
f
er
in
g
a
m
o
r
e
g
r
o
u
n
d
e
d
v
i
ew
o
f
h
o
w
k
n
o
wled
g
e
is
d
ev
elo
p
ed
with
in
th
e
p
r
o
g
r
am
.
T
h
is
ap
p
r
o
ac
h
is
esp
ec
ially
r
elev
an
t
in
m
ath
em
atics
ed
u
ca
tio
n
,
wh
er
e
r
esear
ch
q
u
esti
o
n
s
ar
e
o
f
ten
s
h
ap
ed
b
y
class
r
o
o
m
r
ea
liti
es,
p
o
licy
s
h
if
ts
,
an
d
th
e
ev
o
lv
in
g
n
ee
d
s
o
f
lea
r
n
er
s
-
h
i
g
h
lig
h
tin
g
th
e
o
n
g
o
i
n
g
in
te
r
p
l
ay
b
etwe
en
th
eo
r
y
an
d
p
r
ac
tice.
I
t
is
eq
u
ally
im
p
o
r
tan
t
to
co
n
s
id
er
h
o
w
t
h
ese
r
esear
ch
f
o
c
u
s
es
ch
an
g
e
o
v
er
tim
e.
L
o
o
k
in
g
at
tr
e
n
d
s
m
ak
es
it
p
o
s
s
ib
le
to
tr
ac
e
s
h
if
ts
,
co
n
tin
u
ities
,
a
n
d
e
m
er
g
in
g
p
r
i
o
r
ities
with
in
th
e
p
r
o
g
r
a
m
.
I
n
m
a
n
y
ca
s
es
,
g
r
ad
u
ate
r
esear
ch
r
ef
lects
b
r
o
ad
er
co
n
tex
tu
al
in
f
l
u
en
ce
s
,
s
u
ch
as
cu
r
r
icu
lu
m
r
e
f
o
r
m
s
,
tech
n
o
lo
g
ica
l
d
ev
elo
p
m
e
n
ts
,
o
r
ch
an
g
i
n
g
e
d
u
ca
tio
n
al
d
em
a
n
d
s
.
Fo
r
in
s
tan
ce
,
p
er
io
d
s
o
f
cu
r
r
icu
lar
c
h
an
g
e
o
r
d
is
r
u
p
tio
n
o
f
ten
co
i
n
cid
e
with
in
c
r
ea
s
ed
atten
tio
n
to
in
s
tr
u
ctio
n
al
a
p
p
r
o
ac
h
es
o
r
lear
n
er
-
r
elate
d
f
ac
to
r
s
.
Un
d
er
s
tan
d
i
n
g
th
ese
p
atter
n
s
p
r
o
v
id
es
a
clea
r
er
s
en
s
e
o
f
h
o
w
r
esp
o
n
s
iv
e
an
d
ad
ap
tiv
e
a
p
r
o
g
r
a
m
’
s
r
esear
ch
ag
en
d
a
is
,
wh
ile
also
p
o
in
tin
g
to
ar
ea
s
th
at
m
ay
b
en
ef
it f
r
o
m
d
ee
p
er
e
x
p
lo
r
ati
o
n
o
r
n
ew
d
ir
ec
tio
n
s
.
Desp
ite
th
e
g
r
o
win
g
b
o
d
y
o
f
b
ib
lio
m
etr
ic
an
d
tr
en
d
a
n
aly
s
es
in
ed
u
ca
tio
n
,
ex
is
tin
g
s
tu
d
ies
h
av
e
lar
g
ely
f
o
cu
s
ed
o
n
p
u
b
licatio
n
d
atab
ases
s
u
ch
as
jo
u
r
n
al
a
r
ticles
in
d
ex
ed
i
n
Sco
p
u
s
o
r
W
e
b
o
f
Scien
ce
,
o
f
ten
o
v
er
lo
o
k
in
g
g
r
a
d
u
ate
th
eses
as
a
s
ig
n
if
ican
t
s
o
u
r
ce
o
f
e
m
er
g
in
g
s
ch
o
lar
ly
wo
r
k
.
Mo
r
eo
v
er
,
m
an
y
p
r
io
r
an
aly
s
es
r
ely
h
ea
v
ily
o
n
p
r
e
-
e
s
tab
lis
h
ed
class
if
icatio
n
f
r
am
ewo
r
k
s
o
r
k
ey
wo
r
d
c
o
-
o
cc
u
r
r
e
n
ce
,
wh
ich
m
ay
n
o
t
f
u
lly
ca
p
t
u
r
e
t
h
e
co
n
ce
p
tu
al
in
ten
tio
n
s
em
b
e
d
d
ed
in
r
esear
ch
p
r
o
b
lem
s
tatem
en
ts
.
R
ec
en
t
s
tu
d
ies
em
p
h
asize
th
at
th
esis
-
lev
el
r
esear
ch
r
ef
l
ec
ts
lo
ca
lized
ac
ad
em
ic
p
r
i
o
r
ities
an
d
em
er
g
in
g
s
ch
o
lar
ly
d
ir
ec
tio
n
s
n
o
t
y
et
v
is
ib
le
in
f
o
r
m
al
p
u
b
licatio
n
s
y
s
tem
s
[
6
]
,
[
7
]
.
Ho
wev
er
,
li
m
ited
s
tu
d
ies
in
teg
r
ate
p
r
o
b
l
em
-
b
ased
th
em
atic
class
if
icatio
n
with
lo
n
g
itu
d
in
al
tr
en
d
an
aly
s
is
,
p
a
r
ticu
lar
ly
in
m
ath
em
atics
ed
u
ca
ti
o
n
.
T
h
is
g
ap
co
n
s
tr
ain
s
a
d
ee
p
er
u
n
d
e
r
s
tan
d
in
g
o
f
h
o
w
r
esear
ch
p
r
io
r
ities
ev
o
lv
e
w
ith
in
in
s
titu
tio
n
al
co
n
tex
ts
.
T
h
is
s
tu
d
y
co
n
tr
ib
u
tes
to
m
ath
em
atics
ed
u
ca
tio
n
b
y
i
n
tr
o
d
u
ci
n
g
a
p
r
o
b
lem
-
b
ased
th
em
atic
class
if
icatio
n
o
f
g
r
ad
u
ate
th
e
s
es
g
r
o
u
n
d
e
d
in
r
esear
ch
p
r
o
b
lem
s
tatem
en
ts
,
ab
s
tr
ac
ts
,
an
d
m
eth
o
d
o
lo
g
ical
o
r
ien
tatio
n
s
,
r
ath
er
th
an
r
el
y
in
g
s
o
lely
o
n
p
r
e
-
estab
lis
h
ed
ca
teg
o
r
ies
o
r
k
ey
wo
r
d
-
b
ased
b
ib
lio
m
etr
ic
ap
p
r
o
ac
h
es
co
m
m
o
n
ly
u
s
ed
i
n
p
r
io
r
tr
e
n
d
an
al
y
s
es.
I
t
f
u
r
t
h
er
in
teg
r
ates
th
is
class
if
icati
o
n
with
lo
n
g
itu
d
in
al
tr
en
d
a
n
aly
s
is
s
p
an
n
in
g
m
o
r
e
th
an
two
d
ec
ad
es
o
f
g
r
ad
u
ate
r
esear
ch
with
in
a
l
o
ca
lized
in
s
titu
tio
n
al
co
n
tex
t.
T
h
r
o
u
g
h
t
h
is
co
m
b
in
e
d
an
al
y
tical
ap
p
r
o
ac
h
,
th
e
s
tu
d
y
p
r
o
v
id
es
a
m
o
r
e
co
n
tex
t
-
s
en
s
itiv
e
u
n
d
e
r
s
tan
d
in
g
o
f
h
o
w
r
esear
c
h
p
r
io
r
ities
ev
o
l
v
e
o
v
e
r
tim
e
an
d
h
o
w
m
eth
o
d
o
l
o
g
ical
tr
ad
itio
n
s
s
h
ap
e
k
n
o
wled
g
e
p
r
o
d
u
ctio
n
in
m
ath
em
atics
ed
u
ca
tio
n
.
At
t
h
e
p
r
o
g
r
am
lev
el,
t
h
e
f
i
n
d
in
g
s
m
ay
h
elp
r
e
f
in
e
r
esear
ch
ag
en
d
as,
s
tr
en
g
th
en
alig
n
m
en
t
with
in
s
titu
tio
n
al
p
r
io
r
ities
,
an
d
im
p
r
o
v
e
th
e
o
v
er
all
q
u
ality
o
f
g
r
ad
u
ate
r
ese
ar
ch
.
I
n
th
is
s
en
s
e,
g
r
ad
u
ate
th
eses
ar
e
v
iewe
d
n
o
t
m
er
ely
as
in
d
iv
id
u
al
ac
ad
e
m
ic
o
u
tp
u
ts
b
u
t
as
i
n
d
icato
r
s
o
f
ev
o
lv
in
g
s
ch
o
lar
ly
d
ir
ec
tio
n
s
with
in
m
ath
em
atics
ed
u
ca
tio
n
.
Alth
o
u
g
h
t
h
er
e
is
a
s
u
b
s
tan
tial
b
o
d
y
o
f
r
esear
ch
o
n
m
ath
em
atics
ed
u
ca
tio
n
,
t
h
er
e
is
s
till
lim
ited
lo
ca
lized
ev
id
e
n
ce
s
h
o
win
g
h
o
w
g
r
a
d
u
ate
r
esear
c
h
d
e
v
elo
p
s
with
in
a
s
p
ec
if
ic
i
n
s
titu
tio
n
al
s
ettin
g
o
v
er
tim
e
.
T
h
is
s
tu
d
y
ad
d
r
ess
es
th
at
g
ap
b
y
o
f
f
er
in
g
a
s
y
s
tem
atic
an
d
a
n
aly
tically
g
r
o
u
n
d
e
d
m
ap
p
i
n
g
o
f
Ma
s
ter
o
f
Ar
ts
(
MA
)
m
ath
em
atics
th
eses
,
co
m
b
in
in
g
p
r
o
b
lem
-
b
ased
th
em
atic
class
if
icatio
n
with
lo
n
g
itu
d
in
al
tr
en
d
an
aly
s
is
.
Sp
ec
if
ically
,
th
is
s
tu
d
y
s
o
u
g
h
t to
an
s
wer
th
e
f
o
llo
win
g
q
u
esti
o
n
s
:
−
W
h
at
d
o
m
in
an
t
th
em
atic
d
o
m
ain
s
em
er
g
e
f
r
o
m
t
h
e
p
r
o
b
le
m
s
tatem
en
ts
an
d
m
eth
o
d
o
l
o
g
ical
o
r
ien
tatio
n
s
o
f
MA
m
ath
em
atics th
eses
f
r
o
m
2
0
0
0
–
2
0
2
4
?
−
Ho
w
h
av
e
r
esear
ch
f
o
cu
s
es a
n
d
s
u
b
th
em
es with
in
th
ese
th
e
m
atic
d
o
m
ain
s
ev
o
l
v
ed
o
v
er
ti
m
e?
−
W
h
at
im
p
licatio
n
s
d
o
th
e
o
b
s
er
v
ed
r
esear
ch
tr
e
n
d
s
h
av
e
f
o
r
cu
r
r
icu
lu
m
d
ev
el
o
p
m
en
t,
r
ese
ar
ch
m
en
t
o
r
in
g
,
an
d
f
u
t
u
r
e
m
ath
e
m
atics e
d
u
ca
t
io
n
r
esear
ch
?
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t J E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
5
,
Octo
b
er
20
26
:
4
5
8
8
-
4601
4590
2.
M
E
T
H
O
D
2
.
1
.
Resea
rc
h
des
ig
n
T
h
is
s
tu
d
y
em
p
lo
y
ed
a
q
u
alita
tiv
e
co
n
ten
t a
n
aly
s
is
d
esig
n
to
ex
am
in
e
th
e
th
em
atic
p
atter
n
s
o
f
MA
in
ma
th
em
atics
th
eses
an
d
to
d
ev
elo
p
an
i
n
teg
r
ativ
e
f
r
am
e
wo
r
k
th
at
m
a
y
in
f
o
r
m
cu
r
r
ic
u
lu
m
en
h
an
ce
m
en
t.
C
o
n
ten
t
an
aly
s
is
is
w
id
ely
r
ec
o
g
n
ized
in
e
d
u
ca
tio
n
al
r
es
ea
r
ch
as
a
s
y
s
tem
atic
an
d
f
lex
ib
le
m
eth
o
d
f
o
r
an
aly
zin
g
tex
tu
al
d
ata,
allo
win
g
r
esear
ch
e
r
s
to
id
en
tify
p
atter
n
s
,
tr
en
d
s
,
an
d
m
ea
n
in
g
s
em
b
e
d
d
ed
i
n
d
o
cu
m
e
n
ts
[
1
]
,
[
2
]
.
I
n
th
is
s
tu
d
y
,
th
e
ap
p
r
o
ac
h
ex
te
n
d
ed
b
ey
o
n
d
s
im
p
le
ca
teg
o
r
izatio
n
t
o
in
clu
d
e
th
em
atic
s
y
n
th
esis
,
en
ab
lin
g
n
o
t
o
n
ly
t
h
e
id
en
tific
atio
n
o
f
r
ec
u
r
r
in
g
t
h
em
es
b
u
t
also
th
e
in
ter
p
r
etati
o
n
o
f
r
elatio
n
s
h
ip
s
am
o
n
g
th
em
.
Su
ch
a
n
ap
p
r
o
ac
h
r
ef
lects
co
n
tem
p
o
r
ar
y
v
i
ews
o
f
co
n
ten
t
an
aly
s
is
as
b
o
th
d
escr
ip
tiv
e
an
d
in
ter
p
r
etiv
e,
ca
p
ab
le
o
f
g
en
e
r
a
tin
g
h
ig
h
e
r
-
o
r
d
er
c
o
n
ce
p
tu
al
i
n
s
ig
h
ts
f
r
o
m
tex
t
u
al
co
r
p
o
r
a
[
8
]
,
[
9
]
.
2
.
2
.
Co
rpus
o
f
t
he
s
t
ud
y
T
h
e
co
r
p
u
s
o
f
th
e
s
tu
d
y
co
n
s
is
ted
o
f
1
2
9
MA
in
m
ath
em
a
tics
th
eses
co
m
p
leted
at
B
en
g
u
et
State
Un
iv
er
s
ity
f
r
o
m
2
0
0
0
,
c
o
r
r
e
s
p
o
n
d
in
g
to
th
e
p
r
o
g
r
am
’
s
f
ir
s
t
g
r
ad
u
atin
g
co
h
o
r
t,
th
r
o
u
g
h
2
0
2
4
.
A
to
tal
en
u
m
er
atio
n
a
p
p
r
o
ac
h
was
em
p
lo
y
ed
,
wh
e
r
eb
y
all
av
ailab
le
th
eses
with
in
th
e
s
p
ec
if
ied
p
er
io
d
wer
e
in
clu
d
ed
.
T
h
e
th
eses
wer
e
r
etr
iev
ed
f
r
o
m
d
ep
ar
tm
e
n
t
an
d
th
e
g
r
ad
u
ate
s
tu
d
ies
o
f
f
ice
o
f
th
e
co
lleg
e
o
f
f
er
in
g
th
e
p
r
o
g
r
a
m
.
E
ac
h
th
esis
was
tr
ea
ted
as
a
s
in
g
le
u
n
it
o
f
an
al
y
s
is
.
Fo
r
co
n
s
is
ten
cy
an
d
co
m
p
ar
ab
ilit
y
,
th
e
s
tu
d
y
f
o
cu
s
ed
o
n
th
esis
titl
es,
ab
s
t
r
ac
ts
,
an
d
s
tatem
en
ts
o
f
th
e
p
r
o
b
lem
,
as
th
ese
s
ec
tio
n
s
p
r
o
v
id
e
co
n
cise
an
d
r
eliab
le
r
ep
r
esen
tatio
n
s
o
f
t
h
e
s
tu
d
y
’
s
f
o
cu
s
,
v
ar
iab
les,
an
d
i
n
ten
d
ed
co
n
t
r
ib
u
tio
n
s
.
T
h
is
ap
p
r
o
ac
h
is
co
m
m
o
n
l
y
u
s
ed
in
d
o
cu
m
en
t
ar
y
an
d
tr
en
d
an
aly
s
es
wh
er
e
lar
g
e
d
atasets
r
eq
u
ir
e
s
y
s
te
m
atic
y
et
f
ea
s
ib
le
ex
am
in
atio
n
[
6
]
.
T
o
f
ac
ilit
ate
lo
n
g
itu
d
in
al
a
n
aly
s
is
,
th
e
co
r
p
u
s
was
o
r
g
an
ized
i
n
to
f
iv
e
-
y
e
ar
in
ter
v
als
ac
r
o
s
s
th
e
p
er
io
d
2
0
0
0
–
2
0
2
4
.
2
.
3
.
Da
t
a
a
na
ly
s
is
T
h
e
an
aly
s
is
f
o
cu
s
ed
o
n
th
esi
s
titl
e
s
,
ab
s
tr
ac
ts
,
an
d
s
tatem
e
n
ts
o
f
th
e
p
r
o
b
lem
,
as
th
ese
co
m
p
o
n
en
ts
en
ca
p
s
u
late
th
e
ce
n
tr
al
f
o
cu
s
,
v
ar
iab
les,
an
d
in
ten
t o
f
ea
ch
s
tu
d
y
.
I
n
lar
g
e
-
s
ca
le
d
o
c
u
m
en
ta
r
y
an
d
b
i
b
lio
m
etr
ic
an
aly
s
es,
th
ese
s
ec
tio
n
s
ar
e
wi
d
ely
r
e
g
ar
d
ed
as
v
alid
in
d
icat
o
r
s
o
f
r
esear
ch
d
ir
ec
tio
n
an
d
t
h
em
atic
o
r
ien
tatio
n
,
p
ar
ticu
lar
ly
wh
en
f
u
ll
-
tex
t
ex
a
m
in
atio
n
is
n
o
t
f
ea
s
ib
le
[
2
]
,
[
6
]
,
[
1
0
]
.
As
illu
s
tr
ated
in
Fig
u
r
e
1
,
a
m
u
lti
-
p
h
ase
in
d
u
ctiv
e
co
d
in
g
p
r
o
ce
s
s
was
em
p
lo
y
ed
.
Ph
ase
1
in
v
o
lv
e
d
o
p
en
co
d
in
g
to
id
en
tif
y
k
ey
c
o
n
ce
p
ts
an
d
r
esear
ch
f
o
ci
f
r
o
m
t
h
e
tex
tu
al
d
ata.
I
n
p
h
ase
2
,
ax
ial
co
d
in
g
was
c
o
n
d
u
cte
d
to
g
r
o
u
p
r
elate
d
c
o
d
es
in
to
a
n
aly
tical
ca
teg
o
r
ies
o
r
s
u
b
-
th
em
es.
T
h
ese
ca
teg
o
r
ies
wer
e
th
en
s
y
n
th
esized
in
to
b
r
o
ad
er
th
em
ati
c
d
o
m
ain
s
d
u
r
in
g
p
h
ase
3
th
r
o
u
g
h
co
n
s
tan
t c
o
m
p
ar
is
o
n
,
allo
win
g
p
atter
n
s
to
e
m
er
g
e
d
ir
ec
tly
f
r
o
m
th
e
d
atase
t
[
1
]
,
[
8
]
.
T
h
e
co
d
in
g
an
d
class
if
icatio
n
p
r
o
ce
s
s
was
co
n
d
u
cted
co
llab
o
r
ativ
ely
b
y
th
e
r
esear
ch
er
s
.
Usi
n
g
co
m
m
o
n
co
d
in
g
cr
iter
ia
d
e
r
i
v
ed
f
r
o
m
th
e
p
r
o
b
lem
s
tatem
en
ts
an
d
m
eth
o
d
o
l
o
g
ical
c
h
ar
ac
ter
is
tics
o
f
th
e
th
eses
,
th
e
r
esear
ch
e
r
s
in
d
e
p
en
d
en
tly
ex
a
m
in
ed
an
d
in
itially
class
if
ied
th
e
s
tu
d
ies.
T
h
e
p
r
elim
i
n
ar
y
class
if
icatio
n
s
wer
e
th
en
co
m
p
ar
ed
a
n
d
r
ev
iewe
d
to
id
e
n
tif
y
o
v
e
r
lap
p
in
g
in
ter
p
r
etatio
n
s
an
d
in
c
o
n
s
is
ten
cies.
I
n
ca
s
es
wh
er
e
a
t
h
esis
co
u
ld
r
ea
s
o
n
ab
ly
alig
n
with
m
u
ltip
le
th
em
atic
d
o
m
ain
s
,
class
if
icatio
n
d
ec
is
io
n
s
wer
e
g
u
id
ed
b
y
th
e
s
tu
d
y
’
s
p
r
im
ar
y
r
esear
ch
p
r
o
b
lem
,
d
o
m
in
a
n
t v
ar
iab
les,
an
d
m
eth
o
d
o
l
o
g
ical
o
r
ien
tatio
n
.
Fig
u
r
e
1
.
Data
an
al
y
s
is
p
r
o
ce
d
u
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
Ma
p
p
in
g
tr
en
d
s
in
m
a
th
ema
ti
cs g
r
a
d
u
a
te
th
eses
(
Ju
lie
A
.
B
u
a
s
en
)
4591
T
o
s
tr
en
g
th
en
class
if
icatio
n
v
alid
ity
,
a
s
ec
o
n
d
lay
er
o
f
an
aly
s
is
ex
am
in
ed
m
eth
o
d
o
lo
g
ical
ch
ar
ac
ter
is
tics
,
p
ar
ticu
lar
ly
r
e
s
ea
r
ch
d
esig
n
an
d
d
ata
an
aly
s
is
tech
n
iq
u
es.
T
h
is
s
tep
was
d
o
n
e
to
v
er
if
y
th
e
th
em
atic
class
if
icatio
n
wh
en
cr
o
s
s
-
ch
ec
k
ed
with
th
e
m
eth
o
d
o
lo
g
y
im
p
lem
en
ted
in
th
e
s
tu
d
y
.
W
h
er
e
in
co
n
s
is
ten
cies
wer
e
id
en
tifi
ed
,
iter
ativ
e
r
ec
lass
if
icatio
n
was
co
n
d
u
cted
u
n
til
co
n
ce
p
t
u
al
co
h
e
r
en
ce
was
ac
h
iev
ed
,
co
n
s
is
ten
t
with
r
ec
o
m
m
en
d
e
d
p
r
ac
tices
f
o
r
r
ig
o
r
o
u
s
th
em
atic
an
aly
s
is
[
1
1
]
.
E
ac
h
th
esis
wa
s
ass
ig
n
ed
to
a
s
in
g
le
d
o
m
in
a
n
t
th
em
e
b
ased
o
n
its
p
r
im
ar
y
r
esear
ch
p
r
o
b
lem
an
d
m
eth
o
d
o
lo
g
ical
f
o
c
u
s
.
T
h
is
ap
p
r
o
ac
h
s
u
p
p
o
r
ts
th
e
u
s
e
o
f
m
u
t
u
ally
ex
clu
s
iv
e
ca
teg
o
r
ies
in
co
n
ten
t
an
aly
s
is
,
f
ac
ilit
atin
g
clea
r
er
ag
g
r
eg
atio
n
an
d
m
o
r
e
s
tab
le
t
r
en
d
in
ter
p
r
etatio
n
[
2
]
,
[
6
]
,
[
1
2
]
.
W
h
ile
s
o
m
e
s
tu
d
ies
m
ay
s
p
an
m
u
ltip
le
ar
ea
s
,
ass
ig
n
in
g
a
d
o
m
i
n
an
t th
em
e
e
n
ab
les co
n
s
is
ten
t c
lass
if
icatio
n
f
o
r
la
r
g
e
-
s
ca
le
an
aly
s
is
.
Fo
llo
win
g
th
e
f
in
al
class
if
icatio
n
,
th
e
ca
teg
o
r
ized
d
ata
wer
e
a
n
aly
ze
d
u
s
in
g
f
r
e
q
u
en
cy
an
d
p
er
ce
n
tag
e
d
is
tr
ib
u
tio
n
s
an
d
o
r
g
an
ized
in
t
o
f
iv
e
-
y
e
ar
in
te
r
v
als
to
ex
am
in
e
lo
n
g
itu
d
in
a
l
tr
en
d
s
.
T
em
p
o
r
al
g
r
o
u
p
in
g
allo
ws
th
e
id
en
tific
a
tio
n
o
f
s
h
if
ts
in
r
esear
ch
p
r
io
r
i
ties
wh
ile
m
in
im
izin
g
s
h
o
r
t
-
ter
m
v
ar
iab
ilit
y
[
1
0
]
.
T
h
e
in
teg
r
atio
n
o
f
q
u
a
n
titativ
e
f
r
e
q
u
en
c
y
a
n
aly
s
is
with
th
em
atic
s
y
n
th
esis
s
u
p
p
o
r
ts
m
o
r
e
m
ea
n
in
g
f
u
l
in
ter
p
r
etatio
n
o
f
r
esear
ch
p
at
ter
n
s
[
1
3
]
.
T
o
e
n
s
u
r
e
tr
an
s
p
ar
en
cy
an
d
co
n
s
is
ten
cy
,
co
d
i
n
g
d
ec
is
io
n
s
wer
e
g
u
id
ed
b
y
ex
p
licit
cr
iter
ia
an
d
iter
ativ
ely
r
ev
iewe
d
.
T
h
e
r
ig
o
r
was
s
u
p
p
o
r
ted
th
r
o
u
g
h
s
y
s
tem
atic
co
d
in
g
p
r
o
ce
d
u
r
es,
iter
ativ
e
v
alid
atio
n
,
an
d
alig
n
m
en
t
b
etwe
en
te
x
tu
al
an
d
m
eth
o
d
o
lo
g
ical
f
ea
tu
r
es,
co
n
s
is
ten
t
with
tr
u
s
two
r
th
in
ess
cr
iter
ia
in
q
u
alitativ
e
r
esear
ch
[
1
1
]
.
T
o
f
u
r
th
er
en
h
a
n
ce
m
eth
o
d
o
lo
g
ical
tr
an
s
p
ar
en
cy
a
n
d
au
d
itab
ilit
y
,
s
u
p
p
lem
e
n
tar
y
c
o
d
in
g
m
ater
ials
co
n
s
is
tin
g
o
f
a
co
d
in
g
m
an
u
al
a
n
d
co
d
in
g
g
u
id
e
wer
e
p
r
e
p
ar
ed
d
etailin
g
th
e
c
o
d
in
g
p
r
o
ce
d
u
r
es,
v
alid
atio
n
p
r
o
ce
s
s
,
co
d
in
g
cr
iter
ia,
an
d
illu
s
tr
ativ
e
class
if
icatio
n
ex
am
p
les
u
s
ed
in
th
e
s
tu
d
y
.
E
th
ical
co
n
s
id
er
atio
n
s
wer
e
ca
r
ef
u
lly
o
b
s
er
v
ed
th
r
o
u
g
h
o
u
t
th
e
s
tu
d
y
.
All
th
ese
wer
e
ac
ce
s
s
ed
th
r
o
u
g
h
th
e
in
s
titu
tio
n
al
ar
c
h
iv
es
an
d
u
s
ed
s
o
lely
f
o
r
ac
a
d
em
ic
p
u
r
p
o
s
es,
with
n
o
d
is
clo
s
u
r
e
o
f
p
e
r
s
o
n
al
id
en
tifie
r
s
.
I
n
ad
d
itio
n
,
th
e
s
tu
d
y
a
d
h
er
e
d
to
em
e
r
g
in
g
et
h
ical
g
u
id
eli
n
es
r
eg
a
r
d
in
g
th
e
u
s
e
o
f
a
r
tific
ial
in
tellig
en
ce
(
AI
)
in
r
esear
ch
.
AI
-
ass
is
ted
to
o
ls
wer
e
u
tili
ze
d
in
a
lim
ited
an
d
s
u
p
p
o
r
tiv
e
ca
p
ac
ity
,
p
ar
ticu
lar
ly
f
o
r
o
r
g
an
izin
g
d
ata
an
d
im
p
r
o
v
in
g
clar
ity
o
f
p
r
esen
tatio
n
/n
a
r
r
atio
n
.
R
ec
en
t
s
ch
o
lar
s
h
ip
e
m
p
h
asizes
th
at
wh
ile
g
en
er
ativ
e
AI
ca
n
en
h
an
ce
e
f
f
icien
cy
,
it
also
in
tr
o
d
u
ce
s
co
n
ce
r
n
s
r
elate
d
to
b
ias,
tr
an
s
p
ar
e
n
cy
,
an
d
ac
ad
e
m
ic
in
teg
r
ity
[
1
4
]
,
[
1
5
]
.
As
s
u
ch
,
AI
to
o
ls
s
h
o
u
ld
f
u
n
ctio
n
o
n
ly
as
ass
i
s
tiv
e
tech
n
o
lo
g
ies
an
d
m
u
s
t
n
o
t
r
ep
lace
th
e
r
esear
ch
er
’
s
an
aly
tical
ju
d
g
m
en
t
[
1
6
]
,
[
1
7
]
.
C
o
n
s
is
ten
t
wit
h
th
ese
p
r
in
cip
les,
all
AI
-
ass
i
s
ted
o
u
tp
u
ts
in
th
is
s
tu
d
y
wer
e
c
r
itically
r
ev
iewe
d
,
v
alid
ate
d
,
an
d
s
u
b
s
tan
tiall
y
r
ef
in
e
d
b
y
t
h
e
r
esear
ch
e
r
.
AI
was
n
o
t
u
s
ed
to
g
en
er
ate
p
r
im
ar
y
d
ata,
co
n
d
u
ct
in
d
ep
en
d
en
t
an
al
y
s
is
,
o
r
m
ak
e
in
ter
p
r
etiv
e
d
ec
is
io
n
s
.
T
h
is
ap
p
r
o
ac
h
en
s
u
r
es
ac
co
u
n
tab
ilit
y
an
d
ad
h
er
en
ce
t
o
cu
r
r
e
n
t stan
d
ar
d
s
f
o
r
r
esp
o
n
s
ib
le
AI
in
teg
r
atio
n
in
r
esear
c
h
[
1
8
]
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
T
hem
a
t
ic
cla
s
s
if
ica
t
io
n o
f
M
A
m
a
t
hema
t
ics t
hes
es
T
h
e
co
n
ten
t
a
n
aly
s
is
y
ield
e
d
f
iv
e
m
ajo
r
th
em
atic
d
o
m
ain
s
d
er
iv
ed
f
r
o
m
t
h
e
ce
n
tr
al
r
esear
ch
p
r
o
b
lem
s
an
d
m
eth
o
d
o
l
o
g
ic
al
o
r
ien
tatio
n
s
o
f
th
e
t
h
eses
:
i
)
ass
es
s
m
en
t
o
f
m
ath
em
atics
r
ea
d
in
ess
,
ac
h
iev
em
en
t,
an
d
cu
r
r
icu
lu
m
(
AM
R
AC
)
;
ii
)
af
f
ec
tiv
e,
m
o
tiv
atio
n
al,
an
d
s
elf
-
r
e
g
u
lated
lear
n
in
g
in
m
ath
em
ati
cs
(
AM
SR
L
M)
;
iii
)
p
r
ed
ictiv
e
a
n
d
co
r
r
elatio
n
al
s
tu
d
ies
(
PC
S);
iv
)
in
s
tr
u
ctio
n
al
in
ter
v
en
tio
n
s
a
n
d
in
n
o
v
atio
n
s
(
I
I
I
)
;
a
n
d
v
)
cu
l
tu
r
al
an
d
c
o
n
tex
tu
al
d
im
en
s
i
o
n
s
o
f
m
ath
e
m
atics
lea
r
n
in
g
(
C
C
DM
L
)
.
T
h
ese
th
em
es
em
er
g
ed
th
r
o
u
g
h
an
iter
ativ
e
an
d
s
y
s
tem
atic
co
d
in
g
p
r
o
ce
s
s
,
en
s
u
r
in
g
co
n
ce
p
tu
al
clar
ity
,
m
u
tu
al
ex
clu
s
iv
ity
,
an
d
alig
n
m
en
t w
it
h
b
o
th
t
h
e
s
u
b
s
tan
tiv
e
f
o
cu
s
a
n
d
m
eth
o
d
o
lo
g
ical
ch
ar
ac
ter
is
tics
o
f
ea
ch
s
tu
d
y
.
Fig
u
r
e
2
p
r
esen
ts
an
in
teg
r
ated
v
is
u
aliza
tio
n
o
f
b
o
t
h
th
em
atic
d
is
tr
ib
u
tio
n
a
n
d
s
u
b
-
th
em
e
co
m
p
o
s
itio
n
.
Ov
er
all,
th
e
d
is
tr
ib
u
tio
n
is
n
o
tab
ly
u
n
ev
e
n
.
PC
S
co
n
s
titu
te
th
e
lar
g
est
p
r
o
p
o
r
tio
n
(
3
1
.
7
8
%),
f
o
llo
wed
b
y
I
I
I
(
2
8
.
6
8
%)
an
d
AM
R
AC
(
2
4
.
8
1
%).
I
n
c
o
n
tr
ast,
C
C
DM
L
(
8
.
5
3
%)
an
d
AM
SR
L
M
(
6
.
2
0
%)
r
em
ain
co
m
p
ar
ativ
ely
u
n
d
er
r
ep
r
esen
ted
.
Pre
s
en
tin
g
b
o
th
f
r
eq
u
en
cies
an
d
p
er
ce
n
tag
es
allo
ws
clea
r
er
in
ter
p
r
etatio
n
o
f
r
elativ
e
e
m
p
h
asis
ac
r
o
s
s
d
o
m
ain
s
,
a
d
d
r
ess
in
g
ca
lls
f
o
r
m
o
r
e
tr
an
s
p
ar
e
n
t
r
ep
o
r
tin
g
in
tr
e
n
d
an
aly
s
es
[
6
]
.
A
clo
s
er
ex
am
i
n
atio
n
o
f
t
h
e
in
ter
n
al
c
o
m
p
o
s
itio
n
o
f
ea
c
h
th
em
e
r
ev
ea
ls
im
p
o
r
tan
t
d
is
tin
ctio
n
s
.
W
ith
in
P
C
S,
th
e
d
o
m
in
an
ce
o
f
co
r
r
elatio
n
al
s
tu
d
ies
(
5
6
.
1
0
%)
in
d
icate
s
a
s
tr
o
n
g
p
r
ef
er
en
ce
f
o
r
ex
am
i
n
in
g
r
elatio
n
s
h
ip
s
am
o
n
g
v
ar
ia
b
les,
wh
ile
p
r
ed
ictiv
e
s
tu
d
ies
(
3
1
.
7
1
%)
an
d
p
er
f
o
r
m
an
ce
lin
k
a
g
e
s
(
1
2
.
2
0
%)
ar
e
less
p
r
o
m
in
e
n
t.
T
h
is
p
atter
n
s
u
g
g
e
s
ts
th
at
g
r
ad
u
ate
r
esear
ch
is
p
r
im
ar
ily
o
r
ie
n
ted
to
war
d
id
en
t
if
y
in
g
ass
o
ciatio
n
s
r
ath
er
th
an
d
ev
elo
p
in
g
e
x
p
lan
ato
r
y
o
r
ca
u
s
al
m
o
d
els.
Su
ch
d
o
m
in
an
ce
ca
n
b
e
attr
ib
u
ted
t
o
th
e
ac
ce
s
s
ib
ilit
y
o
f
co
r
r
elatio
n
al
d
esig
n
s
an
d
th
ei
r
alig
n
m
en
t
with
co
m
m
o
n
ly
ta
u
g
h
t
s
tatis
tical
tech
n
iq
u
es
in
g
r
ad
u
ate
p
r
o
g
r
am
s
,
r
ef
lectin
g
b
r
o
ad
er
p
atter
n
s
in
e
d
u
ca
tio
n
al
r
esear
ch
[
1
9
]
,
[
2
0
]
.
W
ith
in
th
e
I
I
I
d
o
m
ain
,
i
n
s
tr
u
ctio
n
al
in
ter
v
e
n
tio
n
s
(
4
5
.
9
5
%)
an
d
teac
h
in
g
s
tr
ateg
ies
(
2
7
.
0
3
%)
ac
co
u
n
t
f
o
r
th
e
m
ajo
r
ity
o
f
s
tu
d
ies,
with
f
ewe
r
s
tu
d
ies
f
o
c
u
s
in
g
o
n
tec
h
n
o
lo
g
y
-
e
n
h
an
ce
d
lear
n
in
g
(
1
6
.
2
2
%
)
an
d
in
s
tr
u
ctio
n
al
in
n
o
v
atio
n
s
(
1
0
.
8
1
%).
T
h
e
d
is
tr
ib
u
tio
n
s
h
o
ws
a
s
tr
o
n
g
p
r
ac
tice
-
o
r
ien
te
d
r
esear
ch
ag
e
n
d
a
aim
ed
at
im
p
r
o
v
in
g
class
r
o
o
m
in
s
tr
u
ctio
n
.
W
h
ile
th
is
ali
g
n
s
with
ev
id
en
ce
em
p
h
asiz
in
g
th
e
im
p
ac
t
o
f
teac
h
in
g
q
u
ality
o
n
s
tu
d
en
t
o
u
tco
m
es
[
2
1
]
,
th
e
r
elativ
ely
l
im
ited
atten
tio
n
to
i
n
n
o
v
atio
n
-
o
r
ien
te
d
r
esear
c
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t J E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
5
,
Octo
b
er
20
26
:
4
5
8
8
-
4601
4592
s
u
g
g
ests
th
at
s
tu
d
ies
d
o
n
e
b
y
g
r
ad
u
ate
s
tu
d
en
ts
ten
d
to
test
ex
is
tin
g
ap
p
r
o
ac
h
es
r
ath
er
th
a
n
d
ev
elo
p
in
g
n
ew
in
s
tr
u
ctio
n
al
m
o
d
els.
R
esear
ch
o
n
d
ig
ital
lear
n
in
g
f
u
r
t
h
er
in
d
icate
s
th
at
ef
f
ec
tiv
e
tech
n
o
lo
g
y
in
teg
r
atio
n
r
eq
u
ir
es a
lig
n
m
e
n
t w
ith
p
ed
a
g
o
g
y
r
at
h
er
th
a
n
m
er
e
a
d
o
p
tio
n
[
2
2
]
.
T
h
e
AM
R
AC
d
o
m
ain
h
ig
h
lig
h
ts
a
d
iag
n
o
s
tic
o
r
ien
tatio
n
,
with
r
ea
d
in
ess
an
d
en
tr
y
s
k
ills
(
3
4
.
3
8
%)
an
d
lear
n
in
g
d
if
f
icu
lties
an
d
er
r
o
r
an
aly
s
is
(
2
5
.
0
0
%)
as
d
o
m
in
an
t
s
u
b
-
th
em
es.
T
h
is
r
ef
lects
a
s
tr
o
n
g
em
p
h
asis
o
n
u
n
d
er
s
tan
d
in
g
lear
n
er
s
’
s
tar
tin
g
p
o
in
ts
an
d
i
d
en
tify
in
g
b
ar
r
ier
s
to
ac
h
iev
em
e
n
t.
Su
ch
f
o
cu
s
is
co
n
s
is
ten
t
with
f
o
r
m
ativ
e
ass
ess
m
en
t
p
r
in
cip
les,
wh
ich
s
tr
ess
th
e
im
p
o
r
tan
ce
o
f
p
r
i
o
r
k
n
o
wled
g
e
in
s
h
ap
in
g
in
s
tr
u
ctio
n
[
2
3
]
.
H
o
wev
er
,
t
h
e
r
elativ
ely
lo
w
r
ep
r
esen
tatio
n
o
f
cu
r
r
ic
u
lu
m
ev
alu
atio
n
(
9
.
3
8
%)
a
n
d
p
r
o
b
lem
-
s
o
lv
in
g
(
1
2
.
5
0
%)
s
u
g
g
ests
th
at
s
y
s
tem
ic
an
d
h
ig
h
er
-
o
r
d
er
d
im
e
n
s
io
n
s
o
f
lear
n
in
g
r
ec
eiv
e
co
m
p
ar
ativ
ely
less
atten
tio
n
,
d
esp
ite
th
eir
r
ec
o
g
n
ized
im
p
o
r
tan
ce
in
m
ath
em
atics
ed
u
ca
tio
n
[
2
4
]
.
C
u
r
r
icu
lu
m
alig
n
m
e
n
t
is
cr
itical
in
en
s
u
r
in
g
c
o
h
er
e
n
ce
b
etwe
en
in
ten
d
e
d
lear
n
i
n
g
o
u
tco
m
es,
in
s
tr
u
ctio
n
al
p
r
ac
tices,
an
d
ass
ess
m
en
t
s
y
s
tem
s
[
2
5
]
.
T
h
e
AM
SR
L
M
d
o
m
ai
n
,
t
h
o
u
g
h
co
m
p
r
is
in
g
o
n
ly
6
.
2
0
%
o
f
t
h
e
d
ataset,
r
ef
lects
em
er
g
in
g
a
tten
tio
n
to
af
f
ec
tiv
e
an
d
s
elf
-
r
e
g
u
lato
r
y
d
im
en
s
io
n
s
o
f
lea
r
n
in
g
.
T
h
e
li
m
ited
v
o
lu
m
e
o
f
s
tu
d
ies
in
th
i
s
ar
ea
s
u
g
g
ests
th
at
s
u
ch
co
n
s
tr
u
cts
h
av
e
o
n
ly
r
ec
en
tly
g
ain
ed
p
r
o
m
in
e
n
ce
with
in
th
e
p
r
o
g
r
am
.
T
h
is
tr
en
d
m
i
r
r
o
r
s
b
r
o
ad
er
s
h
if
ts
in
ed
u
ca
tio
n
al
r
esear
ch
to
wa
r
d
r
ec
o
g
n
izin
g
th
e
r
o
le
o
f
m
o
tiv
atio
n
,
s
elf
-
e
f
f
icac
y
,
an
d
an
x
iety
in
s
h
ap
in
g
lear
n
in
g
o
u
tco
m
es
[
2
6
]
,
[
2
7
]
.
T
h
e
r
elativ
ely
lo
w
r
e
p
r
esen
tat
io
n
in
d
icate
s
an
o
p
p
o
r
tu
n
ity
t
o
f
u
r
th
e
r
in
teg
r
ate
th
ese
d
im
en
s
io
n
s
in
to
f
u
tu
r
e
r
esear
ch
.
I
n
co
n
tr
ast,
PC
S
s
lig
h
tly
d
ec
lin
ed
d
u
r
in
g
th
is
p
er
io
d
,
wh
ile
af
f
ec
tiv
e
an
d
co
n
te
x
tu
al
th
em
es
b
eg
an
to
g
r
o
w.
B
y
2
0
2
0
–
2
0
2
4
,
a
r
eb
alan
cin
g
is
ev
i
d
en
t:
PC
S
an
d
I
I
I
d
ec
r
ea
s
ed
b
u
t
r
em
ai
n
e
d
p
r
o
m
in
en
t,
wh
ile
AM
SR
L
M
an
d
C
C
DM
L
r
ea
ch
ed
th
ei
r
h
i
g
h
est
lev
els.
T
h
is
p
o
in
ts
t
o
a
g
r
a
d
u
al
s
h
if
t
to
war
d
m
o
r
e
h
o
lis
tic
p
er
s
p
ec
tiv
es
th
at
co
n
s
id
er
m
o
tiv
atio
n
,
i
d
en
tity
,
a
n
d
co
n
te
x
t
in
lear
n
in
g
.
E
m
er
g
in
g
s
tu
d
ies
o
n
c
u
ltu
r
ally
g
r
o
u
n
d
ed
m
ath
em
atics,
in
cl
u
d
in
g
et
h
n
o
m
at
h
em
atics
an
d
c
o
n
tex
tu
alize
d
in
s
tr
u
ctio
n
,
r
ef
l
ec
t
ef
f
o
r
ts
t
o
m
a
k
e
lear
n
in
g
m
o
r
e
r
elev
a
n
t a
n
d
in
c
lu
s
iv
e
[
2
8
]
,
[
2
9
]
.
Fig
u
r
e
2
.
T
h
em
atic
d
is
tr
ib
u
tio
n
an
d
s
u
b
-
th
em
e
c
o
m
p
o
s
itio
n
o
f
MA
m
ath
em
atics th
eses
Similar
ly
,
th
e
C
C
DM
L
d
o
m
ain
(
8
.
5
3
%)
r
em
ain
s
u
n
d
er
d
e
v
elo
p
ed
,
with
eth
n
o
m
at
h
em
atics
(
5
4
.
5
5
%)
as
th
e
d
o
m
in
an
t
s
u
b
-
th
em
e.
W
h
ile
th
is
in
d
icate
s
g
r
o
win
g
r
ec
o
g
n
itio
n
o
f
c
u
ltu
r
al
p
er
s
p
ec
tiv
es,
th
e
lim
ited
p
r
esen
ce
o
f
co
n
tex
tu
alize
d
an
d
ap
p
lied
m
ath
em
atics
s
tu
d
ie
s
s
u
g
g
ests
th
at
s
o
cio
cu
ltu
r
al
ap
p
r
o
ac
h
es
r
em
ain
p
er
ip
h
er
al.
T
h
is
is
n
o
tewo
r
th
y
g
iv
en
th
at
m
ath
em
atics
lear
n
in
g
is
in
cr
ea
s
in
g
ly
u
n
d
er
s
to
o
d
as
s
i
tu
ated
with
in
cu
ltu
r
al
an
d
s
o
cial
co
n
tex
ts
,
an
d
in
teg
r
atin
g
th
ese
p
er
s
p
ec
tiv
es
h
as
b
ee
n
s
h
o
wn
to
en
h
an
ce
r
elev
an
ce
an
d
en
g
ag
em
e
n
t
[
2
8
]
,
[
3
0
]
.
T
ak
en
to
g
eth
e
r
,
th
e
f
in
d
in
g
s
i
n
d
icate
a
r
esear
ch
lan
d
s
ca
p
e
t
h
at
is
s
tr
o
n
g
ly
g
r
o
u
n
d
e
d
in
q
u
an
titativ
e
an
d
in
te
r
v
en
tio
n
-
b
ased
ap
p
r
o
ac
h
es
b
u
t
r
elativ
ely
lim
ited
in
af
f
ec
tiv
e
an
d
s
o
cio
cu
ltu
r
al
in
q
u
ir
y
.
T
h
is
p
atter
n
r
ef
lects
n
o
t
o
n
ly
r
esear
ch
in
t
er
ests
b
u
t
also
in
s
titu
tio
n
al
a
n
d
m
eth
o
d
o
lo
g
ical
in
f
lu
e
n
ce
s
s
h
ap
in
g
g
r
ad
u
ate
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
Ma
p
p
in
g
tr
en
d
s
in
m
a
th
ema
ti
cs g
r
a
d
u
a
te
th
eses
(
Ju
lie
A
.
B
u
a
s
en
)
4593
r
esear
ch
p
r
o
d
u
ctio
n
.
As
n
o
te
d
in
s
tu
d
ies
o
f
k
n
o
wled
g
e
p
r
o
d
u
ctio
n
,
r
esear
ch
tr
en
d
s
a
r
e
o
f
ten
s
h
a
p
ed
b
y
m
eth
o
d
o
l
o
g
ical
ac
ce
s
s
ib
ilit
y
,
tr
ain
in
g
,
a
n
d
in
s
titu
tio
n
al
e
x
p
ec
tatio
n
s
[
1
9
]
,
[
3
0
]
.
E
x
p
a
n
d
in
g
r
esear
ch
in
to
u
n
d
er
r
ep
r
esen
ted
d
o
m
ain
s
-
p
a
r
ticu
lar
ly
af
f
ec
tiv
e
,
co
n
te
x
tu
a
l,
an
d
in
ter
d
is
cip
lin
ar
y
ar
ea
s
-
m
ay
co
n
t
r
ib
u
te
to
a
m
o
r
e
b
ala
n
ce
d
an
d
h
o
lis
tic
u
n
d
er
s
tan
d
in
g
o
f
m
ath
em
atics lea
r
n
in
g
.
3
.
2
.
T
re
nd
s
in
re
s
ea
rc
h f
o
cu
s
o
f
M
A
m
a
t
hema
t
ics t
hes
es
Fig
u
r
e
3
s
h
o
ws
h
o
w
MA
m
at
h
em
atics
th
esis
to
p
ics
ev
o
lv
ed
ac
r
o
s
s
f
iv
e
p
er
io
d
s
.
I
n
th
e
ea
r
ly
y
ea
r
s
(
2
0
0
0
to
2
0
0
4
)
,
r
esear
c
h
o
u
tp
u
t
was
lim
ited
an
d
co
n
ce
n
tr
at
ed
m
ain
ly
o
n
PC
S
an
d
I
I
I
,
wit
h
m
in
im
al
atten
tio
n
to
af
f
ec
tiv
e
AM
SR
L
M
an
d
co
n
tex
tu
al
C
C
DM
L
d
im
en
s
io
n
s
.
T
h
is
s
u
g
g
ests
th
at
ea
r
ly
wo
r
k
was
s
till
d
ev
elo
p
in
g
an
d
h
a
d
n
o
t
y
et
d
i
v
er
s
if
ied
.
Fro
m
2
0
0
5
t
o
2
0
0
9
,
r
esear
ch
ac
tiv
ity
in
cr
ea
s
ed
,
p
ar
ticu
lar
ly
in
PC
S,
AM
R
A
C
,
an
d
I
I
I
,
r
ef
lectin
g
a
g
r
o
win
g
f
o
cu
s
o
n
s
tu
d
en
t
p
er
f
o
r
m
a
n
ce
,
ass
ess
m
en
t,
an
d
class
r
o
o
m
in
ter
v
en
tio
n
s
.
Ho
wev
er
,
af
f
ec
tiv
e
an
d
c
o
n
tex
tu
al
th
e
m
es r
em
ain
ed
m
ar
g
i
n
al.
T
h
e
p
er
i
o
d
2
0
1
0
-
2
0
1
4
m
ar
k
e
d
a
clea
r
s
h
if
t,
with
PC
S
r
ea
ch
in
g
its
p
ea
k
.
T
h
is
d
o
m
in
an
ce
r
ef
lects
a
s
tr
o
n
g
em
p
h
asis
o
n
ex
am
i
n
in
g
r
elatio
n
s
h
i
p
s
am
o
n
g
cla
s
s
r
o
o
m
v
ar
iab
les,
an
a
p
p
r
o
a
ch
wid
ely
u
s
ed
in
ed
u
ca
tio
n
d
u
e
to
its
p
r
ac
ticality
[
3
1
]
.
I
t
also
alig
n
s
with
th
e
r
is
e
o
f
ev
id
en
ce
-
b
ased
an
d
d
at
a
-
d
r
iv
en
p
r
ac
tices,
wh
ich
f
a
v
o
r
ed
s
tatis
tical
ap
p
r
o
ac
h
es
lik
e
co
r
r
elatio
n
an
d
r
e
g
r
ess
io
n
[
1
9
]
,
[
3
2
]
,
as
well
as
lar
g
e
-
s
ca
le
s
y
n
th
eses
lin
k
in
g
v
ar
ia
b
les to
s
tu
d
en
t a
ch
iev
em
en
t
[
2
1
]
.
B
etwe
en
2
0
1
5
a
n
d
2
0
1
9
,
t
h
er
e
was
a
s
ig
n
if
ican
t
m
o
v
em
en
t
to
war
d
in
te
r
v
en
tio
n
-
b
ased
a
n
d
p
r
ac
tice
-
o
r
ien
ted
r
esear
ch
,
as seen
b
y
th
e
s
h
ar
p
in
cr
ea
s
e
in
I
I
I
.
T
h
is
is
in
lin
e
with
g
r
o
win
g
ca
lls
f
o
r
cu
r
r
icu
lar
ch
a
n
g
es
an
d
e
v
id
en
ce
-
b
ased
in
s
tr
u
cti
o
n
,
as
s
tr
u
ct
u
r
ed
in
ter
v
e
n
tio
n
s
h
av
e
b
ee
n
d
em
o
n
s
tr
ated
to
r
aise
ar
ith
m
etic
ac
h
iev
em
en
t
[
2
1
]
,
[
3
3
]
.
AM
R
AC
al
s
o
p
ea
k
ed
d
u
r
in
g
th
is
tim
e,
d
em
o
n
s
tr
atin
g
th
e
o
n
g
o
in
g
s
ig
n
if
ican
ce
o
f
ass
es
s
m
en
t
in
d
ir
ec
tin
g
in
s
tr
u
ctio
n
.
W
h
ile
cu
r
r
icu
lu
m
alig
n
m
en
t
-
th
o
u
g
h
less
s
tu
d
ied
-
r
em
ain
s
ess
en
tial
f
o
r
co
h
er
en
t
lea
r
n
in
g
o
u
tco
m
es
[
2
5
]
,
d
ia
g
n
o
s
tic
ass
ess
m
en
t
an
d
er
r
o
r
a
n
aly
s
is
in
p
ar
ticu
lar
co
n
tin
u
e
to
b
e
cr
u
cial
f
o
r
id
en
tif
y
in
g
lear
n
in
g
g
ap
s
an
d
m
is
co
n
ce
p
tio
n
s
[
2
3
]
,
[
3
4
]
,
[
3
5
]
s
tr
o
n
g
er
p
r
o
g
r
a
m
co
m
p
letio
n
r
ates
also
co
r
r
esp
o
n
d
ed
with
th
is
b
o
o
m
,
in
d
icatin
g
s
tr
o
n
g
e
r
g
r
a
d
u
ate
o
u
tp
u
t.
Alth
o
u
g
h
s
till
less
r
ep
r
esen
ted
,
AM
SR
L
M
h
ig
h
lig
h
ts
im
p
o
r
ta
n
t
f
ac
to
r
s
s
u
ch
as
s
elf
-
ef
f
icac
y
,
m
o
tiv
ati
o
n
,
an
d
a
n
x
iety
,
wh
ich
a
r
e
k
n
o
wn
to
in
f
lu
e
n
ce
ac
h
iev
em
en
t
a
n
d
e
n
g
ag
em
e
n
t
[
2
6
]
,
[
3
6
]
,
[
3
7
]
.
T
h
e
in
clu
s
io
n
o
f
s
elf
-
r
eg
u
lated
lear
n
in
g
al
s
o
s
ig
n
als
g
r
o
win
g
r
ec
o
g
n
itio
n
o
f
lear
n
er
s
as a
ctiv
e
p
ar
ticip
an
ts
in
th
ei
r
lear
n
in
g
p
r
o
ce
s
s
es
[
3
8
]
.
Fig
u
r
e
3
.
T
r
en
d
s
o
f
r
esear
ch
t
o
p
ics o
f
th
eses
in
MA
in
m
ath
em
atics
Ov
er
all,
wh
ile
PC
S
an
d
I
I
I
h
av
e
lo
n
g
d
o
m
in
ated
,
th
e
tr
en
d
s
h
o
ws
a
g
r
ad
u
al
d
iv
er
s
if
icatio
n
o
f
r
esear
ch
th
em
es.
T
h
e
p
r
o
g
r
a
m
r
em
ain
s
s
tr
o
n
g
ly
a
n
ch
o
r
ed
in
p
er
f
o
r
m
an
ce
-
an
d
in
te
r
v
en
t
io
n
-
f
o
c
u
s
ed
s
tu
d
ies
b
u
t
is
in
cr
ea
s
in
g
ly
o
p
e
n
in
g
t
o
af
f
ec
tiv
e
an
d
s
o
cio
cu
ltu
r
al
d
i
m
en
s
io
n
s
.
T
h
is
s
h
if
t
s
u
g
g
ests
b
o
th
c
o
n
tin
u
ity
an
d
ch
an
g
e,
w
h
ile
also
p
o
i
n
tin
g
to
o
p
p
o
r
tu
n
ities
f
o
r
b
r
o
ad
e
r
an
d
m
o
r
e
b
ala
n
ce
d
r
esear
c
h
d
ir
ec
tio
n
s
m
o
v
in
g
f
o
r
war
d
.
T
h
e
o
b
s
er
v
ed
s
h
if
ts
in
r
esear
ch
f
o
cu
s
ca
n
b
e
u
n
d
er
s
to
o
d
in
r
elatio
n
to
b
r
o
a
d
er
ed
u
ca
t
io
n
al
an
d
in
s
titu
tio
n
al
d
ev
elo
p
m
en
ts
.
T
h
e
ea
r
ly
d
o
m
i
n
an
ce
o
f
co
r
r
elatio
n
al
an
d
ass
ess
m
en
t
-
o
r
ien
ted
s
tu
d
ies
r
ef
lects
th
e
s
tr
o
n
g
in
f
lu
en
ce
o
f
q
u
a
n
titativ
e
r
esear
ch
tr
ain
in
g
an
d
th
e
em
p
h
asis
o
n
m
ea
s
u
r
ab
le
ac
ad
em
ic
o
u
tco
m
es.
T
h
e
s
u
b
s
eq
u
en
t
r
is
e
o
f
in
s
tr
u
ctio
n
al
in
ter
v
en
tio
n
s
tu
d
ies
co
r
r
esp
o
n
d
s
with
in
c
r
ea
s
in
g
atte
n
tio
n
to
class
r
o
o
m
ef
f
ec
tiv
en
ess
an
d
p
ed
ag
o
g
ical
im
p
r
o
v
em
e
n
t
in
r
esp
o
n
s
e
to
c
u
r
r
icu
lu
m
r
ef
o
r
m
s
.
Mo
r
e
r
ec
e
n
tly
,
th
e
em
er
g
en
ce
o
f
af
f
ec
tiv
e
an
d
s
o
cio
cu
ltu
r
al
th
em
es
alig
n
s
with
g
lo
b
al
tr
en
d
s
in
m
ath
em
atics
ed
u
ca
ti
o
n
th
at
em
p
h
asize
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t J E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
5
,
Octo
b
er
20
26
:
4
5
8
8
-
4601
4594
lear
n
er
d
iv
er
s
ity
,
e
q
u
ity
,
an
d
co
n
tex
tu
alize
d
lear
n
in
g
.
T
h
ese
p
atter
n
s
s
u
g
g
est
th
at
g
r
ad
u
a
te
r
esear
ch
a
g
en
d
as
ar
e
n
o
t
o
n
ly
s
h
ap
e
d
b
y
in
d
i
v
id
u
al
in
ter
ests
b
u
t
ar
e
also
in
f
lu
en
ce
d
b
y
e
v
o
lv
in
g
ed
u
ca
tio
n
al
p
r
io
r
ities
,
m
eth
o
d
o
l
o
g
ical
ex
p
o
s
u
r
e,
a
n
d
in
s
titu
tio
n
al
ex
p
ec
tatio
n
s
[
6
]
,
[
1
9
]
.
3
.
3
.
T
re
nd
s
in
re
s
ea
rc
h t
o
pi
cs a
cr
o
s
s
t
hem
a
t
ic
do
ma
ins
T
h
e
an
aly
s
is
o
f
th
e
th
eses
r
ev
ea
ls
clea
r
an
d
e
v
o
lv
in
g
p
a
tter
n
s
in
th
e
r
esear
ch
p
r
io
r
ities
o
f
MA
m
ath
em
atics
g
r
ad
u
ates.
W
h
en
v
iewe
d
ac
r
o
s
s
th
e
f
iv
e
t
h
em
a
tic
d
o
m
ain
s
,
th
e
f
in
d
in
g
s
s
u
g
g
est
th
at
r
esear
ch
is
n
o
t
s
tatic;
r
ath
er
,
it
r
ef
lects
a
d
y
n
a
m
ic
in
ter
p
la
y
b
etwe
en
e
n
d
u
r
in
g
co
n
ce
r
n
s
in
m
ath
em
a
tics
ed
u
ca
tio
n
an
d
em
er
g
in
g
is
s
u
es
s
h
ap
ed
b
y
ed
u
ca
tio
n
al
r
ef
o
r
m
s
,
tech
n
o
lo
g
i
ca
l
d
ev
elo
p
m
e
n
ts
,
an
d
b
r
o
ad
e
r
s
o
cieta
l
ch
an
g
es.
T
h
e
f
o
llo
win
g
d
is
cu
s
s
es
th
e
tr
en
d
o
f
r
esear
ch
t
o
p
ics
o
f
MA
m
ath
em
atics
g
r
a
d
u
ates
a
lo
n
g
ea
c
h
t
h
em
atic
d
o
m
ain
.
3
.
3
.
1
.
Ass
ess
m
ent
o
f
m
a
t
he
ma
t
ics re
a
din
ess
,
a
chiev
em
ent
,
a
nd
curr
iculu
m
T
h
e
tr
en
d
u
n
d
er
AM
R
AC
s
h
o
ws
a
s
u
s
tain
ed
em
p
h
asis
o
n
r
ea
d
in
ess
an
d
en
tr
y
s
k
ills
as
well
a
s
lear
n
in
g
d
if
f
icu
lties
an
d
er
r
o
r
an
aly
s
is
,
b
o
th
o
f
w
h
ich
ap
p
ea
r
co
n
s
is
ten
tly
ac
r
o
s
s
all
ti
m
e
p
er
io
d
s
.
T
h
is
is
ev
id
en
t
in
Fig
u
r
e
4
,
s
u
g
g
esti
n
g
th
at
g
r
a
d
u
ate
r
esear
ch
e
r
s
co
n
tin
u
e
to
g
r
ap
p
le
with
a
f
u
n
d
am
en
tal
q
u
esti
o
n
:
w
h
at
d
o
s
tu
d
en
ts
b
r
in
g
in
t
o
th
e
m
ath
em
atics c
lass
r
o
o
m
,
an
d
wh
er
e
d
o
t
h
ey
s
tr
u
g
g
le
m
o
s
t?
I
n
c
o
n
tr
ast,
ar
ea
s
s
u
ch
as
cu
r
r
icu
lu
m
ev
alu
atio
n
a
n
d
alig
n
m
en
t
r
em
ain
r
elativ
ely
u
n
d
er
ex
p
lo
r
e
d
,
ap
p
ea
r
in
g
o
n
l
y
o
cc
asio
n
ally
.
T
h
is
im
b
alan
ce
i
n
d
icate
s
th
at
wh
ile
m
u
ch
atten
tio
n
is
g
iv
en
to
d
iag
n
o
s
in
g
lear
n
er
-
lev
el
is
s
u
es,
f
ewe
r
s
tu
d
ies
en
g
ag
e
with
b
r
o
ad
er
,
s
y
s
tem
-
lev
el
co
n
ce
r
n
s
s
u
ch
as
cu
r
r
icu
lu
m
co
h
er
en
ce
an
d
alig
n
m
en
t.
T
h
e
r
elativ
ely
s
tab
le
ex
is
ten
ce
o
f
ass
ess
m
en
t
-
f
o
cu
s
ed
s
tu
d
ies
ac
r
o
s
s
tim
e
s
tr
en
g
th
en
s
t
h
e
id
ea
th
at
ass
ess
m
en
t
r
em
ain
s
im
p
o
r
tan
t
to
m
ath
em
atics
ed
u
ca
tio
n
.
B
ey
o
n
d
s
im
p
ly
m
ea
s
u
r
i
n
g
ac
h
ie
v
em
en
t
o
r
p
er
f
o
r
m
an
ce
,
ass
ess
m
en
t
s
er
v
es
as
a
cr
itical
to
o
l
f
o
r
in
f
o
r
m
in
g
in
s
tr
u
ctio
n
an
d
g
u
id
in
g
cu
r
r
icu
lu
m
d
ec
is
io
n
s
.
E
f
f
ec
tiv
e
ass
ess
m
en
t
p
r
ac
tice
s
,
p
ar
ticu
lar
ly
f
o
r
m
ativ
e
ass
ess
m
en
t,
p
lay
a
p
iv
o
tal
r
o
le
in
im
p
r
o
v
in
g
s
tu
d
e
n
t
lear
n
in
g
b
y
m
a
k
in
g
t
h
in
k
in
g
v
is
ib
le
an
d
ac
tio
n
ab
le
[
2
3
]
.
Similar
ly
,
lar
g
e
-
s
ca
le
ed
u
ca
tio
n
al
f
r
am
ewo
r
k
s
h
ig
h
lig
h
t th
e
r
o
le
o
f
ass
ess
m
e
n
t in
s
h
ap
in
g
b
o
th
p
o
licy
a
n
d
class
r
o
o
m
p
r
ac
tice
[
3
9
]
.
T
h
e
p
r
o
m
i
n
en
ce
o
f
r
ea
d
in
es
s
an
d
er
r
o
r
an
aly
s
is
also
r
ef
lects
a
lo
n
g
-
s
tan
d
in
g
r
ec
o
g
n
itio
n
th
at
s
tu
d
en
ts
’
m
is
co
n
ce
p
tio
n
s
ar
e
n
o
t
r
an
d
o
m
b
u
t
ar
e
o
f
te
n
s
y
s
tem
atic
an
d
r
o
o
ted
in
p
r
io
r
k
n
o
wled
g
e
.
Un
d
er
s
tan
d
in
g
t
h
ese
m
is
co
n
ce
p
tio
n
s
is
ess
en
tial
f
o
r
d
esig
n
in
g
in
s
tr
u
ctio
n
th
at
m
ea
n
in
g
f
u
lly
s
u
p
p
o
r
ts
co
n
ce
p
tu
al
c
h
an
g
e
[
3
5
]
.
At
th
e
s
am
e
tim
e,
th
e
lim
ited
atten
tio
n
to
c
u
r
r
icu
lu
m
ev
al
u
atio
n
s
u
g
g
ests
an
o
p
p
o
r
tu
n
ity
f
o
r
f
u
tu
r
e
r
esear
ch
to
en
g
ag
e
m
o
r
e
d
ee
p
ly
with
h
o
w
cu
r
r
icu
lar
s
tr
u
ctu
r
es
in
f
lu
en
ce
lear
n
in
g
o
u
tco
m
es,
p
a
r
ticu
lar
ly
in
c
o
n
t
ex
ts
u
n
d
er
g
o
in
g
r
ef
o
r
m
.
Fig
u
r
e
4
.
T
r
en
d
s
o
f
r
esear
ch
t
o
p
ics ca
teg
o
r
ized
u
n
d
e
r
AM
R
AC
3
.
3
.
2
.
Af
f
ec
t
iv
e
,
mo
t
iv
a
t
io
na
l
,
a
nd
s
elf
-
re
g
ula
t
ed
lea
rning
in m
a
t
hem
a
t
ics
R
esear
ch
u
n
d
er
th
e
AM
SR
L
M
th
em
e
r
em
ai
n
s
r
elativ
ely
lim
ited
in
ea
r
lier
p
er
i
o
d
s
b
u
t
s
h
o
ws
a
n
o
ticea
b
le
in
c
r
ea
s
e
in
r
ec
en
t
y
ea
r
s
,
p
ar
ticu
lar
l
y
f
r
o
m
2
0
2
0
to
2
0
2
4
,
as
s
h
o
wn
in
Fig
u
r
e
5
.
T
h
is
s
h
if
t
is
n
o
t
s
u
r
p
r
is
in
g
.
T
h
e
d
is
r
u
p
tio
n
s
b
r
o
u
g
h
t
ab
o
u
t
b
y
th
e
C
OVI
D
-
1
9
p
an
d
em
ic
f
o
r
ce
d
ed
u
ca
to
r
s
an
d
r
esear
ch
er
s
alik
e
to
co
n
f
r
o
n
t
t
h
e
em
o
tio
n
al
an
d
p
s
y
ch
o
lo
g
ical
d
im
en
s
io
n
s
o
f
l
ea
r
n
in
g
m
o
r
e
d
ir
ec
tly
.
As
lear
n
in
g
en
v
ir
o
n
m
en
ts
b
ec
am
e
m
o
r
e
f
lex
ib
le
an
d
,
at
tim
es,
m
o
r
e
is
o
latin
g
,
is
s
u
es
s
u
ch
as
m
o
tiv
atio
n
,
an
x
iety
,
an
d
s
elf
-
r
eg
u
latio
n
m
o
v
ed
t
o
th
e
f
o
r
ef
r
o
n
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
Ma
p
p
in
g
tr
en
d
s
in
m
a
th
ema
ti
cs g
r
a
d
u
a
te
th
eses
(
Ju
lie
A
.
B
u
a
s
en
)
4595
T
h
is
g
r
o
win
g
atten
tio
n
to
af
f
e
ctiv
e
f
ac
to
r
s
is
s
tr
o
n
g
ly
s
u
p
p
o
r
ted
b
y
e
x
is
tin
g
liter
atu
r
e.
Ma
th
em
atics
an
x
iety
,
f
o
r
in
s
tan
ce
,
h
as
b
ee
n
s
h
o
wn
to
in
ter
f
er
e
with
wo
r
k
in
g
m
e
m
o
r
y
an
d
h
i
n
d
er
p
er
f
o
r
m
an
ce
[
3
7
]
,
wh
ile
s
elf
-
ef
f
icac
y
p
lay
s
a
cr
u
cial
r
o
le
in
s
h
ap
in
g
s
tu
d
en
ts
’
p
e
r
s
is
ten
ce
an
d
ac
h
iev
em
en
t
[
2
6
]
.
Mo
r
e
r
ec
en
t
s
tu
d
ies
f
u
r
th
er
u
n
d
er
s
co
r
e
th
at
s
tu
d
en
ts
’
em
o
tio
n
al
well
-
b
ein
g
i
s
clo
s
ely
tied
to
th
eir
ac
ad
em
ic
en
g
a
g
em
en
t,
p
ar
ticu
lar
ly
i
n
tim
es
o
f
u
n
ce
r
tain
ty
[
4
0
]
,
[
4
1
]
.
Mo
s
t
o
f
t
h
e
r
esear
ch
in
th
is
f
ield
e
m
p
lo
y
s
co
r
r
elatio
n
al
m
eth
o
d
o
l
o
g
ies,
ass
o
ciatin
g
af
f
ec
tiv
e
v
ar
iab
les
with
ac
ad
em
i
c
r
esu
lts
.
Alth
o
u
g
h
t
h
ese
s
tu
d
ies
y
ield
s
ig
n
if
ican
t
in
s
ig
h
ts
,
th
ey
also
u
n
d
er
s
co
r
e
th
e
n
ec
ess
ity
f
o
r
m
o
r
e
co
m
p
r
eh
en
s
iv
e
an
d
in
ter
v
en
tio
n
-
o
r
i
en
ted
r
esear
ch
th
at
in
v
esti
g
ates
h
o
w
th
ese
af
f
ec
tiv
e
d
im
en
s
io
n
s
ca
n
b
e
ef
f
ec
tiv
ely
f
ac
ilit
ated
in
ed
u
ca
tio
n
al
p
r
ac
tice.
Sti
ll,
th
e
g
r
o
win
g
n
u
m
b
e
r
o
f
AM
SR
L
M
s
tu
d
ies
s
h
o
ws
th
at
th
er
e
is
a
s
ig
n
if
ican
t
s
h
if
t
to
war
d
a
m
o
r
e
co
m
p
lete
u
n
d
er
s
tan
d
i
n
g
o
f
h
o
w
p
e
o
p
le
lear
n
m
ath
.
T
h
is
in
clu
d
es
n
o
t
o
n
ly
h
o
w
well
th
ey
d
o
o
n
test
s
b
u
t
also
th
eir
ex
p
er
ien
ce
s
an
d
p
er
s
o
n
alities
.
Fig
u
r
e
5
.
T
r
en
d
o
f
r
esear
c
h
ca
teg
o
r
ized
u
n
d
er
AM
SR
L
M
3
.
3
.
3
.
P
re
dict
iv
e
a
nd
co
rr
ela
t
io
na
l st
ud
ies
T
h
e
PC
S
d
o
m
in
ate
th
e
r
esear
ch
lan
d
s
ca
p
e
ac
r
o
s
s
m
o
s
t
tim
e
p
er
io
d
s
,
p
a
r
ticu
lar
ly
in
t
h
e
ea
r
lier
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d
m
id
d
le
y
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r
s
.
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h
e
s
tr
o
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g
p
r
e
s
en
ce
o
f
th
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tu
d
ies,
as
s
h
o
wn
in
Fig
u
r
e
6
,
r
ef
lects
a
s
u
s
tain
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in
ter
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d
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r
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s
h
ip
s
am
o
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g
v
ar
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les,
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d
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p
lain
in
g
d
if
f
er
en
ce
s
in
s
tu
d
en
t
ac
h
iev
e
m
en
t.
C
o
r
r
elatio
n
al
s
tu
d
ies
r
em
ain
to
d
o
m
in
ate
ev
en
u
p
to
th
e
last
f
iv
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y
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ar
s
.
T
h
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tr
en
d
alig
n
s
with
b
r
o
ad
e
r
p
atter
n
s
i
n
ed
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ca
tio
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al
r
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ch
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wh
e
r
e
c
o
r
r
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al
d
esig
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ar
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wid
el
y
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ed
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u
e
t
o
th
eir
m
eth
o
d
o
l
o
g
ical
ac
ce
s
s
ib
ilit
y
an
d
ab
ilit
y
to
h
an
d
le
lar
g
e
d
at
asets
[
4
2
]
.
I
n
f
lu
en
tial sy
n
th
ese
s
o
f
ed
u
ca
tio
n
al
r
esear
ch
h
av
e
also
r
ein
f
o
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ce
d
th
e
im
p
o
r
tan
ce
o
f
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e
n
tify
in
g
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ac
to
r
s
th
at
in
f
lu
e
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es
[
2
1
]
.
Ho
wev
er
,
wh
ile
th
ese
ap
p
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o
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h
es a
r
e
v
alu
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o
m
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n
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t c
o
n
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id
er
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C
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co
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tex
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al
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An
o
v
er
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elian
ce
o
n
v
ar
iab
le
-
c
en
ter
ed
ap
p
r
o
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es
m
ay
lim
it
th
e
f
ield
’
s
ab
ilit
y
to
f
u
lly
ca
p
tu
r
e
th
e
co
m
p
lex
ity
o
f
teac
h
in
g
an
d
lea
r
n
in
g
p
r
o
ce
s
s
es
[
4
3
]
.
Fig
u
r
e
6
.
T
r
en
d
s
o
f
r
esear
ch
t
o
p
ics ca
teg
o
r
ized
u
n
d
e
r
PC
S
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t J E
v
al
&
R
es E
d
u
c
,
Vo
l
.
15
,
No
.
5
,
Octo
b
er
20
26
:
4
5
8
8
-
4601
4596
T
h
e
s
lig
h
t
d
ec
lin
e
in
PC
S
s
tu
d
ies
in
m
o
r
e
r
ec
en
t
y
ea
r
s
m
ay
in
d
icate
a
g
r
ad
u
al
d
iv
e
r
s
if
icatio
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o
f
r
esear
ch
in
ter
ests
,
with
g
r
ad
u
ate
s
tu
d
en
ts
b
eg
in
n
in
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to
ex
p
lo
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alter
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ap
p
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ch
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ter
v
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b
ased
o
r
c
o
n
tex
tu
ally
g
r
o
u
n
d
e
d
s
tu
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ies.
Sti
ll,
th
e
p
er
s
is
ten
ce
o
f
p
r
ed
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e
r
esear
ch
,
p
ar
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cu
lar
ly
th
o
s
e
lin
k
e
d
to
ac
ad
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ic
p
er
f
o
r
m
an
ce
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d
licen
s
u
r
e
o
u
tco
m
es,
r
ef
lects
in
s
titu
tio
n
al
p
r
io
r
ities
r
elate
d
to
ac
co
u
n
tab
ilit
y
a
n
d
m
ea
s
u
r
ab
le
s
u
cc
ess
.
I
n
d
ee
d
,
p
r
io
r
r
esear
ch
h
as
s
h
o
wn
th
at
ac
ad
em
ic
i
n
d
icato
r
s
s
u
c
h
as
GPA
r
em
ain
s
tr
o
n
g
p
r
ed
icto
r
s
o
f
f
u
tu
r
e
p
er
f
o
r
m
a
n
ce
[
4
4
]
,
wh
ich
h
elp
s
ex
p
lain
t
h
e
co
n
tin
u
ed
r
elev
a
n
ce
o
f
th
is
lin
e
o
f
in
q
u
ir
y
.
3
.
3
.
4
.
I
ns
t
ruct
io
na
l int
er
v
ent
io
ns
a
nd
inn
o
v
a
t
io
ns
Fig
u
r
e
7
illu
s
tr
ates
th
e
tr
en
d
in
III
r
ev
ea
lin
g
a
clea
r
r
esp
o
n
s
iv
en
ess
to
ed
u
ca
tio
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al
r
ef
o
r
m
s
an
d
ch
an
g
in
g
in
s
tr
u
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n
al
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o
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tex
t
s
.
T
h
e
m
ar
k
e
d
in
cr
ea
s
e
in
s
tu
d
ies
d
u
r
in
g
th
e
2
0
1
4
–
2
0
1
9
p
e
r
io
d
co
in
ci
d
es
with
th
e
im
p
lem
en
tatio
n
o
f
th
e
K
–
1
2
r
ef
o
r
m
in
th
e
Ph
ilip
p
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n
e
s
,
a
tim
e
wh
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ed
u
ca
to
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s
wer
e
ac
tiv
ely
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ee
k
in
g
ef
f
ec
tiv
e
teac
h
in
g
ap
p
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o
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h
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an
d
s
tr
ateg
ies
to
ad
ap
t
t
o
n
ew
cu
r
r
icu
lar
d
em
an
d
s
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W
h
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ter
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ate
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ch
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n
o
t
o
n
ly
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ter
ested
in
u
n
d
er
s
tan
d
in
g
lear
n
i
n
g
b
u
t
also
in
i
m
p
r
o
v
i
n
g
it.
T
h
ese
s
tu
d
ies
o
f
ten
test
s
p
ec
if
ic
in
ter
v
en
tio
n
s
in
ex
is
tin
g
teac
h
in
g
s
tr
ateg
ies,
m
ater
ials
,
o
r
p
r
o
g
r
am
s
,
r
ef
lectin
g
a
p
r
ac
tical
o
r
ien
tatio
n
to
war
d
class
r
o
o
m
im
p
r
o
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em
en
t.
Fig
u
r
e
7
.
T
r
en
d
s
o
f
r
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ch
t
o
p
ics ca
teg
o
r
ized
u
n
d
e
r
I
I
I
T
h
is
tr
en
d
is
co
n
s
is
ten
t
w
ith
g
lo
b
al
s
h
if
ts
to
war
d
lear
n
er
-
c
en
ter
ed
an
d
ev
id
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ce
-
b
ased
i
n
s
tr
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,
wh
er
e
teac
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g
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r
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u
o
u
s
ly
r
ef
in
e
d
th
r
o
u
g
h
r
esear
c
h
[
4
5
]
.
T
h
e
g
r
o
win
g
p
r
esen
ce
o
f
tech
n
o
lo
g
y
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en
h
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ce
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lear
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f
u
r
th
er
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th
e
i
n
cr
ea
s
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g
in
teg
r
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n
o
f
d
i
g
ital
to
o
ls
in
e
d
u
ca
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n
.
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as
s
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wn
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at
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tiv
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o
lo
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en
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tu
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er
s
tan
d
i
n
g
an
d
s
tu
d
en
t
en
g
ag
em
e
n
t
[
2
2
]
,
[
4
6
]
.
I
n
ter
esti
n
g
ly
,
wh
ile
in
ter
v
en
t
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n
s
tu
d
ies
ar
e
ab
u
n
d
an
t,
f
ew
er
s
tu
d
ies
f
o
cu
s
o
n
m
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r
e
ex
p
lo
r
ato
r
y
o
r
d
esig
n
-
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ased
in
n
o
v
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n
s
.
T
h
is
s
u
g
g
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ts
th
at
wh
ile
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h
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g
s
tr
ateg
i
es
ar
e
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ed
,
th
er
e
m
ay
b
e
r
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o
m
to
f
u
r
t
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er
ex
p
an
d
r
esear
ch
in
to
m
o
r
e
tr
an
s
f
o
r
m
ativ
e
a
p
p
r
o
ac
h
es
to
m
ath
em
atics
in
s
tr
u
ctio
n
.
Stu
d
ies
f
o
cu
s
in
g
o
n
III
d
em
o
n
s
tr
ate
a
m
ar
k
ed
in
cr
ea
s
e
d
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r
in
g
th
e
2
0
1
5
-
2
0
1
9
p
er
io
d
,
co
i
n
c
id
in
g
with
th
e
im
p
lem
en
tatio
n
o
f
t
h
e
K
-
1
2
r
e
f
o
r
m
in
th
e
Ph
ilip
p
in
es.
T
h
is
p
e
r
io
d
s
aw
a
s
u
r
g
e
in
r
esear
ch
ex
am
in
i
n
g
teac
h
in
g
s
tr
ateg
ies,
in
clu
d
in
g
s
tr
ateg
ic
in
ter
v
en
tio
n
m
ater
ials
,
th
e
d
y
n
am
ic
lear
n
in
g
p
r
o
g
r
am
,
an
d
o
th
e
r
p
ed
ag
o
g
ical
in
n
o
v
atio
n
s
in
tr
o
d
u
ce
d
in
r
esp
o
n
s
e
to
cu
r
r
icu
la
r
ch
an
g
es.
T
h
e
m
o
s
t
s
ig
n
if
ica
n
t
f
in
d
in
g
is
th
e
r
is
e
in
in
s
tr
u
ctio
n
al
in
ter
v
e
n
tio
n
s
r
ef
lectin
g
g
lo
b
al
s
h
if
ts
to
war
d
lear
n
er
-
ce
n
ter
ed
a
n
d
t
ec
h
n
o
lo
g
y
-
en
h
an
ce
d
ed
u
ca
tio
n
.
R
esear
ch
h
as
s
h
o
wn
th
at
d
ig
ital
to
o
ls
an
d
s
tr
u
ctu
r
ed
in
ter
v
en
tio
n
s
ca
n
e
n
h
an
ce
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
i
n
g
an
d
en
g
ag
em
e
n
t
[
4
6
]
.
T
h
is
tr
en
d
m
a
y
also
b
e
in
f
lu
en
ce
d
b
y
th
e
in
cr
ea
s
in
g
in
teg
r
atio
n
o
f
f
lex
ib
le
an
d
m
o
d
u
lar
lear
n
in
g
s
y
s
tem
s
in
b
o
th
b
asic e
d
u
ca
tio
n
an
d
h
ig
h
er
ed
u
ca
tio
n
.
E
ar
lie
r
,
f
r
o
m
2
0
0
5
-
2
0
0
9
,
in
ter
v
en
tio
n
s
tu
d
ies
wer
e
p
r
im
ar
ily
ce
n
ter
ed
o
n
co
m
p
u
t
er
-
ass
is
ted
in
s
tr
u
ctio
n
,
r
ef
lectin
g
th
e
g
r
o
win
g
in
teg
r
atio
n
o
f
tech
n
o
lo
g
y
in
teac
h
in
g
.
T
h
ese
p
atter
n
s
ar
e
co
n
s
is
ten
t
with
in
ter
n
atio
n
al
f
in
d
in
g
s
th
at
ed
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late
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ter
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ased
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r
ch
[
2
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,
[
4
5
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.
3
.
3
.
5
.
Cultura
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ua
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ic
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T
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o
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ates
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ad
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u
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l
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Fig
u
r
e
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,
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tu
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ies
with
in
th
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o
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ain
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e
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o
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v
is
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le
in
r
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s
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p
ar
ticu
lar
ly
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J E
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&
R
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2252
-
8
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atics
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ch
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d
in
th
e
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iel
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o
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m
ath
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atics
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th
ey
en
a
b
led
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e
ep
er
ex
p
lo
r
atio
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lear
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er
s
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ex
p
e
r
ien
ce
s
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cu
ltu
r
a
l
p
r
ac
tices,
an
d
c
o
n
tex
tu
alize
d
f
o
r
m
s
o
f
k
n
o
wled
g
e
[
4
7
]
.
T
h
e
em
er
g
e
n
ce
o
f
C
C
DM
L
as
a
d
is
tin
ct
th
em
atic
d
o
m
ain
t
h
er
ef
o
r
e
s
ig
n
als
n
o
t
o
n
ly
a
ch
an
g
e
in
r
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ch
to
p
ics
b
u
t
also
an
ex
p
a
n
s
io
n
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ep
is
tem
o
lo
g
ical
o
r
ien
tatio
n
,
m
o
v
in
g
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ey
o
n
d
m
ea
s
u
r
em
e
n
t
to
war
d
in
ter
p
r
etatio
n
an
d
m
ea
n
in
g
-
m
a
k
in
g
.
T
h
e
p
r
ese
n
ce
o
f
s
tu
d
ies
o
n
eth
n
o
m
a
th
em
atics
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d
co
n
tex
tu
alize
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lear
n
in
g
r
e
f
lects
a
b
r
o
ad
er
s
h
if
t
to
war
d
r
ec
o
g
n
i
zin
g
th
at
m
ath
em
atics
is
n
o
t
m
er
ely
ab
s
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u
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ee
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ly
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ed
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e
d
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ltu
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d
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h
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e
r
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o
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ly
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u
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ltu
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ies
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lear
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ich
em
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asize
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at
k
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co
n
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u
cted
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h
r
o
u
g
h
p
ar
ticip
at
io
n
in
cu
ltu
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ally
s
itu
ated
p
r
ac
t
ices
[
3
0
]
.
Similar
ly
,
r
esear
ch
in
cu
ltu
r
ally
r
esp
o
n
s
iv
e
m
ath
e
m
atics
ed
u
ca
ti
o
n
h
ig
h
lig
h
ts
th
e
im
p
o
r
ta
n
ce
o
f
co
n
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tin
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m
ath
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atica
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co
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ce
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ts
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tu
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en
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ed
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ie
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s
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ce
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en
t,
i
d
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ev
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m
e
n
t,
an
d
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
[
4
8
]
.
Desp
ite
th
is
p
o
s
it
iv
e
tr
en
d
,
th
e
r
elativ
ely
lo
w
n
u
m
b
er
o
f
s
tu
d
ies
in
C
C
DM
L
s
u
g
g
ests
th
at
s
o
cio
cu
ltu
r
al
an
d
c
o
n
tex
tu
al
a
p
p
r
o
ac
h
es
r
em
ain
at
t
h
e
m
a
r
g
i
n
s
o
f
th
e
p
r
o
g
r
am
’
s
r
esear
ch
a
g
en
d
a.
T
h
is
p
atter
n
is
n
o
t
u
n
co
m
m
o
n
i
n
p
r
o
g
r
a
m
s
with
s
tr
o
n
g
q
u
a
n
titativ
e
tr
ad
itio
n
s
,
w
h
er
e
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esear
ch
i
s
o
f
ten
s
h
a
p
ed
b
y
estab
lis
h
ed
m
eth
o
d
o
l
o
g
ical
tr
ain
in
g
an
d
ex
p
ec
tatio
n
s
[
4
9
]
.
Mo
r
eo
v
er
,
ev
e
n
in
s
tu
d
ies
th
a
t
in
teg
r
ate
cu
ltu
r
al
elem
en
ts
-
s
u
ch
as
th
e
u
s
e
o
f
in
d
ig
en
o
u
s
m
ater
ials
,
lo
ca
l
co
n
tex
ts
,
o
r
lan
g
u
ag
e
in
m
ath
e
m
atics
in
s
tr
u
ctio
n
-
th
ese
ar
e
f
r
e
q
u
en
tl
y
f
r
am
ed
as
in
s
tr
u
ctio
n
al
s
tr
a
teg
ies
an
d
ev
alu
ated
p
r
im
a
r
ily
in
ter
m
s
o
f
th
eir
ef
f
ec
ts
o
n
s
tu
d
en
t
p
er
f
o
r
m
a
n
ce
.
As
a
r
esu
lt,
cu
ltu
r
e
is
o
f
ten
tr
ea
ted
as
a
s
u
p
p
o
r
tin
g
v
ar
iab
le
with
in
in
ter
v
en
tio
n
o
r
c
o
r
r
elatio
n
al
d
esig
n
s
r
ath
er
th
an
as a
ce
n
tr
al
len
s
o
f
in
q
u
i
r
y
in
its
o
wn
r
ig
h
t
.
Nev
er
th
eless
,
th
e
in
cr
ea
s
in
g
p
r
esen
ce
o
f
C
C
DM
L
s
tu
d
ies
is
s
ig
n
if
ican
t.
I
t
r
ef
lects
a
g
r
o
win
g
o
p
en
n
ess
to
q
u
alitativ
e
an
d
i
n
ter
p
r
etiv
e
ap
p
r
o
ac
h
es
an
d
a
b
r
o
ad
er
r
ec
o
n
ce
p
tu
aliza
tio
n
o
f
wh
at
co
n
s
titu
tes
m
ea
n
in
g
f
u
l
m
ath
em
atica
l
k
n
o
wled
g
e.
I
n
t
h
is
s
en
s
e,
th
e
r
is
e
o
f
C
C
DM
L
r
ep
r
esen
ts
an
im
p
o
r
tan
t
s
tep
to
war
d
a
m
o
r
e
in
clu
s
iv
e
an
d
h
o
lis
tic
u
n
d
er
s
tan
d
i
n
g
o
f
m
at
h
em
atics
ed
u
ca
tio
n
-
o
n
e
th
at
v
alu
es
n
o
t
o
n
ly
p
er
f
o
r
m
a
n
ce
an
d
in
ter
v
e
n
tio
n
,
b
u
t a
ls
o
cu
lt
u
r
e,
id
en
tity
,
an
d
c
o
n
tex
t.
Fig
u
r
e
8
.
T
r
en
d
s
o
f
r
esear
ch
t
o
p
ics ca
teg
o
r
ized
u
n
d
e
r
C
C
D
ML
3.
4
.
I
m
pli
ca
t
i
o
ns
f
o
r
curr
iculu
m
dev
elo
pm
ent
,
re
s
ea
rc
h
m
ent
o
ring
,
a
nd
f
uture
re
s
ea
rc
h
T
h
e
s
tu
d
y
’
s
co
n
clu
s
io
n
s
o
f
f
er
a
n
u
m
b
er
o
f
s
u
g
g
esti
o
n
s
f
o
r
im
p
r
o
v
in
g
g
r
a
d
u
ate
r
esear
ch
d
ev
elo
p
m
e
n
t in
m
ath
em
atics e
d
u
ca
tio
n
.
Pre
d
ictiv
e,
co
r
r
elati
o
n
al,
an
d
in
ter
v
en
tio
n
-
b
ased
s
tu
d
ies p
r
ed
o
m
in
ate,
in
d
icatin
g
th
at
th
e
p
r
o
g
r
am
’
s
r
esear
ch
tr
ain
in
g
h
as
b
ee
n
h
ea
v
ily
f
o
cu
s
ed
o
n
q
u
an
titativ
e
ap
p
r
o
ac
h
es
an
d
p
er
f
o
r
m
an
ce
-
b
ased
in
q
u
ir
y
.
T
h
is
h
as
g
iv
en
em
p
ir
ical
a
n
d
s
t
atis
tically
g
r
o
u
n
d
e
d
r
esear
ch
a
s
tr
o
n
g
f
o
u
n
d
atio
n
,
b
u
t
it
also
s
h
o
ws
th
at
m
eth
o
d
o
lo
g
ical
ex
p
o
s
u
r
e
n
ee
d
s
to
b
e
ex
p
an
d
ed
to
i
n
clu
d
e
q
u
alitativ
e,
m
ix
ed
-
m
eth
o
d
s
,
an
d
d
esig
n
-
b
ased
ap
p
r
o
ac
h
es.
E
x
p
an
d
in
g
m
eth
o
d
o
lo
g
ical
t
r
ain
in
g
m
a
y
allo
w
g
r
ad
u
ate
s
tu
d
en
ts
to
en
g
ag
e
m
o
r
e
th
o
r
o
u
g
h
ly
with
co
m
p
li
ca
ted
,
co
n
tex
t
-
s
en
s
itiv
e
asp
ec
ts
o
f
m
ath
em
atics
lear
n
in
g
,
wh
ich
ar
e
f
r
eq
u
e
n
tly
b
etter
ca
p
tu
r
e
d
th
r
o
u
g
h
in
ter
p
r
etiv
e
an
d
co
n
tex
tu
ally
g
r
o
u
n
d
ed
ap
p
r
o
ac
h
es
[
4
7
]
,
[
4
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.