I
nte
rna
t
io
na
l J
o
urna
l o
f
E
v
a
lua
t
io
n a
nd
Resea
rc
h in E
du
ca
t
io
n (
I
J
E
RE
)
Vo
l.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
,
p
p
.
3
8
5
9
~
3
8
7
1
I
SS
N:
2
2
5
2
-
8
8
2
2
,
DOI
: 1
0
.
1
1
5
9
1
/
ijer
e
.
v
13
i
6
.
2
6
6
7
0
3859
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ere.
ia
esco
r
e.
co
m
Ana
ly
sis
of aca
demic deser
tion a
m
o
ng
ungra
dua
ted
ma
thema
tics st
ud
ents
M
ig
uel A
.
Ro
dríg
uez
-
M
á
rq
u
ez
1
,
Da
g
o
bert
o
Sa
l
g
a
do
-
H
o
rt
a
2
,
Cristina
P
edro
s
a
-
J
esú
s
3
1
D
e
p
a
r
t
me
n
t
o
f
Ec
o
n
o
m
y
,
F
a
c
u
l
t
y
o
f
Ec
o
n
o
mi
c
s a
n
d
A
d
mi
n
i
s
t
r
a
t
i
v
e
S
c
i
e
n
c
e
s,
U
n
i
v
e
r
s
i
t
y
o
f
T
o
l
i
ma
,
T
o
l
i
ma
,
C
o
l
o
mb
i
a
2
D
e
p
a
r
t
me
n
t
o
f
M
a
t
h
e
m
a
t
i
c
s
,
F
a
c
u
l
t
y
o
f
E
d
u
c
a
t
i
o
n
,
U
n
i
v
e
r
s
i
t
y
o
f
T
o
l
i
ma
,
T
o
l
i
ma,
C
o
l
o
m
b
i
a
3
D
e
p
a
r
t
me
n
t
o
f
M
a
t
h
e
m
a
t
i
c
s
,
F
a
c
u
l
t
y
o
f
E
d
u
c
a
t
i
o
n
S
c
i
e
n
c
e
s a
n
d
P
s
y
c
h
o
l
o
g
y
,
U
n
i
v
e
r
s
i
t
y
o
f
C
o
r
d
o
b
a
,
C
o
r
d
o
b
a
,
S
p
a
i
n
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
an
25
,
2
0
2
3
R
ev
is
ed
Ap
r
7
,
2
0
2
4
Acc
ep
ted
May
12
,
2
0
2
4
Un
iv
e
rsity
d
ro
p
o
u
t
is
a
p
h
e
n
o
m
e
n
o
n
t
h
a
t
h
a
s
p
lay
e
d
a
n
imp
o
r
tan
t
ro
le
in
th
e
u
n
d
e
r
g
ra
d
u
a
te
p
ro
g
ra
m
in
m
a
th
e
m
a
ti
c
s
a
t
th
e
Un
i
v
e
rsity
o
f
To
li
m
a
(Co
lo
m
b
ia),
b
e
c
a
u
se
it
h
a
s
b
e
e
n
a
p
ro
g
ra
m
th
a
t
h
a
s
h
i
g
h
d
r
o
p
o
u
t
ra
tes
se
m
e
ste
r
b
y
se
m
e
ste
r.
To
g
e
n
e
ra
te
th
e
re
su
lt
s
p
re
se
n
ted
h
e
re
,
th
e
p
o
p
u
latio
n
wh
o
wa
s
c
o
n
sid
e
re
d
wa
s
stu
d
e
n
ts
e
n
ro
ll
e
d
i
n
t
h
e
2
0
1
2
A
-
2
0
1
8
B
a
c
a
d
e
m
ic
p
e
rio
d
.
In
t
h
is
ti
m
e
fra
m
e
,
th
e
in
fo
rm
a
ti
o
n
o
n
t
h
e
fa
c
to
rs
re
q
u
ired
to
c
h
a
ra
c
teriz
e
stu
d
e
n
t
d
y
n
a
m
ics
is
c
o
n
s
o
li
d
a
te
d
a
n
d
e
v
a
lu
a
ted
u
sin
g
t
h
e
Ka
p
lan
-
M
e
ier
sta
ti
stica
l
m
o
d
e
l,
e
v
a
lu
a
ti
o
n
o
f
a
ss
o
c
iatio
n
s,
c
o
rre
l
a
ti
o
n
s
a
n
d
c
o
m
p
a
riso
n
s
u
sin
g
n
o
n
-
p
a
ra
m
e
tri
c
sta
ti
stics
.
T
h
e
a
im
is
to
d
e
te
rm
in
e
th
e
in
d
i
v
id
u
a
l,
a
c
a
d
e
m
ic,
in
stit
u
ti
o
n
a
l,
so
c
ial
a
n
d
e
c
o
n
o
m
ic
fa
c
to
rs
th
a
t
c
a
u
se
stu
d
e
n
ts
to
d
ro
p
o
u
t.
As
a
re
su
lt
o
f
t
h
e
a
n
a
ly
sis
i
n
c
o
n
tex
t
,
th
e
f
a
c
to
rs
th
a
t
in
flu
e
n
c
e
th
e
p
ro
b
lem
s
o
f
th
e
p
h
e
n
o
m
e
n
o
n
o
f
d
r
o
p
o
u
t
in
th
is
c
o
h
o
rt
we
re
d
e
term
in
e
d
a
n
d
c
h
a
ra
c
teriz
e
d
.
Th
is
m
e
th
o
d
o
lo
g
y
p
re
se
n
ts
c
a
u
sa
l
f
a
c
to
rs
fo
r
stu
d
e
n
t
re
ten
ti
o
n
o
n
wh
ic
h
a
c
ti
o
n
s
sh
o
u
l
d
b
e
tak
e
n
to
p
ro
p
o
se
stra
teg
ies
a
ss
o
c
iate
d
with
o
b
tain
i
n
g
b
e
tt
e
r
p
e
rc
e
n
tag
e
s
o
f
re
ten
ti
o
n
a
n
d
g
ra
d
u
a
ti
o
n
with
in
th
e
Ba
c
h
e
lo
r
’
s
De
g
re
e
p
ro
g
ra
m
in
M
a
t
h
e
m
a
ti
c
s.
K
ey
w
o
r
d
s
:
Data
an
aly
s
is
Deser
tio
n
Dr
o
p
o
u
t
Un
d
er
g
r
a
d
u
ate
m
ath
e
m
atics
R
ete
n
tio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
C
r
is
tin
a
Ped
r
o
s
a
-
J
esú
s
Dep
ar
tm
en
t o
f
Ma
th
em
atics,
Facu
lty
o
f
E
d
u
ca
tio
n
Scien
ce
s
an
d
Ps
y
ch
o
lo
g
y
,
Un
i
v
er
s
ity
o
f
C
o
r
d
o
b
a
San
Alb
er
to
Ma
g
n
o
SN,
C
o
r
d
o
b
a,
Sp
ain
E
m
ail: s0
2
p
ejec
@
u
co
.
es
1.
I
NT
RO
D
UCT
I
O
N
E
d
u
c
a
t
i
o
n
a
t
a
ll
l
e
v
el
s
f
r
o
m
b
as
i
c
t
o
h
i
g
h
e
r
e
d
u
c
at
i
o
n
is
a
v
e
r
y
v
a
l
u
a
b
l
e
t
o
o
l
i
n
t
h
e
d
y
n
a
m
ic
s
o
f
g
r
o
w
t
h
a
n
d
d
e
v
e
l
o
p
m
e
n
t
w
it
h
s
o
ci
a
l
,
ec
o
n
o
m
i
c
,
c
u
l
t
u
r
a
l
a
n
d
a
c
a
d
e
m
ic
e
q
u
i
t
y
i
n
a
c
o
u
n
t
r
y
,
w
h
i
c
h
i
s
w
h
y
,
a
s
a
p
o
l
i
c
y
,
it
i
s
o
n
e
o
f
t
h
e
e
x
p
e
c
t
e
d
g
o
a
ls
i
n
m
a
n
y
c
o
u
n
t
r
i
e
s
,
i
n
r
e
l
a
ti
o
n
t
o
s
t
r
a
t
e
g
i
es
f
o
r
li
n
k
i
n
g
q
u
a
l
i
t
y
a
n
d
c
o
v
e
r
a
g
e
o
f
y
o
u
n
g
p
e
o
p
l
e
i
n
t
h
e
u
n
i
v
e
r
s
i
t
y
e
d
u
c
a
ti
o
n
s
y
s
t
e
m
,
a
n
d
c
o
n
s
e
q
u
e
n
t
l
y
,
r
e
l
e
v
a
n
t
f
a
c
t
o
r
s
a
r
e
e
v
a
l
u
a
t
e
d
a
n
d
d
e
t
e
r
m
i
n
e
d
o
n
w
h
i
c
h
g
u
i
d
e
l
i
n
es
a
r
e
d
r
aw
n
u
p
i
n
o
r
d
e
r
t
o
g
u
a
r
a
n
t
e
e
t
h
e
i
r
p
e
r
m
a
n
e
n
c
e
i
n
t
h
e
s
y
s
te
m
t
o
a
c
h
i
e
v
e
t
h
e
g
o
a
l
o
f
c
o
m
p
l
e
t
i
n
g
s
t
u
d
i
e
s
i
n
t
h
e
v
ar
i
o
u
s
p
r
o
g
r
a
m
s
wi
t
h
a
h
i
g
h
r
a
t
e
o
f
g
r
a
d
u
a
t
es
,
a
ll
o
w
i
n
g
t
h
e
m
t
o
r
et
u
r
n
a
s
p
r
o
f
e
s
s
i
o
n
a
ls
,
w
it
h
g
r
e
a
t
e
r
i
n
d
ic
a
t
o
r
s
o
f
p
e
r
s
o
n
a
l
e
m
p
o
w
e
r
m
en
t
a
n
d
t
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
a
c
o
u
n
t
r
y
.
I
n
a
d
d
i
t
i
o
n
,
u
n
e
m
p
l
o
y
m
e
n
t
l
e
v
e
l
s
a
r
e
l
o
we
r
w
h
e
n
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
a
l
l
e
v
e
l
s
a
r
e
a
c
h
i
e
v
e
d
u
p
o
n
c
o
m
p
l
e
t
i
o
n
o
f
u
n
i
v
e
r
s
i
t
y
s
t
u
d
i
es
,
w
h
ic
h
i
n
c
r
e
as
es
t
h
e
l
i
k
e
l
i
h
o
o
d
o
f
i
m
p
r
o
v
i
n
g
t
h
e
s
t
a
n
d
a
r
d
o
f
l
i
v
i
n
g
o
f
i
n
d
i
v
i
d
u
al
s
a
n
d
t
h
e
a
c
h
i
e
v
e
m
e
n
t
o
f
s
u
s
ta
i
n
a
b
l
e
d
e
v
e
l
o
p
m
e
n
t
o
f
c
o
m
m
u
n
i
t
i
e
s
t
o
i
m
p
r
o
v
e
t
h
e
e
c
o
n
o
m
i
c
a
n
d
s
o
c
i
al
p
r
o
s
p
e
r
i
t
y
o
f
th
e
c
o
u
n
t
r
y
[
1
]
.
I
n
t
h
e
s
p
e
c
i
f
i
c
c
a
s
e
o
f
t
h
e
o
f
f
i
c
i
a
l
u
n
i
v
e
r
s
it
y
s
y
s
t
e
m
p
r
o
v
i
d
i
n
g
t
h
e
p
u
b
l
i
c
s
e
r
v
i
c
e
o
f
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
i
n
C
o
l
o
m
b
i
a
,
it
s
p
o
l
i
c
y
is
t
o
o
f
f
e
r
i
n
c
l
u
s
i
v
e
a
n
d
q
u
a
l
i
t
y
e
d
u
c
a
t
i
o
n
,
w
h
i
c
h
h
a
s
s
e
r
v
e
d
as
s
u
p
p
o
r
t
f
o
r
m
a
n
y
p
e
o
p
l
e
o
f
l
o
w
e
r
i
n
c
o
m
e
i
n
t
h
e
f
i
r
s
t
t
h
r
e
e
o
f
s
i
x
s
o
c
i
al
s
t
r
at
a
:
s
t
r
a
t
u
m
1
(
lo
w
-
l
o
w
)
,
s
t
r
at
u
m
2
(
l
o
w
)
a
n
d
s
t
r
a
t
u
m
3
(
m
e
d
i
u
m
-
l
o
w
)
.
St
r
a
t
a
c
l
as
s
i
f
i
e
d
a
cc
o
r
d
i
n
g
t
o
t
h
e
g
u
i
d
e
li
n
e
s
o
f
t
h
e
N
a
t
i
o
n
a
l
A
d
m
i
n
is
t
r
at
i
v
e
D
e
p
ar
t
m
e
n
t
o
f
St
a
ti
s
ti
cs
(
D
A
N
E
)
i
n
C
o
l
o
m
b
i
a
.
T
h
e
p
u
r
p
o
s
e
o
f
f
o
r
m
a
l
e
d
u
c
a
t
i
o
n
i
s
t
o
e
n
s
u
r
e
t
h
a
t
p
e
o
p
l
e
w
i
t
h
l
o
we
r
i
n
c
o
m
e
s
h
a
v
e
a
n
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
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
8
5
9
-
3
8
7
1
3860
o
p
p
o
r
t
u
n
i
t
y
i
n
t
h
e
s
e
a
r
c
h
f
o
r
b
et
t
e
r
l
i
v
i
n
g
c
o
n
d
i
t
i
o
n
s
,
i
n
r
el
a
t
i
o
n
t
o
i
n
d
i
v
i
d
u
a
l
a
n
d
c
o
l
l
e
ct
i
v
e
d
e
v
e
l
o
p
m
e
n
t
,
a
s
o
n
e
o
f
t
h
e
d
e
te
r
m
i
n
i
n
g
f
a
ct
o
r
s
f
o
r
th
e
r
e
d
u
c
t
i
o
n
o
f
p
o
v
e
r
t
y
a
n
d
i
n
e
q
u
a
l
i
t
i
es
.
H
o
w
e
v
e
r
,
i
n
m
a
n
y
c
a
s
es
,
t
h
es
e
d
r
e
a
m
s
a
r
e
t
r
u
n
c
a
t
e
d
b
y
d
i
f
f
e
r
e
n
t
f
a
c
to
r
s
t
h
a
t
c
a
u
s
e
s
t
u
d
e
n
ts
t
o
d
r
o
p
o
u
t
o
f
u
n
i
v
e
r
s
i
t
y
s
t
u
d
i
es
,
wh
i
c
h
g
e
n
e
r
a
t
es
h
i
g
h
p
e
r
s
o
n
a
l
a
n
d
c
o
l
l
e
c
t
i
v
e
o
p
p
o
r
t
u
n
i
t
y
c
o
s
t
s
i
n
t
h
e
c
u
l
t
u
r
a
l
a
n
d
e
c
o
n
o
m
i
c
s
p
h
e
r
e
i
n
C
o
l
o
m
b
i
a
’
s
p
r
o
d
u
c
t
i
v
e
s
o
c
i
a
l
e
n
v
i
r
o
n
m
e
n
t
.
T
h
e
d
e
t
e
r
m
i
n
a
t
i
o
n
a
n
d
c
h
a
r
a
c
t
e
r
i
z
a
ti
o
n
o
f
t
h
i
s
p
r
o
b
l
e
m
,
g
e
n
e
r
a
t
e
d
b
y
v
a
r
i
o
u
s
c
o
m
p
l
e
x
f
a
c
t
o
r
s
,
is
o
n
e
o
f
t
h
e
p
u
r
p
o
s
e
s
o
f
t
h
e
C
o
l
o
m
b
i
a
n
M
i
n
i
s
t
r
y
o
f
E
d
u
c
a
t
i
o
n
[
2
]
,
f
o
r
w
h
i
c
h
i
t
m
o
n
i
t
o
r
s
g
r
a
d
u
a
t
i
o
n
a
n
d
d
r
o
p
o
u
t
i
n
d
i
c
a
t
o
r
s
f
o
r
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
s
t
u
d
e
n
t
s
.
R
ec
o
r
d
s
i
n
d
i
c
a
t
e
t
h
at
s
t
u
d
e
n
t
s
w
h
o
m
a
n
a
g
e
t
o
g
r
a
d
u
a
t
e
f
r
o
m
u
n
i
v
e
r
s
i
t
y
a
r
e
b
e
l
o
w
5
0
%
i
n
al
l
a
r
e
as
o
f
s
t
u
d
y
,
w
i
t
h
t
h
e
l
o
w
es
t
p
e
r
c
e
n
t
a
g
e
s
o
f
s
t
u
d
e
n
t
r
e
t
e
n
ti
o
n
i
n
th
e
M
a
t
h
e
m
a
ti
c
s
a
n
d
N
a
t
u
r
a
l
S
c
i
e
n
c
es
p
r
o
g
r
a
m
s
,
wi
th
a
l
o
w
p
e
r
c
e
n
t
a
g
e
o
f
2
7
.
2
8
%
o
f
s
t
u
d
e
n
t
s
g
r
a
d
u
a
ti
n
g
(
d
a
t
a
f
r
o
m
2
0
1
6
)
[
3
]
.
Fo
r
th
is
r
ea
s
o
n
,
in
r
ec
en
t d
ec
ad
es th
er
e
h
as b
ee
n
an
in
cr
ea
s
e
in
th
e
n
u
m
b
er
o
f
s
tu
d
ies th
at
i
n
v
esti
g
ate
ed
u
ca
tio
n
al
d
eser
tio
n
,
t
r
y
in
g
t
o
r
ef
lect
o
n
th
e
s
itu
atio
n
an
d
i
ts
ca
u
s
es
to
ac
h
iev
e
a
h
ig
h
er
r
ate
o
f
r
eten
tio
n
an
d
p
er
m
an
en
ce
o
f
s
tu
d
e
n
ts
in
h
i
g
h
er
ed
u
ca
tio
n
.
W
ith
in
t
h
e
r
esear
ch
th
at
h
as
b
ee
n
d
ev
elo
p
ed
to
ex
p
lo
r
e
th
e
p
h
en
o
m
en
o
n
o
f
d
r
o
p
o
u
t,
th
is
s
tu
d
y
was
ca
r
r
ied
o
u
t
with
th
e
aim
o
f
i
d
en
tify
in
g
th
e
ca
u
s
es
th
at
m
o
tiv
ate
u
n
d
er
g
r
ad
u
ate
m
ath
em
atics
s
t
u
d
en
ts
to
ab
an
d
o
n
th
eir
u
n
d
er
g
r
ad
u
ate
s
tu
d
ies,
as
it
is
o
n
e
o
f
th
e
d
e
g
r
ee
s
with
th
e
lo
west
g
r
ad
u
atio
n
r
ate
in
C
o
lo
m
b
ia.
I
t
is
h
o
p
ed
th
at
th
is
r
esear
ch
will
g
en
er
ate
a
d
eb
ate
ab
o
u
t
th
e
s
itu
atio
n
o
f
u
n
iv
er
s
ity
s
tu
d
en
t
s
,
wh
ile
at
th
e
s
am
e
tim
e
d
ec
i
s
io
n
s
will
b
e
tak
en
to
r
ed
u
ce
t
h
e
cu
r
r
en
t
d
r
o
p
o
u
t
r
ates
p
r
esen
ted
in
th
e
B
ac
h
el
o
r
o
f
Ma
th
em
atics
p
r
o
g
r
a
m
,
s
o
th
at,
in
t
h
is
way
,
p
o
s
itiv
e
ch
an
g
es
c
o
u
ld
b
e
g
en
er
ated
at
th
e
ec
o
n
o
m
ic,
s
o
cial,
cu
ltu
r
al,
an
d
ac
ad
em
ic
le
v
el
in
th
e
T
o
lim
a
co
m
m
u
n
ity
an
d
n
atio
n
al.
I
n
th
e
p
r
o
ce
s
s
o
f
r
esear
ch
o
n
d
r
o
p
o
u
t
in
d
if
f
er
e
n
t
co
n
tex
ts
,
it
is
r
elev
an
t
to
k
n
o
w
wh
at
th
is
ter
m
r
ef
er
s
to
an
d
th
e
f
ac
to
r
s
ass
o
c
iated
with
th
is
p
h
en
o
m
e
n
o
n
t
h
at
af
f
ec
ts
s
ch
o
o
l
r
eten
tio
n
r
a
tes,
in
th
e
E
u
r
o
p
ea
n
ar
ea
it
h
as
b
ee
n
r
ef
er
r
ed
to
as
u
n
iv
er
s
ity
d
r
o
p
o
u
t.
I
n
th
e
liter
atu
r
e,
d
ef
in
itio
n
s
o
f
d
r
o
p
o
u
t
a
r
e
r
elate
d
to
f
ac
to
r
s
th
at
h
av
e
an
im
p
ac
t
o
n
u
n
i
v
er
s
ity
d
r
o
p
o
u
t
[
4
]
–
[
6
]
d
e
f
in
in
g
t
h
is
p
h
en
o
m
en
o
n
as
t
h
e
f
a
ct
th
at
s
tu
d
en
ts
d
o
n
o
t
f
o
llo
w
th
e
n
o
r
m
al
p
ath
o
f
th
e
d
eg
r
ee
co
u
r
s
e
in
wh
ich
th
ey
ar
e
en
r
o
lled
,
b
ec
au
s
e
th
ey
with
d
r
aw
o
r
tak
e
lo
n
g
er
th
an
ex
p
ec
te
d
to
f
in
is
h
it.
Al
o
n
g
th
e
s
am
e
lin
es,
m
o
r
e
r
e
c
en
t
d
ef
in
itio
n
s
,
s
u
ch
as
th
e
Glo
s
a
r
io
d
el
S
is
tema
p
a
r
a
la
P
r
ev
en
ció
n
d
e
la
Deserció
n
d
e
la
E
d
u
ca
ci
ó
n
S
u
p
er
io
r
(
g
lo
s
s
ar
y
o
f
t
h
e
s
y
s
tem
f
o
r
th
e
p
r
ev
e
n
tio
n
o
f
d
r
o
p
o
u
t
i
n
h
i
g
h
er
ed
u
ca
tio
n
)
[
7
]
,
d
ef
in
e
d
eser
tio
n
as
th
e
s
tate
o
f
a
s
tu
d
e
n
t
wh
o
d
o
es
n
o
t
g
r
ad
u
ate
b
ec
a
u
s
e
th
ey
h
av
e
n
o
t
g
r
ad
u
ated
in
a
n
y
ac
ad
em
ic
p
er
io
d
o
f
th
e
p
r
o
g
r
am
i
n
wh
ich
th
e
y
en
r
o
lled
;
n
o
tin
g
t
h
at
th
is
s
itu
atio
n
ca
n
b
e
ca
u
s
ed
b
y
d
if
f
er
en
t
in
d
iv
id
u
al,
ac
ad
em
ic,
in
s
titu
tio
n
al
o
r
s
o
cio
ec
o
n
o
m
i
c
f
ac
to
r
s
,
an
d
in
a
v
o
lu
n
tar
y
o
r
f
o
r
ce
d
way
.
I
n
t
h
e
r
ev
iew
o
f
d
r
o
p
o
u
t
in
E
u
r
o
p
ea
n
u
n
iv
er
s
ities
,
d
eser
tio
n
w
as
d
escr
ib
e
d
as
th
e
ab
an
d
o
n
m
en
t
o
f
s
tu
d
ies
b
ef
o
r
e
h
av
in
g
co
m
p
leted
th
e
p
r
o
g
r
am
,
h
ig
h
lig
h
tin
g
th
at
th
ey
d
o
n
o
t
co
n
s
id
er
tem
p
o
r
ar
y
ab
an
d
o
n
m
e
n
t
(
d
u
e
to
illn
ess
o
r
p
r
eg
n
a
n
cy
,
f
o
r
ex
am
p
le)
as
d
r
o
p
o
u
t,
a
n
d
th
at
it
is
a
p
r
o
b
lem
with
m
an
y
co
n
s
eq
u
en
ce
s
f
o
r
s
o
ciet
y
,
f
o
r
th
e
u
n
iv
er
s
ity
an
d
f
o
r
t
h
e
p
er
s
o
n
wh
o
d
r
o
p
s
o
u
t.
T
h
i
s
ter
m
is
lin
k
ed
to
o
th
er
co
n
ce
p
ts
s
u
ch
as g
r
a
d
u
at
io
n
,
r
eten
tio
n
,
p
e
r
s
is
ten
ce
,
o
r
p
er
m
an
en
ce
[
8
]
,
[
9
]
.
Gr
ad
u
atio
n
is
o
f
ten
p
r
esen
te
d
as
th
e
an
tith
esis
o
r
t
h
e
co
m
p
lem
en
tar
y
co
n
ce
p
t
to
d
r
o
p
o
u
t.
T
h
e
g
lo
s
s
ar
y
o
f
t
h
e
s
y
s
tem
f
o
r
th
e
p
r
ev
e
n
tio
n
o
f
d
r
o
p
o
u
t
in
h
ig
h
er
ed
u
ca
tio
n
[
1
0
]
d
ef
in
es
a
g
r
ad
u
ate
as
a
s
tu
d
en
t
wh
o
ac
q
u
ir
es
a
h
ig
h
er
e
d
u
ca
t
io
n
d
eg
r
ee
at
th
e
en
d
o
f
th
e
a
ca
d
em
ic
p
er
io
d
af
ter
p
ass
in
g
all
s
u
b
jects.
W
h
e
n
e
x
p
l
o
r
i
n
g
d
e
f
i
n
i
t
i
o
n
s
o
f
r
eten
t
io
n
an
d
p
er
s
is
ten
ce
,
s
o
m
e
a
u
th
o
r
s
u
s
e
t
h
e
s
e
t
e
r
m
s
e
q
u
a
l
l
y
,
w
h
i
l
e
o
t
h
e
r
s
u
s
e
d
i
f
f
e
r
e
n
t
d
ef
in
itio
n
s
f
o
r
ea
ch
.
So
m
e
liter
atu
r
e
[
1
1
]
u
n
d
er
s
t
an
d
b
o
th
r
ete
n
tio
n
a
n
d
p
er
s
is
ten
ce
as
th
e
ac
t
o
f
r
em
ain
in
g
en
r
o
lled
in
a
h
ig
h
er
ed
u
ca
tio
n
in
s
titu
tio
n
,
with
o
u
t
with
d
r
awin
g
o
r
d
r
o
p
p
in
g
o
u
t.
On
th
e
o
th
er
h
an
d
,
o
th
er
r
esear
ch
[
1
2
]
,
[
1
3
]
r
elat
e
r
eten
tio
n
to
t
h
e
ca
p
ac
ity
o
f
th
e
in
s
titu
tio
n
to
m
ain
tain
th
e
atten
d
an
ce
o
f
its
s
tu
d
en
ts
u
n
til
th
ey
o
b
tain
th
eir
d
eg
r
ee
,
wh
ile
p
er
s
is
ten
ce
is
ass
o
ciate
d
with
th
e
s
tu
d
en
t,
h
is
ab
ilit
y
o
r
m
o
tiv
atio
n
to
co
n
tin
u
e
with
th
eir
s
tu
d
ies
u
n
til
th
ey
r
ea
ch
th
eir
ac
ad
em
ic
g
o
al.
T
h
e
latter
way
o
f
u
n
d
e
r
s
t
a
n
d
i
n
g
t
h
e
s
e
c
o
n
c
e
p
t
s
i
s
t
h
e
m
o
s
t
co
m
m
o
n
i
n
th
e
liter
atu
r
e
a
n
d
,
m
o
r
eo
v
er
,
with
th
e
m
o
s
t
cu
r
r
en
t
r
ef
er
en
ce
s
.
Fin
ally
,
s
tu
d
en
t
p
er
m
an
en
ce
is
d
e
f
in
ed
as
th
e
co
n
d
itio
n
t
h
at
m
a
k
es
th
e
s
tu
d
en
t
r
em
ain
an
ac
tiv
e
m
e
m
b
er
o
f
th
e
h
ig
h
er
ed
u
ca
tio
n
in
s
titu
tio
n
,
with
o
u
t
d
r
o
p
p
in
g
o
u
t
o
f
t
h
e
s
t
u
d
y
p
r
o
g
r
am
th
at
will a
llo
w
h
im
to
g
r
ad
u
ate
[
1
4
]
.
A
liter
atu
r
e
r
ev
iew
o
f
p
r
ev
i
o
u
s
s
tu
d
ies
o
n
d
r
o
p
o
u
t
in
h
ig
h
er
ed
u
ca
tio
n
s
h
o
ws
th
at
it
is
a
p
r
o
b
le
m
s
h
ar
ed
b
y
d
if
f
er
e
n
t
co
u
n
tr
ies,
in
clu
d
in
g
d
if
f
er
e
n
t
co
n
tin
e
n
ts
.
T
h
ey
all
ag
r
ee
o
n
a
co
m
m
o
n
r
esear
ch
in
ten
tio
n
to
d
eter
m
in
e
f
ac
to
r
s
ass
o
ciate
d
with
th
e
d
r
o
p
o
u
t
p
h
e
n
o
m
en
o
n
af
f
ec
tin
g
s
tu
d
e
n
ts
,
th
e
f
a
m
ily
an
d
th
e
s
o
cial
en
v
ir
o
n
m
en
t,
an
d
s
o
m
e
o
f
th
ese
r
esu
lts
wer
e
d
eter
m
in
ed
b
y
im
p
lem
en
tin
g
d
if
f
er
en
t
as
s
ess
m
en
t
m
o
d
els
to
d
eter
m
in
e
th
e
r
elev
a
n
t
ca
u
s
al
f
ac
to
r
s
.
C
o
n
s
id
er
in
g
th
e
h
ig
h
d
r
o
p
o
u
t
r
ate
in
h
ig
h
er
ed
u
c
atio
n
,
s
tu
d
ies
h
av
e
s
h
o
wn
th
e
n
ee
d
t
o
cr
ea
te
m
ec
h
an
is
m
s
to
d
etec
t
it
a
n
d
f
o
r
i
n
s
titu
tio
n
s
to
h
av
e
an
o
r
g
a
n
izatio
n
co
m
p
o
s
ed
o
f
r
ep
r
esen
tativ
es
o
f
s
tu
d
en
ts
,
te
ac
h
er
s
,
ad
m
in
is
tr
ato
r
s
an
d
p
a
r
en
ts
,
in
o
r
d
e
r
to
ac
h
iev
e
s
tu
d
en
t
r
eten
tio
n
[
1
5
]
.
Giv
en
th
is
n
ee
d
,
m
o
s
t
o
f
th
e
s
tu
d
ies
f
o
u
n
d
o
n
th
e
s
u
b
ject
f
o
cu
s
o
n
th
e
s
tu
d
y
o
f
ex
p
lan
at
o
r
y
m
o
d
els
o
n
th
e
r
eten
tio
n
a
n
d
p
er
s
is
ten
ce
o
f
s
tu
d
en
ts
in
h
ig
h
e
r
ed
u
ca
tio
n
[
1
6
]
–
[
1
9
]
,
m
o
r
e
s
p
ec
if
ically
,
o
n
r
esear
ch
o
n
m
o
d
els
o
f
th
e
v
a
r
iab
les
th
at
ca
u
s
e
d
r
o
p
o
u
ts
an
d
,
in
th
is
way
,
to
b
e
a
b
le
to
d
etec
t
th
em
a
n
d
p
r
ev
en
t
d
r
o
p
o
u
ts
,
r
ed
u
cin
g
cu
r
r
en
t
r
ates
[
1
]
,
[
2
0
]
.
I
t
is
n
ec
ess
ar
y
to
h
ig
h
lig
h
t
th
e
p
r
e
v
i
o
u
s
wo
r
k
[
2
1
]
,
[
2
2
]
wh
o
co
n
c
ep
tu
alize
u
n
iv
er
s
ity
s
tu
d
en
t
d
eser
tio
n
,
d
elv
in
g
in
to
wh
at
it
is
,
wh
at
ty
p
es
o
f
d
eser
tio
n
ex
is
t,
wh
at
ar
e
th
e
ass
o
ciate
d
v
ar
iab
les
an
d
th
eir
lev
els
o
f
in
cid
en
ce
,
wh
o
ar
e
th
e
ac
to
r
s
o
f
d
r
o
p
o
u
t,
an
d
wh
at
ar
e
th
e
ed
u
ca
tio
n
al,
s
o
cial,
an
d
p
o
liti
ca
l
p
r
o
b
lem
s
ass
o
ciate
d
with
it.
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
A
n
a
lysi
s
o
f a
ca
d
emic
d
eser
tio
n
a
mo
n
g
u
n
g
r
a
d
u
a
ted
ma
th
em
a
tics
s
tu
d
en
ts
(
Mig
u
el
A
.
R
o
d
r
íg
u
ez
-
Má
r
q
u
ez
)
3861
Am
o
n
g
th
e
lar
g
e
n
u
m
b
er
o
f
r
esear
ch
er
s
wh
o
f
o
cu
s
th
eir
s
tu
d
ies
o
n
th
e
ex
p
lan
ato
r
y
f
ac
to
r
s
o
f
d
eser
tio
n
,
h
ig
h
lig
h
tin
g
th
e
im
p
o
r
tan
ce
o
f
s
tu
d
y
in
g
in
d
e
p
th
th
e
ca
u
s
es
th
at
e
x
p
lain
it
[
2
3
]
,
[
2
4
]
,
m
an
y
au
th
o
r
s
ag
r
ee
th
at
it
h
as
a
m
u
lti
-
ca
u
s
al
s
tr
u
ctu
r
e,
th
at
is
,
a
wid
e
r
a
n
g
e
o
f
v
ar
iab
les
an
d
t
y
p
es
o
f
v
ar
iab
les
th
at
h
av
e
a
s
ig
n
if
ican
t
im
p
ac
t
o
n
th
e
d
r
o
p
o
u
t
o
f
u
n
i
v
er
s
ity
s
tu
d
en
ts
[
1
]
,
[
7
]
,
[
2
0
]
,
[
2
5
]
.
So
m
e
o
f
th
e
v
ar
iab
les
th
at
s
tan
d
o
u
t
as
s
ig
n
if
ican
t
ca
u
s
es
o
f
s
tu
d
en
t
d
eser
tio
n
in
h
ig
h
er
ed
u
ca
tio
n
ar
e
th
e
f
o
llo
win
g
:
p
e
r
s
o
n
al
cir
cu
m
s
tan
ce
s
o
f
th
e
s
tu
d
en
ts
[
2
3
]
,
th
eir
p
s
y
c
h
o
lo
g
ical
n
atu
r
e
[
2
6
]
;
ac
ad
e
m
ic,
m
o
tiv
atio
n
al,
v
o
ca
tio
n
al
an
d
s
o
cio
ec
o
n
o
m
ic
f
ac
to
r
s
[
2
5
]
;
th
eir
o
wn
ed
u
ca
tio
n
al
lev
el
an
d
th
at
o
f
th
eir
p
ar
en
ts
,
ac
ad
em
ic
p
er
f
o
r
m
a
n
ce
,
f
u
n
d
in
g
a
n
d
f
am
il
y
co
n
f
ig
u
r
atio
n
[
2
7
]
;
ag
e
u
n
d
er
3
0
,
lo
w
in
c
o
m
e,
h
av
in
g
to
c
o
m
b
in
e
s
tu
d
ies
with
a
jo
b
,
an
d
th
e
n
ee
d
f
o
r
f
u
n
d
in
g
[
2
5
]
,
[
2
8
]
.
Alo
n
g
th
e
s
am
e
lin
es,
[
2
9
]
,
[
3
0
]
,
wh
o
s
tu
d
ie
d
th
e
s
tate
o
f
d
r
o
p
o
u
t
an
d
t
h
e
ca
u
s
es
th
at
g
e
n
er
ate
it
,
ad
d
r
ess
th
e
p
r
o
b
lem
o
f
d
r
o
p
o
u
t
in
co
m
p
u
ter
s
cien
ce
s
tu
d
e
n
ts
,
f
in
d
in
g
a
c
o
r
r
elatio
n
b
etwe
en
d
r
o
p
o
u
t
a
n
d
th
e
u
s
e
o
f
tech
n
o
lo
g
ical
m
ed
ia,
a
g
e
an
d
p
r
e
v
io
u
s
tr
ain
in
g
;
th
e
y
also
h
ig
h
lig
h
t,
as
th
e
m
ain
r
e
aso
n
s
f
o
r
d
r
o
p
p
in
g
o
u
t,
th
e
d
if
f
icu
lty
in
ca
lcu
lati
n
g
th
e
tim
e
n
ee
d
e
d
to
d
e
d
icate
to
u
n
iv
er
s
ity
-
lev
el
co
u
r
s
es
an
d
th
e
p
er
ce
i
v
ed
d
if
f
icu
lty
in
th
e
cu
r
r
icu
lar
s
u
b
jects
o
f
th
e
C
o
m
p
u
ter
Scien
ce
s
y
llab
u
s
.
Fo
r
th
eir
p
ar
t,
s
tu
d
y
[
3
1
]
,
[
3
2
]
was
co
n
d
u
cte
d
a
with
h
ig
h
er
ed
u
c
atio
n
s
tu
d
en
ts
p
ar
ticip
atin
g
in
co
o
p
er
ativ
e
s
tu
d
y
p
r
o
g
r
am
s
,
wh
ich
co
m
b
in
e
th
eir
s
tu
d
ies
with
tr
ain
in
g
in
a
wo
r
k
co
m
p
a
n
y
,
an
d
th
ey
c
o
n
f
ir
m
th
e
im
p
ac
t
o
f
c
o
g
n
itiv
e
s
k
ills
an
d
o
r
g
an
izatio
n
al
awa
r
en
ess
o
n
d
r
o
p
o
u
t.
F
i
n
a
l
l
y
,
a
f
t
e
r
s
t
u
d
y
i
n
g
t
h
e
s
t
a
te
o
f
d
e
s
e
r
t
i
o
n
a
n
d
t
h
e
c
a
u
s
e
s
th
a
t
p
r
o
v
o
k
e
i
t
,
s
o
m
e
p
u
b
l
i
c
a
t
i
o
n
s
m
a
k
e
p
r
o
p
o
s
a
l
s
t
o
a
ll
e
v
i
a
te
t
h
is
s
it
u
at
i
o
n
,
s
u
c
h
a
s
A
l
b
a
n
a
n
d
M
a
u
r
ic
i
o
[
2
3
]
,
w
h
o
s
u
g
g
e
s
t
i
n
c
r
e
as
i
n
g
t
h
e
li
n
k
s
b
et
w
e
e
n
u
n
i
v
e
r
s
i
t
ie
s
a
n
d
t
h
ei
r
s
t
u
d
e
n
ts
in
o
r
d
e
r
t
o
i
m
p
r
o
v
e
t
h
e
i
r
w
e
l
l
b
ei
n
g
a
n
d
,
i
n
t
h
i
s
wa
y
,
p
r
e
v
e
n
t
t
h
e
m
f
r
o
m
d
e
s
e
r
t
i
o
n
.
O
t
h
e
r
s
t
u
d
i
e
s
[
3
3
]
,
[
3
4
]
s
u
g
g
e
s
t
ed
m
e
as
u
r
es
t
h
a
t
f
a
v
o
r
t
h
e
ad
a
p
t
a
t
i
o
n
o
f
t
h
e
s
t
u
d
e
n
ts
,
e
m
p
h
a
s
i
z
i
n
g
t
h
e
w
o
r
k
o
f
t
h
e
t
e
a
c
h
e
r
s
t
h
a
t
ac
t
as
t
u
t
o
r
s
;
o
r
p
r
e
v
i
o
u
s
r
e
s
e
a
r
c
h
[
3
5
]
,
[
3
6
]
,
w
h
o
r
e
c
o
m
m
e
n
d
c
h
a
r
a
c
t
e
r
iz
i
n
g
s
t
u
d
e
n
ts
a
t
t
h
e
b
e
g
i
n
n
i
n
g
o
f
t
h
e
i
r
s
t
u
d
i
es
t
o
f
i
n
d
o
u
t
t
h
e
i
r
v
u
l
n
e
r
a
b
i
l
it
i
es
,
m
o
n
i
t
o
r
i
n
g
t
h
e
m
w
it
h
s
p
e
ci
a
li
z
e
d
s
o
f
t
w
a
r
e
,
f
a
c
il
i
t
at
i
n
g
t
h
e
i
r
i
n
t
e
g
r
a
t
i
o
n
a
n
d
p
r
o
v
i
d
i
n
g
t
h
e
m
w
i
t
h
g
u
i
d
a
n
c
e
,
a
s
w
el
l
a
s
s
u
p
p
o
r
t
i
n
g
t
h
e
m
f
i
n
a
n
c
ia
l
l
y
.
A
s
i
n
d
i
ca
t
e
d
,
u
n
i
v
e
r
s
i
t
y
d
es
e
r
t
i
o
n
i
s
c
o
n
s
i
d
er
e
d
a
s
t
r
u
ct
u
r
a
l
p
r
o
b
l
e
m
i
n
h
ig
h
e
r
e
d
u
c
a
t
i
o
n
a
n
d
,
t
o
a
as
i
n
d
i
c
a
t
e
d
,
u
n
i
v
e
r
s
i
t
y
d
e
s
e
r
t
i
o
n
is
c
o
n
s
i
d
e
r
e
d
a
s
t
r
u
ct
u
r
a
l
p
r
o
b
l
e
m
i
n
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
a
n
d
,
t
o
a
g
r
e
a
t
e
r
e
x
t
e
n
t
,
i
n
C
o
l
o
m
b
i
a
.
F
o
r
t
h
is
r
e
a
s
o
n
,
t
h
is
r
es
e
a
r
c
h
h
as
b
e
e
n
c
a
r
r
i
e
d
o
u
t
i
n
a
u
n
i
v
e
r
s
i
t
y
i
n
C
o
l
o
m
b
i
a
a
n
d
i
t
b
ec
o
m
e
s
f
u
n
d
am
e
n
t
a
l
t
o
r
e
v
i
e
w
t
h
e
s
t
u
d
i
es
t
h
a
t
c
l
a
r
i
f
y
t
h
e
s
it
u
a
t
i
o
n
o
f
d
r
o
p
o
u
t
i
n
t
h
i
s
c
o
u
n
t
r
y
,
in
t
e
r
m
s
o
f
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
s
tu
d
e
n
t
s
.
I
n
t
h
is
l
i
n
e
,
s
e
v
e
r
a
l
r
es
e
a
r
c
h
[
1
0
]
,
[
2
5
]
r
e
v
i
e
w
e
d
t
h
e
e
x
is
t
i
n
g
t
h
e
o
r
ie
s
o
n
d
r
o
p
o
u
t
a
n
d
t
h
e
r
e
t
e
n
t
i
o
n
p
r
o
g
r
a
m
s
t
h
a
t
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
i
n
s
t
i
t
u
t
i
o
n
s
h
a
d
t
o
r
e
d
u
c
e
i
t
.
F
u
r
t
h
e
r
m
o
r
e
,
t
h
is
s
t
u
d
y
a
n
a
l
y
z
e
d
t
h
e
i
n
f
l
u
en
c
e
o
f
i
n
d
i
v
i
d
u
a
l
,
s
o
c
i
o
e
c
o
n
o
m
i
c
,
ac
a
d
e
m
i
c
,
a
n
d
i
n
s
ti
t
u
t
i
o
n
al
v
a
r
i
a
b
le
s
t
h
a
t
a
f
f
e
c
t
d
e
s
e
r
t
i
o
n
f
r
o
m
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
,
h
i
g
h
l
i
g
h
ti
n
g
t
h
e
a
c
a
d
e
m
i
c
f
a
c
t
o
r
as
t
h
e
m
o
s
t
s
i
g
n
i
f
i
c
a
n
t
.
O
n
t
h
e
o
t
h
e
r
h
an
d
,
a
n
o
t
h
e
r
s
t
u
d
i
es
[
4
]
,
[
1
0
]
i
n
v
e
s
t
i
g
a
te
d
d
r
o
p
o
u
t
t
h
r
o
u
g
h
e
x
p
l
a
n
a
t
o
r
y
a
n
d
f
a
c
t
o
r
i
a
l
a
n
al
y
s
is
,
i
d
e
n
t
i
f
y
i
n
g
t
h
e
f
a
ct
o
r
s
t
h
at
i
n
f
l
u
e
n
ce
d
r
o
p
o
u
t
a
n
d
n
o
n
-
g
r
a
d
u
a
t
i
o
n
o
f
t
h
e
p
o
p
u
l
a
t
i
o
n
,
t
h
e
r
e
s
u
lt
s
c
o
n
f
i
r
m
t
h
e
j
o
i
n
t
i
m
p
a
c
t
t
h
a
t
s
o
cio
e
c
o
n
o
m
i
c
,
i
n
d
i
v
i
d
u
a
l
,
a
c
a
d
em
i
c
a
n
d
i
n
s
t
it
u
t
i
o
n
a
l
f
a
c
t
o
r
s
h
a
v
e
o
n
d
r
o
p
o
u
t
a
n
d
g
r
a
d
u
a
t
i
o
n
,
w
h
i
c
h
i
s
a
d
e
t
e
r
m
i
n
an
t
f
o
r
t
h
e
d
e
s
i
g
n
o
f
t
r
u
l
y
c
o
m
p
r
e
h
e
n
s
i
v
e
s
t
r
at
e
g
i
es
f
o
r
i
t
s
p
r
e
v
e
n
t
i
o
n
.
Oth
er
ar
ticles
also
in
v
esti
g
ate
d
r
o
p
o
u
t
in
h
ig
h
e
r
ed
u
ca
tio
n
i
n
C
o
lo
m
b
ia,
h
ig
h
lig
h
tin
g
th
e
ex
is
tin
g
p
r
o
b
lem
an
d
th
e
n
ee
d
t
o
s
tu
d
y
it,
b
u
t
f
o
c
u
s
in
g
o
n
d
eg
r
ee
s
o
r
f
ac
u
lties
o
th
er
th
a
n
m
ath
e
m
atics
,
s
u
ch
in
th
e
Facu
lty
o
f
Ps
y
ch
o
lo
g
y
[
2
8
]
;
t
h
e
Deg
r
ee
in
B
io
lo
g
y
[
3
7
]
;
o
r
th
e
Deg
r
ee
in
Nu
r
s
in
g
[
2
4
]
,
[
3
8
]
.
T
o
co
n
clu
d
e,
it
is
es
s
en
tial
to
p
o
in
t
o
u
t
th
e
ex
is
ten
ce
o
f
o
th
er
s
tu
d
ies
at
th
e
Un
iv
er
s
ity
o
f
T
o
lim
a,
s
in
ce
th
is
is
th
e
in
s
titu
tio
n
wh
er
e
th
e
p
r
esen
t
r
esear
ch
is
b
ein
g
ca
r
r
ied
o
u
t
.
L
o
u
te
n
[
1
2
]
co
n
d
u
cted
a
s
tu
d
y
s
im
ilar
to
th
e
p
r
esen
t
o
n
e,
b
u
t
in
d
if
f
er
en
t
p
r
o
g
r
am
s
o
f
th
e
S
cien
ce
,
T
ec
h
n
o
l
o
g
y
,
E
n
g
in
ee
r
in
g
,
an
d
Ma
t
h
em
atics.
On
th
e
o
th
er
h
an
d
,
C
astro
-
C
ar
v
ajal
[
2
5
]
f
o
cu
s
ed
o
n
t
h
e
Deg
r
ee
in
Ma
th
em
atics
;
th
ey
f
o
u
n
d
t
h
e
r
elatio
n
s
h
ip
b
etwe
en
s
ch
o
o
l
d
r
o
p
o
u
t
a
n
d
ec
o
n
o
m
ic
co
n
d
itio
n
s
,
th
e
s
atis
f
ac
tio
n
o
f
d
eg
r
ee
e
x
p
ec
tatio
n
s
an
d
in
d
iv
id
u
al
ch
a
r
ac
ter
is
tics
.
R
eg
ar
d
in
g
th
e
m
ath
em
atica
l
m
o
d
els
u
s
ed
in
s
im
ilar
s
tu
d
ies,
we
h
av
e
f
o
u
n
d
d
if
f
er
e
n
t
ap
p
r
o
ac
h
es
,
s
u
c
h
Pellag
atti
[
1
6
]
wh
o
p
r
o
p
o
s
e
th
e
g
en
er
alize
d
m
i
x
ed
-
ef
f
ec
ts
r
an
d
o
m
f
o
r
est
m
o
d
el
(
GM
E
R
F
)
,
wh
ich
in
co
r
p
o
r
ates
th
e
u
s
e
o
f
en
s
em
b
le
m
eth
o
d
s
b
ased
o
n
t
r
ee
s
with
in
th
e
s
tr
u
ctu
r
e
o
f
m
ix
ed
-
ef
f
ec
ts
m
o
d
els;
,
an
im
p
r
o
v
ed
d
ec
is
io
n
tr
ee
a
l
g
o
r
i
t
h
m
b
a
s
e
d
o
n
t
h
e
i
d
3
(
i
ter
a
t
i
v
e
d
i
c
h
o
t
o
m
i
z
e
d
3
)
al
g
o
r
i
t
h
m
[
3
9
]
;
th
e
o
p
e
n
s
o
u
r
ce
Had
o
o
p
s
y
s
tem
[
4
0
]
; a
n
d
u
p
lift
m
o
d
el,
wh
ich
is
a
p
r
e
d
ic
tiv
e
an
aly
tics
tech
n
iq
u
e
t
h
at
esti
m
ates th
e
ef
f
ec
t o
f
in
d
iv
id
u
al
tr
ea
tm
en
t
[
1
5
]
.
I
n
t
h
i
s
s
t
u
d
y
,
a
n
a
n
a
l
y
s
is
o
f
t
h
e
d
i
f
f
e
r
e
n
t
c
a
u
s
e
s
o
f
d
r
o
p
o
u
t
w
a
s
c
a
r
r
i
e
d
o
u
t
t
h
r
o
u
g
h
a
s
t
a
t
is
t
ic
a
l
m
o
d
e
l
,
b
a
s
e
d
o
n
t
h
e
a
c
a
d
e
m
i
c,
i
n
d
i
v
i
d
u
a
l
,
ec
o
n
o
m
i
c
a
n
d
i
n
s
t
i
t
u
t
i
o
n
al
f
a
c
t
o
r
s
o
f
t
h
e
s
t
u
d
e
n
t
s
o
f
t
h
e
B
a
c
h
e
l
o
r
'
s
D
e
g
r
e
e
i
n
M
a
t
h
e
m
a
ti
cs
a
t
t
h
e
U
n
i
v
e
r
s
i
t
y
o
f
T
o
li
m
a
d
u
r
i
n
g
t
h
e
a
c
a
d
e
m
i
c
p
e
r
i
o
d
2
0
1
2
A
-
2
0
1
8
B
,
a
c
c
o
r
d
i
n
g
t
o
g
u
i
d
e
l
i
n
e
s
o
f
t
h
e
M
i
n
is
t
r
y
o
f
Hi
g
h
e
r
E
d
u
c
a
t
i
o
n
(
ME
N
)
,
i
n
C
o
l
o
m
b
i
a
,
wi
t
h
t
h
e
p
u
r
p
o
s
e
o
f
i
d
e
n
t
i
f
y
i
n
g
t
h
e
s
o
c
ia
l
,
e
c
o
n
o
m
i
c
a
n
d
a
c
a
d
e
m
i
c
v
a
r
i
a
b
l
e
s
a
s
s
o
c
i
at
e
d
w
i
t
h
s
t
u
d
e
n
t
d
r
o
p
o
u
t
i
n
t
h
i
s
p
r
o
g
r
a
m
.
T
h
e
e
v
a
l
u
a
t
i
o
n
o
f
r
e
l
e
v
a
n
t
f
a
c
t
o
r
s
b
y
c
a
t
e
g
o
r
i
es
w
as
c
a
r
r
i
e
d
o
u
t
b
y
i
m
p
l
e
m
e
n
t
i
n
g
t
h
e
K
a
p
l
a
n
-
M
e
i
e
r
s
t
at
is
t
i
c
al
m
o
d
e
l
[
2
1
]
.
F
a
c
t
o
r
d
a
t
a
a
c
c
o
r
d
i
n
g
t
o
d
a
t
a
r
e
t
e
n
ti
o
n
g
u
i
d
e
l
i
n
e
s
w
e
r
e
c
o
n
s
o
l
i
d
a
t
e
d
u
s
i
n
g
i
n
f
o
r
m
a
t
i
o
n
p
r
o
v
i
d
e
d
b
y
t
h
e
U
n
i
v
e
r
s
i
t
y
o
f
T
o
l
i
m
a
.
N
o
n
-
p
a
r
a
m
e
t
r
i
c
s
t
a
ti
s
ti
c
a
l
m
o
d
e
l
s
w
e
r
e
i
m
p
l
e
m
e
n
t
e
d
i
n
t
h
e
e
v
a
l
u
a
t
i
o
n
o
f
t
h
e
s
e
v
a
r
i
a
b
l
e
s
t
o
d
e
t
e
r
m
i
n
e
i
n
d
i
v
i
d
u
a
l
,
a
c
a
d
e
m
i
c
,
i
n
s
t
it
u
t
io
n
a
l
a
n
d
e
c
o
n
o
m
i
c
p
a
tt
e
r
n
s
r
e
l
a
t
e
d
t
o
t
h
e
c
a
u
s
es
o
f
a
tt
r
i
ti
o
n
o
f
s
t
u
d
e
n
ts
o
f
t
h
e
B
a
c
h
e
l
o
r
'
s
D
e
g
r
e
e
i
n
M
a
t
h
e
m
at
i
c
s
a
t
t
h
e
U
n
i
v
e
r
s
i
t
y
o
f
T
o
l
i
m
a
d
u
r
i
n
g
t
h
e
a
c
a
d
e
m
i
c
p
e
r
i
o
d
2
0
1
2
A
-
2
0
1
8
B
.
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
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
8
5
9
-
3
8
7
1
3862
2.
M
E
T
H
O
D
2
.
1
.
Resea
rc
h desi
g
n
T
h
e
ap
p
r
o
ac
h
u
s
ed
to
d
e
v
el
o
p
th
is
r
esear
c
h
is
q
u
a
n
titativ
e,
b
ec
a
u
s
e,
r
ec
o
g
n
izin
g
s
o
m
e
in
itial
h
y
p
o
th
eses
r
elate
d
to
th
e
p
h
en
o
m
e
n
o
n
o
f
d
eser
tio
n
an
d
ac
co
r
d
in
g
to
th
e
i
n
f
o
r
m
atio
n
co
llected
,
s
o
m
e
s
tatis
t
ical
an
aly
s
es
ar
e
ca
r
r
ied
o
u
t
f
r
o
m
wh
ich
it
is
in
ten
d
e
d
to
e
x
tr
ac
t
p
atter
n
s
o
f
b
e
h
av
io
r
an
d
co
n
clu
s
io
n
s
ab
o
u
t
t
h
e
r
esu
lts
o
b
tain
ed
[
4
1
]
.
P
r
ev
io
u
s
s
tu
d
ies
[
4
2
]
,
[
4
3
]
d
escr
ib
e
d
th
r
ee
lev
els
o
f
n
o
n
-
ex
p
er
im
en
tal
q
u
an
titativ
e
r
esear
ch
d
esig
n
.
T
h
ese
ar
e
ex
p
lo
r
ato
r
y
,
d
esc
r
ip
tiv
e,
an
d
co
r
r
elatio
n
al.
C
o
n
s
id
er
in
g
th
at
th
e
r
esear
ch
tr
ies
to
ch
a
r
ac
ter
ize
th
e
m
o
s
t
in
f
lu
en
tial
f
ac
to
r
s
in
th
e
d
eser
tio
n
o
f
u
n
d
er
g
r
ad
u
ate
s
tu
d
en
ts
in
m
ath
em
atics
at
th
e
Un
i
v
er
s
ity
o
f
T
o
lim
a,
we
r
eso
r
ted
to
an
ex
p
lo
r
ato
r
y
s
tu
d
y
b
ec
au
s
e
it
a
llo
ws
u
s
to
in
cr
ea
s
e
th
e
d
eg
r
ee
o
f
f
am
iliar
ity
with
r
elativ
ely
u
n
k
n
o
wn
p
h
e
n
o
m
en
a,
o
b
tain
in
g
in
f
o
r
m
atio
n
to
ca
r
r
y
o
u
t
a
m
o
r
e
co
m
p
lete
in
v
esti
g
atio
n
o
n
a
p
ar
ticu
lar
co
n
te
x
t
o
f
r
ea
l
life
,
i
n
th
is
ca
s
e
th
e
U
n
iv
er
s
ity
o
f
T
o
lim
a,
in
o
r
d
e
r
to
d
eter
m
in
e
th
e
ca
u
s
es a
n
d
th
e
d
if
f
er
en
t v
a
r
iab
les th
at
ca
u
s
e
th
ese
p
h
en
o
m
e
n
a
[
2
5
]
,
[
2
8
]
.
I
n
a
d
d
i
t
i
o
n
,
t
h
is
i
s
a
d
e
s
c
r
i
p
t
i
v
e
d
e
s
i
g
n
b
e
ca
u
s
e
i
t
a
i
m
s
t
o
i
d
en
t
i
f
y
,
e
x
p
o
s
e
,
a
n
d
d
es
c
r
i
b
e
t
h
e
v
a
r
i
a
b
l
e
s
t
h
a
t
i
n
f
l
u
e
n
c
e
a
p
h
e
n
o
m
e
n
o
n
[
1
2
]
,
[
1
5
]
,
[
2
8
]
,
m
o
r
e
s
p
e
ci
f
i
c
a
ll
y
,
t
h
e
v
a
r
i
a
b
l
es
t
h
a
t
c
a
u
s
e
d
e
s
e
r
t
i
o
n
i
n
t
h
e
D
e
g
r
ee
i
n
M
a
t
h
e
m
at
i
cs
a
t
t
h
e
U
n
i
v
e
r
s
it
y
o
f
T
o
l
i
m
a
.
T
h
e
t
h
i
r
d
t
y
p
e
o
f
d
e
s
i
g
n
d
e
v
el
o
p
e
d
i
n
t
h
is
r
es
e
ar
c
h
i
s
c
o
r
r
e
l
at
i
o
n
a
l
.
I
t
s
p
u
r
p
o
s
e
i
s
t
o
d
e
t
e
r
m
i
n
e
t
h
e
r
e
l
a
t
i
o
n
s
h
i
p
o
r
d
e
g
r
e
e
o
f
a
s
s
o
c
i
a
t
i
o
n
t
h
a
t
e
x
i
s
ts
b
e
tw
e
e
n
d
i
f
f
e
r
e
n
t
c
a
t
e
g
o
r
i
es
o
r
v
a
r
i
a
b
l
e
s
i
n
a
p
a
r
t
ic
u
l
a
r
s
a
m
p
le
o
r
c
o
n
t
e
x
t
[
1
0
]
,
[
2
5
]
,
t
h
a
t
is
,
t
o
e
x
a
m
i
n
e
t
h
e
r
el
a
ti
o
n
s
h
i
p
b
e
t
w
e
e
n
t
h
e
v
a
r
i
a
b
l
es
t
h
a
t
i
n
f
l
u
e
n
ce
d
r
o
p
o
u
t
i
n
t
h
e
De
g
r
e
e
i
n
Ma
t
h
e
m
a
ti
c
s
a
t t
h
e
Un
i
v
e
r
s
i
t
y
o
f
T
o
l
i
m
a
.
T
h
e
a
b
o
v
e
i
s
d
o
n
e
c
o
n
s
i
d
e
r
i
n
g
w
h
a
t
i
s
p
r
o
p
o
s
e
d
[
1
]
,
[
1
3
]
,
[
1
5
]
.
F
r
o
m
t
h
e
q
u
e
s
t
i
o
n
s
,
h
y
p
o
t
h
e
s
e
s
a
r
e
es
t
a
b
li
s
h
e
d
a
n
d
v
a
r
i
a
b
le
s
a
r
e
d
e
t
e
r
m
i
n
e
d
;
a
p
l
a
n
is
d
e
v
is
e
d
t
o
t
es
t
t
h
e
m
(
d
e
s
i
g
n
)
;
v
a
r
i
a
b
l
es
a
r
e
m
e
as
u
r
e
d
i
n
a
g
i
v
e
n
c
o
n
t
e
x
t
;
t
h
e
m
e
as
u
r
e
m
e
n
t
s
o
b
t
a
i
n
e
d
a
r
e
a
n
a
l
y
z
e
d
u
s
i
n
g
s
t
a
ti
s
t
i
c
a
l
m
e
t
h
o
d
s
;
a
n
d
a
s
et
o
f
c
o
n
c
l
u
s
i
o
n
s
is
d
r
a
w
n
r
e
g
a
r
d
i
n
g
t
h
e
h
y
p
o
t
h
e
s
e
s
.
T
h
e
r
esear
ch
tech
n
i
q
u
e
u
s
ed
t
o
d
ev
elo
p
th
is
r
esear
ch
is
th
e
m
u
ltiv
ar
iate
an
aly
s
is
o
f
th
e
d
ata.
T
h
is
an
aly
s
is
was c
ar
r
ied
o
u
t th
r
o
u
g
h
n
o
n
-
p
ar
a
m
etr
ic
test
s
d
u
e
to
th
e
v
ar
iab
les th
at
ar
e
th
e
o
b
ject
o
f
th
is
s
tu
d
y
,
an
d
tak
in
g
i
n
to
ac
c
o
u
n
t
th
e
ch
ar
ac
ter
is
tics
[
2
]
,
[
2
5
]
.
M
os
t
o
f
th
e
s
e
an
aly
s
es
d
o
n
o
t
r
e
q
u
ir
e
ass
u
m
p
tio
n
s
a
b
o
u
t
th
e
s
h
ap
e
o
f
th
e
p
o
p
u
latio
n
d
is
tr
ib
u
tio
n
.
T
h
e
y
ac
ce
p
t
n
o
n
-
n
o
r
m
al
d
is
tr
ib
u
tio
n
s
(
"f
r
ee
"
d
is
tr
ib
u
tio
n
s
)
.
T
h
e
v
ar
iab
les
d
o
n
o
t
n
ec
ess
ar
ily
h
av
e
to
b
e
m
ea
s
u
r
ed
at
an
in
te
r
v
al
o
r
r
atio
lev
el;
th
ey
ca
n
a
n
aly
ze
n
o
m
in
al
o
r
o
r
d
in
al
d
ata.
I
n
f
ac
t,
if
n
o
n
-
p
ar
am
etr
ic
an
aly
s
es
ar
e
to
b
e
ap
p
lied
to
in
ter
v
al
o
r
r
atio
d
a
ta,
th
ey
n
ee
d
to
b
e
s
u
m
m
ar
ized
to
d
is
cr
ete
ca
teg
o
r
ies (
to
a
f
ew)
.
T
h
e
v
ar
ia
b
les m
u
s
t b
e
ca
teg
o
r
ical.
T
o
m
ak
e
th
e
an
aly
s
is
o
f
th
e
i
n
f
o
r
m
atio
n
p
r
o
v
id
ed
b
y
th
e
s
tu
d
en
ts
o
f
th
e
d
eg
r
ee
i
n
Ma
th
em
atics,
th
e
p
er
s
o
n
al
in
f
o
r
m
atio
n
th
at
ea
ch
o
f
th
em
r
eg
is
ter
ed
in
th
e
SP
A
DI
E
S p
latf
o
r
m
was c
o
llected
.
SP
ADI
E
S
is
a
to
o
l
u
s
ed
to
tr
ac
k
n
u
m
b
er
o
f
s
tu
d
en
ts
d
eser
tin
g
in
h
i
g
h
er
e
d
u
c
atio
n
[
2
]
,
[
6
]
,
[
2
5
]
.
T
h
e
d
ata
co
llected
with
th
is
p
latf
o
r
m
wer
e
s
tatis
tically
an
aly
ze
d
with
s
tatis
tical
s
o
f
twar
e
s
u
ch
as
E
x
ce
l
[
9
]
an
d
I
n
f
o
s
tat
[
4
4
]
.
T
h
is
an
aly
s
is
h
as b
ee
n
ca
r
r
ied
o
u
t ta
k
in
g
2
1
s
tu
d
y
v
ar
iab
les as a
r
ef
er
en
ce
,
am
o
n
g
wh
ic
h
co
r
r
elatio
n
s
an
d
ass
o
ciatio
n
s
wer
e
estab
lis
h
ed
,
s
h
o
win
g
if
th
er
e
a
r
e
v
ar
iab
les
th
at
h
a
v
e
a
g
r
ea
ter
im
p
ac
t
o
n
th
e
f
ac
t
th
at
a
s
tu
d
en
t
d
r
o
p
s
o
u
t
t
h
eir
u
n
d
er
g
r
ad
u
ate
s
tu
d
ies,
u
p
d
atin
g
th
e
in
f
o
r
m
atio
n
we
h
av
e
o
n
th
is
ac
ad
em
ic
p
r
o
g
r
a
m
an
d
,
in
th
is
way
,
g
iv
in
g
th
e
p
o
s
s
ib
ilit
y
o
f
g
e
n
er
atin
g
s
o
lu
tio
n
s
th
at
g
en
e
r
ate
an
in
c
r
e
ase
in
th
e
r
eten
tio
n
o
f
s
tu
d
e
n
ts
.
T
h
e
r
esu
lts
o
b
tai
n
ed
h
av
e
b
ee
n
in
ter
p
r
eted
b
ased
o
n
th
e
Ka
p
lan
-
Me
ier
s
tatis
tical
m
o
d
el,
wh
ich
is
a
non
-
p
ar
am
etr
ic
m
a
x
im
u
m
lik
e
lih
o
o
d
c
o
u
n
t e
s
tim
ato
r
o
f
th
e
s
u
r
v
iv
al
f
u
n
ctio
n
S(t)
a
s
in
(
1
)
.
̂
(
)
=
∏
−
<
(
1
)
W
h
er
e
,
co
r
r
esp
o
n
d
s
to
t
h
e
n
u
m
b
er
o
f
s
tu
d
en
ts
wh
o
d
r
o
p
o
u
t
o
f
th
e
d
eg
r
ee
o
f
m
ath
e
m
atics
at
th
e
tim
e;
to
th
e
tim
e
d
eter
m
i
n
ed
b
y
two
c
o
n
s
ec
u
tiv
e
s
em
ester
s
o
u
t
o
f
t
h
e
d
eg
r
ee
,
a
n
d
co
r
r
esp
o
n
d
s
t
o
th
e
n
u
m
b
e
r
o
f
s
tu
d
en
ts
en
r
o
lled
in
th
e
p
r
o
g
r
a
m
at
p
o
ten
tial
r
is
k
u
n
til
ju
s
t
th
e
tim
e
co
r
r
esp
o
n
d
in
g
to
t
h
e
s
u
b
jects
p
ass
ed
b
y
th
e
s
tu
d
en
ts
.
I
f
th
er
e
is
ce
n
s
u
r
e,
is
th
e
n
u
m
b
er
o
f
s
tu
d
en
ts
r
em
ain
in
g
in
th
e
p
r
o
g
r
am
m
e
m
in
u
s
th
e
n
u
m
b
e
r
o
f
ce
n
s
u
r
ed
ca
s
es.
On
ly
th
e
v
ar
iab
le
co
r
r
esp
o
n
d
in
g
to
th
e
s
u
b
jects
p
ass
ed
b
y
s
tu
d
en
ts
wh
o
r
em
ain
in
th
e
p
r
o
g
r
a
m
is
o
b
s
er
v
e
d
[
4
5
]
.
2.
2
.
Study
v
a
ria
bles
D
u
r
i
n
g
t
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
t
h
e
r
e
s
e
a
r
c
h
,
T
a
b
l
e
1
a
b
o
u
t
v
a
r
i
a
b
l
e
s
g
e
n
e
r
a
t
e
d
b
y
t
h
e
G
E
L
I
M
O
g
r
o
u
p
i
n
t
h
e
i
r
r
e
s
e
a
r
c
h
o
n
d
e
s
e
r
t
i
o
n
a
t
t
h
e
U
n
i
v
e
r
s
i
t
y
o
f
T
o
l
i
m
a
[
2
5
]
w
a
s
t
a
k
e
n
a
s
a
r
e
f
e
r
e
n
c
e
,
d
u
e
t
o
t
h
e
f
a
c
t
t
h
a
t
t
h
e
c
o
n
t
e
x
t
s
e
v
a
l
u
a
t
e
d
a
r
e
s
i
m
i
l
a
r
,
a
s
t
h
e
y
a
r
e
d
e
v
e
l
o
p
e
d
w
i
t
h
i
n
t
h
e
U
n
i
v
e
r
s
i
t
y
o
f
T
o
l
i
m
a
.
T
h
e
t
a
b
l
e
o
f
v
a
r
i
a
b
l
e
s
u
s
e
d
i
n
t
h
i
s
r
e
s
e
a
r
c
h
i
s
p
r
e
s
e
n
t
e
d
i
n
T
a
b
l
e
1
.
T
h
e
f
a
c
t
o
r
s
a
n
d
t
i
m
e
o
f
o
b
s
e
r
v
a
t
i
o
n
a
r
e
f
r
a
m
e
d
d
u
r
i
n
g
t
h
e
p
e
r
i
o
d
2
0
1
2
A
-
2
0
1
8
B
,
a
n
d
t
h
e
s
e
s
t
u
d
y
v
a
r
i
a
b
l
e
s
a
r
e
c
o
n
s
o
l
i
d
a
t
e
d
f
o
l
l
o
w
i
n
g
t
h
e
g
u
i
d
e
l
i
n
e
s
o
f
t
h
e
S
y
s
t
e
m
f
o
r
t
h
e
P
r
e
v
e
n
t
i
o
n
o
n
E
v
a
l
u
a
t
i
o
n
a
n
d
M
o
n
i
t
o
r
i
n
g
o
f
D
r
o
p
o
u
t
P
h
e
n
o
m
e
n
o
n
(
S
P
A
D
I
E
S
)
,
t
o
d
e
t
e
r
m
i
n
e
t
h
e
o
b
s
e
r
v
a
t
i
o
n
o
f
s
o
c
i
o
-
e
c
o
n
o
m
i
c
,
a
c
a
d
e
m
i
c
a
n
d
c
u
l
t
u
r
a
l
a
s
s
o
c
i
a
t
e
d
f
a
c
t
o
r
s
t
h
a
t
c
a
n
p
o
t
e
n
t
i
a
l
l
y
i
n
f
l
u
e
n
c
e
d
r
o
p
o
u
t
a
n
d
t
h
a
t
a
r
e
b
a
s
e
l
i
n
e
i
n
f
o
r
m
a
t
i
o
n
r
e
f
e
r
e
n
t
s
i
n
t
h
e
m
e
t
h
o
d
o
l
o
g
i
c
a
l
d
e
v
e
l
o
p
m
e
n
t
o
f
t
h
i
s
r
e
s
e
a
r
c
h
.
B
a
s
e
d
o
n
t
h
e
r
e
s
u
l
t
s
o
f
t
h
e
r
e
s
e
a
r
c
h
,
p
o
s
s
i
b
l
e
s
t
r
a
t
e
g
i
e
s
f
o
r
r
e
t
e
n
t
i
o
n
a
r
e
p
r
o
j
e
c
t
e
d
i
n
a
c
t
i
o
n
p
l
a
n
s
a
i
m
e
d
a
t
m
i
t
i
g
a
t
i
n
g
t
h
e
p
r
o
b
l
e
m
s
i
n
a
c
h
i
e
v
i
n
g
h
i
g
h
e
r
r
e
t
e
n
t
i
o
n
r
a
t
e
s
i
n
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
f
o
r
s
t
u
d
e
n
t
s
w
i
t
h
a
h
i
g
h
e
r
p
r
o
b
a
b
i
l
i
t
y
o
f
p
o
t
e
n
t
i
a
l
l
y
b
e
i
n
g
d
r
o
p
o
u
t
s
[
2
5
]
,
[
4
5
]
,
[
4
6
]
,
[
4
7
]
.
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
A
n
a
lysi
s
o
f a
ca
d
emic
d
eser
tio
n
a
mo
n
g
u
n
g
r
a
d
u
a
ted
ma
th
em
a
tics
s
tu
d
en
ts
(
Mig
u
el
A
.
R
o
d
r
íg
u
ez
-
Má
r
q
u
ez
)
3863
T
ab
le
1
.
So
cial,
cu
ltu
r
al,
an
d
a
ca
d
em
ic
v
ar
iab
les in
th
e
co
n
f
o
r
m
atio
n
o
f
th
e
o
b
s
er
v
atio
n
b
ase
f
o
r
th
e
ch
ar
ac
ter
izatio
n
o
f
ac
ad
em
ic
d
eser
tio
n
in
th
e
Deg
r
ee
o
f
Ma
th
em
atics
at
th
e
Un
iv
er
s
ity
o
f
T
o
lim
a
[
2
5
]
V
a
r
i
a
b
l
e
De
t
a
i
l
V
a
r
i
a
b
l
e
De
t
a
i
l
M
u
n
i
c
i
p
a
l
i
t
y
o
f
r
e
si
d
e
n
c
e
M
u
n
i
c
i
p
a
l
i
t
i
e
s
o
f
C
o
l
o
m
b
i
a
M
u
n
i
c
i
p
a
l
i
t
y
w
h
e
r
e
t
h
e
sch
o
o
l
i
s
l
o
c
a
t
e
d
M
u
n
i
c
i
p
a
l
i
t
i
e
s
i
n
C
o
l
o
m
b
i
a
S
t
a
t
u
s
0
:
En
r
o
l
l
e
d
1
:
D
e
sert
e
r
C
o
d
e
V
a
l
i
d
p
e
r
s
t
u
d
e
n
t
,
a
c
c
o
r
d
i
n
g
t
o
y
e
a
r
o
f
e
n
t
r
y
F
a
c
u
l
t
y
1
:
Ed
u
c
a
t
i
o
n
P
r
o
g
r
a
m
D
e
g
r
e
e
i
n
M
a
t
h
e
m
a
t
i
c
s
P
r
o
g
r
a
m
m
o
d
a
l
i
t
y
0
:
O
n
-
si
t
e
A
g
e
A
g
e
i
n
y
e
a
r
s
G
e
n
d
e
r
0
:
M
a
l
e
1
:
F
e
ma
l
e
F
i
n
a
n
c
i
a
l
s
u
p
p
o
r
t
0
:
Y
e
s
1
:
N
o
C
i
v
i
l
st
a
t
u
s
1
:
S
i
n
g
l
e
2
:
M
a
r
r
i
e
d
3
:
W
i
d
o
w
e
r
4
:
S
e
p
a
r
a
t
e
5
:
F
r
e
e
u
n
i
o
n
(FU)
6
:
N
o
t
d
e
f
i
n
e
d
(
N
D
)
S
o
c
i
o
e
c
o
n
o
m
i
c
s
t
r
a
t
u
m
1
:
S
t
r
a
t
u
m
-
1
2
:
S
t
r
a
t
u
m
-
2
3
:
S
t
r
a
t
u
m
-
3
4
:
S
t
r
a
t
u
m
-
4
5
:
S
t
r
a
t
u
m
-
5
6
:
S
t
r
a
t
u
m
-
6
Ec
o
n
o
mi
c
s
i
t
u
a
t
i
o
n
1
:
I
n
d
e
p
e
n
d
e
n
t
2
:
D
e
p
e
n
d
e
n
t
3
:
Em
p
l
o
y
e
e
4
:
N
o
t
d
e
f
i
n
e
d
(
N
D
)
Ty
p
e
o
f
s
c
h
o
o
l
1
:
P
u
b
l
i
c
2
:
P
r
i
v
a
t
e
3
:
N
o
t
d
e
f
i
n
e
d
(
N
D
)
N
u
mb
e
r
o
f
p
e
o
p
l
e
i
n
t
h
e
f
a
mi
l
y
n
u
c
l
e
u
s
I
n
t
e
g
e
r
v
a
l
u
e
N
u
mb
e
r
o
f
p
e
o
p
l
e
w
o
r
k
i
n
g
i
n
t
h
e
h
o
u
se
h
o
l
d
I
n
t
e
g
e
r
v
a
l
u
e
S
u
b
j
e
c
t
s
t
a
k
e
n
I
n
t
e
g
e
r
v
a
l
u
e
S
u
b
j
e
c
t
s
p
a
sse
d
I
n
t
e
g
e
r
v
a
l
u
e
I
C
F
ES
R
e
a
l
v
a
l
u
e
C
u
m
u
l
a
t
i
v
e
a
v
e
r
a
g
e
R
e
a
l
v
a
l
u
e
S
e
mest
e
r
s s
t
u
d
i
e
d
I
n
t
e
g
e
r
v
a
l
u
e
Tu
i
t
i
o
n
p
a
y
me
n
t
a
v
e
r
a
g
e
R
e
a
l
v
a
l
u
e
Y
e
a
r
o
f
o
b
ser
v
a
t
i
o
n
Y
e
a
r
2
0
1
2
-
A
Y
e
a
r
2
0
1
8
-
B
To
t
a
l
o
b
ser
v
e
d
v
a
r
i
a
b
l
e
s
2
3
o
b
ser
v
e
d
v
a
r
i
a
b
l
e
s
2.
3
.
P
a
rt
icipa
nts
Du
r
in
g
th
e
d
ev
el
o
p
m
en
t
o
f
th
e
r
esear
ch
,
a
s
am
p
le
o
f
5
0
1
s
t
u
d
en
ts
o
f
th
e
Deg
r
ee
in
Ma
t
h
e
m
atics
wa
s
s
elec
ted
.
Fo
r
th
e
s
elec
tio
n
o
f
th
is
s
am
p
le,
th
e
m
ain
ch
ar
ac
te
r
is
tic
was
s
tu
d
en
ts
wh
o
en
r
o
ll
ed
in
th
e
Deg
r
ee
in
Ma
th
em
atics
d
u
r
in
g
th
e
o
b
s
er
v
atio
n
p
er
io
d
2
0
1
2
A
-
2
0
1
8
B
.
T
h
e
letter
s
A
o
r
B
o
f
th
e
d
ates
r
ef
er
to
th
e
f
ir
s
t
an
d
s
ec
o
n
d
ter
m
o
f
th
e
co
u
r
s
e,
r
esp
ec
tiv
ely
.
I
t
s
h
o
u
l
d
b
e
n
o
t
e
d
t
h
at
,
d
u
r
i
n
g
t
h
e
r
e
s
e
a
r
c
h
,
a
p
e
r
c
e
n
ta
g
e
o
f
s
t
u
d
e
n
ts
w
e
r
e
s
ti
l
l
s
t
u
d
y
i
n
g
a
t
u
n
d
e
r
g
r
a
d
u
a
t
e
l
e
v
e
l
,
s
o
s
o
m
e
r
e
s
u
l
ts
m
a
y
v
a
r
y
a
c
c
o
r
d
i
n
g
t
o
t
h
e
l
e
n
g
t
h
o
f
t
i
m
e
e
a
c
h
s
t
u
d
e
n
t
h
a
s
b
e
e
n
s
t
u
d
y
i
n
g
.
I
n
t
h
i
s
t
i
m
e
p
e
r
i
o
d
,
t
h
e
s
t
u
d
y
was
c
o
n
d
u
c
t
e
d
u
n
d
e
r
t
h
e
g
u
i
d
e
l
in
e
s
o
f
t
h
e
M
i
n
is
t
r
y
o
f
N
a
t
i
o
n
al
E
d
u
c
a
t
i
o
n
(
ME
N
)
e
v
a
l
u
a
t
i
o
n
o
f
t
h
e
d
r
o
p
o
u
t
p
r
o
b
l
e
m
,
w
i
t
h
i
n
t
h
e
l
e
g
al
f
r
a
m
e
wo
r
k
o
f
t
h
e
p
r
i
n
c
i
p
l
e
s
o
f
c
o
n
f
i
d
e
n
t
i
a
l
it
y
,
n
e
c
es
s
it
y
,
t
e
m
p
o
r
a
l
i
t
y
,
t
h
e
d
a
t
a
a
r
e
u
s
e
d
o
n
l
y
f
o
r
t
h
e
p
u
r
p
o
s
e
s
o
f
e
v
a
l
u
a
t
i
o
n
o
f
d
r
o
p
o
u
t
f
o
r
w
h
i
c
h
t
h
e
y
w
e
r
e
c
o
l
l
e
c
t
e
d
,
w
i
t
h
o
u
t
b
e
i
n
g
u
s
e
d
f
o
r
s
u
b
s
e
q
u
e
n
t
o
r
d
i
f
f
e
r
e
n
t
p
u
r
p
o
s
e
s
.
I
n
t
h
i
s
p
r
o
c
e
s
s
,
23
f
a
c
t
o
r
s
w
e
r
e
u
s
e
d
t
o
c
o
n
s
o
l
i
d
a
te
b
a
s
e
l
i
n
e
a
s
s
e
e
n
i
n
T
a
b
l
e
1
,
w
i
t
h
t
h
e
i
n
f
o
r
m
a
t
i
o
n
c
a
p
t
u
r
e
d
b
y
t
h
e
o
f
f
i
c
e
o
f
p
l
a
n
n
i
n
g
a
n
d
i
n
s
t
i
t
u
t
i
o
n
a
l
d
e
v
e
l
o
p
m
e
n
t
o
f
t
h
e
U
n
i
v
e
r
s
i
t
y
o
f
T
o
l
i
m
a
,
i
n
t
h
e
f
r
a
m
e
w
o
r
k
o
f
t
h
e
l
a
w
o
f
t
r
a
n
s
p
a
r
e
n
c
y
a
n
d
t
h
e
r
i
g
h
t
o
f
a
c
c
e
s
s
t
o
n
a
t
i
o
n
a
l
p
u
b
l
i
c
i
n
f
o
r
m
a
ti
o
n
,
i
n
a
c
c
e
s
s
i
b
l
e
f
o
r
m
at
s
,
p
r
o
t
e
ct
i
o
n
o
f
p
e
r
s
o
n
a
l
d
a
t
a
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
r
esu
lts
o
b
tain
ed
f
r
o
m
th
e
an
aly
s
is
o
f
th
e
in
f
o
r
m
atio
n
co
llected
o
n
u
n
d
er
g
r
ad
u
ate
s
tu
d
en
ts
o
f
th
e
d
eg
r
ee
in
m
ath
em
atics
at
th
e
Un
iv
er
s
ity
o
f
T
o
lim
a
ar
e
p
r
esen
ted
.
Acc
o
r
d
in
g
to
th
e
r
e
s
u
lts
p
r
esen
ted
in
Fig
u
r
e
1
,
it
ca
n
b
e
o
b
s
er
v
e
d
t
h
at,
d
u
r
in
g
th
e
p
er
io
d
u
n
d
e
r
e
v
alu
atio
n
,
t
h
e
a
v
er
ag
e
ag
e
o
f
th
e
s
tu
d
en
ts
d
o
es
n
o
t
v
ar
y
g
r
ea
tly
f
r
o
m
y
ea
r
to
y
ea
r
(
s
in
ce
th
e
s
tu
d
en
ts
ar
e
b
etw
ee
n
1
9
a
n
d
2
0
y
ea
r
s
o
l
d
)
.
Si
m
ilar
ch
ar
ac
ter
is
tic
co
n
d
itio
n
s
in
r
elatio
n
to
th
e
v
a
r
iab
les
ag
e
(
a
v
er
ag
e
2
0
y
ea
r
s
)
,
h
ig
h
er
p
ar
ticip
atio
n
o
f
m
ale
s
tu
d
en
ts
an
d
h
ig
h
er
p
er
ce
n
tag
e
o
f
s
tu
d
en
ts
co
m
in
g
f
r
o
m
o
f
f
icial
s
ch
o
o
ls
ar
e
r
eg
is
ter
ed
in
th
e
r
esear
ch
[
2
8
]
,
co
n
s
eq
u
en
tly
t
h
is
p
r
o
p
o
r
tio
n
al
r
elatio
n
s
h
ip
in
p
e
r
ce
n
tag
es
[
6
]
,
[
4
7
]
,
[
4
8
]
.
On
th
e
o
th
er
h
an
d
,
r
e
g
ar
d
in
g
th
e
v
ar
iab
le
av
er
ag
e
g
r
a
d
e,
it
is
o
b
s
er
v
ed
th
at
s
tu
d
en
ts
,
y
ea
r
b
y
y
ea
r
,
p
r
esen
t
a
n
eu
tr
al
av
er
a
g
e
p
er
f
o
r
m
an
ce
,
r
an
g
in
g
b
etwe
en
3
.
1
(
y
ea
r
s
2
0
1
7
an
d
2
0
1
8
)
an
d
3
.
5
(
y
ea
r
2
0
1
3
)
.
T
h
e
av
er
ag
e
m
a
r
k
v
ar
iab
le
is
tak
en
f
r
o
m
all
th
e
s
u
b
jects
tak
e
n
b
y
th
e
s
tu
d
e
n
ts
d
u
r
i
n
g
th
ei
r
ac
ad
em
ic
p
er
io
d
.
T
h
er
ef
o
r
e,
th
e
s
tu
d
en
ts
o
b
s
er
v
ed
f
r
o
m
2
0
1
4
o
n
war
d
s
h
av
e
f
ewe
r
s
u
b
jects
ass
e
s
s
ed
.
E
v
al
u
atin
g
th
e
co
h
o
r
t
in
lo
n
g
itu
d
in
al
an
al
y
s
is
allo
ws
th
e
d
y
n
am
ics
o
f
th
e
f
ac
to
r
s
o
v
e
r
tim
e
to
b
e
d
eter
m
in
ed
[
4
8
]
,
[
4
9
]
.
R
eg
ar
d
in
g
th
e
th
ir
d
v
ar
ia
b
le,
wh
ich
is
th
e
r
esu
lt
o
f
th
e
1
1
test
s
(
I
C
FES)
,
it
ca
n
b
e
co
n
cl
u
d
ed
th
at
th
e
av
er
ag
e
s
co
r
e
f
o
r
ad
m
is
s
io
n
to
th
e
Deg
r
ee
in
M
ath
em
atics
is
with
in
th
e
ce
n
tr
al
s
co
r
e
m
an
ag
ed
b
y
th
e
U
n
iv
e
r
s
ity
o
f
T
o
lim
a
(
5
0
p
o
in
ts
)
,
r
an
g
in
g
f
r
o
m
4
7
(
2
0
1
4
)
to
5
5
(
2
0
1
8
)
.
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
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
8
5
9
-
3
8
7
1
3864
F
i
g
u
r
e
1
.
Qu
an
titativ
e
v
ar
iab
les o
f
th
e
Deg
r
ee
i
n
Ma
th
em
atic
s
s
tu
d
en
ts
in
th
e
p
er
io
d
2012A
-
2018B
Fo
r
th
e
v
ar
iab
le
s
em
ester
s
s
t
u
d
ied
,
it
ca
n
b
e
s
ee
n
th
at
t
h
e
av
er
ag
e
f
o
r
s
tu
d
en
ts
in
2
0
1
2
an
d
2
0
1
3
(
wh
o
at
th
e
tim
e
o
f
t
h
e
r
esear
ch
h
ad
alr
ea
d
y
co
m
p
leted
th
e
f
iv
e
y
ea
r
s
o
f
th
e
s
tu
d
y
p
lan
,
t
h
at
is
,
1
0
s
em
ester
s
)
is
8
s
em
ester
s
,
wh
ich
is
an
in
d
icato
r
o
f
th
e
h
i
g
h
lev
el
o
f
p
r
em
atu
r
e
co
m
p
letio
n
b
y
s
tu
d
e
n
ts
o
f
th
e
Deg
r
ee
in
Ma
th
em
atics.
I
n
t
h
e
o
th
er
y
e
ar
s
,
it
is
o
b
s
er
v
ed
th
at
th
e
av
er
ag
e
r
esu
lt
s
em
ester
b
y
s
em
ester
d
ec
r
ea
s
es,
an
d
th
is
is
b
ec
au
s
e
y
ea
r
b
y
y
ea
r
,
th
e
n
u
m
b
er
o
f
s
em
ester
s
s
ee
n
is
lo
wer
at
th
e
tim
e
o
f
th
e
i
n
f
o
r
m
atio
n
s
ea
r
ch
.
W
ith
r
ef
er
en
ce
to
th
e
s
u
b
ject
s
tak
en
an
d
s
u
b
jects
p
ass
ed
v
ar
iab
les,
it
is
o
b
s
er
v
ed
th
at
s
tu
d
en
ts
wh
o
en
ter
e
d
d
u
r
in
g
2
0
1
2
an
d
2
0
1
3
h
a
v
e
s
im
ilar
av
er
ag
es
in
b
o
th
v
ar
ia
b
les
(
av
er
ag
e
o
f
3
6
i
n
s
u
b
jec
ts
tak
en
an
d
3
4
in
s
u
b
jects
p
ass
ed
)
o
f
5
8
s
u
b
je
cts
th
at
th
e
De
g
r
ee
i
n
Ma
th
em
atics
h
ad
wh
e
n
t
h
e
p
lan
I
I
I
was
o
f
f
er
e
d
.
I
n
s
u
b
s
eq
u
en
t
y
ea
r
s
,
it
is
o
b
s
er
v
e
d
th
at
th
e
av
er
a
g
e
in
b
o
th
v
ar
i
ab
les
is
lo
wer
,
an
d
th
is
is
b
ec
au
s
e
th
e
s
tu
d
y
tim
e
o
f
th
e
s
tu
d
e
n
ts
is
less
th
an
in
2
0
1
2
an
d
2
0
1
3
.
Acc
o
r
d
in
g
to
th
e
in
f
o
r
m
atio
n
in
T
ab
le
2
,
it
is
o
b
s
er
v
ed
th
at
th
er
e
is
a
to
tal
o
f
5
0
1
s
tu
d
en
ts
(
3
0
9
m
ales
an
d
1
9
2
f
e
m
ales)
,
an
d
th
e
av
er
a
g
e
m
ar
k
o
b
tain
ed
b
y
t
h
e
f
em
ales
(
3
.
4
)
is
h
i
g
h
er
t
h
a
n
th
e
av
e
r
ag
e
m
a
r
k
o
b
tain
ed
b
y
th
e
m
ales
(
3
.
2
)
;
s
o
,
it
ca
n
b
e
c
o
n
clu
d
e
d
th
at
f
em
ales,
d
u
r
in
g
th
eir
s
tay
in
th
e
Deg
r
ee
i
n
Ma
th
em
atics,
o
b
tain
b
etter
m
ar
k
s
th
an
m
ales.
T
ab
le
2
s
h
o
ws
th
at
th
er
e
ar
e
s
ig
n
if
ican
t
d
if
f
er
en
ce
s
in
th
e
ac
ad
em
ic
p
er
f
o
r
m
an
ce
o
f
wo
m
en
with
r
esp
ec
t
to
th
e
ac
ad
em
ic
p
er
f
o
r
m
an
ce
o
f
m
en
,
b
ec
au
s
e
th
e
p
-
v
alu
e
(
0
.
0
1
1
7
)
is
less
th
an
0
.
1
.
I
n
s
tu
d
ies
wh
ich
in
clu
d
e
p
r
o
f
ess
io
n
s
wh
er
e
a
p
er
ce
n
tag
e
o
f
m
ath
em
atics
-
r
elate
d
s
u
b
jects a
r
e
r
eq
u
ir
ed
,
th
e
p
e
r
c
en
tag
e
o
f
m
ale
p
ar
ticip
an
ts
is
h
ig
h
er
th
a
n
th
at
o
f
f
em
ales
[
2
5
]
.
T
ab
le
2
.
Qu
alitativ
e
v
a
r
iab
les o
f
th
e
Deg
r
ee
in
Ma
th
em
atics
s
tu
d
en
ts
in
th
e
p
er
io
d
2
0
1
2
A
-
2018B
V
a
r
i
a
b
l
e
S
i
z
e
o
f
t
h
e
g
r
o
u
p
(
N
)
A
v
e
r
a
g
e
mar
k
s
S
t
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
A
v
e
r
a
g
e
r
a
n
k
Le
t
t
e
r
s
a.
G
e
n
d
e
r
F
e
mal
e
1
9
2
(
3
8
%)
3
.
4
0
.
9
3
2
7
1
.
7
A
M
a
l
e
3
0
9
(
6
2
%)
3
.
2
1
.
1
2
3
8
.
2
B
b.
S
t
a
t
u
s
(
D
e
sert
e
r
)
N
o
n
-
d
r
o
p
o
u
t
st
u
d
e
n
t
2
4
4
(
4
9
%)
3
.
8
0
.
4
4
3
4
0
.
8
A
D
r
o
p
o
u
t
s
t
u
d
e
n
t
2
5
7
(
5
1
%)
2
.
7
1
.
1
4
1
6
5
.
7
B
c.
Ty
p
e
o
f
s
c
h
o
o
l
P
r
i
v
a
t
e
sc
h
o
o
l
4
4
(
9
%)
2
.
7
3
1
.
1
8
1
7
5
.
4
A
P
u
b
l
i
c
sc
h
o
o
l
4
5
7
(
9
1
%)
3
.
3
1
.
0
2
2
5
8
.
3
B
d.
F
i
n
a
n
c
i
a
l
su
p
p
o
r
t
N
o
3
3
3
(
6
7
%)
3
.
0
1
.
0
7
1
9
9
.
3
A
Y
e
s
1
6
8
(
3
3
%)
3
.
8
0
.
6
8
3
5
3
.
6
B
e.
Y
e
a
r
c
o
m
p
a
r
i
so
n
Y
e
a
r
-
2
0
1
2
7
8
(
1
6
%)
3
.
3
7
0
.
8
7
2
5
3
.
9
A
Y
e
a
r
-
2
0
1
3
7
6
(
1
5
%)
3
.
4
3
0
.
7
7
2
6
8
.
7
A
Y
e
a
r
-
2
0
1
4
8
6
(
1
7
%)
3
.
2
7
0
.
9
2
4
2
.
7
A
Y
e
a
r
-
2
0
1
5
8
1
(
1
6
%)
3
.
1
1
.
2
8
2
4
5
.
2
A
Y
e
a
r
-
2
0
1
6
6
0
(
1
2
%)
3
.
2
5
1
.
0
7
2
5
9
.
6
A
Y
e
a
r
-
2
0
1
7
8
0
(
1
6
%)
3
.
1
3
1
.
1
7
2
3
7
.
8
A
Y
e
a
r
-
2
0
1
8
4
0
(
8
%)
3
.
1
3
1
.
2
3
2
5
4
.
9
A
(
a
)
A
v
e
r
a
g
e
s
w
i
t
h
a
c
o
mm
o
n
l
e
t
t
e
r
a
r
e
n
o
t
si
g
n
i
f
i
c
a
n
t
l
y
d
i
f
f
e
r
e
n
t
(
p
>
0
.
1
0
)
,
K
r
u
sk
a
l
-
W
a
l
l
i
s
(
K
-
W
)
t
e
s
t
b
y
r
a
n
k
s
,
A
l
p
h
a
=
0
.
1
0
,
p
-
v
a
l
u
e
=
0
.
0
1
1
7
(
*
*
*
)
(
b,
c
)
A
v
e
r
a
g
e
s
w
i
t
h
a
c
o
m
mo
n
l
e
t
t
e
r
a
r
e
n
o
t
si
g
n
i
f
i
c
a
n
t
l
y
d
i
f
f
e
r
e
n
t
(
p
>
0
.
1
0
)
,
K
r
u
s
k
a
l
-
W
a
l
l
i
s
(
K
-
W
)
t
e
st
b
y
r
a
n
k
s
,
A
l
p
h
a
=
0
.
1
0
,
p
-
v
a
l
u
e
=
0
.
0
0
0
1
(
*
*
*
)
(
d
)
A
v
e
r
a
g
e
s
w
i
t
h
a
c
o
mm
o
n
l
e
t
t
e
r
a
r
e
n
o
t
s
i
g
n
i
f
i
c
a
n
t
l
y
d
i
f
f
e
r
e
n
t
(
p
>
0
.
1
0
)
,
K
r
u
s
k
a
l
-
W
a
l
l
i
s
(
K
-
W
)
t
e
st
b
y
r
a
n
k
s
,
A
l
p
h
a
0
.
1
0
,
p
-
v
a
l
u
e
=
0
.
0
0
0
1
(
*
*
*
)
(
e
)
A
v
e
r
a
g
e
s
w
i
t
h
a
c
o
mm
o
n
l
e
t
t
e
r
a
r
e
n
o
t
si
g
n
i
f
i
c
a
n
t
l
y
d
i
f
f
e
r
e
n
t
(
p
>
0
.
1
0
)
,
K
r
u
sk
a
l
-
W
a
l
l
i
s
(
K
-
W
)
t
e
s
t
b
y
r
a
n
k
s
,
A
l
p
h
a
=
0
.
0
5
,
p
-
v
a
l
u
e
=
0
.
8
7
R
eg
ar
d
in
g
th
e
ac
a
d
em
ic
s
tatu
s
o
f
t
h
e
s
tu
d
e
n
t
(
n
o
n
-
d
r
o
p
o
u
t
s
tu
d
en
t=2
4
4
,
d
r
o
p
o
u
t
s
tu
d
en
t
=2
5
7
)
,
th
e
av
er
ag
e
m
ar
k
o
f
th
e
n
o
n
-
d
r
o
p
o
u
t
s
tu
d
e
n
ts
is
3
.
8
,
wh
ile
th
e
a
v
er
ag
e
m
ar
k
o
f
th
e
d
r
o
p
o
u
t
s
t
u
d
en
ts
is
2
.
7
.
Ab
o
u
t
th
e
s
ig
n
if
ican
ce
lev
el,
it
is
o
b
s
er
v
ed
th
at
th
er
e
is
a
h
ig
h
ly
s
i
g
n
if
ican
t
d
if
f
e
r
en
ce
(
p
=0
.
0
0
0
1
)
b
etwe
en
d
r
o
p
o
u
t
an
d
n
o
n
-
d
r
o
p
o
u
t
s
tu
d
en
ts
.
T
h
e
r
esu
lt
o
f
th
is
ca
teg
o
r
y
s
h
o
w
s
u
s
th
at
th
e
ac
ad
em
ic
is
s
u
e
h
as
an
im
p
ac
t
o
n
th
e
19
20
19
20
19
20
19
3
.4
3
.5
3
.3
3
.1
3
.4
3
.1
3
.1
52
52
47
51
53
54
55
8
8
6
5
3
3
1
36
36
30
23
16
13
7
34
34
28
21
15
12
4
0
10
20
30
40
50
60
70
80
90
1
0
0
1
1
0
1
2
0
1
3
0
1
4
0
1
5
0
1
6
0
Y
e
a
r
-
2
0
1
2
Y
e
a
r
-
2
0
1
3
Y
e
a
r
-
2
0
1
4
Y
e
a
r
-
2
0
1
5
Y
e
a
r
-
2
0
1
6
Y
e
a
r
-
2
0
1
7
Y
e
a
r
-
2
0
1
8
A
g
e
Av
e
r
a
g
e
m
a
r
k
ICF
E
S
S
e
m
e
s
t
e
r
s
s
t
u
d
ie
d
S
u
b
je
c
t
s
t
a
k
e
n
S
u
b
je
c
t
s
p
a
s
s
e
d
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
A
n
a
lysi
s
o
f a
ca
d
emic
d
eser
tio
n
a
mo
n
g
u
n
g
r
a
d
u
a
ted
ma
th
em
a
tics
s
tu
d
en
ts
(
Mig
u
el
A
.
R
o
d
r
íg
u
ez
-
Má
r
q
u
ez
)
3865
d
eser
tio
n
o
f
s
tu
d
e
n
ts
o
f
th
e
D
eg
r
ee
in
Ma
th
em
atics,
b
ec
au
s
e
th
e
to
tal
n
u
m
b
e
r
o
f
d
r
o
p
o
u
t
s
tu
d
en
ts
is
h
ig
h
er
th
an
th
e
n
u
m
b
er
o
f
n
o
n
-
d
r
o
p
o
u
ts
,
an
d
th
e
av
er
a
g
e
o
f
th
e
s
tu
d
en
ts
is
lo
wer
th
an
th
e
m
in
im
u
m
p
ass
m
a
r
k
in
th
e
Deg
r
ee
in
Ma
th
em
atics
(
3
.
0
)
,
wh
ich
in
d
icate
s
th
at
lo
w
a
ca
d
em
ic
p
e
r
f
o
r
m
an
ce
is
a
n
i
m
p
o
r
tan
t
f
ac
to
r
f
o
r
d
eser
tio
n
o
f
t
h
e
p
r
o
g
r
am
,
s
o
it
is
n
ec
ess
ar
y
to
s
u
p
p
o
r
t t
h
e
ac
ad
em
ic
p
r
o
ce
s
s
es o
f
th
e
s
tu
d
e
n
ts
.
R
eg
ar
d
in
g
th
e
ty
p
e
o
f
s
ch
o
o
l,
it
is
o
b
s
er
v
ed
th
at
a
h
ig
h
p
e
r
ce
n
tag
e
o
f
s
tu
d
e
n
ts
(
9
1
%)
wh
o
en
ter
th
e
Deg
r
ee
in
Ma
th
e
m
atics
b
elo
n
g
to
p
u
b
lic
s
ch
o
o
ls
,
wh
ich
d
e
m
o
n
s
tr
ates
th
e
im
p
o
r
tan
ce
o
f
p
u
b
lic
ed
u
ca
tio
n
at
th
e
r
eg
i
o
n
al
le
v
el,
s
u
p
p
o
r
tin
g
lo
w
-
in
co
m
e
s
tu
d
e
n
ts
.
I
t
is
a
ls
o
o
b
s
er
v
ed
th
at
s
tu
d
en
ts
f
r
o
m
p
u
b
lic
s
ch
o
o
ls
o
b
tain
b
etter
av
er
ag
e
m
a
r
k
s
th
an
s
tu
d
en
ts
f
r
o
m
p
r
iv
ate
s
c
h
o
o
ls
(
3
.
3
p
u
b
lic
s
ch
o
o
ls
;
2
.
7
3
p
r
iv
ate
s
ch
o
o
ls
)
,
wh
ich
in
d
icate
s
th
at
s
tu
d
en
ts
co
m
in
g
f
r
o
m
th
e
p
u
b
lic
s
ec
to
r
h
av
e
a
g
r
ea
ter
af
f
in
it
y
with
th
e
p
r
o
g
r
am
,
th
er
ef
o
r
e
th
e
y
o
b
tain
m
o
r
e
s
atis
f
ac
to
r
y
r
esu
lts
.
Ab
o
u
t
th
e
lev
el
o
f
s
tatis
tical
s
ig
n
if
ican
ce
,
it
is
o
b
s
er
v
ed
th
at
th
er
e
is
a
h
ig
h
ly
s
ig
n
if
ican
t d
if
f
er
en
ce
(
p
=0
.
0
0
0
1
)
.
Fig
u
r
e
2
s
h
o
ws
th
at
th
e
r
e
is
a
h
ig
h
ass
o
ciatio
n
b
etwe
en
th
e
ac
ad
em
ic
p
er
f
o
r
m
a
n
ce
o
f
th
e
s
tu
d
en
ts
an
d
th
eir
m
o
tiv
atio
n
to
co
n
tin
u
e
o
r
n
o
t
to
co
n
tin
u
e
th
eir
s
tu
d
ies.
I
n
o
th
er
wo
r
d
s
,
if
th
e
s
tu
d
en
ts
o
b
tain
b
etter
m
ar
k
s
,
th
ey
ar
e
less
lik
ely
to
d
r
o
p
o
u
t
o
f
th
e
Deg
r
ee
in
Ma
th
em
atics.
T
h
is
r
elatio
n
s
h
ip
is
test
ed
b
y
th
e
ass
o
ciatio
n
o
f
Sp
ea
r
m
an
(
p
-
v
a
lu
e<
0
.
0
0
1
(
*
*
*
)
)
.
T
a
b
l
e
3
s
h
o
ws
t
h
at
t
h
e
s
t
u
d
e
n
ts
m
o
s
t
l
i
k
el
y
t
o
d
r
o
p
o
u
t
a
r
e
i
n
t
h
e
a
g
e
r
a
n
g
e
b
e
tw
e
e
n
1
6
a
n
d
2
5
y
e
a
r
s
,
s
o
t
h
e
o
l
d
e
r
t
h
e
s
t
u
d
e
n
t
,
t
h
e
l
o
w
e
r
t
h
e
p
r
o
b
a
b
i
l
i
t
y
o
f
d
r
o
p
p
i
n
g
o
u
t
o
f
t
h
e
D
e
g
r
e
e
i
n
Ma
t
h
e
m
a
t
i
cs
,
w
i
t
h
a
s
i
g
n
i
f
i
c
a
n
ce
p
=
0
.
0
3
9
5
(
*
*
)
.
R
eg
a
r
d
i
n
g
t
h
e
t
o
t
a
l
n
u
m
b
e
r
o
f
s
t
u
d
e
n
t
s
w
h
o
d
o
o
r
d
o
n
o
t
r
e
c
e
i
v
e
f
i
n
a
n
c
i
a
l
s
u
p
p
o
r
t
,
i
t
i
s
o
b
s
e
r
v
e
d
t
h
a
t
t
h
e
r
e
is
a
n
a
s
s
o
ci
a
t
i
o
n
w
it
h
r
e
s
p
e
c
t
t
o
d
r
o
p
p
i
n
g
o
u
t
o
r
n
o
t
f
r
o
m
t
h
e
D
e
g
r
e
e
i
n
M
a
t
h
e
m
a
t
i
cs
,
w
h
e
n
r
e
c
e
i
v
i
n
g
a
f
i
n
a
n
c
i
a
l
i
n
c
e
n
t
i
v
e
.
A
c
c
o
r
d
i
n
g
t
o
t
h
e
r
e
s
u
l
t
s
,
t
h
e
n
,
i
t
c
a
n
b
e
i
n
d
i
c
at
e
d
t
h
a
t
,
i
f
t
h
e
s
t
u
d
e
n
ts
r
e
c
e
i
v
e
s
o
m
e
f
i
n
a
n
c
ia
l
s
u
p
p
o
r
t
,
t
h
e
y
a
r
e
l
e
s
s
l
i
k
e
l
y
t
o
d
r
o
p
o
u
t
o
f
u
n
i
v
e
r
s
i
t
y
s
t
u
d
i
es
.
T
h
e
s
o
ci
o
-
e
c
o
n
o
m
i
c
f
a
c
t
o
r
w
a
s
o
b
s
e
r
v
e
d
a
s
o
n
e
o
f
t
h
e
m
a
in
c
a
u
s
e
s
o
f
d
r
o
p
o
u
t
,
c
o
i
n
c
i
d
i
n
g
w
i
t
h
t
h
e
r
es
u
l
ts
f
o
u
n
d
i
n
[
3
]
,
[
6
]
,
[
2
5
]
.
Acc
o
r
d
in
g
to
T
a
b
le
4
,
it
ca
n
b
e
o
b
s
er
v
e
d
th
at
t
h
er
e
is
a
co
r
r
elatio
n
b
etwe
en
ea
c
h
p
ai
r
o
f
v
ar
iab
les,
ex
ce
p
t
f
o
r
I
C
FES
with
s
u
b
jects
p
ass
ed
,
s
u
b
jects
tak
en
,
a
n
d
s
em
ester
s
s
tu
d
ied
.
R
eg
ar
d
in
g
th
e
co
r
r
elatio
n
b
etwe
en
v
ar
iab
les,
th
e
v
ar
ia
b
l
es
s
u
b
jects
p
ass
ed
,
s
u
b
jects
ta
k
en
,
s
em
ester
s
s
tu
d
ied
an
d
I
C
FES
s
h
o
w
a
d
ir
ec
t
co
r
r
elatio
n
,
th
at
is
,
wh
en
o
n
e
o
f
th
ese
v
ar
iab
les
g
r
o
ws
p
o
s
itiv
ely
,
th
e
co
r
r
elate
d
v
ar
ia
b
le
will
al
s
o
g
r
o
w
p
o
s
itiv
ely
,
b
u
t
in
s
tead
,
th
e
a
g
e
v
ar
iab
le
s
h
o
ws
an
in
v
e
r
s
e
c
o
r
r
elatio
n
,
s
o
th
e
y
o
u
n
g
er
t
h
e
ag
e,
th
e
h
ig
h
er
th
e
r
esu
lts
o
f
th
e
c
o
r
r
elate
d
v
ar
ia
b
les.
T
h
is
co
r
r
elatio
n
in
d
icate
s
th
at
attr
itio
n
is
lo
wer
f
o
r
s
tu
d
en
ts
with
a
h
ig
h
er
lev
el
o
f
ac
ad
em
ic
ed
u
ca
tio
n
[
1
]
.
Fig
u
r
e
2
.
R
elatio
n
s
h
ip
b
etwe
e
n
d
eser
tio
n
a
n
d
ac
ad
e
m
ic
p
er
f
o
r
m
an
ce
f
r
o
m
2
0
1
2
-
A
to
2
0
1
8
-
B
T
ab
le
3
.
R
elatio
n
s
h
ip
b
etwe
en
d
eser
tio
n
,
ag
e
r
an
k
s
a
n
d
f
in
a
n
cial
s
u
p
p
o
r
t f
r
o
m
2
0
1
2
-
A
to
2
0
1
8
-
B
V
a
r
i
a
b
l
e
D
r
o
p
o
u
t
(
%)
N
o
n
-
d
r
o
p
o
u
t
(
%)
To
t
a
l
(
%)
A
g
e
r
a
n
k
(
%)
16
-
1
8
y
e
a
r
s
o
l
d
2
0
.
6
25
4
5
.
6
19
-
2
5
y
e
a
r
s
o
l
d
2
8
.
4
2
1
.
6
50
O
l
d
e
r
t
h
a
n
2
6
y
e
a
r
s
2
.
3
2
.
2
4
.
5
To
t
a
l
(
%)
5
1
.
3
4
8
.
7
1
0
0
P
e
a
r
so
n
C
h
i
-
S
q
u
a
r
e
,
a
l
p
h
a
s
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
=
0
.
0
5
,
p
-
v
a
l
u
e
=
0
.
0
3
9
5
(
*
*
)
F
i
n
a
n
c
i
a
l
s
u
p
p
o
r
t
(
%)
N
o
f
i
n
a
n
c
i
a
l
s
u
p
p
o
r
t
4
3
.
3
2
3
.
2
6
6
.
5
Y
e
s,
f
i
n
a
n
c
i
a
l
s
u
p
p
o
r
t
8
.
0
2
5
.
6
3
3
.
5
To
t
a
l
(
%)
5
1
.
3
4
8
.
7
1
0
0
P
e
a
r
so
n
C
h
i
-
S
q
u
a
r
e
,
a
l
p
h
a
s
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
=
0
.
0
5
,
p
-
v
a
l
u
e
=
0
.
0
0
0
1
(
*
*
*
)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
P
o
o
r p
e
rfo
rma
n
c
e
(
%
)
L
o
w
p
e
r
f
o
rman
c
e
(
%
)
Me
d
i
u
m
p
e
rfo
rman
c
e
(
%
)
H
i
g
h
p
e
r
f
o
rman
c
e
(
%
)
Po
o
r
p
e
r
fo
r
m
an
c
e
(%
)
L
o
w
p
e
r
fo
r
m
an
c
e
(%
)
Me
d
i
u
m
p
e
r
fo
r
m
an
c
e
(%
)
H
i
g
h
p
e
r
fo
r
m
an
c
e
(%
)
N
o
n
d
r
o
p
o
u
t S
t
u
d
e
n
t (%
)
0.6
0.6
27.0
20.6
Dr
o
p
o
u
t S
tu
d
e
n
t
(
%
)
17.4
7.0
22.4
4.6
N
o
n
d
ro
p
o
u
t S
t
u
d
e
n
t (%
)
Dr
o
p
o
u
t S
tu
d
e
n
t
(
%
)
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
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
8
5
9
-
3
8
7
1
3866
T
ab
le
4
.
C
o
r
r
elatio
n
b
etwe
en
t
h
e
v
ar
iab
les o
f
ac
ad
em
ic
p
er
f
o
r
m
an
ce
d
u
e
to
d
eser
tio
n
,
in
th
e
p
er
io
d
f
r
o
m
2012
-
A
to
2
0
1
8
-
B
N
u
meri
c
a
l
v
a
r
i
a
b
l
e
s
C
u
m
u
l
a
t
i
v
e
a
v
e
r
a
g
e
S
u
b
j
e
c
t
s
t
a
k
e
n
S
u
b
j
e
c
t
s
p
a
sse
d
S
e
mest
e
r
s c
o
m
p
l
e
t
e
d
A
g
e
I
C
F
ES
C
u
m
u
l
a
t
i
v
e
a
v
e
r
a
g
e
1
0
.
0
0
0
0
.
0
0
0
0
.
0
0
0
0
.
0
0
0
0
.
0
2
0
S
u
b
j
e
c
t
s
t
a
k
e
n
0
.
5
3
1
0
.
0
0
0
0
.
0
0
0
0
.
0
0
0
0
.
0
8
0
S
u
b
j
e
c
t
s
p
a
sse
d
0
.
5
8
0
.
9
9
1
0
.
0
0
0
0
.
0
0
0
0
.
0
6
0
S
e
mest
e
r
s c
o
m
p
l
e
t
e
d
0
.
4
6
0
.
9
5
0
.
9
5
1
0
.
0
1
0
0
.
1
2
0
A
g
e
-
0
.
1
5
-
0
.
1
3
-
0
.
1
4
-
0
.
1
3
1
0
.
0
0
0
I
C
F
ES
0
.
1
1
0
.
0
8
0
.
0
9
0
.
0
7
0
.
1
8
1
S
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
,
a
l
p
h
a
=
0
.
0
5
,
p
-
v
a
l
u
e
=
0
.
0
0
0
Acc
o
r
d
in
g
to
Fig
u
r
e
3
,
it
ca
n
b
e
co
n
cl
u
d
ed
th
at
th
er
e
ar
e
n
o
s
ig
n
if
ican
t
d
if
f
er
en
ce
b
e
twee
n
g
en
d
er
s
in
r
elatio
n
to
th
e
n
u
m
b
er
o
f
s
u
b
jects
p
ass
ed
(
p
=0
.
4
9
6
)
,
th
at
is
,
m
ale
an
d
f
em
ale
p
ass
a
s
im
ilar
n
u
m
b
er
o
f
s
u
b
jects.
Similar
r
esu
lts
in
r
elatio
n
to
g
e
n
d
er
ar
e
r
ep
o
r
te
d
in
p
r
ev
io
u
s
s
tu
d
y
[
2
1
]
.
Fig
u
r
e
4
s
h
o
ws
th
a
t
f
in
an
cial
s
u
p
p
o
r
t
is
r
elate
d
t
o
th
e
n
u
m
b
er
o
f
s
u
b
jects
p
a
s
s
ed
(
p
=0
,
0
0
0
0
)
,
s
o
th
e
r
e
is
a
v
er
y
s
ig
n
if
ican
t
d
if
f
er
en
ce
b
etwe
en
s
tu
d
en
ts
wh
o
r
ec
eiv
e
f
in
a
n
cial
s
u
p
p
o
r
t
an
d
th
o
s
e
w
h
o
d
o
n
o
t.
T
h
er
ef
o
r
e
,
it
ca
n
b
e
co
n
clu
d
e
d
th
at
th
e
ec
o
n
o
m
ic
v
ar
iab
le
is
an
asp
ec
t
to
b
e
co
n
s
id
er
ed
b
y
s
tu
d
en
ts
wh
o
d
r
o
p
o
u
t
o
f
th
eir
De
g
r
ee
in
Ma
th
em
atics.
T
h
er
ef
o
r
e,
it
ca
n
b
e
co
n
clu
d
e
d
th
at
th
e
ec
o
n
o
m
ic
v
ar
ia
b
le
is
an
asp
ec
t
to
b
e
tak
en
in
to
ac
co
u
n
t b
y
s
tu
d
en
ts
wh
o
d
r
o
p
o
u
t o
f
t
h
e
B
ac
h
elo
r
'
s
Deg
r
ee
in
Ma
th
em
atics
[
2
5
]
,
[
2
8
]
.
Fig
u
r
e
3
.
Su
r
v
iv
al
cu
r
v
es b
y
g
en
d
er
Fig
u
r
e
4
.
Su
r
v
iv
al
cu
r
v
es b
y
f
i
n
an
cial
s
u
p
p
o
r
t
Fig
u
r
e
5
s
h
o
ws
th
at
th
er
e
is
n
o
s
ig
n
if
ican
t
d
if
f
er
e
n
ce
b
etwe
en
s
tu
d
en
ts
ac
co
r
d
in
g
t
o
th
e
p
er
io
d
o
f
en
tr
y
to
th
e
p
r
o
g
r
am
(
p
=
0
.
3
3
5
8
)
,
th
at
is
,
th
e
s
em
ester
o
f
en
tr
y
h
as
n
o
d
ir
ec
t
in
f
lu
e
n
ce
o
n
s
tu
d
en
t
d
r
o
p
o
u
t.
Fig
u
r
e
6
s
h
o
ws th
e
v
ar
iab
les s
tr
atu
m
an
d
th
e
n
u
m
b
er
o
f
s
u
b
j
ec
ts
p
ass
ed
,
wh
er
e
th
er
e
is
n
o
d
if
f
er
en
ce
b
etwe
en
th
e
d
if
f
e
r
en
t
s
tr
atu
m
in
r
elatio
n
to
th
e
n
u
m
b
er
o
f
s
u
b
jects
p
a
s
s
ed
(
p
=0
.
2
1
0
4
)
.
Acc
o
r
d
in
g
t
o
Fig
u
r
e
7
,
th
er
e
ar
e
n
o
s
ig
n
if
ican
t
d
if
f
er
e
n
ce
s
b
etwe
en
th
e
ag
e
r
an
g
es
in
r
elatio
n
to
th
e
s
u
b
jects
p
as
s
ed
(
p
=0
,
4
1
1
)
,
s
o
th
e
p
ass
in
g
r
esu
lts
ar
e
clo
s
e
b
etwe
en
all
th
e
ag
e
r
a
n
g
es
an
aly
ze
d
.
Fi
g
u
r
e
8
s
h
o
ws
th
e
s
ig
n
if
ican
t
d
if
f
er
en
ce
b
etwe
en
s
tu
d
en
ts
f
r
o
m
p
u
b
lic
s
ch
o
o
ls
an
d
s
tu
d
en
ts
f
r
o
m
p
r
iv
ate
s
ch
o
o
ls
with
r
esp
ec
t
to
th
e
v
ar
iab
le
p
ass
ed
s
u
b
jects
(p
-
v
alu
e=
0
.
0
0
0
1
9
)
,
th
at
is
,
s
tu
d
en
ts
f
r
o
m
p
u
b
lic
s
ch
o
o
ls
o
b
t
ain
a
b
etter
ac
ad
e
m
ic
p
er
f
o
r
m
an
ce
th
an
s
tu
d
e
n
ts
f
r
o
m
p
r
iv
ate
ed
u
ca
tio
n
al
in
s
titu
tio
n
s
.
I
t
is
n
ec
ess
ar
y
to
p
ay
s
p
ec
ial
atten
tio
n
t
o
s
tu
d
e
n
ts
f
r
o
m
p
r
iv
ate
s
ch
o
o
ls
,
to
m
o
tiv
ate
th
em
t
o
ad
v
a
n
ce
i
n
th
eir
u
n
d
er
g
r
ad
u
ate
s
tu
d
ies
[
4
8
]
,
[
4
9
]
.
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
A
n
a
lysi
s
o
f a
ca
d
emic
d
eser
tio
n
a
mo
n
g
u
n
g
r
a
d
u
a
ted
ma
th
em
a
tics
s
tu
d
en
ts
(
Mig
u
el
A
.
R
o
d
r
íg
u
ez
-
Má
r
q
u
ez
)
3867
Acc
o
r
d
in
g
to
Fig
u
r
e
9
,
th
er
e
ar
e
s
ig
n
if
ican
t
d
if
f
er
e
n
ce
s
in
th
e
ac
ad
em
ic
p
er
f
o
r
m
an
ce
o
f
th
e
s
tu
d
en
ts
with
r
esp
ec
t
to
th
e
to
tal
n
u
m
b
er
o
f
s
u
b
jects
p
ass
ed
(
p
-
v
alu
e=
0
.
0
0
0
0
)
,
s
o
s
tu
d
en
ts
with
lo
w
an
d
p
o
o
r
p
er
f
o
r
m
an
ce
d
o
n
o
t
co
m
p
lete
th
eir
Deg
r
ee
in
Ma
th
em
atics.
T
h
er
ef
o
r
e,
it
is
im
p
o
r
tan
t
to
p
ay
atten
tio
n
to
th
e
ac
ad
em
ic
p
er
f
o
r
m
an
ce
i
n
th
e
Deg
r
ee
in
Ma
th
em
atics,
an
d
t
o
s
u
p
p
o
r
t
t
h
o
s
e
s
tu
d
en
ts
with
lo
w
p
er
f
o
r
m
an
ce
in
o
r
d
er
to
im
p
r
o
v
e
th
e
m
ar
k
s
o
b
tain
ed
d
u
r
in
g
t
h
e
f
ir
s
t
s
em
ester
s
,
ca
u
s
ality
r
esu
lt
th
at
i
s
r
ep
o
r
ted
in
s
ev
e
r
al
s
tu
d
ies
[
2
5
]
,
[
2
8
]
,
[
3
0
]
,
[
4
8
]
.
Fig
u
r
e
5
.
Su
r
v
iv
al
cu
r
v
es b
y
y
ea
r
in
th
e
Deg
r
ee
in
Ma
th
em
at
ics
Fig
u
r
e
6
.
Su
r
v
iv
al
cu
r
v
es b
y
s
t
r
atu
m
in
th
e
De
g
r
ee
in
Ma
th
e
m
atics
Fig
u
r
e
7
.
Su
r
v
iv
al
cu
r
v
es b
y
a
g
e
r
an
g
e
S
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
a
l
p
h
a
=
0
.
0
5
,
T
e
st
L
o
g
r
a
n
g
=
6
.
8
4
1
,
p
-
v
a
l
u
e
=
0
.
3
3
5
8
S
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
a
l
p
h
a
=
0
.
0
5
,
T
e
st
L
o
g
r
a
n
g
=
6
.
8
4
1
,
p
-
v
a
l
u
e
=
0
.
2
1
0
4
S
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
a
l
p
h
a
=
0
.
0
5
,
T
e
st
L
o
g
r
a
n
g
=
6
.
3
8
2
,
p
-
v
a
l
u
e
=
0
.
4
1
1
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
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
8
5
9
-
3
8
7
1
3868
Fig
u
r
e
8
.
Su
r
v
iv
al
cu
r
v
es b
y
t
y
p
e
o
f
s
ch
o
o
l
Fig
u
r
e
9
.
Su
r
v
iv
al
cu
r
v
es b
y
a
ca
d
em
ic
p
er
f
o
r
m
an
c
e
Fig
u
r
e
1
0
s
h
o
ws
a
s
ig
n
if
ican
t
d
if
f
er
en
ce
i
n
th
e
to
tal
n
u
m
b
er
o
f
s
u
b
jects
p
ass
ed
b
e
twee
n
d
r
o
p
o
u
t
s
tu
d
en
ts
an
d
n
o
n
-
d
r
o
p
o
u
t
s
tu
d
en
ts
,
s
o
it
is
n
ec
ess
ar
y
to
g
i
v
e
im
p
o
r
tan
ce
t
o
th
e
s
tu
d
e
n
ts
wh
o
d
r
o
p
o
u
t,
an
d
to
g
en
er
ate
p
o
s
s
ib
le
s
o
lu
tio
n
s
s
o
th
at
th
ese
s
tu
d
en
ts
ca
n
r
e
-
e
n
ter
an
d
co
n
tin
u
e
th
eir
s
tu
d
ies
in
th
e
Deg
r
ee
i
n
Ma
th
em
atics.
Aca
d
em
ic
p
er
f
o
r
m
an
ce
ass
o
ciate
d
with
p
a
s
s
in
g
g
r
ad
es
is
a
s
ig
n
if
ican
t
f
ac
to
r
in
s
tu
d
en
t
r
eten
tio
n
at
u
n
iv
er
s
ity
lev
el,
r
e
s
u
lts
co
n
s
is
ten
t w
ith
p
r
ev
io
u
s
s
tu
d
ies
[
1
]
,
[
2
5
]
,
[
2
8
]
,
[
4
7
]
.
Fig
u
r
e
1
0
.
Su
r
v
iv
al
c
u
r
v
es b
y
ty
p
e
o
f
d
r
o
p
o
u
t
S
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
a
l
p
h
a
=
0
.
0
5
,
T
e
st
L
o
g
r
a
n
g
=
1
8
.
3
3
7
,
p
-
v
a
l
u
e
=
0
.
0
0
0
1
9
(
*
*
*
)
S
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
a
l
p
h
a
=
0
.
0
5
,
T
e
st
L
o
g
r
a
n
g
=
4
0
5
.
4
5
,
p
-
v
a
l
u
e
=
0
.
0
0
0
0
(
*
*
*
)
S
i
g
n
i
f
i
c
a
n
c
e
l
e
v
e
l
a
l
p
h
a
=
0
.
0
5
,
T
e
st
L
o
g
r
a
n
g
=
5
2
3
.
6
2
,
p
-
v
a
l
u
e
=
0
.
0
0
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.