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CC B
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C
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p
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A
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r
:
I
n
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y
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Ace
r
o
Ap
az
a
Ma
th
em
atics,
Ph
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s
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C
o
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p
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ter
Scien
ce
an
d
I
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f
o
r
m
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am
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Facu
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ca
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Un
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id
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Nac
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Altip
lan
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Av
.
Flo
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al
N
o.
1
1
5
3
,
Pu
n
o
,
Per
u
E
m
ail: ia
ce
r
o
@
u
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ap
.
ed
u
.
p
e
1.
I
NT
RO
D
UCT
I
O
N
I
n
th
e
f
ield
o
f
h
ig
h
er
ed
u
ca
tio
n
,
t
h
e
a
n
aly
s
is
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d
u
n
d
er
s
tan
d
in
g
o
f
th
e
s
tu
d
en
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’
lear
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p
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s
s
co
n
s
titu
tes
a
f
u
n
d
am
en
tal
ch
allen
g
e
[
1
]
,
[
2
]
.
T
h
e
co
n
s
tan
t
s
ea
r
ch
f
o
r
ef
f
ec
tiv
e
p
ed
ag
o
g
ical
s
tr
ateg
ies
th
at
p
r
o
m
o
te
ac
ad
em
ic
s
u
cc
ess
an
d
th
e
ac
q
u
is
itio
n
o
f
r
elev
an
t
c
o
m
p
eten
cies
h
as
le
d
to
th
e
ex
p
lo
r
atio
n
o
f
v
ar
i
o
u
s
ap
p
r
o
ac
h
es,
am
o
n
g
wh
ic
h
m
a
th
em
atica
l
m
o
d
els
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er
g
e
as
to
o
ls
o
f
in
d
is
p
u
tab
le
p
o
ten
tial
[
3
]
,
[
4
]
.
Mo
d
elin
g
,
b
y
al
-
lo
win
g
th
e
q
u
an
titati
v
e
r
ep
r
esen
tatio
n
o
f
co
m
p
l
ex
r
elatio
n
s
h
ip
s
b
etwe
en
v
ar
iab
les,
h
as
f
o
u
n
d
f
er
tile
g
r
o
u
n
d
in
ed
u
ca
tio
n
al
r
esear
ch
,
o
f
f
er
in
g
an
an
aly
tical
p
er
s
p
ec
tiv
e
th
at
g
o
es
b
ey
o
n
d
s
u
p
er
f
icial
o
b
s
er
v
atio
n
s
[
5
]
,
[
6
]
.
I
n
th
e
co
n
tex
t
o
f
a
c
o
n
s
tan
tly
ev
o
lv
in
g
u
n
iv
e
r
s
ity
ed
u
ca
tio
n
,
m
ath
em
atica
l
m
o
d
elin
g
p
r
e
s
en
ts
its
e
lf
as
a
p
r
o
m
is
in
g
alter
n
ativ
e
to
ad
d
r
ess
th
e
d
iv
er
s
ity
o
f
f
ac
to
r
s
th
at
in
f
lu
en
ce
lear
n
i
n
g
[
7
]
.
T
h
e
co
m
p
le
x
ity
o
f
th
is
p
r
o
ce
s
s
,
wh
ich
in
v
o
lv
es
co
g
n
itiv
e,
em
o
tio
n
al,
s
o
cial
an
d
p
ed
a
g
o
g
ical
ele
m
en
ts
,
r
eq
u
ir
es
a
m
u
ltid
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cip
lin
ar
y
a
p
p
r
o
ac
h
t
h
at
allo
ws
a
h
o
lis
tic
u
n
d
e
r
s
tan
d
in
g
o
f
ed
u
ca
tio
n
al
p
h
en
o
m
e
n
a
[
8
]
.
I
n
th
is
s
en
s
e,
th
e
p
r
o
p
o
s
ed
s
y
s
tem
atic
r
ev
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w
s
tan
d
s
as
an
o
p
p
o
r
tu
n
ity
to
ex
am
in
e
a
n
d
s
y
n
th
esize
th
e
ex
is
tin
g
s
cien
tific
ev
id
en
ce
r
e
g
ar
d
in
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th
e
u
s
e
o
f
m
ath
em
atica
l m
o
d
els in
th
e
a
n
aly
s
is
o
f
u
n
d
er
g
r
ad
u
ate
lear
n
i
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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&
R
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2252
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8
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2
2
Tr
a
n
s
fo
r
min
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u
n
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ed
u
ca
tio
n
:
a
s
ystema
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r
ev
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w
o
f m
a
th
ema
tica
l …
(
I
n
es Mir
ya
m
A
ce
r
o
A
p
a
z
a
)
2119
Pre
v
io
u
s
r
esear
ch
h
as
p
r
o
v
id
e
d
en
co
u
r
ag
in
g
in
d
icatio
n
s
ab
o
u
t
th
e
v
alu
e
o
f
m
ath
em
atica
l
m
o
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g
in
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atter
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in
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r
n
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p
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s
s
[
9
]
,
[
1
0
]
.
Ho
wev
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r
,
th
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d
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s
ity
o
f
ap
p
r
o
ac
h
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d
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[
1
1
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.
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1
2
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[
1
3
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.
T
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p
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p
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f
th
is
s
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d
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is
to
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h
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c
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en
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th
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s
tu
d
y
o
f
lear
n
in
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in
h
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g
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d
u
ca
tio
n
.
T
h
r
o
u
g
h
a
s
y
s
tem
atic
r
ev
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o
f
t
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liter
atu
r
e,
we
an
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tr
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ed
th
is
to
p
ic.
I
t
also
id
en
tifie
s
th
e
m
ain
f
in
d
in
g
s
d
er
i
v
ed
f
r
o
m
th
is
r
esear
ch
,
a
b
o
u
t
th
e
ef
f
ec
tiv
en
ess
o
f
m
ath
em
atica
l
m
o
d
els
f
o
r
th
e
o
p
tim
izatio
n
o
f
lear
n
in
g
s
tr
ateg
ies
an
d
th
e
im
p
r
o
v
em
en
t
o
f
th
e
ac
ad
em
ic
p
er
f
o
r
m
an
ce
o
f
u
n
iv
er
s
ity
s
tu
d
en
ts
.
I
n
s
h
o
r
t,
th
is
s
y
s
tem
atic
r
ev
iew
aim
s
to
co
n
t
r
ib
u
te
t
o
th
e
en
r
ic
h
m
en
t
o
f
th
e
f
ield
o
f
h
ig
h
er
e
d
u
ca
tio
n
an
d
to
p
r
o
v
id
e
a
c
o
m
p
r
e
h
en
s
iv
e
an
d
cr
itical
v
iew
o
f
th
e
a
p
p
licatio
n
o
f
m
ath
em
atica
l m
o
d
els in
u
n
iv
e
r
s
ity
lear
n
in
g
.
Ma
th
em
atica
l
m
o
d
elin
g
in
h
ig
h
er
ed
u
ca
tio
n
is
an
ad
v
an
ce
d
p
ed
ag
o
g
ical
ap
p
r
o
ac
h
th
at
r
eli
es
o
n
th
e
ap
p
licatio
n
o
f
m
ath
em
atica
l
co
n
ce
p
ts
,
tech
n
iq
u
es,
an
d
t
o
o
ls
to
ad
d
r
ess
r
ea
l
-
wo
r
ld
p
r
o
b
lem
s
with
in
th
e
ac
ad
em
ic
co
n
tex
t
[
1
4
]
,
[
1
5
]
.
T
h
is
ap
p
r
o
ac
h
is
c
h
ar
ac
ter
i
ze
d
b
y
th
e
co
n
s
tr
u
ctio
n
an
d
m
an
ip
u
latio
n
o
f
m
ath
em
atica
l
m
o
d
els,
wh
ich
ar
e
ab
s
tr
ac
t
an
d
s
y
m
b
o
lic
r
ep
r
esen
tatio
n
s
th
at
ca
p
tu
r
e
e
s
s
en
tial
asp
ec
ts
o
f
p
h
en
o
m
en
a,
p
r
o
c
ess
es,
o
r
s
itu
atio
n
s
o
b
s
er
v
ed
in
v
ar
io
u
s
d
is
cip
lin
es
an
d
in
ter
d
is
cip
lin
ar
y
f
ield
s
[
1
6
]
,
[
1
7
]
.
L
ik
ewise,
h
ig
h
er
e
d
u
ca
tio
n
in
v
o
lv
es
a
co
m
p
lex
a
n
d
m
u
ltifa
ce
ted
co
g
n
itiv
e
p
r
o
ce
s
s
th
at
g
o
es
b
ey
o
n
d
th
e
m
er
e
m
em
o
r
izatio
n
o
f
f
o
r
m
u
las an
d
alg
o
r
ith
m
s
[
1
8
]
.
Stu
d
en
ts
,
in
co
llab
o
r
atio
n
wi
th
ex
p
er
t
in
s
tr
u
cto
r
s
,
em
b
ar
k
o
n
f
o
r
m
u
latin
g
p
r
o
b
lem
s
,
i
d
en
tify
in
g
r
elev
an
t
v
ar
ia
b
les,
d
er
iv
in
g
ap
p
r
o
p
r
iate
m
ath
em
atica
l
eq
u
ati
o
n
s
an
d
r
elatio
n
s
h
ip
s
,
an
d
in
te
r
p
r
etin
g
t
h
e
r
esu
lts
o
b
tain
ed
[
1
9
]
.
T
h
is
p
r
o
ce
s
s
r
eq
u
ir
es
cr
itical
an
d
an
aly
tic
al
th
in
k
in
g
,
as
well
as
th
e
ab
ilit
y
to
tr
an
s
late
r
ea
l
-
wo
r
ld
s
itu
atio
n
s
in
to
m
at
h
em
atica
l te
r
m
s
,
an
d
v
ice
v
er
s
a
[
2
0
]
.
On
th
e
o
th
er
h
a
n
d
,
m
at
h
em
atica
l m
o
d
elin
g
in
h
ig
h
er
e
d
u
ca
tio
n
is
n
o
t
lim
ited
to
a
s
in
g
le
d
is
cip
lin
e,
b
u
t
f
in
d
s
a
p
p
licab
ilit
y
i
n
a
wid
e
r
an
g
e
o
f
ac
ad
em
ic
f
ield
s
,
in
clu
d
in
g
,
b
u
t
n
o
t lim
it
ed
to
,
p
h
y
s
ics,
b
io
lo
g
y
,
ec
o
n
o
m
ics,
en
g
in
ee
r
in
g
,
s
o
cial
s
cien
ce
s
an
d
h
ea
lth
[
2
1
]
.
Ma
th
em
atica
l
m
o
d
els
ca
n
b
e
u
s
ed
to
d
escr
ib
e
th
e
e
v
o
lu
tio
n
o
f
b
io
lo
g
ical
p
o
p
u
latio
n
s
,
p
r
ed
ict
th
e
b
eh
av
io
r
o
f
f
in
an
cial
m
ar
k
ets,
s
im
u
late
co
m
p
lex
p
h
y
s
ical
p
r
o
ce
s
s
es,
an
aly
ze
ep
id
em
io
lo
g
i
ca
l
d
ata,
an
d
s
o
lv
e
in
ter
d
is
cip
lin
ar
y
p
r
o
b
lem
s
th
at
r
eq
u
ir
e
a
d
ee
p
u
n
d
er
s
t
an
d
in
g
an
d
q
u
an
titativ
e
ap
p
r
o
ac
h
[
2
2
]
.
T
h
is
p
ed
ag
o
g
ical
ap
p
r
o
ac
h
n
o
t
o
n
l
y
d
r
i
v
es
th
e
d
ev
elo
p
m
en
t
o
f
ad
v
an
ce
d
m
ath
em
atica
l
s
k
ills
,
b
u
t
also
p
r
o
m
o
tes
th
e
ac
q
u
is
itio
n
o
f
tr
a
n
s
f
er
ab
l
e
s
k
ills
,
s
u
ch
as
p
r
o
b
lem
s
o
l
v
in
g
,
e
v
id
en
ce
-
b
ased
d
ec
is
io
n
m
ak
in
g
,
e
f
f
ec
tiv
e
co
m
m
u
n
icatio
n
,
an
d
in
ter
d
is
cip
lin
ar
y
c
o
llab
o
r
atio
n
[
2
3
]
.
Stu
d
en
ts
wh
o
p
ar
ticip
ate
in
m
ath
em
atica
l
m
o
d
elin
g
ex
p
er
ien
ce
s
d
ev
elo
p
a
d
ee
p
er
an
d
m
o
r
e
m
ea
n
in
g
f
u
l
u
n
d
er
s
tan
d
in
g
o
f
m
ath
em
atics
b
y
o
b
s
er
v
in
g
h
o
w
it
is
d
ir
ec
tly
ap
p
lied
i
n
r
ea
l
-
wo
r
ld
s
itu
atio
n
s
[
2
4
]
.
Ma
th
em
atica
l
m
o
d
elin
g
h
as
b
ec
o
m
e
an
ess
en
tial
co
m
p
o
n
e
n
t
o
f
p
ed
ag
o
g
y
i
n
h
ig
h
e
r
ed
u
c
atio
n
,
as
it
p
r
ep
ar
es
s
tu
d
e
n
ts
to
f
ac
e
co
m
p
lex
an
d
ev
o
lv
in
g
ch
allen
g
es
in
th
eir
f
u
tu
r
e
ca
r
ee
r
s
a
n
d
p
r
o
f
ess
io
n
al
ac
tiv
ities
[
2
5
]
,
[
2
6
]
.
I
n
a
wo
r
ld
d
r
iv
e
n
b
y
tech
n
o
lo
g
y
an
d
in
ter
d
is
cip
li
n
ar
ity
,
th
e
ab
ilit
y
to
ad
d
r
ess
r
ea
l
-
wo
r
ld
p
r
o
b
lem
s
q
u
an
titativ
ely
an
d
m
ath
e
m
atica
lly
is
h
ig
h
ly
v
alu
ed
,
an
d
m
at
h
em
atica
l
m
o
d
elin
g
s
tan
d
s
as
an
in
v
alu
ab
le
to
o
l
f
o
r
tr
ain
in
g
ca
p
a
b
le
an
d
c
o
m
p
eten
t in
d
iv
id
u
als to
s
o
lv
e
co
m
p
lex
an
d
m
u
ltifa
ce
ted
p
r
o
b
lem
s
[
2
7
]
,
[
2
8
]
.
T
h
e
teac
h
in
g
o
f
m
ath
em
atics
an
d
th
e
m
ea
n
i
n
g
f
u
l
lear
n
i
n
g
o
f
its
co
n
ten
ts
h
av
e
g
iv
e
n
r
is
e
to
a
n
ew
co
n
ce
p
t
ca
lled
“n
e
u
r
o
-
m
ath
e
m
atics”
f
r
o
m
a
m
u
ch
m
o
r
e
cu
r
r
en
t
p
e
r
s
p
ec
tiv
e.
T
h
is
em
er
g
es
as
a
p
r
o
p
o
s
al
b
ased
o
n
th
e
r
elatio
n
s
h
i
p
b
e
twee
n
n
eu
r
o
s
cien
ce
an
d
m
at
h
em
atics
d
id
ac
tics
,
wh
ich
h
i
g
h
lig
h
ts
th
e
u
s
e
o
f
v
ar
io
u
s
s
tr
u
ctu
r
es,
s
u
ch
as
th
e
Ho
d
g
k
in
-
H
u
x
ley
m
o
d
el,
th
e
I
n
teg
r
ate
-
an
d
-
Fire
m
o
d
el,
n
e
u
r
al
n
etwo
r
k
s
,
an
d
s
y
n
ap
s
es
[
2
9
]
.
I
n
th
is
s
en
s
e,
m
o
d
elin
g
n
o
w
ex
ten
d
s
to
th
e
d
esig
n
o
f
in
n
o
v
ativ
e
s
tr
ate
g
ies.
T
h
ese
s
h
o
u
ld
p
r
o
m
o
te
co
n
ca
ten
ate
d
d
esig
n
ac
tio
n
s
b
etwe
en
c
r
itical
-
r
ef
le
ctiv
e
th
in
k
in
g
an
d
em
o
tio
n
al
ch
ar
g
es
th
at
allo
w
th
e
d
esig
n
an
d
d
ev
elo
p
m
en
t
o
f
m
o
d
els
b
y
s
tu
d
en
ts
.
I
n
th
i
s
s
en
s
e,
th
e
r
e
s
ea
r
ch
q
u
esti
o
n
f
o
r
m
u
lated
f
o
r
th
is
ar
ticle
is
th
e
f
o
llo
win
g
: Wh
at
is
th
e
im
p
ac
t o
f
m
at
h
em
atica
l m
o
d
elin
g
o
n
th
e
lear
n
in
g
o
f
u
n
iv
er
s
ity
s
tu
d
en
ts
?
I
n
o
r
d
er
to
ac
h
iev
e
th
e
co
r
r
ec
t
p
er
f
o
r
m
an
ce
an
d
d
e
v
elo
p
m
en
t
o
f
s
tu
d
e
n
ts
,
th
e
in
s
tit
u
tio
n
m
u
s
t
co
n
s
id
er
d
if
f
er
en
t
s
k
ills
th
at
will
f
ac
ilit
ate
lear
n
in
g
.
I
n
tu
r
n
,
u
n
i
v
er
s
ity
ed
u
ca
tio
n
is
co
m
p
lem
en
ted
with
s
o
f
t
s
k
ills
,
wh
ich
s
er
v
e
as
ad
ap
tatio
n
to
o
ls
f
o
r
d
if
f
e
r
en
t
ed
u
ca
tio
n
al
s
p
ac
es
[
3
0
]
.
I
n
th
e
s
am
e
way
,
th
e
s
tim
u
latio
n
o
f
r
esear
ch
s
k
ills
n
o
t
o
n
ly
r
eq
u
ir
es
th
e
ad
o
p
tio
n
o
f
tech
n
ical
an
d
m
eth
o
d
o
l
o
g
ical
s
k
ills
,
s
i
n
ce
it
en
co
m
p
ass
es
co
g
n
itiv
e,
af
f
ec
tiv
e
a
n
d
b
e
h
av
io
r
al
ex
p
er
ie
n
ce
s
[
3
1
]
,
b
u
t
also
r
esear
ch
s
tr
ateg
ies
th
at
allo
w
co
n
tin
u
o
u
s
s
elf
-
lear
n
in
g
,
s
in
ce
th
e
y
h
av
e
p
o
s
itiv
e
ef
f
ec
ts
b
o
th
i
n
th
e
ac
a
d
em
ic
an
d
w
o
r
k
e
n
v
ir
o
n
m
en
ts
[
3
2
]
.
As
th
e
y
ea
r
s
g
o
b
y
,
th
e
f
o
r
m
ativ
e
n
ee
d
s
o
f
s
tu
d
en
ts
a
d
v
an
ce
an
d
ex
p
a
n
d
,
wh
ich
d
r
iv
es
th
e
d
ev
elo
p
m
e
n
t
o
f
n
ew
ev
alu
at
io
n
m
eth
o
d
s
th
at
en
r
ich
th
e
lear
n
in
g
p
r
o
ce
s
s
es;
o
n
th
e
o
th
er
h
an
d
,
h
ig
h
e
r
ed
u
ca
tio
n
r
eq
u
ir
es
a
cr
itical
an
d
an
aly
tical
ap
p
r
o
ac
h
th
at
f
ac
ilit
ates
th
e
ap
p
licatio
n
o
f
th
eo
r
etica
l
co
n
ce
p
ts
lear
n
ed
in
class
,
as
well
as
th
e
co
n
n
ec
tio
n
b
etwe
en
th
e
tr
ad
itio
n
al
an
d
th
e
d
ig
ital
[
3
3
]
.
Fo
r
th
e
ad
eq
u
ate
ac
ad
em
ic
p
r
o
ce
s
s
,
it
is
n
ec
ess
ar
y
th
e
in
cu
r
s
io
n
o
f
f
o
r
m
ativ
e
s
tr
ateg
ies
th
at
h
elp
t
o
ac
h
iev
e
p
er
s
o
n
a
l
ac
h
iev
em
en
ts
an
d
c
o
m
p
ete
n
cies th
at
ar
e
b
en
ef
icial
f
o
r
lear
n
i
n
g
[
3
4
]
.
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
.
14
,
No
.
3
,
J
u
n
e
20
25
:
2
1
1
8
-
2
1
3
1
2120
I
n
h
ig
h
e
r
ed
u
ca
tio
n
,
th
ese
m
o
d
els
ar
e
u
s
ed
to
m
ak
e
an
e
v
alu
atio
n
r
ec
o
r
d
o
f
s
tu
d
en
ts
,
with
th
e
o
b
jectiv
e
o
f
f
o
llo
win
g
u
p
o
n
th
eir
p
er
f
o
r
m
an
ce
; th
is
allo
ws i
d
en
tify
in
g
h
o
w
im
p
r
o
v
em
en
ts
in
s
tu
d
en
t le
ar
n
in
g
ar
e
d
ev
elo
p
e
d
th
r
o
u
g
h
d
ata
r
ev
iew
an
d
elab
o
r
atio
n
o
f
s
ch
em
es
[
3
5
]
.
T
h
ese
m
o
d
els
attem
p
t
to
tr
an
s
late
a
p
h
en
o
m
en
o
n
o
r
p
r
o
b
lem
i
n
to
a
r
ea
l
s
ce
n
ar
io
,
an
d
b
ec
o
m
e
ess
en
tial
f
o
r
th
e
g
en
er
atio
n
o
f
k
n
o
wled
g
e,
s
in
ce
th
ey
h
elp
to
r
ep
licate
an
d
u
n
d
er
s
tan
d
v
ar
io
u
s
p
r
o
b
lem
s
o
f
r
e
ality
[
3
6
]
.
Ma
t
h
em
atica
l
m
o
d
e
lin
g
,
wh
en
u
s
ed
as
a
p
ed
ag
o
g
ical
ap
p
r
o
ac
h
,
f
av
o
r
s
th
e
u
n
d
er
s
tan
d
in
g
o
f
th
e
d
i
s
cip
lin
e
to
b
e
s
tu
d
ied
,
wh
ile
o
f
f
er
in
g
an
ab
s
tr
ac
t
r
elatio
n
s
h
ip
with
r
ea
lity
th
at
r
ep
r
esen
ts
an
d
s
im
p
lifie
s
it [
3
5
]
,
[
3
7
]
.
Dep
en
d
in
g
o
n
th
e
n
atu
r
e
o
f
ea
ch
m
ath
em
atica
l
m
o
d
el
an
d
its
ap
p
licatio
n
in
th
e
p
h
en
o
m
en
a
o
f
r
ea
lity
,
ce
r
tain
v
alu
es
ar
e
c
o
n
s
id
er
ed
f
o
r
th
eir
r
esp
ec
ti
v
e
s
tu
d
y
,
f
o
r
ex
am
p
le,
v
a
r
i
ab
les,
p
ar
am
eter
s
,
co
n
s
tr
ain
ts
,
r
elatio
n
s
h
ip
s
b
etw
ee
n
v
ar
iab
les
an
d
s
im
p
lifie
d
r
ep
r
esen
tatio
n
s
[
3
8
]
.
T
h
e
latter
,
to
g
eth
er
with
th
e
ac
tiv
ities
g
en
er
ated
f
r
o
m
t
h
e
in
co
r
p
o
r
atio
n
o
f
m
ath
em
atic
al
m
o
d
elin
g
,
allo
ws
th
e
i
n
ter
v
en
tio
n
o
f
r
ea
lis
tic
p
r
o
b
lem
s
th
at
c
o
n
s
o
lid
ate
d
if
f
er
en
t sk
ills
in
th
e
s
tu
d
en
t w
h
e
n
s
u
cc
ess
f
u
l in
p
r
ac
tice
[
3
9
]
.
Ma
t
h
e
m
at
ic
al
m
o
d
el
in
g
i
n
c
o
r
p
o
r
a
tes
le
v
e
ls
o
f
lea
r
n
i
n
g
,
w
h
e
r
e
t
h
e
c
o
g
n
iti
v
e
,
a
f
f
e
cti
v
e
,
a
n
d
m
e
t
a
c
o
g
n
i
t
i
v
e
a
r
e
n
e
c
e
s
s
a
r
y
f
o
r
t
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
c
o
m
p
e
t
e
n
c
i
e
s
;
t
h
u
s
,
t
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
t
e
s
t
s
a
n
d
p
r
a
c
t
i
c
a
l
e
x
e
r
c
i
s
e
s
p
r
o
m
o
t
e
s
e
d
u
c
a
t
i
o
n
u
n
d
e
r
a
h
o
l
i
s
t
i
c
a
p
p
r
o
a
c
h
f
o
r
t
h
e
i
d
e
n
t
i
f
i
c
a
t
i
o
n
o
f
s
t
r
e
n
g
t
h
s
i
n
a
c
a
d
e
m
i
c
c
o
m
p
e
t
e
n
c
e
[
4
0
]
.
Fr
o
m
a
r
es
ea
r
c
h
c
o
n
t
ex
t,
t
h
e
s
tu
d
y
p
u
r
s
u
es
th
e
f
o
ll
o
win
g
o
b
je
cti
v
es
:
i
)
t
o
e
x
p
la
i
n
th
e
im
p
ac
t
o
f
t
h
e
ap
p
li
ca
ti
o
n
o
f
m
at
h
e
m
a
tic
al
m
o
d
els
o
n
s
t
u
d
e
n
t
l
ea
r
n
i
n
g
i
n
h
i
g
h
e
r
e
d
u
ca
ti
o
n
,
t
o
co
n
t
r
i
b
u
t
e
t
o
t
h
e
c
o
n
s
o
l
id
ati
o
n
o
f
ex
is
ti
n
g
k
n
o
wle
d
g
e
;
ii
)
to
d
es
cr
ib
e
h
o
w
m
at
h
e
m
a
tic
al
m
o
d
eli
n
g
i
m
p
r
o
v
es
t
h
e
u
n
d
e
r
s
t
a
n
d
i
n
g
o
f
u
n
i
v
e
r
s
it
y
s
tu
d
e
n
ts
;
iii
)
t
o
d
e
tai
l
t
h
e
ele
m
e
n
ts
ass
o
cia
te
d
wi
th
th
e
d
e
v
el
o
p
m
e
n
t
o
f
p
r
o
b
le
m
-
s
o
l
v
i
n
g
s
k
ills
;
a
n
d
i
v
)
to
an
al
y
ze
t
h
e
c
o
n
n
ec
t
io
n
b
etwe
en
t
h
e
o
r
y
a
n
d
p
r
a
cti
ce
o
f
m
a
t
h
e
m
at
ic
al
m
o
d
eli
n
g
i
n
h
i
g
h
e
r
ed
u
ca
t
io
n
.
I
n
t
h
is
s
en
s
e
,
th
e
d
e
v
elo
p
m
e
n
t
o
f
th
e
estab
lis
h
ed
ex
p
l
o
r
atio
n
will
p
r
o
v
id
e
cr
itical
g
u
id
an
ce
f
o
r
f
u
tu
r
e
r
esear
ch
a
n
d
p
ed
ag
o
g
ical
p
r
a
c
t
i
c
e
s
,
b
a
s
e
d
o
n
t
h
e
f
o
l
l
o
w
i
n
g
r
e
s
e
a
r
c
h
q
u
e
s
t
i
o
n
s
:
i
)
W
h
a
t
i
s
t
h
e
i
m
p
a
c
t
o
f
m
a
t
h
e
m
a
t
i
c
a
l
m
o
d
e
l
i
n
g
o
n
u
n
i
v
e
r
s
i
t
y
s
tu
d
en
ts
'
lear
n
in
g
?
;
ii)
Ho
w
d
o
es
m
ath
e
m
atica
l
m
o
d
ellin
g
im
p
r
o
v
e
u
n
iv
er
s
ity
s
tu
d
en
ts
'
u
n
d
er
s
tan
d
i
n
g
?
;
iii)
W
h
at
ar
e
th
e
elem
en
ts
ass
o
ciate
d
with
t
h
e
d
ev
elo
p
m
en
t
o
f
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
?
;
an
d
iv
)
W
h
at
is
th
e
co
n
n
ec
tio
n
b
et
wee
n
th
e
th
eo
r
y
an
d
p
r
ac
tice
o
f
m
ath
em
atica
l m
o
d
elin
g
in
h
i
g
h
er
ed
u
ca
tio
n
?
2.
M
E
T
H
O
D
T
o
ac
h
iev
e
th
e
estab
lis
h
ed
r
esear
ch
o
b
jectiv
e,
a
q
u
alitativ
e
ap
p
r
o
ac
h
m
eth
o
d
o
lo
g
y
with
an
ex
p
lo
r
ato
r
y
s
co
p
e
was a
d
o
p
te
d
.
T
o
ac
h
iev
e
th
e
estab
lis
h
ed
r
esear
ch
o
b
jectiv
e,
a
q
u
alitativ
e
m
eth
o
d
o
lo
g
y
with
an
ex
p
lo
r
ato
r
y
ap
p
r
o
ac
h
was
ad
o
p
ted
.
T
o
ca
r
r
y
o
u
t
th
is
task
,
th
e
s
y
s
tem
atic
r
ev
iew
m
eth
o
d
s
u
p
p
o
r
te
d
b
y
th
e
p
r
in
cip
les
o
f
th
e
PR
I
SMA
m
eth
o
d
was
ap
p
lied
,
ad
d
r
ess
in
g
th
e
b
asic
s
tag
es
o
f
th
e
m
eth
o
d
s
u
ch
as
d
o
cu
m
en
t
id
en
tific
atio
n
,
ex
h
a
u
s
tiv
e
r
ev
iew,
elig
ib
ilit
y
,
an
d
in
clu
s
io
n
[
4
1
]
,
to
in
v
esti
g
ate
th
e
u
s
e
o
f
m
ath
em
atica
l
m
o
d
elin
g
in
th
e
co
n
tex
t
o
f
u
n
iv
er
s
ity
lear
n
in
g
.
T
h
e
c
h
o
ic
e
o
f
t
h
is
m
eth
o
d
o
lo
g
ical
to
o
l
m
ad
e
it
p
o
s
s
ib
le
to
ca
r
r
y
o
u
t
an
ex
h
a
u
s
tiv
e
an
d
o
r
g
an
ized
s
ea
r
ch
i
n
th
e
r
elev
a
n
t a
ca
d
em
ic
liter
atu
r
e,
p
e
r
f
o
r
m
a
cr
itical
an
aly
s
is
o
f
th
e
s
elec
ted
s
tu
d
ies,
an
d
ac
cu
r
ately
an
d
r
ig
o
r
o
u
s
ly
co
m
p
ile
t
h
e
av
ailab
le
ev
id
e
n
ce
[
4
2
]
.
T
h
is
q
u
alitativ
e
r
esear
ch
ap
p
r
o
ac
h
an
d
s
y
s
tem
atic
r
ev
iew
m
eth
o
d
o
l
o
g
y
p
r
o
v
id
e
a
s
o
lid
f
o
u
n
d
atio
n
f
o
r
ad
d
r
ess
in
g
th
e
to
p
ic
o
f
m
ath
em
atica
l
m
o
d
elin
g
i
n
th
e
f
ield
o
f
u
n
iv
er
s
ity
lear
n
i
n
g
.
B
y
s
y
s
tem
atica
lly
ex
p
lo
r
in
g
th
e
ac
ad
em
ic
liter
atu
r
e,
a
d
ee
p
er
an
d
m
o
r
e
co
m
p
r
eh
en
s
iv
e
u
n
d
er
s
tan
d
in
g
o
f
tr
en
d
s
,
ap
p
r
o
ac
h
es,
an
d
r
esu
lts
in
th
is
s
p
ec
if
ic
f
ield
ca
n
b
e
o
b
tain
ed
.
I
n
ad
d
it
io
n
,
cr
itical
an
aly
s
is
o
f
th
e
s
elec
ted
s
tu
d
ies
will
co
n
tr
ib
u
te
to
ass
ess
in
g
th
e
q
u
ality
an
d
r
elev
an
ce
o
f
th
e
av
a
ilab
le
ev
id
en
ce
,
wh
ich
will
u
l
tim
ately
en
r
ich
th
e
r
esear
ch
an
d
its
co
n
clu
s
io
n
s
.
C
o
n
s
eq
u
en
tly
,
t
h
e
s
ea
r
ch
f
o
r
r
elev
an
t
ac
ad
em
ic
liter
atu
r
e
an
d
p
u
b
licatio
n
s
was
ca
r
r
ied
o
u
t
b
y
ac
ce
s
s
in
g
th
r
ee
p
r
esti
g
io
u
s
elec
tr
o
n
ic
d
ata
b
ases
:
Pu
b
Me
d
,
S
co
p
u
s
,
an
d
W
eb
o
f
Scien
ce
.
Du
r
in
g
th
is
p
r
o
ce
s
s
,
s
p
ec
if
ic
co
m
b
in
atio
n
s
o
f
k
ey
t
er
m
s
,
s
u
ch
as “
m
ath
em
atica
l
m
o
d
elin
g
”
AND
“u
n
iv
er
s
ity
l
ea
r
n
in
g
”
OR
“h
ig
h
e
r
ed
u
ca
tio
n
”
wer
e
u
s
ed
to
p
r
e
cisely
id
en
tify
th
o
s
e
s
tu
d
ies
r
elate
d
to
th
e
im
p
lem
e
n
tatio
n
o
f
m
ath
e
m
atica
l
m
o
d
elin
g
i
n
th
e
co
n
tex
t
o
f
h
ig
h
er
ed
u
ca
tio
n
.
T
o
f
u
r
th
er
s
p
ec
if
y
th
e
s
ea
r
ch
an
d
f
o
cu
s
o
n
th
e
ef
f
icac
y
o
f
im
p
lem
en
tin
g
m
ath
em
atica
l
m
o
d
elin
g
in
c
o
lleg
e
lear
n
i
n
g
,
ter
m
s
s
u
ch
as
“e
f
f
e
ctiv
en
ess
”
OR
“o
u
tco
m
es”
OR
“im
p
ac
t”
wer
e
in
clu
d
ed
.
T
h
es
e
s
ea
r
ch
eq
u
atio
n
s
an
d
B
o
o
lea
n
o
p
er
ato
r
s
y
ield
e
d
a
s
et
o
f
r
esu
lts
r
elev
an
t
to
th
e
s
tu
d
y
o
f
m
at
h
em
atica
l m
o
d
eli
n
g
in
th
e
f
ield
o
f
u
n
i
v
er
s
ity
lear
n
in
g
.
T
o
b
o
o
s
t
th
e
s
ea
r
ch
in
ea
ch
o
f
th
e
d
atab
ases
o
r
s
ea
r
ch
en
g
in
es,
th
e
co
n
f
ig
u
r
atio
n
w
as
ap
p
lied
:
“
m
ath
em
atica
l
m
o
d
elin
g
”
AND
“
u
n
iv
er
s
ity
lear
n
in
g
”
OR
“
h
ig
h
er
e
d
u
ca
tio
n
”
,
f
o
r
Sco
p
u
s
.
I
n
th
e
c
o
n
tex
t
o
f
a
s
y
s
tem
atic
r
ev
iew
o
n
th
e
im
p
o
r
tan
ce
o
f
m
ath
em
atica
l
m
o
d
e
lin
g
in
u
n
d
er
g
r
a
d
u
ate
lea
r
n
in
g
,
it
was
co
n
s
id
er
ed
ess
en
tial
to
estab
lis
h
in
clu
s
io
n
an
d
ex
cl
u
s
io
n
cr
iter
ia
in
a
r
o
b
u
s
t
an
d
clea
r
m
an
n
e
r
.
T
h
e
s
e
c
r
i
t
e
r
i
a
p
l
a
y
e
d
a
k
e
y
r
o
l
e
i
n
t
h
e
c
a
r
e
f
u
l
s
e
l
e
c
t
i
o
n
o
f
r
elev
an
t
s
tu
d
ies
,
wh
ich
,
in
tu
r
n
,
en
s
u
r
ed
th
e
co
n
s
is
ten
cy
an
d
th
o
r
o
u
g
h
n
ess
o
f
th
e
r
ev
iew
.
A
d
escr
ip
tio
n
o
f
t
h
e
i
n
c
l
u
s
i
o
n
c
r
i
t
e
r
i
a
th
at
wer
e
ap
p
lie
d
i
n
t
h
e
ar
t
icle
s
ea
r
ch
p
r
o
ce
s
s
is
p
r
o
v
id
ed
as
:
−
T
h
em
ati
c
r
ele
v
an
ce
:
t
o
b
e
i
n
cl
u
d
e
d
i
n
t
h
e
r
e
v
i
ew,
ea
ch
a
r
tic
l
e
h
ad
to
b
e
r
ela
te
d
,
d
i
r
e
ctl
y
o
r
in
d
i
r
e
ctl
y
,
to
th
e
im
p
o
r
t
an
ce
o
f
m
at
h
e
m
at
ic
al
m
o
d
eli
n
g
i
n
t
h
e
l
ea
r
n
i
n
g
p
r
o
c
ess
o
f
u
n
iv
er
s
it
y
s
t
u
d
e
n
ts
.
T
h
is
ap
p
r
o
ac
h
w
as
s
p
e
ci
f
ic
all
y
d
esi
g
n
e
d
t
o
e
n
s
u
r
e
t
h
at
t
h
e
s
e
lec
te
d
s
tu
d
i
es
ac
cu
r
atel
y
a
d
d
r
ess
e
d
th
e
ce
n
t
r
a
l
r
es
e
ar
ch
q
u
esti
o
n
.
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
Tr
a
n
s
fo
r
min
g
u
n
ivers
ity
ed
u
ca
tio
n
:
a
s
ystema
tic
r
ev
ie
w
o
f m
a
th
ema
tica
l …
(
I
n
es Mir
ya
m
A
ce
r
o
A
p
a
z
a
)
2121
−
T
y
p
e
o
f
s
tu
d
y
:
o
n
ly
em
p
ir
i
ca
l
s
tu
d
ies
th
at
f
o
cu
s
ed
o
n
s
y
s
tem
atic
r
esear
ch
,
eith
er
q
u
an
titativ
e
o
r
q
u
alitativ
e,
o
n
th
e
a
p
p
licatio
n
o
f
m
ath
em
atica
l
m
o
d
elin
g
in
u
n
d
er
g
r
ad
u
ate
lear
n
in
g
wer
e
c
o
n
s
id
er
ed
.
T
h
is
cr
iter
io
n
en
co
m
p
ass
ed
a
wid
e
v
ar
iety
o
f
r
esear
ch
d
esig
n
s
,
in
clu
d
in
g
ex
p
er
im
en
tal
s
tu
d
i
es,
lo
n
g
itu
d
in
al
r
esear
ch
,
ca
s
e
s
tu
d
ies,
s
u
r
v
ey
s
,
an
d
in
ter
v
iews.
T
h
e
r
atio
n
ale
b
eh
in
d
th
is
ch
o
ice
was
to
en
s
u
r
e
th
at
th
e
s
tu
d
ies p
r
o
v
id
ed
co
n
c
r
ete
an
d
s
u
b
s
tan
tial d
ata
o
n
th
e
im
p
o
r
ta
n
ce
o
f
m
at
h
em
atica
l m
o
d
elin
g
.
−
Date
o
f
p
u
b
licatio
n
:
t
h
e
in
c
lu
s
io
n
o
f
ar
ticles
was
lim
ite
d
to
a
s
p
ec
if
ic
r
an
g
e
o
f
y
e
ar
s
,
d
eter
m
in
ed
ac
co
r
d
in
g
to
th
e
n
ee
d
s
an
d
r
e
s
o
u
r
ce
s
av
ailab
le
t
o
th
e
r
ev
ie
wer
.
T
h
is
tem
p
o
r
al
r
an
g
e
,
alt
h
o
u
g
h
v
ar
iab
le,
was
estab
lis
h
ed
,
f
o
r
ex
am
p
le,
f
r
o
m
t
h
e
y
ea
r
2
0
1
8
to
t
h
e
y
e
ar
2
0
2
3
,
with
th
e
p
u
r
p
o
s
e
o
f
co
v
er
in
g
r
ec
en
t
an
d
r
ele
v
an
t
r
esear
c
h
.
I
n
th
is
s
en
s
e,
it
is
in
ten
d
ed
t
o
f
u
lf
ill
th
e
p
u
r
p
o
s
e
o
f
s
elec
tin
g
a
n
d
i
n
clu
d
in
g
r
ec
en
t
an
d
r
elev
a
n
t r
esear
ch
o
n
m
ath
em
atica
l m
o
d
elin
g
.
An
in
itial
co
r
p
u
s
c
o
m
p
o
s
ed
o
f
a
to
tal
o
f
7
5
4
ac
ad
em
ic
ar
ticles
was
ex
am
in
e
d
as
p
ar
t
o
f
th
e
s
y
s
tem
atic
r
ev
iew
o
f
th
e
liter
a
tu
r
e,
s
ec
tio
n
e
d
as:
2
5
4
f
r
o
m
P
u
b
Me
d
,
3
9
8
f
r
o
m
Sco
p
u
s
an
d
3
3
2
f
r
o
m
W
eb
o
f
Scien
ce
s
.
Fro
m
th
is
lar
g
e
s
am
p
le,
a
r
ig
o
r
o
u
s
s
elec
tio
n
p
r
o
c
ess
was
ca
r
r
ied
o
u
t
in
f
o
u
r
s
tag
es:
id
en
tific
atio
n
,
r
ev
iew,
elig
ib
ilit
y
an
d
in
clu
s
io
n
.
I
n
th
e
f
ir
s
t
s
h
ar
ed
r
ev
iew,
1
6
3
ar
ticles
o
r
d
u
p
licate
d
o
c
u
m
en
ts
wer
e
f
o
u
n
d
,
wh
ich
wer
e
d
is
ca
r
d
ed
,
r
ed
u
c
in
g
th
e
n
u
m
b
er
o
f
d
o
cu
m
en
ts
to
5
9
1
.
Nex
t,
a
d
etailed
o
b
s
er
v
atio
n
o
f
th
e
s
tr
u
ctu
r
e
o
f
ea
ch
ar
ticle
was
ca
r
r
ied
o
u
t,
f
r
o
m
wh
ich
5
6
1
wer
e
d
is
ca
r
d
ed
b
ec
au
s
e
th
ey
d
id
n
o
t
h
a
v
e
a
co
m
p
lete
s
tr
u
ctu
r
e.
T
h
is
r
esu
lted
in
a
s
elec
t
s
et
o
f
3
0
s
tu
d
ies
r
elev
an
t
to
th
e
f
in
al
an
a
ly
s
is
as
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
ese
s
tu
d
ies
wer
e
ca
r
ef
u
lly
s
elec
ted
an
d
in
cl
u
d
ed
b
ased
o
n
th
ei
r
r
elev
a
n
ce
an
d
s
u
b
s
tan
tial
co
n
tr
ib
u
tio
n
to
th
e
r
esear
ch
to
p
ic,
i.e
.
,
th
e
im
p
o
r
tan
ce
o
f
m
ath
em
atica
l m
o
d
elin
g
in
u
n
d
er
g
r
ad
u
ate
lear
n
i
n
g
.
I
t
i
s
im
p
er
ativ
e
to
n
o
te
th
at
t
h
is
r
ev
iew
was
s
u
b
ject
to
ce
r
t
ain
lim
itatio
n
s
,
s
u
ch
as
p
u
b
li
ca
tio
n
b
ias
an
d
th
e
r
estrictio
n
o
f
s
tu
d
ies
av
ailab
le
in
lan
g
u
ag
es
o
t
h
er
t
h
an
E
n
g
lis
h
.
Nev
er
t
h
eless
,
m
eticu
lo
u
s
s
tr
ateg
ies
wer
e
ca
r
r
ied
o
u
t
with
th
e
aim
o
f
ad
d
r
ess
in
g
an
d
m
in
im
izin
g
th
ese
p
o
ten
tial
b
iases
.
T
h
ese
s
tr
ateg
ies
in
clu
d
ed
an
e
x
h
a
u
s
t
i
v
e
s
e
a
r
c
h
o
f
t
h
e
e
x
i
s
t
i
n
g
l
i
t
e
r
a
t
u
r
e
,
i
n
a
d
d
i
t
i
o
n
t
o
t
h
e
i
n
c
l
u
s
i
o
n
o
f
s
t
u
d
i
e
s
i
n
v
a
r
i
o
u
s
l
a
n
g
u
a
g
e
s
.
I
n
t
h
i
s
w
a
y
,
w
e
s
o
u
g
h
t
t
o
en
s
u
r
e
t
h
a
t
t
h
e
s
y
s
tem
atic
r
e
v
i
e
w
c
o
v
e
r
e
d
a
s
m
u
ch
r
elev
an
t
a
n
d
r
eliab
le
ev
id
en
ce
as p
o
s
s
ib
le
.
Fig
u
r
e
1
.
T
h
e
alg
o
r
ith
m
d
esig
n
ed
to
ca
r
r
y
o
u
t th
e
a
p
p
licatio
n
o
f
th
e
PR
I
SMA
m
eth
o
d
in
t
h
e
r
esear
ch
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Resul
t
s
T
h
ese
s
p
ec
if
ic
s
tu
d
ies
wer
e
ch
o
s
en
to
p
r
esen
t
a
f
o
cu
s
ed
an
d
r
e
p
r
esen
tativ
e
v
iew
o
f
th
e
in
tr
in
s
ic
r
elatio
n
s
h
ip
b
etwe
en
m
ath
em
atica
l
m
o
d
elin
g
an
d
th
e
im
p
r
o
v
em
en
t
o
f
th
e
ed
u
ca
tio
n
al
ex
p
er
ien
ce
at
th
e
u
n
iv
er
s
ity
lev
el.
E
ac
h
o
f
th
e
s
elec
ted
p
ap
er
s
p
r
o
v
id
es
s
ig
n
if
ican
t
in
s
ig
h
ts
th
at
to
u
c
h
o
n
v
ar
io
u
s
asp
ec
ts
o
f
h
ig
h
er
e
d
u
ca
tio
n
,
r
a
n
g
in
g
f
r
o
m
d
ee
p
e
n
in
g
c
o
n
ce
p
t
u
al
u
n
d
e
r
s
tan
d
in
g
to
o
p
tim
izin
g
ac
ad
e
m
ic
p
er
f
o
r
m
an
ce
,
as
well
as
ad
ap
tin
g
to
th
e
c
h
an
g
in
g
d
y
n
am
ics
o
f
d
ig
ital
en
v
ir
o
n
m
en
ts
.
T
ab
le
1
,
b
y
v
ir
t
u
e
o
f
its
s
elec
tiv
e
an
d
an
aly
tical
ap
p
r
o
ac
h
,
ex
p
o
s
es
th
e
ar
ticles
s
elec
ted
f
o
r
th
e
r
ev
iew,
th
r
o
u
g
h
a
co
n
cise
b
u
t
r
ep
r
esen
tativ
e
s
y
n
th
esis
o
f
th
e
f
in
d
in
g
s
th
a
t
im
p
ly
th
e
im
p
o
r
tan
ce
o
f
m
ath
em
atica
l
m
o
d
elin
g
in
th
e
u
n
iv
er
s
ity
s
ettin
g
,
p
r
esen
tin
g
th
e
q
u
alitativ
e
asp
ec
ts
o
f
ea
ch
s
elec
tio
n
.
T
a
b
le
1
,
d
u
e
t
o
its
s
elec
tiv
e
an
d
a
n
aly
tical
ap
p
r
o
ac
h
,
ex
p
o
s
es
th
e
ar
ticles
s
elec
ted
f
o
r
th
e
r
e
v
iew
th
r
o
u
g
h
a
c
o
n
cise
b
u
t
r
ep
r
esen
tativ
e
s
y
n
th
esis
o
f
th
e
f
in
d
in
g
s
th
at
I
d
e
n
t
i
f
i
c
a
t
i
o
n
N
o
.
o
f
r
e
c
o
r
d
s
i
d
e
n
t
i
f
i
e
d
i
n
t
h
e
se
ar
c
h
=
7
5
4
N
o
.
o
f
i
t
e
m
s
i
d
e
n
t
i
f
i
e
d
f
o
r
r
e
v
i
e
w
:
P
u
b
M
e
d
=
2
5
4
,
S
c
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Evaluation Warning : The document was created with Spire.PDF for Python.
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n
s
fo
r
min
g
u
n
ivers
ity
ed
u
ca
tio
n
:
a
s
ystema
tic
r
ev
ie
w
o
f m
a
th
ema
tica
l …
(
I
n
es Mir
ya
m
A
ce
r
o
A
p
a
z
a
)
2123
I
n
r
elatio
n
to
th
e
q
u
an
titativ
e
r
esu
lts
,
it
wa
s
p
o
s
s
ib
le
to
ap
p
r
ec
iate
th
e
u
s
e
o
f
v
ar
io
u
s
m
at
h
em
atica
l
m
o
d
els
in
th
e
s
elec
ted
p
u
b
licatio
n
s
,
with
a
g
r
ea
ter
p
ar
ticip
atio
n
o
f
m
o
d
els
with
s
tr
u
ctu
r
a
l
eq
u
atio
n
s
,
m
o
d
els
r
elate
d
to
ad
ap
tiv
e
p
r
o
f
iles
a
n
d
v
ir
tu
al
m
at
h
em
atica
l
m
o
d
els.
I
n
t
h
e
f
ir
s
t
p
lace
,
with
t
h
e
s
am
e
lev
el
o
f
f
r
eq
u
e
n
cy
an
d
p
er
ce
n
tag
e
d
is
tr
ib
u
tio
n
,
t
h
e
u
s
e
o
f
s
tr
u
ctu
r
al
eq
u
atio
n
s
,
ad
a
p
tiv
e
p
r
o
f
ile
m
ath
em
atica
l
m
o
d
els
an
d
v
ir
t
u
al
m
o
d
els
s
tan
d
o
u
t w
ith
1
0
%
ea
ch
.
I
n
a
s
ec
o
n
d
g
r
o
u
p
with
a
lo
wer
f
r
eq
u
en
cy
ar
e
p
r
ed
ictiv
e
m
o
d
els,
lin
ea
r
r
eg
r
ess
io
n
an
d
m
u
ltil
ev
el
m
o
d
els
with
6
.
6
6
%
ea
ch
.
Fin
ally
,
n
e
u
r
al
n
etwo
r
k
s
,
d
y
n
am
ic
s
im
u
latio
n
m
o
d
els,
m
o
d
els b
ased
o
n
s
et
t
h
eo
r
y
,
an
d
p
h
y
s
ico
-
m
ath
em
ati
ca
l m
o
d
els,
wer
e
f
o
u
n
d
with
3
.
3
3
% e
ac
h
.
T
h
e
n
u
m
b
er
o
f
an
n
u
al
s
tu
d
ie
s
clea
r
ly
s
h
o
ws
an
e
v
o
lu
tio
n
o
v
er
s
ix
y
ea
r
s
.
An
in
c
r
ea
s
in
g
tr
en
d
in
r
esear
ch
ac
tiv
ity
is
o
b
s
er
v
ed
f
o
r
2
0
2
0
,
wh
ich
r
em
ain
ed
c
o
n
s
tan
t
u
n
til
2
0
2
1
;
h
o
wev
er
,
a
s
ig
n
if
ican
t
u
p
t
u
r
n
is
o
b
s
er
v
ed
f
o
r
2
0
2
2
,
as we
ll a
s
a
s
m
all
d
ec
r
ea
s
e
in
2
0
2
3
,
in
d
icatin
g
a
g
r
o
wth
in
th
e
p
r
o
d
u
ct
io
n
o
f
s
tu
d
ies in
t
h
is
ar
ea
in
r
ec
en
t
y
ea
r
s
as p
r
esen
ted
in
Fig
u
r
e
2
.
T
h
is
is
m
ain
ly
b
ec
au
s
e
tech
n
o
lo
g
ical
ad
v
a
n
c
es m
ay
f
ac
ilit
ate
th
e
d
ev
elo
p
m
e
n
t
o
f
r
esear
ch
in
ce
r
tain
ar
ea
s
,
wh
ich
c
o
u
ld
lea
d
t
o
an
in
c
r
ea
s
e
in
th
e
p
r
o
d
u
ctio
n
o
f
s
tu
d
ies
in
t
h
ese
f
ield
s
.
T
h
e
s
elec
ted
ar
ticles
also
d
em
o
n
s
tr
ate
th
e
ex
is
ten
ce
o
f
p
o
s
itiv
e
an
d
n
eg
ativ
e
f
i
n
d
in
g
s
i
n
r
elatio
n
to
th
e
y
ea
r
o
f
p
u
b
licatio
n
as
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
is
an
al
y
s
is
f
ac
ilit
ates
a
r
etr
o
s
p
ec
tiv
e
v
ie
w
o
n
th
e
d
is
tr
ib
u
tio
n
an
d
tr
en
d
o
f
p
o
s
itiv
e
an
d
n
e
g
ativ
e
f
in
d
in
g
s
in
ac
ad
em
ic
r
esear
ch
.
An
o
v
er
all
p
r
e
d
o
m
in
an
ce
o
f
p
o
s
itiv
e
f
in
d
in
g
s
is
o
b
s
er
v
ed
i
n
th
e
y
e
ar
s
2
0
1
9
,
2
0
2
0
,
2
0
2
1
,
a
n
d
2
0
2
2
,
in
co
n
tr
ast
to
2
0
2
3
;
h
o
wev
e
r
,
p
o
s
itiv
e
f
in
d
in
g
s
(
n
=1
8
)
p
r
e
d
o
m
in
ate
o
v
er
n
eg
ativ
e
f
in
d
in
g
s
(
n
=1
2
)
.
T
h
is
o
v
er
v
iew
co
n
tr
i
b
u
tes
to
th
e
u
n
d
er
s
tan
d
in
g
o
f
th
e
ev
o
lu
tio
n
o
f
r
esear
c
h
f
in
d
i
n
g
s
in
th
e
ex
am
in
e
d
f
ield
o
v
er
a
s
ix
-
y
ea
r
p
er
io
d
.
Fig
u
r
e
2
.
Nu
m
b
er
o
f
r
esear
ch
p
er
y
ea
r
s
tu
d
y
Fig
u
r
e
3
.
R
atio
o
f
p
o
s
itiv
e
an
d
n
eg
ativ
e
f
in
d
in
g
s
b
y
y
ea
r
o
f
p
u
b
licatio
n
On
t
h
e
o
t
h
e
r
h
an
d
,
s
el
ec
t
ed
r
e
s
ea
r
c
h
f
i
n
d
i
n
g
s
f
r
o
m
2
0
1
8
t
o
2
0
2
3
r
e
v
ea
l
r
em
ar
k
a
b
l
e
d
e
v
el
o
p
m
en
ts
in
th
e
r
e
lat
io
n
s
h
i
p
b
et
wee
n
m
at
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em
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tic
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4
4
10
9
0
1
2
3
4
5
6
7
8
9
10
11
2018
2019
2020
2021
2022
2023
Pu
b
li
c
a
tio
n
s
Ye
a
r
o
f
Pu
b
li
c
a
tio
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s
1
1
3
3
6
4
1
0
1
1
4
5
0
1
2
3
4
5
6
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2018
2019
2020
2021
2022
2023
Po
s
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ti
ve
N
e
g
ati
ve
Fi
n
d
in
g
s
Ye
a
r
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f
P
u
b
li
c
a
ti
o
n
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
.
14
,
No
.
3
,
J
u
n
e
20
25
:
2
1
1
8
-
2
1
3
1
2124
s
er
i
es,
a
f
o
cu
s
o
n
i
d
e
n
t
if
y
i
n
g
c
o
g
n
iti
v
e
a
n
d
n
o
n
-
c
o
g
n
it
iv
e
p
r
e
d
ic
to
r
s
o
f
s
t
u
d
en
t
ac
h
i
ev
em
en
t
s
ta
n
d
s
o
u
t
.
St
u
d
i
es
s
u
c
h
as
V
o
r
o
n
i
n
et
a
l.
[
4
3
]
la
y
th
e
g
r
o
u
n
d
w
o
r
k
b
y
ex
p
l
o
r
i
n
g
th
e
i
n
f
l
u
en
ce
o
f
t
h
es
e
p
r
ed
ict
o
r
s
i
n
t
h
e
c
o
n
te
x
t
o
f
u
n
if
ie
d
s
tat
e
ex
am
s
a
n
d
ad
v
an
ce
d
m
a
th
em
ati
cs
cu
r
r
ic
u
l
a.
Sim
u
l
ta
n
e
o
u
s
l
y
,
s
t
u
d
e
n
t
a
d
o
p
ti
o
n
o
f
e
-
l
ea
r
n
i
n
g
s
y
s
te
m
s
,
as
s
t
u
d
ie
d
b
y
Ha
n
i
f
et
a
l
.
[
4
4
]
,
b
e
c
o
m
es
a
c
r
i
tic
al
to
p
ic
o
f
i
n
t
er
est;
e
d
u
ca
ti
o
n
al
t
ec
h
n
o
l
o
g
y
ca
n
b
e
a
v
al
u
ab
le
r
eso
u
r
c
e
f
o
r
a
d
d
r
ess
i
n
g
t
h
e
ap
p
l
ica
ti
o
n
o
f
m
at
h
e
m
a
tica
l
m
o
d
els
wit
h
s
t
r
u
ct
u
r
al
e
q
u
at
io
n
s
.
T
h
e
y
ea
r
s
2
0
2
0
,
2
0
2
1
,
2
0
2
2
,
a
n
d
2
0
2
3
m
ar
k
a
p
e
r
io
d
o
f
d
ee
p
en
in
g
th
e
r
o
le
o
f
m
ath
em
atic
al
r
esear
ch
an
d
m
o
d
elin
g
in
h
ig
h
er
ed
u
c
atio
n
.
T
h
ese
s
tu
d
ies
h
ig
h
lig
h
t
th
e
p
o
s
itiv
e
in
f
lu
en
ce
o
f
s
tu
d
en
t
r
esear
ch
o
n
ac
ad
em
ic
o
u
tco
m
es,
em
p
h
asizin
g
th
e
im
p
o
r
tan
ce
o
f
ea
r
l
y
im
m
er
s
io
n
o
f
s
tu
d
en
ts
in
r
esear
c
h
ac
tiv
ities
[
4
6
]
.
I
n
ad
d
itio
n
,
th
e
u
s
ef
u
ln
ess
o
f
m
at
h
em
atica
l
m
o
d
elin
g
i
n
p
r
o
f
ess
io
n
al
ed
u
ca
tio
n
p
lan
n
in
g
a
n
d
m
an
ag
em
en
t
o
f
f
er
s
a
v
alu
ab
le
p
er
s
p
ec
tiv
e
f
o
r
a
d
d
r
ess
in
g
th
e
ad
ap
tatio
n
o
f
ac
ad
em
ic
p
r
o
g
r
a
m
s
to
th
e
ev
er
-
ch
an
g
in
g
d
em
a
n
d
s
o
f
th
e
lab
o
r
m
a
r
k
et
[
5
0
]
.
Su
b
s
eq
u
en
tly
,
in
th
e
y
ea
r
s
2
0
2
2
an
d
2
0
2
3
,
in
n
o
v
atio
n
an
d
ev
alu
atio
n
o
f
h
i
g
h
er
ed
u
ca
tio
n
is
p
r
esen
ted
,
wh
e
r
e
m
ath
em
atic
al
m
o
d
elin
g
em
er
g
es
as
a
n
ef
f
ec
tiv
e
to
o
l
to
im
p
r
o
v
e
c
o
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
in
tech
n
ical
d
is
cip
lin
es in
en
g
i
n
ee
r
in
g
an
d
p
h
y
s
ics;
as we
ll
a
s
th
e
ap
p
licatio
n
o
f
th
eo
r
etica
l c
o
n
ce
p
ts
in
a
d
ee
p
way
[
5
3
]
.
I
n
th
is
s
en
s
e,
th
e
u
s
e
o
f
th
ese
m
o
d
els
ca
n
f
ac
ilit
ate
th
e
teac
h
in
g
an
d
ev
alu
atio
n
o
f
o
n
li
n
e
lear
n
in
g
;
an
ex
am
p
le
o
f
th
is
ca
n
b
e
th
e
u
s
e
o
f
an
o
n
lin
e
lear
n
in
g
al
g
o
r
ith
m
u
s
in
g
f
u
zz
y
n
eu
r
al
n
etwo
r
k
s
.
C
o
llectiv
ely
,
th
is
s
er
ies
o
f
r
esear
ch
tr
ac
es
an
ev
o
lu
tio
n
at
th
e
in
te
r
s
ec
tio
n
o
f
m
ath
em
atica
l
m
o
d
elin
g
an
d
ed
u
ca
tio
n
.
Fro
m
u
n
d
er
s
tan
d
i
n
g
f
ac
to
r
s
th
at
d
r
i
v
e
s
tu
d
en
t
s
u
cc
ess
to
im
p
le
m
en
tin
g
ed
u
ca
tio
n
al
tech
n
o
l
o
g
ies
an
d
p
r
o
m
o
tin
g
s
tu
d
en
t
r
esear
ch
i
n
h
ig
h
er
e
d
u
ca
tio
n
,
th
ese
in
v
esti
g
atio
n
s
co
n
tr
ib
u
te
s
ig
n
if
ican
tly
to
t
h
e
im
p
r
o
v
em
en
t
o
f
p
ed
ag
o
g
ical
p
r
ac
tice.
T
h
is
an
aly
s
is
h
ig
h
lig
h
ts
th
e
n
e
ed
f
o
r
m
o
r
e
in
ter
d
is
cip
lin
ar
y
a
n
d
c
o
llab
o
r
ativ
e
r
esear
ch
,
as we
ll
as
th
e
ap
p
licatio
n
o
f
m
o
d
elin
g
a
p
p
r
o
ac
h
es
in
p
ed
ag
o
g
ical
d
ec
is
io
n
m
ak
in
g
.
I
t
also
u
n
d
e
r
s
co
r
es
th
e
r
elev
an
ce
o
f
co
n
tin
u
o
u
s
ad
a
p
tatio
n
t
o
th
e
ch
an
g
in
g
d
em
a
n
d
s
o
f
t
h
e
e
d
u
ca
tio
n
al
en
v
ir
o
n
m
en
t
an
d
th
e
im
p
o
r
tan
ce
o
f
r
ig
o
r
o
u
s
ass
es
s
m
en
t
to
en
s
u
r
e
th
e
q
u
ality
o
f
teac
h
in
g
at
all
lev
els.
T
h
ese
f
in
d
in
g
s
p
r
o
v
id
e
a
s
o
lid
f
o
u
n
d
atio
n
f
o
r
f
u
tu
r
e
r
esear
c
h
,
as we
ll a
s
f
o
r
d
r
iv
in
g
e
d
u
ca
tio
n
al
i
n
n
o
v
a
tio
n
in
th
e
2
1
s
t c
en
tu
r
y
.
3
.
2
.
Dis
cus
s
io
n
T
h
e
r
esear
ch
q
u
esti
o
n
g
u
id
i
n
g
th
is
an
aly
s
is
f
o
cu
s
es
o
n
th
e
im
p
ac
t
o
f
m
ath
em
atica
l
m
o
d
elin
g
o
n
co
lleg
e
s
tu
d
en
ts
'
lear
n
in
g
.
T
o
ad
d
r
ess
th
is
q
u
esti
o
n
,
af
ter
ex
am
in
in
g
th
e
co
n
tr
ib
u
tio
n
s
o
f
th
e
3
0
p
u
b
licatio
n
s
s
elec
ted
an
d
s
h
o
wn
in
th
e
p
r
e
v
io
u
s
s
ec
tio
n
,
th
e
in
f
o
r
m
atio
n
was sy
n
th
esized
in
o
r
d
er
to
p
r
esen
t th
e
d
is
cu
s
s
io
n
in
an
o
r
d
er
l
y
an
d
ar
ticu
late
d
m
an
n
er
.
I
n
th
is
c
o
n
tex
t,
th
r
ee
m
ain
ax
es
h
a
v
e
b
ee
n
estab
lis
h
ed
f
o
r
th
e
d
is
cu
s
s
io
n
,
s
tar
tin
g
with
th
e
im
p
r
o
v
e
m
en
t
o
f
co
n
ce
p
tu
al
u
n
d
e
r
s
tan
d
in
g
,
t
h
en
th
e
d
ev
elo
p
m
e
n
t
o
f
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
an
d
,
f
in
ally
,
th
e
co
n
n
ec
tio
n
b
etwe
en
t
h
eo
r
y
a
n
d
p
r
ac
tice.
3
.
2
.
1
.
I
m
pro
v
ed
co
ncept
ua
l
un
dersta
n
din
g
T
h
e
im
p
r
o
v
e
m
en
t
o
f
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
in
th
e
u
n
iv
er
s
ity
co
n
tex
t
is
a
to
p
ic
o
f
g
r
ea
t
r
elev
an
ce
in
h
ig
h
er
ed
u
ca
tio
n
.
I
n
th
is
s
en
s
e,
p
r
ev
io
u
s
r
esear
ch
[
5
2
]
,
[
5
3
]
h
ig
h
lig
h
ted
th
at
t
h
e
in
co
r
p
o
r
atio
n
o
f
m
ath
em
atica
l
m
o
d
elin
g
in
th
e
r
em
o
te
teac
h
in
g
o
f
d
if
f
er
e
n
tial
eq
u
atio
n
s
lead
s
to
a
s
ig
n
if
ican
t
im
p
r
o
v
em
e
n
t
in
th
e
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
i
n
g
o
f
u
n
iv
e
r
s
ity
s
tu
d
en
ts
.
T
h
ei
r
f
o
c
u
s
was
o
n
a
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
th
e
co
n
ce
p
ts
an
d
an
en
h
an
ce
d
a
b
ilit
y
to
ap
p
ly
t
h
em
in
v
a
r
io
u
s
co
n
tex
ts
.
C
o
m
p
lem
en
tar
il
y
,
Pen
g
e
t
a
l.
[
4
2
]
p
r
o
p
o
s
ed
a
m
ath
em
atica
l
eq
u
atio
n
-
b
ased
lear
n
in
g
m
o
d
el
o
f
th
e
s
tatis
tical
m
em
o
r
y
cu
r
v
e;
th
is
s
tr
en
g
th
en
e
d
th
e
co
n
n
ec
tio
n
b
etwe
en
p
o
liti
ca
l
id
eo
lo
g
y
an
d
ac
ad
em
ic
d
is
cip
lin
es
in
u
n
i
v
er
s
ity
e
d
u
ca
tio
n
a
n
d
also
k
n
o
wled
g
e
r
eten
tio
n
a
n
d
u
n
d
e
r
s
tan
d
in
g
o
f
p
o
liti
ca
l c
r
iter
ia.
I
n
a
p
r
ec
is
e
co
n
tex
t,
Saleem
et
a
l
.
[
6
8
]
h
ig
h
lig
h
t
ed
th
e
im
p
o
r
tan
ce
o
f
p
r
e
d
ictiv
e
m
o
d
els
in
s
tu
d
ies
r
elate
d
to
p
u
b
lic
h
ea
lth
p
r
o
b
lem
s
,
s
u
ch
as
th
o
s
e
g
en
e
r
ated
b
y
e
p
id
em
ics
an
d
d
ec
is
io
n
-
m
ak
in
g
,
wh
ile
W
ei
et
al
.
[
6
9
]
em
p
h
asize
d
th
a
t w
ith
th
ese,
elem
en
tar
y
s
ch
o
o
l stu
d
en
ts
ca
n
tak
e
ad
v
a
n
tag
e
o
f
th
eir
ap
p
licatio
n
to
m
o
d
el
en
v
ir
o
n
m
en
ts
an
d
ca
s
es
o
n
ev
er
y
d
a
y
p
r
o
b
lem
s
an
d
im
p
r
o
v
e
b
o
th
co
g
n
itiv
e
an
d
cr
ea
tiv
e
s
k
ills
.
Similar
ly
,
Af
r
if
a
et
a
l
.
[
7
0
]
co
n
f
ir
m
ed
th
r
o
u
g
h
r
ef
e
r
en
tial
ex
p
lo
r
atio
n
th
at
p
r
ed
ictiv
e
m
o
d
e
ls
ca
n
co
n
tr
i
b
u
te
to
th
e
u
n
d
e
r
s
tan
d
in
g
o
f
p
h
en
o
m
en
a
alr
ea
d
y
ev
id
e
n
ce
d
,
b
y
s
im
u
latin
g
s
im
ilar
s
itu
atio
n
s
in
th
e
f
u
tu
r
e,
co
m
p
lem
en
tin
g
au
to
m
atic
lea
r
n
in
g
in
s
tu
d
en
ts
.
On
th
e
o
th
er
h
an
d
,
B
er
g
et
a
l
.
[
7
1
]
s
h
ar
e
d
th
eir
ex
p
er
ien
ce
with
th
e
u
s
e
o
f
in
v
iv
o
im
a
g
es
with
in
m
ath
em
atica
l
m
o
d
elin
g
,
wh
ich
r
ep
r
esen
ts
a
way
to
im
p
r
o
v
e
th
e
u
n
d
er
s
tan
d
i
n
g
o
f
s
p
ec
if
ic
co
n
t
en
ts
s
u
ch
as b
lo
o
d
f
lo
w
b
eh
a
v
io
r
an
d
c
o
n
d
itio
n
s
.
On
th
e
o
th
er
h
an
d
,
Z
iat
d
in
o
v
an
d
Valles
[
5
4
]
h
ig
h
lig
h
t
ed
th
at
t
h
e
ap
p
licatio
n
o
f
m
a
th
em
atica
l
m
o
d
elin
g
i
n
u
n
iv
e
r
s
ity
STE
M
ed
u
ca
tio
n
,
b
o
o
s
ted
in
co
n
ce
p
tu
al
u
n
d
e
r
s
tan
d
in
g
a
n
d
as we
ll a
s
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
T
h
is
in
cr
ea
s
ed
ac
ad
em
ic
p
er
f
o
r
m
a
n
ce
in
s
tu
d
en
ts
.
I
n
th
e
ca
s
e
o
f
Me
r
ck
et
a
l
.
[
5
1
]
,
th
ey
p
r
o
p
o
s
ed
a
m
ath
em
atica
l
m
o
d
el
in
th
e
co
n
tex
t
o
f
h
y
d
r
o
lo
g
ical
d
esi
g
n
a
n
d
d
em
o
n
s
tr
ated
a
n
in
c
r
ea
s
e
in
c
o
n
ce
p
tu
al
u
n
d
er
s
tan
d
i
n
g
,
wh
ich
u
n
d
er
li
n
es
th
e
r
elev
an
ce
o
f
m
ath
e
m
a
tical
m
o
d
elin
g
to
co
n
tex
t
u
alize
th
eo
r
y
in
p
r
ac
tice
an
d
im
p
r
o
v
e
u
n
d
er
s
tan
d
i
n
g
in
p
ar
ticu
lar
f
ield
s
.
I
n
th
e
ca
s
e
o
f
T
a
r
asy
ev
et
a
l
.
[
4
7
]
,
th
ey
t
o
o
k
th
e
d
is
cu
s
s
io
n
b
ey
o
n
d
p
u
r
e
m
ath
em
atica
l
m
o
d
elin
g
b
y
d
e
v
elo
p
in
g
f
u
zz
y
lo
g
ic
-
b
ased
m
o
d
elin
g
s
o
f
twar
e
to
an
aly
ze
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
Tr
a
n
s
fo
r
min
g
u
n
ivers
ity
ed
u
ca
tio
n
:
a
s
ystema
tic
r
ev
ie
w
o
f m
a
th
ema
tica
l …
(
I
n
es Mir
ya
m
A
ce
r
o
A
p
a
z
a
)
2125
ed
u
ca
tio
n
al
tr
ajec
to
r
ies.
T
h
eir
r
esear
ch
h
ig
h
lig
h
ted
th
e
im
p
o
r
tan
ce
o
f
p
e
r
s
o
n
aliza
tio
n
i
n
h
ig
h
e
r
ed
u
ca
tio
n
,
s
u
g
g
esti
n
g
th
at
tailo
r
in
g
in
s
tr
u
ctio
n
to
s
tu
d
en
ts
'
in
d
iv
id
u
al
p
r
ef
e
r
en
ce
s
an
d
n
ee
d
s
ca
n
i
m
p
r
o
v
e
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
i
n
g
an
d
ac
ad
em
ic
p
er
f
o
r
m
a
n
ce
.
T
ak
en
to
g
et
h
er
,
th
e
f
in
d
in
g
s
o
f
th
ese
elev
en
p
u
b
licatio
n
s
co
n
s
is
ten
tly
in
d
icate
th
at
m
at
h
em
atica
l
m
o
d
elin
g
is
o
f
g
r
ea
t
im
p
o
r
ta
n
ce
f
o
r
th
e
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
o
f
co
lleg
e
s
tu
d
e
n
ts
.
T
h
is
is
in
d
ir
ec
t
ag
r
ee
m
en
t
with
p
r
e
v
io
u
s
s
tu
d
i
es
[
3
]
,
[
4
]
wh
ich
p
o
i
n
t
o
u
t
th
a
t
m
o
d
elin
g
f
ac
ilit
ates
th
e
ac
q
u
is
itio
n
o
f
r
ele
v
an
t
s
k
ills
,
b
y
k
n
o
win
g
its
n
atu
r
e,
ap
p
licatio
n
s
,
an
d
b
en
ef
its
to
r
ef
in
e
th
e
h
a
n
d
lin
g
o
f
m
ath
e
m
atica
l
f
u
n
ctio
n
s
an
d
o
p
er
atio
n
s
an
d
o
t
h
er
r
elate
d
d
is
cip
lin
es.
Similar
ly
,
th
e
r
eten
tio
n
o
f
k
n
o
wled
g
e
a
n
d
t
h
e
ab
ilit
y
to
a
p
p
l
y
co
n
ce
p
ts
in
p
r
ac
tical
s
itu
atio
n
s
s
u
p
p
o
r
t
t
h
e
u
s
ef
u
ln
ess
o
f
m
ath
em
atica
l
m
o
d
elin
g
as
an
ef
f
ec
tiv
e
to
o
l
f
o
r
m
ea
n
in
g
f
u
l
lear
n
in
g
in
h
ig
h
er
ed
u
ca
tio
n
,
asp
ec
ts
th
at
a
r
e
in
d
ir
ec
t
ag
r
ee
m
e
n
t
with
th
e
c
o
n
t
r
ib
u
tio
n
s
g
e
n
er
ated
by
th
e
s
tu
d
ies
[
5
]
,
[
6
]
,
wh
o
em
p
h
asize
th
e
p
o
ten
tial
f
o
r
u
n
d
er
s
tan
d
i
n
g
an
d
an
aly
s
is
o
f
v
ar
io
u
s
ar
ea
s
o
f
k
n
o
wled
g
e,
s
u
ch
as
b
io
lo
g
y
,
p
h
y
s
ics,
ec
o
n
o
m
ics,
a
n
d
en
g
in
ee
r
in
g
.
T
h
is
en
r
ich
es
th
e
ed
u
ca
tio
n
al
ex
p
e
r
ien
c
e
o
f
s
tu
d
en
ts
to
f
ac
e
ac
ad
em
ic
a
n
d
p
r
o
f
ess
io
n
al
ch
allen
g
es m
o
r
e
ef
f
ec
tiv
ely
.
3
.
2
.
2
.
Dev
elo
pm
ent
o
f
pro
ble
m
-
s
o
lv
ing
s
k
ills
C
o
n
tem
p
o
r
ar
y
h
ig
h
er
e
d
u
ca
ti
o
n
f
ac
es
a
g
r
o
win
g
d
em
a
n
d
t
o
p
r
ep
ar
e
s
tu
d
e
n
ts
n
o
t
o
n
ly
with
a
d
ee
p
u
n
d
er
s
tan
d
i
n
g
o
f
c
o
n
ce
p
ts
,
b
u
t a
ls
o
with
th
e
ab
ilit
y
to
ap
p
ly
th
at
k
n
o
wled
g
e
i
n
ch
allen
g
in
g
co
n
tex
ts
an
d
s
o
lv
e
p
r
o
b
lem
s
ef
f
ec
tiv
ely
.
I
n
th
is
co
n
tex
t,
m
ath
em
atica
l
m
o
d
elin
g
h
as
em
er
g
ed
as
a
p
r
o
m
in
en
t
p
ed
ag
o
g
ical
s
tr
ateg
y
th
at
s
ee
k
s
n
o
t
o
n
ly
to
en
h
an
ce
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
i
n
g
,
b
u
t
also
to
cu
ltiv
ate
cr
itical
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
I
n
t
h
is
r
eg
ar
d
,
Z
iatd
i
n
o
v
an
d
Valles
[
5
4
]
s
tate
d
th
at
m
ath
em
atica
l
m
o
d
elin
g
n
o
t
o
n
l
y
im
p
r
o
v
es
co
n
ce
p
tu
al
u
n
d
e
r
s
tan
d
in
g
,
b
u
t
also
p
r
o
m
o
tes
s
u
b
s
tan
tial
d
ev
elo
p
m
en
t
o
f
p
r
o
b
l
em
-
s
o
lv
in
g
s
k
ills
.
T
h
eir
r
esear
ch
in
d
icate
s
th
at
th
e
in
te
g
r
atio
n
o
f
m
ath
em
at
ical
m
o
d
elin
g
,
v
is
u
aliza
tio
n
,
an
d
p
r
o
g
r
am
m
in
g
th
r
o
u
g
h
Geo
Geb
r
a
in
u
n
d
e
r
g
r
ad
u
ate
STE
M
ed
u
ca
ti
o
n
lead
to
im
p
r
o
v
ed
ac
a
d
em
ic
p
er
f
o
r
m
an
ce
,
a
p
h
en
o
m
en
o
n
th
at
ca
n
b
e
attr
ib
u
ted
to
th
e
ac
q
u
is
itio
n
o
f
s
tr
o
n
g
er
p
r
o
b
lem
-
s
o
lv
i
n
g
s
k
ills
.
On
th
e
o
th
er
h
a
n
d
,
o
th
er
r
esear
ch
[
6
5
]
,
[
6
6
]
a
d
d
ed
a
cr
itical
d
im
en
s
io
n
b
y
h
ig
h
lig
h
tin
g
th
e
im
p
o
r
tan
ce
o
f
s
tu
d
y
an
d
r
esear
ch
tr
ac
k
s
in
u
n
iv
er
s
ity
teac
h
er
ed
u
ca
tio
n
.
T
h
eir
s
tu
d
y
h
i
g
h
lig
h
ts
th
at
th
ese
tr
ac
k
s
n
o
t
o
n
ly
p
r
o
m
o
te
th
e
ef
f
ec
tiv
e
co
n
n
ec
tio
n
b
etwe
en
th
eo
r
y
an
d
p
r
ac
tice,
b
u
t
also
en
ab
le
s
tu
d
en
ts
to
ac
q
u
ir
e
a
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
t
h
eir
f
u
tu
r
e
p
r
o
f
ess
io
n
an
d
im
p
r
o
v
e
th
eir
p
ed
a
g
o
g
ical
s
k
ills
,
wh
ich
in
clu
d
e
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
T
h
e
wo
r
k
o
f
Fas
in
u
et
a
l
.
[
5
8
]
f
ac
ilit
ates
v
is
u
aliza
tio
n
o
f
h
o
w
a
m
ath
em
atica
l
p
ed
ag
o
g
ical
m
o
d
el
b
ased
o
n
em
p
ir
ical
ev
id
en
ce
ca
n
p
o
s
itiv
ely
im
p
ac
t
th
e
d
ev
elo
p
m
e
n
t
o
f
s
p
ec
if
ic
s
k
ills
r
eq
u
ir
ed
f
o
r
an
te
n
n
a
d
esig
n
.
T
h
e
s
tu
d
en
ts
wh
o
p
a
r
ticip
ated
in
t
h
is
s
tu
d
y
p
r
o
v
i
d
ed
i
n
f
o
r
m
atio
n
to
d
en
o
te
a
n
im
p
r
o
v
e
d
co
n
ce
p
t
u
al
u
n
d
er
s
tan
d
in
g
,
b
u
t
m
o
r
e
s
ig
n
if
ica
n
tly
,
th
ey
wer
e
ab
le
to
ef
f
ec
tiv
ely
ap
p
ly
th
is
k
n
o
wled
g
e
i
n
p
r
ac
tical
p
r
o
ject
s
,
r
ef
lectin
g
th
e
tan
g
ib
le
d
e
v
elo
p
m
en
t
o
f
p
r
o
b
lem
-
s
o
l
v
in
g
s
k
ills
.
I
n
tu
r
n
,
Atalla
et
a
l
.
[
5
7
]
ex
p
lo
r
e
d
h
o
w
m
at
h
em
atica
l
m
o
d
e
lin
g
ca
n
p
er
s
o
n
alize
ac
ad
em
ic
ad
v
is
in
g
an
d
c
u
r
r
icu
l
u
m
p
lan
n
in
g
i
n
c
o
lleg
e.
T
h
eir
r
esear
ch
h
ig
h
lig
h
ts
th
at
s
tu
d
e
n
t
wh
o
b
e
n
ef
ited
f
r
o
m
a
n
in
tellig
e
n
t
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
b
ase
d
o
n
p
er
f
o
r
m
an
ce
m
o
d
elin
g
r
ec
eiv
ed
m
o
r
e
p
er
s
o
n
alize
d
r
e
co
m
m
en
d
atio
n
s
an
d
ex
p
er
ien
ce
d
g
r
ea
ter
ac
a
d
em
ic
s
u
cc
ess
,
im
p
ly
in
g
s
ig
n
if
ican
t
d
ev
elo
p
m
en
t
o
f
p
r
o
b
lem
-
s
o
l
v
in
g
s
k
ills
in
th
eir
ac
ad
em
ic
p
ath
way
.
T
h
e
co
n
tr
i
b
u
tio
n
o
f
L
ee
an
d
R
ec
k
er
[
5
5
]
f
o
cu
s
es o
n
th
e
im
p
o
r
tan
ce
o
f
ac
tiv
e
p
ar
ticip
atio
n
an
d
o
n
li
n
e
in
ter
ac
tio
n
i
n
u
n
d
er
g
r
ad
u
ate
ac
ad
em
ic
ac
h
ie
v
e
m
en
t.
T
h
eir
f
o
cu
s
o
n
m
ath
e
m
atica
l
m
o
d
elin
g
to
p
r
ed
ict
s
tu
d
e
n
t
ac
h
iev
e
m
en
t
h
ig
h
lig
h
ts
h
o
w
p
r
o
b
lem
s
o
lv
in
g
is
en
r
ic
h
ed
w
h
en
s
tu
d
en
ts
a
ctiv
ely
p
ar
ticip
ate
in
asy
n
ch
r
o
n
o
u
s
d
is
cu
s
s
io
n
s
in
o
n
lin
e
m
ath
em
atics c
o
u
r
s
es.
T
h
e
s
tu
d
y
b
y
Me
l
n
y
k
o
v
et
a
l
.
[
4
6
]
p
r
o
v
i
d
es
an
ad
d
itio
n
al
ar
g
u
m
e
n
t,
as
it
s
h
o
ws
th
a
t
r
esear
ch
co
n
d
u
cte
d
b
y
u
n
iv
e
r
s
ity
s
tu
d
en
ts
,
as
a
f
o
r
m
o
f
m
o
d
elin
g
t
h
e
r
ea
l
wo
r
ld
,
tr
an
s
lates
in
to
h
ig
h
er
g
r
a
d
es
in
f
in
al
ce
r
tific
atio
n
s
.
T
h
is
r
esu
lt
h
ig
h
lig
h
ts
th
e
r
elatio
n
s
h
ip
b
et
wee
n
s
tu
d
en
t
r
esear
ch
a
n
d
t
h
e
d
ev
elo
p
m
en
t
o
f
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
,
wh
ich
is
cr
u
cial
in
th
e
u
n
iv
er
s
ity
co
n
tex
t.
I
n
an
o
t
h
er
v
ein
,
Kar
y
y
et
a
l
.
[
5
9
]
an
d
Gu
im
ar
ãe
s
an
d
L
im
a
[
6
0
]
e
x
p
lo
r
e
d
h
o
w
ar
tific
ial
in
telli
g
en
ce
an
d
m
o
d
elin
g
ca
n
f
u
r
th
er
p
e
r
s
o
n
alize
th
e
ed
u
ca
tio
n
al
p
r
o
ce
s
s
.
T
h
eir
d
e
v
elo
p
ed
m
o
d
el
illu
s
tr
ates
h
o
w
ar
tific
ial
in
tellig
en
ce
ca
n
a
d
ap
t
lear
n
in
g
to
th
e
in
d
iv
id
u
al
n
ee
d
s
o
f
s
tu
d
en
ts
,
im
p
r
o
v
in
g
th
e
ef
f
icien
c
y
o
f
th
e
ed
u
ca
tio
n
al
p
r
o
ce
s
s
an
d
s
tr
en
g
th
en
in
g
th
e
d
ev
elo
p
m
e
n
t o
f
p
r
o
b
lem
-
s
o
lv
i
n
g
s
k
ills
.
B
ar
k
er
[
5
0
]
ad
d
s
ev
id
en
ce
b
y
d
em
o
n
s
tr
atin
g
th
at
m
o
d
elin
g
u
s
in
g
s
tr
u
ctu
r
al
eq
u
atio
n
s
ca
n
im
p
r
o
v
e
co
n
ce
p
tu
al
u
n
d
e
r
s
tan
d
in
g
an
d
k
n
o
wled
g
e
r
eten
tio
n
c
o
m
p
ar
ed
to
m
o
r
e
p
ass
iv
e
ap
p
r
o
a
ch
es
in
en
g
i
n
ee
r
in
g
ed
u
ca
tio
n
.
T
h
is
f
i
n
d
in
g
s
u
p
p
o
r
ts
th
e
h
y
p
o
t
h
esis
th
at
m
ath
e
m
atica
l
m
o
d
elin
g
f
o
s
ter
s
m
o
r
e
ef
f
ec
tiv
e
lear
n
in
g
an
d
th
e
d
ev
elo
p
m
en
t
o
f
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
I
n
th
is
r
eg
ar
d
,
Fo
n
tan
a
an
d
Gr
o
en
wald
[
6
1
]
f
u
r
th
er
ex
p
lo
r
e
th
e
ap
p
licatio
n
o
f
m
ath
e
m
atica
l
m
o
d
elin
g
i
n
ad
d
r
ess
in
g
b
u
s
in
ess
p
r
o
b
lem
s
in
h
ig
h
er
e
d
u
c
atio
n
.
T
h
eir
r
esu
lts
in
d
icate
th
at
th
is
ap
p
r
o
ac
h
p
r
o
m
o
tes
a
d
ee
p
an
d
ap
p
licab
le
u
n
d
er
s
tan
d
in
g
th
at
h
elp
s
s
tu
d
en
ts
d
ea
l
with
p
r
o
b
lem
s
itu
atio
n
s
in
b
u
s
in
ess
co
n
tex
ts
,
wh
ich
f
u
r
th
er
r
ein
f
o
r
ce
s
th
e
r
elev
an
ce
o
f
m
o
d
elin
g
in
th
e
d
ev
elo
p
m
e
n
t o
f
p
r
o
b
lem
-
s
o
lv
i
n
g
s
k
ills
.
S
e
v
e
r
a
l
r
es
e
a
r
c
h
[
6
3
]
,
[
6
4
]
d
e
v
e
l
o
p
a
m
a
t
h
e
m
a
t
i
c
al
m
o
d
e
l
to
a
s
s
es
s
t
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e
q
u
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li
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f
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o
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t
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c
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k
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m
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
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8
8
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2
I
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t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
3
,
J
u
n
e
20
25
:
2
1
1
8
-
2
1
3
1
2126
t
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
s
k
il
ls
.
Fi
n
a
l
l
y
,
A
b
i
d
em
i
e
t
a
l
.
[
6
2
]
p
r
e
s
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t
s
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a
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C
O
V
I
D
-
1
9
o
n
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
i
n
d
e
v
e
l
o
p
i
n
g
c
o
u
n
t
r
ie
s
.
T
h
e
r
es
u
l
ts
h
el
p
t
o
u
n
d
e
r
s
t
a
n
d
t
h
e
i
m
p
l
i
c
a
t
i
o
n
s
o
f
t
h
e
p
a
n
d
e
m
i
c
o
n
e
d
u
c
a
t
i
o
n
a
n
d
t
o
p
l
a
n
a
p
p
r
o
p
r
i
a
t
e
r
e
s
p
o
n
s
e
s
t
r
at
e
g
i
es
,
h
i
g
h
l
i
g
h
t
i
n
g
t
h
e
r
e
l
e
v
a
n
c
e
o
f
m
o
d
e
l
i
n
g
i
n
c
r
i
s
i
s
s
i
t
u
at
i
o
n
s
a
n
d
i
t
s
a
b
i
l
it
y
t
o
a
d
d
r
e
s
s
c
o
m
p
l
e
x
p
r
o
b
l
e
m
s
.
T
h
u
s
,
a
s
m
e
n
t
i
o
n
e
d
b
y
s
e
v
e
r
a
l
s
t
u
d
i
es
[
1
4
]
,
[
1
5
]
,
[
2
0
]
,
m
a
t
h
e
m
a
t
i
c
a
l
m
o
d
e
l
i
n
g
i
n
h
i
g
h
e
r
e
d
u
c
a
t
i
o
n
i
s
a
m
e
c
h
a
n
i
s
m
o
f
g
r
e
a
t
i
m
p
o
r
t
a
n
c
e
f
o
r
t
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
s
k
i
ll
s
i
n
u
n
i
v
e
r
s
i
t
y
s
t
u
d
e
n
t
s
,
u
s
i
n
g
c
r
i
t
i
c
al
a
n
d
r
e
f
l
e
c
t
i
v
e
t
h
i
n
k
i
n
g
.
L
i
k
e
w
i
s
e
,
t
h
is
i
s
s
u
p
p
o
r
t
e
d
b
y
p
r
e
v
i
o
u
s
s
t
u
d
i
e
s
[
1
6
]
,
[
1
7
]
,
w
h
o
e
m
p
h
a
s
i
z
e
t
h
e
g
o
o
d
n
e
s
s
o
f
r
e
p
r
e
s
e
n
t
i
n
g
i
n
a
s
i
m
p
l
i
f
i
e
d
f
o
r
m
a
l
a
r
g
e
-
s
c
a
l
e
p
h
e
n
o
m
e
n
o
n
t
o
b
e
a
n
a
l
y
z
e
d
a
n
d
i
n
t
e
r
p
r
e
t
e
d
u
s
i
n
g
o
b
j
e
c
t
i
v
e
f
u
n
c
ti
o
n
s
,
v
a
r
i
a
b
l
es
,
c
o
n
s
t
r
ai
n
t
s
,
a
n
d
o
t
h
e
r
s
p
e
ci
f
i
c
a
t
i
o
n
s
,
a
n
d
t
h
u
s
o
b
t
ai
n
a
co
n
d
i
t
i
o
n
a
l
o
p
t
i
m
a
l
s
o
l
u
t
i
o
n
.
O
n
t
h
e
o
t
h
e
r
h
a
n
d
,
R
o
d
r
í
g
u
e
z
-
N
i
et
o
e
t
a
l
.
[
2
1
]
ar
g
u
e
t
h
a
t
m
a
t
h
e
m
a
ti
c
a
l
m
o
d
el
i
n
g
e
m
e
r
g
e
s
as
a
f
u
n
d
a
m
e
n
t
a
l
e
d
u
c
a
t
i
o
n
a
l
s
t
r
a
te
g
y
t
h
a
t
c
a
n
p
o
s
i
t
i
v
el
y
t
r
a
n
s
f
o
r
m
t
h
e
u
n
i
v
e
r
s
i
t
y
l
e
a
r
n
i
n
g
ex
p
e
r
i
e
n
c
e
.
A
l
l
t
h
is
a
l
l
o
ws
c
a
te
g
o
r
i
c
a
l
l
y
s
u
p
p
o
r
t
i
n
g
m
a
t
h
e
m
a
t
i
ca
l
m
o
d
e
l
i
n
g
i
n
u
n
i
v
e
r
s
i
t
y
c
u
r
r
ic
u
l
a
t
o
b
o
o
s
t
u
n
d
e
r
g
r
a
d
u
a
t
e
d
e
c
i
s
i
o
n
-
m
a
k
i
n
g
.
3
.
2
.
3
.
Co
nn
ec
t
io
n bet
wee
n t
heo
ry
a
nd
pra
ct
ice
T
h
is
s
u
b
s
ec
tio
n
d
etails
th
e
s
tr
ateg
ies
em
p
lo
y
ed
to
m
er
g
e
,
c
o
m
p
ar
e,
o
r
tr
ian
g
u
late
b
o
th
q
u
an
titativ
e
an
d
q
u
alitativ
e
d
ata
s
ets.
I
t
ex
p
lain
s
h
o
w
th
e
s
y
n
th
esis
o
f
th
ese
d
iv
e
r
s
e
d
ata
s
o
u
r
c
e
s
co
n
tr
ib
u
tes
to
a
co
m
p
r
eh
e
n
s
iv
e
u
n
d
er
s
tan
d
in
g
o
f
t
h
e
r
esear
ch
p
r
o
b
lem
.
T
h
e
co
n
v
e
r
g
en
ce
b
etwe
en
t
h
eo
r
y
an
d
p
r
ac
tice
in
th
e
f
ield
o
f
h
ig
h
er
e
d
u
ca
tio
n
h
as b
ee
n
m
eticu
lo
u
s
ly
ex
am
in
ed
th
r
o
u
g
h
o
u
t sev
er
al
in
v
esti
g
atio
n
s
,
wh
ich
h
av
e
b
ee
n
f
o
cu
s
ed
o
n
d
ec
ip
h
e
r
in
g
th
e
tr
an
s
ce
n
d
en
tal
in
f
lu
en
ce
o
f
m
a
th
em
atica
l
m
o
d
elin
g
o
n
t
h
e
l
ea
r
n
in
g
p
r
o
ce
s
s
o
f
u
n
iv
er
s
ity
s
tu
d
en
ts
.
T
h
r
o
u
g
h
a
m
o
r
e
d
etailed
an
aly
s
is
o
f
th
e
co
n
tr
ib
u
tio
n
s
o
f
th
ese
s
tu
d
i
es,
it
is
p
o
s
s
ib
le
t
o
d
ee
p
en
th
e
r
ich
n
ess
an
d
s
co
p
e
o
f
th
e
r
elatio
n
s
h
ip
b
etwe
en
m
ath
em
atica
l m
o
d
elin
g
a
n
d
h
ig
h
er
ed
u
ca
tio
n
.
S
t
u
d
i
e
s
b
y
F
u
e
t
a
l
.
[
6
6
]
b
r
i
n
g
u
p
t
h
e
r
e
l
e
v
a
n
c
e
o
f
s
t
u
d
y
a
n
d
r
e
s
e
a
r
c
h
p
a
t
h
s
a
s
v
e
h
i
c
l
e
s
o
f
i
n
t
e
g
r
a
t
i
o
n
b
e
t
w
e
e
n
t
h
e
o
r
y
a
n
d
p
r
a
c
t
i
c
e
.
T
h
i
s
r
e
s
e
a
r
c
h
r
e
v
e
a
l
s
t
h
a
t
t
h
e
s
e
t
r
a
j
e
c
t
o
r
i
e
s
p
l
a
y
a
c
r
i
t
i
c
a
l
r
o
l
e
i
n
t
h
e
t
r
a
i
n
i
n
g
o
f
u
n
i
v
e
r
s
i
t
y
t
e
a
c
h
e
r
s
,
i
n
w
h
i
c
h
m
a
t
h
e
m
a
t
i
c
a
l
m
o
d
e
l
i
n
g
b
e
c
o
m
e
s
a
n
e
f
f
e
c
t
i
v
e
p
e
d
a
g
o
g
i
c
a
l
t
o
o
l
t
o
f
o
s
t
e
r
a
d
e
e
p
e
r
u
n
d
e
r
s
t
a
n
d
i
n
g
o
f
t
h
e
i
r
f
u
t
u
r
e
p
r
o
f
e
s
s
i
o
n
.
T
h
u
s
,
t
h
e
r
e
l
a
t
i
o
n
s
h
i
p
b
e
t
w
e
e
n
t
h
e
o
r
y
a
n
d
p
r
a
c
t
i
c
e
b
e
c
o
m
e
s
m
o
r
e
e
x
p
l
i
c
i
t
a
s
s
t
u
d
e
n
t
s
e
m
b
a
r
k
o
n
r
e
s
e
a
r
c
h
a
n
d
a
p
p
l
y
t
h
e
o
r
e
t
i
c
a
l
c
o
n
c
e
p
t
s
t
o
r
e
a
l
s
i
t
u
a
t
i
o
n
s
i
n
a
n
e
d
u
c
a
t
i
o
n
a
l
s
e
t
t
i
n
g
.
I
n
th
e
wo
r
k
o
f
Sh
er
s
to
b
it
o
v
a
et
a
l
.
[
5
6
]
,
th
e
y
f
o
cu
s
o
n
t
h
e
ad
ap
tatio
n
an
d
s
tab
ilit
y
o
f
e
d
u
ca
tio
n
al
in
s
titu
tio
n
s
in
th
e
ch
an
g
in
g
d
ig
ital
en
v
ir
o
n
m
e
n
t,
an
d
co
n
clu
d
e
th
at
m
ath
em
atica
l
m
o
d
elin
g
is
a
to
o
l
th
at
allo
ws
co
m
p
etitio
n
b
etwe
en
u
n
iv
er
s
ities
to
im
p
lem
en
t
p
e
d
ag
o
g
ical
th
e
o
r
y
a
n
d
d
ig
ital
r
ea
lity
,
in
cr
ea
s
in
g
ef
f
icien
cy
in
th
eir
ad
m
i
n
is
tr
ativ
e
p
r
o
ce
d
u
r
es.
I
n
th
e
s
am
e
way
,
ac
co
r
d
in
g
to
B
ar
k
er
[
5
0
]
,
th
e
u
s
e
o
f
v
ir
tu
al
d
esig
n
m
o
d
u
les
in
en
g
in
ee
r
i
n
g
co
u
r
s
es
s
tr
en
g
th
en
s
th
e
p
r
o
f
ess
io
n
al
id
en
tity
o
f
s
tu
d
en
ts
,
th
u
s
m
ath
em
atica
l
m
o
d
elin
g
b
ec
o
m
es a
b
r
id
g
e
b
e
twee
n
ac
ad
em
ic
th
eo
r
y
an
d
p
r
o
f
ess
io
n
al
tr
ain
in
g
.
On
th
e
o
th
er
h
an
d
,
Pin
ev
ich
et
a
l
.
[
1
0
]
ad
d
an
eth
ical
d
im
e
n
s
io
n
,
b
y
e
x
p
lo
r
i
n
g
h
o
w
m
o
d
eli
n
g
ca
n
b
e
em
p
lo
y
ed
to
ad
d
r
ess
h
u
m
an
it
ar
ian
p
r
o
b
lem
s
,
it
is
n
o
ted
th
at
it
i
s
im
p
lem
en
ted
as
a
ca
ta
ly
s
t
f
o
r
eth
ical
an
d
s
o
cial
p
r
o
b
lem
s
o
lv
in
g
.
T
h
is
is
ev
id
en
ce
d
in
th
e
wo
r
k
K
en
g
er
an
d
Ozc
ey
lan
[
6
7
]
,
wh
o
p
r
o
v
id
e
a
m
ix
e
d
in
teg
er
lin
ea
r
p
r
o
g
r
am
m
in
g
(
MI
L
P)
m
o
d
el
an
d
a
n
im
p
r
o
v
ed
o
n
lin
e
lear
n
in
g
alg
o
r
ith
m
f
o
r
g
e
n
er
al
f
u
zz
y
m
in
-
m
ax
n
e
u
r
al
n
etwo
r
k
s
,
wh
ich
b
ec
o
m
e
a
b
r
id
g
e
co
n
n
ec
ti
n
g
p
ed
a
g
o
g
ical
th
eo
r
ies
with
teac
h
in
g
s
tr
ateg
ies
tailo
r
ed
to
th
e
c
h
an
g
i
n
g
n
ee
d
s
o
f
lear
n
e
r
s
.
T
h
e
a
p
p
r
o
ac
h
o
f
T
ar
asy
ev
et
a
l
.
[
4
7
]
,
p
r
io
r
itize
s
p
er
s
o
n
aliza
tio
n
in
ed
u
ca
tio
n
th
r
o
u
g
h
th
e
u
s
e
o
f
f
u
zz
y
lo
g
ic
-
b
ased
m
o
d
elin
g
s
o
f
twar
e,
wh
ich
allo
ws
its
co
n
v
er
s
io
n
to
in
d
iv
id
u
al
s
tu
d
en
t
n
ee
d
s
,
r
ein
f
o
r
cin
g
th
e
in
ter
twin
in
g
o
f
ed
u
ca
tio
n
th
e
o
r
y
an
d
p
er
s
o
n
alize
d
ap
p
licatio
n
.
I
n
tu
r
n
,
s
tu
d
en
t
s
af
ety
ca
n
also
b
e
en
s
u
r
ed
th
r
o
u
g
h
p
r
ed
ictiv
e
m
ath
e
m
atica
l
m
o
d
els,
ac
co
r
d
in
g
to
Ap
p
el
an
d
Du
r
an
d
t
[
4
5
]
,
f
ac
ilit
ates e
ar
ly
in
ter
v
en
tio
n
in
s
tu
d
en
t w
ell
-
b
ein
g
a
n
d
s
u
p
p
o
r
t.
I
n
th
is
s
en
s
e,
m
ath
em
atica
l
m
o
d
elin
g
em
er
g
es
as
a
v
ital
an
d
m
u
ltifa
ce
ted
lin
k
b
etwe
en
t
h
eo
r
y
an
d
p
r
ac
tice
in
h
ig
h
e
r
ed
u
ca
tio
n
.
T
h
e
af
o
r
em
en
tio
n
ed
s
tu
d
ies,
b
y
d
elv
in
g
d
ee
p
er
in
t
o
th
eir
r
esu
lts
an
d
ap
p
licatio
n
s
,
r
ev
ea
l h
o
w
m
ath
em
atica
l m
o
d
elin
g
n
o
t o
n
ly
en
r
ich
es th
eo
r
etica
l u
n
d
er
s
tan
d
i
n
g
,
b
u
t a
ls
o
d
ir
ec
tly
in
f
lu
en
ce
s
th
e
tr
ain
i
n
g
o
f
p
r
o
f
ess
io
n
als,
in
s
titu
tio
n
al
d
e
cisi
o
n
m
ak
in
g
,
h
u
m
a
n
itar
ian
p
r
o
b
lem
s
o
lv
in
g
,
ef
f
ec
tiv
e
teac
h
in
g
an
d
s
tu
d
e
n
t
ca
r
e.
Ultim
ately
,
m
ath
em
atic
al
m
o
d
elin
g
is
co
n
s
o
lid
ated
as
an
ess
en
tial
to
o
l
in
th
e
co
n
tin
u
o
u
s
im
p
r
o
v
em
en
t
o
f
h
ig
h
er
e
d
u
ca
tio
n
a
n
d
in
th
e
c
o
n
s
tr
u
ctio
n
o
f
a
s
o
lid
b
r
id
g
e
b
etwe
en
th
eo
r
y
an
d
p
r
ac
tice
in
th
is
ac
ad
em
ic
co
n
t
ex
t.
I
n
a
p
r
e
c
i
s
e
d
i
r
e
c
t
i
o
n
,
t
h
e
co
n
n
e
c
t
i
o
n
b
e
t
w
e
e
n
t
h
e
o
r
y
a
n
d
p
r
a
c
t
i
c
e
i
n
t
h
e
c
a
s
e
o
f
m
a
t
h
e
m
a
t
i
ca
l
m
o
d
e
l
i
n
g
p
r
e
s
e
n
t
s
t
h
e
f
u
n
d
a
m
e
n
t
a
l
f
o
u
n
d
a
t
i
o
n
s
f
o
r
t
h
e
g
r
a
d
u
a
l
d
e
v
e
l
o
p
m
e
n
t
o
f
e
m
e
r
g
i
n
g
t
e
c
h
n
o
l
o
g
i
e
s
.
A
n
e
x
a
m
p
l
e
o
f
t
h
is
is
t
h
e
s
t
u
d
y
d
e
v
e
l
o
p
e
d
b
y
F
i
n
o
t
e
ll
i
a
n
d
E
u
s
ta
c
h
e
[
2
9
]
,
w
h
o
d
e
l
v
e
i
n
t
o
t
h
e
m
o
d
e
l
i
n
g
o
f
h
u
m
a
n
m
e
m
o
r
y
t
o
r
e
p
r
e
s
e
n
t
t
h
e
m
o
t
i
v
a
t
i
o
n
a
l
s
ta
t
e
o
f
t
h
e
l
e
a
r
n
e
r
a
n
d
i
t
s
e
f
f
e
c
t
o
n
t
h
e
l
e
a
r
n
i
n
g
p
r
o
c
e
s
s
.
T
h
is
i
s
p
e
r
c
e
i
v
e
d
w
h
e
n
q
u
a
n
t
i
t
a
t
i
v
el
y
e
x
p
o
s
i
n
g
t
h
e
r
a
t
e
o
f
c
h
a
n
g
e
o
f
l
e
a
r
n
i
n
g
t
h
a
t
i
s
a
s
s
o
c
i
at
e
d
w
i
t
h
v
a
r
i
at
i
o
n
i
n
m
o
t
i
v
a
t
i
o
n
,
a
s
w
e
l
l
as
a
n
i
n
it
i
a
l
f
a
c
t
o
r
i
n
t
h
e
g
a
i
n
e
q
u
a
t
i
o
n
,
e
.
g
.
,
t
h
e
c
h
a
n
g
e
in
m
o
t
i
v
a
t
i
o
n
a
t
t
h
e
b
e
g
i
n
n
i
n
g
o
f
a
l
e
a
r
n
i
n
g
t
as
k
.
I
n
ad
d
itio
n
,
s
ev
e
r
al
r
esear
ch
es
[
3
5
]
–
[
3
7
]
,
[
4
2
]
th
r
o
u
g
h
t
h
e
r
esu
lts
o
f
t
h
eir
r
esp
ec
tiv
e
r
esear
ch
,
s
h
o
w
ed
th
e
co
n
v
er
g
e
n
ce
b
et
wee
n
th
e
th
eo
r
y
an
d
p
r
ac
tice
o
f
m
ath
em
atica
l
m
o
d
elin
g
.
T
h
is
is
d
etec
ted
b
y
ex
p
licitly
h
ig
h
lig
h
tin
g
ef
f
ec
tiv
e
an
d
s
u
s
tain
ab
le
in
n
o
v
atio
n
s
,
as we
ll a
s
th
e
cr
ea
tio
n
o
f
s
y
s
tem
atize
d
r
esp
o
n
s
es
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
Tr
a
n
s
fo
r
min
g
u
n
ivers
ity
ed
u
ca
tio
n
:
a
s
ystema
tic
r
ev
ie
w
o
f m
a
th
ema
tica
l …
(
I
n
es Mir
ya
m
A
ce
r
o
A
p
a
z
a
)
2127
th
at
b
r
in
g
a
p
o
s
itiv
e
im
p
ac
t
o
f
m
ath
em
atica
l
m
et
h
o
d
s
an
d
m
o
d
els
in
th
e
tr
ea
tm
en
t
o
f
m
em
o
r
y
d
u
r
i
n
g
th
e
lear
n
in
g
p
r
o
ce
s
s
.
I
n
th
is
way
,
o
n
e
ca
n
em
p
h
asize
th
e
o
p
ti
m
izatio
n
o
f
p
r
o
ce
s
s
es
o
f
a
s
o
cial
n
atu
r
e
s
u
ch
as
en
g
in
ee
r
in
g
p
r
o
jects,
m
e
d
icin
e,
as
well
as
m
an
u
f
ac
tu
r
in
g
s
y
s
tem
s
,
th
e
ex
p
a
n
s
io
n
o
f
AI
th
r
o
u
g
h
ad
v
an
ce
d
alg
o
r
ith
m
s
,
an
d
th
e
r
ee
n
g
in
ee
r
in
g
o
f
n
an
o
tec
h
n
o
lo
g
y
.
Fin
ally
,
Ma
r
tín
-
L
ar
a
an
d
R
o
n
d
a
[
4
8
]
p
r
esen
t
ed
a
wa
y
to
b
r
id
g
e
th
e
g
a
p
b
etwe
en
th
e
o
r
y
a
n
d
p
r
ac
tice
in
th
e
u
s
e
o
f
m
ath
em
atica
l
m
o
d
els
in
th
e
ed
u
ca
tio
n
al
f
ie
ld
.
I
n
th
is
co
n
tex
t,
in
d
e
v
elo
p
in
g
th
e
s
tu
d
y
,
th
e
y
co
m
p
ar
ed
t
h
e
r
esu
lts
o
b
tain
ed
af
ter
th
e
less
o
n
s
th
at
wer
e
tr
ad
itio
n
ally
p
er
f
o
r
m
ed
,
with
th
o
s
e
o
b
tain
ed
a
f
ter
th
e
im
p
lem
en
tatio
n
o
f
s
ev
er
a
l
co
m
p
u
ter
ac
tiv
ities
with
m
o
d
elin
g
an
d
s
im
u
latio
n
o
f
b
i
o
r
ea
cto
r
s
to
teac
h
b
io
r
ef
in
er
y
co
n
ce
p
ts
f
o
cu
s
ed
o
n
b
io
eth
an
o
l
p
r
o
d
u
ctio
n
.
T
h
is
is
a
liv
in
g
e
x
am
p
le
in
w
h
ich
m
ath
em
atica
l
m
o
d
elin
g
p
r
o
v
id
es th
e
p
r
ac
tic
al
in
f
o
r
m
atio
n
to
co
r
r
o
b
o
r
ate
t
h
e
th
eo
r
etica
l a
s
p
ec
ts
lear
n
ed
.
4.
CO
NCLU
SI
O
N
I
t
is
f
o
u
n
d
t
h
at
th
e
in
teg
r
ati
o
n
o
f
m
at
h
em
atica
l
m
o
d
elin
g
i
n
th
e
teac
h
in
g
an
d
lear
n
in
g
p
r
o
ce
s
s
es
a
t
th
e
u
n
iv
er
s
ity
lev
el
p
r
o
m
o
tes
a
s
u
b
s
tan
tial
im
p
r
o
v
em
en
t
in
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
in
g
.
T
h
is
im
p
r
o
v
em
en
t
is
n
o
t
lim
ited
o
n
l
y
to
a
s
u
p
er
f
ici
al
ass
im
ilatio
n
o
f
co
n
ce
p
ts
,
b
u
t
tr
an
s
lates
in
to
a
d
ee
p
e
r
u
n
d
er
s
tan
d
in
g
a
n
d
th
e
ab
ilit
y
to
ap
p
ly
th
ese
co
n
ce
p
ts
in
a
v
ar
iety
o
f
ac
ad
em
ic
co
n
tex
ts
.
T
h
e
ev
id
e
n
ce
p
r
ese
n
ted
in
th
e
s
tu
d
ies
an
aly
ze
d
co
n
s
is
ten
tly
s
u
p
p
o
r
ts
th
is
claim
,
h
ig
h
lig
h
tin
g
th
e
v
alu
e
an
d
h
ig
h
im
p
o
r
tan
c
e
o
f
m
ath
em
atica
l
m
o
d
elin
g
as a
p
ed
ag
o
g
ical
r
es
o
u
r
ce
to
e
n
r
ich
t
h
e
co
n
ce
p
tu
al
u
n
d
er
s
tan
d
i
n
g
o
f
co
lleg
e
s
tu
d
en
ts
.
Ma
th
em
atica
l
m
o
d
elin
g
is
f
o
u
n
d
t
o
b
e
an
ef
f
ec
tiv
e
to
o
l
f
o
r
f
o
s
ter
in
g
th
e
d
ev
elo
p
m
en
t
o
f
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
R
esea
r
ch
f
in
d
i
n
g
s
s
u
g
g
est
th
at
s
tu
d
en
ts
ex
p
o
s
ed
to
m
ath
em
atica
l
m
o
d
elin
g
ac
q
u
ir
e
s
tr
o
n
g
s
k
ills
to
tack
le
co
m
p
lex
p
r
o
b
lem
s
an
d
to
e
f
f
ec
tiv
ely
ap
p
ly
m
ath
e
m
atica
l
p
r
in
cip
les
in
p
r
ac
tical
s
itu
atio
n
s
.
T
h
is
p
r
o
b
lem
-
s
o
l
v
in
g
ab
ilit
y
em
e
r
g
es
as
a
cr
u
cial
co
m
p
eten
c
y
in
h
ig
h
er
ed
u
ca
tio
n
a
n
d
i
n
p
r
ep
ar
in
g
s
tu
d
e
n
ts
to
f
ac
e
ac
ad
em
ic
an
d
p
r
o
f
ess
io
n
al
ch
al
len
g
es,
th
u
s
,
it
is
co
n
clu
d
e
d
th
at
m
ath
em
atica
l
m
o
d
elin
g
h
as a
h
ig
h
lev
el
o
f
im
p
o
r
tan
ce
f
o
r
u
n
iv
e
r
s
ity
lear
n
in
g
.
I
t
is
al
s
o
estab
li
s
h
ed
th
at
m
ath
em
atica
l
m
o
d
elin
g
f
ac
ilit
ates
th
e
co
n
n
ec
tio
n
b
etwe
en
th
eo
r
y
an
d
p
r
ac
tice
in
h
ig
h
er
ed
u
ca
tio
n
.
T
h
e
s
tu
d
ies
an
aly
ze
d
h
ig
h
lig
h
t
h
o
w
m
ath
em
atica
l
m
o
d
elin
g
allo
ws
s
tu
d
en
ts
to
ex
p
er
ien
ce
th
e
co
n
cr
ete
a
p
p
l
icatio
n
o
f
th
eo
r
etica
l
k
n
o
wl
ed
g
e
in
r
ea
l
-
w
o
r
ld
s
itu
atio
n
s
.
T
h
is
co
n
n
ec
tio
n
b
etwe
en
th
eo
r
y
a
n
d
p
r
ac
tice
n
o
t
o
n
ly
en
r
ich
es
ac
ad
em
ic
tr
ai
n
in
g
,
b
u
t
also
s
tr
en
g
th
e
n
s
s
tu
d
en
ts
’
p
r
o
f
ess
io
n
al
id
en
tity
b
y
p
r
o
v
id
in
g
t
h
em
with
m
ea
n
in
g
f
u
l a
n
d
ap
p
licab
le
e
x
p
er
ien
ce
s
in
th
eir
f
ield
s
o
f
s
t
u
d
y
.
T
ak
en
to
g
eth
e
r
,
th
ese
f
in
d
i
n
g
s
p
r
o
v
i
d
e
a
s
o
lid
b
asis
f
o
r
u
n
d
er
s
tan
d
in
g
an
d
ap
p
r
ec
iatin
g
m
ath
em
atica
l
m
o
d
elin
g
as
a
v
alu
ab
le
ed
u
ca
tio
n
al
r
eso
u
r
ce
i
n
h
ig
h
er
ed
u
ca
tio
n
,
as
well
as
f
o
r
a
p
p
r
ec
iatin
g
its
im
p
o
r
tan
ce
i
n
f
ac
ilit
atin
g
s
tu
d
en
t
lear
n
in
g
.
T
h
e
in
teg
r
ated
an
d
s
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