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1274
Ma
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r
o
g
r
e
s
s
io
n
[
1
6
]
,
[
1
7
]
.
R
esear
ch
er
s
r
eg
ar
d
b
ib
lio
m
etr
ic
an
aly
s
es
as
p
iv
o
tal
in
d
elin
ea
tin
g
b
ib
lio
g
r
a
p
h
ic
d
etails
in
s
p
ec
if
ic
s
ec
to
r
s
[
1
8
]
–
[
2
0
]
.
I
n
t
h
e
co
n
tex
t
o
f
th
is
in
v
esti
g
atio
n
,
th
e
ar
ticle
lev
er
ag
es
th
e
b
ib
lio
m
etr
ic
m
eth
o
d
o
lo
g
y
to
g
ath
er
an
d
s
cr
u
t
in
ize
b
ib
lio
g
r
ap
h
ic
co
n
ten
t
ass
o
ciate
d
with
m
ath
em
atica
l
ab
ilit
y
.
T
h
is
s
tr
ate
g
y
tap
s
in
to
p
er
tin
e
n
t
s
ch
o
last
ic
an
d
s
cien
tific
liter
atu
r
e
d
atab
ases
,
aim
in
g
to
p
in
p
o
in
t
p
u
b
licatio
n
co
u
n
ts
,
y
ea
r
ly
p
u
b
licatio
n
d
is
tr
ib
u
tio
n
,
jo
u
r
n
al
r
an
k
in
g
ca
teg
o
r
izatio
n
,
a
n
d
r
esear
ch
af
f
iliatio
n
s
co
n
ce
r
n
in
g
m
ath
e
m
atica
l
ab
ilit
y
[
2
1
]
–
[
2
3
]
.
Su
ch
a
b
ib
lio
m
etr
ic
ass
es
s
m
en
t
ca
n
s
p
o
tlig
h
t
th
e
f
r
esh
est
r
esear
ch
d
ir
ec
tio
n
s
o
n
m
ath
em
atica
l
ab
ilit
y
an
d
h
i
g
h
lig
h
t
th
e
r
o
les
o
f
d
iv
er
s
e
in
s
titu
tio
n
s
an
d
n
atio
n
s
in
en
r
ich
in
g
th
e
co
m
p
r
eh
en
s
io
n
o
f
m
ath
em
atica
l
co
m
p
eten
cies
[
2
4
]
–
[
2
6
]
.
T
h
is
in
f
o
r
m
ati
o
n
ca
n
p
r
o
v
i
d
e
im
p
o
r
tan
t
i
n
s
ig
h
ts
f
o
r
r
esear
c
h
er
s
,
ed
u
ca
t
o
r
s
,
an
d
p
r
ac
titi
o
n
er
s
o
f
m
ath
em
atics
ed
u
ca
tio
n
in
d
esig
n
in
g
s
y
llab
u
s
an
d
cu
r
r
icu
la
as
well
as
te
ac
h
in
g
s
tr
ateg
ies
to
en
h
an
ce
m
ath
em
atica
l
ab
ilit
y
p
ar
ticu
lar
ly
am
o
n
g
s
ch
o
o
l c
h
il
d
r
en
[
2
7
]
–
[
3
0
]
.
T
h
e
r
ea
lm
o
f
m
ath
em
atics
ed
u
ca
tio
n
r
esear
ch
is
co
n
tin
u
a
lly
ex
p
an
d
in
g
,
as
ev
id
en
ce
d
b
y
r
ec
en
t
s
tu
d
ies
f
o
cu
s
in
g
o
n
v
ar
io
u
s
asp
ec
ts
o
f
s
tu
d
en
ts
'
m
ath
em
ati
ca
l
ab
ilit
ies.
On
e
s
u
ch
s
tu
d
y
aim
ed
to
u
n
d
er
s
tan
d
m
ath
em
atics
teac
h
er
s
'
p
er
ce
p
tio
n
s
o
f
s
tu
d
en
ts
'
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies.
T
h
e
r
esear
c
h
also
h
ig
h
lig
h
te
d
d
if
f
er
en
ce
s
in
s
tu
d
en
ts
'
p
r
o
b
le
m
-
s
o
lv
in
g
s
k
ills
d
u
r
in
g
o
n
lin
e
an
d
o
f
f
lin
e
lear
n
in
g
,
u
n
d
e
r
s
co
r
in
g
th
e
n
e
ed
f
o
r
f
u
r
th
er
in
v
esti
g
atio
n
an
d
im
p
r
o
v
em
en
t
in
th
is
ar
ea
[
3
1
]
.
T
h
is
s
tu
d
y
c
o
n
tr
ib
u
tes
to
th
e
g
r
o
win
g
b
o
d
y
o
f
liter
atu
r
e
o
n
m
at
h
em
atics
ed
u
ca
tio
n
an
d
o
f
f
er
s
in
s
ig
h
ts
th
a
t
ca
n
b
e
u
s
ed
t
o
en
h
a
n
ce
an
d
ev
alu
ate
s
tu
d
en
ts
'
m
ath
em
atica
l p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies in
s
ch
o
o
ls
ac
r
o
s
s
Su
m
atr
a.
I
n
an
o
th
er
v
ein
,
r
esear
ch
h
a
s
d
elv
ed
in
t
o
th
e
d
esig
n
a
n
d
q
u
ality
ass
ess
m
en
t
o
f
d
ig
ital
lear
n
in
g
p
latf
o
r
m
s
f
o
r
d
iag
n
o
s
in
g
s
ev
e
n
th
-
g
r
a
d
e
s
tu
d
en
ts
'
m
ath
em
atica
l
ab
ilit
ies
in
m
ea
s
u
r
em
en
t
a
n
d
g
e
o
m
etr
y
.
T
h
e
f
in
d
in
g
s
af
f
ir
m
ed
th
e
p
latf
o
r
m
'
s
h
ig
h
lev
el
o
f
u
s
ef
u
ln
ess
,
s
u
itab
ilit
y
,
an
d
ac
cu
r
ac
y
,
alth
o
u
g
h
its
f
ea
s
ib
ilit
y
was
d
ee
m
ed
m
o
d
e
r
ately
ap
p
r
o
p
r
ia
te
[
2
]
.
T
h
is
d
ig
ital
to
o
l
s
tan
d
s
as
a
v
alu
ab
le
r
eso
u
r
ce
f
o
r
d
i
ag
n
o
s
in
g
s
tu
d
en
ts
'
m
ath
em
atica
l
ab
ilit
ies.
Ad
d
itio
n
ally
,
s
tu
d
ies
h
av
e
e
x
p
lo
r
e
d
th
e
r
elatio
n
s
h
ip
b
etwe
en
c
o
g
n
itiv
e
f
lex
ib
ilit
y
an
d
g
eo
m
etr
ic
ab
ilit
ies
in
p
r
o
b
le
m
-
s
o
lv
in
g
,
a
d
v
o
ca
tin
g
f
o
r
t
h
e
u
s
e
o
f
au
x
iliar
y
lin
es
to
f
o
s
ter
cr
ea
tiv
e
th
in
k
in
g
s
k
ills
in
g
eo
m
etr
y
[
3
2
]
.
Fu
r
t
h
er
m
o
r
e
,
in
v
esti
g
atio
n
s
in
to
s
tu
d
en
ts
'
m
ath
em
atica
l
co
n
n
e
ctio
n
ab
ilit
ies
h
av
e
r
ev
ea
led
v
a
r
y
in
g
lev
els
o
f
p
r
o
f
icien
cy
ac
r
o
s
s
d
if
f
er
en
t
i
n
d
icato
r
s
,
h
ig
h
lig
h
tin
g
ar
ea
s
f
o
r
im
p
r
o
v
e
m
en
t
[
1
7
]
.
R
esear
ch
em
p
lo
y
in
g
a
n
o
p
en
ap
p
r
o
ac
h
to
o
r
g
an
ize
lear
n
in
g
ac
tiv
ities
h
as
also
s
h
o
wn
p
r
o
m
is
e
in
d
ev
elo
p
in
g
s
tu
d
en
ts
'
m
ath
em
atica
l
p
r
o
b
l
em
-
s
o
lv
in
g
a
n
d
r
ea
s
o
n
in
g
s
k
ills
,
d
em
o
n
s
tr
atin
g
th
e
ef
f
e
ctiv
en
ess
o
f
ac
tio
n
r
esear
ch
in
ac
h
iev
in
g
e
d
u
ca
ti
o
n
al
g
o
als
[
3
2
]
.
T
h
ese
s
tu
d
ie
s
co
llectiv
ely
co
n
tr
ib
u
te
to
t
h
e
en
h
an
ce
m
e
n
t
o
f
m
ath
em
atics e
d
u
ca
tio
n
,
p
r
o
v
id
in
g
ev
i
d
en
ce
-
b
ased
s
tr
ateg
ies f
o
r
im
p
r
o
v
i
n
g
s
tu
d
en
ts
'
m
ath
em
atica
l a
b
ilit
ies.
Desp
ite
th
e
ab
u
n
d
an
ce
o
f
lite
r
atu
r
e,
n
o
co
m
p
r
eh
en
s
iv
e
b
ib
lio
m
etr
ic
s
tu
d
y
o
f
m
ath
em
ati
ca
l
ab
ilit
y
h
as
b
ee
n
co
n
d
u
cted
in
th
e
last
10
y
ea
r
s
,
p
a
r
ticu
lar
ly
th
o
s
e
u
s
in
g
Sco
p
u
s
an
d
Go
o
g
le
Sch
o
lar
as
d
atab
ases
.
I
n
th
is
co
n
tex
t,
th
is
ar
ticle
aim
s
to
co
m
p
lem
en
t
o
th
er
im
p
o
r
ta
n
t
asp
ec
ts
o
f
m
ap
p
in
g
r
esear
c
h
o
n
m
ath
e
m
atica
l
ab
ilit
y
,
s
o
th
at
th
e
m
ap
p
in
g
b
ec
o
m
es
m
o
r
e
co
m
p
r
eh
e
n
s
iv
e.
T
h
e
f
o
cu
s
o
f
th
is
s
tu
d
y
is
a
b
i
b
lio
m
etr
ic
an
aly
s
is
o
f
th
e
m
ath
em
atics
ab
ilit
y
m
o
d
el
b
y
co
n
s
id
er
in
g
p
u
b
licatio
n
tr
en
d
s
,
s
ig
n
if
ican
t
jo
u
r
n
al
co
n
tr
ib
u
tio
n
s
,
citatio
n
p
atter
n
s
,
au
th
o
r
k
ey
w
o
r
d
s
,
an
d
co
llab
o
r
atio
n
o
f
au
th
o
r
s
wh
o
p
u
b
lis
h
ar
ticles.
T
h
is
r
esear
ch
aim
s
to
ex
p
lo
r
e
th
e
lan
d
s
ca
p
e
o
f
s
ch
o
lar
ly
w
o
r
k
o
n
m
ath
em
atica
l a
b
ilit
y
b
y
a
d
d
r
ess
in
g
th
e
f
o
llo
win
g
q
u
esti
o
n
s
:
i)
W
h
at
ar
e
th
e
tr
en
d
s
in
th
e
p
u
b
licatio
n
o
f
ar
ticles o
n
m
ath
em
atica
l a
b
ilit
y
f
r
o
m
2
0
1
4
to
2
0
2
3
?
ii)
W
h
at
is
th
e
citatio
n
p
atter
n
f
o
r
ar
ticles o
n
m
ath
em
atica
l a
b
ili
ty
f
r
o
m
2
0
1
4
to
2
0
2
3
?
iii)
W
h
at
ar
e
th
e
k
ey
wo
r
d
tr
en
d
s
u
s
ed
b
y
a
u
th
o
r
s
in
a
r
ticles o
n
m
ath
em
atica
l a
b
ilit
ies f
r
o
m
2
0
1
4
to
2
0
2
3
?
iv
)
W
h
at
is
th
e
p
atter
n
o
f
c
o
llab
o
r
atio
n
b
etwe
en
au
t
h
o
r
s
in
ar
ticles
o
n
m
ath
em
atica
l
ab
ilit
y
f
r
o
m
2
0
1
4
to
2023?
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
Ma
th
em
atica
l
ab
ilit
y
is
a
cr
u
cial
co
g
n
itiv
e
co
m
p
eten
ce
i
n
to
d
ay
'
s
er
a.
Nu
m
er
o
u
s
s
tu
d
ies
h
av
e
attem
p
ted
to
ex
p
lain
v
ar
i
o
u
s
asp
ec
ts
r
elate
d
to
m
ath
em
atica
l
ab
ilit
ies
an
d
th
eir
im
p
lic
atio
n
s
in
d
if
f
er
en
t
s
itu
atio
n
s
.
T
h
e
r
o
le
o
f
m
ath
e
m
atica
l
ab
ilit
ies
in
th
e
r
ea
lm
o
f
ed
u
ca
tio
n
al
a
n
d
ac
ad
em
i
c
g
r
o
wth
h
as
b
ee
n
in
v
esti
g
ated
[
3
3
]
,
[
3
4
]
.
T
h
eir
wo
r
k
ac
ce
n
tu
ates th
e
n
ee
d
f
o
r
ad
ep
t m
ath
em
atica
l p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
an
d
an
in
tr
icate
g
r
asp
o
f
m
ath
em
atica
l c
o
n
ce
p
ts
f
o
r
tr
iu
m
p
h
in
m
at
h
em
atics a
n
d
ad
jace
n
t d
is
cip
lin
es.
A
s
ep
ar
ate
s
tu
d
y
f
o
c
u
s
es
o
n
i
d
en
tify
in
g
f
ac
to
r
s
th
at
in
f
lu
en
ce
s
tu
d
en
ts
'
m
ath
em
atica
l
ab
i
liti
es
an
d
th
e
ef
f
ec
tiv
en
ess
o
f
in
n
o
v
ati
v
e
teac
h
in
g
m
et
h
o
d
s
in
en
h
a
n
cin
g
th
eir
ac
a
d
em
ic
p
er
f
o
r
m
an
ce
.
E
m
p
h
asis
is
p
lace
d
o
n
t
h
e
im
p
o
r
tan
ce
o
f
en
g
ag
in
g
s
tu
d
en
ts
in
ch
allen
g
in
g
an
d
r
elev
an
t
m
at
h
em
atica
l
s
itu
atio
n
s
,
wh
ich
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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&
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ilit
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d
e
to
war
d
s
m
ath
em
atics
[
3
5
]
,
[
3
6
]
.
T
h
e
r
esear
c
h
f
in
d
in
g
s
s
u
g
g
est
th
at
in
s
tr
u
ctio
n
al
ap
p
r
o
ac
h
es
b
ase
d
o
n
u
n
d
er
s
tan
d
in
g
,
co
llab
o
r
ativ
e
lear
n
in
g
,
an
d
h
an
d
s
-
o
n
in
v
o
lv
em
e
n
t
ca
n
s
ig
n
if
ican
tly
im
p
r
o
v
e
s
tu
d
e
n
t
s
'
m
ath
em
atica
l
ab
ilit
ie
s
[
3
7
]
,
[
3
8
]
.
T
h
e
s
ig
n
if
ican
ce
o
f
d
ee
p
an
d
s
y
s
tem
atic
lear
n
in
g
in
e
n
h
an
ci
n
g
m
ath
e
m
atica
l
ab
ilit
ies
is
em
p
h
asized
,
h
i
g
h
lig
h
tin
g
th
e
n
ec
ess
ity
f
o
r
a
n
e
d
u
ca
tio
n
al
ap
p
r
o
ac
h
f
o
c
u
s
ed
o
n
au
t
h
en
ti
c
p
r
o
b
lem
s
o
lv
in
g
task
s
an
d
t
h
e
ad
o
p
tio
n
o
f
a
d
ap
tab
le
c
o
g
n
itiv
e
s
tr
ateg
ies
[
3
3
]
,
[
3
4
]
.
T
h
is
r
esear
c
h
also
h
ig
h
lig
h
ts
th
e
cr
u
cial
r
o
le
th
at
te
ac
h
er
s
p
lay
in
p
r
o
v
id
in
g
o
n
g
o
in
g
s
u
p
p
o
r
t
a
n
d
f
ee
d
b
ac
k
.
T
h
is
r
o
le
is
ess
en
tial f
o
r
s
tu
d
en
ts
to
h
o
n
e
t
h
eir
m
at
h
em
atica
l sk
ills
.
Sig
n
if
ican
t
r
esear
ch
in
th
e
f
i
eld
o
f
m
ath
em
atica
l
a
b
ilit
y
h
as
b
ee
n
h
ig
h
lig
h
ted
,
f
o
cu
s
i
n
g
o
n
th
e
v
ar
iab
les
th
at
s
h
ap
e
m
ath
em
atica
l
ab
ilit
y
,
p
o
wer
f
u
l
p
ed
a
g
o
g
ical
m
eth
o
d
o
lo
g
ies,
an
d
th
e
im
p
o
r
tan
ce
o
f
f
o
s
ter
in
g
a
co
n
s
tr
u
ctiv
e
m
in
d
s
et
to
war
d
s
m
ath
em
atics
to
ac
h
iev
e
h
ig
h
m
ath
em
atica
l
c
o
m
p
e
ten
ce
.
At
th
e
s
am
e
tim
e,
th
er
e
ar
e
o
th
er
in
v
esti
g
a
tio
n
s
th
at
f
u
r
th
er
en
r
ich
o
u
r
u
n
d
er
s
tan
d
in
g
o
f
m
ath
em
atica
l
ab
ilit
ies.
On
e
s
tu
d
y
ex
p
lo
r
es
th
e
elem
en
ts
th
at
in
f
lu
en
ce
s
tu
d
en
ts
'
ac
h
iev
em
en
ts
in
m
ath
em
atics.
T
h
eir
f
in
d
in
g
s
s
u
g
g
est
th
at
asp
ec
ts
s
u
ch
as
s
tu
d
en
t
s
elf
-
c
o
n
f
id
en
ce
,
in
tr
i
n
s
ic
m
o
tiv
atio
n
,
an
d
th
e
ef
f
icac
y
o
f
ed
u
ca
to
r
s
p
lay
a
cr
u
cial
r
o
le
in
s
h
ap
in
g
th
eir
m
ath
em
atica
l
ab
ilit
ies
[
3
9
]
–
[
4
1
]
.
T
h
e
co
n
tex
t
o
f
e
v
alu
atin
g
m
at
h
em
a
tical
co
m
p
eten
cies
h
ig
h
lig
h
ts
th
e
cr
ea
tio
n
o
f
e
v
al
u
ativ
e
to
o
ls
ca
p
ab
le
o
f
h
o
lis
tically
m
ea
s
u
r
in
g
m
ath
e
m
atica
l
ab
ilit
ies
[
4
2
]
,
[
4
3
]
.
T
h
e
p
r
im
ar
y
f
o
cu
s
is
o
n
d
ev
elo
p
in
g
in
s
tr
u
m
en
ts
th
at
co
v
er
b
o
th
co
g
n
itiv
e
an
d
c
o
n
ce
p
tu
al
m
ath
em
atica
l
d
im
en
s
io
n
s
.
T
h
is
in
clu
d
es p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
an
d
m
ath
e
m
atica
l c
o
m
m
u
n
icatio
n
ab
ilit
ies.
E
m
o
tio
n
al
f
ac
to
r
s
s
u
ch
as
m
ath
em
atics
an
x
iety
p
lay
a
cr
u
cial
r
o
le
in
th
e
r
eso
lu
tio
n
o
f
ar
ith
m
etic
p
r
o
b
lem
-
s
o
lv
in
g
ev
e
n
d
u
r
in
g
th
e
ea
r
ly
y
ea
r
s
o
f
f
o
r
m
al
e
d
u
ca
tio
n
[
4
4
]
.
E
m
o
tio
n
al
in
tellig
en
ce
,
s
elf
-
esteem
,
an
d
s
elf
-
ef
f
icac
y
h
av
e
a
s
ig
n
i
f
ican
t
in
f
lu
en
ce
in
p
r
ed
ictin
g
s
tu
d
en
ts
'
ac
ad
em
ic
ac
h
iev
em
en
t
in
m
ath
em
atics,
af
f
ir
m
in
g
th
at
th
ese
f
ac
to
r
s
a
r
e
k
ey
d
eter
m
i
n
an
ts
in
th
eir
s
u
cc
ess
in
th
e
f
ield
[
4
5
]
,
[
4
6
]
.
T
h
ese
f
in
d
i
n
g
s
u
n
d
er
s
co
r
e
th
e
im
p
o
r
tan
ce
o
f
ad
d
r
ess
in
g
em
o
tio
n
al
an
d
p
s
y
ch
o
lo
g
ical
asp
ec
ts
in
m
ath
em
atics
ed
u
ca
tio
n
to
en
h
an
ce
s
tu
d
en
ts
'
o
v
er
all
p
er
f
o
r
m
an
ce
an
d
co
n
f
id
en
ce
in
th
e
s
u
b
ject.
Ma
th
em
atics
ed
u
ca
to
r
s
n
ee
d
to
b
e
s
k
illed
an
d
u
s
e
ef
f
ec
tiv
e
s
tr
a
teg
ies
to
teac
h
m
ath
em
atica
l
co
n
ce
p
ts
.
T
h
eir
ab
ilit
y
to
li
n
k
s
tu
d
e
n
ts
'
b
asi
c
k
n
o
wled
g
e
with
a
d
v
an
ce
d
m
a
th
em
atica
l
th
em
es
is
k
e
y
t
o
th
eir
ap
p
r
o
ac
h
.
T
h
ese
m
eth
o
d
s
g
r
ea
tly
e
n
h
an
ce
th
e
o
v
er
all
d
ev
el
o
p
m
en
t
o
f
lear
n
e
r
s
'
m
ath
em
atica
l a
b
ilit
ie
s
[
4
7
]
,
[
4
8
]
.
T
h
ese
in
v
esti
g
atio
n
s
illu
s
tr
ate
th
e
in
tr
icac
ies
o
f
m
ath
em
atica
l
ab
ilit
ies
an
d
th
e
m
y
r
iad
elem
en
ts
th
at
s
h
ap
e
th
em
.
A
p
r
o
f
o
u
n
d
c
o
m
p
r
eh
en
s
io
n
o
f
m
ath
em
atica
l
a
b
ilit
y
,
co
u
p
led
with
in
s
ig
h
ts
in
to
its
in
f
lu
en
ci
n
g
f
ac
to
r
s
,
ca
n
aid
in
cr
af
tin
g
e
f
f
icien
t
p
ed
a
g
o
g
ical
m
eth
o
d
s
,
p
in
p
o
in
tin
g
s
tu
d
en
t
lear
n
in
g
r
eq
u
ir
e
m
en
ts
,
an
d
f
o
r
m
u
latin
g
p
er
tin
en
t
an
d
s
tim
u
latin
g
ed
u
ca
tio
n
al
tactics.
Su
ch
s
tr
ateg
ies
n
o
t
o
n
ly
f
o
s
ter
a
d
ee
p
er
u
n
d
er
s
tan
d
i
n
g
o
f
m
ath
em
atic
al
co
n
ce
p
ts
b
u
t
also
p
r
o
m
o
te
a
p
o
s
itiv
e
lear
n
i
n
g
e
n
v
ir
o
n
m
e
n
t
th
at
en
c
o
u
r
a
g
es
s
tu
d
en
t e
n
g
ag
e
m
en
t a
n
d
p
er
s
e
v
er
an
ce
.
3.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
is
s
tu
d
y
a
d
o
p
ts
a
b
ib
lio
g
r
a
p
h
ic
r
esear
c
h
f
r
am
ewo
r
k
,
u
tili
zin
g
s
y
s
tem
atic
an
d
ex
p
licit
m
ap
p
i
n
g
tech
n
iq
u
es
s
o
u
r
ce
d
f
r
o
m
v
ar
i
o
u
s
p
r
ev
io
u
s
p
u
b
licatio
n
s
[
4
9
]
.
T
h
e
liter
atu
r
e
r
ev
iew
is
s
tr
u
ctu
r
ed
in
to
f
o
u
r
d
is
tin
ct
p
h
ases
:
s
ea
r
ch
p
r
o
ce
d
u
r
e,
f
ilter
b
ib
lio
g
r
ap
h
y
,
b
ib
lio
g
r
ap
h
ic
co
m
p
leten
ess
,
a
n
d
b
i
b
lio
m
etr
ic
an
aly
s
is
[
5
0
]
,
[
5
1
]
.
T
h
e
ap
p
licatio
n
o
f
s
y
s
tem
atic
m
ap
p
in
g
tech
n
i
q
u
es
in
b
ib
lio
m
etr
ic
s
tu
d
ies,
th
e
in
teg
r
atio
n
o
f
b
ib
lio
m
etr
ic
e
v
alu
atio
n
s
with
m
ap
p
in
g
th
e
r
esear
ch
lan
d
s
ca
p
e,
th
e
s
ig
n
if
ican
ce
o
f
b
ib
lio
m
etr
ic
tech
n
iq
u
es
in
m
ea
s
u
r
in
g
r
esear
ch
ca
lib
er
an
d
im
p
ac
t,
an
d
i
n
s
ig
h
ts
in
to
u
s
in
g
co
m
p
u
tatio
n
al
t
o
o
l
s
f
o
r
b
ib
lio
m
etr
ic
m
o
n
ito
r
in
g
ar
e
all
ex
p
lo
r
ed
[
5
2
]
.
T
h
r
o
u
g
h
c
o
m
p
r
e
h
en
s
iv
e
b
ib
lio
m
etr
ic
ev
alu
atio
n
,
th
i
s
r
esear
ch
aim
s
to
em
p
lo
y
estab
lis
h
ed
m
eth
o
d
o
l
o
g
ies
an
d
en
h
an
ce
u
n
d
er
s
tan
d
in
g
o
f
m
ath
em
atica
l
ab
ilit
ies,
lev
er
ag
in
g
th
e
af
o
r
em
en
tio
n
ed
s
ch
o
la
r
ly
wo
r
k
s
.
3
.
1
.
Sea
rc
h pro
ce
du
re
T
h
e
s
o
f
twar
e
Pu
b
lis
h
o
r
Per
i
s
h
(
Po
P)
was
u
tili
ze
d
to
p
r
o
b
e
b
ib
lio
g
r
ap
h
ic
d
ata
b
ases
,
s
p
ec
if
ically
Sco
p
u
s
an
d
Go
o
g
le
Sch
o
lar
.
T
h
ese
d
atab
ases
s
tan
d
o
u
t
as
th
e
p
r
ed
o
m
in
an
t
r
eser
v
o
i
r
s
o
f
f
er
in
g
ex
p
er
t
-
r
ev
iewe
d
liter
atu
r
e.
T
h
e
s
elec
t
io
n
o
f
Sco
p
u
s
an
d
Go
o
g
le
Sch
o
lar
s
tem
s
f
r
o
m
th
eir
co
m
p
r
eh
en
s
iv
e
s
p
ec
tr
u
m
o
f
co
n
ten
t
in
co
m
p
ar
is
o
n
to
o
t
h
er
ar
ch
iv
es
[
2
3
]
,
[
4
9
]
.
No
tab
l
y
,
th
ey
en
co
m
p
ass
r
o
u
g
h
ly
7
0
%
m
o
r
e
p
u
b
lis
h
ed
wo
r
k
s
th
an
W
eb
o
f
Scien
ce
[
5
0
]
.
I
n
th
is
an
aly
s
is
,
cr
iter
ia
wer
e
d
ef
in
e
d
f
o
r
all
b
ib
lio
g
r
a
p
h
ies
to
b
e
in
clu
d
ed
,
in
clu
d
in
g
ty
p
es
o
f
b
ib
lio
g
r
a
p
h
ies
co
n
s
is
tin
g
o
n
l
y
o
f
jo
u
r
n
als,
ar
ticle
titl
es
th
at
in
clu
d
ed
“
m
ath
e
m
atica
l
ab
ilit
y
”
,
an
d
a
y
ea
r
lim
it
o
f
s
ea
r
ch
es
f
o
r
t
h
e
p
ast
1
0
y
ea
r
s
,
i.e
.
,
b
etwe
en
2
0
1
4
an
d
2
0
2
3
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
b
ib
lio
g
r
a
p
h
ic
s
ea
r
ch
p
r
o
ce
s
s
u
s
in
g
th
e
Po
P a
p
p
licatio
n
.
R
esu
lts
f
r
o
m
b
ib
lio
g
r
a
p
h
ic
s
e
ar
ch
es
ar
e
f
ir
s
t
s
to
r
ed
in
th
e
Me
n
d
eley
ap
p
licatio
n
,
a
p
o
p
u
l
ar
r
ef
er
e
n
ce
m
an
ag
em
en
t
to
o
l
p
o
p
u
lar
wit
h
r
esear
ch
er
s
.
On
ce
th
e
d
ata
h
as
b
ee
n
s
u
cc
ess
f
u
lly
im
p
o
r
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li
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ase
d
o
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t
h
e
f
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ll
o
w
in
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as
p
ec
ts
:
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)
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u
b
lic
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t
r
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n
d
s
;
ii
)
m
o
s
t
f
r
e
q
u
en
tl
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ci
te
d
a
r
ti
cles
;
iii
)
a
u
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k
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y
w
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at
a
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n
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Evaluation Warning : The document was created with Spire.PDF for Python.
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ic
lan
d
s
ca
p
e
w
h
er
e
s
ch
o
la
r
ly
o
u
tp
u
t
an
d
co
llab
o
r
atio
n
ar
e
b
o
t
h
in
f
lu
en
ce
d
b
y
a
n
d
co
n
tr
ib
u
te
t
o
ev
o
lv
i
n
g
r
esear
ch
th
em
es.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
P
ub
lica
t
io
n
t
re
nd
-
ba
s
ed
a
na
ly
s
is
Fig
u
r
e
2
d
ep
icts
th
e
p
r
o
g
r
es
s
io
n
in
th
e
p
u
b
licatio
n
o
f
jo
u
r
n
al
ar
ticles
ad
d
r
ess
in
g
m
ath
em
atica
l
ab
ilit
y
b
etwe
en
2
0
1
4
an
d
2
0
2
3
.
T
h
e
ch
ar
t
h
ig
h
lig
h
ts
th
e
a
n
n
u
al
f
lu
ctu
atio
n
s
in
th
e
co
u
n
t o
f
s
u
ch
a
r
ticles.
T
h
is
tr
en
d
r
ef
lects
th
e
g
r
o
win
g
in
ter
est
an
d
f
o
c
u
s
with
in
th
e
ac
ad
em
ic
co
m
m
u
n
ity
o
n
u
n
d
er
s
tan
d
i
n
g
an
d
im
p
r
o
v
in
g
m
ath
em
atica
l a
b
ilit
ies.
Fig
u
r
e
2
d
is
p
lay
s
th
e
an
n
u
al
co
u
n
t
o
f
a
r
ticles
f
o
cu
s
ed
o
n
m
ath
em
atica
l
ab
ilit
y
b
etwe
en
2
0
1
4
a
n
d
2
0
2
3
,
r
an
g
in
g
f
r
o
m
1
5
8
to
1
8
1
ar
ticles
in
an
y
g
iv
en
y
ea
r
.
O
n
in
s
p
ec
tio
n
,
th
e
v
o
l
u
m
e
o
f
ar
ticles
s
tay
s
m
o
r
e
o
r
less
co
n
s
i
s
ten
t
th
r
o
u
g
h
o
u
t
th
e
s
e
y
ea
r
s
.
T
h
e
ze
n
ith
was
in
2
0
2
2
with
1
8
1
ar
ticles,
wh
ile
th
e
tr
o
u
g
h
s
wer
e
s
ee
n
in
2
0
1
5
an
d
2
0
2
0
,
r
eg
is
ter
in
g
1
7
1
an
d
1
7
3
ar
ticles,
r
esp
ec
tiv
ely
.
I
t
is
cr
u
cial
to
m
en
tio
n
th
at
th
e
2
0
2
3
d
at
a
was
ac
cu
m
u
lated
o
n
ly
u
p
t
o
Ma
y
,
m
ak
i
n
g
t
h
e
c
o
u
n
t
f
o
r
t
h
is
y
ea
r
p
r
o
v
is
io
n
al
a
n
d
n
o
t
n
ec
ess
ar
ily
r
ep
r
esen
tativ
e
o
f
th
e
en
tire
y
ea
r
.
Ho
wev
er
,
t
h
e
en
d
u
r
in
g
p
atter
n
in
tim
ates
a
s
u
s
tain
ed
r
esear
ch
in
clin
atio
n
to
war
d
s
m
ath
em
atica
l a
b
ilit
y
o
v
er
th
is
d
u
r
atio
n
.
T
h
e
d
ata
in
d
icate
s
a
r
elativ
ely
s
tab
le
tr
en
d
,
d
esp
ite
v
ar
iati
o
n
s
in
th
e
n
u
m
b
e
r
o
f
ar
ticles
ea
ch
y
ea
r
.
Alth
o
u
g
h
th
e
p
ea
k
o
cc
u
r
r
ed
in
2
0
2
2
,
it
is
im
p
o
r
tan
t
to
n
o
te
th
at
th
e
d
ata
f
o
r
2
0
2
3
o
n
ly
in
clu
d
es
ar
ticles
p
u
b
lis
h
ed
u
n
til
Ma
y
.
T
h
is
s
u
g
g
ests
th
at
co
n
clu
s
io
n
s
ab
o
u
t
th
e
o
v
er
all
tr
en
d
f
o
r
th
at
y
ea
r
n
ee
d
to
b
e
ca
r
ef
u
lly
co
n
s
id
er
ed
.
Fu
r
th
e
r
m
o
r
e
,
th
e
f
o
cu
s
o
n
th
e
to
p
1
0
jo
u
r
n
als
f
ea
tu
r
in
g
ar
ticles
o
n
m
ath
em
at
ical
ab
ilit
y
r
esear
ch
h
ig
h
lig
h
ts
th
e
r
ele
v
an
ce
a
n
d
im
p
o
r
tan
ce
o
f
th
is
r
esear
c
h
in
v
ar
io
u
s
asp
ec
ts
o
f
life
.
Ho
wev
er
,
to
b
etter
u
n
d
er
s
tan
d
th
e
u
n
d
e
r
ly
in
g
f
a
cto
r
s
d
r
iv
in
g
th
ese
tr
e
n
d
s
,
f
u
r
th
er
a
n
aly
s
is
o
f
c
h
an
g
es
i
n
r
esear
ch
f
u
n
d
in
g
,
ed
u
ca
tio
n
al
p
o
licies,
o
r
em
e
r
g
in
g
r
esear
ch
ar
ea
s
i
n
th
e
f
ield
o
f
m
ath
e
m
atica
l
ab
ilit
y
is
n
ee
d
ed
.
Su
c
h
a
n
aly
s
is
ca
n
p
r
o
v
id
e
d
ee
p
er
in
s
ig
h
ts
in
t
o
th
e
d
y
n
am
ics o
f
r
esear
ch
in
t
h
is
f
ield
.
Su
b
s
eq
u
en
t
d
ata
p
r
esen
t
th
e
lead
in
g
1
0
j
o
u
r
n
als
th
at
f
ea
tu
r
ed
ar
ticles
o
n
m
ath
em
ati
ca
l
ab
ilit
y
r
esear
ch
f
r
o
m
2
0
1
4
to
2
0
2
3
.
Su
ch
r
esear
ch
u
n
d
er
s
co
r
es
a
co
m
p
r
eh
e
n
s
iv
e
d
esire
to
b
o
th
co
m
p
r
e
h
en
d
an
d
en
h
an
ce
m
ath
em
atica
l
ab
ilit
ies
in
d
iv
er
s
e
f
ac
ets
o
f
e
x
is
ten
ce
.
T
h
ese
jo
u
r
n
als
s
er
v
e
as
k
ey
p
latf
o
r
m
s
f
o
r
d
is
s
em
in
atin
g
cr
itical
f
in
d
in
g
s
an
d
ad
v
a
n
ce
m
en
ts
in
th
e
f
ield
,
f
u
r
th
er
e
m
p
h
asizin
g
th
e
im
p
o
r
tan
ce
o
f
th
is
ar
ea
o
f
s
tu
d
y
.
Fig
u
r
e
2
.
Pu
b
licatio
n
tr
en
d
s
p
er
y
ea
r
T
ab
le
2
in
d
icate
s
th
at
s
tu
d
ies
o
n
m
ath
em
atica
l
ab
ilit
y
ar
e
d
is
s
em
in
ated
ac
r
o
s
s
a
r
an
g
e
o
f
jo
u
r
n
als.
T
h
is
in
clu
d
es
th
o
s
e
th
at
ex
cl
u
s
iv
ely
d
elv
e
in
t
o
m
ath
em
ati
cs
ed
u
ca
tio
n
,
as
well
as
th
o
s
e
with
a
b
r
o
ad
e
r
m
u
ltid
is
cip
lin
ar
y
f
o
c
u
s
.
T
ak
in
g
th
e
lead
is
th
e
J
o
u
r
n
al
o
f
E
x
p
er
im
en
tal
C
h
ild
Ps
y
ch
o
lo
g
y
,
f
ea
tu
r
in
g
a
t
o
tal
o
f
173
171
172
172
177
172
173
173
181
158
140
150
160
170
180
190
N
u
m
be
r o
f P
ub
l
i
c
a
ti
o
ns
20
14
20
15
20
16
20
17
20
18
20
19
20
20
20
21
20
22
20
23
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
.
2
,
Ap
r
il
20
25
:
1
2
7
3
-
1
28
5
1278
4
8
ar
ticles
th
at
ce
n
ter
o
n
m
at
h
em
atica
l
ab
ilit
ies
in
th
e
y
o
u
n
g
d
em
o
g
r
a
p
h
ic.
B
r
o
a
d
ly
s
p
ea
k
in
g
,
t
h
ese
jo
u
r
n
als
ad
d
r
ess
m
u
ltip
le
f
ac
ets
o
f
m
ath
em
atica
l
ab
ilit
y
.
T
o
p
ics
s
p
an
d
ev
el
o
p
m
en
tal
p
s
y
ch
o
lo
g
y
,
ed
u
ca
tio
n
,
s
u
s
tain
ab
ilit
y
,
an
d
d
is
tin
ctio
n
s
at
an
in
d
iv
i
d
u
al
lev
el.
Su
c
h
a
s
p
r
ea
d
u
n
d
er
s
co
r
es
th
e
s
ig
n
if
ican
ce
o
f
ad
o
p
tin
g
a
co
m
p
r
e
h
en
s
iv
e
p
e
r
s
p
ec
tiv
e
wh
en
s
ee
k
in
g
to
co
m
p
r
eh
e
n
d
an
d
n
u
r
tu
r
e
m
ath
em
atica
l
ab
ili
ties
ac
r
o
s
s
d
if
f
er
en
t
s
ce
n
ar
io
s
.
Giv
en
th
is
ar
r
a
y
o
f
p
u
b
licatio
n
s
,
t
h
e
ac
ad
em
ic
a
n
d
p
r
o
f
ess
io
n
al
co
m
m
u
n
ity
is
well
-
eq
u
ip
p
e
d
with
d
iv
er
s
e
s
o
u
r
ce
s
to
ta
p
in
to
th
e
m
o
s
t
r
ec
e
n
t
f
i
n
d
in
g
s
in
th
e
r
ea
lm
o
f
m
ath
em
atica
l
a
b
ilit
y
r
esear
ch
.
A
m
o
r
e
v
is
u
al
r
ep
r
esen
tatio
n
o
f
th
is
d
a
ta,
in
th
e
s
h
ap
e
o
f
a
p
ie
ch
ar
t,
ca
n
b
e
f
o
u
n
d
in
Fig
u
r
e
3
.
Fro
m
Fig
u
r
e
3
,
th
e
J
o
u
r
n
al
o
f
E
x
p
er
im
en
tal
C
h
ild
Ps
y
ch
o
lo
g
y
is
a
lead
in
g
s
o
u
r
ce
f
o
r
ar
ticles
o
n
m
ath
em
atica
l
ab
ilit
ies,
co
m
p
r
i
s
in
g
1
8
.
6
%
o
f
th
e
p
u
b
licatio
n
s
,
h
ig
h
lig
h
tin
g
its
s
ig
n
if
ican
t
r
o
le
in
th
is
r
esear
ch
ar
ea
.
PLo
S
ONE
f
o
llo
ws,
ac
c
o
u
n
tin
g
f
o
r
1
2
.
4
%,
r
ei
n
f
o
r
ci
n
g
its
im
p
o
r
tan
ce
in
d
is
s
em
in
atin
g
r
esear
ch
r
elate
d
to
m
ath
em
atica
l
ab
ilit
y
.
Oth
er
jo
u
r
n
als
in
clu
d
in
g
Dev
el
o
p
m
en
tal
Scien
ce
,
Fro
n
tier
s
in
Ps
y
ch
o
lo
g
y
,
J
o
u
r
n
al
o
f
E
d
u
ca
tio
n
al
Ps
y
ch
o
l
o
g
y
,
Su
s
tain
ab
ilit
y
(
Switzer
lan
d
)
,
J
o
u
r
n
al
o
n
Ma
t
h
em
atics
E
d
u
ca
ti
o
n
,
Dev
elo
p
m
en
tal
Ps
y
ch
o
lo
g
y
,
E
a
r
ly
C
h
ild
h
o
o
d
R
esear
ch
Qu
ar
ter
ly
,
an
d
L
ea
r
n
in
g
a
n
d
I
n
d
iv
id
u
al
Dif
f
er
en
ce
s
,
th
o
u
g
h
co
n
tr
ib
u
tin
g
lo
wer
p
er
ce
n
tag
e
s
,
s
till
p
lay
a
cr
u
cial
r
o
le
in
th
e
o
n
g
o
i
n
g
s
tu
d
y
o
f
m
ath
em
ati
ca
l a
b
ilit
ies.
Fro
m
th
e
an
aly
s
is
,
it is
ev
id
en
t th
at
th
e
J
o
u
r
n
al
o
f
E
x
p
er
im
e
n
tal
C
h
ild
Ps
y
ch
o
lo
g
y
is
a
p
iv
o
tal
s
o
u
r
ce
f
o
r
r
esear
ch
o
n
m
at
h
em
atica
l
ab
ilit
ies.
T
h
is
jo
u
r
n
al'
s
lea
d
in
g
p
o
s
itio
n
ca
n
b
e
attr
ib
u
t
ed
to
its
f
o
cu
s
o
n
co
m
p
r
eh
e
n
s
iv
e
em
p
i
r
ical
s
tu
d
ies
th
at
ex
p
l
o
r
e
c
o
g
n
itiv
e
d
ev
elo
p
m
e
n
t
p
r
o
ce
s
s
es,
in
clu
d
in
g
m
ath
em
atica
l
s
k
ills
,
in
ch
ild
r
en
.
T
h
e
jo
u
r
n
al'
s
r
ig
o
r
o
u
s
p
ee
r
r
ev
ie
w
p
r
o
ce
s
s
an
d
its
r
ep
u
tati
o
n
f
o
r
p
u
b
lis
h
in
g
m
eth
o
d
o
l
o
g
ically
s
o
u
n
d
r
esear
ch
co
n
tr
ib
u
te
to
its
p
r
o
m
in
e
n
ce
in
th
e
f
ield
.
Fo
llo
win
g
c
lo
s
ely
,
PLo
S
ONE
ac
co
u
n
ts
f
o
r
1
2
.
4
%
o
f
th
e
a
r
ticles,
h
ig
h
lig
h
tin
g
its
r
o
le
i
n
b
r
o
ad
ly
d
is
s
em
in
atin
g
d
iv
er
s
e
a
n
d
in
ter
d
is
cip
lin
ar
y
r
esear
ch
o
n
m
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em
atica
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ab
il
ities
.
Oth
er
jo
u
r
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s
u
ch
as
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elo
p
m
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tal
Scien
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Fro
n
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y
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o
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o
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u
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tio
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y
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g
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d
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Switzer
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d
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th
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g
h
c
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n
tr
ib
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tin
g
s
m
aller
p
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tag
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s
till
s
ig
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if
ican
tly
im
p
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t
th
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f
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y
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v
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s
asp
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ts
o
f
ed
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tio
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d
p
s
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ch
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lo
g
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p
m
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n
t
th
at
in
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e
s
tu
d
ies
o
n
h
o
w
ch
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r
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lear
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an
d
d
ev
elo
p
m
ath
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l
s
k
ills
.
E
ac
h
jo
u
r
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al'
s
u
n
iq
u
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ed
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r
ial
f
o
cu
s
an
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co
m
m
itm
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t
to
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t
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s
u
r
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th
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th
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ic
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s
e
o
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m
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l a
b
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m
th
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am
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co
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ar
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a
n
u
m
b
er
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f
jo
u
r
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als
th
at
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lay
a
n
im
p
o
r
tan
t
r
o
le
in
th
e
p
u
b
licatio
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o
f
ar
ti
cles
r
elate
d
to
m
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atica
l
ab
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.
T
h
is
h
ig
h
lig
h
ts
th
e
wid
esp
r
ea
d
cu
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io
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ity
ac
r
o
s
s
m
u
ltip
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d
is
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lin
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m
p
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n
d
in
g
an
d
en
h
an
cin
g
m
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ab
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in
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iv
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e
s
ettin
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s
.
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ch
in
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ig
h
ts
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le
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ca
to
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r
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m
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m
ater
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h
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jo
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T
ab
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2
.
T
h
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jo
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th
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r
ticles o
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m
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b
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r
o
m
2
0
1
4
t
o
2
0
2
3
Jo
u
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a
l
N
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r
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p
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m
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t
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C
h
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c
h
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g
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48
P
Lo
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32
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29
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y
27
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P
sy
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24
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24
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To
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8
Fig
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19%
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in
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ticle
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[
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in
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[
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d
o
c
u
m
en
t.
Fro
m
th
e
an
aly
s
is
o
f
1
8
3
au
th
o
r
s
,
o
n
l
y
a
p
air
o
f
a
u
th
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s
s
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m
ed
to
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av
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a
clo
s
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co
n
n
ec
tio
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.
T
h
is
h
ig
h
lig
h
ts
a
p
o
ten
tial
d
ef
icien
cy
i
n
co
llab
o
r
atio
n
with
in
th
e
r
ea
l
m
o
f
m
ath
em
atica
l
ab
ilit
y
d
u
r
in
g
th
e
tim
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f
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am
e
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s
er
v
ed
.
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h
e
d
ata
s
u
g
g
ests
th
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two
au
th
o
r
s
m
ay
h
av
e
w
o
r
k
ed
to
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o
n
a
p
ar
ticu
lar
p
iece
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estab
lis
h
in
g
a
s
tr
o
n
g
b
o
n
d
b
etwe
en
th
em
.
T
h
is
s
ig
n
if
ies
th
at
co
-
o
p
er
ati
o
n
in
m
ath
em
atica
l
ab
ilit
y
r
e
s
ea
r
ch
ap
p
ea
r
s
t
o
b
e
in
f
r
e
q
u
en
t,
with
v
e
r
y
f
ew
au
th
o
r
s
jo
in
in
g
f
o
r
ce
s
.
T
h
is
s
ca
r
city
o
f
co
llab
o
r
ativ
e
ef
f
o
r
ts
in
th
e
ex
p
lo
r
atio
n
o
f
m
ath
em
atica
l
ab
ilit
y
ca
n
lead
to
s
ev
er
al
r
ep
er
cu
s
s
io
n
s
.
Firstl
y
,
lim
ite
d
co
llab
o
r
atio
n
co
u
ld
h
in
d
er
th
e
e
x
p
an
s
iv
e
s
h
ar
in
g
o
f
i
d
ea
s
,
in
s
ig
h
ts
,
an
d
co
m
p
r
eh
e
n
s
iv
e
u
n
d
er
s
tan
d
in
g
in
th
is
ar
en
a.
M
o
r
e
in
clu
s
iv
e
an
d
d
iv
e
r
s
if
ied
co
llab
o
r
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s
co
u
ld
f
o
s
ter
v
ar
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v
iewp
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in
ts
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f
r
esh
id
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an
d
g
r
o
u
n
d
b
r
ea
k
in
g
f
in
d
in
g
s
wh
en
it
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m
es
to
u
n
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er
s
tan
d
i
n
g
an
d
cu
ltiv
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g
m
ath
em
atica
l
ab
ilit
ies.
Seco
n
d
ly
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th
is
lac
k
o
f
c
o
llab
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r
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m
ig
h
t
also
im
p
ed
e
th
e
p
r
o
g
r
es
s
o
f
th
is
d
o
m
ai
n
in
its
en
tire
ty
.
E
x
p
a
n
d
ed
team
wo
r
k
ca
n
s
p
u
r
m
o
r
e
a
d
v
an
ce
m
en
ts
an
d
p
iv
o
tal
r
ev
elatio
n
s
in
m
ath
em
atica
l
ab
ilit
y
r
esear
ch
.
T
o
b
o
ls
ter
co
llab
o
r
atio
n
i
n
m
a
th
em
atica
l
ab
ilit
y
r
esear
ch
,
f
o
s
ter
in
g
d
ialo
g
u
e
an
d
p
ar
tn
er
s
h
ip
s
am
o
n
g
s
ch
o
lar
s
in
th
is
d
o
m
ain
is
p
ar
am
o
u
n
t.
Ven
u
es
s
u
ch
as
s
y
m
p
o
s
iu
m
s
,
s
em
in
ar
s
,
a
n
d
c
o
llo
q
u
ia
ca
n
ac
t
as
ca
taly
s
ts
to
s
p
ar
k
co
llab
o
r
ati
o
n
am
o
n
g
s
ch
o
lar
s
with
alig
n
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in
ter
ests
an
d
s
k
ills
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Fu
r
t
h
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m
o
r
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,
s
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u
r
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g
f
u
n
d
in
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b
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f
r
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m
i
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s
titu
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th
at
p
r
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m
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co
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d
k
n
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s
s
u
r
r
o
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n
d
in
g
m
ath
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m
atica
l a
b
ilit
ies.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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[
1
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A
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