Int
ern
at
i
onal
Journ
al of
R
obot
ic
s
and
Autom
ati
on (I
JRA)
Vo
l.
8
,
N
o.
4
,
D
ece
m
ber
201
9
,
pp.
269
~
276
IS
S
N:
20
89
-
4856
,
DOI: 10
.11
591/
i
jra
.
v
8
i
4
.
pp
269
-
276
269
Journ
al h
om
e
page
:
http:
//
ia
escore.c
om/j
ourn
als/i
ndex.
ph
p/IJRA
Model of
absorb
ed
ga
mm
a radi
ation in
the in
teract
ion with
rock fo
rm
atio
n
A.
A. Az
ar
yan
1
,
A. N
. Gr
itse
nko
2
,
A
. A. Tr
achuk
1
,
V.
M.
Serebreni
k
ov
3
,
D
. V.
Sh
vet
s
1
*
1
Depa
rtment of
M
odel
ing and
S
oftwa
re
,
Kr
y
v
yy
Rih
Na
ti
ona
l
U
nive
rsit
y
,
Ukra
in
e
2
Stat
e
Educat
ion
a
l
Inst
it
u
t
ion
,
Kr
y
v
y
y
R
i
g
Na
ti
on
al
Univ
ersity
,
U
kra
ine
3
Depa
rtment of
Higher
Math
ema
ti
cs
and
Inform
a
ti
on
S
y
s
te
m
s
,
D
onet
sk National
Univer
sit
y
of
E
c
onom
ic
s a
nd
Trade
N
amed
after
M.
Tuga
n
-
Bar
anovsk
y
,
Ukrai
n
e
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
v
ed
A
pr
21
,
201
9
Re
vised
A
ug
22
,
2019
Accepte
d
Oct
6
,
201
9
The
art
i
cl
e
discu
ss
es
issues
of
improving
th
e
a
cc
u
racy
of
oper
at
io
nal
qu
al
i
t
y
cont
rol
of
iron
ore
in
m
ountai
n
ran
g
es.
The
r
e
was
proposed
the
use
of
the
absorbe
d
g
a
m
m
a
rad
ia
ti
on
i
ndic
a
tor
as
an
i
m
prove
m
ent
of
the
nu
cl
e
ar
ph
y
sics
m
et
hod
for
de
te
rm
ini
ng
the
iron
content
in
ore
m
ass
ar
e
proposed.
The
re
wer
e
obt
ai
ned
th
e
relat
i
onships
of
the
sensiti
vity
of
th
e
absorbe
d
gamm
a
rad
i
at
io
n
intensit
y
on
th
e
d
ista
n
ce
bet
wee
n
th
e
d
et
e
ct
or
and
the
i
rra
di
ated
s
urfa
ce
,
as
wel
l
as
on
th
e
dist
an
ce
b
et
we
en
th
e
source
and
the
d
et
e
ct
or
of
g
amm
a
rad
iation
.
Ke
yw
or
d
s
:
Ab
s
orbe
d gam
m
a ray
Iron ore
Op
e
rati
onal
contr
ol
Copyright
©
201
9
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
D.
V. S
hv
et
s
,
Dep
a
rtm
ent o
f M
od
el
in
g
a
nd
So
ft
war
e
,
Kr
yvyy
Ri
h N
at
ion
al
Uni
ver
s
it
y
,
11
Vita
li
ya
Mat
us
evica st
r.
,
K
ryvyy
Ri
h 500
27
,
Ukraine
.
Em
a
il
:
i.a
m
.d
m
it
riy
.sh
vets@
gm
ail.co
m
1.
INTROD
U
CTION
Current
re
quir
e
m
ents
f
or
t
he
qu
al
it
y
of
m
ined
i
ron
ores
in
di
cat
e
the
nee
d
f
or
bo
t
h
m
or
e
a
ccur
at
e
an
d
op
e
rati
onal
det
erm
inati
on
of
the
ir
on
co
ntent
in
them
.
On
e
of
t
he
ways
to
i
m
pr
ove
the
op
erati
on
al
c
ontr
ol
of
the
iro
n
c
on
te
nt
in
the
ore
m
a
ss
is
the
use
of
loggin
g
s
onde
(LS)
in
ro
ll
er
well
s.
I
n
real
c
ondit
ions
,
m
ea
su
ri
ng
the
iro
n
co
nten
t
ta
kin
g
int
o
ac
count
al
l
the
in
flue
ncin
g
facto
rs
on
the
acc
uracy
of
co
ntr
ol
is
qu
it
e
a
chall
eng
e
.
On
e
of
the
possible
ways
to
ov
e
rc
om
e
the
se
dif
ficult
ie
s
is
to
us
e
the
r
esult
of
t
he
in
te
racti
on
of
ga
m
m
a
rad
ia
ti
on
with
iro
n
o
res
as
a
source
of
i
nfo
rm
ation
a
bout
the
i
ron
c
onte
nt.
H
ow
e
ve
r
,
t
he
inte
ns
it
y
of
the
gam
m
a
-
ray
fl
ux
ref
le
ct
ed
fro
m
the
ro
c
k
m
a
ss
us
ed
in
the
m
easur
em
ent
do
e
s
no
t
car
ry
en
ough
in
for
m
at
ion
about
t
he
i
ron
con
te
nt
,
since
this
fl
ux
is
rat
her
sm
al
l
and
char
act
e
r
iz
es
t
he
c
onte
nt
of
t
he
us
e
fu
l
com
pone
nt
on
ly
i
n
t
he
sur
face
la
ye
r
of
th
e
ar
ray.
I
n
t
his
re
gard
,
it
see
m
s
app
r
opriat
e
w
he
n
m
easur
i
ng
the
ir
on
c
on
te
nt
in
the
or
e
to
us
e
t
he
i
ntensity
of
the
fl
ux
of
abs
orbe
d
gam
m
a
rad
ia
ti
on
,
w
hic
h
is
m
uch
la
r
ge
r
tha
n
the
int
e
ns
it
y
of the
ref
le
ct
ed
f
lu
x of gam
m
a
r
a
diati
on
,
an
d l
arg
el
y cha
ract
erizes t
he
i
ron c
on
te
nt w
it
hin
the ore
body.
An
al
ysi
s
of
t
he
res
ults
of
stu
dies
an
d
publi
cat
ion
s
on
the
con
t
ro
l
of
iro
n
co
ntent
in
ore
arr
ay
s
us
in
g
LS in well
s show
e
d
that i
n
m
os
t case
s in
s
uff
ic
ie
nt att
ention i
s p
ai
d
to t
he
issues
of
m
easu
rem
ent accur
ac
y [1
]
.
Nu
cl
ea
r
ph
ysi
c
s
m
et
ho
ds
for
determ
ining
th
e
co
ntent
of
th
e
us
e
fu
l
com
po
ne
nt
i
n
the
or
e
we
re
c
onside
red
i
n
works
[
2
-
4]
,
w
her
e
at
te
m
pts
wer
e
m
ade
to
i
m
pr
ov
e
the
ac
cur
acy
of
m
ea
su
rem
ents
depend
i
ng
on
t
he
nu
m
ber
of
gam
m
a
qu
a
nta
ref
le
ct
ed
f
ro
m
the
su
rf
a
c
e
of
the
a
bsor
ber.
I
n
w
ork
[
5]
,
the
pa
ram
e
te
rs
of
sci
ntil
la
ti
on
sens
or
s
for
re
cordin
g
scat
te
red
gam
m
a
qu
anta
a
re
co
nsi
der
e
d.
Also
in
[
3
]
,
a
m
ath
em
atical
m
o
del
wa
s
dev
el
op
e
d
f
or
determ
ining
th
e
iro
n
c
onte
nt
in
the
ore
by
r
egiste
rin
g
scat
t
ered
gam
m
a
qu
anta.
T
he
a
ut
hors
of
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2089
-
4856
I
nt
J
R
ob
&
A
uto
m
,
Vo
l.
8
,
No.
4
,
Decem
ber
2019
:
269
–
276
270
this
arti
cl
e
pro
po
s
ed
acco
unti
ng
f
or
ab
sorbe
d
gam
m
a
rad
i
at
ion
in
the
irr
adiat
ed
m
at
erial
[
6
]
,
w
hich
a
ll
ow
s
increasin
g
t
he a
ccur
acy
of de
te
rm
inati
on
of t
otal i
ron
i
n
the
or
e
un
d
er
stu
dy
.
In
a
ddit
ion
to
nu
cl
ea
r
physi
c
s
m
e
tho
ds
f
or
determ
ining
th
e
ir
on
co
ntent
,
m
agn
et
om
et
er
[
7
-
9
]
a
nd
ultraso
nic
m
eth
ods
[
10
-
12
]
a
re
kn
own.
H
oweve
r
,
t
he
m
a
gn
et
om
et
er
m
e
thod
al
lo
ws
de
te
rm
ining
th
e
con
te
nt
of
only
m
agn
e
ti
c
iro
n
in
the
stu
died
r
oc
k
m
ass
an
d
it
is
dif
ficult
t
o
use
ultras
onic
c
on
t
ro
l
w
hen
l
ogging
exp
l
os
ive
w
el
l
s.
2.
RESEA
R
CH MET
HO
D
The
ai
m
of
t
he
w
ork
is
to
i
m
pr
ov
e
t
he
ac
cur
acy
of
op
e
rati
on
al
qual
it
y
con
t
ro
l
of
m
ineral
ra
w
m
at
erial
s
by
us
ing
the
i
ntensit
y
of
abs
orbe
d
gam
m
a
rad
ia
ti
on.
To
ac
h
ie
ve
this
go
al
,
t
he
f
ollow
i
ng
ta
s
ks
wer
e
form
ulate
d:
‐
The
c
hoic
e of t
he param
et
ers
of the
ge
om
et
r
y of m
easur
ing t
he
inte
ns
it
y o
f gam
m
a rad
ia
ti
on
;
‐
Dev
el
op
m
ent of a
functi
onal
s
chem
e fo
r
t
he
i
nteracti
on
of gamm
a rad
ia
ti
on
with a
substa
nce;
‐
Dev
el
op
m
ent of a m
a
the
m
at
ical
m
od
el
of t
he
interact
io
n of
gam
m
a rad
ia
ti
on w
it
h a s
ubsta
nce.
In
m
od
er
n
c
onditi
on
s
of
i
ron
or
e
m
ining
,
s
uffici
ent
at
te
nti
on
s
hould
be
pa
id
to
issue
s
re
la
te
d
to
t
he
accuracy of
m
easur
i
ng
the
ir
on
c
on
te
nt
,
w
hi
ch
la
r
gely
de
pe
nd
s
on
the
res
ul
ts
of
t
he
intera
ct
ion
o
f
t
he
ga
m
m
a
-
rad
ia
ti
on f
l
ux
with the
roc
k
f
or
m
at
ion
.
An
a
naly
sis
of
the
gam
m
a
-
ra
diati
on
fl
ux
a
bsor
be
d
by
the
or
e
m
ass
,
wh
i
ch
is
m
uch
la
r
ger
tha
n
the
ref
le
ct
ed
gam
m
a
-
rad
ia
ti
on
flux
us
e
d
i
n
m
oder
n
de
vices
,
will
m
ake
it
possible
to
inc
r
ease
the
acc
uracy
of
m
easur
in
g
the
iro
n
c
onte
nt
in
the
or
e
.
As
one
of
the
ef
fecti
ve
ways
to
im
plem
ent
the
m
at
hem
atical
m
od
el
of
the
interact
io
n
of
g
am
m
a
rad
ia
ti
on
w
it
h
ir
on
or
e
,
wh
ic
h
wil
l
al
low
to
i
den
t
ify
the
m
ai
n
factor
s
i
nf
lue
nci
ng
the
process
of
m
ea
su
ri
ng
t
he
iro
n
con
te
nt
in
the
or
e
m
ass.
Du
e
to
the
fact
that
at
pr
ese
nt
co
nsi
der
a
ble
at
te
ntion
is
paid
to
co
ntr
ol
m
et
ho
ds
that
ens
ur
e
an
increase
i
n
the
eff
ic
ie
ncy
and
reli
abili
ty
of
the
pro
du
ct
io
n
process
[
13
-
14
]
,
these st
ud
ie
s
seem
to
be qu
i
te
r
el
eva
nt.
3.
RESU
L
TS
A
ND AN
ALYSIS
The
gam
m
a
-
ga
m
m
a
m
et
ho
d
ba
sed
on
t
he
ef
f
ect
of
the
i
nter
act
ion
of
lo
w
-
e
nergy
gam
m
a
-
qu
a
nta
with
a
su
bst
ance
is
us
e
d
to
m
easur
e
the
co
ntent
of
total
iro
n
in
t
he
ore.
T
he
c
ontr
olled
ore
m
ass
is
irrad
ia
te
d
,
a
nd
then
the
i
ntens
it
y
of
the
integra
te
d
flu
x
of
scat
te
red
gam
m
a
rad
ia
ti
on
(t
he
so
-
cal
le
d
C
om
pto
n
scat
te
r
ing)
is
recorde
d.
A
s
pe
ci
fic
featur
e
of
m
od
el
ing
the
m
easur
em
ent
process
is
to
buil
d
s
uch
a
m
od
el
that
,
with
c
entra
l
geo
m
et
ry
,
w
ou
ld
ta
ke
int
o
ac
count
t
he
de
pe
nd
e
nce
of
t
he
i
ntensity
of
th
e
abs
orbed
gam
m
a
-
rad
ia
ti
on
flux
on
the
ge
om
et
ric
par
am
et
ers:
the
distance
between
t
he
ra
dia
ti
on
s
ource
an
d
the
detect
or
,
the
distance
be
tween
the d
et
ect
or
a
nd the
r
e
flect
ing su
rf
ace
.
It is log
ic
al
to
beg
i
n
the
synth
esi
s o
f
the m
odel
as a g
a
uge of ir
on
c
ont
ent i
n
the
ore
with
well
-
kn
own
and
pro
ve
n
for
m
ulas
descr
ibi
ng
the
distrib
ut
ion
of
t
he
ga
m
m
a
-
rad
ia
ti
on
flu
x
in
the
m
edium
[1
5
].
A
di
agr
a
m
of the sim
ulate
d
inte
racti
on of
g
am
m
a rad
ia
tio
n wit
h a s
ubsta
nce is s
how
n
i
n
Fi
g
ure
1.
Figure
1.
The
s
chem
e o
f
int
e
r
act
ion
of g
am
m
a rad
ia
ti
on wi
th a s
ub
sta
nce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
R
ob
&
A
uto
m
IS
S
N:
20
89
-
4856
Mo
del o
f
absor
bed ga
mma
r
adiati
on in
the
interacti
on wi
th
...
(D
. V
. Shvet
s)
271
The
flo
w
of
ga
m
m
a
-
qu
anta
e
m
anates
from
a
point
B
in
t
he
f
or
m
of
a
ci
r
cular
c
one
with
a
s
ol
ution
ang
le
of
a
co
ne
2*α
.
Furthe
r
,
this
stream
re
aches
t
he
ir
ra
di
at
ed
surface
,
f
or
m
ing
a
“sp
ot
”
in
the
f
or
m
of
a
ci
rcle.
Each
point
of
this
“
s
po
t”
is
a
s
our
ce
of
seco
ndar
y
(r
eflect
ed
)
gam
m
a
rad
ia
ti
on
.
Re
flect
e
d
gam
m
a
rad
ia
ti
on
car
ries
the
nece
ssary
inf
or
m
at
ion
about
the
sta
te
of
t
he
ar
ray
,
w
hich
incl
udes
inf
or
m
at
ion
ab
ou
t
th
e
con
te
nt
of
ir
on
in
it
[
3
,
5
,
16
-
20
]
.
T
he
detect
or
locat
e
d
at
t
he
point
P
re
gi
ste
rs
a
nd
m
easur
es
th
e
i
ntens
it
y
of
gam
m
a
rad
ia
ti
on.
Accord
i
ng
to
the
schem
e
of
pro
pa
gation
of
gam
m
a
rad
ia
ti
on
,
pr
e
s
ented
i
n
Fi
g
ure
1
,
a
gam
m
a
-
qu
a
ntum
that
reache
d
an
ir
rad
ia
te
d
s
urface
at
a
point
C(
x
,
y)
,
from
an
gam
m
a
-
radi
at
ion
s
ource
w
it
h
a
n
intensit
y
Q
l
oc
at
ed
at
a
point
,
is rec
orde
d
as
d
xd
y
h
y
x
h
Q
y
x
dN
2
3
2
2
2
)
(
)
,
(
+
+
=
(1)
wh
e
re
Q
-
gam
m
a
rad
ia
ti
on
s
ource
i
ntensity
,
1/sec
,
h
-
distance
fro
m
ga
m
m
a
rad
ia
ti
on
s
ource
t
o
the
ir
rad
ia
te
d
su
r
face
,
m
,
dxdy
-
area ele
m
ent in Cartesi
an
coor
din
at
e syst
e
m
,
m
2
.
The
n
th
e
total
i
ntensity
o
f
the
g
am
m
a
rad
ia
ti
on
fl
ux r
eachi
ng
t
he
s
urface
is
f
ound b
y
i
nteg
rati
ng
ove
r
the r
e
gion
D
i
n t
he fo
rm
o
f
a c
ircl
e
,
2
3
2
2
2
)
(
h
y
x
d
x
d
y
h
Q
N
D
+
+
=
(2)
To
cal
culat
e
t
he
double
inte
gral
,
f
orm
ula
(2)
,
it
is
nece
ssary
to
reduce
it
to
re
peated
i
nteg
rals.
The
dom
a
in
of
integrati
on
D
i
s boun
de
d by a
circl
e
,
the
can
on
ic
al
e
quat
ion o
f
w
hic
h has t
he fo
rm
,
2
2
2
R
y
x
=
+
(3)
wh
e
re
R
-
the
r
a
diu
s
of the
circ
le
b
ou
nd
i
ng th
e “sp
ot”
on the
irr
a
diati
on sur
face
,
m
.
In the tra
ns
it
io
n
to
polar
co
ordinate
c
o
s
=
R
x
,
s
i
n
=
R
y
fo
rm
ula
(
3)
is
writ
te
n as
R
r
=
,
(
2
0
)
(4)
Accor
ding t
o
E
qu
at
io
n
(
4)
t
he i
ntegr
al
,
f
or
m
ula
(2)
ta
ke
s the
for
m
r
d
r
d
h
r
h
Q
N
D
2
3
2
2
)
(
1
+
=
(5)
wh
e
re
r
drdφ
a
rea
el
em
ent
in
pola
r
co
ordin
at
es
,
m
2
,
=
=
•
2
0
;
)
;
(
R
r
r
D
–
regi
on
of
inte
gr
at
ion
i
n
po
la
r
c
oord
i
nat
es.
To
cal
c
ulate
th
e double i
nte
gral
,
f
or
m
ula
(5)
,
we nee
d
to
r
e
duce it
to re
peated inte
gr
al
s.
G
i
ven the
integrati
on
bounda
ries
,
t
he doub
le
i
nteg
ra
l
,
f
or
m
ula
(5)
is
w
ritt
en
as
2
3
2
2
0
2
0
)
(
h
r
r
d
r
d
h
Q
N
R
+
=
(6)
By
integr
at
in
g
,
we
c
onsist
ently
f
in
d
r
d
r
h
r
h
Q
N
R
2
3
2
2
0
2
0
)
(
1
+
=
r
d
r
h
r
h
Q
R
2
3
2
2
0
)
(
1
2
+
=
2
2
3
2
2
0
)
(
1
dr
h
r
h
Q
R
+
=
=
=
+
−
=
R
h
r
h
Q
0
2
1
2
2
)
(
1
2
)
1
)
(
1
(
2
2
1
2
2
h
h
R
h
Q
−
+
−
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
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4856
I
nt
J
R
ob
&
A
uto
m
,
Vo
l.
8
,
No.
4
,
Decem
ber
2019
:
269
–
276
272
)
1
(
2
2
2
h
R
h
Q
N
+
−
=
.
(7)
Takin
g
i
nto
ac
c
ount
t
hat
the
rad
i
us
of
the
"
sp
ot"
ci
rcle
on
the
i
rr
a
diati
on
s
urface
is
f
ound
by
t
he
form
ula
tg
h
R
=
.
F
orm
ula (
7)
is c
on
sist
ently
co
nve
rted
t
o
)
1
(
2
2
2
2
h
tg
h
h
Q
N
+
−
=
)
1
1
1
(
2
2
tg
Q
+
−
=
)
c
o
s
1
(
2
2
−
=
Q
,
2
s
i
n
2
=
Q
N
.
(8)
The
n
the
inten
sit
y of
the
f
l
ow of
gam
m
a rad
i
at
ion
ref
le
ct
ed
from
the su
r
fac
e is f
ound
by the
form
ula
2
s
i
n
2
=
А
Q
M
(9)
wh
e
re
A
-
al
be
do c
oeffici
ent.
The
a
lbe
do
c
oe
ff
ic
ie
nt
A
sho
ws
t
he
fr
act
io
n
of
t
he
i
ntensit
y
of
the
fl
ux
in
ci
den
t
on
t
he
s
urfac
e
of
the
irrad
ia
ti
on
re
fl
ect
ed
from
the
irrad
ia
te
d
surf
ace
.
It
is
obvi
ou
s
t
hat
the
in
te
ns
it
y
of
the
abs
orbed
gam
m
a
-
ray
flu
x
ca
n be fo
und as t
he diffe
r
ence
in
for
m
ula
(
8)
a
nd
(9)
M
N
N
п
−
=
or
)
1
(
s
i
n
2
2
А
Q
N
п
−
=
(10)
In
tur
n
,
the
el
e
m
ent
of
the
i
ntensity
of
t
he
flo
w
of
gam
m
a
rad
ia
ti
on
,
def
i
ned
by
f
orm
ula
(1
)
,
is
a
so
urce
of sec
onda
ry g
am
m
a rad
ia
ti
on
.
In thi
s case
,
t
he
inte
ns
it
y of
t
he
sec
onda
ry g
am
m
a
-
ray fl
ux en
te
ring the
detect
or locat
e
d
at
a
point
P
f
rom
the point
)
,
(
y
x
С
is
fou
nd b
y t
he
f
orm
ula:
)
,
(
)
;
(
)
,
(
3
y
x
dN
y
x
L
S
h
A
y
x
dM
=
(11)
wh
e
re
L(x
,
y)
-
distance f
ro
m
point
C(
x
,
y)
to point
P
of
detect
or locat
io
n
,
m
,
S
-
detect
or area
,
m
2
.
Accor
ding
to
the
schem
e
of
pro
pa
gation
of
t
he
flo
w
of
ga
m
m
a
rad
ia
ti
on
,
pr
ese
nted
i
n
F
ig
ure
1
,
it
is
po
s
sible t
o rec
ord [2
1
]
2
2
2
)
(
)
,
(
H
y
l
x
y
x
L
+
−
+
=
(12)
wh
e
re
−
l
distanc
e b
et
wee
n ra
diati
on
s
ource a
nd
detect
or
,
m
.
Takin
g
i
nto
ac
count
(1)
a
nd (11)
,
the
form
ula (10) take
s the
for
m
:
d
x
d
y
Н
y
l
x
h
y
x
S
H
h
A
Q
y
x
d
М
5
,
1
2
2
2
2
2
2
))
)
(
)(
((
)
,
(
+
−
+
+
+
=
(13)
To
fi
nd
the
t
otal
intensit
y
of
t
he
sec
onda
ry
gam
m
a
ra
diati
on
flu
x
e
nterin
g
the
de
te
ct
or
,
it
is
necessa
ry to i
nt
egr
at
e
ov
e
r
t
he
r
e
gion
D
5
,
1
2
2
2
2
2
2
))
)
(
)(
((
H
y
l
x
h
y
x
d
xd
y
S
H
h
A
Q
М
D
+
−
+
+
+
=
(14)
To
cal
c
ulate
th
e
double
inte
gral
form
ula
(13)
,
we
nee
d
t
o
re
du
ce
it
to
rep
e
at
ed
inte
gr
al
s.
By
pa
ssin
g
to the p
olar
c
oor
din
at
es
,
the
integ
ral
f
or
m
ula
(
14)
is
reduc
ed
to
r
e
peated
integ
rals an
d
ta
kes
t
he
f
orm
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
R
ob
&
A
uto
m
IS
S
N:
20
89
-
4856
Mo
del o
f
absor
bed ga
mma
r
adiati
on in
the
interacti
on wi
th
...
(D
. V
. Shvet
s)
273
5
,
1
2
2
2
2
2
2
))
)
s
i
n
(
)(
((
H
r
l
с
o
s
r
h
r
r
d
r
d
S
H
h
A
Q
М
D
+
−
+
+
=
,
5
,
1
2
2
2
2
2
2
2
2
))
s
i
n
s
i
n
2
c
o
s
)(
((
H
r
r
l
l
r
h
r
r
d
r
d
S
H
h
A
Q
М
D
+
+
−
+
+
=
,
2
3
2
2
2
2
2
0
2
0
))
s
i
n
2
)(
((
H
l
l
r
r
h
r
r
d
r
d
S
H
h
A
Q
М
tg
h
+
+
−
+
=
(15)
Fo
rm
ula
(
15)
a
ll
ow
s
fin
ding
t
he
value
of
the
a
lbed
o
c
oeffic
ie
nt
by
the
m
agn
it
ude
of
the
intensit
y
of
the f
l
ux of
ref
l
ect
ed
gam
m
a rad
ia
ti
on
m
easu
red by t
he dete
ct
or
,
5
,
1
2
2
2
2
2
0
2
0
))
s
i
n
2
)(
((
H
l
rl
r
h
r
r
d
r
d
S
H
h
Q
М
A
tg
h
+
+
−
+
=
(16)
The
n
,
ta
king in
to acco
unt (
16)
,
f
or
m
ula (10) t
akes t
he
f
orm
:
)
))
s
i
n
2
)(
((
1
(
s
i
n
2
5
,
1
2
2
2
2
2
0
2
0
2
H
l
r
l
r
h
r
r
d
r
d
S
H
h
Q
M
Q
N
tg
h
п
+
+
−
+
−
=
(17)
An
al
ysi
s
of
f
orm
ula
(1
7)
s
ho
ws
t
hat
t
he
int
ensity
of
the
a
bs
or
bed
gam
m
a
-
ray
fl
ux
N
n
dep
e
nds
on
seve
n
va
riable
s:
Q
,
M
,
S
,
h
,
H
,
l
,
α
,
.
T
he
st
ud
y
of
f
or
m
ula
(17)
as
a
funct
ion
of
seve
n
va
riables
ca
us
es
certai
n
diff
ic
ulti
es.
Th
eref
or
e
,
the
quest
ion
of
the
num
ber
of
si
gn
i
ficant
va
riable
s
,
de
fine
d
as
c
om
bin
at
ion
s
of
seve
n
var
ia
bles
,
is
of
exce
ptio
nal
i
m
po
rta
nce.
The
a
ppli
cat
ion
of
the
t
heory
of
sim
il
ari
t
y
and
analy
s
is
of
dim
ension
s
[2
2
]
all
ow
s
us
t
o
r
epr
ese
nt the
fo
rm
ula (
17)
i
n
t
he fo
rm
)
))
ˆ
ˆ
s
i
n
ˆ
ˆ
2
ˆ
)(
1
ˆ
((
ˆ
ˆ
ˆ
ˆ
ˆ
1
(
s
i
n
2
ˆ
5
,
1
2
2
2
2
0
2
0
2
H
l
r
l
r
r
r
d
r
d
S
H
M
N
tg
п
+
+
−
+
−
=
(18)
wh
e
re
Q
N
N
п
п
=
ˆ
,
Q
M
M
=
ˆ
,
h
H
H
=
ˆ
,
h
r
r
=
ˆ
,
h
l
l
=
ˆ
.
An
al
ysi
s
of
form
ula
(1
8)
s
hows
that
the
num
ber
o
f
sign
ific
a
nt
var
i
ables is
five
t
ha
t i
s
,
dec
rease
d by tw
o u
nits [
2
3
].
In
order
t
o
c
om
par
e
the
m
agn
it
ud
e
s
of
t
he
ref
le
ct
ed
a
nd
a
bs
or
bed
gam
m
a
ra
diati
on
upon
i
rr
a
diati
on
of
t
he
sam
ples
unde
r
co
ndit
ion
s
of
ce
ntr
al
geo
m
et
ry
,
the
co
rr
es
pondin
g
num
erical
cal
culat
ion
s
wer
e
perform
ed.
F
or
this
pur
pos
e
,
the
rati
o
f
or
m
ula
(
15)
t
o
(10)
was
c
om
piled
,
al
lo
wing
est
im
ati
ng
th
e
corres
pondin
g value i
n
a
dim
e
ns
io
nless
form
2
3
2
2
2
2
0
2
0
2
))
ˆ
ˆ
s
i
n
ˆ
ˆ
2
ˆ
)(
1
ˆ
((
ˆ
ˆ
s
i
n
2
ˆ
ˆ
1
H
l
l
r
r
r
r
d
r
d
S
H
A
A
E
tg
+
+
−
+
−
=
(19)
wh
e
re
п
N
M
E
=
,
2
ˆ
h
S
S
=
.
Ca
lc
ulati
on
s
usi
ng
f
or
m
ula
(
19)
we
re
perf
orm
ed
us
in
g
th
e
Ma
thca
d
s
oft
war
e
pac
ka
ge
[
2
4
].
I
n
the
cal
culat
i
on
s
w
ere
ta
ke
n
s
uch
val
ues
of
the
pa
ram
et
ers
1
ˆ
=
H
,
7
,
0
ˆ
=
S
.
In
F
ig
ure
2
s
hows
the
dep
e
ndenc
e
diag
ram
E
cal
culat
ed by t
he
for
m
ula (
19
)
,
de
pendin
g o
n
th
e d
ist
ance
l
ˆ
,
f
or
diff
e
re
nt v
al
ue
s of
a
lbe
do
A
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2089
-
4856
I
nt
J
R
ob
&
A
uto
m
,
Vo
l.
8
,
No.
4
,
Decem
ber
2019
:
269
–
276
274
Figure
2. The
dep
e
ndent
of t
he rat
io
E
from
the
distance
l
at
v
ari
ou
s
v
al
ue
s of a
al
bedo
An
al
ysi
s o
f
t
he
gr
a
phs
s
how
n
in
Fig
ure
2
sho
ws
that
t
he
pro
portio
n
of
t
he
r
eflect
ed
gam
ma
-
ra
diati
on
intensit
y
,
as
c
om
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ed
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a
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d
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m
a
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rad
ia
ti
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en
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ti
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More
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e
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he
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ti
on
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le
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al
lo
ws
us
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e
t
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e
dient
t
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agn
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ud
e
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t
he
inte
ns
it
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bsor
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a
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on
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on
te
nt
i
n
t
he
ore
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le
ads
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s
m
al
le
r
error
s
.
Estim
at
ion
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t
he
i
ro
n
con
te
nt
in
the
or
e
s
houl
d
be
carried
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acc
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g
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t
he
f
or
m
ula
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,
wh
ic
h
,
us
in
g
i
nfor
m
at
ion
ab
ou
t
t
he
inte
ns
it
y
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e
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le
ct
e
d
ga
m
m
a
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ia
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flu
x
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akes
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lc
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ab
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l
ux
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t t
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al
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rm
ula
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te
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se
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ti
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t
he
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ntensity
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ab
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gam
m
a
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ray
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ux
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h
res
pect
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the
inten
sit
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th
e
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le
ct
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gam
m
a
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ray
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ux
m
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e
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detect
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F
or
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orm
ul
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18)
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te
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a
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.
REFERE
NCE
S
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Aza
r
y
an
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“
Mobile
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l
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Dete
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”
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ud
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“
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ra
torno
go
Metoda
Kont
rolj
a
Soder
zha
n
i
ja
Zhe
l
ez
a
Magnitnogo
V
Produktah
Obogashhenija
,
”
Kac
hestvo
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l
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nogo
S
yr
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ja
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Sb
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Nauc
h
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Trudov
.
Akad
e
m
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a
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kra
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6
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7
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9
1
l
ˆ
5
,
0
ˆ
=
H
1
ˆ
=
H
5
,
1
ˆ
=
H
dM
dN
п
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2089
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4856
I
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J
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&
A
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ai
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ste
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Eu
rope
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iz
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[16]
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ser
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pti
m
iz
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the
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Proce
ss
at
T
h
y
ss
enKrupp
S
t
ee
l
Europe
,
Duisburg
,
Germ
an
y
,
”
Proce
ed
ings
Iron
Ore
Confer
en
ce
,
Perth
W
A
,
The
Aus
tra
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