A Ekhtesasi
20
ﻛﺸﻮر از ﺧﺎرج ﺳﺮاﺳﺮي90 آﻣﻮزش ﻓﺮﻫﻨﮕﻲ ﻛﺎﻧﻮن1 اﺷﺘﺮاك) ﺑﺮﻗﺮار ﻫﻤﻮاره( وﺳﻄﻴﻦ ﻃﺮﻓﻴﻦ) ﺑﺮﻗﺮار ﻫﻤﻮاره( ) * ( ) log (log ) log (log ) (log ) (log A 2 5 2 5 2 5 2 2 + − = − = 101 - ﮔﺰﻳﻨﻪ ي» 2 « ) رﻳﺎﺿﻲ2 - ﺻﻔﺤﻪ ﻫﺎي79 ﺗﺎ84 ( درﺟﻪ ﺗﺎﺑﻊ دوم يc bx ax y + + = 2 اﺳﺖ ﻣﺜﺒﺖ ﻫﻤﻮاره. ﻫﺮﮔﺎه: D D > < ∆ a , ﻋﺒﺎرت در ﭘﺲ1 2 6 1 2 + + + − m x x ) m ( داﺷﺖ ﺧﻮاﻫﻴﻢ: ⎪ ⎩ ⎪ ⎨ ⎧ > ⇒ > − ⇒ > < − + − ⇒ < ∆ 1 1 1 1 2 4 6 2 m m a ) m ( ) m ( ) ( D D D D ⎪ ⎩ ⎪ ⎨ ⎧ > > − − ⇒ 1 40 4 8 2 m m m D ⎪ ⎩ ⎪ ⎨ ⎧ < > − + ⇒ > − − ⇒ 1 5 2 2 10 2 2 m ) m ( ) m ( m m D D ⎪ ⎩ ⎪ ⎨ ⎧ > > ⇒ > ⎯ ⎯→ ⎯ > − < ⇒ 1 5 2 2 5 2 5 2 m / m m m m ∪ 102 - ﮔﺰﻳﻨﻪ ي» 4 « ) ﺣﺴﺎﺑﺎن- ﺻﻔﺤﻪ ﻫﺎي71 و91 ( 1 1 1 − − − = ) fog ( of g ﺗـﺎﺑﻊ اﺑﺘـﺪا ﭘﺲfog ﻣـﻲ ﺗـﺸﻜﻴﻞ را ﻣﻌﻜـﻮس را آن ﺳـﭙﺲ و دﻫـﻴﻢ ﻣﻲ ﻛﻨﻴﻢ. ﺗﺎﺑﻊ ﺗﺸﻜﻴﻞ ﺑﺮايfog داﻣﻨﻪ از ﺗﺎﺑﻊ يg ﻣﻲ ﺷﺮوع ﻛﻨﻴﻢ. fog ) , ( ) ( f )) ( g ( f : x ∈ ⇒ = = = 2 2 2 1 2 2 fog ) , ( ) ( f )) ( g ( f : x ∈ ⇒ = = = 3 3 3 2 3 3 fog ) , ( ) ( f )) s ( g ( f : x ∈ ⇒ = = = 5 5 5 4 5 ﺗﺎﺑﻊ ﭘﺲfog اﺳﺖ زﻳﺮ ﺻﻮرت ﺑﻪ: { } ) , ( , ) , ( , ) , ( fog 5 5 3 3 2 2 = ﺗﺎﺑﻊ ﻧﻬﺎﻳﺖ در و1 − ) fog ( ﻣﻲ را ﻳﺎﺑﻴﻢ: { } ) , ( , ) , ( , ) , ( ) fog ( 5 5 3 3 2 2 1 = − 103 - ﮔﺰﻳﻨﻪ ي» 2 « ) رﻳﺎﺿﻲ2 - ﺻﻔﺤﻪ ﻫﺎي169 و170 ( ﻣﺎﺗﺮﻳﺲ در⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = d c b a A دﺗﺮﻣﻴﻨﺎن، A ﺑﺮاﺑﺮ ﺑﺎ اﺳﺖ: bc ad A − = ﻣﺎﺗﺮﻳﺲ در ﭘﺲ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 5 2 2 5 log log log log A دارﻳﻢ: آن از ﻛﻪ ﺟﺎb a log b log a log , ab log b log a log = − = + دارﻳﻢ: 5 2 1 5 2 10 2 5 1 / log / log log log A * = × = × = ⎯→ ⎯ 104 - ﮔﺰﻳﻨﻪ ي» 4 « ) ﺣﺴﺎﺑﺎن- ﺻﻔﺤﻪ ﻫﺎي2 و5 ( ﺧﻮاﺳﺘﻪ ﺟﻤﻼت ﻣﺠﻤﻮع ﻣﺴﺄﻟﻪ ي7 a ﺗﺎ18 a اﺳﺖ ؛ ﻳﻌﻨﻲ: 18 8 7 a ... a a S + + + = ﻛـﻪ اﻳﻦ ﺑﻪ ﺗﻮﺟﻪ ﺑﺎ6 15) n ( n S n − = ﻣﺤﺎﺳـﺒﻪ ﺑـﺮاي دارﻳـﻢ را يS ﺟﻤﻠـﻪ ﺷﺶ ﻣﺠﻤﻮع اﺳﺖ ﻛﺎﻓﻲ ﻣﺠﻤـﻮع از را اول ي18 ﺟﻤﻠـﻪ اول ي ﻛﻨﻴﻢ ﻛﻢ. ﺑﻨﺎﺑﺮاﻳﻦ: 6 15 6 6 6 15 18 18 6 18 ) ( ) ( S S S S − − − = ⇒ − = 18 9 9 = − − = ) ( 105 - ﮔﺰﻳﻨﻪ ي» 1 « ) ﺣﺴﺎﺑﺎ ن- ﺻﻔﺤﻪ ﻫﺎي130 ﺗﺎ132 ( { } f g fog D ) x ( g D x D ∈ ∈ = داﻣﻨﻪ اﺑﺘﺪا ﺑﻨﺎﺑﺮاﻳﻦ ﺗﻮاﺑﻊ يf وg ﻣﻲ را ﻳﺎﺑﻴﻢ: 2 2 1 1 2 1 1 2 1 ≤ ≤ ⇒ ≤ − ≤ − ⇒ − = − x x ) x ( sin ) x ( f D 1 ≤ ≤ ⇒ x D R D x x ) x ( g g = ⇒ + = 2 2 1 ﺑﻨﺎﺑﺮاﻳﻦ: ⎪ ⎪ ⎭ ⎪ ⎪ ⎬ ⎫ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ∈ + ∈ = D ) * ( fog ] , [ x x R x D 1 1 2 2 اﻳﻦ ﺑﺮاي راﺑﻄﻪ ﻛﻪ ي) * ( ﺑﺮﻗﺮا ﺑﺎﺷﺪ ر، ﺑﺎﻳﺪ: ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ + ≤ ⎯ ⎯ ⎯ → ⎯ ≤ + ≥ + ⇒ ≤ + ≤ > + 1 1 1 1 1 1 2 2 1 2 2 2 2 2 2 2 x x x x x x x x x D D D ﺗﺎﺑﻊ ﻧﺘﻴﺠﻪ درfog ﻫﺮ ازاي ﺑﻪR x ∈ ﻣﻲ ﺗﻌﺮﻳﻒ و ﺷﻮدR D fog = . ﻳﺎدآوري: ﺗﺎﺑﻊ درu sin ) x ( f 1 − = داﻣﻨﻪ ﻧﺎﻣﻌﺎدﻟـﻪ ﺣـﻞ از ﺗـﺎﺑﻊ ي ي1 ≤ u ﻣﻲ دﺳﺖ ﺑﻪ آﻳﺪ. 106 - ﮔﺰﻳﻨﻪ ي» 3 « ) ﺣﺴﺎﺑﺎن- ﺻﻔﺤﻪ ﻫﺎي71 ﺗﺎ77 ( ) * ( x ) x ( f 2 2 − − = ﺗـﺸﻜﻴﻞ ﺑـﺮاي)) x ( f ( f ﻫـﺮ ﺟـﺎي ﺑـﻪx ﺗـﺎﺑﻊ درf ، ) x ( f ﻗـﺮار را ﻣﻲ دﻫﻴﻢ: 2 2 2 2 2 2 − − − = − − − − = ⎯→ ⎯ x x )) x ( f ( f ) * ( ﻣﻲ داﻧﻴﻢu u , u u = − = ﺑﻨﺎﺑﺮاﻳﻦ اﺳﺖ: ) x ( f ) * ( x )) x ( f ( f 2 2 − − = ⇒ 107 - ﮔﺰﻳﻨﻪ ي» 2 « ) ﺣﺴﺎﺑﺎن- ﺻﻔﺤﻪ ﻫﺎي71 ﺗﺎ77 ( اﻳﻦ ﺑﻪ ﺗﻮﺟﻪ ﺑﺎ ﻛـﻪ} , ( 2 2 αβ β α ﻣﺠﻤﻮﻋـﻪ ﺟـﻮاب ي ﻣﻌﺎدﻟـﻪ ﻫـﺎي يD = − + 1 8 2 kx x ﻣﺤﺎﺳـﺒﻪ ﺑـﺮاي ﻫـﺴﺘﻨﺪ ﻣﻘـﺪار يk اﺳـﺖ ﻛـﺎﻓﻲ رﻳﺸﻪ ﻣﺠﻤﻮع ﺑﻴﺎﺑﻴﻢ را ﻫﺎ: 8 2 2 k a b S − = αβ + β α ⇒ − = ′ ) * ( k ) ( ) ( 8 − = β + α αβ ⇒ آن از اﻣﺎ ﻛـﻪ ﺟـﺎα وβ رﻳـﺸﻪ ﻣﻌﺎدﻟـﻪ ﻫـﺎي يD = − − 1 3 2 2 x x ﻫﺴﺘﻨﺪ، ﺑﻨﺎﺑﺮاﻳﻦ: ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ − = αβ = − − = β + α 2 1 2 3 2 3 ﭘﺲ: 6 8 2 1 2 3 = ⇒ − = − ⎯ ⎯→ ⎯ k k ) ( ) * ( ﺳﺮاﺳﺮ ﻛﺸﻮر از ﺧﺎرج ي90 رﻳﺎﺿﻴﺎت
description
A Ekhtesasi
Transcript of A Ekhtesasi
-
1 09
( )
( )
==+ 22 525252 Agol()gol()gol(gol)gol(gol)(*)
(48 97 -2 ) 2 -101 . 2 =++ yxaxbc
,a DD : : (m)xxm +++ 2 1621
>>>>
12 8404
m D mm
+>
12 201225
m DD mm(m)(m)
>>>
1225
5225
m
mmmm/
(19 17 -) 4 -201 gfo(gof) = 111
gof . g gof .
221222 === x:f(g())f()(,)gof 332333 === x:f(g())f()(,)gof 54555 === x:f(g(s))f()(,)gof
: gof =223355 gof(,),(,),(,)} {
: (gof)1 = 1223355 (gof)(,),(,),(,)} {
(071 961 -2 ) 2 -301
=cdab
: A A
= Adacb
25 =52
golgolgolgol
: A
b : +== golagolbgolba,golagolbgola
20125125 === *Agolgolgol/gol/ 1 5
(5 2 -) 4 -401 : a81 a7
=+++ Saa...a 7881 6
nSn(n)51 S =
81 :.
6 6651
6818151
816 == SSSS()()
() == 9981
(231 031 -) 1 -501 = DxDg(x)D gofgf} {
: g f
D f(x)nis(x)xx = 121121122 Dx 1
DR x
+= g g(x)x2 =
2
1
:
=+
D
(*)
[,] gofx
1 DxRx21
2
: (*)
++
+
+
11 +>1
112122 1
22
22
22
xxx
xx
x
x
x
D x
D D
.= gofDR xR gof =1 f(x)nisu :
. u1 (77 17 -) 3 -601
= 22 f(x)x(*) f(x) f x f(f(x))
:
(*)f(f(x))xx == 222222 : == uu,uu
= 22 f(f(x))x(*)f(x) (77 17 -) 2 -701
22 (,} k xxk 2 81 +=D
:
8 k 22
a =+= Sb
8 ()()k(*) +=
xx 2 231 =D :
=+==
21
23
23
286 :1
2 (*)()kk == 3
09
-
09 2
(921 421 79 29 -) 3 -801
=+
4144 f(x)xnisxf(x)socx =+
: socu 11
1414444
socxsocx
1414414 socx(*) +
+
f f>D (*) .
= yx f f1 f : .
=D
=
44 f(x)xxnisxxnisx =+
== 44 xkxk
19 [,] 4 3 f1 f . D48 {,,} .
(561 161 -) 4 -901milf(x)f(a) = xa
xa=
.
==DD
ax
xx
x=D f(x)nis
:
=
=f()a
:x
milf(x)milnisxx
D DD
. x=D f (181 -) 1 -011
x= :
===
221
f() xf()
= :yf()f()(x)(*) . D2 A(,)
D (*)()() == 21212 222 211f() ===D
:
22 SCBA == 22
(721 621 -) 3 -111 = xC f
:
. (921 421 -) 4 -211
nisxnisxnisx += 2 321 = 3122 nisxnisxnisx(*)
: 222122 nispnisqnispqsocpq,nisxsocx
=+= 2 :
22 (*)nisxxsocxxsocx 3
2= 23
+
= 222 nisxsocxsocx 222221 nisxsocxsocxsocx(nisx) == DD
=+
=+==
==+=+
62526
2211
22224
xk
xknisxnisx
socxxkxk
D
D
: D2 [,]
=
=
=
656
47
45
43
4
x
x
x,,,
. 6 (52 81 -) 2 -311
:
2 1
1nn ++=+=
milnnn
milnnn
89 : 1
891
2121
891
21
1++ 13131313 271612371271333
xKKK =
-
9 09
y
(15 83 1 ) 3 -651
.
mg N1
N2 :
NN NN
natN30806 natgm
1 35084111
D ====
1 (N) : 1 (N)
== 1106 NNN
(32 61 1 ) 2 -751
:
(t)i(t)j td =+==+ 3263 232 r(t)itjVdr
: =2 ts ==+ 22121 tsVij
x =2 ts :
21154D ==== 21
x
y
VV
nat
(61 31 1 ) 1 -851
:
sVm
V/
gV
D === 240142 t DD
36 /s
:s DD =+=+= 013663 VtgVV()(/)Vm
:
sVm
sVm
VV()266 V
6342== 2
D =+=+
(31 3 1 ) 1 -951 =4 ts :
x :
42 433
s DD =+=+= VtaVaam
t :
434 3
21
2 DD xtaVtxx()tt =++=++ 22 1
834 xtt =++ 2 3
883844 tsxxm = =++= 82 3
:
) =4 ts . (
x
=8 ts t=D .
(33 72 1 ) 4 -061
=
g(Vnis)
2 H2
D
. (V.nis)
09
-
09 01
d
=
g(Vnis)
D t 2
(1 )
( 3 )
( 3)
( 3) ( 4 )
3 (.2 )
(15 83 1 ) 2 -161
. F :
2 == FaMFgMaM Mgk
ag3 FM(ag)MF
001201
+= 222002 =+=+=
(82 91 1 ) 3 -261 :
=+ Cab 2222 Cabbasoc =++
222 215017520175 ///socsoc =++=D
2 =
2 01 7/5
= ab/ 215 :
(33 72 1 ) 1 -361
003mc
003mc
.
(2 ) .
: 21 = EEWf
= k VmhgmVmgm(dsoc)
+
2 2212D + 1
2 1
s2210501642 V/Vm
201311
== 2222
+
V2 (2)
: ( 2)
/m g
(Vnis)g
V02042 y h
5421
20163
423
2222
22
22= 2
=
===+
=42 hmc :
=+=+= 00342423 HhhHmc (37 46 1 ) 4 -461
:
() (Rh)
VeMG(Rh)
MmG
RhVm
ee
e
e221
2
+=+=+
eMGRg() : R
e gGeMe
== 222
-
11 09
.
:
3123
004600801() =+=+ 00460198
/(Rh)
VRge
e (),()
sVm
/ /
60046 ==
763004694
72016 00460198
3
:
h
60046360462408862 V/Vmk === 7
(55 15 1 ) 2 -561
:
B
A
A
B
A
PVmBmm
PP
KK
m KVmKP
= = ==
22222
1
BB KKJ mBmA
36 PAPB,KAJ8111
23
== 81=
==
(651 841 ) 3 -661 .
mVmgk V ==== 00010101 58 m
:
QCm === 98 0012010100245D === 2122 552503DC
(861 461 221 911 ) 2 -761 : :
0011 LL/LL/() 01
00101
=== 111
:
001 ()VV()VV(/) =+=+ 12121 13103
= 21 13002 V/V()
:
13001300 1
221
/V/ 2m
V === m
:
0010011300001 1
11
121
1
=
= /
~(%03 /) /
1300 = / 03
. 0/3
0011 LL/LL/() : 01
00101
=== 111
/() V0012 () VV()V
3031
1 == 1
V2 dmVd
V = = m m
VVdVd
m
= = =
: ( )
V d~V
= 001001
V :V
001001 = :/(%03 /) 2() 03
(71 9 ) 4 -861
b a = PVPV aabb 1== ab (TTT).
ba T1 T2
ba > TT 21 .
(6 4 ) 2 -961 :
052 0051
837232= 53 8015101
===TR()
VPTRnnVP
=6 nlom
6 . / = 66013601 3242
(71 9 ) 3 -071 DC BA T-P
T V
= PRn
WW BADC ==D . (1 . )
PT
-
09 21
. > VV DCBA :
V(PP) R
C == 2121 VVMVVM QCn(TT)Q
> VV DCBA PP 21 (.3 . ) > QQ DCBA
AD CB :
P(VV) R
C == 2121 PPMPPM QCn(TT)Q
> PP CBAD VV 21 (.2 . ) > QQ CBAD
W R
CPM Q
=
AD CB : > QQ CBAD
(4 ) > WW CBAD (001 39 ) 3 -171
. 08D
. = 208061 DD (611 001 ) 2 -271
()
:
==+=+==+
=()
fpmcqf
()f
pmcqf
pfqfp
022 pqf0202
0611110606
22
11
025 02
06f = ++= 1212 506
ff
(),() qqmcf
ff 2 7080021 =D 7022202
ffmcrf ==== 04001
=04 rmc (821 321 69 39 ) 3 -371
:
2 2
12
103nisi === 2
nis
nisinn
nisrnisi
D
i =54D ji ==54D
. ij +=+= 545409 DDD
(651 341 ) 1 -471
=+=2 qppp .
===2pq
BA mAB
.
(421 321 ) 4 -571
. .
.
.
-
31 09
(831 921 ) 1 -671
:
==+=+
==+=+
=
()hgP()hg()PhgPhgPP
()hgP()hg()PhgPhgPP
PPBBBB
AAAA
MN
2
1
21222121222
21112111121
MN PPhgghhh ==>>D 213()
( 3) ( 2) (1) > hh 21 > PP 21 :
(221 911 ) 1 -771 :
33 3
00870501/m 009301
mV
V ==== m
=05 V/til
:
==05 VV/til :
mV/mg V ==== 00805004 m
. : 1 : 2
.
(06 24 ) 3 -871 q2
.
FN r(/)
qq09 Fk
080221 901801801
669
221
12=== 21
FN r(/)
qq06 Fk
060223 901301801
669
223
32=== 23
=+= rr(mc) 6801 2422224222
FN
(/)/
rqq
Fk
0901
90121501801
24
2966
224
4124
=
==
:
01 6
01 soc,nis == 8
: y x F24
0127 x (F)FsocN === 2424098
0145 (F)yFnisN === 2424096
: y x =+=+= 2124092781 xxx FF(F)FN
=== 242345066 yyy F(F)FFN FFF Txy =+=+= 2222 816601
(031 111 ) 1 -971 :
+= 030602 =+=
030612
12RRR TT
RR R
3 :
3 === 02
2332
rR
rIr
TT RI
-
09 41
R
:
IA Rr
I2 T
3
30202
= 04+
+= =
: R103 =
IIA RR
R21 I
30306
061
122
=+=+= 1
: R103 = === 111221 03103 PRIPW
(401 201 ) 4 -081 :
2
2
4
B ===A
A
B
A
B
A
BDD
ll
RR
Dl
A Rl
== ==
208 ==
41511
2
451
2B
B
ll,R
R ,DDR
ABA
BAAB
(031 611 ) 4 -181 K2 K1
:
IIIA RR
41 IR3
43
33
=+== 1
+=+= 16 =
T 17TT
RRrR
I
+== 48 =
363RR 3
RR TRRR
R k2 k1
:
:
+= 3 =
61861861
RR TT
IA Rr
I91 T
1231
61= 7+
+= =
91 IIIA 41
9112
32
86161
=+== 11 (031 611 ) 2 -281
:
4 IIIIA 5
2151
66212
== 2 D ==
A : B A
4 ABAB VIVVVI === 6665
=751 AB VV/V() :
D 11 ++==+ VVVVVV BCAABC =+= 175615 ()CC /VV/V
: 4156 === C qVC/qC
(59 09 ) 3 -381 C1
(V1=. ) :
23 == , CF 6
23
234369 =+= ,, CF
-
51 09
C5 C,, 234
2342 . V,,=
232 C, 23 C4 V,=
C3 C2
24 23
2 : VV, ==
4 4
66
21
21
21
2= 1
===qq
VV
CC
qq
qVC
(641 041 ) 4 -481( N )
( 4 1 )
( 4)
. (261 551 ) 2 -581
.
.
:
RI
(R)I
BB=
12224 == DD
() RI
1221 BB D =+=
() RI
322 B ==D
( 2) ( 1)
( 1) ( 2) .
(881 681 ) 1 -681 ( 1)
N ( 1) . B A ( 1)
(2)
N ( 2) . C D ( 2)
(991 691 ) 1 -781 .
:
s
darT/
020001 ==== T/s 02022
001 =+=+ xamxam (nist)(nist) 020001 = /(nist)
:
(/(nist) tdd
td 05020001 == Nd
001001 = (soct) (19 87 ) 2 -881
:
.
-
09 61
..
.
:
.
D : D < D
=>a > :ttt CBA
: : 1 >> PPP ABC : : 3
y x . . y x C B A : 4 A
. 3 -422
R1= R2= 06 05
45 01060
01072
21
2/ 1
RR
/
/
R = R
.( B )
H|
HCONO|
HCONO|
HCONO|
H
2
2
2
-
09 02
1 -522 ++ 422 222 lCH(g)O(g)lC(g)HO(g)
2 2172 222
/lClom 362OlomlClom
== ?lClom/Olom
441010 211 5
72/lom.L.s ==
/
lCR 2 -622
N(g)O(g)ON(g)K/L.lom += 2201 2221 .
21 > QK2
805211
22== 1
Q/L.lom =()
Q()
. K Q 3 -722
HO(g)OC(g)OC(g)H(g),K ++= 22201 0/6 x D D y -6/0 y-x y y 0/3 x-0/3 0/3 0/3
/ZZ
//011
01
303
303
303
= 01
=
[OC[]HO][OC][H]
K2
=22
== 1 0103030 Z/lom.LL/lom == 03030033 x//x/lom
1 -822
. 1 -922
: : 1 .
: > 23 HCHOOClCHCHOOC 3HCOOC 2HCOOClC
. 2HCOOC 3HCOOC : 2
.
Hp Hp . .
. ( )OP43 : 3 01 : 4
. Hp 4 -032
: 5. 7/4 Hp : 1
lom.L1 0051Lm .
: 2
.
aC(HO)2 aB(HO)2: 3
. : 4
. 4 -132
/lom g
040200 ?lomHOaNglom1
0001 == 08
020121 /lom.L === 0200
M/VMn
(HO)
pHOgol[HO]HOp ==2 HpHOpHp +== 4121
[HO][HO][H] == ++ 0101 34121 01
3+ =01
[HO]
[HO]
++2 HOaN(qa)lCH(qa)lCaN(qa)HO(l) == lCHHOaNlCH (VM)(VM)(/V)/ 020001010
05 lCHVLm
00012
011
==
4 -232 :
lCOPxx ==+ 32305 1 OSlCxx ==+ 224206
OnMaBxx ++==+ 42806 2 OnMKxx ++==+ 41807
HOPxx ++==+ 242815 3 OlCxx ==+ 4817
OrCxx ==+ 3606 4 HSOxx ++==+ 227224106
2 -332 :
: 1 ED ED
. +gA(qa) : 2
.2+ eF(qa) ED ED : 3
.
: 4 . .
2 -432 .
2 -532
. .
