Polyester Blend Fabric Effect of Alkali
13/&0 12 ) * +,* -. "
** + 892
!!" #$
7 12 4 8 * *4 5 : 2 ;
()0/ // & :+ , -., #$
0 >=
% &' ( )
16 1 1 8 ?1@!= )
* ) /(/ & : ! " #$
)
!" # " $ % &! ' $ $ ( A ;1 @ .0 3$ 4 5 &6 7 $ $ 8 -9 & 0&1 2 $" # . ! ) *+ $ , -. + &- 0 $ 4 5 2 ) ! ? @ 2 A &-B> C + - : ;2 -9 0.L 06 O K " # $ MN °c L GK°c I-+9 J GH D &EF & , -. $ A &-B> 6 1 C . ! 7 $ $ &- " BO &WXL V .0 U " ( TK $ HK 0 E $ : + - 8 -9 RS J $ QPF $ QPF Q9$ F ) ! S Q F@ $ A &-B> .0 # $ # ! [B Q PP Y 7 &Z S Y 7 -] O Q F. $ Q & \ &- " BO J Q $ ! ) 0 E 8 -9 + \- ? $ % B> U6 ! I&_`L => $ + F S " a.+ Ca&6 ! S 0 ^ ;$ (&+ ;9 +P&$ J @ J O L S J ;P L J QPF $ 06 O \b &- A &-B> . ! + # Z J $ J &;$ 1 \+E $ S + - : RS Y 7 &- A &-B> QP Q1 Ca&6 ! J L 0; c ] 7 F \# ![B $@ .0E& 0&B b O " a.+: 0: Q :F D : &:EF & \ &- A &-B> + - : 8 -9 RS " # : 41 B + C * S \# ! [B \PPF
Hot Mercerizing of Cotton/Polyester Blend Fabric Effect of Alkali Treatment Temperature on Tensile Properties, Weight Loss and Shrinkage of Fabric S.M. Mortazavi and M. Sedighipoor Textile Engineering Department, Isfahan University of Technology
Abstract: The presence of defects in cold mercerizing of cotton goods led to the creation of a new method, called hot mercerizing in which caustic soda solution is used at a high temperature. Hot mercerizing is successfully used in cotton blended with some other fibers. In cotton/polyester blend fabrics, this treatment serves a dual purpose: subjectively, it imparts a silklike + 3
4 2 **
2*
soft handle to the polyester and brings about mercerizing of the cotton. In this work, the mercerizing operation with caustic soda solution was performed on a 65/35 polyester/cotton fabric in sixteen different temperatures (from 15°C to 90°C), in two states: with tension and without tension. Finally, the effect of temperature of treatment on some properties of fabric such as tensile properties, weight loss, and shrinkage have been studied. Alkali treatment cause weight loss in cotton/polyester blend fabrics, the main part of the weight loss attributed to the polyester component of the blend. Increasing temperature leads to a corresponding increased in weight loss. The resulting weight loss leads to more yarn release and consequently, to the improvement of the drape and soft handle in the fabric. However, it decreases the tensile strength and causes weakness of the fabric, therefore, an optimum of temperature must be considered. In the alkali treatment, the internal stresses in the fabric can be released. Release of tension in the fabric causes shrinkage, particularly in the warp direction. The effect of tension on properties of cotton/polyester blend fabric is not considerable in alkali treatment. Keywords: Hot mercerizing, Cotton/Polyester blend fabric, Alkali treatment, Caustic soda solution, Weight loss, Handle, tensile properties, Shrinkage
]j 24 ^ 24 +L 2 X2
A >J" @
cJ< AB v _7P Yr,
#62., @
4 >J, ,B
? _7 w u
D J, ? r< + J J ? j 3 $ 22 k
2 +2" @ 2< 2, AB C
GH°C 2:
JL+" L;
2";
2< EF: 2 D
#-7 8 J D
2< 24 + 2j u 7 +
"
+" h D A "C ]j 4 [D < ; , 22 +22" @> 22 "
22L ;
22
2J,
I H ! E F*10
~, "
~, "
7
L =3 >
7 ~, @ ,
: ~, @ ,
(Ne)
(Ne)
G |Z
G
O
" A 3D #9: _! # .
`: :
|5Z
G
2 + 7 2 637
`:
C
OH
O-CH 2 -CH 2
O
-
O -CH 2 -C H 2
C OH
+" @ < , AB
OH -
6 K G H 2637 2
2 +2 7 2u 7
2ˆ ( ) C
I H ! AEAJ
2c "CB @ g 2
AB 8 d-c" 4 #
2j u 7
7
: ~, s #
.#
" Qu 7
? J!
#4
#R %} lJ
w " #4
#R l
4 J 2
#R U
8 3< 4 2
< #4 ;) 9 2" l2J C #4 2 #R 2
)
N T9
: 2 #R
? JL@C , @ k
2
C O-
,+
C @
a
. 3R 7
CA
2
2L =3 > 2 " [D < P { l C 4 •J: :
2 +7#
CA
, L Uc < [D < k P {C @ . [ G*}]
+rJ2
2{
: 2 #4 2 #R 2 Š32 #2< { @ k
3
u 7#
< 2< A 2 9" C 2k +j L • ,C #
23j hJTc: ? > C l j ?
#R
H 2O
#22" " ] >22$ +22j C 7 ]j 224
2
#4
+
O -C H 2 -CH 2
< `_ [D < 8 J D q
@k
iJ: " ,
MA40-00V2 11401125
Jj + 2J e
2$ L
2e +2
3 ) G H )
* O 3 J F*10
lJ, J,B – lJ, A , A < I
#V z
(gr/li) H:
^ 4 AC
J!
:
+" +
AC ]j 4 2I
C
#
C
6< @
: h< e #J j
2$ >2J, AC ]j 24 2" ] >2$ K
+" Vp "
A 4 + J e C r
2$ ? Jk 2cu
2{ 2< AC ]j 24 :^
2" ? j u 7
2cJ< u 7
(o)
I p AC ]j 4
24 2 +2 7 2 637 € -" ? j u 7
#
6
"
+I P j
-, ? CB Ye ]j 4 K
C AB @ 2 j
J" qJ -: ? < +6 3"
0)
ƒ>2
24 +! 2p
@ T, + .9" JJ\: 637 ƒ>
@ j 2c" +, 2 L , ] >2$ ^ 2< ? 2j "
2< +" ] >$ 8
AC
+ " 2D 2
@
P 2J!
C AC ]j 4 < A :+"
] % I &P
2: ?>!
P J! „4
2 6! . , 2 +" + J e 8 J D AC ]j 4 < m3" 4 3 .j C 8 g"?
p : AC ]j 4 $
AJAM
2" Q ^ ‘, 3u
J, j@ gp q 2{
Jj
2
@ 7 +r’ " ? JL
Jj
]j 24 2< qTJ2! . 2, @
] >$ q # D
< +" ] >$
#6., P J! +! {
2 2637 € 2 -" +L 7 ? J, A 2c, 2 < 637 ƒ> ]j 24 ]2 , 24
T9
9"
"
2
J! 26,
< @ 4
U24 +! T! " AC < + > #! p q ]j 24 [2D < @ 2
$ Š
7 AC
: < ]34
9"
FI dR ^
J!
Jj ? j Jm,C
Jj ? , lJ 3J ?S , ^ < ? j "
@ j
$ hJ.4 4
.
9" ]34 yJ9"
. cJ" ? J 7
2:#2p
Jj K
p hJ, < 4 @ L < hJ.4
+, L , ] >$ l
] >$ C + , 4
+2" 2 p 4 # •! z 637 ƒ>
+2
3: @ c, hI p
$ ] >$ }H °C ? "
[ |]#
?j"
+c >$ ™Jj (G)hT +
+2 , +L 7 ? J, ] >$ < AC ]j 4 K
"
"
4 # AB C +4 p
% / GC
P J! ZY
#29: =3 > 2 " C i27 ? 2637 % HH ?^ 4 T9
9"
+ .9" JJ\: }H °C
6,
A "C G5Hgr/li #V z
#D 2
WJr’ ? Y , A 3D < 4 u .[ }
2 +2 7 ƒ> ?2 ,
J.4
637 WJ! "B +"
"
Je
°C ? 2"
% / 5 2
P 2J! Ye ]j 4 . < +" ]j 4 P J! Ye U
L =3 >
? 2637 ? 2j 2, , AC ]j 24
+" R 7 € -"
9" < P J! A 4 h D K
637 % HH ? j u 7
+! @ 6,
J : ? < . < +" ]j 4 8
? >2 C l2 2j +L 27 ? J, < U
2: 2K
2 $ L 8 2I 8 J 9: .[ 5] # >Ju , p =3 >
4 @ c,
2< +L 27 ? 2J, 2" ] >2$ 2< :^ < ? j "
C
TJ: 4 ˜$ 9" Q ^
8 2I 2< =3 > 2 " C +2 ,
" •.p
! 2
!!" #$
C •2 -:
"C
@
+ p + J e 8 J D qJp
#62., 2 +2 7 2 2637 € 2 -"
2 2637 € 2 -" 2j
24
AC ]j 24 A >2J"
"
€ -" + 7 ƒ>
2 +2" $ L mJ , h4 *5H °C
29"
+" +7
]j 4 5H°c?^ < < " ] >$ < .# qJ 7 € -" ƒ>
5H
180
(N(N) ) +L 7 ? 4* J,=
170 160 150 140 130 15
25
35
45
55
65
75
;13 ] % 4 . = &= 4
@$
45
75
85
95
((°c) ºC) )" t=5min + , * C=260gr/li `a b ) ) _>'
I
^
) &= J N@3
205
185
4* =
(N) +L 7 ? J,
195
(N )
175
165
155
145 15
25
35
55
65
85
95
((°ºC c) )) " t=5min + , * C=260gr/li `a b ) ) _>'
#2
^ 4 T9
8 JJ\: ,
< c" AB 8 JJ\: , .
? J, +393" AC ]j 4 2 5
2 9" 2< + 2J e >J!
T9
. "
@$
€ -"
I
I p +L 7
^
) &= M N@3
" Q637 ƒ> #6., A < .
6J" :
qJ< € 6: q $ ?
J!
Jj ?^ 4
175
4* =
155
(N)
165
145 135 125 0
2
4
6
8
10
+,* -. B12 )
g
4 ) Ef ) e 1 1 >B* 1 . F $
] % I &P ) +,* -. B 12 ) *
t=5min
8 2I 2
2J" 24
C
. 2, 27 C
0)
U
2"
+L 7 ? J, 4
+" @ j c"
2< H/}|G +k 2.6 j • 2’ 2< +2YR ! r" l C , :+" Y= - 4.0743X + 168.09 X
c:
+ 7 P J! Ye ]j 4 A 4
2R ZY2 A u @ .
AC ]j 4 I •.p
2J, +L 27 ? 2J, _2! #2 >Ju 2, p AC ]j 24 ] >2$ # D < " ] >$ < +!
+" ^ 4 +L X
. < +" ]j 4 8
+72 $ J, +, 3u
< +L 7 ? J,
Ye ]j 4 . < +" ]j 4 P J! Ye + J e C < ~, +k -
$ [D < ~,
+" Vp " qJ3‘ j ( )hT
2cJ< ? 2Vp " h2< e #62., 2" q2
.(o)hT2
+L X
2 : _22! #22 @ 2 hJT22c: 2 +2 7
C W22 -" ? 2"
>J, ? k ? j " 7
2: [2D < …ˆ 2J e 8 2J D < U4 p y
2
< m3" 4
C 4 , hJR + J e 8 J D qJp
+ 2J e C i27 637 P J!
2 < 2 m3"
hT2 q2
}H 2:
AC ]j 24 2I h< "
#6., Relaxation #! p
2 2637 € 2 -" Q2u 7 +L 2 X2 < A :+"
kJ , 2 Q22
2 +2" 2Vp " ( ) hT
AB A 2: +2" 24 2< +2" ] >$ u 7
]3: ?C
c:
r: #! p < +< J
+" + J e 8 J D C i7 u 7 +L X
) &= d N#3
+ , * C=260gr/li `a b )
^ 2 4 Relaxation +TJ, 2 T" ? 2J, #22< { 2" ] >22$ 2< . 2j +2" A 2c, +L 2 X2
4* =
2{ 2< u 7 : #
< A :+"
2cJ< 2: #2
`: .
1 3/ &0 1 2 )
] % I &P
AMAM
+" +L
+2cc4 ? 2j J, 2K
P 2J!
AB # D # ? 7 #
C + 2j C i7^ 24 . 2, JL +"
2u 7
. 234+" #p
" ? c3: 4
2u 7 ~, J! : qJp R
** + 892
!!" #$
7 12 4 8 * *4 5 : 2 ;
()0/ // & :+ , -., #$
0 >=
% &' ( )
16 1 1 8 ?1@!= )
* ) /(/ & : ! " #$
)
!" # " $ % &! ' $ $ ( A ;1 @ .0 3$ 4 5 &6 7 $ $ 8 -9 & 0&1 2 $" # . ! ) *+ $ , -. + &- 0 $ 4 5 2 ) ! ? @ 2 A &-B> C + - : ;2 -9 0.L 06 O K " # $ MN °c L GK°c I-+9 J GH D &EF & , -. $ A &-B> 6 1 C . ! 7 $ $ &- " BO &WXL V .0 U " ( TK $ HK 0 E $ : + - 8 -9 RS J $ QPF $ QPF Q9$ F ) ! S Q F@ $ A &-B> .0 # $ # ! [B Q PP Y 7 &Z S Y 7 -] O Q F. $ Q & \ &- " BO J Q $ ! ) 0 E 8 -9 + \- ? $ % B> U6 ! I&_`L => $ + F S " a.+ Ca&6 ! S 0 ^ ;$ (&+ ;9 +P&$ J @ J O L S J ;P L J QPF $ 06 O \b &- A &-B> . ! + # Z J $ J &;$ 1 \+E $ S + - : RS Y 7 &- A &-B> QP Q1 Ca&6 ! J L 0; c ] 7 F \# ![B $@ .0E& 0&B b O " a.+: 0: Q :F D : &:EF & \ &- A &-B> + - : 8 -9 RS " # : 41 B + C * S \# ! [B \PPF
Hot Mercerizing of Cotton/Polyester Blend Fabric Effect of Alkali Treatment Temperature on Tensile Properties, Weight Loss and Shrinkage of Fabric S.M. Mortazavi and M. Sedighipoor Textile Engineering Department, Isfahan University of Technology
Abstract: The presence of defects in cold mercerizing of cotton goods led to the creation of a new method, called hot mercerizing in which caustic soda solution is used at a high temperature. Hot mercerizing is successfully used in cotton blended with some other fibers. In cotton/polyester blend fabrics, this treatment serves a dual purpose: subjectively, it imparts a silklike + 3
4 2 **
2*
soft handle to the polyester and brings about mercerizing of the cotton. In this work, the mercerizing operation with caustic soda solution was performed on a 65/35 polyester/cotton fabric in sixteen different temperatures (from 15°C to 90°C), in two states: with tension and without tension. Finally, the effect of temperature of treatment on some properties of fabric such as tensile properties, weight loss, and shrinkage have been studied. Alkali treatment cause weight loss in cotton/polyester blend fabrics, the main part of the weight loss attributed to the polyester component of the blend. Increasing temperature leads to a corresponding increased in weight loss. The resulting weight loss leads to more yarn release and consequently, to the improvement of the drape and soft handle in the fabric. However, it decreases the tensile strength and causes weakness of the fabric, therefore, an optimum of temperature must be considered. In the alkali treatment, the internal stresses in the fabric can be released. Release of tension in the fabric causes shrinkage, particularly in the warp direction. The effect of tension on properties of cotton/polyester blend fabric is not considerable in alkali treatment. Keywords: Hot mercerizing, Cotton/Polyester blend fabric, Alkali treatment, Caustic soda solution, Weight loss, Handle, tensile properties, Shrinkage
]j 24 ^ 24 +L 2 X2
A >J" @
cJ< AB v _7P Yr,
#62., @
4 >J, ,B
? _7 w u
D J, ? r< + J J ? j 3 $ 22 k
2 +2" @ 2< 2, AB C
GH°C 2:
JL+" L;
2";
2< EF: 2 D
#-7 8 J D
2< 24 + 2j u 7 +
"
+" h D A "C ]j 4 [D < ; , 22 +22" @> 22 "
22L ;
22
2J,
I H ! E F*10
~, "
~, "
7
L =3 >
7 ~, @ ,
: ~, @ ,
(Ne)
(Ne)
G |Z
G
O
" A 3D #9: _! # .
`: :
|5Z
G
2 + 7 2 637
`:
C
OH
O-CH 2 -CH 2
O
-
O -CH 2 -C H 2
C OH
+" @ < , AB
OH -
6 K G H 2637 2
2 +2 7 2u 7
2ˆ ( ) C
I H ! AEAJ
2c "CB @ g 2
AB 8 d-c" 4 #
2j u 7
7
: ~, s #
.#
" Qu 7
? J!
#4
#R %} lJ
w " #4
#R l
4 J 2
#R U
8 3< 4 2
< #4 ;) 9 2" l2J C #4 2 #R 2
)
N T9
: 2 #R
? JL@C , @ k
2
C O-
,+
C @
a
. 3R 7
CA
2
2L =3 > 2 " [D < P { l C 4 •J: :
2 +7#
CA
, L Uc < [D < k P {C @ . [ G*}]
+rJ2
2{
: 2 #4 2 #R 2 Š32 #2< { @ k
3
u 7#
< 2< A 2 9" C 2k +j L • ,C #
23j hJTc: ? > C l j ?
#R
H 2O
#22" " ] >22$ +22j C 7 ]j 224
2
#4
+
O -C H 2 -CH 2
< `_ [D < 8 J D q
@k
iJ: " ,
MA40-00V2 11401125
Jj + 2J e
2$ L
2e +2
3 ) G H )
* O 3 J F*10
lJ, J,B – lJ, A , A < I
#V z
(gr/li) H:
^ 4 AC
J!
:
+" +
AC ]j 4 2I
C
#
C
6< @
: h< e #J j
2$ >2J, AC ]j 24 2" ] >2$ K
+" Vp "
A 4 + J e C r
2$ ? Jk 2cu
2{ 2< AC ]j 24 :^
2" ? j u 7
2cJ< u 7
(o)
I p AC ]j 4
24 2 +2 7 2 637 € -" ? j u 7
#
6
"
+I P j
-, ? CB Ye ]j 4 K
C AB @ 2 j
J" qJ -: ? < +6 3"
0)
ƒ>2
24 +! 2p
@ T, + .9" JJ\: 637 ƒ>
@ j 2c" +, 2 L , ] >2$ ^ 2< ? 2j "
2< +" ] >$ 8
AC
+ " 2D 2
@
P 2J!
C AC ]j 4 < A :+"
] % I &P
2: ?>!
P J! „4
2 6! . , 2 +" + J e 8 J D AC ]j 4 < m3" 4 3 .j C 8 g"?
p : AC ]j 4 $
AJAM
2" Q ^ ‘, 3u
J, j@ gp q 2{
Jj
2
@ 7 +r’ " ? JL
Jj
]j 24 2< qTJ2! . 2, @
] >$ q # D
< +" ] >$
#6., P J! +! {
2 2637 € 2 -" +L 7 ? J, A 2c, 2 < 637 ƒ> ]j 24 ]2 , 24
T9
9"
"
2
J! 26,
< @ 4
U24 +! T! " AC < + > #! p q ]j 24 [2D < @ 2
$ Š
7 AC
: < ]34
9"
FI dR ^
J!
Jj ? j Jm,C
Jj ? , lJ 3J ?S , ^ < ? j "
@ j
$ hJ.4 4
.
9" ]34 yJ9"
. cJ" ? J 7
2:#2p
Jj K
p hJ, < 4 @ L < hJ.4
+, L , ] >$ l
] >$ C + , 4
+2" 2 p 4 # •! z 637 ƒ>
+2
3: @ c, hI p
$ ] >$ }H °C ? "
[ |]#
?j"
+c >$ ™Jj (G)hT +
+2 , +L 7 ? J, ] >$ < AC ]j 4 K
"
"
4 # AB C +4 p
% / GC
P J! ZY
#29: =3 > 2 " C i27 ? 2637 % HH ?^ 4 T9
9"
+ .9" JJ\: }H °C
6,
A "C G5Hgr/li #V z
#D 2
WJr’ ? Y , A 3D < 4 u .[ }
2 +2 7 ƒ> ?2 ,
J.4
637 WJ! "B +"
"
Je
°C ? 2"
% / 5 2
P 2J! Ye ]j 4 . < +" ]j 4 P J! Ye U
L =3 >
? 2637 ? 2j 2, , AC ]j 24
+" R 7 € -"
9" < P J! A 4 h D K
637 % HH ? j u 7
+! @ 6,
J : ? < . < +" ]j 4 8
? >2 C l2 2j +L 27 ? J, < U
2: 2K
2 $ L 8 2I 8 J 9: .[ 5] # >Ju , p =3 >
4 @ c,
2< +L 27 ? 2J, 2" ] >2$ 2< :^ < ? j "
C
TJ: 4 ˜$ 9" Q ^
8 2I 2< =3 > 2 " C +2 ,
" •.p
! 2
!!" #$
C •2 -:
"C
@
+ p + J e 8 J D qJp
#62., 2 +2 7 2 2637 € 2 -"
2 2637 € 2 -" 2j
24
AC ]j 24 A >2J"
"
€ -" + 7 ƒ>
2 +2" $ L mJ , h4 *5H °C
29"
+" +7
]j 4 5H°c?^ < < " ] >$ < .# qJ 7 € -" ƒ>
5H
180
(N(N) ) +L 7 ? 4* J,=
170 160 150 140 130 15
25
35
45
55
65
75
;13 ] % 4 . = &= 4
@$
45
75
85
95
((°c) ºC) )" t=5min + , * C=260gr/li `a b ) ) _>'
I
^
) &= J N@3
205
185
4* =
(N) +L 7 ? J,
195
(N )
175
165
155
145 15
25
35
55
65
85
95
((°ºC c) )) " t=5min + , * C=260gr/li `a b ) ) _>'
#2
^ 4 T9
8 JJ\: ,
< c" AB 8 JJ\: , .
? J, +393" AC ]j 4 2 5
2 9" 2< + 2J e >J!
T9
. "
@$
€ -"
I
I p +L 7
^
) &= M N@3
" Q637 ƒ> #6., A < .
6J" :
qJ< € 6: q $ ?
J!
Jj ?^ 4
175
4* =
155
(N)
165
145 135 125 0
2
4
6
8
10
+,* -. B12 )
g
4 ) Ef ) e 1 1 >B* 1 . F $
] % I &P ) +,* -. B 12 ) *
t=5min
8 2I 2
2J" 24
C
. 2, 27 C
0)
U
2"
+L 7 ? J, 4
+" @ j c"
2< H/}|G +k 2.6 j • 2’ 2< +2YR ! r" l C , :+" Y= - 4.0743X + 168.09 X
c:
+ 7 P J! Ye ]j 4 A 4
2R ZY2 A u @ .
AC ]j 4 I •.p
2J, +L 27 ? 2J, _2! #2 >Ju 2, p AC ]j 24 ] >2$ # D < " ] >$ < +!
+" ^ 4 +L X
. < +" ]j 4 8
+72 $ J, +, 3u
< +L 7 ? J,
Ye ]j 4 . < +" ]j 4 P J! Ye + J e C < ~, +k -
$ [D < ~,
+" Vp " qJ3‘ j ( )hT
2cJ< ? 2Vp " h2< e #62., 2" q2
.(o)hT2
+L X
2 : _22! #22 @ 2 hJT22c: 2 +2 7
C W22 -" ? 2"
>J, ? k ? j " 7
2: [2D < …ˆ 2J e 8 2J D < U4 p y
2
< m3" 4
C 4 , hJR + J e 8 J D qJp
+ 2J e C i27 637 P J!
2 < 2 m3"
hT2 q2
}H 2:
AC ]j 24 2I h< "
#6., Relaxation #! p
2 2637 € 2 -" Q2u 7 +L 2 X2 < A :+"
kJ , 2 Q22
2 +2" 2Vp " ( ) hT
AB A 2: +2" 24 2< +2" ] >$ u 7
]3: ?C
c:
r: #! p < +< J
+" + J e 8 J D C i7 u 7 +L X
) &= d N#3
+ , * C=260gr/li `a b )
^ 2 4 Relaxation +TJ, 2 T" ? 2J, #22< { 2" ] >22$ 2< . 2j +2" A 2c, +L 2 X2
4* =
2{ 2< u 7 : #
< A :+"
2cJ< 2: #2
`: .
1 3/ &0 1 2 )
] % I &P
AMAM
+" +L
+2cc4 ? 2j J, 2K
P 2J!
AB # D # ? 7 #
C + 2j C i7^ 24 . 2, JL +"
2u 7
. 234+" #p
" ? c3: 4
2u 7 ~, J! : qJp R
