Iùuhoçvqlqj 45

Lqyhuvlrqviruphoq rfk
idowqlqj

Ghw ylnwljdvwh wlooçpsqlqjvrpuèghw iùu irxulhuwudqviruphq çu olqhçud glh0

uhqwldohnydwlrqhu1 Wloovdppdqv phg glvwulexwlrqvwhrul çu irxulhudqdo|v hww
nudiwixoow kmçosphgho iùu dww ehvnulyd iùuorss rfk oùvd sureohp phg dqnq|w0
qlqj wloo eègh ruglqçud rfk sduwlhood glhuhqwldohnydwlrqhu1 Iùu dww xwq|wwmd
irxulhuwudqviruphq pèvwh yl hphoohuwlg kd hww hq0hqw|gljw vdpedqg phoodq
hq glvwulexwlrq x rfk ghvv wudqvirup x e1 Ghwwd jhv dy lqyhuvlrqviruphoq1

4514 Lqyhuvlrqviruphoq l V 3
j e
Hqoljw yèu jdpod lqyhuvlrqvirupho/ vdwv 5;/ çu 5i @ ie iùu dood ghulyhuedud
ixqnwlrqhu i 5 O +U, vègdqd dww ie 5 O +U,1 Vshflhoow jçoohu ghq gè iùu dood
whvwixqnwlrqhu * 5 V rfk gçuphg rfnvè iùu dood glvwulexwlrqhu x 5 V  1 Yl
ylvdu iùomdqgh vdwv1

e j
Vdwv 7; Rp x 5 V  jçoohu dww x e @ 5x1
G H G H G j
H G j H
Ehylv1 Yl kdu x e
e> * @ ke e @ x> *
x> *l ee @ x> 5* @ 5x> * iùu dood
* 5 V1
Lqyhuvlrqviruphoq l ghqqd doopçqqd irup çu iudpiùudoow dy whruhwlvnw lq0
wuhvvh jhqrp dww ghq ylvdu dww irxulhuwudqviruphq çu hq elmhnwly dyelogqlqj
I = V  $ V  1 Ghq lqyhuvd wudqviruphq xe :$ x ehwhfnqdu yl I 3 1 Ylg uçnqlqj
phg ydqoljd ixqnwlrqhu rfk glvwulexwlrqhu çu ghw vrp uhjho eçwwuh dww nrp0
elqhud nçqgd wudqviruphu phg uhjohuqd iùu wudqvodwlrq rfk vndoqlqj çq dww
iùuvùnd dqyçqgd lqyhuvlrqviruphoq gluhnw1

H{hpsho 6; Ehuçnqd lqyhuvwudqviruphq wloo ixqnwlrqhq

5d
$ :$
$2  d2

;6
;7 IÙUHOÇVQLQJ 451 LQYHUVLRQVIRUPHOQ RFK IDOWQLQJ

Nrqvwdqwhq d çu uhhoo1
Oùvqlqj1 Yl ièu phg kmços dy h{hpsho 69 rfk iùuvnmxwqlqjvuhjhoq dww
4 l 5 5 3 l ~@|
@ :$ h V
$ d 5 l +$ d, 5
ylonhw jhu
5d 4 4 5 3 l  @|  vlq dw
2 2
@  : $ V h  h3@| @ V vlq dw @ mwm

$ d $d $.d 5 w

Yl ndq rfnvè iùueçwwud ghq jdpod lqyhuvlrqviruphoq qèjrw/ vè dww iùuxw0

e
vçwwqlqjhq rp ghulyhuedukhw ndq vwu|ndv hiwhuvrp ie çu yçoghqlhudg vè vqduw
ie 5 O +U,1 Yl nrpelqhudu uhvxowdwhq iuèq vdwvhuqd 69 rfk 7; rfk ièu sè vè
vçww
e
Vdwv 7< Rp i> ie 5 O +U, vè jçoohu iruphoq 5i +w, @ ie+w, iùu ydumh w gçu
i çu nrqwlqxhuolj1
j e
es @ x
Ehylv1 Hqoljw vdwv 7; jçoohu 5xj @ 5 xs @ x ese @ xee rfk gè iùomhu
s s
e e
dy vdwv 69 dww 5i+w, @ ie+w, jçoohu gçu eègd ohghq çu nrqwlqxhuoljd/ phq ie
çu nrqwlqxhuolj ùyhudoow hqoljw vdwv 58 rfk gçuphg çu sèvwèhqghw ylvdw1
Dy vdwv 7< iùomhu dww iùuxwvçwwqlqjhq rp ghulyhuedukhw l Sduvhydov irupho
+vdwv 63, çu rqùglj1

4515 Glhuhqwldohnydwlrqhu
Vnlooqdghq phoodq glvwulexwlrqhu l V  rfk G eho|vhv sè hww eud vçww qçu
pdq iùuvùnhu oùvd olqhçud glhuhqwldohnydwlrqhu phg nrqvwdqwd nrh!flhqwhu
jhqrp irxulhuwudqviruphulqj1 Yl looxvwuhudu phg hww sdu h{hpsho1
H{hpsho 6< Oùv glhuhqwldohnydwlrqhq x  x @ 51
Oùvqlqj1 Irxulhuwudqviruphudu yl hnydwlrqhq ièu yl +l$,2 x exe @ 5e @ 5
 2
3
e @ 5 4 . $
ylonhw jhu x rfk gçuphg oùvqlqjhq x +w, @ h3ƒ|ƒ 1 Iuèq
whrulq iùu glhuhqwldohnydwlrqhu rfk glvwulexwlrqhu l G yhw yl hphoohuwlg dww
ghq krprjhqd hnydwlrqhq x  x @ 3 kdu ghq doopçqqd oùvqlqjhq x +w, @
Dh| . Eh3| > gçu D rfk E ndq ydud jrgw|fnoljd nrpsoh{d nrqvwdqwhu1 Ghq
ixoovwçqgljd oùvqlqjhq eolu gçuiùu
x +w, @ h3ƒ|ƒ . Dh| . Eh3|
Dww yl hqgdvw ièu sduwlnxoçuoùvqlqjhq x +w, @ h3ƒ|ƒ qçu yl irxulhuwudqviru0
phudu ehuru sè dww ixqnwlrqhuqd h| rfk h3| lqwh çu glvwulexwlrqhu l V  rfk
vdnqdu gçuiùu irxulhuwudqvirup1
Qçvwd h{hpsho ylvdu dww rp oùvqlqjduqd wloo ghq krprjhqd hnydwlrqhq
oljjhu l V  vè nrpphu gh rfnvè phg ylg irxulhuwudqviruphulqjhq1
45161 IDOWQLQJ ;8

H{hpsho 73 Oùv glhuhqwldohnydwlrqhq x . x @ 51

Oùvqlqj1 Vrp iùuxw çu +l$,2 x e.ex @ 5e @ 5 ylonhw jhu +l$ . l, +l$  l, x
e@
e
5 @ 51 Qx iùomhu ghw hphoohuwlg lqwh dww
5 l l
e@
x @ 
+l$ . l, +l$  l, l$ . l l$  l
hiwhuvrp ghq krprjhqd hnydwlrqhq +$ . 4, +$  4, x e @ 3 kdu doopçqqd oùv0
qlqjhq xe @ d . e3 phg jrgw|fnoljd nrpsoh{d nrqvwdqwhu d rfk e1 Ghq
ixoovwçqgljd oùvqlqjhq kdu vèohghv irxulhuwudqviruphq
l l
e@
x  . d . e3
l$ . l l$  l
vrp hiwhu lqyhuvwudqviruphulqj +vh h{hpsho 6;, jhu oùvqlqjhq
vlq w
x +w, @ mwm . Dh| . Eh3|
w
gçu D rfk E çu jrgw|fnoljd nrpsoh{d wdo1
Hq dqqdq ydqolj sureohpvwçooqlqj l vdpedqg phg glhuhqwldohnydwlrqhu
çu ehj|qqhovhyçughvsureohp1 Ghvvd kdqwhudv grfn eçvw phg odsodfhwudqv0
iruphq/ yduiùu yl vsdu ghwwd wloo qçvwd iùuhoçvqlqj1 Yl vndoo lvwçoohw qçupduh
xqghuvùnd vdpedqghw phoodq idowqlqj rfk irxulhuwudqviruphu1

4516 Idowqlqj
L dyvqlww <1; ghqlhudgh yl idowqlqjhq x  G
* dy hq glvwulexwlrq
H x 5 G rfk hq
j
whvwixqnwlrq * 5 G vrp ixqnwlrqhq w :$ x> * 1 Dy vdwv 75 iùomhu rfnvè
|
dww x  * 5 F " 1 Sè vdppd vçww ndq yl ghqlhud x  * gè x 5 V  rfk * 5 V1
Gè jçoohu iùomdqgh vdwv rp idowqlqjhq1
G j H
Vdwv 83 Rp x 5 V  rfk * 5 V çu idowqlqjhq x  * = w :$ x> * hq
|
rçqgoljw ghulyhuedu ixqnwlrq yduv ehorss kùjvw yç{hu sro|qrplhoow gè w $
41
Ehylv1 Ghulyhuedukhwhq ndq ylvdv phg olnqdqgh dujxphqw vrp gè x 5 G
rfk * 5 G phq yl dyvwèu iuèq ghwdomhuqd1 Dqwdj vhgdqSdww yl phg oçpsoljd
nrqvwdqwhu D> p rfk q kdu xssvndwwqlqjhq mkx> *lm  D f$$6 pd{| mw *E +w,m
f$$?
iùu dood whvwixqnwlrqhu
 * 5 V1 Oèw * ydud { rfk vçww i +w, @ kx> !l > gçu
j
! + , @ * + , @ * +w   ,1 Gè eolu
|
     
  E     
pd{  ! + , @ pd{   *E +w   , @ pd{ +w  {, *E +{,
%
  
[  
l  
 mwm& pd{ { *E +{,
n %
&'f
;9 IÙUHOÇVQLQJ 451 LQYHUVLRQVIRUPHOQ RFK IDOWQLQJ

Gçuphg çu
?
[
mi +w,m @ mkx> !lm  D& mwm&
&'f
gçu nrh!flhqwhuqd D& lqwh ehuru dy w1
Hq iùomg dy vdwvhuqd 78 rfk 83 çu dww x* 5 V  rp yl ehwudnwdu idowqlqjhq
vrp hq glvwulexwlrq1 Ghw çu gè ulpoljw dww plvvwçqnd dww iruphoq

x^ e*
*@x e +4514,

rfnvè vndoo jçood1 Plvvwdqnhq ehnuçiwdv dy vdwv 85 qhgdq1 Yl ehkùyhu grfn

iùomdqgh uhvxowdw1

Vdwv 84 Rp i @ x  *> gçu x 5 V  rfk * 5 V/ jçoohu dww

] " j 
xs +#, @ i +w, # +w, gw @ x *  #
3"

iùu dood # 5 V1

Ehylv1 Ehylvhw çu lqwh khow wulyldow rfk yl uhgrylvdu lqwh dood ghwdomhu1
j
Lgìq çu dww dssur{lphud *  # phg hq ulhpdqqvxppd
? 2
j 4 [ j
*  # +w, @ olp * +w  m@q, # +m@q, @ olp !? +w,
?<n" q ?<n"
2 '3?

Hiwhuvrp x çu olqhçu/ jçoohu dww

?2    ?2
4 [ j 4 [
x +!? , @ x * # +m@q, @ i +m@q, # +m@q,
q 2
*? q 2
'3? '3?
G j H
hiwhuvrp i @ x  * rfk gçuphg i +w, @ x> * 1 Vèohghv çu
|

? 2 ] "
4 [
olp x +!? , @ olp i +m@q, # +m@q, @ i +w, # +w, gw
?<n" ?<n" q 3"
2 '3?

Sèvwèhqghw iùomhu gçuiùu rp yl ylvdu dww

j   
x *# @x olp !? @ olp x +!? ,
?<n" ?<n"

gçu ghw qdwxuoljwylv çu ghw vlvwd ohghw vrp çu sureohphw1 Hq ndon|o olnqdqgh
ghq l ehylvhw iùu vdwv 75/ phq qèjrw rpvwçqgoljduh/ ylvdu çyhq ghw vlvwd ohghw
rfk gçuphg çu ehylvhw noduw1
Iruphoq +4514, iùomhu vhgdq gluhnw dy vdwv 841
45171 OWL0ILOWHU ;:

Vdwv 85 Rp x 5 V  rfk * 5 V jçoohu dww x^ e*

*@x e rfk x e @ 5xg
e*  *1
 G H
Ehylv1 Hqoljw ghqlwlrq 49 rfk vdwv 84 çu x^  *> # @ x  *> #e @
G j H j
x> *  #e 1 Ylgduh çu hqoljw vdwv 77 5*  #e @ * ee  #e @ 5* ^
e  # rfk vè0
G j H G H
ohghv x> *  #e @ x> * ^
e  # @ ke e  #l @ k*
x> * exe> #l ylonhw ehylvdu ghq
iùuvwd uhodwlrqhq1 Ghq dqgud iùomhu dy lqyhuvlrqviruphoq hiwhuvrp yl ghov kdu
j j j j
5xgg e^
 * @ +5,2 x  * rfk ghov q|vv ylvdw dww x e@x
* e
e*ee @ +5,2 x  *1

4517 OWL0owhu
Hww OWL0owhu çu hq dyelogqlqj X = F " $ F " vrp çu

41 Olqhçu= X +d* . e#, @ dX +*, . eX +#, rfk

51 W udqvodwlrqvL qyduldqw= i @ X +*, , i| @ X +*| ,1

Olqhdulwhw rfk wudqvodwlrqvlqyduldqv lqqheçu l sudnwlnhq riwdvw hq lgh0

dolvhulqj/ phq çu çqgè yçughixood ehjuhss vrp kmçosphgho iùu dqdo|v rfk
iùuvwèhovh dy yhunoljkhwhq1 Pdq ndq vçjd dww hww owhu çu wudqvodwlrqvlqydul0
dqw l wlghq  wlgvlqyduldqw  rp owuhwv olyvoçqjg çu p|fnhw oèqj l iùukèoodqgh
wloo yduldwlrqhuqd l gh vljqdohu vrp sdvvhudu
 j owuhw1
Rp X çu hww OWL0owhu ghqlhudu x * @ i +3, > gçu i @ X +*, > hq
olqhçu dyelogqlqj vrp/ lidoo ghq rfnvè çu hq glvwulexwlrq/ ylvdu sè hww ylnwljw
vdpedqg phoodq idowqlqj rfk OWL0owhu1
j
Vdwv 86 Oèw X ydud hww OWL0owhu vègdqw dww x 5 G hoohu V  > gçu x * @
i +3, rp i @ X +*, rfk * 5 G hoohu V1 Gè jçoohu dww X +*, @ x  * iùu dood
* 5 G hoohu V1

dww i3| @ X +*3| , rfk gè jço0

Ehylv1 Dy wudqvodwlrqvlqyduldqvhq iùomhu 
 j j
ohu dww i +w, @ i3| +3, @ x +*3| , @ x * @ x  * +w, hiwhuvrp
j
j |
+*3| ,j + , @ * + . w, @ * +  w, @ * + ,
|
Glvwulexwlrqhq x vrp kùu wloo OWL0owuhw X +*, @ x  * ndoodv owuhwv
lpsxovvydu1
Rp i @ X +*, @ x  * rfk x 5 V  jçoohu hqoljw vdwv 85 ie @ x e* e
e @ ie@*1
ylonhw/ rp glylvlrqhq çu wlooèwhq/ jhu x e Glvwulexwlrqhq x
e ndoodv owuhwv
ùyhuiùulqjvixqnwlrq1

H{hpsho 74 Ehvwçp ùyhuiùulqjvixqnwlrq rfk lpsxovvydu wloo UF0owuhw l 0

jxu 45141 Wlgvnrqvwdqwhq çu ydog vè dww UF @ 41
;; IÙUHOÇVQLQJ 451 LQYHUVLRQVIRUPHOQ RFK IDOWQLQJ


) -  s

Iljxu 4514= Hww hqnhow UF0owhu1

Oùvqlqj1 Nrqwlqxlwhwvodjhq iùu vwuùppduqd jhqrp gh wuh nrpsrqhq0

whuqd jhu vdpedqghw
g i gi
F +*  i , @ . F
gw U gw
rfk hiwhu iùuhqnolqj hukèoohv glhuhqwldohnydwlrqhq 5i  . i @ * 1 Irxulhu0
wudqviruphulqj jhu vhgdq +5l$ . 4, ie @ l$*e rfk ùyhuiùulqjvixqnwlrqhq eolu

ie l$ 4 4 4
e +$, @
x @ @ 
*e 5l$ . 4 5 7 l$ . 4@5

Hiwhu lqyhuvwudqviruphulqj hukèoohv lpsxovvyduhw x @ I 3 +e

x,

4 4
x @   h3|*2 K
5 7
rfk vdpedqghw phoodq lq0 rfk xwvljqdo eolu i @ x  *> hoohu l noduwh{w
]
4 4 "
i +w, @ * +w,  * +w   , h3 *2 g
5 7 f

4518 Ùyqlqjdu
41 Ehvwçp x 5 V  vè dww | @ x  * çu hq oùvqlqj wloo | . 5|  . | @ *1
Vnuly oùvqlqjhq vrp hq lqwhjudo1

51 Vdppd xssjliw vrp ùyqlqj 4 phq phg glhuhqwldohnydwlrqhq | . |  

5| @ 6*1 Dqjh rfnvè oùvqlqjviruphoq phg lqwhjudohu1

61 +Whqw1 3334,1 Ehvwçp dood glvwulexwlrqvoùvqlqjdu x 5 V  uhvshnwlyh G

vrp vdwlvhudu glhuhqwldohnydwlrqhq x . 5x . x @ 1

71 +Whqw1 <<43,1 Ehvwçp dood glvwulexwlrqvoùvqlqjdu x 5 V  uhvshnwlyh G

vrp vdwlvhudu glhuhqwldohnydwlrqhq x . x @ 4 . 1
45181 ÙYQLQJDU ;<

81 +Whqw1 333;,1 Ehvwçp dood oùvqlqjdu x 5 V  vrp vdwlvhudu lqwhjudohnyd0

wlrqhq ] "
2 2
h3E|3  x + , g @ +4 . w, h3|
3"
Idowqlqjvlqwhjudohq ièu wrondv l glvwulexwlrqvphqlqj1