>hfZrgyy jZ[hlZ ih ]_hf_ljbb aZ deZkk d mq_[gbdm ©=_hf_ljby deZkkª : < Ih]hj_eh\ F ©Ijhk\_s_gb_ª ] mq_[gh ijZdlbq_kdh_ ihkh[b_
KH>?J@:GB? Â&#x2020; Ih^h[b_ nb]mjBBBBBBBBBBBBBBBBBBBBBBBBBBBB Â&#x2020; J_r_gb_ lj_m]hevgbdh\ BBBBBBBBBBBBBBBBBB Â&#x2020; Fgh]hm]hevgbdb BBBBBBBBBBBBBBBBBBBBBBBBB Â&#x2020; IehsZ^b nb]mj BBBBBBBBBBBBBBBBBBBBBBBBBB
Â&#x2020; IH>H;B? NB=MJ Â&#x2039;
Ijb ]hfhl_lbb lhqdZ O i_j_oh^bl \ lhqdm O Z lhqdZ < ² \ lhqdm < DZd gZclb p_glj ]hfhl_lbb _keb lhqdb ; ; < < g_ e_`Zl gZ h^ghc ijyfhc"
Ih hij_^_e_gbx ij_h[jZah\Zgby ]hfhl_lbb ± p_glj ]hfh l_lbb e_`bl gZ h^ghf emq_ k ^Zggufb lhqdZfb ihwlhfm lhqdZ i_j_k_q_gby ijyfuo ;; b << y\ey_lky p_gljhf Wlb ijyfu_ i_j_k_dmlky lZd dZd lhqdb ; ;c < b <c g_ e_`Zl gZ h^ghc ijyfhc ih mkeh\bx Â&#x2039;
Ijb ]hfhl_lbb lhqdZ O i_j_oh^bl \ lhqdm ; Ih kljhcl_ p_glj ]hfhl_lbb _keb dhwnnbpb_gl ]hfhl_ lbb jZ\_g
LZd dZd bkdhfuc p_glj ]hfhl_lbb e_`bl gZ h^ghc ijy fhc k lhqdZfb O b ; lh ^ey gZoh`^_gby p_gljZ ijh\_^_f ijyfmx ;; Mkeh\by aZ^Zgbc ijb\h^ylky \ mq_[guo p_eyo b \ g_h[oh^bfhf h[t_f_ ² dZd beexkljZlb\guc fZl_jbZe Bfy Z\lhjZ b gZa\Zgb_ pblb jm_fh]h ba^Zgby mdZaZgu gZ lblmevghf ebkl_ ^Zgghc dgb]b Kl i AZdhgZ JN h[ Z\lhjkdhf ijZ\_ b kf_`guo ijZ\Zo hl bxgy ]
LZd dZd N lh ih hij_^_e_gbx ]hfhl_lbb HO 2O ]^_ H ² p_glj ]hfhl_lbb agZqbl hleh`bf hl lhqdb ; hlj_ ahd HO HO b ihemqbf bkdhfmx lhqdm H Â&#x2039;
GZq_jlbl_ lj_m]hevgbd Ihkljhcl_ ]hfhl_lbqguc _fm lj_m]hevgbd ijbgy\ aZ p_glj ]hfhl_lbb h^gm ba _]h \_jrbg b dhwnnbpb_gl ]hfhl_lbb jZ\guf
Ihkljhbf ':<K b ijbf_f lhqdm : ² p_glj ]hfhl_lbb GZ ijh^he`_gbb :< hleh`bf hlj_ahd :< :< ihemqbf lhqdm < ]hfhl_lbqgmx lhqd_ < :gZeh]bqgh gZ ijh^he`_gbb :K hleh`bf hlj_ahd :K :K ihemqbf lhqdm K ]hfhl_lbqgmx lhqd_ K Ijh\_^_f hlj_adb :< :K <K b ihemqbf û$< K ]hfh l_lbqguc û:<K k N Â&#x2039;
Qlh ij_^klZ\ey_l kh[hc nb]mjZ ih^h[gZy lj_m]hev gbdm" Nb]mjZ ih^h[gZy lj_m]hevgbdm lZd`_ y\ey_lky lj_m]hev gbdhf Â&#x2039;
M ih^h[guo lj_m]hevgbdh\ :<K b $ % & Â&#x2018;: Â&#x192; :< f <K f % & f Q_fm jZ\gu m]he $ b klhjhgZ $ % " LZd dZd ih^h[b_ khojZgy_l m]eu lh Â&#x2018;: Â&#x2018;: Â&#x192; >Ze__ < & N%& Z agZqbl N
% & %&
LZd`_ $ < N$% Â&#x2DC; f Hl\_l Â&#x2018;: Â&#x192; : < f
Â&#x2039;
>hdZ`bl_ qlh nb]mjZ ih^h[gZy hdjm`ghklb _klv hdjm`ghklv
>hdZ`_f qlh hlghr_gb_ jZ^bmkh\ hdjm`ghkl_c jZ\gh N Lh]^Z jZkkfhljbf ij_h[jZah\Zgb_ ih^h[by k wlbf dhwnnbpb _glhf N ijb dhlhjhf lhqdZ 2 i_j_oh^bl \ lhqdm 2 Lhqdb gZoh^ysb_ky gZ jZkklhygbb 5 hl lhqdb H l _ lhqdb i_j\hc hdjm`ghklb [m^ml gZoh^blvky gZ jZkklhygbb N5 hl lhqdb H l _ [m^ml e_`Zlv gZ hdjm`ghklb k jZ^bmkhf N5 : agZqbl hd jm`ghklv i_j_c^_l \ hdjm`ghklv Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
>Zgu m]he b \gmljb _]h lhqdZ : Ihkljhcl_ hdjm` ghklv dZkZxsmxky klhjhg m]eZ b ijhoh^ysmx q_j_a lhqdm : Ihkljh_gb_ Ijh\_^_f [bkk_dljbkm m]eZ 14 Hlf_lbf gZ g_c lhqdm H himklbf i_ji_g^bdmeyju 2) b H? gZ klhjhgu m]eZ Ihkljhbf hdjm`ghklv k p_gljhf \ lhqd_ H b jZ^bmkhf H? Ijh\_^_f emq 1$ dhlhjuc i_j_k_dZ_l hdjm`ghklv \ lhqd_ L Ijh\_^_f ijyfmx $H lZd qlh $H __ 72 Lh]^Z '172 b '1$2 ih^h[gu lZd qlh :H LH
$1 17
2 1 12
N
Ihkljhbf hdjm`ghklv k p_gljhf \ lhqd_ 2 b jZ^bmkhf 2 $ F
>hdZ`_f qlh wlZ hdjm`ghklv bkdhfZy lh _klv :H H F H J ]^_ H F b H J ² i_ji_g^bdmeyju ba lhqdb H gZ klhjhgu m]eZ LZd dZd '1F2 b '1)2 ih^h[gu lh
_klv
02 27
02 )2
2 1 12
N Lh
N FH N27 $2 JZ\_gkl\h H F H J ke_^m
_l ba jZ\_gkl\Z '102 b '132 AgZqbl hdjm`ghklv k p_g ljhf \ lhqd_ H b jZ^bmkhf H : bkdhfZy Â&#x2039;
<ibrbl_ \ ^Zgguc lj_m]hevgbd d\Z^jZl m dhlhjh]h ^\_ \_jrbgu e_`Zl gZ h^ghc klhjhg_ Z ^\_ ^jm]b_ \_jrbgu ² gZ ^\mo ^jm]bo klhjhgZo
KgZqZeZ ihkljhbf d\Z^jZl ' ( ) * lZd qlh[u \_jrbgu ) b * e_`Zeb gZ klhjhg_ $& D \_jrbgZ ' ² gZ klhjhg_ :< =hfhl_lby hlghkbl_evgh \_jrbgu : i_j_\h^ysZy lhqdm ? \ lhqdm ? e_`Zsmx gZ klhjhg_ <K i_j_\h^bl ' \ ' ) \ ) * \ * LZd dZd ]hfhl_lby i_j_\h^bl nb]mjm \ ih^h[gmx nb]mjm lh q_luj_om]hevgbd '()* ² bkdhfuc d\Z^jZl
Â&#x2039;
>hdZ`bl_ ih^h[b_ jZ\gh[_^j_gguo lj_m]hevgbdh\ k jZ\gufb m]eZfb ijb \_jrbgZo ijhlb\he_`Zsbo hk gh\Zgbyf Imklv Â&#x2018;% Â&#x2018;% B û:<K b û$ % & ² jZ\gh[_^j_ggu_
Lh]^Z Â&#x2018;: Â&#x2018;$ b Â&#x2018;& Â&#x2018;& lZd dZd Â&#x2018;: Â&#x2018;K b Â&#x2018;: Â&#x2018;<
Â&#x2018;K Â&#x192; b Â&#x2018;$ Â&#x2018;K Â&#x2018;K
Â&#x192; ± Â&#x2018;< :gZeh]bqgh Â&#x2018;:
Â&#x192; ± Â&#x2018;< LZd qlh û:<K a û: % K ih ^\mf
m]eZf Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
M ^\mo jZ\gh[_^j_gguo lj_m]hevgbdh\ m]eu f_`^m [hdh\ufb klhjhgZfb jZ\gu ;hdh\Zy klhjhgZ b hk gh\Zgb_ h^gh]h lj_m]hevgbdZ jZ\gu kf b kf hkgh\Zgb_ ^jm]h]h jZ\gh kf GZc^bl_ _]h [hdh\mx klhjhgm
Imklv û:<K b û$ % K ² jZ\gh[_^j_ggu_ Â&#x2018;< Â&#x2018;% $& kf $ & kf : < kf Lh]^Z û$%& a û$ % & ke_^m_l ba aZ^Zqb Â&#x2039; agZqbl $& $ &
$% $ %
lh _klv :<
$& Â&#x2DC; $ % $ &
Hl\_l :< kf
Â&#x2039;
Â&#x2DC;
Ff
M lj_m]hevgbdh\ $<K b : % K Â&#x2018;: Â&#x2018;: Â&#x2018;< Â&#x2018;< :< f <K f : % f $ & f GZc^bl_ hklZevgu_ klhjhgu lj_m]hevgbdh\
û:<K a û: < K ih ^\mf m]eZf AgZqbl
LZd qlh
< K
$ % Â&#x2DC; %& $%
$% $ %
Â&#x2DC;
%& % &
$& $ &
f b :K
Hl\_l :K f < K f
$% Â&#x2DC; $ & $ %
Â&#x2DC;
f
Â&#x2039;
J_rbl_ aZ^Zqm ijb mkeh\bb qlh :< kf <K kf : % kf $& ± $ & Ff û$<K a û$ < K ih ^\mf m]eZf >Ze__ N
$% $ %
² dhwnnbpb_gl ih^h[by agZqbl $& :K ± : K
$ & b ihkdhevdm
$ & ± : K $ & : K kf
Lh]^Z :K kf >Ze__
< K Â&#x2DC; %&
Â&#x2DC;
kf
Hl\_l :K kf : K kf < K kf
Â&#x2039;
>hdZ`bl_ qlh \ukhlZ ijyfhm]hevgh]h lj_m]hevgbdZ hims_ggZy ba \_jrbgu ijyfh]h m]eZ jZa[b\Z_l _]h gZ ^\Z lj_m]hevgbdZ ih^h[gu_ bkoh^ghfm K
Imklv û$<& ² ijyfhm]hevguc Â&#x2018;K Â&#x192; &' ² \ukhlZ JZkkfhljbf û:<K b û$&' Z Â&#x2018;$&% Â&#x2018;&'$ Â&#x192; [ Â&#x2018;K:< Â&#x2018;':K h[sbc m]he AgZqbl û$%& a û$&' ih ^\mf m]eZf :gZeh]bqgh ^hdZau\Z_lky qlh û:<K a ûK<'
Â&#x2039;
IjyfZy iZjZee_evgZy klhjhg_ :< lj_m]hevgbdZ :<K i_j_k_dZ_l _]h klhjhgm :K \ lhqd_ : Z klhjh gm <K \ lhqd_ < >hdZ`bl_ qlh ¨:<K a ¨: % K AZ^ZqZ j_r_gZ \ mq_[gbd_ gZ klj i
Â&#x2039;
< lj_m]hevgbd_ k hkgh\Zgb_f Z b \ukhlhc K \ibkZg d\Z^jZl lZd qlh ^\_ _]h \_jrbgu e_`Zl gZ hkgh\Z gbb lj_m]hevgbdZ Z ^jm]b_ ^\_ ² gZ [hdh\uo klhjh gZo <uqbkebl_ klhjhgm d\Z^jZlZ
Imklv \ ':<K %' ยฒ \ukhlZ >Ze__ 0134 ยฒ d\Z^jZl 1 ย <K F ย :< 3 b 4 ย $& Lh]^Z $& D %' K ih mkeh \bx JZkkfhljbf รป$<K b รป0%1 Z ย :<K ย 0%1 h[sbc m]he [ ย <:K ย %01 dZd h^ghklhjhggb_ m]eu ijb iZjZe e_evguo ijyfuo :K b 01 b k_dms_c :< Ke_^h\Zl_evgh รป:<K a รป0%1 ih ^\mf m]eZf AgZqbl klhjhgu b \ukhlu lj_m]hevgbdh\ :<K b 0%1 ijhihjpbh gZevgu Lh _klv 01 $&
<? %'
Imklv o ยฒ klhjhgZ d\Z^jZlZ Lh]^Z %( K ยฑ [ Lh _klv K [ K
[ D
D K ยฑ o K[ DK ยฑ D[ K[ DK [ K D [
Hl\_l ย
DK K D
IjyfZy iZjZee_evgZy klhjhg_ :< lj_m]hevgbdZ :<K ^_ebl _]h klhjhgm :K \ hlghr_gbb l i kqb lZy hl \_jrbgu K < dZdhf hlghr_gbb hgZ ^_ebl klhjhgm <K" 1
DK K D
0
&1 $1
P Q $& û:<K a ûK10 AgZqbl &1 $1 &1 0% &0 bf__f &1 $1 0% LZd qlh lh _klv &1 &0
Imklv F1 __ :<
&0 %0
Hl\_l Â&#x2039;
Ba aZ^Zqb Â&#x2039; ke_^m_l qlh %& gh :K &1 $1 %& &0 0% &0 $1 0% beb &0 &1 &0
&1 1$
P Q
P Q
< lj_m]hevgbd_ :<K ijh\_^_g hlj_ahd '( iZjZe e_evguc klhjhg_ :K dhg_p ' hlj_adZ e_`bl gZ klh jhg_ :< Z ? ² gZ klhjhg_ <K GZc^bl_ $' _keb :< kf :K kf b '( kf
Ba aZ^Zqb Â&#x2039; ke_^m_l qlh û:<K a û'<( Lh]^Z $% %'
$& '(
>Ze__ %' :< ± $' lZd qlh $% $% $'
$& '( $'
± $' $' $' kf
Hl\_l $' kf
Â&#x2039;
< aZ^Zq_ gZc^bl_ hlghr_gb_ $' %' _keb ba \_klgh qlh :K '(
LZd dZd
$% %'
$& '(
b :< %' $' lh %' $' %'
$' %'
$' %'
Hl\_l Â&#x2039;
$' %'
GZc^bl_ ^ebgm hlj_adZ '( \ aZ^Zq_ _keb :K kf :< kf b %' kf :K ^f :< ^f b $' ^f
Bf__f
$% %'
$& '(
hldm^Z ihemqZ_f qlh '(
$& Â&#x2DC; %' $%
%' :< ± $' lh _klv
Â&#x2DC; kf
%' ± ^f b '(
Hl\_l kf ^f
$& Â&#x2DC; %' $%
Â&#x2DC; ^f
ย
>bZ]hgZeb ljZi_pbb $%&' i_j_k_dZxlky \ lhqd_ ? >hdZ`bl_ ih^h[b_ lj_m]hevgbdh\ <K? b '$(
JZkkfhljbf รป%K? b รป'$( Z ย %?K ย $(' dZd \_jlbdZevgu_ m]eu [ ย &%? ย ('$ dZd gZdj_kl e_`Zsb_ m]eu ijb i_j_k_ q_gbb iZjZee_evguo ijyfuo $' b <K k_dms_c %' AgZqbl รป<K? a รป$(' ih ^\mf m]eZf Qlh b lj_[h\Zehkv ^hdZaZlv ย
GZc^bl_ hlghr_gb_ hlj_adh\ ^bZ]hgZeb ljZi_pbb gZ dhlhju_ hgZ jZa[b\Z_lky ^jm]hc ^bZ]hgZevx _keb hkgh\Zgby ljZi_pbb hlghkylky dZd P i
รป$(' a รป<K? kf j_r_gb_ ย AgZqbl
Hl\_l ย
P Q
$( (&
$' %&
P Q
IjyfZy ijhoh^ysZy q_j_a lhqdm i_j_k_q_gby ^bZ]h gZe_c ljZi_pbb ^_ebl h^gh hkgh\Zgb_ \ hlghr_gbb l i < dZdhf hlghr_gbb hgZ ^_ebl ^jm]h_ hkgh\Z gb_"
Imklv
%0 0&
P Q
JZkkfhljbf รปFK? b รป$?1 ย F?K ย $?1 m]eu \_jlbdZevgu_ ย FK? ย ?$1 dZd gZdj_kl e_`Zsb_ m]eu ijb i_j_k_ q_gbb iZjZee_evguo ijyfuo 0& b $1 k_dms_c $& AgZqbl รปFK? a รป$?1 ih ^\mf m]eZf Lh]^Z 0& $1
0( 1(
0% 1'
0( 1(
:gZeh]bqgh ^hdZau\Z_lky qlh รป<F? a รป'1( Z agZqbl
LZd qlh
Hl\_l ย
0( 1(
Q P
0& $1
0% agZqbl 1'
FKย 1' 0%ย $1 $1 1'
0& 0%
Q P
< ljZi_pbb $%&' k ^bZ]hgZevx :K m]eu :<K b $&' jZ\gu GZc^bl_ ^bZ]hgZev :K _keb hkgh\Zgby <K b $' khhl\_lkl\_ggh jZ\gu f b f JZkkfhljbf รป$&' b รปK<:
Z ย $&' ย $%& iR mkeh\bx
[ Â&#x2018;&$' Â&#x2018;%&$ dZd gZdj_kl e_`Zsb_ m]eu ijb i_j_k_ q_gbb iZjZee_evguo ijyfuo $' b <K k_dms_c :K LZd qlh û$&' a ûK<: Ihwlhfm $&
$& &%
$& &%Â&#x2DC;$'
&% Â&#x2DC; $'
Â&#x2DC;
$' lh _klv $&
kf
Hl\_l :K kf
Â&#x2039;
Ebgby iZjZee_evgZy hkgh\Zgbyf ljZi_pbb ^_ebl h^gm [hdh\mx klhjhgm \ hlghr_gbb l i < dZdhf hlghr_gbb ^_ebl hgZ \lhjmx [hdh\mx klhjhgm" (
Imklv $%&' ² ljZi_pby $' b <K ² __ hkgh\Zgby F1 __ $' __ <K $0 0%
P Q
;hdh\u_ klhjhgu ljZi_pbb i_j_k_dZxlky \ lhqd_ ? Ih l_hj_f_ h ijhihjpbhgZevguo hlj_adZo iZjZee_evgu_ ijyfu_ $' 01 b <K i_j_k_dZxsb_ klhjhgu Â&#x2018;? hlk_dZxl hl klhjhg ijhihjpbhgZevgu_ hlj_adb lZd qlh
Hl\_l
P Q
$0 0%
'1 1&
P Q
ย
Ijh^he`_gby [hdh\uo klhjhg :< b &' ljZi_pbb $%&' i_j_k_dZxlky \ lhqd_ ? GZc^bl_ klhjhgu lj_m]hevgbdZ $(' _keb :< kf <K kf &' kf $' kf
JZkkfhljbf รป$(' b รป<?K LZd dZd $' __ <K lh wlb lj_ m]hevgbdb ih^h[gu kf j_r_gb_ aZ^Zqb ย AgZqbl gh :? :< <? lZd qlh $% %( %(
$( %(
$' %&
$' %( %& %(
<? <? <? <? kf
Lh]^Z $( :< <? kf :gZeh]bqgh ba ih^h[by lj_m]hevgbdh\ :?< b <?K bf__f '( &(
: lZd dZd '( &' K? lh &' &( &(
$' %&
$' &( %& &(
K? K? K? K? kf '( K? &' kf
Hl\_l :? kf '( kf
Â&#x2039;
GZc^bl_ \ukhlm lj_m]hevgbdZ $(' ba aZ^Zqb Â&#x2039; hims_ggmx gZ klhjhgm $' _keb <K kf $' kf b \ukhlZ ljZi_pbb jZ\gZ kf
Imklv ?1 ² \ukhlZ lj_m]hevgbdZ $(' 01 ² \ukhlZ ljZi_pbb '$(' a '<?K [ueh ^hdZaZgh \ aZ^Zq_ Â&#x2039; Ihwlhfm $( %(
$' %&
>Ze__ jZkkfhljbf û$?1 b û<?F Z Â&#x2018;: Â&#x2018;< m]eu ijb i_j_k_q_gbb iZjZee_evguo ijyfuo %0 b $1 k_dms_c $% [ Â&#x2018;1 Â&#x2018;F Â&#x192; Lh]^Z û$(1 a û<?F b (1 (0
Gh (1 (0 01 lZd qlh
$( %(
(0 (0
?F ?F ?F ?F kf
lh]^Z ?1 (0 01 kf Hl\_l kf Â&#x2039;
>bZ]hgZeb ljZi_pbb i_j_k_dZxlky \ lhqd_ ? Z ijh ^he`_gby [hdh\uo klhjhg i_j_k_dZxlky \ lhqd_ )
>hdZ`bl_ qlh ijyfZy () ^_ebl hkgh\Zgby ljZi_pbb ihiheZf
')0& a ')1' lZd dZd Â&#x2018;)0& Â&#x2018;)1' ² h^ghklhjhggb_ 0& )0 m]eu ijb %& __ $' b Â&#x2018;1)' ² h[sbc LZd qlh 1' )1 %0 )0 lZd qlh :gZeh]bqgh ')0< a ')1: b $1 )1 0& %0 %0 $1 lh _klv N 0' $1 0& 1' %0 $1 lZd qlh < aZ^Zq_ Â&#x2039; [ueh ^hdZaZgh qlh 0& 1' N
N
b <F FK 1' $1 Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
M jZ\gh[_^j_ggh]h lj_m]hevgbdZ :<K k hkgh\Zgb_f :K b ijhlb\he_`Zsbf m]ehf Â&#x192; ijh\_^_gZ [bkk_d ljbkZ $' >hdZ`bl_ ih^h[b_ lj_m]hevgbdh\ $%& b &$' GZc^bl_ hkgh\Zgb_ lj_m]hevgbdZ :<K _keb _]h [hdh\Zy klhjhgZ jZ\gZ Z :< <K Z
LZd dZd Â&#x2018;% Â&#x192; lh
Â&#x2018;<:K Â&#x2018;:K< Â&#x192; ± Â&#x192; Â&#x192;
Ihkdhevdm $' ² [bkk_dljbkZ Â&#x2018;: lh
Â&#x2018;&$' Â&#x2018;'$% Â&#x192; Â&#x192;
JZkkfhljbf ¨$<& b ¨&$' LZd dZd Z Â&#x2018;<:K Â&#x2018;:K< Â&#x192; [ Â&#x2018;:<K Â&#x2018;&$' Â&#x192; AgZqbl ¨$<& a ¨&$' ih ^\mf m]eZf Qlh b lj_[h\Zehkv ^hdZaZlv Ba ih^h[by lj_m]hevgbdh\ :<K b :K' ke_^m_l $% $&
$& &'
Imklv %' [ kf ke_^h\Zl_evgh '& Z ± [ >Ze__ %' $' $& klRjhgu jZ\gh[_^j_gguo lj_m]hev gbdh\ lh _klv %' $' $& [ kf Ih^klZ\eyy \ ijhihjpbx
D [
[ ihemqbf D [
[ D ± D[ o Zo ± Z ' D D D [ [
D D
D
g_ m^h\e_l\hjy_l mkeh\bx aZ
^Zqb lZd dZd [ ! [
D r D
D D
D kf Hl\_l :K D
D D
D
!
AgZqbl $&
Â&#x2039;
M]eu < b % lj_m]hevgbdh\ :<K b : < K jZ\gu Klhjhgu lj_m]hevgbdZ :<K ijbe_`Zsb_ d m]em < \ jZaZ [hevr_ klhjhg lj_m]hevgbdZ : < K ijbe_ `Zsbo d m]em % GZc^bl_ :K b : K _keb bo kmffZ jZ\gZ f %
%
:< : <
$
& $
&
<K b Â&#x2018;< Â&#x2018;< lZd qlh ':<& a '$ % & < K
ih ijbagZdm ih^h[by lj_m]hevgbdh\ k dhwnnbpb_glhf ih^h [by jZ\guf Imklv : K o f ke_^h\Zl_evgh :K o f gh : K :K f
LZd qlh o o o o f Lh]^Z : K f ke_^h\Zl_evgh :K ± : K ± f
Hl\_l : K f :K f
Â&#x2039;
< hkljhm]hevghf lj_m]hevgbd_ :<K ijh\_^_gu \u khlu $' %( &) GZc^bl_ m]eu lj_m]hevgbdZ '() agZy m]eu lj_m]hevgbdZ :<K
Ba ij_^u^ms_c aZ^Zqb ihemqZ_f qlh ')%' a 'ù<K ke_ ^h\Zl_evgh Â&#x2018;%') Â&#x2018;$ Â&#x2018;%)' Â&#x2018;& >Ze__ ''&( a ':<K lZd qlh Â&#x2018;&'( Â&#x2018;$ b Â&#x2018;&(' Â&#x2018;% Â&#x2018;' Â&#x192;± Â&#x2018;%') Â&#x2018;&'( Â&#x192;± Â&#x2018;$ Â&#x2018;$ Â&#x192;± Â&#x2018;$
LZd dZd '$() a ':<K lh Â&#x2018;$() Â&#x2018;% Â&#x2018;$)( Â&#x2018;& LZd qlh Â&#x2018;( Â&#x192;± Â&#x2018;&(' Â&#x2018;$() Â&#x192;± Â&#x2018;% Â&#x2018;% Â&#x192;± Â&#x2018;% Â&#x2018;) Â&#x192;± Â&#x2018;$)( Â&#x2018;%)' Â&#x192;± Â&#x2018;& Â&#x2018;& Â&#x192;± Â&#x2018;&
Hl\_l Â&#x2018;' Â&#x192;± Â&#x2018;$ Â&#x2018;( Â&#x192;± Â&#x2018;% Â&#x2018;) Â&#x192;± Â&#x2018;&
Â&#x2039;
>hdZ`bl_ qlh [bkk_dljbku lj_m]hevgbdZ '() \ aZ ^Zq_ Â&#x2039; e_`Zl gZ \ukhlZo lj_m]hevgbdZ :<K
Â&#x2018;)%$ Â&#x2018;%'$ ± Â&#x2018;%') lZd qlh Â&#x2018;)'$ Â&#x192; ± Â&#x2018;$ b Â&#x2018;$'( Â&#x2018;$'& ± Â&#x2018;&'( Â&#x192; ± Â&#x2018;$ agZqbl $' ² [bkk_d ljbkZ Â&#x2018;' :gZeh]bqgh ^hdZau\Z_lky qlh ?< ² [bkk_dljbkZ Â&#x2018;( b )& ² [bkk_dljbkZ Â&#x2018;) lh _klv [bkk_dljbku wlbo m]eh\ e_`Zl gZ \ukhlZo ':<K Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039; Ih^h[gu eb ^\Z jZ\ghklhjhggbo lj_m]hevgbdZ" LZd dZd klhjhgu jZ\ghklhjhgg_]h lj_m]hevgbdZ jZ\gu lh ljb klhjhgu h^gh]h lj_m]hevgbdZ ijhihjpbhgZevgu lj_f klh jhgZf ^jm]h]h lZd qlh jZ\ghklhjhggb_ lj_m]hevgbdb ih^h[ gu
Â&#x2039;
Ih^h[gu eb lj_m]hevgbdb ù<K b ù ú K _keb :< f :K f <K f $ % Ff $ & kf % K kf :< f :K f <K f $ % ^f $ & ^f % K ^f :< f :K f <K f $ % Ff $ & kf % K kf Lj_m]hevgbdb [m^ml ih^h[gu _keb [m^_l \uihegylvky jZ \_gkl\h $% $ %
$& $ &
%& % &
² lj_m]hevgbdb ih^h[gu ² g_\_jgh ihwlhfm lj_m]hevgbdb g_ ih
^h[gu ih^h[gu
² g_\_jgh ihwlhfm lj_m]hevgbdb g_
Â&#x2039;
Klhjhgu lj_m]hevgbdZ jZ\gu f f b f GZc ^bl_ klhjhgu ih^h[gh]h _fm lj_m]hevgbdZ i_jbf_lj dhlhjh]h jZ\_g f '$%& a '$ % & J ² i_jbf_lj '$%& 3 ² i_jbf_lj '$ % & :< f <K f :K f J f Lh]^Z 3 :< <K :K f
<hkihevam_fky aZ^Zq_c Â&#x2039;
lh]^Z N
3 3
$ % $%
AgZqbl
% & %&
$ & $&
N
: < NÂ&#x2DC;:< < K NÂ&#x2DC;<K : K NÂ&#x2DC;:K
Â&#x2DC; O f
Â&#x2DC;O f
Â&#x2DC; f
Hl\_l $ % O f % & f $ & f Â&#x2039;
I_jbf_lj h^gh]h lj_m]hevgbdZ khklZ\ey_l
i_jb
f_ljZ ih^h[gh]h _fm lj_m]hevgbdZ JZaghklv ^\mo khhl\_lkl\mxsbo klhjhg jZ\gZ f GZc^bl_ wlb klhjhgu
'$%& a '$ % & 3'$%& J ': < K J ':<K
Imklv :< o lh]^Z
3 '$ % & : < ± :< f : < :<
: < o b
[ [
o o o o f
Lh _klv :< f Z : < f Hl\_l f f Â&#x2039;
Ih^h[gu eb ^\Z ijyfhm]hevguo lj_m]hevgbdZ _keb m h^gh]h ba gbo _klv m]he Â&#x192; Z m ^jm]h]h ² m]he jZ\guc Â&#x192; Â&#x192;" M ih^h[guo lj_m]hevgbdh\ m]eu jZ\gu d lhfm `_ kmffZ hkljuo m]eh\ ijyfhm]hevgh]h lj_m]hevgbdZ Â&#x192; Z h h h lj_m]hevgbdb ih^h[gu [ h h h lj_m]hevgbdb g_ ih^h[gu
Â&#x2039;
Hkgh\Zgb_ \ukhlu ijyfhm]hevgh]h lj_m]hevgbdZ hims_gghc gZ ]bihl_gmam ^_ebl __ gZ hlj_adb kf b kf GZc^bl_ klhjhgu lj_m]hevgbdZ
< '$%& Â&#x2018;K Â&#x192; &' ² \ukhlZ $' kf '% kf '$&' a '&%' lZd dZd Â&#x2018;&'$ Â&#x2018;&'% Â&#x192; b Â&#x2018;$&'
Â&#x192; ± Â&#x2018;$ Â&#x2018;% AgZqbl
$' &'
&' $' Â&#x2DC; '%
&' &' $'Â&#x2DC;%' %'
Â&#x2DC;
Â&#x2DC; kf
>Ze__ ba '$&' ih l_hj_f_ IbnZ]hjZ bf__f :K
$' &'
Ba '&%' ih l_hj_f_ IbnZ]hjZ bf__f K< '% &'
kf kf
:< $' %' kf
Hl\_l $& kf &% kf :< kf
Â&#x2039;
=bihl_gmaZ ijyfhm]hevgh]h lj_m]hevgbdZ jZ\gZ kf Z h^bg ba dZl_lh\ jZ\_g kf GZc^bl_ ijh_d pbx ^jm]h]h dZl_lZ gZ ]bihl_gmam
< '$%& Â&#x2018;K Â&#x192; &' ² \ukhlZ :< kf :K kf
Imklv $' [ kf ke_^h\Zl_evgh
'% ± [ kf
< '$&' ih l_hj_f_ IbnZ]hjZ bf__f
&' $& ± $' O ± [
Ih ^hdZaZgghfm \ j_r_gbb aZ^Zqb Â&#x2039; LZd qlh
&' $'Â&#x2DC;'% [Â&#x2DC; ± [ [ ± [
± [ [ ± [ [ [ kf %' ± [ kf
Hl\_l %' kf
Â&#x2039;
>hdZ`bl_ qlh khhl\_lkl\mxsb_ \ukhlu ih^h[guo lj_m]hevgbdh\ hlghkylky dZd khhl\_lkl\mxsb_ klh jhgu
'$<& a '$ < K Imklv %' ² \ukhlZ '$%& % ' ² \u khlZ '$ % & JZkkfhljbf '$%' b '$ % ' Z Â&#x2018;: Â&#x2018;: lZd dZd ':<K a ': < K [ Â&#x2018;' Â&#x2018;' ijyfu_ m]eu AgZqbl '$%' a '$ % ' ih ^\mf m]eZf lh _klv % ' %'
Qlh b lj_[h\Zehkv ^hdZaZlv
$ % $%
Â&#x2039;
DZl_lu ijyfhm]hevgh]h lj_m]hevgbdZ hlghkylky dZd P Q DZd hlghkylky ijh_dpbb dZl_lh\ gZ ]bihl_gmam" K
Imklv \ '$%& Â&#x2018;K Â&#x192; '$K' a ':%& lZd qlh e__ ':<K a '%&' hldm^Z qlh
Hl\_l Â&#x2039;
P Q
$' '%
$& %&
$& $%
<& $%
$& %& $% $%
P Q
<
$' hldm^Z $' $&
<' lh _klv '% <& $& %&
P Q
$& >Z $%
%& LZd $%
>ebgZ l_gb nZ[jbqghc ljm[u jZ\gZ f \ wlh `_ \j_fy \_jlbdZevgh \hldgmluc \ a_fex dhe \ukhlhc f ^Z_l l_gv ^ebghc f GZc^bl_ \ukhlm ljm [u
%havf_f '$%& b '$ % & ]^_ Â&#x2018;K Â&#x2018;K Â&#x192; :K f <K f : K f GZc^_f % & ^ebgZ ljm[u
K\_l gZ dhe b ljm[m iZ^Z_l k h^ghc klhjhgu b ih^ h^gbf m]ehf agZqbl Â&#x2018;: Â&#x2018;$ d lhfm `_ Â&#x2018;K Â&#x2018;K Â&#x192; AgZqbl '$%& a '$ % & b
: K :K
% &
Hl\_l < K | f
Â&#x2039;
< K lh _klv <K
$ & Â&#x2DC; %& $&
| f
< lj_m]hevgbd :<K \ibkZg jhf[ $'() lZd qlh m]he : m gbo h[sbc Z \_jrbgZ ? gZoh^blky gZ klhjhg_ <K GZc^bl_ klhjhgm jhf[Z _keb :< k b :K E
)
&
LZd dZd '(__$& ih hij_^_e_gbx jhf[Z lh ':<K a ''%( '% $% lZd qlh
lh]^Z
'% $%
%( %&
'( $&
%( %&
'( >Ze__ %' $% ± $' F ± $' '( $' $&
F $' F
$' E
EF EÂ&#x2DC;$' FÂ&#x2DC;$' EF $' E F lZd qlh $'
Hl\_l $'
EÂ&#x2DC;F E F
EÂ&#x2DC;F E F
Â&#x2039;
;bkk_dljbkZ \g_rg_]h m]eZ lj_m]hevgbdZ :<K ijb \_jrbg_ K i_j_k_dZ_l ijyfmx :< \ lhqd_ ' >hdZ `bl_ qlh $' %' :K <K
Ijh\_^_f %( __ &' Lh]^Z Â&#x2018;K<? Â&#x2018;%&' dZd m]eu gZ dj_kl e_`Zsb_ ijb iZj_k_q_gbb iZjZee_evguo ijyfuo ?< b &' k_dms_c K< Â&#x2018;<?K Â&#x2018;'&) Â&#x2018;'&% dZd khhl\_lkl\_g gu_ m]eu ijb l_o `_ iZjZee_evguo ijyfuo Â&#x2018;'&) Â&#x2018;'&% l d K' [bkk_dljbkZ Â&#x2018;%&) AgZqbl '(&% ² jZ\gh[_^j_g guc b ?K %K Ba j_r_gby aZ^Zqb Â&#x2039; bf__f _keb klhjhgu m]eZ i_j_k_ q_gu iZjZee_evgufb ijyfufb lh hlk_dZ_fu_ gZ klhjhgZo m] eZ hlj_adb ijhihjpbhgZevgu lh _klv $' %'
Gh lZd dZd ?K <K lh
aZlv
Â&#x2039;
$' %'
$& (&
$& qlh b lj_[h\Zehkv ^hdZ %&
>hdZ`bl_ qlh ]_hf_ljbq_kdh_ f_klh lhq_d hlghr_ gb_ jZkklhygbc hl dhlhjuo ^h ^\mo ^Zgguo lhq_d ih klhyggh g_ jZ\gh _^bgbp_ _klv hdjm`ghklv 0
$
1
%
3
<havf_f ijhbahevgmx lhqdm 0 lZdmx qlh
0$ 0%
O z
Ijh\_^_f [bkk_dljbkm 01 b [bkk_dljbkm \g_rg_]h m]eZ 03 \ ':F< $1 $0 k\hckl\h [bkk_dljbku Lh]^Z O 1% %0 $0 %0
$3 %3
O kf aZ^Zqm Â&#x2039; Lh _klv iheh`_gb_ lhq_d 1 b
3 aZ\bkbl lhevdh hl \u[hjZ qbkeZ O b g_ aZ\bkbl hl lhqdb 0 Â&#x2018;103 Â&#x2018; Â&#x2018; Gh Ã&#x201A;Â&#x2018; Ã&#x201A;Â&#x2018; Â&#x192; AgZqbl Â&#x2018;103 Â&#x192; Z ke_^h\Zl_evgh ]_hf_ljbq_kdh_ f_klh lhq_d hlghr_gb_ jZk klhygbc hl dhlhjuo ^h ^\mo ^Zgguo lhq_d ihklhyggh b g_ jZ\ gh ² wlh fgh`_kl\h lhq_d ba dhlhjuo nbdkbjh\Zgguc hl j_ahd 13 \b^_g ih^ ijyfuf m]ehf lh _klv hdjm`ghklv ihkljh_ggZy gZ ^bZf_lj_ 13 Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
GZc^bl_ ^hihegbl_evgu_ iehkdb_ m]eu agZy qlh h^bg ba gbo \ jZa [hevr_ ^jm]h]h h^bg ba gbo gZ Â&#x192; [hevr_ ^jm]h]h jZaghklv bo jZ\gZ Â&#x192; Imklv c m]he jZ\_g oÂ&#x192; lh]^Z c [m^_l oÂ&#x192; Z l d kmffZ ^\mo iehkdbo m]eh\ jZ\gZ Â&#x192; lh o o Â&#x192; o Â&#x192; [ Â&#x192;
AgZqbl c m]he ² Â&#x192; Z c ² Â&#x192; Imklv c m]he jZ\_g oÂ&#x192; lh]^Z c [m^_l [ Â&#x192; Z bo kmffZ Â&#x192; l _ o o Â&#x192; Â&#x192; o Â&#x192; o Â&#x192; Â&#x192; o Â&#x192;
AgZqbl c m]he ² Â&#x192; Z c ² Â&#x192; Imklv c m]he jZ\_g oÂ&#x192; lh]^Z c [m^_l [ Â&#x192; Z bo kmffZ Â&#x192; l _ [ [ Â&#x192; Â&#x192; [ Â&#x192; [ Â&#x192; Â&#x192; o Â&#x192;
AgZqbl c m]he ² Â&#x192; Z c ² Â&#x192; Hl\_l Â&#x192; Â&#x192; Â&#x192; Â&#x192; Â&#x192; Â&#x192;
Â&#x2039;
Lhqdb : < K e_`Zl gZ hdjm`ghklb Q_fm jZ\gZ ohj ^Z :K _keb m]he :<K jZ\_g Â&#x192; Z ^bZf_lj hdjm`gh klb kf"
LZd dZd \ibkZgguc m]he :<K Â&#x192; lh khhl\_lkl\mxsbc _fm p_gljZevguc m]he [m^_l Â&#x192; ih l_hj_f_ lh _klv Â&#x2018;:HK Â&#x192; JZkkfhljbf '$HK LZd dZd :H HK dZd jZ^bmku hdjm` ghklb Z Â&#x2018;H Â&#x192; lh '$<K ² jZ\ghklhjhggbc agZqbl :K :H HK U
Hl\_l :K kf
Â&#x2039;
kf
Lhqdb : < K e_`Zl gZ hdjm`ghklb Q_fm jZ\_g m]he :<K _keb ohj^Z :K jZ\gZ jZ^bmkm hdjm`ghklb" >\Z kemqZy
Â&#x2018;:HK y\ey_lky p_gljZevguf ^ey Â&#x2018;:<K LZd dZd :K :H HK lh ':HK jZ\ghklhjhggbc ke_^h \Zl_evgh Â&#x2018;:HK Â&#x192; Z Â&#x2018;:<K
Â&#x2018;:HK Â&#x192;
Â&#x2018;:HK \ ':HK jZ\_g Â&#x192; gh p_gljZevguc m]he khhl \_lkl\mxsbc gZr_fm \ibkZgghfm _klv m]he ^hihegbl_evguc d Â&#x2018;:HK b jZ\_g Â&#x192; ± Â&#x192; Â&#x192; Lh]^Z Â&#x2018;:%K
Â&#x192; Â&#x192;
Hl\_l Â&#x2018;:<K Â&#x192; beb Â&#x192;
Â&#x2039;
>hdZ`bl_ qlh p_gljhf hdjm`ghklb hibkZgghc hdh eh ijyfhm]hevgh]h lj_m]hevgbdZ y\ey_lky k_j_^bgZ ]bihl_gmau Imklv '$<& \ibkZg \ hdjm`ghklv k p_gljhf H
Ba ke_^kl\by l_hj_fu h \ibkZgghf m]e_ bf__f qlh Â&#x2018;< Â&#x192; hibjZ_lky gZ ^bZf_lj hdjm`ghklb agZqbl ]bihl_gm aZ lj_m]hevgbdZ :K ² ^bZf_lj hdjm`ghklb b lhqdZ H ² p_glj hdjm`ghklb gZoh^blky \ __ k_j_^bg_ Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
>hdZ`bl_ qlh f_^bZgZ ijyfhm]hevgh]h lj_m]hevgb dZ ijh\_^_ggZy d ]bihl_gma_ jZa[b\Z_l _]h gZ ^\Z jZ\gh[_^j_gguo lj_m]hevgbdZ Hibr_f hdheh '$<& hdjm`ghklv
P_glj hdjm`ghklb [m^_l kh\iZ^Zlv k k_j_^bghc ]bihl_gm au ih ^hdZaZgghfm \ aZ^Zq_ Â&#x2039; AgZqbl <H ² f_^bZgZ gh
'$%H b '<KH jZ\gh[_^j_ggu_ lZd dZd :H H< b H< HK ² jZ^bmku h^ghc hdjm`ghklb Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
Ihkljhcl_ ijyfhm]hevguc lj_m]hevgbd ih ]bihl_gm a_ b \ukhl_ hims_gghc ba \_jrbgu ijyfh]h m]eZ gZ ]bihl_gmam Imklv $& ² ]bihl_gmaZ %' E ² \ukhlZ <
Z :
E
'
'
H
< &
Ihkljh_gb_ ijh\_^_f hlj_ahd :K jZa^_ebf _]h ihiheZf ijbgy\ H aZ k_j_^bgm :K ijh\_^_f hdjm`ghklv k p_gljhf \ lhqd_ H b jZ^bmkhf :H ijh\_^_f ijyfmx Z __ :K gZ jZkklhygbb E hl ijyfhc :K IjyfZy Z i_j_k_q_l hdjm`ghklv \ ^\mo lhqdZo < b < LZd qlh ':<K b ':< K ² bkdhfu_ Â&#x2039;
GZ hdjm`ghklb hlf_q_gu q_luj_ lhqdb : < K ' Q_fm jZ\_g m]he $'& _keb m]he :<K jZ\_g D" >\Z kemqZy
% $
'
D
2
&
c kemqZc Â&#x2018;$'& b Â&#x2018;$%& ² \ibkZggu_ hibjZxsb_ky gZ
h^gm ohj^m Ihwlhfm Â&#x2018;:'K
Â&#x2018;:2K Â&#x2018;:%K .
$ '
D
2
% &
c kemqZc \ ':HK Â&#x2018;:HK Â&#x192; ± D lZd dZd ^hihegb l_evguc d g_fm m]he Â&#x2018;:HK D dZd p_gljZevguc m]he khhl \_lkl\mxsbc hibkZgghfm Â&#x2018;< D Â&#x2018;:'K
Â&#x2018;:2K Â&#x192; ± . Â&#x192; ± .
Hl\_l . Â&#x192; ± . Â&#x2039;
Ohj^u hdjm`ghklb $' b <K i_j_k_dZxlky M]he $<K jZ\_g Â&#x192; m]he $&' jZ\_g Â&#x192; GZc^bl_ m]he &$'
Â&#x2018;$'& Â&#x2018;$%& Â&#x192; ² dZd \ibkZggu_ hibjZxsb_ky gZ h^gm ohj^m Lh]^Z Â&#x2018;&$' Â&#x192; ± Â&#x2018;$'& ± Â&#x2018; $&' Â&#x192; ± ± Â&#x192; ± Â&#x192; Â&#x192; Hl\_l Â&#x192;
Â&#x2039;
>hdZ`bl_ qlh m q_luj_om]hevgbdZ \ibkZggh]h \ hd jm`ghklv kmffZ ijhlb\he_`Zsbo m]eh\ jZ\gZ Â&#x192; Imklv q_luj_om]hevgbd $%&' \ibkZg \ hdjm`ghklv Ih l_hj_f_ bf__f
Â&#x2018;'2% Â&#x2018;%2' Â&#x2018;'2% Â&#x2018;%2' Â&#x192; Â&#x192;
Â&#x2018;$ Â&#x2018;&
lZd dZd Â&#x2018;'2% b Â&#x2018;%2' ^hihegbl_evgu_
:gZeh]bqgh Â&#x2018;' Â&#x2018;< Â&#x192; Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
>hdZ`bl_ qlh ]_hf_ljbq_kdh_ f_klh \_jrbg ijyfuo m]eh\ klhjhgu dhlhjuo ijhoh^yl q_j_a ^\_ ^Zggu_ lhqdb _klv hdjm`ghklv
Imklv kms_kl\m_l lZdZy lhqdZ ' qlh Â&#x2018;$'% h Hibr_f hdjm`ghklv \hdjm] ijyfhm]hevgh]h '$'% Lh]^Z __ p_gljhf y\ey_lky lhqdZ H ² k_j_^bgZ :< : jZ^bmk jZ\_g
:< :H
lh _klv g_ aZ\bkbl hl lhqdb ' LZd qlh ex[Zy lhqdZ ² \_jrb gZ ijyfh]h m]eZ ba mkeh\by aZ^Zqb ijbgZ^e_`bl hdjm`ghklb k p_gljhf H ² k_j_^bgZ :< b jZ^bmkhf :H lj_[h\Zehkv ^hdZaZlv
:< Qlh b
Â&#x2039;
>hdZ`bl_ qlh ]_hf_ljbq_kdh_ f_klh \_jrbg m]eh\ k aZ^Zgghc ]jZ^mkghc f_jhc klhjhgu dhlhjuo ijhoh ^yl q_j_a ^\_ ^Zggu_ lhqdb Z \_jrbgu e_`Zl ih h^ gm klhjhgm hl ijyfhc kh_^bgyxs_c wlb lhqdb _klv ^m]Z hdjm`ghklb k dhgpZfb \ wlbo lhqdZo Imklv :< ² ijyfZy M]he :;< ² \ibkZg \ hdjm`ghklv ?keb \_jrbgZ ; ijbgZ^e_`bl ^m]_ hdjm`ghklb H U lh \k_ m]eu \_jrbgu dhlhjuo e_`Zl gZ hdjm`ghklb ih h^gm klhjhgm hl ijyfhc :< jZ\gu [hc
Â&#x2018;:H< ihwlhfm hgb jZ\gu f_`^m kh
>hdZ`_f l_i_jv qlh ^Zgguf k\hckl\hf h[eZ^Zxl lhevdh lhqdb wlhc qZklb hdjm`ghklb JZkkfhljbf ^\Z \ZjbZglZ Z \_jrbgZ J e_`bl \gmljb hdjm`ghklb lh]^Z Â&#x2018;:J< ! Â&#x2018;:;< [ \_jrbgZ . e_`bl \g_ hdjm`ghklb lh]^Z Â&#x2018;:;< ! Â&#x2018;:.< LZd qlh \_jrbgu ^he`gu e_`Zlv gZ hdjm`ghklb lh _klv gZ ^m]_ hdjm`ghklb Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
>hdZ`bl_ qlh hkljuc m]he f_`^m ohj^hc hdjm`gh klb b dZkZl_evghc d hdjm`ghklb \ dhgp_ ohj^u jZ\_g iheh\bg_ m]eZ f_`^m jZ^bmkZfb ijh\_^_ggufb d dhgpZf ohj^u Imklv H$ b H% ² jZ^bmku hdjm`ghklb H U :< ² ohj ^Z K< ² dZkZl_evgZy Lh]^Z Â&#x2018;2<K Â&#x192; ih k\hckl\m dZkZ l_evghc Z Â&#x2018;2%' Â&#x2018;2$' dZd m]eu jZ\gh[_^j_ggh]h lj_ m]hevgbdZ Lh]^Z Â&#x2018;2%'
q Â&#x2018;$2%
q
Â&#x2018;$2%
>Ze__ Â&#x2018;K%: Â&#x2018;2%K ± Â&#x2018;2%' Â&#x192; ± Â&#x192; ± Â&#x192; ± Â&#x192;
Â&#x2018;$2% Â&#x2018;$2%
$2%
Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
Ihkljhcl_ lj_m]hevgbd ih klhjhg_ ijhlb\he_`Zs_ fm _c m]em b \ukhl_ ijh\_^_gghc ba \_jrbgu wlh]h m]eZ
Imklv Z ² klhjhgZ ':<K Â&#x2018;: . KD ² \ukhlZ hims_g gZy ba Â&#x2018;: Ihkljh_gb_ Ihkljhbf jZ\gh[_^j_gguc lj_m]hevgbd < 0 K k Â&#x2018;0 Â&#x2018;: . GZ emq_ K< hleh`bf hlj_ahd K< Z hl lhqdb K Ijh\_^_f <F __ < 0 q_j_a lhqdm < Hdheh '0K< hibr_f hdjm`ghklv Ijh\_^_f ijyfmx E__%& gZoh^ysmxky gZ jZkklhygbb KD H[hagZqbf lhqdm i_j_k_q_gby E b hdjm`ghklb : '$<& ² bkdhfuc lZd dZd Â&#x2018;: Â&#x2018;F Z dZd \ibkZggu_ m]eu e_`Zsb_ ih h^gm klhjhgm hl ijyfhc <K <K Z ih ih kljh_gbx :G KD ih ihkljh_gbx
Â&#x2039;
Ba lhqdb K hdjm`ghklb ijh\_^_g i_ji_g^bdmeyj &' d ^bZf_ljm :< >hdZ`bl_ qlh &' $'Ã&#x201A;%' Imklv :< ² ^bZf_lj hdjm`ghklb &' A $%
Ijh\_^_f emqb K: b K< ihemqbf '$&< m dhlhjh]h Â&#x2018;K Â&#x192; l d hibjZ_lky gZ ^bZf_lj Ih ijbagZdm ih^h[by ijyfhm]hevguo lj_m]hevgbdh\ bf__f '$&' a '&'% lZd qlh Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
$' &'
&' l _ &' $'Â&#x2DC;<' %'
>hdZ`bl_ qlh ijhba\_^_gb_ hlj_adh\ k_dms_c hd jm`ghklb jZ\gh d\Z^jZlm hlj_adZ dZkZl_evghc ijh \_^_gghc ba lhc `_ lhqdb :KÃ&#x201A;<K &'
'
Â&#x2018;$%' Â&#x2018;$'& JZkkfhljbf '&%' b '$&' Â&#x2018;&%' Â&#x2018;&'$ iR mkeh\bx Â&#x2018;K ² h[sbc ihwlhfm '&%' a '$&' ih ^\mf m]eZf agZqbl %& &'
&' hldm^Z bf__f &' $&
dZaZlv
:KÂ&#x2DC;<K Qlh b lj_[h\Zehkv ^h
Â&#x2039;
DZd ^Ze_dh \b^gh ba kZfhe_lZ e_lys_]h gZ \ukhl_ df gZ^ A_fe_c _keb jZ^bmk A_feb df" <
:
df H
df
Imklv < ² lhqdZ gZoh`^_gby kZfhe_lZ Ijh\_^_f dZkZ l_evgmx <: Lh]^Z \ '$2< Â&#x2018;: Â&#x192; :H df 2% df Ih l_hj_f_ IbnZ]hjZ $%
Hl\_l § df
Â&#x2039;
Â&#x2DC; | df
<uqbkebl_ jZ^bmk ]hjbahglZ \b^bfh]h k \_jrbgu l_e_[Zrgb \ HklZgdbg_ \ukhlZ dhlhjhc f <
df H
:
df
:gZeh]bqgh aZ^Zq_ Â&#x2039; ihemqZ_f
$%
Hl\_l § df
Â&#x2DC; | df
Â&#x2020; J?R?GB? LJ?M=HEVGBDH< Â&#x2039;
Klhjhgu lj_m]hevgbdZ f f f GZc^bl_ dhkb gmku m]eh\ lj_m]hevgbdZ
Imklv $< f <K f :K f Lh]^Z ih l_hj_f_ dhkb gmkh\ lh _klv FRVÂ&#x2018;& ZgZeh]bqgh FRVÂ&#x2018;$ FRVÂ&#x2018;%
:< <K :K ± <KÂ&#x2DC;$&Â&#x2DC;FRVÂ&#x2018;& %& $& $% %& Â&#x2DC; $&
Â&#x2DC; Â&#x2DC;
%$ $& %& $% Â&#x2DC; $&
Â&#x2DC; Â&#x2DC;
$% %& $& $% Â&#x2DC; %&
Hl\_l FRVÂ&#x2018;K FRVÂ&#x2018;:
Â&#x2DC; Â&#x2DC;
FRVÂ&#x2018;<
Â&#x2039;
M lj_m]hevgbdZ ^\_ klhjhgu jZ\gu f b f Z kbgmk m]eZ f_`^m gbfb jZ\_g GZc^bl_ lj_lvx klhjhgm
Imklv $< f $& f VLQÂ&#x2018;$ Bf__f FRV Â&#x2018;$ ± VLQ Â&#x2018;$
FRVÂ&#x2018;$ r VLQ $
r
>Ze__ ih l_hj_f_ dhkbgmkh\
r
r
<K :< :K ± :<Â&#x2DC;:KÂ&#x2DC;FRVÂ&#x2018;$
ihemqZ_f qlh Z <K ± Â&#x2DC; Â&#x2DC; Â&#x2DC; ± f b <K f [ <K ± Â&#x2DC; Â&#x2DC; ± f b <K Hl\_l Z f [ f
Â&#x2039;
f
Klhjhgu lj_m]hevgbdZ jZ\gu D E k >hdZ`bl_ qlh _keb D E ! F lh m]he ijhlb\he_`Zsbc klhjhg_ k hkljuc ?keb Z E F lh m]he ijhlb\he_`Zsbc klhjhg_ F lmihc
J ² m]he lj_m]hevgbdZ ijhlb\he_`Zsbc klhjhg_ k Ih l_hj_f_ dhkbgmkh\ bf__f
F D E ± DEFRVJ
hldm^Z ihemqZ_f FRV J
D E F DE
?keb D E ! F lh D E ± F ! lh]^Z FRV ! Z lZd dZd Â&#x192; lh ² hkljuc ?keb D E F lh FRV b m]he ² lmihc Qlh b lj_[h \Zehkv ^hdZaZlv Â&#x2039;
>Zgu ^bZ]hgZeb iZjZee_eh]jZffZ k b G b m]he f_`^m gbfb . GZc^bl_ klhjhgu iZjZee_eh]jZffZ
Imklv $%&' ² iZjZee_eh]jZff :K k %' G Â&#x2018;:H< D %' G ih k\hckl Lh]^Z HK :H $& F <H \m ^bZ]hgZe_c iZjZee_eh]jZffZ Â&#x2018;:H< D lZd qlh ih l_h j_f_ dhkbgmkh\ bf__f :< :2 <2 ± :HÂ&#x2DC;<HÂ&#x2DC;FRVÂ&#x2018;$2% F G FG Â&#x2DC; FRV D
$%
F G FG Â&#x2DC; FRV D
F G FG Â&#x2DC; FRV D
< '<2& ih l_hj_f_ dhkbgmkh\ bf__f
<K <H HK ± <HÂ&#x2DC;HKÂ&#x2DC;FRV Â&#x192; ± D F G FG Â&#x2DC; FRV q D
F G FG Â&#x2DC; FRV D
L d FRV Â&#x192; ± D ± FRVD ihwlhfm
F G FG Â&#x2DC; FRV D
%&
>Ze__ :< &' b $' %& Hl\_l Â&#x2039;
G F FG Â&#x2DC; FRV D
F G FG Â&#x2DC; FRV D G F FG Â&#x2DC; FRV D
>Zgu klhjhgu iZjZee_eh]jZffZ D b E b h^bg ba m] eh\ D GZc^bl_ ^bZ]hgZeb iZjZee_eh]jZffZ Imklv $%&' ² iZjZee_eh]jZff :< Z $' E Â&#x2018;: D
% '%$' ih l_hj_f_ dhkbgmkh\ %'
D E DE FRV D
$% $' $% Â&#x2DC; $' Â&#x2DC; FRV D
< ':<K ih l_hj_f_ dhkbgmkh\ $&
$% %& $% Â&#x2DC; %& Â&#x2DC; FRV E
D E DE FRV q D
Hl\_l %'
Â&#x2039;
D E DE FRV D
D E DE FRV D $&
D E DE FRV D
Klhjhgu lj_m]hevgbdZ f f b f GZc^bl_ ijh _dpbb klhjhg f b f gZ ijyfmx kh^_j`Zsmx klh jhgm f
%'A$& :< f <K f :K f $' ² ijh_dpby :< gZ $& '& ² ijh_dpby <K gZ :K Ih l_hj_f_ dhkbgmkh\ $% $& %& $% Â&#x2DC; $&
FRVÂ&#x2018;$
FRVÂ&#x2018;&
Â&#x2DC; Â&#x2DC;
%& $& $% %& Â&#x2DC; $&
Â&#x2DC; Â&#x2DC;
>Ze__ \ ijyfhm]hevghf '$%' bf__f $%FRVÂ&#x2018;$
Â&#x2DC;
f
'&
%&FRVÂ&#x2018;&
Â&#x2DC;
f
Hl\_l $' f '& f
$'
: \ '%&'
Â&#x2039;
GZc^bl_ \ukhlu lj_m]hevgbdZ \ aZ^Zq_
GZc^_f KD KE KF Ba aZ^Zqb agZ_f qlh FRV Â&#x2018;$ FRV Â&#x2018;% FRV Â&#x2018;&
E F D DE
D F E DF
D E F DE
Â&#x2DC; Â&#x2DC;
Â&#x2DC; Â&#x2DC;
Â&#x2DC; Â&#x2DC;
Ba hkgh\gh]h ljb]hghf_ljbq_kdh]h lh`^_kl\Z ihemqZ_f FRV Â&#x2018;:
VLQ Â&#x2018;$ VLQ Â&#x2018;%
FRV Â&#x2018;%
VLQ Â&#x2018;&
FRV Â&#x2018;&
>Ze__ gZoh^bf ba ¨$%+ KD FÂ&#x2DC;VLQÂ&#x2018;% Â&#x2DC;
ba '<KG KE DÂ&#x2DC;VLQÂ&#x2018;& Â&#x2DC; ba '$&+ KF EÂ&#x2DC;VLQÂ&#x2018;$ Â&#x2DC; Hl\_l KD Â&#x2039;
f KE
f KF
f f f
f
GZc^bl_ f_^bZgu lj_m]hevgbdZ \ aZ^Zq_ Â&#x2039; Â&#x2020;
$
GZc^_f f_^bZgu PD PE b PF < '$<F :< k f <0
Z <K
kf aZ^Zqm Â&#x2039; Â&#x2020; Ih l_hj_f_ dhkbgmkh\
f FRV Â&#x2018;%
PD
$0
F D Â&#x2DC; F Â&#x2DC; Â&#x2DC; FRV Â&#x2018;%
Â&#x2DC; Â&#x2DC; Â&#x2DC;
< '%&0 %& Z f <F
Ba l_hj_fu dhkbgmkh\ PE
%0
LZd qlh
Hl\_l P D Â&#x2039;
$& E f FRV Â&#x2018;&
< '$0 & $& E f $0
&0
§ · § · D ¨ E ¸ D¨ E ¸ Â&#x2DC; FRV Â&#x2018;& © ¹ © ¹
Â&#x2DC; Â&#x2DC; Â&#x2DC;
PF
$%
F
f FRV Â&#x2018;$
§ · § · E ¨ F ¸ E¨ F ¸ Â&#x2DC; FRV Â&#x2018;$ © ¹ © ¹
Â&#x2DC; Â&#x2DC; Â&#x2DC;
P E
P F
GZc^bl_ [bkk_dljbku lj_m]hevgbdZ \ aZ^Zq_ Â&#x2039;
Imklv $/ OD %/ OE &/ OF ² [bkk_dljbku Ih k\hc kl\m [bkk_dljbku lj_m]hevgbdZ
$% %/
$& &/
Ba\_klgh qlh :< f :K f Imklv </ [ f ke_^h \Zl_evgh / & ± o hldm^Z [
agZqbl </
± o o ± o ± [ [
FRVÂ&#x2018;% kf aZ^Zqm Â&#x2039; Ih l_hj_f_ dhkbgmkh\ ihemqZ_f
< ':</ :< f %/
$% %/ $% Â&#x2DC; %/ Â&#x2DC; FRV Â&#x2018;%
:/
$/
Â&#x2DC; Â&#x2DC; Â&#x2DC;
:gZeh]bqgh
$% $/
%& l _ / & \
]^_ $/ \ f \
± \ \ ± \ ± \ ke_^h\Zl_evgh $/
f
< '$</ $% f $/ %/
f FRV Â&#x2018;$
$% $/ $% Â&#x2DC; $/ Â&#x2DC; FRVÂ&#x2018;$
lh]^Z
Â&#x2DC; Â&#x2DC; Â&#x2DC;
>Ze__
$& l _ $/ ]
%& %/
]^_ %/ ] f ]
± ] ] ± ] ± ]
l _ %/
< 'K</
&/
Hl\_l $/ Â&#x2039;
%& %/ %& Â&#x2DC; %/ FRVÂ&#x2018;%
%/
&/
DZd baf_gy_lky klhjhgZ $% lj_m]hevgbdZ $<K _keb m]he K \hajZklZ_l Z ^ebgu klhjhg :K b <K hklZxlky [_a baf_g_gbc"
Bf__f
:< :K K< ± :KÂ&#x2DC;K<Â&#x2DC;FRVÂ&#x2018;&
?keb :K b :< g_ baf_gyxlky Z Â&#x2018;K \hajZklZ_l lh FRVÂ&#x2018;& ² m[u\Z_l ke_^h\Zl_evgh :< \hajZklZ_l AgZqbl :< \hajZk lZ_l
Â&#x2039;
M lj_m]hevgbdZ :<K :< kf :K kf Fh`_l " eb VLQ
Ih l_hj_f_ kbgmkh\
$& Â&#x2DC; VLQÂ&#x2018;& $%
VLQ
lh _klv VLQÂ&#x2018;&
$% VLQ Â&#x2018;&
VLQE lh VLQ Â&#x2018;&
$& hldm^Z bf__f VLQ Â&#x2018;%
Â&#x2DC; VLQÂ&#x2018;&
Â&#x2DC; VLQÂ&#x2018;&
gh ± VLQÂ&#x2018;& D ! lZd qlh VLQ g_ fh`_l [ulv jZ\_g Hl\_l G_ fh`_l
?keb VLQ
Â&#x2039;
Â&#x2DC;
DZd gZclb jZ^bmk hdjm`ghklb hibkZgghc hdheh lj_ m]hevgbdZ agZy _]h klhjhgu" GZc^bl_ jZ^bmk hd jm`ghklb hibkZgghc hdheh lj_m]hevgbdZ kh klhjh gZfb f f f D VLQ D
Ih l_hj_f_ kbgmkh\ 5 imklv E f Lh]^Z VLQE E VLQ Â&#x2018;%
5
Hl\_l
E VLQ E
F >Ze__ VLQ J
S kfhljb aZ^Zqm Â&#x2039; LZd qlh
Â&#x2DC;
Â&#x2DC;
Â&#x2DC;
Â&#x2039;
H[tykgbl_ dZd gZclb jZkklhygb_ hl lhqdb : ^h g_ ^hklmighc lhqdb < agZy jZkklhygb_ :K b m]eu . b
Ih l_hj_f_ kbgmkh\
$% VLQ
$& lh]^Z $% VLQÂ&#x2018;%
$& Â&#x2DC; VLQ VLQ Â&#x2018;%
l d Â&#x2018;< Â&#x192; ± . lh VLQ< VLQ O Â&#x192; ± D VLQ D b $%
Â&#x2039;
$& Â&#x2DC; VLQ VLQ .
H[tykgbl_ dZd gZclb \ukhlm [ a^Zgby ih m]eZf D b b jZkklhygbx D
< ':<K Â&#x2018;: Â&#x192; ± D lh]^Z Â&#x2018;K Â&#x192; ± E ± Â&#x192; ± D D ± E >Ze__ ih l_hj_f_ kbgmkh\
$&
$% Â&#x2DC; VLQ VLQ .
$K VLQ
$% lZd qlh VLQÂ&#x2018;&
'$&' ² ijyfhm]hevguc ihwlhfm o &' :KVLQD
$%VLQ. Â&#x2DC; VLQ VLQ .
Â&#x2039;
< lj_m]hevgbd_ :<K Â&#x2018;: Â&#x192; Â&#x2018;< Â&#x192; Â&#x2018;K Â&#x192; DZdZy ba klhjhg lj_m]hevgbdZ gZb[hevrZy dZdZy ² gZbf_gvrZy"
Ih l_hj_f_ kbgmkh\
$% VLQÂ&#x2018;K
<& VLQÂ&#x2018;:
:K Ba mkeh\by VLQ Â&#x2018;%
ke_^m_l qlh VLQÂ&#x2018;& ! VLQÂ&#x2018;% ! VLQÂ&#x2018;$ lh]^Z :< ! $& ! %& l _ klhjhgZ :< ² gZb[hevrZy Z klhjhgZ <K ² gZbf_gvrZy Â&#x2039;
M lj_m]hevgbdZ :<K klhjhgu :< f <K f :K f DZdhc ba m]eh\ lj_m]hevgbdZ gZb[hev rbc dZdhc ² gZbf_gvrbc"
Ih l_hj_f_ kbgmkh\
$% VLQÂ&#x2018;K
<& VLQÂ&#x2018;:
:K LZd dZd ih VLQ Â&#x2018;%
mkeh\bx $K ! <& ! :% lh b VLQÂ&#x2018;< ! VLQÂ&#x2018;: ! VLQÂ&#x2018;K agZqbl b Â&#x2018;% ! Â&#x2018;$ ! Â&#x2018;& Ihwlhfm Â&#x2018;< ² gZb[hevrbc Z Â&#x2018;& ² gZb f_gvrbc Â&#x2039;
Qlh [hevr_ ² hkgh\Zgb_ beb [hdh\Zy klhjhgZ jZ\ gh[_^j_ggh]h lj_m]hevgbdZ _keb ijbe_`Zsbc d hk gh\Zgbx m]he [hevr_ Â&#x192;" LZd dZd ijbe_`Zsbc d hkgh\Zgbx m]he [hevr_ Â&#x192; lh m]he ijb \_jrbg_ f_gvr_ Â&#x192; Ih l_hj_f_ kbgmkh\ ijhlb\ f_gvr_ ]h m]eZ e_`bl f_gvrZy klhjhgZ lZd qlh [hdh\Zy klhjhgZ [hevr_ Â&#x2039;
M lj_m]hevgbdZ :<K m]he K lmihc >hdZ`bl_ qlh _keb lhqdZ ; e_`bl gZ klhjhg_ :K lh <O :< %
Ijh\_^_f <G A :K LZd dZd O e_`bl gZ :K lh :G ! OG Z agZqbl gZdehggZy :< ! <; l d ba ^\mo gZdehgguo [hevr_ lZ ijh_dpby dhlhjhc [hevr_ Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
M lj_m]hevgbdZ :<K m]he K lmihc >hdZ`bl_ qlh _keb lhqdZ ; e_`bl gZ klhjhg_ :K Z lhqdZ < ² gZ klhjhg_ <K lh ;< :<
Kh_^bgbf ; k < ih ^hdZaZgghfm \ ij_^u^ms_c aZ^Zq_ O< :< b ;< ;% LZd qlh ;< $< qlh b lj_[h\Zehkv ^h dZaZlv Â&#x2039;
GZ klhjhg_ :< lj_m]hevgbdZ $<K hlf_q_gZ lhqdZ ' >hdZ`bl_ qlh hlj_ahd &' f_gvr_ ih djZcg_c f_j_ h^ghc ba klhjhg :K beb <K
Ijh\_^_f KD A $% LhqdZ ' e_`bl beb f_`^m < b D beb f_`^m : b D ?keb ' e_`bl f_`^m lhqdZfb D b < lh .% ! .' Z _keb ijh_dpby [hevr_ lh [hevr_ b gZdehggZy l _ :< ! &' :gZeh]bqgh ^hdZau\Z_lky qlh &' :K _keb lhqdZ ' e_ `bl f_`^m lhqdZfb : b D ?keb ' kh\iZ^Z_l k D lh &' &% lZd dZd gZdehggZy [hevr_ i_ji_g^bdmeyjZ Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
>Zg lj_m]hevgbd :<K &' ² f_^bZgZ ijh\_^_ggZy d klhjhg_ :< >hdZ`bl_ qlh _keb :K ! <K lh m]he $&' f_gvr_ m]eZ %&'
Ijh^he`bf f_^bZgm &' b hleh`bf gZ g_c hlj_ahd '( &' ihemq_gguc q_luj_om]hevgbd :K<? ² iZjZee_eh ]jZff %( :K b K< :?
< ':K? Â&#x2018;$&' e_`bl ijhlb\ klhjhgu :? K< < 'K<? Â&#x2018;%&' e_`bl ijhlb\ klhjhgu %( $& LZd dZd :K ! <K lh Â&#x2018;:&' Â&#x2018;%&' Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
>hdZ`bl_ qlh [bkk_dljbkZ lj_m]hevgbdZ g_ f_gvr_ \ukhlu b g_ [hevr_ f_^bZgu ijh\_^_gguo ba wlhc `_ \_jrbgu Imklv \ ':<K :. ² \ukhlZ $1 ² [bkk_dljbkZ Â&#x2018;: $( ² f_^bZgZ $
&
(
1
.
%
Ba lhqdb : d ijyfhc <K ijh\_^_gu i_ji_g^bdmeyj :. \ukhlZ b ^\_ gZdehggu_ Ke_^h\Zl_evgh lhqdZ 1 ijbgZ^e_ `bl eb[h .< eb[h .( LhqdZ 1 kh\iZ^Z_l k . lh]^Z $1 :. $( LhqdZ 1 kh\iZ^Z_l k ( lh]^Z $1 $( ! $. LhqdZ 1 e_`bl f_`^m lhqdZfb . b ( lh]^Z $. $1 $( lZd dZd __ ijh_dpby 1. f_gvr_ (. ² ijh_dpbb $( Ih ^hdZaZgghfm \ aZ^Zq_ Â&#x2039; $1 g_ fh`_l [ulv [hevr_ $( l _ lhqdZ 1 g_ fh`_l e_`Zlv f_`^m ( b K Qlh b lj_[h\Z ehkv ^hdZaZlv
Â&#x2039;
>Zgu klhjhgZ b ^\Z m]eZ lj_m]hevgbdZ GZc^bl_ lj_ lbc m]he b hklZevgu_ ^\_ klhjhgu _keb Z Â&#x192; Â&#x192; D D Â&#x192; D Â&#x192; Â&#x192; E D Â&#x192; Â&#x192; k D Â&#x192; Â&#x192;
.
D Â&#x192; ± ± Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; Bkihevamy l_hj_fm kbgmkh\ E F
D VLQ E VLQ D
D VLQ J VLQ D
D VLQ .
VLQ ο VLQ ο
VLQ ο VLQ ο
E VLQ
§ §
Â&#x192; ± D ± Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; Bkihevamy l_hj_fm kbgmkh\ E F
D Â&#x2DC; VLQ E VLQ D
D Â&#x2DC; VLQ J VLQ D
D VLQ D
Â&#x2DC; VLQ ο VLQ
ο
Â&#x2DC; VLQ ο VLQ
ο
E VLQ E
Bkihevamy l_hj_fm kbgmkh\
D VLQ D
F ihemqZ_f VLQ J
Â&#x2DC; | Â&#x2DC; |
D O ± E ± J Â&#x192; ± h ± h h h
F ihemqZ_f VLQ J
E VLQ E
F ihemqZ_f VLQ J
E
D Â&#x2DC; VLQ E VLQ D
D Â&#x2DC; VLQ J VLQ D
F
Â&#x2DC; VLQ ο VLQ
ο
VLQ
ο
Â&#x2DC; VLQ ο
Â&#x2DC; |
Â&#x2DC; |
h ± D ± E Â&#x192; ± h ± h Â&#x192; D VLQ D
Bkihevamy l_hj_fm kbgmkh\ E Â&#x2DC; VLQ J E VLQ D
F
D
Â&#x2DC; VLQ ο VLQ
E Â&#x2DC; VLQ D VLQ E
ο
|
E VLQ E
Â&#x2DC;
F ihemqZ_f VLQ J
Â&#x2DC; |
Â&#x192; ± D ± E Â&#x192; ± Â&#x192; ± Â&#x192; h D E F ihemqZ_f Bkihevamy l_hj_fm kbgmkh\ VLQ D VLQ E VLQ J D
F Â&#x2DC; VLQ D VLQ J E
Â&#x2039;
Â&#x2DC; VLQ ο VLQ
F Â&#x2DC; VLQ E VLQ J
ο
Â&#x2DC; |
Â&#x2DC; |
>Zgu ^\_ klhjhgu b m]he f_`^m gbfb GZc^bl_ hklZevgu_ ^\Z m]eZ b lj_lvx klhjhgm _keb Z E Â&#x192; D E Â&#x192; E F D Â&#x192; E k D Â&#x192; Z k Â&#x192; D k Â&#x192; Bkihevamy l_hj_fm dhkbgmkh\ gZoh^bf
k
D E DE FRV J
Â&#x2DC; Â&#x2DC;
|
>Ze__ FRVD
E F D EF
| lZd qlh Â&#x2DC; Â&#x2DC;
D Â&#x192; Z Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; Bkihevamy l_hj_fm dhkbgmkh\ gZoh^bf k
D
D E DE FRV J
>Ze__ FRVD
Â&#x2DC; Â&#x2DC; Â&#x2DC;
E F D EF
| lZd qlh Â&#x2DC; Â&#x2DC;
Â&#x192; Z Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; Bkihevamy l_hj_fm dhkbgmkh\ gZoh^bf E F EF FRV D
D
>Ze__ FRV E
FRV ο
D F E DF
Â&#x2DC; Â&#x2DC;
lZd qlh Â&#x192; Z Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; Bkihevamy l_hj_fm dhkbgmkh\ gZoh^bf D
E F EF FRV D
|
|
|
D F E | lZd qlh DF Â&#x2DC; Â&#x2DC; Â&#x192; Z Â&#x192; ± D ± Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; Bkihevamy l_hj_fm dhkbgmkh\ gZoh^bf
>Ze__ FRV E
E
D F DF FRV E
Â&#x2DC;
|
E F D | EF Â&#x2DC; Â&#x2DC; lZd qlh D Â&#x192; Z Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; Bkihevamy l_hj_fm dhkbgmkh\ gZoh^bf
>Ze__ FRV D
E
D F DF FRV E
Â&#x2DC; FRV ο | |
>Ze__ FRV D
E F D EF
| lZd qlh Â&#x2DC; Â&#x2DC;
D Â&#x192; Z Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; Â&#x2039;
< lj_m]hevgbd_ aZ^Zgu ^\_ klhjhgu b m]he ijhlb\h e_`Zsbc h^ghc ba klhjhg GZc^bl_ hklZevgu_ m]eu d klhjhgm lj_m]hevgbdZ _keb D E D Â&#x192; D E D Â&#x192; D E D Â&#x192; D E D Â&#x192; D E D Â&#x192;
Ih l_hj_f_ kbgmkh\ bf__f
ihemqZ_f
VLQ E
E Â&#x2DC; VLQ D D
Â&#x2DC; VLQ ο
D VLQ D
E VLQ E
F hldm^Z VLQ J
Â&#x2DC; |
l _ Â&#x192; Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; b F
D Â&#x2DC; VLQ J VLQ D
Â&#x2DC; VLQ ο VLQ
ο
Ih l_hj_f_ kbgmkh\ bf__f
ihemqZ_f
VLQ E
E Â&#x2DC; VLQ D D
Â&#x2DC; VLQ ο
Â&#x2DC; |
D VLQ D
D Â&#x2DC; VLQ J VLQ D
Â&#x2DC; VLQ ο VLQ
ο
F hldm^Z VLQ J
Â&#x2DC; |
l _ | Â&#x192; Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; b F
E VLQ E
Â&#x2DC; |
Ih l_hj_f_ kbgmkh\ bf__f
ihemqZ_f
VLQ E
E Â&#x2DC; VLQ D D
Â&#x2DC; VLQ ο
D VLQ D
l _ h Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; b F
D Â&#x2DC; VLQ J VLQ D
VLQ E
E Â&#x2DC; VLQ D D
F hldm^Z VLQ J
Â&#x2DC; |
Â&#x2DC; |
Ih l_hj_f_ kbgmkh\ bf__f
ihemqZ_f
E VLQ E
D VLQ D
Â&#x2DC;
E VLQ E
F hldm^Z VLQ J
gh VLQE ^he`_g [ulv f_gvr_ agZqbl aZ^ZqZ g_ bf__l j_r_ gby Ih l_hj_f_ kbgmkh\ bf__f
ihemqZ_f
VLQ E
E Â&#x2DC; VLQ D D
D VLQ D
E VLQ E
F hldm^Z VLQ J
Â&#x2DC; |
l _ h beb h Lh]^Z h ± D ± l _ h beb h >Ze__ F Â&#x2039;
D Â&#x2DC; VLQ J lZd qlh k § beb k § VLQ D
>Zgu ljb klhjhgu lj_m]hevgbdZ GZc^bl_ _]h m]eu _keb D E F D E F D E F D E F
D E k D E F Ih l_hj_f_ dhkbgmkh\ bf__f FRV D FRV E
E F D EF
D F E DF
Lh]^Z h ± h ± h h Ih l_hj_f_ dhkbgmkh\ bf__f FRV D FRV E
E F D EF
Â&#x2DC; Â&#x2DC;
FRV E
FRV E
§ h
D h
Â&#x2DC; Â&#x2DC;
E F D EF
Â&#x2DC; Â&#x2DC;
| D Â&#x192;
D F E DF
Â&#x2DC; Â&#x2DC;
Lh]^Z h ± h ± h h Ih l_hj_f_ dhkbgmkh\ bf__f FRV D
h
D F E DF
Lh]^Z h ± h ± Â&#x192; h Ih l_hj_f_ dhkbgmkh\ bf__f FRV D
D §
E F D EF
D F E DF
Â&#x192;
| Â&#x192;
| D Â&#x192; Â&#x2DC; Â&#x2DC;
Â&#x2DC; Â&#x2DC;
Â&#x192;
Lh]^Z Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; ± Â&#x192; Â&#x192;
Ih l_hj_f_ dhkbgmkh\ bf__f FRV D
FRV E
E F D EF
D F E DF
| D Â&#x192; Â&#x2DC; Â&#x2DC;
| Â&#x192; Â&#x2DC; Â&#x2DC;
Lh]^Z Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192; Ih l_hj_f_ dhkbgmkh\ bf__f FRV D FRV E
Lh]^Z
E F F DF
D F E DF
| D Â&#x192; Â&#x2DC; Â&#x2DC; | Â&#x192; Â&#x2DC; Â&#x2DC;
Â&#x192; ± Â&#x192; ± Â&#x192; Â&#x192;
Â&#x2020; FGH=HM=HEVGBDB Â&#x2039;
>Zgu ^\_ hdjm`ghklb k jZ^bmkZfb 5 b 5 b jZkklhy gb_ f_`^m p_gljZfb G ! 5 5 Q_fm jZ\gu gZb [hevr__ b gZbf_gvr__ jZkklhygby f_`^m lhqdZfb ; b < wlbo hdjm`ghkl_c AZ^ZqZ j_r_gZ \ i mq_[gbdZ klj
Â&#x2039;
J_rbl_ aZ^Zqm ijb mkeh\bb qlh G 5 ± 5
Imklv ; b < ² lhqdb gZ hdjm`ghklyo Ih l_hj_f_ h ^ebg_ ehfZghc ^ey ehfZghc ;2 2 < bf__f ;< d ;2 2 2 2 <
lh _klv OH H H H < 5 5 G ² gZb[hevr__ jZkklhy gb_ >ey ehfZghc ;<2 2 bf__f ;H d ;< <2 2 2 5 d ;< 5 G ;< t 5 ± 5 ± G
agZqbl 5 ± 5 ± G ² gZbf_gvr__ jZkklhygb_
Â&#x2039;
>hdZ`bl_ qlh _keb \_jrbgu ehfZghc g_ e_`Zl gZ h^ghc ijyfhc lh ^ebgZ ehfZghc [hevr_ ^ebgu hl j_adZ kh_^bgyxs_]h __ dhgpu Imklv : : $ :Q± :Q ² ehfZgZy lhqdb : $ :Q g_ e_`Zl gZ h^ghc ijyfhc
>hdZaZlv qlh : $ : : :Q :Q ! : :Q Lhqdb : : : g_ e_`Zl gZ h^ghc ijyfhc ih g_jZ\_gkl\m lj_m]hevgbdZ bf__f $ $ : : ! : $
$ $ : : ! : $
>ey ehfZghc : : : ihemqbf Ih^klZ\b\ \ ihemqbf
$ $ : : : : ! : $
Ijh^he`Zy ij_h[jZah\Zgby ^Zevr_ ZgZeh]bqgh ihemqbf $ $ : : « :Q :Q ! : $Q
qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
>hdZ`bl_ qlh m aZfdgmlhc ehfZghc jZkklhygb_ f_ `^m ex[ufb ^\mfy \_jrbgZfb g_ [hevr_ iheh\bgu ^ebgu ehfZghc
Imklv $%&'($ ² aZfdgmlZy ehfZgZy ebgby JZkklhygb_ f_`^m ^\mfy \_jrbgZfb gZijbf_j : b ' [m ^_f kqblZlv hlj_adhf kh_^bgyxsbf dhgpu ehfZghc ke_^h\Z l_evgh ih l_hj_f_ h ^ebg_ ehfZghc bf__f $'d$% %& &' b $'d$( (' keh`b\ ^\Z g_jZ\_gkl\Z ihemqbf $' d $% %& &' '( ($
$' d
$% %& &' '( ($
Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
>hdZ`bl_ qlh m aZfdgmlhc ehfZghc ^ebgZ dZ`^h]h a\_gZ g_ [hevr_ kmffu ^ebg hklZevguo a\_gv_\ LZd `_ dZd b \ j_r_gbb aZ^Zqb Â&#x2039; ihemqZ_f qlh $( d $% %& &' '(
>ey ^jm]bo a\_gv_\ ZgZeh]bqgh Â&#x2039;
Fh`_l eb aZfdgmlZy ehfZgZy bf_lv a\_gvy ^ebghc f f f f f" H[tykgbl_ hl\_l >ey aZfdgmlhc ehfZghc ^ebgZ kZfh]h [hevrh]h a\_gZ ^he`gZ [ulv f_gvr_ kmffu ^ebg \k_o hklZevguo a\_gv_\ >ey ^Zgghc ehfZghc ^he`gh \uihegylvky ! lh _klv qlh g_\_jgh Hl\_l G_ fh`_l Â&#x2039;
>hdZ`bl_ qlh _keb dhgpu ehfZghc e_`Zl ih jZagu_ klhjhgu hl ^Zgghc ijyfhc lh hgZ i_j_k_dZ_l wlm ijyfmx
>hdZ`_f qlh m ijyfhc b ehfZghc gZc^_lky ohly [u h^gZ h[sZy lhqdZ IjyfZy Z jZa[b\Z_l iehkdhklv gZ ^\_ ihemiehkdhklb Z b Z \ dhlhjuo e_`Zl dhgpu : b :Q ehfZghc $ $ ÂŤ$Q >hdZ `_f qlh m ijyfhc Z b ehfZghc gZc^_lky ohly [u h^gZ h[sZy lhqdZ >himklbf qlh $ Â? D :Q Â? Z DZ`^Zy ba \_jrbg $ $ ÂŤ$Q ijbgZ^e_`bl h^ghc ba ihemiehkdhkl_c beb ijyfhc Z ?keb : Â? Z lh hlj_ahd : $ i_j_k_dZ_l ijyfmx Z _keb : Â? Z lh : y\ey_lky h[s_c lhqdhc ijyfhc b ehfZghc ?keb : Â? Z lh jZkkfhljbf \_jrbgm : b l ^ Lh _klv _keb : Â? D lh hlj_ahd : : i_j_k_q_l ijyfmx Z _keb : Â? Z lh : y\ey _lky h[s_c lhqdhc ijyfhc b ehfZghc ?keb : Â? Z i_j_c^_f d jZkkfhlj_gbx \_jrbgu : b l ^ >himklbf qlh kj_^b \_j rbg $ $ ÂŤ$Q g_ gZc^_lky gb h^ghc dhlhjZy [u e_`ZeZ \ Z beb gZ ijyfhc Z lh \ wlhf kemqZ_ hlj_ahd :Q :Q i_j_k_q_l ijyfmx D Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039; Kdhevdh ^bZ]hgZe_c m Q m]hevgbdZ" Ba dZ`^hc \_jrbgu Q m]hevgbdZ fh`gh ijh\_klb ^bZ]hgZ eb dh \k_f \_jrbgZf djhf_ kZfhc k_[y b ^\mo khk_^gbo l _ Q Âą ^bZ]hgZeb Ihkdhevdm dZ`^Zy ^bZ]hgZev kh_^bgy_l ^\_ \_jrbgu lh h[s__ dhebq_kl\h ^bZ]hgZe_c G
Q Q
Â&#x2039;
M]eu \uimdeh]h q_luj_om]hevgbdZ ijhihjpbhgZev gu qbkeZf GZc^bl_ bo Ih l_hj_f_ h kmff_ m]eh\ fgh]hm]hevgbdZ bf__f 6 Â&#x192; Q Âą Â&#x192;Ă&#x201A; Âą Â&#x192;Ă&#x201A; Â&#x192;
Imklv ]jZ^mkgZy f_jZ ]h m]eZ NÂ&#x192; ]h ² NÂ&#x192; ]h ² NÂ&#x192; b ]h ² NÂ&#x192; LZd dZd kmffZ \k_o m]eh\ Â&#x192; ihemqbf mjZ\g_ gb_ N N N N Â&#x192; N Â&#x192; N h
AgZqbl m]he ² Â&#x192; c ² Â&#x192; c ² Â&#x192; c ² Â&#x192;
Â&#x2039;
>hdZ`bl_ qlh m q_luj_om]hevgbdZ hibkZggh]h hdh eh hdjm`ghklb kmffu ^ebg ijhlb\he_`Zsbo klhjhg jZ\gu Imklv $%&' ² q_luj_om]hevgbd hibkZgguc hdheh hd jm`ghklb
Ih k\hckl\m dZkZl_evghc $3 $4 '3 '1 &1 &0 b %4 %0 ihemqZ_f qlh $% &' $4 %4 &1 '1 %& $' %0 &0 $3 '3
Ke_^h\Zl_evgh
$% &' %& $'
Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
Kdhevdh klhjhg bf__l ijZ\bevguc fgh]hm]hevgbd dZ`^uc ba \gmlj_ggbo m]eh\ dhlhjh]h jZ\_g Â&#x192; Â&#x192;" M]he ijZ\bevgh]h Q m]hevgbdZ \uqbkey_lky ih nhjfme_ D
Â&#x192;
qQ q Ã&#x203A;Q Ã&#x203A;Q ± Ã&#x203A; ± Ã&#x203A;Q ± Ã&#x203A; Q
Â&#x192;
qQ q Ã&#x203A;Q Ã&#x203A;Q ± Ã&#x203A; ± Ã&#x203A;Q ± Ã&#x203A; Q
Q Â&#x192; Â&#x192; Q
Q Â&#x192; ± Â&#x192; Q
q Q
Q
Â&#x2039;
Kdhevdh klhjhg bf__l ijZ\bevguc fgh]hm]hevgbd _keb dZ`^uc ba \g_rgbo _]h m]eh\ jZ\_g Â&#x192; Â&#x192;" 6D Â&#x192; D
q Q
q Â&#x192;Q Â&#x192; Q Â&#x192; Â&#x192; Q Q q Â&#x192; Â&#x192;Q Â&#x192; Q Â&#x192; Â&#x192; Q Q
Â&#x192;
Â&#x2039;
>hdZ`bl_ qlh \aylu_ q_j_a h^gm \_jrbgu ijZ\bev gh]h Q m]hevgbdZ y\eyxlky \_jrbgZfb ijZ\bevgh]h Q m]hevgbdZ Imklv $%&'() ² ijZ\bevguc Q m]hevgbd
JZkkfhljbf '$<) b '%&' ): <K :< &' dZd klhjhgu ijZ\bevgh]h fgh]hm]hev gbdZ Â&#x2018;: Â&#x2018;K dZd m]eu ijZ\bevgh]h fgh]hm]hevgbdZ AgZqbl ')$< '%&' ih fm ijbagZdm l _ )< %' :gZeh]bqgh ^hdZau\Z_lky qlh \k_ klhjhgu Q m]hevgbdZ %') jZ\gu ke_^h\Zl_evgh Q m]hevgbd ² ijZ\bevguc Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
>hdZ`bl_ qlh k_j_^bgu klhjhg ijZ\bevgh]h Q m]hevgbdZ y\eyxlky \_jrbgZfb ^jm]h]h ijZ\bev gh]h Q m]hevgbdZ Imklv $%&'( ² ijZ\bevguc Q m]hevgbd :: $ % << < K b l ^ JZkkfhljbf '$ << b '% &&
'
: < % & %% && dZd iheh\bgu jZ\guo klhjhg Q m]h evgbdZ Â&#x2018;< Â&#x2018;K ba mkeh\by AgZqbl '$ << '< && lZd qlh $ < % & :gZeh]bqgh ^hdZau\Z_lky qlh \k_ klhjhgu ihemq_ggh]h Q m]hevgbdZ jZ\gu lh _klv Q m]hevgbd ² ijZ\bevguc Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
Ohj^Z i_ji_g^bdmeyjgZy jZ^bmkm b ijhoh^ysZy q_ j_a _]h k_j_^bgm jZ\gZ klhjhg_ ijZ\bevgh]h \ib kZggh]h lj_m]hevgbdZ >hdZ`bl_
Gm`gh ^hdZaZlv qlh
$% D 5
]^_ 5 ² jZ^bmk hdjm`ghklb JZkkfhljbf '2?<
Â&#x2018;? Â&#x192; l d 2'A:< ih mkeh\bx 2% 5 2(
mkeh\bx Ih l_hj_f_ IbnZ]hjZ ?< H< ± H? 5 ±
5 5 (%
5
5 ih
5
>Ze__ '$(2 '?<2 lZd dZd :H H< b dZl_l H? ² h[
sbc LZd qlh ($ (%
5 Lh]^Z
$% $( (%
5 5
Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
5
M ijZ\bevgh]h lj_m]hevgbdZ jZ^bmk \ibkZgghc hd jm`ghklb \ ^\Z jZaZ f_gvr_ jZ^bmkZ hibkZgghc hd jm`ghklb >hdZ`bl_
Imklv \ ':<K :< Z HK 5 ² jZ^bmk hibkZgghc hdjm` ghklb 2' U ² jZ^bmk \ibkZgghc hdjm`ghklb JZkkfhljbf ''2& Â&#x2018;' Â&#x192; $& ² dZkZl_evgZy Â&#x2018;2&'
Â&#x192; Â&#x192; Â&#x2018;&
dZd [bkk_dljbkZ jZ\gh[_^j_ggh]h lj_m]hevgbdZ Lh]^Z VLQÂ&#x2018;2&'
2' Lh _klv 2&
VLQ Â&#x192;
U 5
Qlh b lj_[h\Zehkv ^hdZaZlv
U 5 U 5
Â&#x2039;
KlhjhgZ ijZ\bevgh]h \ibkZggh]h \ hdjm`ghklv lj_ m]hevgbdZ jZ\gZ Z GZc^bl_ klhjhgm d\Z^jZlZ \ib kZggh]h \ wlm hdjm`ghklv >Zgh '$<K ² ijZ\bevguc \ibkZgguc \ hdjm`ghklv D Z GZc^_f D
LZd dZd Z >Ze__ D Â&#x2039;
5 lh D 5 5 5
D
Â&#x2DC;
D
D
< hdjm`ghklv jZ^bmk dhlhjhc ^f \ibkZg ijZ\bev guc lj_m]hevgbd gZ klhjhg_ dhlhjh]h ihkljh_g d\Z^jZl GZc^bl_ jZ^bmk hdjm`ghklb hibkZgghc hdheh d\Z^jZlZ
Imklv ':<K ² ijZ\bevguc \ibkZgguc \ hdjm`ghklv H< 5 ^f $%'( ² d\Z^jZl 5 ² jZ^bmk hibkZgghc hdheh d\Z^jZlZ hdjm`ghklb Lh]^Z Z 5 ^f Z Z ^f >Ze__ D
5 5 5
Hl\_l 5
DQ
l _ Â&#x2DC;
^f
Â&#x2DC; Â&#x2DC; Â&#x2DC;
^f
Â&#x2039;
Dhg_p \ZebdZ ^bZf_ljhf kf hibe_g ih^ d\Z^jZl Hij_^_ebl_ gZb[hevrbc jZaf_j dhlhjuc fh`_l bf_lv klhjhgZ d\Z^jZlZ <ibkZgguc \ hdjm`ghklv d\Z^jZl bf__l [yevrmx klhjhgm GZc^_f __ 5 G Ff D
Hl\_l kf
5
kf
Â&#x2039;
Dhg_p \bglZ ]Zah\hc aZ^\b`db bf__l ijZ\bevgmx lj_o]jZggmx nhjfm DZdhc gZb[hevrbc jZaf_j fh `_l bf_lv dZ`^Zy ]jZgv _keb pbebg^jbq_kdZy qZklv \bglZ bf__l ^bZf_lj kf" Lj_[m_lky gZclb klhjhgm \ibkZggh]h \ hdjm`ghklv lj_m]hevgbdZ
Hl\_l kf
Â&#x2039;
Z
5 G O Ff 5 Â&#x2DC;
kf
>hdZ`bl_ qlh klhjhgZ ijZ\bevgh]h m]hevgbdZ \u qbkey_lky ih nhjfme_ D 5 ]^_ 5 ² jZ^b mk hibkZgghc hdjm`ghklb
Imklv \ hdjm`ghklv k jZ^bmkhf 5 \ibkZg ijZ\bevguc m]hevgbd $%&'()*+
Lh]^Z \ '+$< +< D 5 :G :< Z Â&#x2018;$ h Ih l_hj_f_ dhkbgmkh\ +% +$ $% ± G:Â&#x2DC;:<Â&#x2DC;FRVÂ&#x2018;$ l _ 5 D D ± D Ã&#x201A;FRVO Â&#x192;
l d FRVO Â&#x192; ±FRV Â&#x192;
lh
5 D D D
hlkx^Z D
5 Â&#x2DC;
D
5 Â&#x2DC;
5
Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
5
5
>hdZ`bl_ qlh klhjhgZ ijZ\bevgh]h m]hevgbdZ \uqbkey_lky ih nhjfme_ D 5 ]^_ 5 ² jZ^bmk hibkZgghc hdjm`ghklb
Imklv \ hdjm`ghklv k jZ^bmkhf 5 \ibkZg :<K ² ijZ \bevguc m]hevgbd < ':<K $& D 5 :< <K Z Â&#x2018;< Â&#x192; ba l_hj_ fu dhkbgmkh\ ihemqZ_f :K :< <K ± :<Â&#x2DC;<KÂ&#x2DC;FRVÂ&#x2018;% lZd dZd FRVO Â&#x192; ±FRV Â&#x192;
lh
5 D
D D D Â&#x2DC;
5
D D
5 Â&#x2DC;
D
5
5
l _ D 5 5 Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
GZc^bl_ klhjhgu ijZ\bevgh]h iylbm]hevgbdZ b ijZ \bevgh]h m]hevgbdZ \ibkZgguo \ hdjm`ghklv jZ ^bmkZ 5
Imklv $%&' ² ijZ\bevguc m]hevgbd :K? ² ijZ \bevguc m]hevgbd $H 5 JZkkfhljbf '$<2 :< Z H: H< 5 Â&#x2018;$ Â&#x2018;%
ο Â&#x2DC;
Â&#x2DC;
h
lh]^Z Â&#x2018;H Â&#x192; ± Â&#x2018;: ± Â&#x2018;< Â&#x192; < aZ^Zq_ Â&#x2039; Â&#x2020; ^hdZaZgh qlh hkgh\Zgb_ jZ\gh[_^j_ggh ]h lj_m]hevgbdZ k lZdbfb m]eZfb jZ\gh Z
5
5
l _
Ba ':<K ih l_hj_f_ dhkbgmkh\ ihemqZ_f
Z :K :< <K ± :<Ã&#x201A;<KÃ&#x201A;FRVÂ&#x2018;%
D
5 5 5 FRV ο Â&#x2DC; 5 FRV q
lZd dZd FRV Â&#x192; ±FRV Â&#x192; Ba '$<2 FRV R
ih^klZ\b\ ihemqbf
ih l_hj_f_ dhkbgmkh\ lZd qlh
Z 5 Â&#x2039;
KlhjhgZ ijZ\bevgh]h fgh]hm]hevgbdZ jZ\gZ Z Z jZ ^bmk hibkZgghc hdjm`ghklb 5 GZc^bl_ jZ^bmk \ib kZgghc hdjm`ghklb
Imklv H ² p_glj hdjm`ghklb :< Z ² klhjhgZ ijZ\bev gh]h fgh]hm]hevgbdZ H: 5 ² jZ^bmk hibkZgghc hdjm`gh klb HK U ² jZ^bmk \ibkZgghc hdjm`ghklb D < 'H<K Â&#x2018;K Â&#x192; K< H< 5 lZd qlh ih l_hj_f_ IbnZ]hjZ ihemqZ_f U U
5
D
5
D
Â&#x2039;
5
KlhjhgZ ijZ\bevgh]h fgh]hm]hevgbdZ jZ\gZ Z Z jZ ^bmk \ibkZgghc hdjm`ghklb U GZc^bl_ jZ^bmk hib kZgghc hdjm`ghklb
Ihevamykv j_r_gb_f aZ^Zqb Â&#x2039; fu ihemqbeb U
Â&#x2039;
D lZd qlh 5
U
D
<ujZabl_ klhjhgm E ijZ\bevgh]h hibkZggh]h fgh]h m]hevgbdZ q_j_a jZ^bmk 5 hdjm`ghklb b klhjhgm Z ijZ\bevgh]h \ibkZggh]h fgh]hm]hevgbdZ k l_f `_ qbkehf klhjhg Imklv : : $Q ² ijZ\bevguc Q m]hevgbd \ibkZgguc \ hdjm`ghklv jZ^bmkZ 5 Z < < <Q ² ijZ\bevguc Q m]hevgbd hibkZgguc hdheh lhc `_ hdjm`ghklb $ $ D % % E
JZkkfhljbf '2$ ' b '2< K Â&#x2018;H ² h[sbc Â&#x2018;' Â&#x2018;K Â&#x192; AgZqbl '2$ ' a '2< K Ba ih^h[by lj_m]hevgbdh\ ke_^m_l qlh
_klv % &
2& Â&#x2DC; $ ' 2'
2' 2&
$ ' lh % &
>Ze__ HK 5 $ '
IbnZ]hjZ 2'
D 2' gZc^_f ba û2'$ ih l_hj_f_ §D· 5 ¨ ¸ © ¹
2$ $ '
lZd qlh
D
5Â&#x2DC; Â&#x2DC;
< K
Hl\_l E Â&#x2039;
D5
5 D
5 D
5D
5 D
E % &
5 D
D5
5 D
<ujZabl_ klhjhgm D ijZ\bevgh]h \ibkZggh]h fgh]h m]hevgbdZ q_j_a jZ^bmk 5 hdjm`ghklb b klhjhgm E ijZ\bevgh]h hibkZggh]h fgh]hm]hevgbdZ k l_f `_ qbkehf klhjhg Imklv % % %Q ² ijZ\bevguc Q m]hevgbd hibkZgguc hdheh hdjm`ghklb jZ^bmkZ 5 % % E : : :Q ² ijZ\bev guc Q m]hevgbd \ibkZgguc \ lm `_ hdjm`ghklv : : Z
û2% & a û2$ ' ih ^\mf m]eZf hldm^Z
2' 2&
$ ' $ ' % &
2' Â&#x2DC; % & 2&
lh
LZd dZd HK 5 % '
$ '
Â&#x2039;
5 D Â&#x2DC; 5
E
D
E b 2'
$ '
5
D
E Â&#x2DC; 5
5 E
5 D E5
5 E
<ibrbl_ \ hdjm`ghklv ijZ\bevguc m]hevgbd
<u[_j_f ijhba\hevgmx \_jrbgm $ gZ hdjm`ghklb Ba g__ jZ^bmkhf jZ\guf jZ^bmkm hdjm`ghklb ^_eZ_f aZk_qdb gZ hd jm`ghklb b ihemqZ_f \_jrbgu : : : dhlhju_ kh_^bgbf hlj_adZfb Ihemqbf ijZ\bevguc r_klbm]hevgbd >Ze__ ih kljhbf k_j_^bggu_ i_ji_g^bdmeyju d klhjhgZf r_klbm]hev gbdZ Hgb jZa^_eyl ^m]b hdjm`ghklb gZ jZ\guo qZkl_c Kh _^bgb\ wlb lhqdb hlj_adZfb k \_jrbgZfb r_klbm]hevgbdZ ihemqbf m]hevgbd Â&#x2039;
Hibrbl_ hdheh hdjm`ghklb ijZ\bevguc lj_m]hev gbd d\Z^jZl ijZ\bevguc \hkvfbm]hevgbd JZkkfhljbf ihkljh_gb_ ijZ\bevgh]h lj_m]hevgbdZ GZ hdjm`ghklb \u[_j_f ijhba\hevgmx lhqdm : Ba g__ ijh\_^_f ^m]m jZ^bmkZ hdjm`ghklb b ihemqZ_f \_jrbgu : b : ² lhqdb i_j_k_q_gby ^m]b b hdjm`ghklb Ijh\_^_f q_j_a lhqdb : : : dZkZl_evgu_ d hdjm`ghklb Lhqdb i_j_k_q_ gby dZkZl_evguo [m^ml \_jrbgZfb bkdhfh]h lj_m]hevgbdZ
>ey ihkljh_gby q_luj_om]hevgbdZ b \hkvfbm]hevgbdZ ijh \h^bf ^\Z i_ji_g^bdmeyjguo ^bZf_ljZ >Ze__ ihkljh_gb_ ZgZeh]bqgh jZkkfhlj_gghfm Â&#x2039;
JZ^bmku \ibkZgghc b hibkZgghc hdjm`ghkl_c h^gh ]h ijZ\bevgh]h Q m]hevgbdZ jZ\gu U b 5 Z jZ^bmk \ibkZgghc hdjm`ghklb ^jm]h]h ijZ\bevgh]h Q m]hev gbdZ jZ\_g U Q_fm jZ\_g jZ^bmk hibkZgghc hdjm` ghklb ^jm]h]h Q m]hevgbdZ" LZd dZd ijZ\bevgu_ Q m]hevgbdb ih^h[gu lh ihemqZ_f
qlh
U U
Â&#x2039;
5 hldm^Z bf__f 5 5
5 U U
I_jbf_lju ^\mo ijZ\bevguo Q m]hevgbdh\ hlghkyl ky dZd Z E DZd hlghkylky jZ^bmku bo \ibkZgguo b hibkZgguo hdjm`ghkl_c" M ijZ\bevguo Q m]hevgbdh\ hlghr_gby i_jbf_ljh\ jZ\gh hlghr_gbx jZ^bmkh\ \ibkZgguo b hibkZgguo hdjm`ghkl_c lZd qlh hlghr_gby jZ^bmkh\ [m^ml Z E Â&#x2039;
<uqbkebl_ ^ebgm hdjm`ghklb _keb jZ^bmk jZ\_g f f >ebgZ hdjm`ghklb \uqbkey_lky ih nhjfme_ O S5
5 f O Â&#x152;5 Â&#x2DC; Â&#x2DC; f 5 f O Â&#x152;5 Â&#x2DC; Â&#x2DC; f
Â&#x2039;
GZ kdhevdh baf_gblky ^ebgZ hdjm`ghklb _keb jZ^b mk baf_gblky gZ ff" >himklbf jZ^bmk jZ\_g 5 ff ke_^h\Zl_evgh O Â&#x152;5 ff ihke_ baf_g_gby jZ^bmk klZg_l 5 ff b O Â&#x152; 5 Â&#x152;5 Â&#x152; O S LZd qlh ^ebgZ hdjm`ghklb baf_gblky gZ S beb | ff Â&#x2039;
GZc^bl_ hlghr_gb_ i_jbf_ljZ ijZ\bevgh]h \ibkZg gh]h m]hevgbdZ d ^bZf_ljm b kjZ\gbl_ _]h k ijb [eb`_gguf agZq_gb_f Â&#x152;
KlhjhgZ ijZ\bevgh]h m]hevgbdZ jZ\gZ 5 kf aZ
^Zqm Â&#x2039; lh]^Z 3 3 G
Hl\_l §
Â&#x2039;
5 b agZqbl
5 5
| S
J_rbl_ aZ^Zqm Â&#x2039; ^ey ijZ\bevgh]h m]hevgbdZ
Z 5 kf aZ^Zqm Â&#x2039; Lh]^Z J 5 Z agZqbl 3 G
Hl\_l §
5 5
| S
Â&#x2039;
GZc^bl_ jZ^bmk a_fgh]h rZjZ bkoh^y ba lh]h qlh f khklZ\ey_l h^gm fbeebhggmx ^hex ^ebgu wd\Z lhjZ Imklv O ² ^ebgZ wd\ZlhjZ lh]^Z O Â&#x152;5 b 5 O Â&#x152; >Ze__ lZd dZd ^ebgZ wd\ZlhjZ f lh 5
Hl\_l | df
| df S
Â&#x2039;
GZ kdhevdh m^ebgbeky [u a_fghc wd\Zlhj _keb [u jZ^bmk a_fgh]h rZjZ m\_ebqbeky gZ kf" Ba aZ^Zqb Â&#x2039; bf__f qlh k baf_g_gb_f jZ^bmkZ gZ ff ^ebgZ hdjm`ghklb baf_gblky gZ Â&#x152; ff AgZqbl ijb m\_ebq_ gbb jZ^bmkZ a_feb gZ kf ^ebgZ wd\ZlhjZ m\_ebqblky gZ Â&#x152; kf § kf Hl\_l § kf Â&#x2039;
<gmljb hdjm`ghklb jZ^bmkZ 5 jZkiheh`_gu Q jZ\ guo hdjm`ghkl_c dhlhju_ dZkZxlky ^jm] ^jm]Z \ ^Zgghc hdjm`ghklb GZc^bl_ jZ^bmk wlbo hdjm`gh kl_c _keb qbkeh bo jZ\gh Imklv \gmljb hdjm`ghklb jZ^bmkhf 5 F p_gljhf \ lhqd_ H jZkiheh`_gu jZ\guo hdjm`ghklb ² hdj : U hdj < U b hdj K U
û$<K ² jZ\ghklhjhggbc lZd dZd $% %& $& U 2( A $% Â&#x2018;?<H Â&#x192; <? U < û2<? bf__f ?< 2%Â&#x2DC;FRVÂ&#x2018;(%2 lZd qlh 2%
(% FRV Â&#x2018;(%2
%' U 5 %' 2% U U
U
5
U FRV q
U
U
§ · ¸ Lh]^Z U ¨¨ ¸¹ ©
· § ¨ ¸ ¹ ©
5
2' 5 $' U 2( A $% $% U 2' '$ $2 gh $2 U dZd iheh\bgZ ^bZ]hgZeb d\Z^jZlZ
AgZqbl 5 U U 5 U
5
U hldm^Z
5
5
2' 5 %' U &% U 2& A $% 2% :< U dZd jZ ^bmk hibkZgghc hdjm`ghklb r_klbm]hevgbdZ
Lh]^Z 2' 2% %' 5 U hldm^Z bf__f U ย
5
J_rbl_ ij_^u^msmx aZ^Zqm _keb hdjm`ghklb jZk iheh`_gu \g_ ^Zgghc hdjm`ghklb Ljb jZ\gu_ hdjm`ghklb dZkZxlky ^jm] ^jm]Z H? 5 Ijh\_^_f 6' A H? b 01 A H? lh]^Z 6' __ 01 JZkkfhljbf รป2F' b รป2(1 ย F ย ? dZd ijyfu_ ย 1 ย ' khhl\_lkl\_ggu_ Lh]^Z รป20' a รป2?1
Ihwlhfm
2' 21
0' hldm^Z bf__f (1
0'
2' Â&#x2DC; (1 21
< û2(1 Â&#x2018;( Â&#x192; Â&#x2018;H Â&#x192; lh]^Z Â&#x2018;1 h agZqbl 2(
21 l _ 5
21 21 5 lh]^Z
(1 5 5
5
< û(1' Â&#x2018;'(0 ² iheh\bgZ m]eZ \ibkZggh]h ijZ\bevgh]h m]hevgbdZ ihwlhfm Â&#x2018;'(0
q
Â&#x2DC;
Â&#x2DC; q q
Lh]^Z Â&#x2018;'(1 Â&#x192; Â&#x2018;('1 Â&#x192; ihwlhfm û(1' ² jZ\gh [_^j_gguc b ?G 1' 5 ihemqZ_f qlh 2' 21 1' 5 5
Ih^klZ\bf \ ijhihjpbx 0'
5 5 Â&#x2DC; 5 5
5 5
û:6' ² jZ\ghklhjhggbc lZd qlh
$' 6' 0' Â&#x2DC;
5
5
5
Imklv q_luj_ jZ\gu_ hdjm`ghklb dZkZxlky ^jm] ^jm]Z b hdjm`ghklv k p_gljhf \ lhqd_ H b jZ^bmkhf H? 5
D
Ijh\_^_f dZkZl_evgmx ?F d hdj H 5 hgZ i_j_k_q_l HD \ lhqd_ F ?F A H< < û2<. b û2?F Â&#x2018;. Â&#x2018;? dZd ijy fu_ Â&#x2018;H Â&#x2018;H h[sbc agZqbl û2<. a û2?F Ihwlhfm 2% 20
%.
%. (0
2% Â&#x2DC; (0 20
< û2?F Â&#x2018;? Â&#x192; Â&#x2018;H Â&#x192; lh]^Z Â&#x2018;F Â&#x192; b H? ?F
5 agZqbl 20 5 5 5 < ûH<D H< 5 ?< 5 <D l d ?< %. Ihemq_ggu_ \ujZ`_gby ih^klZ\bf \ %. Â&#x2DC; 5 Â&#x2DC; 5
%. Â&#x2DC; 5
%. Â&#x2DC; 5 %. Â&#x2DC; 5
%.
5
%. 5 5
5
%. 5 5
%. l _ 5
5
5
5
5
û2$& a û2'0 iR ^\mf m]eZf
$& gh 2$ 5 '$ \ û2'0 Â&#x2018;' h '0 Â&#x2018;2 h lh]^Z '0 HF HF '0 ih l_hj_f_ IbnZ 5 5 20 ]hjZ 5 '0 ± '0 5 '0 '0
AgZqbl
2$ 20
Ih^klZ\bf ihemq_ggu_ agZq_gby '0 b 20 \ 5 '$ 5
5
Â&#x2039;
5 '$
'$ 5
5
'$
5 5 '$ 5Â&#x2DC;'$ 5 5Â&#x2DC;'$ 5Â&#x2DC;'$ 5Â&#x2DC;'$ ± 5Â&#x2DC;'$ 5 '$ 5 ± 5 5 '$Â&#x2DC;5 5 '$ 5
Rdb\ bf__l \ ^bZf_lj_ f b ^_eZ_l h[hjhlh\ \ fbgmlm GZc^bl_ kdhjhklv lhqdb gZ hdjm`ghklb rdb\Z f lZd qlh 5 f O Â&#x152;5 § Â&#x2DC; Â&#x2DC; § G § f gh Q ON ]^_ N ² qbkeh h[hjhlh\ \ fbgmlm lZd qlh § Â&#x2DC; § f fbg
Â&#x2039;
GZc^bl_ ^ebgm ^m]b hdjm`ghklb jZ^bmkZ kf hl\_ qZxs_c p_gljZevghfm m]em Â&#x192; Â&#x192; Â&#x192; Â&#x192;
>ebgZ ^m]b \uqbkey_lky ih nhjfme_ O
kemqZ_ 5 kf lZd qlh
O
O O O O Â&#x2039;
O
S Â&#x2DC; Â&#x2DC; q q S Â&#x2DC; Â&#x2DC; q q S Â&#x2DC; Â&#x2DC; q q S Â&#x2DC; Â&#x2DC; q q
S kf S kf S kf S kf
S5 Â&#x2DC; Dq < gZr_f q
SDq kf q
Kdhevdh ]jZ^mkh\ kh^_j`bl p_gljZevguc m]he _keb khhl\_lkl\mxsZy _fm ^m]Z khklZ\ey_l hdjm`ghklb" Imklv O ² ^ebgZ hdjm`ghklb Z O ² ^ebgZ ^m]b Lh]^Z S5 O
S5 Â&#x2DC; Dq LZd qlh q
D D D
Â&#x2DC; q q Â&#x2DC; q q
O Â&#x2DC; q S5
O Â&#x2DC; q O
D D D D Â&#x2039;
Â&#x2DC; q q Â&#x2DC; q q Â&#x2DC; q q Â&#x2DC; q q
DZdhc m]he h[jZamxl jZ^bmku A_feb ijh\_^_ggu_ \ ^\_ lhqdb gZ __ ih\_joghklb jZkklhygb_ f_`^m dh lhjufb jZ\gh df" JZ^bmk A_feb jZ\_g df 5 df ² jZ^bmk A_feb O df ² jZkklhygb_ f_`^m ^\mfy lhqdZfb gZ ih\_joghklb A_feb D ² m]he f_`^m jZ^bm kZfb S5 Bf__f O Â&#x2DC; D Lh]^Z q D Â&#x2039;
Â&#x2DC; q Â&#x2DC;
cc
Ih jZ^bmkm 5 f gZc^bl_ ^ebgm ^m]b hl\_qZxs_c p_gljZevghfm m]em Â&#x192; Â&#x192; Â&#x192; Â&#x192; Â&#x192; Â&#x192;
S5 Â&#x2DC; D hldm^Z bf__f q Â&#x2DC; Â&#x2DC; q O | f q Â&#x2DC; Â&#x2DC; q O | f q Â&#x2DC; Â&#x2DC; q O | f q Â&#x2DC; Â&#x2DC; q O | f q O
O Â&#x2DC; q S5
Â&#x2DC; Â&#x2DC; q f q Â&#x2DC; Â&#x2DC; q O | f q
O |
Â&#x2039;
Ih ^Zgghc ohj^_ Z gZc^bl_ ^ebgm __ ^m]b _keb ]jZ^mkgZy f_jZ ^m]b jZ\gZ Â&#x192; Â&#x192; Â&#x192; Imklv ^ZgZ hdjm`ghklv k p_gljhf H ohj^Z :< Z Z ]jZ ^mkgZy f_jZ ^m]b jZ\gZ Â&#x192; Â&#x192; Â&#x192; D Â&#x192; JZkkfhljbf û2$<
:H 2% dZd jZ^bmku hdjm`ghklb b Â&#x2018;:H< D Â&#x192; Lh]^Z Â&#x2018;: Â&#x2018;< Â&#x192; ± Â&#x192; Â&#x192; agZqbl û$2< ² jZ\gh klhjhggbc b 5 $2 D >Ze__ O
S5 Â&#x2DC;D q
S Â&#x2DC; D Â&#x2DC; q q
SD
D Â&#x192; û$2% ² ijyfhm]hevguc jZ\gh[_^j_gguc
5
Ih l_hj_f_ IbnZ]hjZ ihemqbf D 5 5 5 hldm^Z D 5
D
O
>Ze__ ihemqZ_f S5 Â&#x2DC;D q
SÂ&#x2DC;
D
Â&#x2DC; q
q
SD
D Â&#x192; < û$2% Â&#x2018;:H< D Â&#x192; ih l_hj_f_ dhkbgm kh\ ihemqbf :< :H H< ± :HÂ&#x2DC;H<Â&#x2DC;FRVÂ&#x2018;$2%
LZd qlh D 5 5 ± 5 Â&#x2DC; ± O
S5 Â&#x2DC;D q
5 5
S Â&#x2DC; D Â&#x2DC; q q
SD
D
>Ze__
Â&#x2039;
Ih ^Zgghc ^ebg_ ^m]b O gZc^bl_ __ ohj^m _keb ^m]Z kh^_j`bl Â&#x192; Â&#x192; Â&#x192; D Â&#x192;
O
S Â&#x2DC; 5 Â&#x2DC; q hldm^Z bf__f 5 q
ghklhjhggbc lh D Â&#x192;
:< 5
O LZd dZd ':<H ² jZ\ S O S
O
S Â&#x2DC; 5 Â&#x2DC; q 5 q
O >Ze__ û$2< ² ijyfhm]hevguc lZd S
qlh ih l_hj_f_ IbnZ]hjZ :H H< :< 5 5 $% 5
$%
5
D Â&#x192;
O
S Â&#x2DC; 5 Â&#x2DC; q l _ 5 q
O S
O < ':H< ih l_hj_f_ dhkbgmkh\ S
:H H< ± :HÂ&#x2DC;H<Â&#x2DC;FRVD $% 5 5 ± 5 FRVO h $% 5 :< $% 5 Â&#x2039;
GZc^bl_ jZ^bZggmx f_jm m]eh\ Â&#x192; Â&#x192; Â&#x192;
S q S q Â&#x2DC; q S q Â&#x2DC; q
q Â&#x2DC;
Â&#x2039;
O S
S S S
GZc^bl_ jZ^bZggmx f_jm m]eh\ lj_m]hevgbdZ :<K _keb Â&#x2018;: Â&#x192; Â&#x2018;< Â&#x192; LZd dZd Â&#x2018;: Â&#x192; lh Â&#x2018;$
q Â&#x2DC;
S q
S
LZd dZd Â&#x2018;< Â&#x192; lh Â&#x2018;%
S q
S
S q
S
q Â&#x2DC;
Â&#x2018;K Â&#x192; ± Â&#x192;± Â&#x192; Â&#x192; lZd qlh Â&#x2018;&
Hl\_l Â&#x2039;
S S S b
q Â&#x2DC;
GZc^bl_ ]jZ^mkgmx f_jm m]eZ _keb _]h jZ^bZggZy S S S S S S f_jZ jZ\gZ S q Â&#x2DC; q S S q Â&#x2DC; q S S q Â&#x2DC; q S S q Â&#x2DC; q S S q q Â&#x2DC; S S q Â&#x2DC; q S
Â&#x2020; IEHS:>B NB=MJ Â&#x2039;
>hdZ`bl_ qlh kmffZ iehsZ^_c d\Z^jZlh\ ihkljh _gguo gZ dZl_lZo ijyfhm]hevgh]h lj_m]hevgbdZ jZ\gZ iehsZ^b d\Z^jZlZ ihkljh_ggh]h gZ ]bihl_gm a_ Imklv dZl_l :K E <K Z ]bihl_gmaZ :< k ke_^h\Z l_evgh 6$$ & & E 6%% & & D 6$%% $ F
Ba l_hj_fu IbnZ]hjZ bf__f D E F lh _klv 6$$ & & 6%% & & 6$%% $
Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
D 6 6 6
Klhjhgu ^\mo mqZkldh\ a_feb d\Z^jZlghc nhjfu jZ\gu f b f GZc^bl_ klhjhgm d\Z^jZlgh]h mqZkldZ jZ\gh\_ebdh]h bf f Z f 6 0 6 Z Â&#x2DC; f Z Â&#x2DC; f 6 6 f
Gh 6 Z hldm^Z bf__f Z
6
Hl\_l Z § f
Â&#x2039;
f | f
GZc^bl_ iehsZ^v d\Z^jZlZ 6 ih _]h ^bZ]hgZeb Z
$%&' ² d\Z^jZl :K Z < û:<K Â&#x2018;< Â&#x192; ih l_hj_f_ IbnZ]hjZ $< <K :K l d :< <K lh :< :K lh _klv $% D $%
ke_^h\Zl_evgh
6 $%
Hl\_l 6 D
Â&#x2039;
D
D
<h kdhevdh jZa iehsZ^v d\Z^jZlZ hibkZggh]h hdheh hdjm`ghklb [hevr_ iehsZ^b d\Z^jZlZ \ibkZggh]h \ lm `_ hdjm`ghklv"
Imklv $%&' ² d\Z^jZl \ibkZgguc \ hdjm`ghklv $ % & ' ² d\Z^jZl hibkZgguc hdheh hdjm`ghklb JZkkfhljbf û$$ < Â&#x2018;$ Â&#x192; ih l_hj_f_ IbnZ]hjZ :< :: : < lh _klv $%
$ % $ %
$ %
lZd dZd :% 6$%&' $ % 6$ % & ' lh 6$ % & ' 6$%&'
:< :<
Â&#x2039;
DZd baf_gblky iehsZ^v d\Z^jZlZ _keb dZ`^mx _]h klhjhgm m\_ebqblv \ jZaZ" KlhjhgZ d\Z^jZlZ jZ\gZ Z _]h iehsZ^v jZ\gZ Z ?keb klh jhgm m\_ebqblv \ jZaZ lh hgZ klZg_l ² Z Z iehsZ^v ² Z >Ze__
D D
Hl\_l IehsZ^v m\_ebqblky \ jZa
Â&#x2039;
<h kdhevdh jZa gZ^h mf_gvrblv klhjhgu d\Z^jZlZ qlh[u _]h iehsZ^v mf_gvrbeZkv \ jZa" Imklv Z ² iehsZ^v d\Z^jZlZ mf_gvr_ggh]h \ jZa lh ]^Z D ² iehsZ^v d\Z^jZlZ ke_^h\Zl_evgh klhjhgZ d\Z^jZ lZ Z ]^_ Z ² klhjhgZ mf_gvr_ggh]h d\Z^jZlZ AgZqbl klhjh gm d\Z^jZlZ ke_^m_l mf_gvrblv \ jZa Â&#x2039;
Q_fm jZ\gu klhjhgu ijyfhm]hevgbdZ _keb hgb hlghkylky dZd Z _]h iehsZ^v f " Imklv h^gZ klhjhgZ ijyfhm]hevgbdZ [m^_l o f lh]^Z ^jm ]Zy ² o f iehsZ^v oÂ&#x2DC; o [ f qlh ih mkeh\bx aZ^Zqb jZ\gh f [ [ [
Lh]^Z o f b o f AgZqbl y klhjhgZ ² f y klhjhgZ ² f
Â&#x2039;
Q_fm jZ\gu klhjhgu ijyfhm]hevgbdZ _keb _]h i_ jbf_lj ^f Z iehsZ^v f " Imklv h^gZ klhjhgm ijyfhm]hevgbdZ o ^f Z ^jm]Zy \ ^f lh]^Z i_jbf_lj [m^_l o \ Â&#x2DC; qlh jZ\gh ^f Z iehsZ^v [\ ^f ih mkeh\bx jZ\gZ ^f  [ \ Â&#x2DC; ® ¯ [\
 [ \  [ \ ® ® ¯ [\ ¯ \ \
±\ \ ± \ ± \
l _ \ ^f Z \ ^f Lh]^Z o ^f Z o ^f Hl\_l H^gZ klhjhgZ ² ^f ^jm]Zy ² ^f Â&#x2039;
IZjZee_eh]jZff b ijyfhm]hevgbd bf_xl h^bgZdh \u_ klhjhgu GZc^bl_ hkljuc m]he iZjZee_eh]jZf fZ _keb iehsZ^v _]h jZ\gZ iheh\bg_ iehsZ^b ijy fhm]hevgbdZ
Imklv $%&' ² iZjZee_eh]jZff k hkljuf m]ehf : $ % & ' ² ijyfhm]hevgbd Lh]^Z $' $ ' D $% $ % E O 6 $ % & ' DE 6$%&' DK
6$ % & '
< û$<? Â&#x2018;? Â&#x192; lZd qlh VLQÂ&#x2018;$
Â&#x2018;: Â&#x192; Hl\_l Â&#x192; Â&#x2039;
E DE Lh]^Z K K E agZqbl E E
D\Z^jZl b jhf[ bf_xl h^bgZdh\u_ i_jbf_lju DZ dZy ba nb]mj bf__l [hevrmx iehsZ^v" H[tykgbl_ hl\_l Imklv Jd\ Jjhf[Z Gh Jd\ Z Z Jjhf[Z Z
Lh]^Z Z Z 6d\ ZÂ&#x2DC;Z 6jhf[Z Z Â&#x2DC;K gh K Z lZd dZd dZl_l f_gvr_ ]bihl_gmau Z agZqbl b ZÂ&#x2DC;Z ! Z Â&#x2DC;K lZd qlh 6d\ ! 6jhf[Z Â&#x2039;
GZc^bl_ iehsZ^v jhf[Z _keb _]h \ukhlZ kf Z hkljuc m]he Â&#x192; Imklv $%&' ² jhf[ <G kf ² \ukhlZ Â&#x2018;: Â&#x192;
< û:<G Â&#x2018;G Â&#x192; lZd qlh <G :<Â&#x2DC;VLQ. hldm^Z $%
%+ VLQ D
VLQ ο
kf
>Ze__ 6jhf[Z $'Â&#x2DC;%+ $%Â&#x2DC;%+ Â&#x2DC; kf Hl\_l kf
Â&#x2039;
GZc^bl_ iehsZ^v jhf[Z _keb _]h \ukhlZ kf Z f_gvrZy ^bZ]hgZev kf Imklv $%&' ² jhf[ %' kf f_gvrZy ^bZ]hgZev <G kf ² \ukhlZ
< û%'+ Â&#x2018;+ Â&#x192; %' kf <G kf ih l_hj_f_
IbnZ]hjZ +' kf %' %+ < û$<+ Â&#x2018;+ Â&#x192; <G kf $+ $' ± +' $% ± Ff ih l_hj_f_ IbnZ]hjZ bf__f $% $+ %+ lh _klv
$% $% ± $% ± $%
:< :< LZd qlh $' $% kf >Ze__ 6$%&' :'Â&#x2DC;<G Â&#x2DC; kf
Hl\_l 6$%&' kf
Â&#x2039;
>hdZ`bl_ qlh iehsZ^v jhf[Z jZ\gZ iheh\bg_ ijhba\_^_gby ^bZ]hgZe_c Imklv $%&' ² jhf[ :K b %' ² ^bZ]hgZeb
Bf__f
6$%&' 6û:<K 6û$&'
:KÂ&#x2DC;<H $&Â&#x2DC;'2 :K <H '2 $& Â&#x2DC; %' :KÂ&#x2DC;%'
Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
GZc^bl_ klhjhgu jhf[Z agZy qlh _]h ^bZ]hgZeb hlghkylky dZd Z iehsZ^v jhf[Z jZ\gZ kf
Imklv $%&' ² jhf[ :K b %' ² ^bZ]hgZeb
6$%&' kf
%' $&
6$%6'
agZqbl
$&Â&#x2DC;%' kf Imklv %' o kf lh]^Z :K o kf [ Â&#x2DC; [ [
[
AgZqbl %' kf :K kf
JZkkfhljbf û$2< Â&#x2018;H Â&#x192; dZl_l :H dZl_l <H
%' kf Lh]^Z ih l_hj_f_ IbnZ]hjZ
:<
Hl\_l kf
Â&#x2039;
:K kf
:H <H
kf
JZa^_ebl_ ^Zgguc lj_m]hevgbd gZ ljb jZ\gh\_ebdb_ qZklb ijyfufb ijhoh^ysbfb q_j_a h^gm \_jrbgm
JZa^_ebf :K gZ $' '( (& Lh]^Z 6 $%' 6 '%( 6 (%&
LZd qlh 6$%' 0'%( 6(%&
$' Â&#x2DC; %+ '( Â&#x2DC; %+ (& Â&#x2DC; %+
Â&#x2039;
J_rbl_ ij_^u^msmx aZ^Zqm \ay\ \f_klh lj_m]hev gbdZ iZjZee_eh]jZff Ijh\_^_f ^bZ]hgZev :K û:<K û$&' iR lj_f klhjh gZf lh]^Z 6$%K 6$&'
JZa^_ebf dZ`^uc ba lj_m]hevgbdh\ :<K b :K' gZ jZ\ gh\_ebdb_ qZklb l d kZfb lj_m]hevgbdb jZ\gu lh bo qZklb [m^ml jZ\gh\_ebdb LZd qlh ihemqblky r_klv jZ\gh\_ebdbo lj_m]hevgbdh\ gh lh]^Z 6$%( 6$( &. 6$. ' LZd dZd wlb nb ]mju kh^_j`Zl ih lj_m]hevgbdZ Â&#x2039;
Q_fm jZ\gZ iehsZ^v jZ\gh[_^j_ggh]h lj_m]hevgbdZ _keb _]h hkgh\Zgb_ f Z [hdh\Zy klhjhgZ f" û:<K ² jZ\gh[_^j_gguc :< <K f :K f
Ijh\_^_f %' A $& ih k\hckl\m jZ\gh[_^j_ggh]h lj_
m]hevgbdZ %' ² f_^bZgZ b \ukhlZ Lh]^Z $'
$& f
< û$%' Â&#x2018;' Â&#x192; :< f $' f ih l_hj_f_
IbnZ]hjZ %' >Ze__
6 $%&
Hl\_l f
$% $'
$& Â&#x2DC; %'
Â&#x2DC; Â&#x2DC;
f
f
Â&#x2039;
GZc^bl_ iehsZ^v jZ\gh[_^j_ggh]h ijyfhm]hevgh]h lj_m]hevgbdZ k ]bihl_gmahc Z JZkkfhljbf û:<K Â&#x2018;K Â&#x192; <K :K :< Z ² ]bihl_ gmaZ
Ih l_hj_f_ IbnZ]hjZ bf__f :K <K :< <K Z
<K <K Lh]^Z :K <K 6 '$%&
Hl\_l Â&#x2039;
D
Z
Z Z
>Ze__
$& Â&#x2DC; %&
D D Â&#x2DC; Â&#x2DC;
D
M lj_m]hevgbdZ kh klhjhgZfb kf b kf ijh\_^_gu \ukhlu d wlbf klhjhgZf <ukhlZ ijh\_^_ggZy d klh jhg_ kf jZ\gZ kf Q_fm jZ\gZ \ukhlZ ijh\_^_g gZy d klhjhg_ kf"
Imklv \ û:<K :K kf :< kf %+ KZ Ff Lh]^Z k h^ghc klhjhgu Â&#x2DC; $& Â&#x2DC; KD
6 '$%&
K ^jm]hc klhjhgu
6'$%&
ihemqZ_f qlh Hl\_l kf
Â&#x2039;
KE
6 '$%& $%
Â&#x2DC; Â&#x2DC; kf
Â&#x2DC; $% Â&#x2DC; KE
kf
>hdZ`bl_ qlh klhjhgu lj_m]hevgbdZ h[jZlgh ijh ihjpbhgZevgu _]h \ukhlZf l _ D E F
K D KE KF
Imklv \ û:<K %& D $$ KD $& E %% KE $% F && KF
Lh]^Z ihwlhfm
6 '$%& D
DKD 6 E KD
EKE 6 F KE
FKF 6 KF
Ba ihemq_gguo jZ\_gkl\ ihemqZ_f D E F
6 6 6 KD KE KF
Qlh b lj_[h\Zehkv ^hdZaZlv
KD KE KF
Â&#x2039;
GZc^bl_ iehsZ^v jZ\ghklhjhgg_]h lj_m]hevgbdZ kh klhjhghc Z Imklv û$<K ² jZ\ghklhjhggbc :< Z
Lh]^Z Â&#x2018;: Â&#x2018;< Â&#x2018;K Â&#x192; ke_^h\Zl_evgh 6 $%&
$% Â&#x2DC; $& Â&#x2DC; VLQ Â&#x2018;$ D
Hl\_l Â&#x2039;
D Â&#x2DC; D Â&#x2DC; VLQ q
D Â&#x2DC;
D
GZc^bl_ iehsZ^v ijZ\bevgh]h lj_m]hevgbdZ \ibkZggh]h \ djm] jZ^bmkZ 5 Imklv û:<K ² ijZ\bevguc \ibkZgguc \ hdjm`ghklv :H 5
Lh]^Z Z
6 $%&
5 Lh _klv :< <K :K 5 Gh lh]^Z
$% ih ij_^u^ms_c aZ^Zq_ b 6 $%&
5
Â&#x2039;
GZc^bl_ iehsZ^v ijyfhm]hevgh]h lj_m]hevgbdZ _k eb _]h \ukhlZ ^_ebl ]bihl_gmam gZ hlj_adb kf b kf Imklv \ lj_m]hevgbd_ :<K Â&#x2018;K Â&#x192; &' ² \ukhlZ $' kf '% kf GZclb 6û$%&
û$&' a û&%' ihwlhfm &'
$' Â&#x2DC; '%
Â&#x2DC;
Â&#x2DC;
kf
:< $' %' kf 6 û$%&
Hl\_l kf
$% Â&#x2DC; &'
Â&#x2DC;
kf
Â&#x2039;
Q_fm jZ\gu dZl_lu ijyfhm]hevgh]h lj_m]hevgbdZ _keb _]h ]bihl_gmaZ jZ\gZ kf Z iehsZ^v jZ\gZ kf " Imklv \ û:<K Â&#x2018;K Â&#x192; :< kf 6 kf
>himklbf :K [ kf Z <K \ kf lh]^Z ih l_hj_f_ IbnZ
]hjZ bf__f [ m Z ih nhjfme_ iehsZ^b LZd qlh
[\
 [ \ ° ® [\ ° ¯
° [ \
® °¯ [\
Keh`bf b \uql_f ba ihemqbf ° [ [\ \ ® °¯ [ [\ \ ° [ \ ® °¯ [ \
 [ \ ® ¯[ \
Hldm^Z o lh]^Z \ <K kf Hl\_l kf kf Â&#x2039;
[±
Lh _klv :K
kf
M lj_m]hevgbdZ $<K :K Z <K E Ijb dZdhf m]e_ K iehsZ^v lj_m]hevgbdZ [m^_l gZb[hevr_c" &
LZd dZd 6û$%&
$&Â&#x2DC;%&Â&#x2DC;VLQÂ&#x2018;&
DEVLQÂ&#x2018;& lh iehsZ^v
[m^_l gZb[hevr_c ijb gZb[hevr_f agZq_gbb VLQÂ&#x2018;& : VLQÂ&#x2018;& ² gZb[hevrbc m Â&#x2018;K Â&#x192; VLQÂ&#x2018; Â&#x192; AgZqbl ijb Â&#x2018;K Â&#x192; 6 [m^_l gZb[hevr_c b jZ\ghc
DE
Â&#x2039;
GZc^bl_ iehsZ^v jZ\gh[_^j_ggh]h lj_m]hevgbdZ m dhlhjh]h [hdh\u_ klhjhgu jZ\gu f Z m]he f_`^m gbfb jZ\_g Â&#x192;
Imklv û:<K ² jZ\gh[_^j_gguc $% <K f Â&#x2018;< Â&#x192; Lh]^Z 6 û$%&
Â&#x2DC; $% Â&#x2DC; %& Â&#x2DC; VLQ Â&#x2018;%
Hl\_l f
Â&#x2DC; Â&#x2DC; Â&#x2DC; VLQ q
Â&#x2DC;
f
Â&#x2039;
GZc^bl_ iehsZ^v iZjZee_eh]jZffZ _keb _]h klhjh gu f b f Z h^bg ba m]eh\ jZ\_g Â&#x192; Imklv $%&' ² iZjZee_eh]jZff $' f :< f Â&#x2018;: Â&#x192;
Lh]^Z 6$%&' $'Â&#x2DC;$%Â&#x2DC;VLQÂ&#x2018;$ Â&#x2DC; Â&#x2DC;VLQ Â&#x192; Â&#x2DC; f Hl\_l f
Â&#x2039;
GZc^bl_ iehsZ^v lj_m]hevgbdZ ih klhjhg_ Z b ijb e_`Zsbf d g_c m]eZf . b Imklv û:<K <K Z Â&#x2018;K . Â&#x2018;<
Ih l_hj_f_ kbgmkh\ bf__f D VLQ q D E
$& lh _klv VLQÂ&#x2018;%
E D VLQ E VLQ D E
D Â&#x2DC; VLQ E >Ze__ VLQ D E
hldm^Z bf__f E 6 '$%&
%& VLQÂ&#x2018;&
DE VLQ D
D Â&#x2DC; D VLQ D Â&#x2DC; VLQ E VLQ D E
E VLQ E
D VLQ D Â&#x2DC; VLQ E VLQ D E
Â&#x2039;
<u\_^bl_ nhjfmem =_jhgZ ^ey iehsZ^b lj_m]hevgb dZ 6 S S D S E S F ]^_ D E F ² ^ebgu klhjhg lj_m]hevgbdZ S ² ihemi_gjbf_lj AZ^ZqZ j_r_gZ \ i mq_[gbdZ klj
Â&#x2039;
GZc^bl_ iehsZ^v lj_m]hevgbdZ ih lj_f klhjhgZf
O D E F
D E F S
S
Ih nhjfme_ =_jhgZ ihemqZ_f
6 '$%&
S S D S E S F
Â&#x2DC; Â&#x2DC; Â&#x2DC;
D E F S
Â&#x2DC;
Â&#x2DC; Â&#x2DC;
D E F S
Â&#x2DC; Â&#x2DC; kf
Ih nhjfme_ =_jhgZ ihemqZ_f 6$%&
S S D S E S F
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2DC; kf
D E F S
Ih nhjfme_ =_jhgZ ihemqZ_f
6$%&
S S D S E S F
D
E
k S
Â&#x2DC;
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Ih nhjfme_ =_jhgZ ihemqZ_f 6$%& S S D S E S F
D E S
F
6$%& S S D S E S F
Â&#x2DC;
Â&#x2DC; Â&#x2DC; kf
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Ih nhjfme_ =_jhgZ ihemqZ_f
Â&#x2DC; Â&#x2DC;
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2DC; Â&#x2DC;
Â&#x2DC;
kf
D S
E F
Ih nhjfme_ =_jhgZ ihemqZ_f
6$%& S S D S E S F
Â&#x2DC; Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2039;
Klhjhgu lj_m]hevgbdZ Z E k GZc^bl_ \ukhlm lj_ m]hevgbdZ hims_ggmx gZ klhjhgm k Imklv KF ² \ukhlZ Lh]^Z F Â&#x2DC; KF
6 û$%&
K ^jm]hc klhjhgu ih nhjfme_ =_jhgZ 6û$%&
]^_ S
D E F LZd qlh KF
6 û$%& F
S S D S E S F
F
S S D S E S F
Â&#x2039;
;hdh\u_ klhjhgu lj_m]hevgbdZ kf b kf GZc ^bl_ \ukhlm lj_m]hevgbdZ hims_ggmx gZ hkgh\Zgb_ jZ\gh_ kf kf Imklv D E k ² klhjhgu lj_m]hevgbdZ Z kf E kf k kf Lh]^Z S
kf
6
S S D S E S F
KF
6 F
Â&#x2DC; kf
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2DC;
kf
Z kf E kf k kf Lh]^Z
j 6
S S D S E S F
KF
6 F
kf
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2DC;
Â&#x2DC; Â&#x2DC; kf
kf
Â&#x2039;
I_jbf_lj jZ\gh[_^j_ggh]h lj_m]hevgbdZ jZ\_g kf Z _]h [hdh\Zy klhjhgZ gZ kf [hevr_ hkgh \Zgby GZc^bl_ \ukhlm lj_m]hevgbdZ hims_ggmx gZ [hdh\mx klhjhgm Lj_m]hevgbd :<K ² jZ\gh[_^j_gguc $& ² hkgh\Zgb_ :< :K kf 3 kf K$% ² \ukhlZ hims_ggZy gZ :< %
Imklv :K [ kf lh]^Z :< <K o kf Z i_jbf_lj jZ\_g [ [ lZd qlh [ [ o ± [
AgZqbl :K kf :< <K kf >Ze__ S
kf
Â&#x2DC; Â&#x2DC; Â&#x2DC; Â&#x2DC; Â&#x2DC; kf
S S $% S $& S %&
6
Lh]^Z K $%
Â&#x2DC; kf
6 $%
Hl\_l kf
Â&#x2039;
GZc^bl_ \ukhlu lj_m]hevgbdZ m dhlhjh]h klhjhgu jZ\gu kf kf b kf Imklv D E k ² klhjhgu lj_m]hevgbdZ D kf E kf k kf S
Z E F lh]^Z S
6$%&
>Ze__
S S D S E S F
KD
6 D KE
KF
Hl\_l Â&#x2039;
k
6 F
Â&#x2DC;
6 E
kf Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2DC;
Â&#x2DC;
kf kf b kf
GZc^bl_
\ukhlm
Â&#x2DC; Â&#x2DC; kf
kf
kf
kf
lj_m]hevgbdZ
kh
klhjhgZfb
ijh\_^_ggmx d klhjhg_ Imklv Z E k ² klhjhgu lj_m]hevgbdZ D E
Ba aZ^Zqb Â&#x2039; 6 kf lh]^Z 6 D
KD
Hl\_l kf
Â&#x2039;
Â&#x2DC;
Â&#x2DC;
kf
GZc^bl_ gZbf_gvrmx \ukhlm lj_m]hevgbdZ kh klh jhgZfb b gZb[hevrmx \ukhlm lj_m]hevgbdZ kh klhjhgZfb
Ba aZ^Zqb Â&#x2039; ke_^m_l qlh gZbf_gvrZy ² \ukhlZ him s_ggZy d gZb[hevr_c klhjhg_ Z gZb[hevrZy ² \ukhlZ him s_ggZy d gZbf_gvr_c klhjhg_ GZbf_gvrZy \ukhlZ KF O D E F Ba aZ^Zqb Â&#x2039; 6 kf lh]^Z Kk
6 k
Â&#x2DC;
kf
Z E k Ba aZ^Zqb Â&#x2039; 6 kf lh]^Z Kk
6 k
Â&#x2DC;
kf
GZb[hevrZy \ukhlZ KD D E F Ba aZ^Zqb Â&#x2039; 6 kf lh]^Z KD
6 D
Â&#x2DC;
Â&#x2DC; Â&#x2DC;
kf
F Ba aZ^Zqb Â&#x2039; 6 kf lh]^Z
D E
KD
Â&#x2039;
6 D
Â&#x2DC;
kf
GZc^bl_ iehsZ^v ljZi_pbb m dhlhjhc iZjZee_evgu_ klhjhgu kf b kf Z g_iZjZee_evgu_ ² kf b kf
Imklv $%&' ² ljZi_pby $' b <K ² hkgh\Zgby $' kf <K kf :< kf &' kf 6 $%&'
$% %& Â&#x2DC; %+
Imklv :G [ kf G? <K kf lh]^Z (' $'±$+±+( ± ± o ± o kf < û$<+ Â&#x2018;G Â&#x192; ih l_hj_f_ IbnZ]hjZ bf__f <G :< ± :G ± o
< û&'( Â&#x2018;( Â&#x192; ih l_hj_f_ IbnZ]hjZ
&( &' ± '( ± ± [ ± [ ± [ [ ± [ ±
Gh <G K? lZd qlh
± [ [ ± [ ± ± [ ± ± ± o ± [ AgZqbl :G kf lh]^Z
<+ ± %+
<G kf
Ke_^h\Zl_evgh 6$%&'
Hl\_l kf
Â&#x2DC;
Â&#x2DC;
kf
Â&#x2039;
< jZ\gh[hdhc ljZi_pbb hkgh\Zgby jZ\gu kf b kf [hdh\Zy klhjhgZ kf GZc^bl_ iehsZ^v ljZi_pbb Imklv $%&' ² ljZi_pby :< &' kf $' kf <K kf
û:<G '&(' Â&#x2018;+ Â&#x2018;( Â&#x192; $% &' %+ &( Lh]^Z $+ (' $' ± %& ± kf
Lh]^Z ih l_hj_f_ IbnZ]hjZ <G
:< :G
Ke_^h\Zl_evgh 6$%&'
$' %& Â&#x2DC; %+
Hl\_l kf
Â&#x2039;
Â&#x2DC; Â&#x2DC;
kf kf
< jZ\gh[hdhc ljZi_pbb [hevr__ hkgh\Zgb_ jZ\gh f [hdh\Zy klhjhgZ f b ^bZ]hgZev f GZc^b l_ iehsZ^v ljZi_pbb
Imklv $%&' ² ljZi_pby :< &' f :K f $' f < û:K? Â&#x2018;? Â&#x192; $& f $( ± (' Ih l_hj_f_ IbnZ]hjZ K? :K ± :( ± ± (' ± (' ± (' ± (' ± ('
lh _klv &( (' (' ± < û&'( Â&#x2018;( Â&#x192; &' f Ih l_hj_f_ IbnZ]hjZ bf__f (' K? &'
IhemqZ_f qlh
(' ± (' (' f
ke_^h\Zl_evgh $+ (' f <K ± Â&#x2DC; f K? ± K? f Lh]^Z 6$%&'
$' %& Â&#x2DC; K?
Hl\_l f
Â&#x2039;
Â&#x2DC;
Â&#x2DC;
f
>hdZ`bl_ qlh kj_^b \k_o iZjZee_eh]jZffh\ k ^Zg gufb ^bZ]hgZeyfb gZb[hevrmx iehsZ^v bf__l jhf[
Imklv $%&' ² iZjZee_eh]jZff $& b K' ² ^bZ]hgZeb Â&#x2018;$.% . 6$%&'
Ã&#x201A;:%Ã&#x201A;K'Ã&#x201A;VLQ.
6$%&' [m^_l gZb[hevr_c dh]^Z VLQ. lh _klv D Â&#x192; ke_^h\Zl_evgh ^bZ]hgZeb ^Zggh]h iZjZee_eh]jZffZ i_j_k_
dZxlky ih^ ijyfuf m]ehf Z lZdhc iZjZee_eh]jZff y\ey_lky jhf[hf Qlh b lj_[h\Zehkv ^hdZaZlv Â&#x2039;
<u\_^bl_ ke_^mxsb_ nhjfmeu ^ey jZ^bmkh\ hib kZgghc 5 b \ibkZgghc U hdjm`ghkl_c lj_m]hevgb dZ 5
DEF U 6
V ]^_ D E F ² klhjhgu lj_ D E F
m]hevgbdZ Z 6 ² _]h iehsZ^v AZ^ZqZ j_r_gZ \ i mq_[gbdZ klj
Â&#x2039;
GZc^bl_ jZ^bmku hibkZgghc 5 b \ibkZgghc U hd jm`ghkl_c ^ey lj_m]hevgbdZ kh klhjhgZfb D E F Ihemi_jbf_lj lj_m]hevgbdZ S
Z E F
Ih nhjfme_ =_jhgZ ihemqZ_f 6'
Ke_^h\Zl_evgh
S S D S E S F
5 U
DEF 6
D E F Ihemi_jbf_lj lj_m]hevgbdZ S
Ih nhjfme_ =_jhgZ ihemqZ_f
6'
Â&#x2DC;
S S D S E S F
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2DC; Â&#x2DC; Â&#x2DC;
6 D E F
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Ke_^h\Zl_evgh
DEF 6
5 U
Â&#x2DC; Â&#x2DC; Â&#x2DC;
6 D E F
D E F Ihemi_jbf_lj lj_m]hevgbdZ S
Ke_^h\Zl_evgh
S S D S E S F
5 U
DEF 6
D E F Ihemi_jbf_lj lj_m]hevgbdZ S
Ke_^h\Zl_evgh
Â&#x2DC;
Ih nhjfme_ =_jhgZ ihemqZ_f 6'
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2DC; Â&#x2DC; Â&#x2DC;
6 D E F
U
DEF 6
6 D E F
Â&#x2DC; Â&#x2DC;
Â&#x2DC;
S S D S E S F
5
Â&#x2DC;
Ih nhjfme_ =_jhgZ ihemqZ_f 6'
Â&#x2DC;
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2039;
;hdh\Zy klhjhgZ jZ\gh[_^j_ggh]h lj_m]hevgbdZ kf \ukhlZ ijh\_^_ggZy d hkgh\Zgbx kf GZc^b l_ jZ^bmk hibkZgghc hdjm`ghklb Imklv :<K ² jZ\gh[_^j_gguc lj_m]hevgbd :< <K kf <G kf ² \ukhlZ ijh\_^_ggZy d hkgh\Zgbx
Lh]^Z \ û:<G Â&#x2018;G Â&#x192; Ih l_hj_f_ IbnZ]hjZ ihemqZ_f :G
:< <G
Lh]^Z :K :G kf b 6 '$%&
Ke_^h\Zl_evgh
5
Hl\_l kf
Â&#x2039;
$& Â&#x2DC; %+
DEF 6
kf
Â&#x2DC; Â&#x2DC; kf
Â&#x2DC; Â&#x2DC; Â&#x2DC;
kf
GZc^bl_ jZ^bmku hdjm`ghkl_c hibkZgghc hdheh jZ\gh[_^j_ggh]h lj_m]hevgbdZ k hkgh\Zgb_f Z b [h dh\hc klhjhghc E b \ibkZgghc \ g_]h Imklv :<K ² jZ\gh[_^j_gguc lj_m]hevgbd :< <K E :K Z GZclb 5 U
:< <K :K
Lh]^Z S 6 $%&
E D
5
U
DEE 6
6 D E
Â&#x2DC; Â&#x2DC;
E D
E D E D
DE
D
D
D
E D E D D D Â&#x2DC; Â&#x2DC; Â&#x2DC;
S S D S E
Ke_^h\Zl_evgh
E
E
E D
E D
E D
E D E D
E D
E D E D
E D E D
D E D
E D
E D
Â&#x2039;
GZc^bl_ jZ^bmk U \ibkZgghc b jZ^bmk 5 hibkZgghc hdjm`ghkl_c ^ey jZ\gh[_^j_ggh]h lj_m]hevgbdZ k hkgh\Zgb_f kf b [hdh\hc klhjhghc kf Imklv :<K ² jZ\gh[_^j_gguc lj_m]hevgbd :< <K kf :K kf
Lh]^Z S 6 $%&
kf
S S D S E
Ke_^h\Zl_evgh
Â&#x2DC; Â&#x2DC; Â&#x2DC;
Â&#x2DC; Â&#x2DC;
kf
5 U
Â&#x2DC; Â&#x2DC; Â&#x2DC;
DEk 6
6 D E k
Â&#x2DC;
kf kf
Â&#x2039;
>hdZ`bl_ qlh \ ijyfhm]hevghf lj_m]hevgbd_ jZ^b mk \ibkZgghc hdjm`ghklb jZ\_g iheh\bg_ jZaghklb f_`^m kmffhc dZl_lh\ b ]bihl_gmahc Imklv \ û:<K Â&#x2018;K Â&#x192; &% D $& E $% F >hdZ`_f
qlh U
D E k
6 gh 6 D E k
Bf__f U U
DE Â&#x2DC;
D E k
DE D E k
DE D E k
DE D E k
D E k D E k
D E DE k
qlh lj_[h\Zehkv ^hdZaZlv Â&#x2039;
DE lZd qlh
DE D E k
DE
DE D E k
D E k
D E F
DZl_lu ijyfhm]hevgh]h lj_m]hevgbdZ jZ\gu kf b kf GZc^bl_ jZ^bmku hibkZgghc b \ibkZgghc hd jm`ghkl_c Imklv \ û:<K Â&#x2018;K Â&#x192; :K kf <K kf
$& Â&#x2DC; %&
Lh]^Z 6 '$%&
IbnZ]hjZ
Â&#x2DC;
kf >Ze__ ih l_hj_f_
$% $& %& kf :<
kf
Imklv :< k :K E <K Z Lh]^Z 5 U
DEF 6
6 D E k
Hl\_l kf kf
Â&#x2039;
Â&#x2DC; Â&#x2DC;
Â&#x2DC;
kf
kf
>hdZ`bl_ qlh iehsZ^v fgh]hm]hevgbdZ hibkZggh]h hdheh hdjm`ghklb jZ\gZ iheh\bg_ ijhba\_^_gby i_ jbf_ljZ fgh]hm]hevgbdZ gZ jZ^bmk hdjm`ghklb
Imklv $ $ :Q ² fgh]hm]hevgbd hibkZgguc hdheh hd jm`ghklb $ $ $ $ $Q $Q ² klhjhgu fgh]hm]hevgbdZ 2$ 2$ 2$ Q U Kh_^bgbf \_jrbgu fgh]hm]hevgbdZ k p_gljhf hdjm`gh klb Fgh]hm]hevgbd jZa[bl gZ Q lj_m]hevgbdh\ Lh]^Z
6$ $ $ Q
6û$ 2$ 6û$ 2$ 6û$ Q 2$ Q
$ $ Â&#x2DC; U $ $ Â&#x2DC; U $ Q $ Q Â&#x2DC; U U $ $ $ $ $ Q $ Q
U Â&#x2DC; 3$ $ Q
Qlh b lj_[h\Zehkv ^hdZaZlv
Â&#x2039;
Q_j_a k_j_^bgm \ukhlu lj_m]hevgbdZ ijh\_^_gZ i_j i_g^bdmeyjgZy d g_c ijyfZy < dZdhf hlghr_gbb hgZ ^_ebl iehsZ^v lj_m]hevgbdZ" Imklv û:<K <G ² \ukhlZ <H HG
':<K a '0%1 ihwlhfm
Lh]^Z
6û:<K 6û0%+
Ihwlhfm
Hl\_l Â&#x2039;
6'%0+ 6'$%&
<H <G
01 lZd qlh :K 01 $&
$&Â&#x2DC;%+ 01Â&#x2DC;%+
01Â&#x2DC;%2 01Â&#x2DC;%+
6'$%& 6'%0+
01 Â&#x2DC; %+ Â&#x2DC; 01 Â&#x2DC; %+ Â&#x2DC;
IjyfZy i_ji_g^bdmeyjgZy \ukhl_ lj_m]hevgbdZ ^_ ebl _]h iehsZ^v ihiheZf GZc^bl_ jZkklhygb_ hl
wlhc ijyfhc ^h \_jrbgu lj_m]hevgbdZ ba dhlhjhc ijh\_^_gZ \ukhlZ _keb hgZ jZ\gZ : Imklv \ û:<K <G ² \ukhlZ 01 A %+ %+ K 6û%01 6$01&
û:<K a ûF<1 lZd dZd 01 __ $&
LZd dZd 6û%01 6$01& lh 6û%01 6 '$%& 6 '0%1
hldm^Z ihemqZ_f
%(
Hl\_l Â&#x2039;
§ %+ · ¨ ¸ © %( ¹
6 '$%& 6 '0%1
%+ %(
%+
K
6û$%&
K
I_jbf_lju ijZ\bevguo Q m]hevgbdh\ hlghkylky dZd Z E DZd hlghkylky bo iehsZ^b"
Hl\_l D E
6 6
§ 3 ¨¨ © 3
· ¸¸ ¹
§D· ¨ ¸ ©E¹
D E
Â&#x2039;
GZc^bl_ iehsZ^v djm]Z _keb ^ebgZ hdjm`ghklb O
O Â&#x152;5 hldm^Z bf__f 5 6
Hl\_l Â&#x2039;
O S
S5
§ O · S¨ ¸ © S ¹
O Lh]^Z S SÂ&#x2DC;
O
S
O S
GZc^bl_ iehsZ^v djm]h\h]h dhevpZ aZdexq_ggh]h f_`^m ^\mfy hdjm`ghklyfb k h^gbf b l_f `_ p_g ljhf b jZ^bmkZfb kf b kf f b f Z b E Z ! E
6dhevpZ 6dj ± 6dj S5 ± S5 S 5 ± 5
LZd qlh 6dhevpZ Â&#x152; ± S kf 6dhevpZ Â&#x152; ± Â&#x152; ± S kf 6dhevpZ Â&#x152; D ± E kf
Â&#x2039;
<h kdhevdh jZa m\_ebqblky iehsZ^v djm]Z _keb _]h ^bZf_lj m\_ebqblv \ jZaZ \ jZa \ P jZa" ?keb ^bZf_lj m\_ebqblv \ Q jZa lh jZ^bmk m\_ebqblky lh`_ \ Q jZa lh]^Z iehsZ^v m\_ebqblky \ Q jZa Q lZd qlh 6 6
Q
l _ 6 djm]Z m\_ebqblky \ jZaZ
:gZeh]bqgh _keb ^bZf_lj m\_ebqblv \ jZa lh 6 djm]Z m\_ebqblky \ jZa ?keb ^bZf_lj m\_ebqblv \ P jZa lh 6 djm]Z m\_ebqblky \ P jZa Â&#x2039;
GZc^bl_ hlghr_gb_ iehsZ^b djm]Z d iehsZ^b \ib kZggh]h \ g_]h d\Z^jZlZ ijZ\bevgh]h lj_ m]hevgbdZ ijZ\bevgh]h r_klbm]hevgbdZ Imklv $%&' ² d\Z^jZl \ibkZgguc \ djm]
$
Lh]^Z D l_evgh
5 b 6 d\
5
6 dj 6 d\
D
S5
5
5 6dj
Â&#x152;5 ke_^h\Z
S
Imklv $%& ² lj_m]hevgbd \ibkZgguc \ djm] Lh]^Z 5 b 6 '$%&
D Â&#x2DC; D Â&#x2DC; VLQ q
6dj Â&#x152;5 ke_^h\Zl_evgh 6 dj
6 ':<K
S5 5
5 Â&#x2DC; 5 Â&#x2DC; Â&#x2DC;
S5 Â&#x2DC; 5
S
5
Imklv $%&'() ² r_klbm]hevgbd \ibkZgguc \ djm]
Lh]^Z D
5 b 6
ke_^h\Zl_evgh
Â&#x2DC; 6 '$%&
Â&#x2DC;
5Â&#x2DC;5Â&#x2DC; Â&#x2DC;
5 6dj Â&#x152;5
6 dj
S5 Â&#x2DC;
6
Hl\_l Â&#x2039;
Â&#x2DC; 5
S S S
S
GZc^bl_ hlghr_gb_ iehsZ^b djm]Z \ibkZggh]h \ ijZ\bevguc lj_m]hevgbd d iehsZ^b djm]Z hibkZg gh]h hdheh g_]h 6\i djm]Z Â&#x152;U 6hi djm]Z Â&#x152;5
5 lh _klv 5
LZd dZd D LZd qlh 6\i djm]Z
§5· SÂ&#x2DC;¨ ¸ © ¹
6hi djm]Z
Hl\_l Â&#x2039;
D
b U
S5 Ihwlhfm
6\i djm]Z
S5 S5
D
GZc^bl_ hlghr_gb_ iehsZ^b djm]Z hibkZggh]h hdh eh d\Z^jZlZ d iehsZ^b djm]Z \ibkZggh]h \ g_]h
>Ze__ bf__f D §5 · ¸ SÂ&#x2DC;¨ ¨ ¸ © ¹
6hi djm]Z
Hl\_l
5
6RQ djm]Z Â&#x152;5 6\Q djm]Z Â&#x152;U
6\i djm]Z
lh U
6\i djm]Z
5 b U S5 Â&#x2DC;
D lZd qlh U
S5 LZd qlh
S5 S5
S5 Â&#x2DC;
Â&#x2DC; S5
5
b
Â&#x2039;
GZc^bl_ iehsZ^v k_dlhjZ djm]Z jZ^bmkZ 5 _keb kh hl\_lkl\mxsbc wlhfm k_dlhjm p_gljZevguc m]he jZ \_g Â&#x192; Â&#x192; Â&#x192; Â&#x192; Â&#x192; Â&#x192;
6k_dlhjZ
S5
ο
6k_dlhjZ 6k_dlhjZ 6k_dlhjZ 6k_dlhjZ 6k_dlhjZ 6k_dlhjZ Â&#x2039;
5
D lZd qlh ihemqZ_f
S5
ο S5
ο S5
ο S5
ο S5
ο S5
ο
S5
ο ο ο ο
S5
S5
S5
ο ο
S5
S5
>ZgZ hdjm`ghklv jZ^bmkZ 5 GZc^bl_ iehsZ^v k_dlhjZ khhl\_lkl\mxs_]h ^m]_ k ^ebghc jZ\ghc 5 O
S5 Â&#x2DC; D hldm^Z D q 6k_dlhjZ
q Â&#x2DC; 5 SÂ&#x2DC; 5
S5 Â&#x2DC;D q
q S
S5 Â&#x2DC; q q Â&#x2DC; S
5
D
q Â&#x2DC; O lZd qlh SÂ&#x2DC; 5 6k_dlhjZ
Hl\_l Â&#x2039;
5 5O
S5 Â&#x2DC; qO q Â&#x2DC; S5
5O
GZc^bl_ iehsZ^v djm]h\h]h k_]f_glZ k hkgh\Zgb_f D D b \ukhlhc ² Imklv $'% ² djm]h\hc k_]f_gl :< ² hkgh\Zgb_ :< D D &' ² \ukhlZ k_]f_glZ
< û:HK Â&#x2018;K $&
$%
Â&#x192; :H
D Ih l_hj_f_ IbnZ]hjZ
:H HK :K
5 5
§ D· D ·¸ § 5 ¨ ¸ ¨¨ ¸ ¹ © © ¹
5 5D
lh _klv 5D D lZd qlh 5
5 2& 2' &'
D D
D D
D
5
D b
< û:H< :H <H Z :<
gmkh\
D D D
FRV Â&#x2018;$2%
lh _klv Â&#x2018;:H< Â&#x192; b 6 '$2%
>Ze__ S5
D
Â&#x2DC; D Â&#x2DC; D Â&#x2DC; VLQ Â&#x2018;$2%
Â&#x2DC; D 6 '$2% ο §S
Hl\_l D ¨ ¨ ©
SD Â&#x2DC; ο
ο
·¸ ¸¹
D
6k_]f_glZ 6k_dlhjZ ± 6$2%
Â&#x2039;
D Lh]^Z ih l_hj_f_ dhkb
D
§S ·¸ D ¨ ¨ ¸¹ ©
GZc^bl_ iehsZ^v lhc qZklb djm]Z dhlhjZy jZkiheh `_gZ \g_ \ibkZggh]h \ g_]h d\Z^jZlZ ijZ\bev gh]h lj_m]hevgbdZ ijZ\bevgh]h r_klbm]hevgbdZ JZ^bmk djm]Z 5 Imklv $%&' ² d\Z^jZl \ibkZgguc \ djm]
6dj Â&#x152;5 D
5 lh]^Z 6d\ D
5
5
6 6dj ± 6d\ Â&#x152;5 ± 5 5 Â&#x152; ±
Imklv :<K ² lj_m]hevgbd \ibkZgguc \ djm]
6dj Â&#x152;5 D
5 ihwlhfm 6û
Ke_^hZ\l_evgh
5 D Â&#x2DC; D VLQ Â&#x192;
6 6dj ± 6û$%& S5
5
5
§ ·¸ 5 ¨S ¨ ¸¹ ©
Imklv $%&'() ² r_klbm]hevgbd \ibkZgguc \ djm]
6dj Â&#x152;5
6 Â&#x2DC;6û$H% Â&#x2DC; 5 Â&#x2DC; 5 Â&#x2DC; VLQ q 5 Â&#x2DC; 6 S5
5 § ¨ ©
Hl\_l 5 Â&#x152; ± 5 ¨ S
5 LZd qlh
§ ·¸ 5 ¨S ¨ ¸¹ ©
§ ·¸ ·¸ 5 ¨ S ¸ ¨ ¹ ¸¹ ©