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∂F Y
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∂F YV
= 'YV ∆F YV − α NF YV − F Y F V ∂W
∂F V
= ' V ∆F V + α NF YV − F Y F V ∂W
ε = α NF YV − F Y F V H[hagZqbf
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ρ ²iehlghklv^bkehdZpbc\a_jg_
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η = −
=γ
= γλ
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W =
W =
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;
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FY
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µ VE
= µV
I
I
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µ YV
= µ VE
I
I
+ µY
I
= µV
I
+ µY
I
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FE
a
µ VE = ψ V E + β F VE + 7 OQ V E − FV
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F VE
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I
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I
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i_j_jZkij_^_e_gby dhlhjuc ijb g_fZeuo F VE W ^he`_g aZ\bk_lv hl dhgp_gljZpbb
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]jZgbp_khhl\_lkl\_gghIj_^iheZ]ZyjZkl\hjkeZ[uf\]jZgbp_ψ VE << ihemqZ_fkh
hlghr_gb_=_gjb
F VE
I
= γ FV
I
= γλ W gZ]jZgbp_a_jgZbf__f
( M YV + M V ) I
=G
G F VE
GW
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MV
M YV
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I
I
=S
'V
D
(F
V I
'Y
N F YV
D
(
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− FaV I
:
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jZkiZ^Zbh[jZah\Zgbydhfie_dkh\m]jZgbpu FaYV = F YH F V N <mjZ\g_gbb:^eyihlhdZijbf_kbgZ]jZgbpmi_j\ucqe_g²wlhihlhdijbf_kb
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\ZdZgkbx < ; i_j\uc qe_g γ N F YV ² ihlhd dhfie_dkh\ gZ ]jZgbpm dhlhju_ ijb
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]jZgbpmijhbkoh^ylh^gh\j_f_ggh\lhjhcqe_g γ N Fa ²ihlhddhfie_dkh\hl]jZgb
YV
pu JZaghklv wlbo ihlhdh\ \ ; _klv lh qlh ih]ehsZ_lky ]jZgbp_c Dhwnnbpb_gl
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b klj_fe_gb_ \ dZ`^hc lhqd_ dhgp_gljZpbb \ZdZgkbc d jZ\gh\_kghfm agZq_gbx ]^_ W S ²\j_fyih^kljhcdb\ZdZgkbcd__jZ\gh\_kghfmagZq_gbx W ²fhf_gl\j_f_gbdh]^Z
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r_gbyihemq_ggu_aZ\j_fyj_eZdkZpbbGZc^_ghkmq_lhfk\ya_cf_`^m F V b FYV fh
(
)
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wnnbpb_glhf^bnnmabb 'HII dhlhjh_kmq_lhfk\yabf_`^m F V b FYV bf__l\b^
(
)(
'HII = N'V + F YH 'YV N + F YH
)
−
'V 'YV ±dhwnnbpb_glu^bnnmabbk\h[h^ghcijbf_kbbdhfie_dkZkhhl\_lkl\_g
gh >ey fh^bnbpbjh\Zggh]h mjZ\g_gby ijbf_kb F V k fhf_glZ W >> W S l_ ihke_ j_
eZdkZpbb \ujZ\gb\Zgby kdhjhklb jZkiZ^Z b h[jZah\Zgby dhfie_dkh\ gZc^_gu gZ
qZevgu_ b ]jZgbqgu_ mkeh\by Ba \ujZ`_gby ^ey 'HII \b^gh qlh ijb N → 'HII → 'YV l_\kbkl_f_g_ljZkiZ^Zdhfie_dkh\bq_j_ag_dhlhjh_\j_fy\kyk\h[h^gZy
ijbf_kv \ a_jg_ [m^_l k\yaZgZ \ dhfie_dku Ijb N → ∞ 'HII → 'V l_ \j_fy `bagb
dhfie_dkh\ [m^_l klj_fblvky d gmex dhfie_dk h[jZah\Z\rbkv [m^_l kjZam `_ jZkiZ
^ZlvkynZdlbq_kdbboihijhklmg_[m^_lkms_kl\h\ZlvLZdbfh[jZahf\fZkkhi_j_ghk_
dhfie_dku[m^ml^hfbgbjh\Zlvijbmkeh\bb 'HII >> 'V <>@bkke_^h\Zg^bnnmabhggucijhp_kki_j_ghkZijbf_kb\khklZ\_dhfie_dkh\\
]jZgbpua_j_ggZgZb[he__\Z`ghfbgl_j\Ze_\j_f_gb W ≥ W >> W S gZdhlhjhfkh[kl\_g
gh b ijhbkoh^bl ijhp_kk k_]j_]Zpbb \ ]jZgbpm a_jgZ JZkkfhlj_gb_ \_^_lky \ kemqZ_
keZ[h]h jZkl\hjZ \ a_jg_ ijb ijhba\hevghc l_fi_jZlmj_ dh]^Z g_l jZ\gh\_kby f_`^m
]jZgbp_cba_jghf
JZkkfhlj_gZ^bnnmabyijbf_kb^eyiehkdhiZjZee_evgh]ha_jgZoZjZdl_jgh]hjZaf_jZ
/ = O b]jZgbp_cf_`^ma_jgZfbrbjbghc G GZc^_gZw\hexpby\h\j_f_gbijhnbeydhgp_gljZpbbijbf_kb\a_jg_kmq_lhf^bn
nmabb dhfie_dkh\ Ihemq_gh k ^hklZlhqghc lhqghklvx j_r_gb_ keh`gh]h bgl_]jh
^bnn_j_gpbZevgh]h mjZ\g_gby dhlhjh_ ij_^klZ\ey_l kh[hc ijb[eb`_ggh_ Ze]_[jZbq_
kdh_mjZ\g_gb_ijbijhba\hevghc λ (W )^eydhgp_gljZpbbijbf_kb\]jZgbp_dZdnmgd
pbb\j_f_gb\\b^_
G HII
O
(F
E
V
(W ) − F VE ()) = [F ′V − λ (W )] 6 (W )
6 W = ∑ Q = ∞
 ' N W 

 − H[S− HII Q  O 
N Q 



(
)
]^_ G HII = N N + F YH G F VE (W ) F VE ( ) dhgp_gljZpby ijbf_kb \ ]jZgbpZo a_jgZ \
fhf_gl \j_f_gb W b \ gZqZevguc fhf_gl \j_f_gb khhl\_lkl\_ggh F ′V gZqZevgZy
dhgp_gljZpbyijbf_kb\a_jg_ihke_lh]hdZdijhbahreZj_eZdkZpbyih^kljhcdZl_k
(
)
fhf_glZ W >> W S F ′V = N N + F YH F V F V gZqZevgZy dhgp_gljZpby ijbf_kb \ a_jg_
N Q = π (Q + ) Hlf_lbfqlhZe]_[jZbq_kdh_mjZ\g_gb_ihemq_gh\h[s_f\b^_^ey
ijhba\hevghc k\yab dhgp_gljZpbb ijbf_kb m ]jZgbpu b \ ]jZgbp_ a_jgZ l_ ijb]h^gh
dZd\kemqZ_keZ[h]hlZdbdhgp_gljbjh\Zggh]hjZkl\hjZijbf_kb\]jZgbp_
>ey bahl_jfu =_gjb l_ keZ[h]h jZkl\hjZ ijbf_kb \ ]jZgbp_ihemq_gZbaw\h
expby\h\j_f_gbdhgp_gljZpbbijbf_kb\]jZgbp_a_jgZ
[
]η +6 (6W)(W ) F VE (W ) = F VE ( ) + γ F ′V − F VE ( )
(
)
]^_ η wnn_dlb\gZyhlghkbl_evgZy_fdhklv]jZgbpu η = N N + F YH (γ G O )NhjfmeZ
hibku\Z_lk_]j_]Zpbxijbf_kb\]jZgbpm\ex[hcfhf_gl\j_f_gb\jZfdZoba\_kl
guodhwnnbpb_glh\^bnnmabbijbf_kbjZ\gh\_kghcdhgp_gljZpbb\ZdZgkbcgZqZevguo
dhgp_gljZpbcijbf_k_cdhwnnbpb_glh\i_j_jZkij_^_e_gbyf_`^m]jZgbp_cba_jghf
LZd`_jZkkfhlj_gZk_]j_]Zpbyijbf_kb\a_jgZobahljhighcnhjfu\ijb[eb`_gbyo
kn_jbq_kdh]hbpbebg^jbq_kdh]ha_jgZ>@Ihemq_gu\ujZ`_gbyZgZeh]bqgu_
\ dhlhjuo ^ey kemqZy Z kn_jbq_kdh]h a_jgZ \f_klh O klhbl 5 jZ^bmk a_jgZ
N Q = πQ b G \oh^ys__\ G HII ihemrbjbgZ]jZgbpul_rbjbgZrZjh\h]hkehyih]eh
sZxs_]hZlhfuijbf_kb[pbebg^jbq_kdh]ha_jgZ\f_klh O klhbl 5 jZ^bmkpbebg^
jZ N Q wlhgmebnmgdpbb;_kk_eyi_j\h]hihjy^dZ - R (N Q ) = Z G hagZqZ_lihemrb
jbgm]jZgbpul_pbebg^jbq_kdh]hkehyih]ehsZxs_]hZlhfuijbf_kb
< jZ[hlZo > @ ihdZaZgh qlh \ujZ`_gb_ b \ujZ`_gby ihemq_ggu_ \ kemqZ_
kn_jbq_kdhcbpbebg^jbq_kdhcnhjfua_j_g^eydhgp_gljZpbbijbf_kb\]jZgbp_hib
ku\ZxldZdijhp_kkh[_^g_gbya_jgZijbf_kvxb\uoh^Z__gZ]jZgbpmlZdbijbhij_
^_e_gguo mkeh\byo h[jZlguc ijhp_kk i_j_oh^Z ijbf_kb ba ]jZgbpu \ a_jgh Dhgdj_l
gucijhp_kkhij_^_ey_lkyagZq_gb_fdhwnnbpb_glZi_j_jZkij_^_e_gby γ (7 ) bagZq_gby
fb N (7 ) b F YH ijb^Zgghcl_fi_jZlmj_ 7 JZkkfhljbfkbkl_fm\kemqZ_ihklhygghcl_fi_jZlmju 7 Imklv\gZqZevgucfhf_gl
W ]jZgbpZ iheghklvx ebr_gZ ijbf_kb l_ F VE (W = ) = Wlh hagZqZ_l qlh
λ ( ) = F VE ( ) γ (7 ) Dhgp_gljZpbhggu_ ijbf_kb ^ey wlh]h kemqZy ko_fZlbq_kdb bah[jZ
`_gugZjbkAZf_lbfqlhdhgp_gljZpby\a_jg_\[ebabih\_joghklbjZa^_eZbah[jZ
`_gZ g_ij_ju\ghc ld __ jZaju\ghklv mkljZgy_lky aZ hq_gv dhjhldb_ \j_f_gZ
≥ D (β' V ) E
V
V
]jZgbpZ
FV¶
O
W a_jgh
λ [
JbkDbg_lbdZi_j_jZkl\hj_gbyijbf_kb
ko_fZlbq_kdbkbkl_fZkgZqZevgufkhklhy
gb_fFEW FV¶ ≠
< lh`_ \j_fy dh]^Z ]jZgbpZ aZiheg_gZ ^h g_dhlhjh]h gZqZevgh]h agZq_gby F VE ≠ f_gvr_jZ\gh\_kgh]hdhgp_gljZpbhggu_ijhnbeb^ey W = ko_fZlbq_kdbij_^klZ\e_
gugZjbk
E
V
]jZgbpZ
FVE
V
a_jgh W FV¶
λ FVE γ7
[
O
JbkDbg_lbdZi_j_jZkl\hj_gbyijbf_kb
ko_fZlbq_kdbkbkl_fZkgZqZevgufkhklhy
gb_fFEW FE≠F¶≠
< kemqZ_ ihklhygghc l_fi_jZlmju 7 kbkl_fZ k gZqZevgufb agZq_gbyfb F VE ( ) ≠ [m^_lw\hexpbhgbjh\ZlvdjZ\gh\_kghfmkhklhygbxkfjbk
AZf_lbf qlh \u[hj ^ey ^Zevg_cr_]h jZkkfhlj_gby gme_\h]h gZqZevgh]h mkeh\by
F VE ≠ h[mkeh\e_gl_fqlhkh^ghcklhjhgulZdh_mkeh\b_y\ey_lkygZb[he__h[sbfZk
^jm]hciha\hey_lm\b^_lvi_j_oh^kbkl_fubajZ\gh\_kgh]hkhklhygbyijbh^ghcl_f
i_jZlmj_djZ\gh\_kghfmkhklhygbxijb^jm]hcl_fi_jZlmj_
E
V
V
FVE∞ γ7λ∞
a_jgh W
]jZgbpZ
FV¶
O
λ FV [
JbkDbg_lbdZi_j_jZkl\hj_gbyijbf_kb
ko_fZlbq_kdbkbkl_fZw\hexpbhgbjm_l
djZ\gh\_kghfmkhklhygbxkmf_gvr_gghc
dhgp_gljZpb_cFV ∞FV¶ \a_jg_bm\_eb
q_gghc\]jZgbp_ FVE∞ γ7FVE ∞> FVE
?kebbaf_gblvl_fi_jZlmjmk 7 gZ 7 lhjZ\gh\_kb_gZjmrblkyb\aZ\bkbfhklbhl
khhlghr_gbyf_`^m 7 b 7 [m^_lijhbkoh^blvh^bgbaijhp_kkh\
•
_keb 7 > 7 l_ γ (7 ) < γ (7 ) lhhkms_kl\ey_lky^hihegbl_evguci_j_oh^ijbf_kb
\]jZgbpmkfjbk
E
V
]jZgbpZ
G
a_jgh
FVE∞ γ7λ∞
λ7 =
γ7γ7
V
FV =
FVE
γ7 λ∞
=
γ7 γ7
F VE
= λ ∞ γ 7 [
O
JbkDbg_lbdZi_j_jZkl\hj_gbyijbf_kb
ko_fZlbq_kdb\kbkl_f_baf_g_gb_l_f
i_jZlmjuhl7^h7ijbq_fγ7 γ7 •
_keb 7 < 7 l_ γ (7 ) > γ (7 ) lhqZklvijbf_kbihdbg_l]jZgbpmbi_j_jZkl\hjblky
\a_jg_kfjbk
E
V
V
]jZgbpZ
FVE∞ γ7 λ∞
G
λ7 =
γ7 λ ∞
FVE
=
γ7
γ7 O
γ7 >γ7
a_jgh
FV =
F VE
= λ ∞ γ 7 [
JbkDbg_lbdZi_j_jZkl\hj_gbyijbf_kb
ko_fZlbq_kdb\kbkl_f_baf_g_gb_l_f
i_jZlmjuhl7^h7ijbq_fγ7 !γ7 AZf_lbfqlh_keb\jZkkfZljb\Z_fhckbkl_f_dhfie_dkuhlkmlkl\mxll_\j_fy`ba
gb dhfie_dkZ klj_fblky d gmex ijb N → ∞ lh\ujZ`_gb_^eyijhnbeydhgp_gljZpbb
ijbf_kb\a_jg_b\ujZ`_gby^eydhgp_gljZpbbijbf_kb\]jZgbpZoi_j_
oh^yl\khhl\_lkl\mxsb_bf\ujZ`_gbyihemq_ggu_\jZ[hl_>@^ey^bnnmabbk\h[h^
ghcijbf_kbDZdhlf_qZehkvjZg__ 'HII → ' V ijb N → ∞ >_ckl\bl_evghba
ijb N → ∞ kmq_lhf 'HII → ' V F ′V → F V ihemqZ_fdZdb\>@
G E
a
F V (W ) + F VE ( ) = F V − λ (W ) 6 (W ) O

 'W  
 − H[S− N Q   
 O

Q = N Q 
(
a
6 (W ) =
) (
)
∞
∑
Khhlghr_gb_ \ kemqZ_ bahl_jfu =_gjb i_j_oh^bl ijb N → ∞ \ khhl\_lkl
\mxs__\ujZ`_gb_>@
F VE
(W ) = () + (γ
]^_ ηa = γ
F VE
F V
−
F VE
a
6 (W )
() a a η + 6 (W )
)
a
G a
= G γ ²hlghkbl_evgZy_fdhklv]jZgbpu G = G O O
<f_kl_kl_f\>@>@[ueZijhZgZebabjh\ZgZhlghkbl_evghijhklZykblmZpbydh]^Z
bf__lkylhevdhh^bglbiijbf_kbdhgp_gljZpbydhlhjh]h\a_jg_b\]jZgbp_fZeZH^
gZdh_kebdhgp_gljZpbyijbf_kb\]jZgbp_m\_ebqb\Z_lky\ijhp_kk_k_]j_]ZpbbbklZ
gh\blky g_fZehc \ughk ijbf_kb \ ]jZgbpmfh`_laZf_^eblvkyohly[ubaaZmf_gvr_
gbyk\h[h^guof_kl\]jZgbp_Djhf_lZdh]h³ehdZevgh]h´\aZbfh^_ckl\by\dhgp_gljb
jh\ZgghfjZkl\hj_kms_kl\_ggufklZgh\blkyg_ihkj_^kl\_ggh_³g_ehdZevgh_´\aZbfh
^_ckl\b_ khk_^gbo Zlhfh\ ijbf_kb < kemqZ_ dh]^Z h^gh\j_f_ggh k_]j_]bjmxl jZagu_
ijbf_kb lZdh]h jh^Z dhgdmj_gpby aZ f_klh b \aZbfh^_ckl\b_ khk_^gbo Zlhfh\ fh]ml
ijb\_klbdg_fhghlhgghfmbaf_g_gbxdhgp_gljZpbbh^ghcbaijbf_k_c\h\j_f_gb
Bkke_^h\Zgbx k_]j_]Zpbb h^ghc beb h^gh\j_f_ggh g_kdhevdbo lbih\ ijbf_kb \
]jZgbpm ba a_jgZ dhg_qgh]h jZaf_jZ \ kemqZ_ dh]^Z dhgp_gljZpby ijbf_kb \ ]jZgbp_
hdZau\Z_lky g_fZehc ihk\ys_gZ >@ Ijb wlhf ij_^iheZ]Z_lky qlh \ jZkkfZljb\Z_fhc
kbkl_f_dhfie_dkuhlkmlkl\mxlMjZ\g_gb_hibku\Zxs__baf_g_gb_kh\j_f_g_fdhg
p_gljZpbx ijbf_kb \ ]jZgbp_ bf__l \b^±\kemqZ_^bnnmabbdhfie_dkh\±\
kemqZ_^bnnmabbk\h[h^ghcijbf_kbDhgp_gljZpbxijbf_kb\a_jg_[m^_fkqblZlvfZ
ehc F V [ W << Z\]jZgbp_ijhba\hevghc\_ebqbghc ≤ F VE W ≤ Khhl\_lkl
\mxs__mkeh\b_gZ]jZgbp_ij_^klZ\ey_lkh[hcbahl_jfmE_g]fxjZ]^_ γ dhwn
nbpb_gli_j_jZkij_^_e_gbydhlhjucijbg_fZeuo F VE W ^he`_gaZ\bk_lvhldhgp_gljZ
pbb\\b^_>@ γ = H[S
( + ( ′ F VE (W )
A^_kv ( b ( ′ wg_j]_lbq_gkdb_iZjZf_ljuk\yaZg
7
(
)
gu_kjZaghklvxwg_j]bcjZkl\hj_gbyijbf_kb\a_jg_b\]jZgbp_AZ\bkbfhklv γ F VE (W ) hibku\Z_l\aZbfh^_ckl\b_[ebadhjZkiheh`_gguogZkhk_^gbomaeZoZlhfh\ijbf_kb
ijbly`_gb_ ( ′ > bebhllZedb\Zgby ( ′ < >jm]h]hjh^Z\aZbfh^_ckl\b_gZh^ghf
mae_ beb ehdZevgh_ \aZbfh^_ckl\b_ hibku\Z_lky hlebqb_f hl _^bgbpu agZf_gZl_ey \
e_\hcqZklbHghh[mkeh\e_ghdhgdmj_gpb_caZf_klh±g_\hafh`ghklvxihf_klblv
[he__h^gh]hZlhfZijbf_kb\h^ghfmae_<hlebqb_hlehdZevgh]h\aZbfh^_ckl\byZlh
fh\ ijbf_kb \aZbfh^_ckl\b_ hibku\Z_fh_ iZjZf_ljhf ( ′ mkeh\gh gZah\_f g_ehdZev
guf
?keb\l\_j^hfjZkl\hj_bf_xlkyjZaebqgu_Zlhfuijbf_kbdhlhju_fh]mlh^gh\j_
f_gghk_]j_]bjh\Zlv\]jZgbp_a_jgZ\aZbfh^_ckl\myijbwlhf^jm]k^jm]hfkblmZpby
hdZau\Z_lky gZfgh]h keh`g__ Ihkdhevdm mjZ\g_gb_ g_ aZ\bkbl hl \u[hjZ mkeh\by
jZ\gh\_kbygZ]jZgbp_wlbkhhlghr_gby\fgh]hdhfihg_glghfkemqZ_ijbh[j_lZxl
\b^
G E
F V L (W ) − F VE L ( ) = F V L − λ L (W ) 6 L (W ) O
[
] (
F VE L (W )
1
− ∑
N
F VE N
(W )
)
= γ L  F VE 7 λ L (W ) 

]^_ L = 1 hagZqZ_lghf_jijbf_kb 1 boqbkeh
(
)
γ L F VE 7 = H[S
7
1


 ( L + ∑ ( LM F VE M (W ) 

M


Hlf_lbfqlhmjZ\g_gb_kijZ\_^eb\h^eyex[h]h\aZbfh^_ckl\byijbf_kb\]jZ
gbp_<>@jZkkfhlj_gZih^jh[ghh^gh\j_f_ggZyk_]j_]ZpbyjZaguoijbf_k_cgZijbf_
j_ ^\modhfihg_glgh]h jZkl\hjZ  IhdZaZgh qlh _keb γ < γ X
' > ' lh
fh`_l bf_lv f_klh g_fhghlhggh_ baf_g_gb_ dhgp_gljZpbb ijbf_kb \ ]jZgbp_ BlZd
\b^ghqlhih^oh^jZ[hlu>@iha\heyxsbckihfhsvxijhkluoZe]_[jZbq_kdbomjZ\g_
gbchibku\Zlvbaf_g_gb_kh\j_f_g_fdhgp_gljZpbbijbf_kbk_]j_]bjmxs_c\]jZgbpm
baa_jgZdhg_qgh]hjZaf_jZijbf_gbf\kemqZ_dhgp_gljbjh\Zggh]hjZkl\hjZijbf_kb\
]jZgbp_ Mkeh\b_f jZ\gh\_kby gZ ih\_joghklb jZa^_eyxs_c ]jZgbpm b a_jgh \ wlhf
kemqZ_y\ey_lkybahl_jfZE_g]fxjZ
?kebdhgp_gljZpbyijbf_kbg_fZeZg_h[oh^bfmq_l\aZbfh^_ckl\byZlhfh\ijbf_kb
EhdZevgh_ \aZbfh^_ckl\b_ beb dhgdmj_gpby aZ f_klh l_ g_\hafh`ghklv ihf_klblv \
h^ghf f_kl_ [he__ h^gh]h ZlhfZ ijbf_kb y\gh mql_gh \ bahl_jf_ E_g]fxjZ AZ\bkb
fhklv dhwnnbpb_glZ i_j_jZkij_^_e_gby γ hl dhgp_gljZpbb F VE mqblu\Z_l g_ehdZevgh_
\aZbfh^_ckl\b_khk_^gboZlhfh\H[Z\b^Z\aZbfh^_ckl\bykms_kl\_ggh\ebyxlgZijh
p_kkk_]j_]Zpbbijbq_f_kebdhgdmj_gpbyaZf_klhmf_gvrZ_lk_]j_]Zpbxlhg_ehdZev
gh_ \aZbfh^_ckl\b_ fh`_l dZd kihkh[kl\h\Zlv k_]j_]Zpbb \ kemqZ_ ijbly`_gby Zlhfh\
ijbf_kblZdbh]jZgbqb\Zlv__ijbhllZedb\ZgbbZlhfh\
?keb\]jZgbpmk_]j_]bjmxl^\Zbebg_kdhevdh\b^h\ijbf_kbgZjy^mkhkemqZyfb
dh]^Z\]jZgbp_ij_bfms_kl\_ggh\uiZ^Z_lh^gZbaijbf_k_c\hafh`gZkblmZpbydh]^Z
f_^e_gg__ ^bnnmg^bjmxsZy gh emqr_ jZkl\hjyxsZyky \ ]jZgbp_ ijbf_kv gZqg_l kh
\j_f_g_f\ul_kgylvba]jZgbpum`_ihiZ\rmxlm^Z[ukljh^bnnmg^bjmxsmxijbf_kv
Dhgp_gljZpby ihke_^g_c \ dZdhc lh fhf_gl \j_f_gb gZqg_l mf_gvrZlvky < a_jg_ dh
g_qguojZaf_jh\fZdkbfmfdhgp_gljZpbbwlhcijbf_kbZlZd`_hlghkbl_evgu_baf_g_
gbydhgp_gljZpbcijhy\eyxlkyg_klhevyjdhdZd\[_kdhg_qgh[hevrhfa_jg_Wlh_kl_
kl\_gghlZddZdf_gvrZyfhsghklvdhg_qgh]ha_jgZdZdbklhqgbdZijbf_kbh]jZgbqb\Z
_lk_]j_]Zpbx
GZdhg_p hlf_lbf qlh agZy jZkl\hjbfhklv ijbf_kb \ ]jZgbp_ k ihfhsvx kjZamfh`ghkdZaZlvdZdh\Z^he`gZ[ulvfZdkbfZevgZygZqZevgZydhgp_gljZpbyijbf_
kb\a_jg_ F V bebbjZaf_ja_jgZ O qlh[u\]jZgbp_g_\hagbdeb\u^_e_gbygh\hcnZau
k^Zgghcijbf_kvxeb[hijbaZ^Zgguo F V F VE O mdZaZlv\j_fygZqZeZ__\uiZ^_gby
<hh[s_]h\hjykihfhsvxfh`ghgZclbbgl_j\Ze\j_f_gb\l_q_gb_dhlhjh]h
dhgp_gljZpby ijbf_kb \ ]jZgbp_ ^hklb]Z_l hij_^_e_ggh]h agZq_gby ij_\ur_gb_ dhlh
jh]hgZijbf_jg_^himklbfhihmkeh\byfwdkiemZlZpbbfZl_jbZeZIhke_wlh]h\j_f_gb
ijhp_kkk_]j_]Zpbbfh`ghh[jZlblvih\ukb\gZg_dhlhjh_\j_fyl_fi_jZlmjmh[jZapZb
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