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\ZdZgkbb khhl\_l kl\_ggh 7 l_fi_jZlmjZ <qe_g αNF YV ²hibku\Z_ljZkiZ^Zqe_g αF Y F V ²h[jZah\Zgb_dhfie_dkh\ Hlf_lbfqlh^eygZoh`^_gbyklZpbhgZjgh]hihlhdZ\ZdZgkbcgZ^bkehdZpbbg_h[oh^bfh j_rZlvaZ^Zqm^ey\k_]hZgkZf[ey^bkehdZpbcld\[_kdhg_qghf^\mof_jghfijhkljZg kl\_ klZpbhgZjgh_j_r_gb_lZdhcaZ^ZqbdZdba\_klghhlkmlkl\m_lLZdh_kZfhkh]eZkh \Zggh_j_r_gb_^eyZgkZf[eyihemq_gh\>@bijb\h^bld\ujZ`_gbx η'Y ρ F Y − F YH ]^_ dhwnnbpb_gl η ihjy^dZ_^bgbpu>eyijh\_^_gbyhp_ghqguojZkq_lh\fh`ghiheh`blv η = − =γ = γλ H[hkgh\Zgb_gZqZevguob]jZgbqguomkeh\bcih^jh[ghjZkkfZljb\Z_lky\>@GZ qZevgu_mkeh\by\u[bjZ_f^hklZlhqghhq_\b^gufh[jZahf FV W = = F V ( ) = F V F YV FY W = = F YH F VE W = W = = = F VE ( ) : ; ]^_bg^_dk E hagZqZ_lqlh\_ebqbgZhlg_k_gZd__agZq_gbx\gmljb]jZgbpua_jgZ =jZgbqgu_mkeh\by^ey\ZdZgkbcdhfie_dkh\bZlhfh\ijbf_kbbf_xl\b^ Zm]jZgbpua_jgZdhgp_gljZpby\ZdZgkbcih^^_j`b\Z_lkyjZ\gh\_kghc FY = F YH I ]^_ I ²ijhba\hevgZylhqdZmih\_joghklba_jgZ [jZ\_gkl\hobfbq_kdboihl_gpbZeh\ijbf_kb\]jZgbp_b\a_jg_ µ VE = µV I I \m]jZgbpua_jgZbf__f µ YV = µ VE I I + µY I = µV I + µY I Hlkx^Z mqblu\Zy qlh dhgp_gljZpby ijbf_kb \ ]jZgbp_ fh`_l [ulv ^hklZlhqgh [hevrhcihemqZ_fqlhobfbq_kdbcihl_gpbZeijbf_kb\]jZgbp_bf__l\b^>@ FE a µ VE = ψ V E + β F VE + 7 OQ V E − FV <wlhf\ujZ`_gbb\lhjh_keZ]Z_fh_\ijZ\hcqZklbmqblu\Z_l\aZbfh^_ckl\b_ijbf_ kbgZkhk_^gbomaeZolj_lv_keZ]Z_fh_mqblu\Z_lkbevgh_[ebadh^_ckl\b_l_lhlnZdl qlhgZh^ghfmae_fh`_lgZoh^blvkylhevdhh^gZqZklbpZDZdijZ\beh\aZbfh^_ckl\b_ ijbf_kb gZ khk_^gbo maeZo^hklZlhqghfZehihkjZ\g_gbxk\deZ^hfhklZevguokeZ]Z_ fuo\ BabihemqZ_fqlhgZ]jZgbp_\uihegy_lkykhhlghr_gb_E_g]fxjZ>@ F VE − F VE I = γ FV I = γλ W ]^_ λ W ² dhgp_gljZpby ijbf_kb m ]jZgbpu a_jgZ γ = H[S{∆* 7 } ² dhwnnbpb_gl i_j_jZkij_^_e_gby dhlhjuc ijb g_fZeuo F VE W ^he`_g aZ\bk_lv hl dhgp_gljZpbb ∆* = ψ V − ψ VE 7 a^_kv ψ V ψ VE ²ba[ulhqgZywg_j]byjZkl\hj_gbyijbf_kb\a_jg_b\ ]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 A^_kvmql_ghqlh]jZgbpZa_j_gmadZyZdhwnnbpb_gl^bnnmabb\gmljb]jZgbpu^hk lZlhqgh \_ebd b ihwlhfm ^bnnmabhggu_ ijhp_kku [ukljh \ujZ\gb\Zxl dhgp_gljZpbx ijbf_kbke_^h\Zl_evgh F VE \]jZgbp_lhevdhnmgdpby\j_f_gb LZdbf h[jZahf ihemq_gZ ihegZy kbkl_fZ ^bnnmabhgguo mjZ\g_gbc k gZ qZevgufb :; b ]jZgbqgufb mkeh\byfb AZf_lbf qlh _keb ehdZevgh_jZ\gh\_kb_gZ]jZgbp_g_mki_\Z_lmklZgh\blvkyaZ\j_fyfgh]hf_gvr__\j_ f_gbjZkkfZljb\Z_fh]hijhp_kkZlhgZ]jZgbp_\uihegyxlkymkeh\by[he__h[s_]h\b ^ZLh]^Zg_h[oh^bfhgZibkZlv]jZgbqgh_mkeh\b_lj_lv_]hjh^Zdhlhjh_bf__l\b^>@ MV M YV =β I I =S 'V D (F V I 'Y N F YV D ( ) − FaV I : ) − FaYV ; ]^_ FaV ²jZ\gh\_kgZydhgp_gljZpbyijbf_kbdhlhjZyhij_^_ey_lkybamkeh\byjZ\_g kl\Z obfbq_kdbo ihl_gpbZeh\ m ]jZgbpu b \ ]jZgbp_ a_jgZ FaYV ² jZ\gh\_kgZy dhg p_gljZpby^eyjZkiZ^Zdhfie_dkh\m]jZgbpudhlhjZygZoh^blkybamkeh\byjZ\gh\_kby jZkiZ^Zbh[jZah\Zgbydhfie_dkh\m]jZgbpu FaYV = F YH F V N <mjZ\g_gbb:^eyihlhdZijbf_kbgZ]jZgbpmi_j\ucqe_g²wlhihlhdijbf_kb \ ]jZgbpm Z \lhjhc ² wlh ihlhd ba ]jZgbpu Dhwnnbpb_gl ' V′ D = β ' V D ( < β < ) _klvwnn_dlb\gZykdhjhklvi_j_oh^ZZlhfZijbf_kb\]jZgbpma_jgZ<mjZ\g_gbb; ijbgZibkZgbbihlhdZq_j_a]jZgbpm^eydhfie_dkh\mqblu\Z_lkyqlhm]jZgbpu\ZdZg kbybadhfie_dkZi_j_oh^blq_j_a[Zjv_jZihlhfZlhfijbf_kbi_j_oh^bl\m`_]hlh\mx \ZdZgkbx < ; i_j\uc qe_g γ N F YV ² ihlhd dhfie_dkh\ gZ ]jZgbpm dhlhju_ ijb jZkiZ^_ i_j_ghkyl ijbf_kv q_j_a ]jZgbpm l_ jZkiZ^ dhfie_dkh\ b i_j_oh^ ijbf_kb \ ]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 'Y′ D = S 'Y D ²wnn_dlb\gZykdhjhklvi_j_oh^Z\ZdZgkbbq_j_a]jZgbpm < jZkkfZljb\Z_fhc kbkl_f_ kms_kl\m_l b_jZjoby \j_f_g l_ jZkkfZljb\Z_fuc ijh p_kkijhbkoh^bl\^\_klZ^bb>@:bf_gghgZklZ^bbgZfZehffZkrlZ[_bgl_j\Ze_ \j_f_gbijb W S << ∆W << W dh]^Zfh`ghij_g_[j_qvhllhdhflhq_qguo^_n_dlh\bafZeh ]hfZdjhh[t_fZijhbkoh^bl\ujZ\gb\Zgb_ijhp_kkh\h[jZah\ZgbybjZkiZ^Zdhfie_dkh\ b klj_fe_gb_ \ dZ`^hc lhqd_ dhgp_gljZpbb \ZdZgkbc d jZ\gh\_kghfm agZq_gbx ]^_ W S 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dhlhjhc mqblu\Zxlky khhlgh r_gbyihemq_ggu_aZ\j_fyj_eZdkZpbbGZc^_ghkmq_lhfk\ya_cf_`^m F V b FYV fh ( ) ^bnbpbjh\Zggh_ mjZ\g_gb_ ^ey ijbf_kb F V ]^_ ε = α NF YV + F YH F V k wnn_dlb\guf dh 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 ( 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