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L_ieh\hc [ZeZgk \ha^moZ \ ihf_s_gbb

<ha^mo ihf_s_gby khijbdZkZykv k gZ]j_lufb ih\_joghklyfb gZ]j_\Z_lky beb hoeZ`^Z_lky Djhf_ lh]h hg ihemqZ_l beb hl^Z_l l_ieh \ ijhp_kk_ \ha^mohh[f_gZ < g_[hevrbo ihf_s_gbyo ih^ \ebygb_f dhg\_dlb\guo lhdh\ b \_glbeypbhgguo kljmc \ha^mo ^hklZlhqgh ohjhrh i_j_f_rb\Z_lky \ ke_^kl\bb q_]h _]h W\ ijb jZkq_l_ l_iehh[f_gZ fh`gh kqblZlv ihklhygghc \h \k_f h[t_f_ ihf_s_gby Hkj_^g_ggZy l_fi_jZlmjZ ih\_joghklb lZd`_ ijbgbfZ_lky ihklhygghc MjZ\g_gb_ l_ieh\h]h [ZeZgkZ \ha^moZ \ ihf_s_gbb bf__l \b^

α DL (τ τ \ ) )L ± 4< =

]^_ α .L kj_^g__ agZq_gb_ dhwnnbpb_glZ dhg\_dlb\gh]h l_iehh[f_gZ gZ ih\_joghklb 4\ dhebq_kl\h dhg\_dlb\gh]h l_ieZ dhlhjh_ g_ihkj_^kl\_ggh i_j_^Z_lky \ha^mom ihf_s_gby beb aZ[bjZ_lky hl g_]h

< \_ebqbgm 4\ \oh^bl l_ieh \ghkbfh_ ijblhqghc \_glbeypb_c b \ j_amevlZl_ g_hj]Zgbah\Zggh]h ijh\_ljb\Zgby ihf_s_gby Z lZd`_ dhg\_dlb\gh]h l_iehh[f_gZ \u^_ey_lky beb hl[bjZ_lky l_ieh \ dhg\_dlb\guo dZgZeZo gZ]j_\Zl_evguo ijb[hjh\ b ^jm]h]h l_ieh\h]h h[hjm^h\Zgby

>ey kljmb ijblhqgh]h \ha^moZ g_h[oh^bfh kZfhklhyl_evgu_ mjZ\g_gby l_ieh\h]h [ZeZgkZ < gZijZ\e_gbb ^\b`_gby kljmx jZa[b\Zxl gZ we_f_glZjgu_ h[f_gu \ khhl\_lkl\bb k jZa[b\dhc gZ we_f_glZjgu_ iehsZ^db hfu\Z_fhc ih\_joghklb MjZ\g_gb_ l_ieh\h]h [ZeZgkZ ^ey dZ`^h]h we_f_glZjgh]h h[t_fZ jbk bo ]jZgbpu gZ jbkmgd_ h[hagZq_gu imgdlbjhf fh`gh aZibkZlv \ \b^_

/Q− F ρ WQ− + ∆ /Q F ρ W\ − /Q F ρ Wg + α .Q τ Q − Wg ∆ )Q =

]^_ /Q− /Q h[t_fgu_ jZkoh^u \ha^moZ \ kljm_ f_`^m we_f_glZjgufb h[t_fZfb (Q − )− Q b Q − (Q + )

Jbk L_iehh[f_g gZklbeZxs_cky kljmb Z l_ieh\hc [ZeZgk we_f_glZjgh]h h[t_fZ \ha^moZ \ kljm_ [ l_ieh\hc [ZeZgk \ha^moZ ihf_s_gby

< nhjfme_ kρ h[t_fgZy l_ieh_fdhklv \ha^moZ

WQ− b WQ kj_^g__ agZq_gb_ l_fi_jZlmju \ha^moZ \ ij_^_eZo we_f_glZjguo h[t_fh\ kljmb gZ mqZkldZo Q b Q

∆ /Q h[t_fguc jZkoh^ \ha^moZ dhlhjuc ih^f_rb\Z_lky d kljm_ ba ihf_s_gby k W\ \ ij_^_eZo we_f_glZjgh]h h[t_fZ Q

τ Q kj_^gyy l_fi_jZlmjZ ih\_joghklb \ ij_^_eZo we_f_glZjgh]h h[t_fZ Q

α .Q kj_^gbc dhwnnbpb_gl dhg\_dlb\gh]h l_iehh[f_gZ gZ ih\_joghklb \ ij_^_eZo we_f_glZjgh]h h[t_fZ Q

LZd dZd /Q = /Q−

+ ∆ /Q lh mjZ\g_gb_ i_j_ibr_f \ \b^_

/Q− F ρ

WQ− − Wg + ∆ /Q F ρ W\ − /Q F ρ W\ − WQ + α .Q τ Q − WQ ∆ )Q =

JZkoh^ \ we_f_glZjghf h[t_f_ D kljmb jZ\_g

 

/. = ∆ /Q + /

< h[s_f kemqZ_ dh]^Z l_fi_jZlmjZ moh^ys_]h ba ihf_s_gby \ha^moZ W mo ≠ W\

/. F ρ . W5 ∆ /Q F ρ \ W\ = (/. − / ) F ρ (W. − W\ )+ / F ρ (W. − W mo )

]^_ /. b W. jZkoh^ \ha^moZ b l_fi_jZlmjZ \ dhgp_ ihke_^g_]h we_f_glZjgh]h h[t_fZ D gZ ]jZgbp_ k \ha^mohf ihf_s_gby ]^_ mkeh\gh aZdZgqb\Z_lky kljmy

/ dhebq_kl\h ijblhqgh]h \ha^moZ ih^Z\Z_fh]h \_glbeypb_c

MjZ\g_gb_ l_ieh\h]h [ZeZgkZ \ha^moZ ihf_s_gby \ wlhf kemqZ_ bf__l \b^

α DL (τ L τ \ ) )L + /. F ρ (W. − W\ )+ / F ρ (W. − W mo )± 4< =

=

< kmffm i_j\h]h keZ]Z_fh]h \oh^yl \k_ khklZ\eyxsb_ dhg\_dlb\gh]h l_iehh[f_gZ djhf_ ih\_joghklb hfu\Z_fhc kljm_c <lhjh_ b lj_lv_ keZ]Z_fu_ mqblu\Zxl l_ieh ijblhqghc gZklbeZxs_c kljmb >ey k\h[h^ghc kljmb \ ihf_s_gbb ihemq_gu h[h[s_ggu_ aZ\bkbfhklb k ihfhsvx dhlhjuo fh`gh hij_^_eblv \k_ __ iZjZf_lju g_h[oh^bfu_ ^ey jZkq_lZ h[s_]h l_iehh[f_gZ \ ihf_s_gbb

Ihwlhfm ijb k\h[h^guo kljmyo h[uqgh g_ gm`gh ijb[_]Zlv d jZa[b\d_ gZ we_f_glZjgu_ h[t_fu

IhegZy kbkl_fZ mjZ\g_gbc h[s_]h l_iehh[f_gZ \ ihf_s_gbb

< h[s_f l_iehh[f_g_ \ ihf_s_gbb mqZkl\mxl \k_ _]h ih\_joghklb \ha^mrgu_ kljmb b \ha^mo ihf_s_gby

JZkkfZljb\Zy ihegmx nbabdh fZl_fZlbq_kdmx ihklZgh\dm aZ^Zqb h l_iehh[f_g_ \ ihf_s_gbb ijbgbfZxl \ dZq_kl\_ hkgh\ghc kbkl_fm mjZ\g_gbc khklhysmx ba mjZ\g_gbc l_ieh\h]h [ZeZgkZ ih\_joghklb we_f_glZjguo ih\_joghkl_c b h[t_fh\ gZklbeZxsboky kljmc h[t_fh\ k\h[h^guo kljmc b mjZ\g_gb_ l_ieh\h]h [ZeZgkZ \ha^moZ Ijbf_qZgb_ y __ g_ ijb\h`m ihkdhevdm hgZ hq_gv ]jhfha^dZy b keh`gZ d \hkijbylbx

Kbkl_fZ mjZ\g_gbc ;h]hkeh\kdbc KLN khklhbl ba [hevrh]h qbkeZ mjZ\g_gbc qlh aZljm^gy_l __ j_r_gb_ M^h[gh j_rZlv ihegmx kbkl_fm mjZ\g_gbc l_iehh[f_gZ \ ihf_s_gbb gZ we_dljbq_kdhc ZgZeh]h\hc fh^_eb ;h]hkeh\kdbc KLN ξ Djhf_ lh]h wlh j_r_gb_ fh`_l [ulv mki_rgh ijh\_^_gh k ihfhsvx dhfivxl_jZ

Kbkl_fZ ba ^\mo mjZ\g_gbc h[s_]h l_iehh[f_gZ \ ihf_s_gbb

>ey oZjZdl_jbklbdb h[s_c l_fi_jZlmjghc h[klZgh\db \ ihf_s_gbb h[uqgh ^hklZlhqgh bf_lv kj_^g__ agZq_gb_ l_fi_jZlmju lj_o oZjZdl_jguo ]jmii ih\_joghkl_cgZ]j_\Zxsbo hoeZ`^Zxsbo b g_cljZevguo b \ha^moZ jbk

< wlhf kemqZ_ ^ey \k_o ih\_joghkl_c hlghkysboky d h^ghc dZl_]hjbb fh`gh khklZ\blv h^gh mjZ\g_gb_ l_ieh\h]h [ZeZgkZ

< kbkl_fm mjZ\g_gbc l_iehh[f_gZ \ ihf_s_gbb \hc^ml mjZ\g_gb_ l_ieh\h]h [ZeZgkZ ^ey \k_o h[h]j_\Zxsbo ih\_joghkl_c mjZ\g_gb_ ^ey \k_o hoeZ`^Zxsbo ih\_joghkl_c gZjm`guo HD mjZ\g_gb_ ^ey \k_o ih\_joghkl_c \gmlj_ggbo HD b mjZ\g_gb_ ^ey \ha^moZ

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