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"!#%$'&)(+*",.-0/1.$23! 465 ,7 598;:=<>< ?A@7BDCFE G B G BC2HIJBDKLNMPOQBSRUTPV.W"XZY\[+T]KDBSRU^`_N@abBdc7eJBDLbKDBSRU^`[email protected] GNi I.LbB6jM G HkjM G Yl_+KDBdcmOkTPa G anBdc`eJBDLbKdopqYlV.rsBDL+jM G YlKdodt u M]KLNMvIJBdc`wkWxRMPV.TyI`z+YUr{BDL+jT G BSRUTPV.WkC'abHkj|I.zbHQR7pSMP}dB7~XZY\[+T]KdM7EIJBDKc`~abH G Hk~o_F@`_QH G H~`BPpRDS~7 G R7W\_QH3B)RU^7pkV.MPjc IJBdc7wkY G WV7kK G HLn^`_N@ zbHp i I.W\abjMMa'o7jeJBd} i M G ~t\EI`zbHkO G G HabYRdB7~`V`Wa G LNMPVUc jM G HSjM G Yl_NKPOST]a G YtJ)HQRo7}\c`Oc]CnY R7[NM]KJEwHanH G M G BjM]KULNMqV7K7~o6pkjSV`WEI`L+B G BDwHRD G [+YlV.MqY\V`rsBDL+jM G Yl_+KU^7_F@6B G T]pHK6c7L+OkY G V`He.c`~`HpI`LNMP_QBSRTPV.M a'o`a G kjHkj~7HV`Yl_HRD G M~ i KUM]p~ i a+}Hk~`HK G M]KJE`CbMKC'anBdcpI`LNMP_BSRUTPVdojM G HkjM G Y\_+KDB G T]pKUodE I.LbB G B e.c.~`cBPeJMBDKUL+c`@doB G TpkHKqB~.~7k}lBSRUM G t 7DvnUDU`D3.D` `¡k¢;¤£.¥¥"N¦k§U¢¡1+¦P¨77©Dª]§U«ªDd¬ HLbpH®e.c`~`cOW\ab}lBSRUM G IJBOkWlV.M]C2HOW\ab}lHkj°¯MavKUMwS~7Bdc~.MP}l[+WI`z+YlO G cC'Hk~`V`Y\O+K7ct ± Bdc`r²TPjEdwH)RUMP[+W.pTPab}lc.@7Bdcpk~`H)ec`~7BdcpkI`LNMP_QBSRMPV7)B G T]pKUoI`zNYed^RM G t7³DH G Hk´VMV7KDBdj|C'YlV`kjE7M]edoa+Y G BRpSMP} V.Mqa G ML+BDa G t kV`BSRUMP}JC'abHkj G Bdjcµ~`Bda G OkMPabcMq`abY\}lW¤E MKUL+BDj G [email protected]_N@dRUMP}1KUM]wk~.Tq~.c`[nH¶)BdanIJB7~`Y\V.M7Ec`wjTPj anBdc`eJBDLbKcpSManHeBDc t · H¸R7[bHkjY ~7B G M]pQodEMP}H@`}sMR7V`®I`z+YIBDjWlV`KdMPjYZMBDI`LNMRMPjY anH®BDe`LNMP_QHnC G HV.MjBDc M]~`LbHka+c ¹ `©Dº].»`©P¼P§JP.º+¦P¨ TP[ P½]¾ gJ¿ À"ÁmÂÃÄÅ Æ z+YlIJBdjWlV`KdojMPYl}\c]C G H®VMMP~7LbHka+c .ª 7¡©Sªd»]£JP7¥d¬7¨"N¦]¨ Ç È ÉËÊÍÌ°Î Ï.Ð Æ B7OW G MPOHMBDIJHkLNMPOV`W a'o`a G kj®otPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtÒÑ Ï.Ð¤Ï BdVyHSc`jMPV`V`BSRUMM]L+_F@`Y G HkK G c7LNMIJB7OW G MPOQHtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtÒÑ Ï.Ð{Ó Æ MPjQÔ6tDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtÖÕ Ï.Ðs×ÙØ eab}[email protected]L+c`[bHkV`W1tDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtÛÚ Ï.Ð\Ü ±u ?ÞÝ ± YL+Hk_ G u HkjBDLno?A__HkabaFß®tDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtÖà Ï.Ð{áãâbäDØ pMzNWpHkV.WtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtÖå Ï.Ðsæ f>oIUoMP~7LbHkabBSRUTPV.W MYlV`a G L+c7KdOV`WLbHkIJHL G BUT]L1tDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtÖå Ï.вçèØ IJHkLNMPOV`W a'o`a G kjoéRdB7~®tDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt ÇDÇ Ï.Ðsê · I`LFTRUMI.LbB_HkanBDL+ctPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt Ç ¯ Ï.Ðsë pSTC'HkjV`RUo`}Bdc`OHkV`WMa'[email protected]pSMPOV.WI`L+Y\jY G YxRMÞtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt ÇSì Ï.ФÏí · I`LFTRUMIJM]j G YtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt Ç Õ Ï.ФÏÏ · o`a G kjÛabBdc7eJBDL i tDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt Ç à ÓÐ Æ LbBDîDLNMPjBSRMP_WCbM]pQoKUoïtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt Ç å ÓÐ¤Ï )HI`LbB7_QHk~.c7LNTP}\V`WE`I.LbB_Hk~`c7LNTP}\V`WZMBDe`C'HK G BSRd¸I.LbBDîDLNMPjBSRM]_kWCnM]poKdotDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt Ç å ÓÐ{Ó ± M G BSRDMz+Wl~.Wl_WZa G L+c7K G c7LnoqRUo`[b[bW\_N@I`LbBDîDLNMPjBSRUMP_W\_N@CnM]pQoK i MAC2HbC'Yl_F@YljI.}HSjHkV G MP_HtPtDt Ç å ÓÐs×ÙØ LbîUMPV`YlpSMP_QH®IMPj G YÍtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯]ð ×Ð Æ zbHK7}\MP~.MPOHtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯ Ç ×Ð¤Ï · G L+c7K G c7LNMI`zbHK7}\MP~M]OHïtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯ Ç ×Ð{Ó X HQñ`YKUTP}lV.WZMPV.MP}^pSMtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯ Ç ×Ðs× · o`V G M]K G Y\_+KUTMPV.MP}^pSM%tDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯ Ç ×Ð\Ü u H G B7~oa'o`V G M]K G Y\_+KDM]VMP}x^7pQoòtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯D¯ ×Ð{á XZX3Ý Ç ß;MPV.MP}x^7pSMpT]abBDe.V`WlKPBSR^7j°MPc G BdjM G HkjtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯ ì ×Ðsæ XZX3Ý Ç ß;MPV.MP}x^7pSMLbHkKc7LbpSYxR`V`Wlj#abHka G c`IJHkj|tPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯ ì ×Ð²ç · XóÝ Ç ßMPVM]}^pMôtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯ ì ×ÐsêÙõ B G MRDHkV.Wp®_N@doeötDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯Ñ Ü Ð ± M G M]eT]pBSRda'o7a G kj®otDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯D÷ Ü Ð¤Ï óvHS}\MPOV`W ~M G BSR^jB7~7Hk}tDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯D÷ Ü Ð{ÓØ e`C'HK G BSR^jB7~7Hk}`tPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯PÕ Ü Ðs×ÙØ e`C'HK G BSRd®LbHk}\MPOkV`W tDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯PÕ Ü Ð\Ü fLNMPV`a+M]Kd_QH6tDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯PÕ áÐ ^7LbBDKPBSRTMI`L+Hk~`YlKdT G BSRT}BDîdYlKdMtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯På áÐ¤Ï ^LbBDKDBSRUT}lBDîdYKUM®tdtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ¯På áÐ{Ó Æ LbHk~`YlKdT G BSRT}lBPîdYlKdMvtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt ì Ñ áÐs× G MB7I.}\V7Bda G Y>ÝøAù7~7Hk}{߸tPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt ì Ú æÐ ?Ac G BdjM G oMACbM]pQoKUo®tdtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt ì å æФÏãõ T]K}sMP~`V`WIJBDC'joMBDpkVM]OHkV`WtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt ì å æÐ{Ó ?)KD_HI G BDLnoMLbHîdc`}sTLNV`W7CnM]pQo7KdoÖtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDt ì å æÐs×Ùõ TPanBDe.V.WKDBSRDMPc G BdjM G o|tDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑ Ç æÐ\Ü f1c7L+Y\V7îDBSRUoa G LbBDC2HútPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒѯ æÐ{á øALNMPjM G YlKdoÞtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑ ì ¯ æÐsæÙû @7BdjabKPS@7B@`YHkLNM]L+_N@`YlH"tdtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑDÑ æвçãü pSTRdLbBSRdR`}\MPa G V`BDa G Y1tDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑ÷ æÐsê )HLbBDpk@7B7~`Vc G Hk}\V7®I`LbBDe.}lkj®o G HBDL+YlH;CbMpoK i tPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑUÕ Jç Ð ?A}lîPBDLNY G j®oMAC2HnCnYl_N@ ab}lBDwkY G Bda G tDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑÚ çJÐ¤Ï · }lBDwkY G Bda G MP}lîDBDL+Y G j i tDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑÚ çJÐ{Ó f[email protected]`YKUoV.TR7L+@UcHkr{HK G YR7V`W\_N@6MP}îDBDL+Y G j i tDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑÚ çJÐs× f;z+Wl~.Wl_WMP}îDBDL+Y G joýR`V`Y G z+V.W G z+Wl~7SV`WtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑUà çJÐ\Ü f;z+Wl~.Wl_WMP}îDBDL+Y G joýR`V7nC'[+W G z+Wl~`kV`WtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÒÑUå çJÐ{á o7@`}lHk~.TRTPV`W3tDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷]ð çJÐsæÿþ óvBDpk~`k} MIMPVUc]C ytDtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷]ð çJÐ²ç ± o7VM]jYl_NKP®I.LbBDîPLFM]jBSRUTPV.WtPtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷ Ç çJÐsêÙõ T]K}sMP~`V`WîDLNMPrsBSRdM]}lîDBDL+Y G jo tDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷ Ç çJÐsë · G LbBdjBSRd®~.M G BSRd®a G L+c7K G c`LnoÒtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷ Ç çJÐ¤Ï í YeJBdVM]_k_Yl@`B@M]}\~otDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷ ì çJФÏÏ Æ 7I.}\V7Bda G tPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷Ñ ê Ð XYlV7HT]L+V`WI`LbBDîDLNMPjBSRTPV`WDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷PÕ êÐ¤Ï Æ L+YlV._YI ~.c.MP}lY G otDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷PÕ êÐ{Ó ML+KdMPanBRDB}lHkjjMtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷DÚ êÐs× ¿ }sMPabY\_+Kd^~7BDI`LNMR`V`WI`L+BPe}kjtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷Pà êÐ\Ü · Y\jI.}lHQñBSRdjH G B7~o}lY\V7HST]L+V.Wl@7BI`LbBDîDLNMPjBSRTPV`WZtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÛ÷Pà ë Ð Æ BDpkVT]jKdodE.~`BDI.} `KdoMBDI`LFMRUoKYlV`r{BDL+jM G Yl_QHtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕd¯ ëÐ¤Ï ¿ ~ i ab}lHk~7K7cRD G oBKPBdjIM]K G V7Bda G YI`LbBR^LbBDKDBSRdBDc}lBDîdYK7cmÝ G CQt7B7~`a G MRDHk_®OW\ab}B÷t àdßµtDtPtDtÖÕd¯ ëÐ{Ó ¿ ~`H.V`Y\_Y I`LNMR`~`YxRdBda G Y>Ý G CFt`B7~`a G MRdHk_¸OkWla+}Bq÷t ì7Ç ßtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕd¯ ëÐs× ¿ a+c7e.a G Y G c7BSRM G Hk}lV`BDa G Y®tDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕd¯ ëÐ\Ü ¿ Mñ`YBdj i jÖI`L+Hk~`YlKdT G BSRd®}lBDîdYKUoÝ G CFt`B7~`a G MRdHk_¸OkWlab}lBq÷t ì Õdß®tDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕd¯ ëÐ{á ¿ I.z+WK7}\MP~`cI.zbHQRdB~.cVMI`LbHkV`HQñ7V.W G RUM]LÝ G CFt`B7~`a G MRDHk_®OW\ab}B÷t ÑUàdß tDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕd¯ ëÐsæ ¿ BdjIJM]K G V7Bda G I`LbBI.LbHk~`YlKdT G BSRdBdc}BDîdYK7cytDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕd¯ ëÐ²ç ¿ V`Hk~7H G HLNjYlV.Yla G Y\_+KDkjcpSTPanBDe.V.WKDBSRDSjc MPc G BdjM G cÝ G CFt`B~.a G MRDHS_¸OW\ab}lBÕ7t Ç ÚPßAtDtDtDtDtDtPtDtÖÕ ì ëÐsê u MPa G HkL G @`HBDLbHkj tDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕ ì ëÐs ë YlV.~M â V.anHL G ce.Y\V.T]L+V`W\_N@RUo`@`}lHk~.TRMP_Wl_F@ a G LbBdj i Ý G CFt`B7~`a G MkRDHk_®OWla+}B÷t ÑUàdß tPtDtDtDtDtDtPtDtÖÕ ì ëФÏí ¿ H®K}sM]a+Yl_NKPSjc~7BDI.LNMR7V`W\jcI`L+BPe}kjcÝ G CFt`KUM]I.Y G Bd}sMà7t ì ßmtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕ ì ëФÏÏ ¿ }sMPabY\_+Kd^~7BDI`LNMR`V`WI`L+BPe}kjÛIJB~`L+c`@79tPtDtDtDtPtDtDtDtDtDtDtPtDtDtDtPtDtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕ ì ëФÏ7Ó ¿ .}BDpHX Æ RLbBSR`V`Y\_QBSRDSj G RM]L+cÝ G CFt`B7~`a G MkRDHk_®OWla+}Bqà7t Ç ÕdßmtDtDtDtDtPtDtDtDtDtPtDtDtDtDtPtDtDtDtDtDtPtDtÖÕ ì ì NËy ?)[email protected] G HK G c`LnoqIJB7OW G MPO i t7?)L+_F@`Y G HkK G c7LnoMr²c`V7KdOV`W7C2Hk~.V7B G KdoqI`L+B_HkanBDL i E G oIUoY\V`a G L+c`KD_W¤E.MP~7L+HkanBSRTPV`W¤t a G c7I.V`W MRU^7a G c7I.V.WpSM]z+WlpHkV.WEZKDBdjc.V`YKUMP_QHaI`LbB7_QHkabBPL+HkjE I`zbHkL+c`[nHSV`WE ±u ?t · G L+c7K G c`LNMBDIJHkLNMPOV`W\_N@mano7a G Sj i jB V7Bd}\Y G Yl_NKPdE.jYKLbBDCnTP~7LbB.ER7YlL G c.TP}lV`W a G LbBDC2HDt · I`LNTkRUMI`LbB7_QHka i MR`}\T]KDHkVE`I.}\TPV`BSRUTPV`W¤t u HpkYlI`LbB7_QHkabBSRUTKDBDjc`V`YlKUM]_HDE KULNY G Yl_NKP3abHKD_HDERUo7}lBdc`OQHSV`WEa'[email protected]pSMPOV.WDI`L+Y\jY G YRUM7EkK7}\MPabY\_+KD3a'[email protected]pSMPOV.WDI`LbBDe.}lkjodt · I.LNTRM;I`LbBda G zbHk~`K i E pSM]e.}lBDKPBSRTPV`W"MjBDwkV7Bda G YC'Hk@7Bz+Hk[nHkV.WE û B jMPV7BSRoµIJB7~`jWlV`KdodE eMPV7KDz i RmMP}lîDBPLNY G jc.at Ø LbîUMPV`YlpSMP_QHIJMPj G YE I`z+Y\~7k}lBSRM]_kWda G LFM G HkîDYlHDt YlL G c.TP}\V`WDIMPjÔkESa G LNTPV`KPBSRTPV`WUMvanHkîDjHkV G MP_QHdt â jI}HkjHkV G MP_QH3a G LNTPV7KDBSRTPV`WESa G LNTPV7KPBSRMP_W G M]e.c`}lKdodEBd[nH G z+HkV`W.RU^7IMP~7K i E`MP}îDBDL+Y G joR^7jkVDoqa G LNTPV7HKE7MPanB7_YsM G YR7V.WIMPjQÔSt · Bdc7eJBDLbBSRda'o7a G kj®oUEMP~`LbHka+T]zbHDE anI.LNTRUMRDBd}\V7k@7BI`LbBda G BDL+c E.MP}BDKUMPOV`WZjH G B7~odt.?)}lîDBDL+Y G joqI.z+Wla G c`I.cV.M~`Y\anKt ! 4 *3&#" 5%$ -0/"&)&y*%&"/0/>,('*)A$= 5 3 $ 7, /,+®*-/./- 5 :! : 7o [email protected]]pkWpÍKDBdV`_QHkI_QHÍRpkV.YK7}R ü · ?R }H G HS_N@ Ç å]ÑDð10 Ç å]Ñ÷E1C2HbC'Wwm@.}\MR`V`W G R i L+_QHC2H³PBd@`VúRdBdV )Hkc.jMPV`Vt V`Y G zNV`Wa G L+c`K G c7L+cIJB7OW G MPOQH G RDBDzNW.IMPjQÔSEDR7a G c7I EdRU^7a G c7IM¸I`LbB7_QHSanBDLkt · G L+c7K7c7LNM®IJB7OW G MPOQHAanHAV7HkjkV`Wa G oIJHSj `}lBd@Dodt1³PH¸C2HS~`V7B G V.TIMPjQÔI`LbB G HQñ G I`LbBDîDLNMPjcY>~.M G M7tZóvBDpk~`W\}>jHpSY I.LbBDîPLFM]jHkj M~.M G oC2H~T]VC2HSVC'HnC'Y\_N@ YlV G HLbI`L+H G M]_kWt Æ MPjQÔ1C2HIJBdab}Bdc`I.V7Bda G a G HnC'V`)RDHS}KU^7_N@qIMPjQÔ+BSRU^`_N@qjW\a G t Æ BOkW G MPO"C2HAz+WlpHkV G BDKDHkjÞYlV`a G L+c7Kd_W` G oanH®I`LbBSRTP~7nC'W¤E`K7~owVMV7~7BPCn~7H¸zFM]~M7t KUM]wk~7kjÛBDKdMPjwkYK7cI`LbBDe.W\@.TAC'HkVC'Hk~`VMOY\V`V7Bda G t à ?BADCÁmÄ.Ã1%à <E8;F (Ä GIHIJLKNM1APOQM1C%G7F Ï.ФÏ.Ð 2 *Ä 3547698/:;8=<(>8=<@ TPab}lHk~7BSRMP}BpMRDHk~`HkV`WMPano7V`_F@7LbBdV`V.Wl_N@ ä BDIJHkLNMP_WEOY\}lYJanHc`jBDwkV.Yl}lBabBdc`OkMPabV`k@7BI`LbBSRTP~7kV`W ä BPIH LNMP_kWDa7CnYlV`BDcOYlV.V7Bda G WDI`LbB7_QHkabBPLNct ~ i ab}lHk~7K7c G Bd@7BveUo7}sM;pSMRDHS~7HkV.MvjBDwkV7Bda G I.zbHL+c`[bHkV`WPI.LbBDîDLNMPjct pkV.YK}o I.LnR7V`WBDIJHLNMPOV.Wano7a G Sj®o Ý Ç åd÷PÕdßNt Æ BDwSMP~MRKUoÍc7wSYxRM G HS} i abY RUo`VUc G Y\}xoÍLbBDpS[bWz+HkV`W"MR7pkV`YlKµV`BSRU^`_N@[email protected] V.Ylabj i t RD G [+WIMPjQÔ;ýRpkV.YKqR7YL G cTP}lV`W IMPj G Y Lno7_N@.}HnCn[bWIJMPjQÔ;ýRpkV.YKRoLbBSR`V.TRMP_Wl_F@IJMPj G W Lno7_N@.}HnCn[bWI`LbB7_QHkabBDLno Ro7[+[bWr{LbHKdRdHkV._QHMpSMRdHk~7HkV.WI.LbBdc`~7BSRdk@7BpI.LNMP_QBSRT]V.WÝ G pQR(t R K R AE3SKLà K%à T ß KdM]wk~TOkTPa G I`L+B_QHSanBDL+cpI.LNMP_QBSRTRUTC'Y\V7Bdcr²T]pkYL i pSVD^[email protected] G L+c7Kd_W RU^URdBDCMLN_N@`Y G HK G c7Lno ó â · û ݤóyHk~`c`_Hk~ â V`a G L+c._ G YBdV · H G û BdjIc G HLF߸ RD G [+YlV7Bdc abHIJBdc`wkWxRMCnW1C2HkV RDHk}\jY7C2Hk~.V7B7~`c`_F@7YlV.a G L+c7Kd_QHDEMLbHSMP}\YpSMP_H®a+}BDwkY G ^7_F@Y\V`a G L+c`KD_kWJRI`LbB7_QHSanBDL+ca+V`YwSc]C2H®Lno7_F@`}lBDa G I`LbBSRT ~7kV`W G k_N@C'Hk~`V7B7~`c._N@d^7_N@ EDI`LbB7_QHSanBDL G HS~oe.c.~7HvpQR`}\TP~M G C2HSVjMP}lvjV7BDwka G R`W]C2Hk~.V7B7~`c`_F@D^7_F@YlV`a G L+c7Kd_W Ï.Ð{ÓÐ Ï.Ðs×Ð] Ä Jà 1ÁÄÃ1Ã%<E8/F ÄYG1HZJLKNM7AEO=MIC[G7F pSMPa G M]LNMP}\T V.MRL+@`BSRUTPVMACnM]KDBanHkKdRdHkV`OV.W V7HB7~7IJBSR`Wl~.TIJB G zbHeTPj ·P\ é~.M G BSRd®a G L+c7K G c`LnodE7RDBd}sT]V.WI`LbB7_QHk~.c7L . . . ?APUL<*VWM EM1OQFX8=< @?AEC ]ÃÄEMIK^8ZÃL63Ä(G1HZJLKNM1APO=MIC%G7F IJBOkW G MPOzNWpHkVd^ G BDKPHSj ~.M G DB IJHkLNMP_QHqanHqI`LbBRDHk~`HDECnM]K7jY\}HC'abBdcmpkVTPj®oR7[nHS_N@`VdoC2HbC'W"BDIJHLFM]V.~odE ~.M G MIc G c]C'WRDHrsBDL+j®IM]KPH G+i E`IJ7B OW G MPO®jTR7W\_QH®I`LbB7_QHkanBDL i RDBdVú)Hkc.jMPV`V i RöIJB7OW G MPOC2H · â · ± Ý · YlV`îD}lH â V`a G L+c`_ G YBdV · Y\V7îd}lH ± M G MdßFEMP} G HkL+V.M G YxRomC'anBdc · â u6± E u â u6± 3NM1APG Ï.ФÏ.ФÏ.Ð _ KÃ1%à <*VWM`8=<JÃ@?AEC1ÁÄÃ1Ã%<E8JÄ R </aP6NMÄ(abA u TIJHQR`V7~.MPVd^LbHIJHL G BUT]Lya G L+BPC2BRU^7_F@Y\V`a G L+c7Kd_W KÃ%VWM1GIC%O*aUÃL6cVd<=C%ef<*G Ð ¿ M]wk~Ta G LbBDC2BSRTYlV.a G L+c7Kd_QH®BDea+M @UcPC2H < R APGÄYaUÃL6hgUÃÄYO c`L+Oc]C'HBDIJHLNMP_Y¤EIJBOH G C'HnC'W\_N@ÍIM]LNMPjH G L i . . . M < R APGÄÃ%U%<D8=<=CiaPj(VWM c.jW\a G kV`W C2HS~`V7B G }lYRU^`_N@BDIJHLNMPV`~ i t Æ LbBSRdka G YlV.a G L+c7Kd_YpkVMPjHkV.TDk Ç ß VM]OkWla G YlV`a G L+c7Kd_Yp¸IJMPj G Y ~7BI`LbB7_QHSanBDL+cmÝ l A M1HZJ ß ¯Dß°pnCnYla G Y G E`B¸CnM]KDBdcY\V`a G L+c`KD_kY7C'~7HÝ ULAPHb<;U%A ß ì ß°I.z+YI`LFMR7Y G pk~7LbBDC2BSRd®BDIJHLNMPV`~o Ñß°I.LbBSRDSa G BDIJHLNMP_Y>Ý APn;APHPC;M1A ß ÷Dß c.}BDwkY G _W\}BSRd®BDIJHLNMPV.~o Ñ Å Æ û Ý Æ LbBDîDLNMPj û DB c.V G HLFß BDe.aNMP@Uc]C'HMP~7L+HkabcI.z+Wl[ G W Y\V`a G LNc7KD_H â óòÝ â V`a G LNc`_ G YBdVóyHîdYla G HLF.ß .... . BDea+MP@UcPC2H®I`LNTRd¸I.LbBSRUTP~`kV7BdcYlV`a G L+c7Kd_Y · Æ Ý · G MP_+K Æ BdYlV G HkLFß c`KdM]pSM G Hk} VMRLN_N@7Bd}pSTPabBPeV`WK7c u ?AóòÝ u HkjBDLno?A~`~7. Lb.HS.abayóvHîdY\a G HLFß . . . MP~7LbHkaNM~`BBDIJHLNMPOV`WIJM]j G Y urs óÒÝ u HkjBDLno s Dc JHLyóyHîdYla G HLFß . . . ~M G MO G HSV.T ä pSM]I.YlabBSRM]VTp ä ~7BIJMPj G Y Æ z+Y>I`L+BSRDHk~`HkV`W3a G LbBDC2BSRdqM]Kd_QHqanHIJBda G c`I.V7I`LbBSRTP~7nCnW"~.Wl}\OW3M]Kd_QH t Á K5O/G1<;< R APGYÄ HbA Ð Æ zbHk~7IYlaB G BdjE.CnM]KP jYlKULbBBDIJHLNMP_HMRCnM]KDkjIJBDzNMP~`W"anHjM]C'W>I`LbBSRT]~` G I`z+Y>I`LbBSRdHk~7HSV`W"a G LbBDC2BSRdY\V`a G L+c`KD_QHdEanHV.M]pQ^RUT ÁtK5O/G1<Yu R G1<*T*GÄÁ Ð Ï.Ð\Ü Ðo 1à <YM7p1AEe %qrG1AET=K5VWM1G7F Ï.Ð{áÐv C Ã%O*aUÃL6Áw</UC%3^F LbHîdYla G Lno RDHS}ljYLbo7_N@.}\TIJMPjQÔ)jMP}l¸KUM]IMP_Y G omÝ~`HkabW G KdoeJß BDIJHLNMP_QH®pST]I.Y\abcE.O G HkV.WE.V`K~7oYlV`KULbHkjHkV G E.~7HkKULbHkjHkV G E`KDBdjI.}lHkjHSV G E7RUo7Vc`}lBSRUTPV`W¤E}lBPî.t`IJBda+c`V R7[[email protected]BDIJHLFM]_H;C'abBdcBSR`}\TP~.TPVdoz+Wl~.Wl_W\jY a+YîdV.TP}o KPBdje.YlVM]OkV`WBDeURDB7~o I`LbBSRTP~7nCnWvI.z+WljBDc G LNMPV`a+rsBDL+jMP_Y;R7a G c7I.V`W\_N@ú~.M G V.MÍRU^`a G c7IV`W; LbHSMP}lYlpkc]CnW)c7L+OY G Bdc }lBDîdYl_NKPBdc r{c`V`KD_kYEV.M]I`zkt.anHSOW G TPV`W OkWlanHS} V7HBDe.aNMP@Uc]CnWIMPjQÔ r{c`V`KD_HLbHSMP}\YpBSRMPV.T)KDBdje.Y\V.MPOV.Wlj9BDedRdB7~7Hkj V`Hkjc.abWUeU^ G IJHQR`V.Tvè}pkH1C'YURDBd}\Y G ~.MP}\[bW\j%R7a G c`IJHkj IMPj G Y av}\YeJBRDBd}\VD^7jÖR^eJkLbHkj z+WpkHkV`WIJBdjB7_W abYlîdV.TP} i ó ± E \ ó%MLbHîdYla G LNcó g ? ± x aneJL+V.Yl_QH ab}lBdc7wkWKqI`LbBDIJBDC2HkV.WC'Hk~`V7B G }\YxR^7_N@ jB7~`c.} i IJBOkW G MPOQH BDedRoK}lHV7KDBd}lYlKR`a G c7I i MR^7a G c`I i RqKUM]wk~7SjÖBDKUMPjwkYlKcabjWeU^ G B G HQRz+HkVV`HnCR^7[bHvC2Hk~7HSVqR`a G c7I ~7L+c`@doaneJkL+V`Yl_ y R`V`Y G z+V.WZI`LbBDIJBPCnc]C2HLbHîdYla G LnoÍMKDBdjeYlV.MPOkV`W1BDeURDB7~odEBDeURUoK7}x^µpkI i anBDeLbHSMP}lYlpSMP_QHC'HIJB jB7_W z Á CL3NM1K R 35APn;<*GIC ýKDBdje.Y\V.MPOV.WJBDeURDB7~E7K G HLn^RoeWLNTAC2Hk~`HkVqpkH¸a'R^7_N@qR`a G c7I i M G HSV I`LbBDIJBdc.[ G WVMRU^`a G c7I y ano7a G kjBSRD6 I`L+BPIBPC'cPC2HÍI`LbB7_QHkabBDLkE3BDIJHLktIMPjQÔ M ä C2Hk~.V7B G KdodEvV7K7~o anH~7k}\WV.M MP~7LbHSanBSRdBdcE.~.M G BSRDBdc Mz+Wl~.Wl_W ä e`LNTPVdo }pkH;C'H®[email protected]]IM G CnM]KDBLbHîdY\a G Lnoc`jBD7w Uc]CnWl_WIJBdc7pkH®O G HSV`W V7HeJBIJBdc7pH®pST]I.Y\a Ï.ÐsæÐ{ YÄ UK5a pSM]C'Y\['ÔNc]C'HvI`LbBSRTP~7kV.W.jYlKULbBDI`L+BPîDLNMPj i dt ³PHvKDBdV7KLb G V`W`LbHSMP}\YpSMP_W G pQRtdanHKURDHSV`OV`W\@7Ba G LbBPC'HDt u i wHyed^ G pMP~7LNT G BSRTPVݤ@.M]L+E~ |)YlLbHk~J}ß k Lno7_N@.}x^ IJHQR7V`®c`L+OQHkV.Tr{c`V`KD_QH V7HkjBDwkV`Bda G }\MP~7SV`W ab}BDwSY G V`HeJBLbHSMP}\YpBSRTPVanBdr G |vM]LbBSRD G pQRt t Á K5O/G1< R G1<=T*GÄ.Áw<E8/:XpÄYUK5a`Å C2Hk~`V`B G VTa G L+c7K G c7LNM jBDwkV7Bda G abVMP~`V7®pkjSVDor{c`V7Kd_QH ÷ Æ M]KC2H®zNMP~`YlO þ IJB7OW G MPORjMP}Sjt~ u YlKULbBBDIJHLNMP_QH¸RLNTPj_Y jYlKULbBdY\V`a G L+c`KD_W }lpH¸RUo]CnTP~7z+Y G k pSM]ZK 7~7BSRMPV7éjc`a+WHQñ7Y\a G BSRM G ~7HKDB7~7LkE`K G HkLn^V.MpST]K7}\MP~7®K ~.cjYKLbBBPIHLNMP_QHRoîDHkV7HkL+c]C2H®z+W\~`W\_W abYîdVTP}xodE`KDBdV`a G MPV G o G W\jÛabH®jYlV`Y\jMP}\YpkcPC2H[bWz+KdMY\V`a G LNc7KD_H LbBDpHI.aNMPV7 ~7BC'Hk~`V7.B .G .}\YxRU^`_N@ z+W\~`W\_Wl_F@ abYlîdV.TP} i EKDBdV`a G MPV G . . . 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u ݤó)MPV`~`BDjqßéV7HpT]}lHwkWZV.MIJBda+}Hk~7oIJBdc wkY G kjÛIMPjÔbBSRdkjÛjWla G DE.jW\a G Bc7L+OkWljHMP~7LbHkabBdc a)IJBda G c7IVD^`j#RU^7eJLbHSj ݤanHkKdRdHkV`OV.Wsß; · ? u Ý · 7H Uc7HSV G Y\MP}{ßMP~7LbHkaNMRU^7eJL+cC2HYljI}lY\_Y G V`~.TPV.M c7KdM]pM G Hk}lHkjÛI`zbHkabBdcRUM]C'W\_W\jÛabH®V.ManBdc`anHS~`V`WIMPjQÔ+BSRDjW\a G B a®MPanB7_YsM G YR7V.Wlj R^eJkLbHkj Ý=MPanB7_YsM G YxR`V`Wsßv û ? u Ý û BdV G HkV G ßvIMPjQÔ+BSRdjWla G BC2Hc`L+OQHkV7BanRU^`j BPea+MP@7HSjE7LbHM]}\YpMP_QH k LbHîdY\a G LvK}\WlOQHÝC'Hk@7BBDea+MP@abHRo7@`}lHk~.TRTdß LbHîdY\a G LyjMPanKUoÍݲRdH¸K G HLbOkTPa G Y ab}BRUMabHRUo`@`}lHk~.TRTdß I`z+WlpkV.M]Kab@`B~7oÍݤV.MPa G MRDHkV G MPjE`K~7H~7Bd[+}BKDH®a+@7B7~7ß BPIHLNMP_QHMPabB_kY\M G YxR`V`W\_N@IMPj G WSk _QBdjIJML+H IJBDLbBSR`V.TPV`W3R`[nHk_F@ôIMPjQÔ+BSR^7_N@ jWla G aLbHkîdYla G LbHSj K}\WlOQH ~`}lHjMPanKUoôMÍV.MPa G MRdHkV`W I`z+WlpkV.M]K i |yL+Y G HAýpST]IYla;BDe.aNMP@UcLbHîdY\a G L+c~7BR`[nHk_F@IMPjÔbBSR^7_F@jWla G avV.MPa G MRdHkVD^`jÖI`z+WlpkV.M]KDHkjÛab@`B~7o anHk}lHk_ G .L+a G ýRUo`VUc`}lBSRT]V.WR7[[email protected] G MRdHkVD^`_N@I.z+WpkVM]K i ab@`B~7oqKLbBdj;C'Hk~`V`BD@`B LbHSMP~ V.MPO G HkV`WyBDe.aNMP@Uc R7[nHS_N@öIMPjQÔ+BSRU^`_N@öjWla G ~`BmRoeMRdBSRM]_kWl@7B L+HîdYla G L+c9Ý G MPjãR7pkV`YlKUT anBdc`OH G C2Hk~.V7B G }lYRU^`_N@e.Y GNi ß I`z+WlpkV.M]KanBdjH ä V7BdV7HAéc`~TRUT7E`pk~MAC2HV.MPa G MRdHkV MP}HkabIJbB C'Hk~7HkVI.z+WpkVM]Kqa+@7B7~o R7[nHS_N@`VMIJBDLbBSR7VTRUTPV.W"I`LbBDeJ[email protected] Ø Ý Ç ß MPanB7_YsM G YR7V.W>IJMPjQÔanHqIJBdc7wkWRUT I`LbB RoLbBSR`V.TRM]_kW IMPj G Y MM]~`LbHka+T]zbHa G LNTPV7HK Ï.ФÏ7ÓcÐ (Ä HZJ%A8/F[G1<E8Z%à jb8(Ä HP6 R ÄÁb Z ³DHKDBDjI`LbBdjY\anHkj jHkpkY"Lno7_F@`}Bda G W3M _HkV7Bdct û MP_N@`HC'HqjMP}\TLno7_F@`}\T IMPjQÔc.jWla G kV.T jHpSY>I.LbB_HkanBDLM @.}\MR`V`WvIJM]jQÔSE C'anBdc R V`WvI`LNTkRD IJBdc7wSWxRM]V` e.}lBDKdo @.}\MR`V`WvIJMPj G Y p6V`Y\_N@ö~7BDKUT]wH6c`abIJBDKPBDC'Y G Ú]1ð 0åd÷ IJBDwSMP~MRK i t AY Ä 3SK5gdYÄ HbA.Å;Æ MPjQÔOk}HkV`kV.MÍV.M6e}BDKUo IÑ 0 ì ¯ eUo GNi E~M G MÍanHV`HnC2I.LnRDH@.}Hk~MCnW3RdHqRoLbBSR`V.TRMP_WIJMPj G YE HG I.LnRDH®K~7ow G MPjÛV7HnCnanBdcÝ G pQRt 8/: R YÄ U%AEOe35<*O;C ßFE`@.}Hk~MC'WZanHR@`}sMR7V.WtAMPOkW G TanH_QHk}^e.}lBDKJt _kMP_N@7HvC2H û ? 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BdjY\_Y G o G LNMPV`aNMKd_QHanH G RT]z+W7CnM]KPB®C2Hk~7HSV_Hk}HkKJEjc`a+Wec`´I`LbBDeJ[email protected] G _QHk}sTV`HeJBR i eJHk_®V7HE _QBdV.abY\a G HkV`_Qo G LNMPV`aNM]KD_H G LNMPV`abr{BDL+jcPC2H®~.M G M]eT]pkYp;C'Hk~`V7Bd@`BKDBDV`pkYla G HkV G V`W\@7Ba G MR`c~`B¸C'YlV`[email protected] Y\V`~7HkIJHkV`~7HSV`_QHA G LNMPV`a+M]Kd_QHC'abBdcV7HpTR7Y\ab}lDE G CFt`~`W\}lOWHSrsHK G o G LFM]V.a+M]Kd_QH¸V7HnCnanBdcR`Yl~`Y G Hk}\V7;C'Y\VD^`j G LNMPV`aNM]K _W\jE ~.c7LNM]e.Y\}lY G o Hkr{HK G oq.anIJk[+V7¸c7KDBdV`OQHkV`ݲIJB G R7LbpHkV7]ß G LNMPV`aNMKd_QHC'anBdc G LnRUMP}lH¸c`}BDwkHkVDoq~`B~.M G M]eT]pHÝ G G B R`}\MPa G V`Bda G Y G M]KD®abH¸z+WlKdTIJHL+a+Yla G HSV`_QHßFt Ü ÐsæÐ <*g 8[GIJ V7HIJ%AEULCL35AY C'H¸KDBdV7KUL+ G V`WIJBDzNMP~`WBDIJHLNMP_kWt Ü Ð²çJÐ qEGIK5<E8/:XG1<*g 8;GZJ C'H G M]KDBSRU^LbBDpRL+@E.K~7H¸R~.MPVd^BDKdMPjwkYKqeJkwkW7C2HSVC2Hk~`Y\V.T G LNMPV`a+M]Kd_QHDt.f CQt.jHpSYI.LnR7V.WZMIJBda+}Hk~.V`WBDIJHLNMP_W V`nCnM]KD G LFM]V.a+M]Kd_QH®abH®V7HI.LbBSRdHk~7H®wSTP~`V.TBDIJHLNMP_QHvCnM]KPkKPBd}\Y7C'Y\V7 G LNMPV`a+M]Kd_QHDt Ü ÐsêÐ éV R <=p1j(U1DÄ M7AD3[à <=VWM · L+YBSRdLbBDpQR7L+@DopSMP_N@`BSRUTRMCnW BDIJHLNMP_QHKdM]wk~` G LNMPV`aNM]KD_H®IJBd@7LbBdjMP~`Dt Æ LbBpkW\anKUT]V.W KPBDLbHkK G V`W\@7BR^7a+}Hk~`Kc R`[+M]Kj i wHkjH)IJBdc7wSW G YLbBDpQR7L+@Uc EUK~`H"CnanBdcBDIJHLNMP_QHVMRpST]C2HkjÒI`LbBDK7}\TP~.TPVdo6Ý=MvC'H G BV7HnCnanI.W\["R^7@7B7~`V`nC'[+WsßFt Æ z+YlLbBDpHkVd^7jÖIJBDwSMP~.MR7KPHkjÛVMKPBDLbHkK G V7Bda G C2HDE.M]eUoqHkrsHkK G IM]LNMP}Hk}\V`W\@7BpI`LFMP_QBSRUTPV.W G LFM]V.a+M]Kd_Wedo`} G ^7wDE]CnM]KDB eUoedo7}o G LNMPV`aNM]KD_QH®I`LbBSRdHk~7HSVDoqRV7bCnM]KPSjÛabL+YlBSRDSjÖLbBDpQR7L+@Uc t Á F[OYÄ HP6 R G1<(M1<*O*<=3^F Ü ÐsëÐ égdÄ o G RT]zbHkV`WULbBDpQRL+@ i M G HSa G BSRUTPV.WkC2HnC'Y\_N@c`anIBPzFT]~M G HS}lV7Bda G YdV7HSV`WdI`LbB)I.LNMñ7YdpkzbHnC'j G HkVV7HnCR`@7B7~`V7bC'[bWUpI i abBDe I.LNTP_QHDt _;MPabBSRD VTL+BPKUo G M]KPBSRdk@`BmI`z+Wla G c7I.c edoôpz+HnC'jI.zbHka+MP@`BSRUMP}oôLbBDpkc.jV7Bdc jWlL+ct ü KUT]wHkjH ~T]}lHDE wHC'HjBDwkV`KDBdV`a G L+c`BSRUM GG LNMPV`aNM]KD_QHIJB7~`}HC'Y\a G ^`_N@ I.LNMR7Y\~7Hk} G M]KEwHpSMc7L+OY G ^7_F@ I`zbHk~7IBPK7}\MP~ i e.c`~7H KUM]wk~^AC'HnC'Y\_N@LbBDpQR7L+@c`abIJBDzNTP~.M G Hk}lVd^dt · Bdc.a G MRD G M]KPBSR^[email protected]R7Y\~7Hk}`abH;BDeJHk_V`;z+WlKdTI`LbB G BDKPBd}¤tP)HnC'pkV.TPjnC'[bW I.LbB G BDKDBd}xoC'abBdcúpSMP}BDwHSVDo V.M ~o`V.MPjY\_+KDkj pSMPj®o7KdTPV`W¸MB7~7HkjoKUTPV`WABDe`C2HK G+i Rú~.M G M]eT]pkY¤t õ MPj®o7KdTPV`W ÝBDIJHLNMP_HX Ø®û ¿ ß C2H®M]Kd_QHDE7K G HLbBdcRUoURdBd}\T G LNMPV`aNM]KD_HV.MBPe`C'HK G c E`MeUoq@7BB7_N@`LNTPV`Y\}\MI`zbHk~qI`z+W\a G c7IJHkjÞB7~ Bda G M G V`W\_N@ G LNMPV`a+M]Kd_Wt Á <E8Ä.%à jzM1GÄ.%à VkYÄ O*HbA Ü Ð¤Ïí Ð 2 <*eLp1A l <=G] Æ zbHS~I`z+W\a G c7IHkjÖKqBDe`C2HK G cI.LbBSRUTP~.Wc`pSMPjK7VUc G WBDe`C2HkK G cX ظû ¿ ݲBDe`C'HK G ß yHkI`LbBSRTP~`W X Ø®û ¿ ÝßV.MBDe`C2HK G E`K G HLn^c7wc7pSMPjK}\M yHkI`LbBSRTPV`W ü )X ظû ¿ Ý=ßV.MBDe`C'HK G E`K G HkLn^V7HpSMPjK}\M Æ zbHS~KDBdV`_QHkjÛI`LbBSRdHk~7H ü AX Ø®û ¿ ÝßV.MR7[[email protected]BDe`C2HkK G odE.K G HLb®pSMPjK}sM Ü Ð¤ÏÏÐ d APT*j*3Là 6cG1<*g 8;GIJ yHkpSMPj®o7KdTc`w®c7pSMPjOQHkVd^qBDe`C'HK G X pH®I`L+Yla G c7IJBSRM G IJBdc7pHV.Mc7pM]jOQHkVd^BPe`C'HK G ¯DÚ » XH Á F[OYÄ HP6 R G1<YM7<*O=<=3 Ü Ð¤Ï7ÓÐ2 8=<=C l j(gb<D8/:@C[gdÄ ± RdBdc`r²T]pBRUT G LNMPV`a+M]Kd_QHqRmI`LbR7V`WrT]pkYc7pSMPjoKUTR`[nHDE _QBC2HqIJB G zbHeJM7E M6B~ I`LnR`V`Wl@`BµB7~7HkjKVUc G WAݤ~7LNc`@.T rTpkHß anH G LNMPV`a+M]Kd_W7pSMPjOQHkV7vBDe`C2HK G oIJBdc`pHvB7~`j®o7KdM]C'W¤E G CQtDV7HkV.W]C'YlwvIJBdc`wkY G B¸wTP~`V7vBDIJHkLNMP_QHyX ظû ¿ tDfHk~o G LNMPV`aNM]KD_H®jc.abW jW G R`[nHk_F@`VDoBDe7C'HK G oc`pSMPjOQHSV7¸I`z+Hk~ G W\jE.V7wV7nCbM]Kd^BDe`C2HK G B7~7HkjKV7Hdt Ü Ð¤Ï× Ð éV R <*p1jYU1EÄ M1AE3%à <*VWMßU%8=<=C l jYgb<E8=qEJ%< R GI<(M7<=O*<=3SC ³DHka G }\YwH;R`[nHk_F@`VDo G LNMPV`a+M]Kd_QH;R~.MPV7yjV`BPwSYlV7 G LNMPV.a+M]KD_kW]C'anBdc~7BDe.zbHvr{BDL+jBSRMPV7)M~RdBDc.r²T]pBSRdDEDIM]KKUM]wk~^ C'HnC'Y\_N@}lHîUTP}lV`W LbBDpQRL+@C2Hc`anIBPzFT]~M G HS}lVd^dtZݤAM~7LNc`@7Bdca G LNMPVUc G MP~oa G TP}HvC2Hk[ G @7LbBDpkW ~7HMP~`}B7_+Ktxß Ä ×M1Kw Á APVWMÄ.Á R VZ Ü Ð¤ÏUÜZcÐ _ (Ä Vd<E8QjùG](Ä gP6NM1O@ ³DHk~`V.TanHBC'Y\V7BdcmjH G B7~`cI`LbBpMC'Y\[ G kV.W>c`anIJBDzNTP~M G HS}lV7Bda G Y¤t ¿ HKUM]wk~7kjcBDe`C2HK G cC'abBdcÍI.z+YzNM]pkHkV.M~RD LNM]pSW G KdDM kZOkMPa®IJBdab}lHk~`V.Wl@7B6O G HkV`Wyݤf · ó߸MOkMPa¸IJBdab}lHk~`V.Wl@7B pST]I.Y\abcöݤf b· \ ßFt ¿ M]wk~T G LNMPV`a+M]Kd_QHf ~`Bda G MPV7H VMa'RdkjÖpM]OST G K7c@`B~.V7B G cf · ݤf)ßFE`K G HLNTAC'H®c.V`YKUT G V`WZMLbBda G HÝVM]I`zkt`IJBDzNMP~7BSRd®OW\ab}lB G LNMPV`aNM]KD_QH]ßNt fZLNMPV.a+M]Kd_QH®f RdBd}\TBDIJHLNMP_Y \ ó â f g Ýh®ß C2Hka G }lYlwH T SR Ý X ß > T S Ý T ß , pkL+c`[ G LNMPV.a+M]Kd_YZf%MI.LbBSRdHk´ ó Ø XZX s ? û ¿ ݤf)߸ÝV`nCnM]KUT G LNMPV`aNMKd_QH a;LFMpSW G KDHkjÞRd G [bW\jÛV7Hkw®f · Ýf)ßCnYwOQH G }sMh9I`zbHk~ G WljE`V`Hw®f|jk}lB[NMPV`_YI`L+BSRDka G pST]I.Y\aNß C2Hka G }lYlwH T SW Ý X ß > T S Ý T ß , pL+c.[BDIJHLNMP_Y \ ó â f g Ýh¸ßMIJBDKLNMPOc]CݤV7bCnM]KdT G LNMPV`aNM]KD_HaLNM pkW G KDHkjÖRD G [+Wlj#V7Hwf · ݤf)ßC'Ylw®pSM]I.YlabBSRUMP}sMhE þ V.TP}[ pST]IYlavedoeUo7}I`zbHkI.a+TPVJß C'Y\V.M]K \ ó â f g Ýh®ßFE`f P· \ Ýh®}ß k¦f · ݤf)ß fZLNMPV.a+M]Kd_QH®f RdBd}\TBDIJHLNMP_Y ó g ? ± Ýh¸ß C2Hka G }lYlwH T SW Ý X ß > T S Ý T ß , pL+c`[ G LNMPV.a+M]Kd_YJf MI`L+BSRDHk´ó Ø XZX s ? û ¿ Ýf)ß)ݤV7nCnM]KUT G LNMPV`aNMKd_QH a;LFMpSW G KDHkjÞRd G [bW\jÛV7Hkw®f · Ýf)ßCnYw®pSM]I.Y\anBSRMP}\Mh9I.zbHk~ G WljE`V7Hkw®fïjk}B[NMPV`_Y OW\a G ß C'Y\V.M]Kó g ? ± Ýh¸ßFE.f · óݲh®ß k¦9jMñ ݤf · ݤf)ßFE f · óÝh®ßbß Ü Ð¤Ï7áÐË C%G][à j*3¥ 35<*T/ û @ G k}lY edo`_N@7BdjE M]edoµY1I.z+YRU^7IMP~7KcV.M]IT]C2HkV.W1edo`}\MqpSMP_N@`BSRUTPVMKDBdV7pkY\a G HkV._QH~.M G M]eT]pHDt Æ BDIWl[bcqC'Hk~7HSVµp jBDwkVD^`_N@pI i abBDe i þ G RDBDLbeMwSc7L+V.TP}\cavB7~`}lBPwkHkVD^`jYLbHSMP}\YpSMP_HkjYpkjkV*Ek s k@7HSjïI`L+BSRUTP~7SV`W G LNMPV.a+M]KD_H"fC'anBdc¸R7[[email protected]®BPIHLNMP_QH \ ó â f g B7~`}lBDwHkVdo®~7B)BDKdMPjwSYK7cESV7Hkw3anH G LNMPV.a+M]Kd_QH ~`BDa G MPV7H~7Ba G MR7c G kabV7®I.zbHk~BDIJHkLNMP_W ûvØ u6u â fòÝ Æ û ßNt [nHk_F@`VDopkjSVDoC'anBdcpM]I.YlabBSRUTPVdo~`BwSc7L+V.TP}\cE C'Hk@7BDwÍpST]pkVM]joúBDe.aNMP@Uc]CnW G LbBDC'Y\_QH < T, jm no atributu, nov T hodnota > . M IJB7OkT G K7c I`LbBSRTP~7kV`W G LNMPV`aNM]KD_Hf anH¸~`Bwkc`L+V.TP}\cqpSM]I.Wl[bH < T, ST ART >, RdH¸a G MR7c Æ û < T, COM M IT > . fHI.LnRDHIB G Bdj ~`[email protected]]pkW K pST]I.Y\abcÍpkjSVÍ~7B~M G M]eJTpkHDt ± BDC'~`H }lY Kµ_N@Do7eJRÍOkMPanHI`zbHk~Í~7BdaNM]wHkV`W\j Æ û Ea G MPOW YlV.rsBDL+jMP_Y Rmwkc7L+VTP}lcYlîdV7BDLbBSRM G MabI.c`a G Y G ó g · f1?Aó f°Ý G CFt1jBDwSV7Bda G R7pkV`YlKc V`BSRD G LNMPV.a+M]Kd_QHßFt I`z+WlIMP~7_N@doedoUE K7~o OkMPaA_N@doeUoC2HpSMIJB7OkT G KDHkj°a G MR7c Æ û EdC'abBDc pST]pkVMPj®owkc`L+V.TP}lc K~.YlabIJBDpkYl_kYZI`LbBqI`LbBSRdHk~7HSV`WZBDIJHkLNMP_QH ó g ± Ø Ý¤f)ßNE`K G HLNTRo7c7wkY C2H®pST]pSV.MPj i jHpkY < T, ST ART > M < T, COM M IT > . ¯Pà Ìß ÍÏÎ A¸ V®ÐQ n A¸ÑQnm]ÐF ³dM]pQo7KJErsBDL+jc.}HDEUabkjMPV G YlKUME G MPc G Bd}lBDîDYlHDtUóyBDpk@7B7~`Vc G Hk}\V7Bda G EUanI}lV`Y G Hk}lV`Bda G EdI.LNMR7~`YRdBDa G EU~7BDKUM]pSM G Hk}lV`BDa G t G oB KDBDjIM]K G V`BDa G YM7I.}\V7Bda G Y1RU^7LbBDKPBRDMqI`LbHk~.YKUT G BRD}BDîdYlKdodt )BDL+jT]}\V`W G RM]Lno R^LbBDKDBSRU^`_N@r{BPLNjc`}\WEI`LbHSV7HQñ`V`W G RUM]LnorsBDL+jc`}\WI`LbHk~.YKUT G BSRd}BDîdYlKdodt Å: ! : 4 y,7*">[* &" ¸8* v3$2>/ áФÏ.Ðv <*G]Áj*3ÃL6cVF[VWM7q7Á 8/:;GI<*O*<E8=qz35<=T=K5OQF ³dM]pQoK ?vñ`YBdjo Ø ~RdBDpBSRM]_kWI`LFMR7Y\~`}\M áÐ{ÓÐg Ä(g F;O ³UMpoKRU^7LbBDKDBSRD}lBDîDYlKdoBPea+MP@UcPC2H RU^L+BPKDBSRd®I`LbBdjSV`V7DE anIJBDC2KdoÓ ÒE E E ↔ E ¬ E IJBdjB7_V7®ano7j∨eJBd}x→ oÝ'EJßFgE ÔxE<Õ . . . Á CL35A áÐs×Ð :;G1<=O*<E8=j l <=G]z 7^ LbBDKPBSRTrsBDLNjc`}lH;C2H Ç ß KdM]wk~TRU^7LbBDKPBSRTI.LbBdjkV`VT7E ¯DßãÝ A Ò B ß , Ý A ∨ B ß , Ý A → B ß , Ý A ↔ B ß , ¬A, IJBDKc`~CnanBdc ì ßrsBDL+jc.}H¸RpkV`YlK}sTKPBdV`HkOVD^`jÛIJB7O G HkjÛc7wkY G W Ç M¯t áÐ\Ü Ðo A, B rsBDL+jc`}HdE ]Á ]Á <;U l <=G zCL35A o <;U l <=G zCL53 A C2H¸IJB7~7z+H G pHk_ݤYV`HQR7}sMPa G V`W{ß3zbH G kpk_QHDE`K G HLn^C'H®aNTPj ¼.Wt áÐ{áÐo GÄb8;UK^8=<=VWMÃL6c<QJ[<;U [à <;HbALà 6 U ÏZ`§d k ^ ð Ç anHVMp^URT ¤7¢= Z`ÖW¬Y¬=ÎO Û˨ ¢ ¤d¢h¤WÕ®Z®7¯I ¨7©$RÖ Z õ BPe.LNM]pHkV`W v R GÄP8;UK^8=<*VWM]L C2HS~`prom. V7BDpkVM]Ok→ V7{LbBD,pk[+W}z+Y G V.M v G wDt à 6<=J%<;U1%à </HbA7Là 6 Ð ¿ vM]wk~`I`LNMR7~.YxRdBda G V`WBd@7B7~`V7B7_QHkV.vW v v}lpHrok. k ð Ç M v f le → { , } Ç ß Ý ß Ý ß3I`LbBI`LbBdjkV`V7Bdc P E ¯Dß vv Ý P¬A8ß v ð P↔ v Ý A ß Ç E Ý ß Ý ß Ç E ì ß Ý Ò ß Ç Ñß vv Ý AA ∨ BB ß ð ↔↔ vv Ý AA ß vv Ý BB ß ð7E ÷Dß Ý ß ð ↔ v Ý Aß Ç Ò v Ý B ß ð`E Bß Õdß vv Ý AA → Ý ß v Ý B ßFt ↔B ↔v A áÐsæÐ 7q ÁÄÃ*MIK5OÄù8/:[G1<*O*<E8Qqz35<*T=K5O/F C2H MS*Ä C/M1<=35<=T=K5A EPC2Hka G }lYlwH v Ý Aß Ç I`LbBKUM]wk~7 v. }lH A C2H R V 3L à KNM1AE3%à j E]C2Hka G }lYwkH®HQñ7Y\a G c]C'H G wdt Ý ß Ç f MKDBSRT V.M]pQ^RUTPjH Áw</ULAE35A7ÁØ×A ?t }lH M ¼.W T C2H V R 3Là KNM7AD3%à j E C2HSa G }lYlwH v Hñ7Yla G vc]C2AH v G wD.t v Ý A ß v Ç I`LbB }lYle t A ∈ T. f M]KDBSRD v C2H u V7BDAwkY\V. Á </ULAD35AÁ T t æ WKUTPjHdEwù H ¼`H C2H MS*Ä C;M7<=35<=T=K5HIOQ:Á U[V735AEULAPO jV`BPwSYlVdo T M I.W\[nHkjH T | A E1C'Hka G }\YwHI`LbB }lYleJBSRDBd}\VD^jB7~7Hk} Av jV7BDwSYlVDo T I}\M G W v Ý A8ß Ç t áвçJÐ u ±  M Ä <wO*<Á R ÄYO=MÃ%<=VWM1K V7BDwkYlVM¼.W T C'H®abI.}\V`Y G Hk}\V.T7E.I`LNTRd¸K7~ow®KUM]wk~.TKDBdV7HkOkV.T i KdM]p k MdÛ ß Ú → Ük Æ }sM G W G L+YR7YsTP}lV`Dt ¯På TÙ ⊆ T C2H®abI.}lV.Y G Hk}\V.T7t eßÛÚ ← Ük â V`~`c7Kd_QHV7HeJBfvYl_F@7BdV7BSRdBSRUM6RD G M6BÍabBdc`OY\VUc KDBdjIM]K G V`Wl_F@ I`LbBda G BPL i U ¬Ym¡é¬Q¢W¦ÚN«Z¨¤WÚS¡Ú^Û˨ Ü¢`©¦ ¢5¤W`Ö /I£¨bª}¤WÚS¡Úm®7È©1¢W¬YÚZb± áÐsêÐ2 %V735APULAEO I`LFTRD®K~o7w®HQñ7Y\a G c]C'H®KPBdV7HSOV.T TÙ ⊆ T E`wkH TÙ | A t áÐsëÐ] n[K5<ÁFi×M7pZKcVdHZJ%qÁmEÄ M=Ä ³danBdc }\Y A E B E C ¼.HDE`IM]KKUM]wk~.Tp®VTPab}lHk~`c]CnWl_W\_N@B¼.W7C2HMñ7YlBDjt Ý? Ç ß A → Ý B → Aß Ý?¸¯DßÍÝ Ý ßbß ÝbÝ ß Ý ßbß Ý? ì ßÍÝ A¬B→→B¬A→ß C→ Ý A→→ AB ß→ B → A → C T | A Á </UC%V R <JÃ%AÃ%V áФÏí Ð ´ÝU%8=<*gb<E8Ä(HP6 R GÄb8%K5U35<ÝÜ w õ ¼W A M A → B B~7RDB7´ B. fB G BpkVM]OkWljH o A, A → B . B áФÏÏÐ2 AbLà K5HbAU[OJ(Ä gPC C2H¸KDBdV7HkOVTIJBda+}Bdc7I.V`Bda G ¼.W C'H e.c`´Mñ`YBdj 2 %OÄYg ¼`H G wDt C2H MI`LbBKUM]wk~7 V`HeJBB7~RdBDpAHkV.Tqpݼ.W A E A , j, k < i I`LNMAR`Yl¶ ~., }.Hk.j . , Au nB~.c`aAIJnBdV7HSV`Aat g ñ`Yla G cPC2H }\YV7ib≤CnM]Kdn^Í~ i AKdiM]pݼ`H A EJRdH XIWl[bHkjH ` A Mz+WKUTPjj HdE7wkkH A >ArUL<*OÄYgdÄEM1AE3Ã%j ݲRDH X1ßV7HeJB A >A8JÂbMSÄ d)t áФÏ7ÓÐ 2 [OJ(Ä gBg R p1AEU R <=O;3²(Ä UC )Hk_F@DÔ C2HjV7BDwkYlVÍM ¼.W1M ¼`Hdt æ WlKdTPjHdE.wH C'H Ug%OYÄ gbAÁ g R p1A R <=O;3²ÄYULC ݲRdH X ßNE .,A C'Hka G }\YwH TA C2H A MI`LbBKdM]wkA~` i ≤ n C2H A e.c`´ AMS¶ ñ`, .YBd.jÛ V7HneBI`LnRdHK T V7HkeJABC'HB7~RdBDpHkVMI.LNMR7TY\~`}lHkj u Æ p ¼.W A E An , j, k < i t g ñ7Y\a G c]C'H }\Y ~ i KdM]p iA p T, I.Wl[bHkjH T ` A Mz+WlKdTPjHdE7wkH A >ArUL<*OYÄ gdEÄ M1AE3%à jg T t Þ j k Ä <wULAEULC%O=HPK áФÏ× Ð b MS )Hk_F@DÔ T C2HjV7BDwkY\V.M ¼.WZM A E B CnanBdé c ¼`HDt Æ B G Bdj I.LNTRD®K7~ow T ∪ {A} ` B. T `A→B à j.w Á OÄÅ T ∪ {A} ` B pkV.MPOW\jH¸pkKULNTP_QHSV7 T, A ` B t o <*gU% áФÏUÜZgÐ AEU1%à </UC%HZJ%qB8J MWF Ý{R Ç ß ` A → A Ý{R¯Dß ` ¬A → Ý A → B ß Ý{R ì ß ` ¬¬A → A Ý{R7Ñß ` A → ¬¬A Ý{R÷Dß ` Ý A → B ß → Ý ¬B → ¬Aß Ý{R.Õdß ` A → Ý ¬B → ¬ Ý A → B ßbß Ý{RÚDß ` Ý ¬A → A ß → A ± i KdM]p k Ý{R Ç ß k HpkjkjHMñ7YlBdjݤ? Ç ßFE7K~`H A C'H A M B C2H A → A ÝnÝ ß ß `A→ A→A →A . ± TP}lHMñ`YBdj Ý?¸¯DßFE7K7~7H A C2H A E B C2H A → A M C C2H A Ô ÝnÝ ß ß Õ ÔÝ Ý ßbß Ý ß Õ ` A→ A→A →A → A→ A→A → A→A . Æ Bdc7wSY G WljÛI`LFMR7Y\~`}\M u Æ ~7Bda G M]V`HkjH Ý Ý ßbß Ý ß ` A→ A→A → A→A . ìð ± TP}lH®c7RUM]wkcPC'jHMñ7YlBdjݤ? Ç ßFE7K~`H A C'H A M B C2H Ý A M~M]}\[bW\jÖIBDc`wkY G W\j u Æ ~`Bda G TRUTPjH `A→ A→A ß ` A → A. ݲR¯Pßk Ý Ý ß ß ` ¬A → ¬B → ¬A ¬A ` ¬B → ¬A ` ¬B → ¬A → A → B ¬A ` A → B ` ¬A → A → B Ý Ý ß Ý ß Ý¤? Ç ß ²Ý RD G MB~7Hk~`c`KD_kYsß Ý¤? ì ß Ý u Æ V.MI`zbHS_N@7BDpkW ~7RDß Ý²Rd G MB~7Hk~.c7KD_kYsß ß áФÏ7áÐ d AÁÁÄ< Ã[ADC;M7G1j*3Ã%6 l <*G]ÁùCL3SK )Hk_F@DÔ T C2HjV7BDwkY\V.M¼.W¤E A E B V7HS_N@dÔ>C'abBDcé¼`HDt³DH }\Y T, A ` B M T, ¬A ` B E`IJB G Bdj T ` B t áФÏæ Ð ´ÝgUÃÄ(abA7Là 6 )Hk_F@DÔ v C'H¸I`LFMR7~`YRDBda G V`WBd@7B7~`V7B7_QHSV`WZM A ¼`HDt Ø pkV.MPOjH Av ¼Y G MKDBSRdBdcE`wH C2H }\Y v Ý A ß Ç , A v C2H C2H }\Y v Ý A ß ð . A ¬A Æ BDpBDLbBSRTPV`mW k Av C2H®I`LNMR`~`YRUTI`z+Y v t áФÏ`çÐ d AÁÁÄ )Hk_F@DÔvR`[nHk_F@`VDoqR^LbBDKDBSRd®I`LbBdjkV.V7Ë ¼`H A CnanBdcjHpkY p ¶ , . . . , p t.)Hk_F@DÔ v C2H®I`LNMR`~`YRDBda G V.WBd@7B7~`V7B7_QHkV.Wt n Æ B G Bdj pv¶ , . . . , pvn ` Av . ± i KdM]p k â V`~`c7Kd_W IJB7~`}Hab}lBDwkY G Bda G /Y ¼`H A t.ykKPBd}\YKqI.z+WIMP~ i k Mdß C2H®aNMPjMR^LbBDKDBSRdBDcI.LbBdjkV.V7Bdc t Æ B G BDj0C2H V7K G HLNTp M t eß AA C'H G RUM]L+c ¬B MI`LbB B C2H)CnYw}Hkjjp M~7BDKdT]pT]V`B.pt Æ }sM G W G Hk~o ppi v¶ , .p.vi. ,`ppv vi` B v ݤY\V`~`c7KdOV.WI`zbHS~7IJB n K}\MP~JßNt ³PH }\Y v Ý Aß Ç E7IJB G Bdj v Ý B 8ß ð G CQt B v C2H ¬B E.M G B¸C'H Av t ³PH }\Y v Ý Aß ð`E7IJB G Bdj v Ý B 8ß Ç G CQt B v C2H B t u TPjH G Hk~o ݤY\V`~t.I`zbHk~7Iß pv¶ , . . . , pvn ` B ݲRÑß pv¶ , . . . , pvn ` B → ¬¬B Æ BdjB_kW u Æ pSWlabKdTPjH _ß pv¶ , . . . , pvn ` ¬¬B. v o`V`W c7wabY a G MPOW7C2HSV7BdjÛc7RDk~`BdjY G E`wH Av C2H ¬A G CQt ¬¬B t C2H G RUM]L+c M v t`óvBDpk@7B7~`cPC'Wl_kW@7B7~`V7B G oCnanBdc v Ý B ß3M v Ý C ßAÝÑI`z+WIJMP~odE¯ v v v A jMCnWa G HbC'VD^B~ i →KdM]Cp]ßNt p ¶ , . . . , pn ` B , C Y{ß ³PH }lY v Ý B ß ð7E`IJM]K v Ý A ß Ç , G CQt Av C'H B → C t B v C2H ¬B M G Hk~7oqpYlV.~t`I`z+Hk~7I t Æ B~.}HݲR.¯Dß pv¶ , . . . , pvn ` ¬B. Ý ?%IJBdjB7_W u Æ pkWlabKdTPjH¸p®I`zbHk~._N@7BDpkW\_N@~7RDBdc ß ` ¬B → B → C . pv¶ , . . . , pvn ` B → C. ì7Ç YlY{ß ³PH }lY v Ý B ß Ç M v Ý C ß8 ð`E`IM]K Bv B M Cv ¬C t õ RD G oݲR.ÕdßjTPjH Ý Ý ßnß ± RDBDC'W\jÖIJBdc`wkY G W\j u Æ MYlV`~.c7KdOV`W\@7BI`zbHk~`IJBDK}sM]~.c~7Bda G MPV7HSjH Ý ß pv¶ , . . . , pvn ` ¬ B → C . ?9V.M]KDBDV`Hk_ Ý ßC'H v E7I.LbB G BPwkH Ý ß ð`t YlY\Ysß³PH }lY v Ý B ß8 ¬ Ç BM →v Ý CCß8 Ç AE`IM]K B v vBAM C v C t v Ý A8ß Ç M G Hk~7o I`zbHk~`I t.jTPjH ` B → ¬C → ¬ B → C . Av C2H B→C t õ YlV.~t pv¶ , . . . , pvn ` C. ¿ ~o7w®IJBdc7wkY C2HkjHMñ7YlBdjݤ? Ç ß>RdH G RM]L+c Ý ~7Bda G MPV7HSjH¸IJBdjB7_W u Æ ß `C→ B→C , pv¶ , . . . , pvn ` B → C. Uà Á ÄÅ%Æ z+Y YlV`~.c7Kd_Y1I`zbHka¸ab}lBPwSY G Bda G ¼`H C'abjHV7Hkjc`anHk}\Y cRUM]wkBSRUM G I`z+WlIMP~oôÝ A Ò B ßFE Ý A ∨ B ß)M Ý A ↔ B ßFE7V7HeJBPÔ G o G BAC'abBDc_N@TIJTPVDoCnM]KDBpKULNM AG KUopSM ¬ Ý A → ¬B ßFE ¬A → B MÝbÝ A → ß$ÒÝ B → A ßbßNt B o ¼`HvC'~7Bdc G Hk~oV.M]I.aNM G IJBdjB7_WpST]K7}\MP~`V.Wl_F@}BDîdY\_+Kd^`_N@ anIJBDC2HK ¬ M → t [bHk_N@`Vd Ä <Þa R 3%à <*VWMIK o <*VWM áФÏê Ð b MS c ¼.Y A I.}\M G W Æ LbB}\YeJBSRdBd}lV`Bdé I.LNTRD®K~7ow ` A. | A ± i KdM]p k MdÛ ß Ú ← ZÝKPBDLbHK G V7Bda G rsBDL+jT]}\V`W\@7Ba'o`a G kjcß k W\jHDE wHR`[nHk_F@`VDomMñ`YBdjoqC'abBdc G MPc G Bd}BDîdYHdt Ø ~RDBDpkBSRUMP_W>I`LNMR7Y\~`}lB u Æ C2HKDBDLbHK G V`W1I.LbBKUM]wk~7 BD@`B~.V7B7_QHkV`W v G wDt v Ý Aß v Ý A → B ß I.}o7V7H v Ý B ß Ç tdf;pkV t u Æ p G MPc G Bd}BDîdY\W`B7~RdBDpkc]C'H G MPc G Bd}BDîdYHdt c ¼`H A ~7Bda G MPV7HkjH â V`~`c7Kd_W ~.}H~7k}lKdo~ i KUM]pké o <=g [j wO ` A ⇒ | A. eßÛÚ → Ük C'anBdcR7[bHk_N@`VdoRU^7LbBDKDBSRDI`LbBdjkV`V7¼`H A tJ)Hk_F@DÔ v C2H Æ Bdc`wkY C'HkjH}HSjjM G cµ÷t Ç ÚtJ)Hk_N@dÔ BD@`B~.V7B7_QHkV`W G wDt v Ý p ß8 Ç t Æ M]KjpTP¶j, .H . . , pn n pv¶ , . . . , pvn− ¶ , pn ` Av , I`z+YlOHkjw v R Av j i wkHkjHRUo`V7Hk_N@M G E.V7HkeJBPÔ @7B7~`V7B G o v Ý p Nß t n ݲpM]abH®j i w HkjH A C'H G PM c G Bd}BDîdYHÝ | pv¶ , . . . , pvn− ¶ , ¬pn ` Av ß v¶ ßFt A v¶ V7Hk_F@DÔvRpkV.YK7V7H¸p v pkjkV`Bdc [email protected] G ßFt õ l} HkjjM G cBV7HSc G NL TP}lV`W r{BDL+jc.}lY 7~ Bda G MPV`HkjH pv¶ , . . . , pvn− ¶ ` A. v o`V`W a G MPOW G HkV G BIBDa G c7IBDIJMKDBSRM G C2Hk[ G Ý n − Ç ß3KULNT G t áФÏë Ð KS3Ã[j l <=G]ÁÄù8 MFX<àa R 3Ã%<*VWMIK ³DH }lY T jV7BDwSYlV.M ¼.WM A ¼.HDE I`LFTRD®K~7ow T ` A. T | A ì¯ ± i KdM]p k MdßÛÚ ← Ük ± i KdM]pC2HIJB7~7BDe.Vd^ ~ i KUM]pkcRD G oBÍ7I.}\V7Bda G Y¤t )Hk_N@dÔ A ¶ , . . . , An ≡ A C2H~ i KUM]p A p T t T | A ~7BDKdT]wHSjH®Y\V`~`c`KD_kWIJB7~`}lH i ≤ n t Y{ß ³PH }lY Mñ7YlBdj X"E7IJB G Bdj M G WljÛabI.Wl[yY t YlY{ß ³PH }lY AAi ∈ T E`IJM]KCnYla G T | | A AÝiIJ, B7~`}lH®~`H.V`Y\_QH T|¸| ßFt Ai YlY\Ysß A C'HB7i~RDBDpHSV7BI`LNMR7Y\~`}lHkj u Æ i p A E A , K7~7H j, k < i t M]I`zkt A C2H A → A t)Hk_F@DÔ v C2H jiB7~7Hk} T t W\jH ݤ~`}lHYlV.~t I`zbHS~7IJBDK}sMPj~`cßFkE wH T | A M T | A k→ A tZj fZHS~o iv Ý A ßN Ç M j Ý ß Ç t õ G Bd@7BI}xo`V7HDE`wH v Ý A ß Ç EM G c`~`jWlw®jTPjH T j| A t i v Aj → Ai i i eÛ ß Ú → Ük fZHSV G BI`z+WIJMP~6pLbHk~.c7KcPC2HkjHV.MRD G cµB7I.}\V7Bda G Y¤EMP}lHjc.abW\jHI`LNMP_QBSRM G C'HkVµaKPBdV7HSOV7Bdc6IB~.jV7B wkYlV`BDc TÙ ⊆ T t õ Rd G o BmKDBdjIM]K G V`Bda G Y)M T | A RUo7I.}x^RUT7E3wH HQñ7Y\a G c]C'H KDBdV7HkOVT TÙ ⊆ T G wDt t Æ zbHk~`IJBDK}sT]~TPjH G Hk~7odE.wkH TÙ {A ¶ , . . . , A } t õ ~`H.V`Y\_QH |0j i wHSjHc`OkYlV`Y G V.TPab}lHk~`c]CnWl_W T N IJBDÙ p|BDLbBSARUTPV.SW k I`LNTRd¸K7~o7w {A ¶ , . . . , A ¶ } | A → A. {A ¶ , . . . , AN } | A N− N ¿ ~o7w G B G Bc7wkY C2HkjH N KLNT G E`~`BDa G MPV7HkjH Ý Ý ß ß | A ¶ → A · → . . . AN → A . . . . õ RD G oB`I.}lV`Bda G Y jTPjH Ý Ý ß ß ` A ¶ → A · → . . . AN → A . . . Mc7wkY G W\j N KULNT G Rd G oB~7Hk~.c7KD_kYpkW\anKUTPjH {A ¶ , . . . , AN } ` A. fZHS~o T ` A t áÐ{Ó.í Ð R <*G]%à <*VWM l <=G]Áj*3Ã%6mJ[<tVF;VWM1qÁzC C'H tÝ Æ BDpkV.TPjKUMDk BDL+jTP}lV.WZa'o`a G kj X BDL+jTP}\V`WZa'o`a G kj C2H V R <*G]ÃQ: EDC'Hka G }\YwHI`LbBq}lYleJBSRdBd}lV7Bdc¼.Y A `A C'H¸eJHkpHkanIBPLNVD^dtxß Ä <wU%OYÄ gPC@G1<*gbef<*G1A7Á R pI6 R YÄ Ug áÐ{ÓÏÐ b MS ³DH }lY T jV7BDwSYlV.M ¼.W¤E A E B E C ¼`HDE`IJB G Bdj I.LNTRD®K~7ow T, A ` C M T, B ` C. T, A ∨ B ` C áÐ{ÓÓÐ2 A <*G1TJÄ.Ã%<E8JÄ R GÄP8[K5U3²Ä Ý? Ç ß ¬ Ý A Ò B ß ↔ Ý ¬A ∨ ¬B ß Ý?¸¯Dß ¬ Ý A ∨ B ß ↔ Ý ¬A Ò ¬B ß áÐ{Ó.× Ð ?B<=G]Áj*3ÃL6M78JÄYG7F8/:[G1<*O*<E8;:;HZJ R G1<JÁmÂÃ1Qà :;HZJ d KNM1APG1j*3 C'H3ec`´RU^7LbBDKPBSRT)I`LbBdjkV.V.T)V7HkeJB3C2HbC'WV7HkîUM]_HDt }lH1C2H3R O*<JÃD>dC1Ã[OQM1K^8ÃZÂbuUK5V×>dC1Ã[OQM1K^8ÃL6Á G RM]L+cE IJBDK7c`~C'H G BKDBdV]Cnc`V7Kd_QH~`Y\aC'c.V7Kd_W}lY G HLNTP} i t }HyC'H®R UK5V×>dC1Ã%O=MIK^8Zàu}O*<JÃD>dC1Ã[OQM1K^8Ã%6Á G RUM]L+c E.IJBDK7c`~C2H G B~`Y\aC'c.V7Kd_QH®KDBDVPC'c`V`KD_WZ}\Y G HLNTP} i t Ä <%à <=G] Á j*3%à 6Á Md8JYÄ GICX8;:;G1<*O=<E8/:[HZJ R G1<ÁÂ7ÃQà :;HZJ áÐ{Ó`ÜZÐ b MS ¿ HKUM]wk~7 ¼.Y A }lpHanHka G LbBPCnY G HkKdR`YxRMP}HkV G V`%W ¼.Y A RKPBdV]Cnc`V7K G YxR7V` ~`Y\aCnc`V7K G YR7V.Wlj G RM]L+c6MHKUR7YRUMP}lHkV G V`Y ¼Y R~.Yla¤C'c`V7K G YxR`V7 KDBdV]C'c.V7K G YR7V`W\j G RMLNct K AD ± i KdM]p k £ 7©1§dZ¢W =¦ÚÐ/¨bZØÍ= ¬ ¨ Ò ¨Ë/ZbÕ5mÚ^#P¢¥áZYb¨Z¬=Z®7¯ ¡W°=ȨZ®7mP¢± ìDì : : Å , 5 ì $2 *%&" ¸ *8v3$'/ áÐ{ÓáÐg ÄYg F;O ³UMpoKqI`LbHS~`YKUT G BSRD}lBDîdYKUoÝCnM]pQoK Ç t`zNTP~`cß3BDea+MP@UcPC2H I`LbBdjkV.V7ݤV7HBdjHpHkV`®jV`BD@`Bß x E y E z E x ¶ E x· . . . E r{c`V7KdOV.W a'o`jeBD}oÍÝI.LbBKUM]wk~7BdcOH G V7Bda G ðKPBdV7HSOV7V7HeJBV7HKDBdV7HkOV`jV7Bd@7Bß> E E I`LbHk~`YlKUT G BSRda'o`jeJBd}oÍÝI`L+BKdM]wk~`BDcOQH G V`nBda ≥G n ≥ ðKDBdV7HkOkV7V7HeBV7HKDBdV7HkOV`jV7Bd@7BßFfE g }BDîdYl_NKPabIJBPC'KdoÓ ÒE E E E E KdRM]V G Y.KdT G BDLno ∀ E ∃∨E → ↔ ¬ IJBdjB7_V7®ano7jeJBd}xoÝ'EJßFgE Ôx<E Õ . . . áÐ{Ó.æ Ð h. . . E ]Á Ç ß ¿ M]wk~.TI.LbBdjkV`VTAC2H G HkL+jt D¯ ß ³PH }\Y f n T]L+V.W r{c`V7KdOV`WZa'o`jeJBd}ZM t ¶ , . . . , t CnanBdc G HLNj®odE`IM]KRU^7LNM]p f Ý t ¶ , . . . , t ßC2H G HL+jt n ì ß ¿ M]wk~7®KDBDV`HkOV7®IJBdc7wSY G W Ç M¯)C2H G HL+jt n c APG áÐ{ÓJçÐv Çß ¯Dß ìß Ñß PÁ ³PH }\Y T]L+V`W1I`L+Hk~t a'o7jeJBd}M t ¶ , . . . , t CnanBdc G HL+j®oUEIM]KRU^7LNM]p p Ý t ¶ , . . . , t ß>C'H ÄEM1<JÁwK5HIO=j n n Á CL35A pt n z ³DanBdc }lY A E B rsBDL+jc`}lHDE`IM]KÍÝ A Ò B ß , Ý A ∨ B ß , Ý A → B ß , Ý A ↔ B ß , ¬A C'anBdcrsBDL+jc`}Hdt ³PH }\Y rsBDL+jc`}HM I`LbBdjSV`V.T7E`IM]K M C'anBdcrsBDL+jc`}Hdt BO G HkjÛ∃xA c7wkY G WI`LNMR`Yl~7HS} Ç M]w ì t ¿ M]wk~.ATr{BDL+jc`}lHR7pkxV`YlKV`H®KPBdV`HkOVD^`jÛIJ∀xA <*G zCL35A l <*Gdu áÐ{Ó.ê Ð q ÁmÄ.Ã=M1K5OJÄ R G1APUK5O*jDM1<E8=qr35<=T=K5OQF ³DH }lY CnM]pQo7K Ç tzNTP~`c EIJM]K KÃ=M7AEG R G1A MÄ(HbAtÈG1AUÄ*3SK5gdÄYHbA( CnM]pQo7KdM L C2H¸LbHk}sM]OkV`Wa G L+c`K G c7LNM M E7K G HkLNTBDe.aNM @c]C2Hbk L u V7BDwkY\VUc M 6 ∅ t.M]pQ^URTPjHvC'Y C1Ã%K^8QAPG1gbA7Á M MAC2HnCnWI`LnR7Kdo m ¶ , m· , . . . V.M]pQ^URTPjH KÃ[UK^8%K5ULCÄ t Æ LbBKUM]wk~^ n T]L+V.W r{OV`W ano7jeJBd} f BDe.aNM]@c]C2H M pBDe`LNM]pHSV`W f k M n → M t E M BPea+MP@UcPC2H n T]L+V.WDLbHk}sMP_Y p ⊆ M n t Æ LbBA}\YeJBSRdBd}lVd^ n T]L+V`WdI`LbHk~.YKUT G p EkKLbBdj"I`LbHk~.YKUT G cLbBSR`V7Bda G Y¤M M áÐ{Ó.ë Ð ´`J%</U %à </HbA7%à 6 R G1<JÁÂ7Ã1Ã[q C'HKUMwS~7pBDe`LNM]pHkV.W e EK G HLbKdM]wk~`I`LbBdjkV`V7I`z+YlzNMP~`WYlV`~.Y ´`J%<;U1Ã%<;HbAÃL6 R G1<ÁÂ7ÃÃ%q RLbHSMP}\YpSMP_kY M R`Yl~`c.c`j e Ý xß ∈ M t Á C áÐs×í Ð AU*Ä 3SK5gd(Ä HbABM7AEG]z )Hk_F@DÔ e C'HABd@7B7~`V7B7_QHkV.WI`LbBdjSV`V7)R M t7)Hk_N@dÔ t C'H G HL+jt AUÄ*3SK5gdÄ(HbAM1APG]ÁzC t R pIK<=J%</U Ã%</HbA7ÃL6 e C2H Y\V`~`YR7Y\~`c`c.j t Ô eÕ ∈ M G wDt t Ç ß Ô Õ` Ý ßFEPC2H }\Y ¯Dß t³PH e }\Y t eG RUxM]L+c f Ý s ¶t,≡. . .x, s ß , IJM]K t Ô eÕ` f Ý s ¶ Ô eÕ , . . . , s Ô eÕ²ßFt n M n áÐs× ÏÐo GPÄ 8;UK^8=<*VWM æ WKUTPjHDE`wH ×A R MI.Wl[bHkjH M | A Ô eÕE]C'Hka G }\YwH >A R GÄP8;UK^8=j I.z+YBd@`B~.V7B7_QHkV`W A e M ß;MÝ Ô Õ Ô Õß Ç ß C2H Ý ¯Dß AA C2H pt ¶ t ¶ , t. ·. .M , ttn¶ Ô eÕ` t ¶ t· eÔ e,Õ . . . , tn e ∈ M M M 6| B Ô eÕ ì ß C2H Ñß AA C2H ¬B M Ô ÕZV7HkeJB Ô Õ ÷Dß A C2H BB ∨→CCM MM| 6| BBÔ eeÕV7HeJB MM| | CCÔ eeÕ C2H Ò M Ô Õ1M | C Ô eÕ A C2H B C M M | B eÔ Õ I`M LFTRD®K~7ow Ô Õ B ↔ MC M | Ô BÝ e ß ÕI`LbB}lYle t M | CEKe~7H Ý Õdß AA C2H ∀xB ä ä ß3anH¸ab@`B~.c]C2H®a e V.M®R`[nHk_F@qI`LbBdjkV`Vd^7_N@ aR^C'Y\jKDBdc xME`K |G HkLbB¸I`ezNYxzNM]mpkcPC2H m ∈ Mm ∈ M e x m ÚDß A C2H ∃xB M M | B Ô e Ý xä m ß ÕZI.LbBV7nCnM]KD m ∈ M ìÑ áÐs×JÓÐ R 3Là KNM1AE3%à <*VWM æ WKUTPjHDE.wkHÞ¼.H MIWl[bHkjH M | A EDC2H }\Y A I`LNMR`~`YxRTR M I`z+Y KUM]wk~7kj >AùV R 3¤ÃZÂ7ÃÄù8@G1AÄY3SK5gdÄYHPK M Bd@7B7~`V`B_HkV`W e t A áÐs×× Ð ´ÝgUÃ(Ä abA7Là 6 ³DH }lY G HL+jE ¼`H®M I`LbBdjSV`V7DEIJB G Bdj Ô ÕRpkV.YKV`Hp abBdc`OkMPabVd^7jÖ~7Bda+M]pkH ¶ , . . . , tn tj tV`Vd^7jY E7IM]KRU^LFMp V.Wlj G tHL+j i t ApSMI`LbBdjx ¶ k,V`. V7. . ,xxnt Æ B7~7BDe.V7DE]CnanBdc }\Y x ¶ t,x.ß .,...,x k H k p Y d R D B \ } D V ` ^ j Y ` I b L d B j k i Ô Õ R7pkV`YlKV7Hp i anBdc.OkMPabVD^`jÛ~7BdaNM]pHkV`W\j . , xG HnL+j i t pMR7[bHk_N@`VdoqRdBd}lV7¸R^7abKdAo G o x t Ax ß ,...,x t ¶ , . . . , tn A i i áÐs×.ÜZÐ C[eLVWMIKNM1C%<E8JDÄ M1AE3%à <*VWM æ WKUTPjHDE7wkH G HL+j >ABV7C%eLVWM1KNMIC%<E8JD Ä M7AD3=à : pSMI`L+BDjkV`V`BDc x ~7ÝB ¼`H A E]C2HSa G }lYlwH¸I`L+BKdM]wS~7BdcI`LbBdjkV.V7Bdc t RU^`anKUo I.LbBdjkV.V7 p w ] T . ~ D V q ^ d R d B l } d V q ^ R V7HkV.W anBdc`OSTPa G WwTP~`V7¸IB(~ ¼`H Qy B ¼`H A t G y t x A Á 3SC;8Ä áÐs×JáÐ t Ô Õ C'HkVK7~o7w®KdM]wk~7^ G HL+j C'H®a+c7e.a G Y G c7BSRM G HS}lVd^pSMI`LbBdjkV`V7Bdc x t Æ W\[nHkjH A ß ti x ,...,x t ¶ , . . . , tn , i Á j*3%à 6cVF[VWM7q7Á U%O(Ä g+ R G1APUK5O*jDM7<E8Qqr35<=T=K5OQF áÐs×æ Ð v <*GP Ø e.a+MP@c]C2H ³dM]pQoK ?vñ`YBdjo · _N@`kjM G Mݤ? Ç fß 0µÝ¤? ì ß"p X ± RDab_F@7kjM G MI`L+B ∀ ± RDab_F@7kjM G MI`L+BLbBSR7V`BDa G Ý}lBDîdYKUMavLbBSR7V`BDa G Wsß Ø ~RdBDpBSRM]_kWI`LFMR7Y\~`}\M u B7~`c`avIJBdV7HkV.a Æ LNMR7Y\~`}BîDHkV7HLFM]}\YpMP_QH n n n áÐs×çÐo G ÄP8[K5U35<wT*A7Ã%APGÄ*3SK5gdÄ(HbA ³DH }lY A ¼.HDE x I`LbBdjkV`V.T7E`IM]KqB7~RDB7´ ∀xA t`fB G BpSV.MPOW\jH A . ∀xA áÐs×ê Ð HZJ[q7ÁÄDMSÄ R G1< ∀ Ç ß ] n%K5<JÁ V R AEHPK^OÄYHbA P³ H }\Y ¼`HDE G HL+jE7IM]K¼`H ∀xA → A Ô tÕ`C'HMñ`YBdjÖI.LbHk~`YlKdT G BSRd}BDîdYlKdodt x ¯Dß HZJ%qAÁmÄ R G1t A7Ã%Abn;A ³DanBdc }lY A E B ¼`HdE x I`LbBdjkV`V.T7E1K G HLNT6V7HkV.W>RdBd}lVTR A EIJM]K¼`H ∀x Ý A → B ß → Ý A → ∀xB ß;C'H MSñ`YBdjt Á 3SC;8Ä áÐs×ë Ð t [email protected]]IJHkjH;CbMKDBpkKULNM G KcpSM ¬∀x¬B t }\Y ∃xB áÐ\ÜJí Ð o GPÄ 8[K5U35<wgdbÄ 8QAPULALà 6 ∀ ³DH }lY ` A → B M x V`HkV`WRdBd}lV`R A E`IM]K ` A → ∀xB t áÐ\ÜZÏÐ d AÁÁÄ Ô Õ t Çß ¯Dß `³PH A }\Yx `t A→→∃xA M V7HkV`WRDBd}\V7R B E`IM]K ` ∃xA → B Ý o GbÄ 8%K5UL35<tgdbÄ 8=AEULALà 6 ∃ ßFt B x áÐ\ÜÓÐ 2 K5VWM7GIK5eC%HbAOQ8Ä.=à M1K5LO=jEM1<*G ³DH }lY ` A → B E`IM]K ` ∀xA → ∀xB M ` ∃xA → ∃xB. áÐ\ÜJ× Ð (Ä GZK²Ä.=à MSÄ æ WKUTPjHDEJwk H ¼.H 0 C2H 8J(Ä GZK²Ä.=à M7<QC ¼`H A EUC2Hka G }lYlwH A0 R7pkV`YlKV7Hp A KPBdV7HSOVD^`j IJB7O G Hkj VM]@`LNM]pHkV`W G RM]L+c/k IJB7D~ ¼Y QxB V.MP@7ALNMPé ´ ¼.W QyB Ô yÕE`K~7H x Ç ß y C2Ha+c7e.a G Y G c7BSRM G HS}lV7®pSM x ~`B B M ¯Dß y V7HSV`WRDBd}\V7¸R B t ì÷ áÐ\ÜÜZÐ ÂbMSÄ<8Ä(GIK²ÄÃ=M7jYHZJ ³DH }lY A0 RM]L+YsM]V G Bdc¼`H A E`IM]K ` A ↔ A0 t áÐ\ÜáÐ ÂbMSÄ<wULAEULC%O=HPK )Hk_F@DÔ T C2HjV7BDwkY\V.M ¼.W¤E A c7pSMR7zbHkV.Tͼ`HM .HDt Æ M]K I.LNTRD®K~7ow T `A→B B ¼ T, A ` B. áÐ\ÜJæ Ð o G1A7[à APnZLà 6fMd8(Ä G7F l <*G]ÁùCL3S6 æ WKUTPjHDE1wH¼`H C2HRR G1A7Ã%AbnÃ%6Á Md8Ä(GIC EJC2Hka G }\YwkHC2H G RM]L+c EK~7H x ¶ , . . . , x n CnanBdcL i pkV7®I`LbBdjAkV`V7M B C'H¸B G HQRz+HkV.TݤV7HkBDe.a+MP@c]C2H®wSTP~`V`¸KdRMPV QG Yl¶ `xKU¶ T QG BD· xLno· ßF.t . . Qnxn B áÐ\ÜçÐ o p1AP8=</U ÃÄ R G1A%à AbnÃL6fMd8JÄYG c ¼.Y A }pHabHka G LbBDC'Y G ¼Y A0 RI.LbHkV7HQñ`V`W\j G RM]L+c G M]KE7wkH ` A ↔ A0 t Æ LbBKUM]wk~7Bdé ± i KdM]p k A0 anHka G LbBPCnWljH¸IJBdjB_WI`LbHkV`HQñ7V.Wl_F@BDIJHLNMP_mW k Ç ß Æ B7D~ ¼Y VMP@7LNMP´V`nCnM]KDBDcC'HnC'WRM]L+Y\MPV G BDc 0 ݲpTPjkV.MRT]pSMPVD^`_N@I`LbBdjkV`Vd^7_N@C'H®VUc G VTh ß ¯Dß ¬QxC CV.MP@7LNMP´ Qx¬C E`K~`H ∀ C2H ∃ M ∃ C'H C∀ t V.MP@7LNMP´ Qx Ý B → C ßFt ì ßyHSV`W }lY RdBd}lVTRdËH ¼.Y E`IJB7D~ ¼.Y QxC ÑßyHSV`W }lY xx RdBd}lVTRdËH ¼.Y BC E`IM]KqIJBB(~ ¼.→Y QxB VMP@7LNMP´ Ý B → C ßFt ÷DßyHS_N@DÔ ♥ C2á H Ú ∨ V7HkeJÝ B Ú¦ÒnM x V7HSV`WZRdBd}lV`R →BCEJIJM]KÝ B ♥Qx ßyVMP@7LNMP´ Qx Ý B ♥ C ßFt Ý QxC ♥ B ß QxC V.MP@7LNMP´ Qx Ý C ♥ B ßFt u c`abW\jHMP}lHvC2Hk[ G ~7BDKdT]pM G E`wH®KdM]wS~.TBDIJHLNMP_H®V.MP@7LFMpSc]C2H®IJB7D~ ¼.YHKUR7YRUMP}lHkV G ;W ¼.mW k M]~ Ç k G MBRM]L+YsM]V G TP_N@t M]~6¯Ek M G Hk~7o ` ¬∀xC ↔ ∃x¬C ݲR7Ylp®~7Hk.V`Y\_Y ∃ ßNt ` M]~ ¬∀xC ì k ↔ ¬∀x¬¬C, Æ LbB Q ≡ ∀ k Ú Ük y←HS_N@DÔ x V`HkV`WRdBd}lV`¸R B t Æ MK ` ∀x Ý B → C ß → Ý B → ∀xC ßÝI`LbHkV7HñHßFt Ú Ük õ →U PI«7YI£L£d¢®©7¨ ¨ß¬Q¢©¬=ÎZÝË= bª/ ¨ SÚ . . . Z Ý ß ÝbÝ ß Ý ßnß ` B → ∀xC → ∀xC → C → B → C IJBdc7wkY G W\jÞRd G oB~7HS~`c7Kd_YM u Æ a Ý=Mñ7YlBdjÛanIHk_Y.KdMP_QH®I.LbB t xß ` ∀xC → C pkWlabKdTPjH Ý ß Ý ß ` B → ∀xC → B → C . ?%I`LbB G BDwH¸I`zbHk~`IJBDK}sMP~V7HBDe.aNMP@Uc]C'HRdBd}lV` x E.j i wHkjH¸IJBdc7wkW G I`LNMR`Yl~.}BpSMRdHk~7HkV.W ∀ M~7Bda G TRTPjH Ý ß Ý ß ` B → ∀xC → ∀x B → C . Æ LbB Q ≡ ∃ k Ú ← Ük ݤYlV.~t`I.zbHk~7IJBDK7}\MP~ß ÝbÝ ß Ý ßbß ` C → ∃xC → B → C → B → ∃xC Ý ß Ý ß Ý u Æ p®I`zbHk_F@7BDpkWl_F@Ý9I`LNMRt7pMRt ∃ ß ` ∃x B → C → B → ∃xC ` C → ∃xC Ú Ük Æ →BdjB_kW~ i KdM]pkcLbBDpeJBDLbHkj9I.z+WIJM]~ i t B → ∃xC C'H ¬B ∨∃xC M G c`~`Wlwvjc`a+WljH;~7BDKdT]pSM G Ý ßFt ∃x B → C Mdç ß Ä ` ∃xC → ∃x Ý B → C ßÄ u TPjH Ý ß ¤Ý ? Ç ß . `C→ B→C ìÕ ¬B ∨∃xC ` yo7V`W a G M]OkWIJBdc`wkW G ~`Yla G L+Ye.c._Y t eJßçÄ ` ¬B → ∃x Ý B → C ßÄ ∃ õ }lHkjjM G cµ÷t Ñ Ç jTPjH ` Ý B → C ß → ∃x Ý B → C ßFt ± TP}lHR7W\jHݲR¯PßFEwkH ` ¬B → ∃x Ý B → ßFt.M]KPBdV7HS_IJBdc7wkY C2HkjHRd G cB~7Hk~.c7Kd_YZM u Æ t C M]~YÑ k Ý ß Ý ¬C → ¬∀xB ß ↔ Ý ¬C → ¬∀x¬¬B ß ↔ Ý ¬C → ∃x¬B ß ↔ ∃x Ý ¬C → ¬B ß ↔ ` Ý ∀xB → ßFCt ↔ Æ LbB ∃ IJB7~7BDe.V`Dt ∃x M]~6E÷ Bk → C LbBDpHIWl[+cIJBdjB_kW ¬ M → E`IM]KqI`zbHRDHk~.cIJBdjB7_WBDIJHkLNMP_W Ç M]w®Ñ.t ♥ á Ð\ÜJê Ðo pI65O[3²(Ä U R p1Ab8=<;UCöÃÄ R G1A%à AbnLà 6fMd8JYÄ G Ý ß Ý ß B ↔ ∀xC Ò B → ∀xC ∀xC → B Ò Ô Õ B → ∀xC ∀yCx y → B Ò Ô Õ ∀x B → C ∃y Cx y → B Ý Ý ß Ý ÝbÝ ß ∃y∀x B → C Ý ß$Ò Ý C Ô Õ x ß ß y →B ßbß áÐ\ÜJë Ð2 AbÃLK5HbA yHS_N@DÔ C'HjV7BDwkY\V.MݼW R V7bCnM]KPSj CbM]pQo7_H Ç tzNTP~`c tJyHS_N@DÔ C2HLbHM]}\YpMP_QH G wDtKUM]wk~.T`¼`Hp C2HanI.}\V7TkVMR M t Æ M]K z+WlKdTPjHdEwH M C2H ÁL<;ULAE35AÁ M1AP<*GZK5A( MT tM]I`zktjB7~7HSL}Hkj G HBDL+YHîDL+c7IC2TH KdM]wk~TîDL+c7IM7t ³PH }\/Y ¼`H A anI.}\V7kVMRKdM]wk~7Sj#jB7~7Hk}\c G HBDL+YH T E`z+WKUTPjHdE7wH A >A T u R 3²ÄEM]Ã%j MI.W\[nHSjH T | A t C2H®}lBDîdYl_+KUoI.LNMR7~`YRTÝ | A ßC2H }\Y abI.}lV`kV.MRKUM]wk~7®LbHSMP}\YpSMP_kY7CnM]pQo7KdM7t A Ä <wO=<*G1APOQM%à <*VWMIK áÐ{á.í Ð b MS ³DH }lY T G HBDL+YH¸RCnM]pQo7Kc L M A C2ÞH ¼`HDE`IM]K K~o7w T ` A E7IJB G Bdj T | A. áÐ{áÏÐ2 [V135APULAPO8J MWF<tO*<*G1AEO=M]Ã%<*VWM1K u T }lY G HBDL+YlH T jB~`Hk}E G M]KC'H¸eHpHkabIJBDL+V.T7t Å:=8;: 4 / *âÔ+¥¸'&y*9·d.$ Â&ã³ä ì 5 ¸ à G MB7I.}\V7Bda G YZanH®~TV.M]I.aNM G RdH®~7RDBdc G RUM]LbHS_N/@ k Ç ß I`LFTRD®K~o7w ¯Dß TT |C'H¸eAHpHkabIJBDL+V.T7E`I`LNTTRd`¸A. K7~ow T jTjB7~7Hk}¤t õ I`LNMRM~`Bd}HQRMyCn~7HARBDeJBdcI`z+WlIMP~7HS_N@qBRd G cqBKPBDLbHkK G V7Bda G Y¤t ± TanH G M]KD~7BDKUT]pSM G HKUR7YRUMP}lHkV`_QH G RL+pHkV`W Ç M¯Ut s c`~7HkjH G Hk~o~`BPKUM]pBSRM G ~7L+c.@7 G R7LbpHkV`WM~`WlKdoqRd G ¸BKDBDLbHK G V`BDa G YIJBdc7pHabjLvpk}HQRM~7BDI`LNMRM7t áÐ{áÓÐ R 3%à jrM7AE<*GIK5A æ WKUTPjHDE`wH C'H a R 3¤[à j E]C'H }lY eJHpkHkanIJBDL+VTMI.LbBKdM]wS~7Bdcc`pSMRz+HkV7Bdé c ¼.Y A I.}sM G W T ` A V`HeJB T ` ¬A t T Ä M7AE<*GIK5A áÐ{á.× Ð A7%à O;K%à <E8Jz fHBDL+YlH T C2H A7[à O[K%à <E8JÄ EPC2HSa G }lYlwHI`LbBKdM]wS~7Bdcc`pSMRzbHSV7Bdé c ¼.Y G RMLNc ∃xA HQñ7Y\a G c]C'H®KDBdV`a G MPV G M c ݤ¶)HkV7K7Y V`BSRUMKPBdV`a G M]V G MI`LbB ∃xA ß G wDt T ` ∃xA → A Ô cÕt x áÐ{á`ÜZÐ d AÁÁÄ ³DH }lY T 7I.}\V.T¶)HSV7KY\V7BSRM G HBDL+YlHDE`IM]K T jTjB~`Hk}t áÐ{ááÐ <*gb4765p1A7%à 6 Ç ß 0 C2H G1<*gb4765p1ALà 6Á >QYÄ g F;OJÄ EPC2Hka G }\YwkH 0 BDe.aNMP@Uc]C'HR`[nHS_N@`Vdoa'o`jeJBd}op RDHa G HbC'V7kjÖRU^7pkV.MPjct ¯Dß LT 0 a"CnM]pQoKDHkj L0 C2H G1<*gb4765p1A7L%à 6Á M1AP<=GILK5A T a>CbMpoKDHkj L EdC2H }lY L0 LbBDpk[bWlzbLHkV`W\j L MI`L+Bq}lYleJBSRDBd}\V7Bdc ¼.Y CnM]pQo7KdM I}\M G WE.wH YljI.}lYlKcPC2H 0 t ì ßfZHkBPALNYH T 0 a"CbLM]pQoKDHkj L0 TC'H `O*A<J%à gbAPG78EÄ MIK^8ZLà T6Á ` G1A<*gb4765pIALà 6Á G HBDL+YH T a>CbM]pQoKDHkj L EdC'H }lY T 0 LbBDpk[bW zbHkV`W\j G HBDL+YlH T MI.LbB}lYleJBSRdBD}\V7Bdé c ¼Y A CbMpoKUM L I}\M G WE.wH T 0 ` A Y\jI.}\YK7c]C'H T ` A t ìÚ Ä A7Ã%O;Kà áÐ{á.æ Ð b MS@ ¿ M]wk~7Bdc G HkBDL+YlY T }lpH®KPBdV7pkHLnRM G YR7V`®LbBDpk[bWlz+Y G ~`B¶)HkV7K7YlV7BSRo G HBDL+YlH T t H Ä d KÃ[ULA7ÃQe1Ä*CÁ áÐ{áJçÐ b MS@ ¿ M]wk~7BdceJHpHkabIJBDL+V7Bdc G HkBDL+YlY T }lpH®LbBDpk[bWlz+Y G ~`B7I.}\V7 G HBDL+YH T na Ha G HnCnVD^7j0CnM]pQo7KPHSjt U (¢k^~ T å ¢W¬(«15¬=Z®I¨IÛQ/¨I« TL ¤7¢Ê¨I«XW å ¢W¬Y«75¬=Z®I¨P± Z L áÐ{á.ê Ð 2 AbLà K5HbA u nC'jHvCnM]pQo7K L MAC2Hk@`BLbBDpk[bWlzbHkV`W¤EPCbMpoK L0 t ³PH }\Y M hM, f k f ∈ L, p k p ∈ Li EIJMK6a G L+c7K G c7LNc M0 hM, f k f ∈ L f k f ∈ M M M k k V.M]pQ^URTPjH Abn R ÄÃ%gP6 M UL< L0 t M 0 0 p ∈ L p p ∈ L − Li L − L, p M M ³PH }\Y M0 p;I`z+Hk~`_N@`BDpkWl@`B¸B~.a G MRU_QH;LbHSMP}\YpSMP_H CnM]pQo7KdM L0 EPIM]K M p;I.zbHk~`_F@7BDpkWl@`B¸B7~`a G MRU_QH C'H G1APUC%O*HP6 VMLbHSMP}lYlpSMP_Y M CbMpoKUM L MpkVM]OkWljHvC'Y M0 |L t M0 áÐ{á.ë Ð d AÁÁÄ ³DH }lY T 0 LbBDpk[bWlzbHkV`W T ݤaCnM]pQo7KPHSj Lß;MAC2H }lY M0 jB~`Hk} T 0 E`IJM]K M0 |L C'H®jB7~7Hk} T t áÐsæí Ð 2 [OJ(Ä gé8 MFX<àa R 3%à <*VWMIK u T]jHqeJHkpHkanIBPLNV7Bdc G HkBPLNYlY M ec`~7HkjH@.}Hk~M G C2HbC'W;jB7~7Hk}¤t Æ B~.}HqRd G o ÷tx÷PÕ6j i wHkjH LbBDpk[bWlz+Y G V.M eJHkpHkanIBPLNV7Bdc¶)HkV7K7YlV`BSR7c G HBDTL+Y\Y T t ± TP}lH¸j i wHkjH T LbBDpk[bWlz+Y G IJB7~`}lHARd G o÷tx÷DÚV.M7I}lV7BdTc¶)HkV7K7YlV`BSR7c G HBDL+Y\Y TL M G M®jT¸IB~.}HA}lHkjjM G cqH÷tx÷ÑjB7~7HS}tU)Hk_F@DÔ HM0 C2HAjB7~7HS} G HkBDL+YH TL t õ ed^RUTc`w"C2HkV7BdjòIJBdc7wkW G }lHkjjM÷tx÷På7E7pV7k@7BDw®pkW\anKUTRUTPjH M0 |L jB~`Hk} G HBDLNYH T t 0 0 ìà æ ç q Í ¸ ;q èp;er û 7@ BdjanKDk@7B%@`YlHLNM][email protected][email protected]]LNM]K G HL+YpM]_HC'Hk~`V7B G }\YxR^7_N@ G z+Wl~ïCnM]pQoK i I`LbBda G zbHS~7Kdo0îDLNMPjM G YK MïMPc G BdjM G+i E ݤV7Hß'~7H G HkL+jY\V`Yla+jc.at ü pSTRDkLbBSRD¸R`}\MPa G V7Bda G Yt.)HLbBDpk@`B~.VUc G Hk}\V7®I`LbBDe.}lkjo G HBDL+YlH;CbM]pQoK i t ¸2/ ì& .+¸* -ï!#/0*" &yf/ - 5 h& . ê;: ! : ¨ > æФÏ.Ð fÀ jYO;3²YÄ U %à 6cULAP Là K5HbA C2H)}\YeJBSRdBd}lVT®jV7BDwkY\V.M Æ LnR7KdoM]eJHS_QHk~o¸C'anBd`c R 65VS Á A7ÃÄ L+HkanI t VFZr Á ef<Q3^F ÐO 35<E8=< C2HyKdM]wk~T ] efAPHbAEU1Ä KDBdV7HkOVTIJBdAab}lBdc7I.V`Bda G I.W\abjHSVt o G1jYA. gbU [ à qùV735<D8=< ݤab}lBSRdBq~7k}lKdo6ðdßvabHpkV.MPOkW . u V7BDwkY\V.MR`[nHS_N@6ab}lBSRVMP~ M]eJHk_Hk~7Bdc anHpkV.MPOW u V7BDwkY\V.MAV7HI`LFTpS~`VD^`_N@ab}lBSRV.MP~ anHpkV.MPOW YÄ g F;O=AÁ V.MP~ V.M]pRDHkjH CbMKDBdc7KDBd}lYRAIJB7~`jV`BDwkYlAVcq∗. jV`BPwSYlVdo A∗ . Æ LbBa+}BSRM α a ¶ . .A. a M β Abé ¶ .. . . b Ý m, nL∈ ? ß"A~7HVUc]C'HkjH m n BDIJHLFMP_Y V735<=ÿbALà 6cV735<E8 CnM]KPB αβ a ¶ . . . a b ¶ . . . b . m n ' 5 +v7*",!#/ , 5 v $ ¸>,.& .wd/ !y3! ê;: : Á 9 æÐ{ÓÐ] O*HbA R M7<*G O*HbA R 7 M <*G1A 7Á A LbBDpkc.jW\jH¸IJ G Yl_kY A Ý Q, X, δ, qÙ , F ß , K~7H C'H¸KDBdV7HkOkV.TjV7BDwkYlVMa G MR i Q C2H®KPBdV`HkOV.TR7a c7I.V`WZM]eJHS_QHk~.M G Xk 2 C H®I`zbHk_F@7B7~7BSRTr{c.V7Kd_QH δ C2Q × X → QW a MR ® H J I 7 B k O T k H O ` V G G qÙ 2 C H j ` V P B S w l Y . V MKPBdV`_QBRU^7_F@mÝI`z+Y C'W\jMP_W\_N@ß;a G MR i t F ⊆Q à <=VWM1K3(Ä O*HbA R M7<*GIC o GIKÃ%HPK R aPKÃ% ?)KD_HI G BDLabYPI.zbHk~`a G MR`jH CnM]KDBypSM]z+WpHSV`WEkK G HkLb"jTz+W\~`W\_WC2Hk~`V`B G K7cEbC2Hw3j i wkH"V.M]ed^RUM G KDBDV`HkOV73jV7Bd@M;a G MR i ESM R7a G c7I.V.WUIJTPanKc t Æ TPanKUM"C2HL+BPpS~7k}lHkV.MAVM"C2Hk~.V7B G }lYRUTAIJBd}lW\O+KUM7E]K G HLFT"C'anBdcBOW\ab}lBSRT]VM)I`zNYLbBDpHSVD^7jY7OWla+}xodt a G c7I.V`W ab}lBSRdB α a ¶ . . . a C2H)V.M]I.aNTPV7BVMI.LnR7V`W\_N@ n IBD}\WlONKdTP_F@R`a G c7I.V.W`IJTPanKdoUt Æ B¸R`a G c7IV`W.ITPab_QH)abHvIBD@doec]C2HAO G Hk_W @`}sMRUM7t MqIJB7OkT G KncÍOY\V`V7Bda G YabHM]KD_QHkI G BDL®[email protected]]pkW1RdHa G MR7c qÙ MO G Hk_kW @`}sMRMC2HV.MI.LnR7V.WljIJBd}\WlONKcÍITPabKdodt ?)KD_HI G BDLvI.LNMP_c]C'H¸R G MK G Hk_N@q RC2Hk~.V7Bdj G M]K G c@`}sMRMV.MR`a G c7I.V.WITPa+_QH®I`zbHkO G HvC'Hk~`V7BI.W\abjHSV7BpkHR`a G c7I.c MIJBdabc`V`H6anH6V.MmVT]a+}HS~`c]C'W\_WyIBD}\WlONKPB.t pSTR`Yla+}Bda G Y)V.MI`zbHkO G HSV7kjèIWla+jHkVcúMma G MR7cöz+Wl~`W\_W>C2Hk~.V7B G KdoöanHR z+W\~`Wl_kWC'Hk~`V7B G _QHVM]a G MR7WÝBDeJHS_V7ßyC'YlVd^ôa G MR8t _Y\V`V7Bda G M]Kd_QHI G BDL+c KDBdV`OW3RBDKUM]jwkYK7cE K~o edo abHjk}lBÍOW\a G I`LnR`V`W.I`LNT]pk~`V`yIJBd}lW\O+KDB®pMKDBdV`_QHkjòa+}BSRM7tU³DH }lYjBdjHSV G TP}lV.W`a G MRz+Wl~.Wl_WDC2HS~`V7B G Kdo¸C2Hk~.V`WljòpvKDBdV`_QBSR^7_F@a G MR i E IJBSRM]wkc]C2HabH®a+}BSRdBpSMI.z+Y CbM G dE.V7HkV`W }lY¤EM]Kd_QHI G BDL)ab}lBSRdBV7HI.z+Y CbM]}¤t æÐs×Ð <*gb4165p1ALà 6 R p1APHZJ%</UL<E8=q l C%à O*HPA C'H®r²c`V7Kd_QH δ∗ k Q × X ∗ → Q ~7Hk.V7BSRMPV.TLbHKc`LbpkYR7V7 G M]K G YB k Ý ß Ý ß Ý Ý ß ß δ ∗ q, ≡ q, δ ∗ q, αa ≡ δ δ ∗ q, α , a . ] æÐ\Ü Ð : R <;abA Mbü R pIK >6ÁmÄ=à :r>QÄYg F;O Æ Bdab}lBdc7I.V`Bda G a G MR i rÙ , . . . , rn VMpRDHkjH 8;: R </aZM1AÁ V.MP~a+}BSRdHkj α 0Ý a ¶ , . . . , an ß , C'Hka G }lYlwH δ Ý ri− ¶ , ai ß8 I`L+B i Ç , . . . , n. æ HK7V7HkjHdE>wHR^IJB7OQH G C2HrR pIK >d6ÁÄYHP6ü C2HSa G }lYlwH rÙ qÙ M r ∈ F. · }lBSRDB α C2H rR i pIK >d6w Á j.%à < M]Kd_QHI G BDLbHSj A, IBPK7c`~VM]~mV`Wlj HQñ`Yla G c]C2HI`z+Y CnWljM]_kW1R^IJB7OQH G E G Hk~oÍIJBDnKc`~ δ∗ Ý qÙ , α ß ∈ F. ³UMpoX K R pIK >d6ÁÄ=à : M]Kd_QHI G BDLbHSj C'H G RdBPz+HkVöjV7BDwkYlV`Bdc R7[bHk_N@úab}lBSR I`z+Y C'WljMPVD^7_F@ G W\j G BôM]KD_HI G BDLbHkjE pkVMPOWljH@7B L Ý Aß . Ø ~7RDBdcöM]KD_QHkAI G BDLbHk_N@ A ¶ , A· zbHK7V7HkjHdE wkHC'abBdc AEOQ8[K^8ÄY35A7Ã*M]ÃL6ü IJBDK7c`~ôI.z+Y C'W\jM]C'W a G HnC'Vd^CbM]pQoKE G Hk~o L Ý A ¶ ß L Ý A· ß . æÐ{áÐ 2 <*VkYÄ ÿPKNM1AE3Qà :VWMbÄ 8 · G MR q MKd_QHkI G BDL+c A Ý Q, X, δ, qÙ , F ß`C2H UL<*VkYÄ ÿPKNM7AD3=à :Yü K7~o7w3HQñ`Yla G cPC2H α ∈ X ∗ G M]KDBSRDDEwH q δ∗ Ý qÙ , α ß . æÐsæÐ AET=CL35j(G]Là 6/>YÄ g F;O ³UMpoKV.M]pQ^RUTPjH G1AET=CL35j(G]Là 6ü C2H }lYI.z+Y CnWljTPVV7bCnM]Kd^`jÖKDBdV7HkOVd^7j°M]Kd_QHI G BDLbHkjt æвçJÐ FZ=à M(Ä OQM1K5HIO*qrO*<J%à T=GIC[A7%à HbA u nC'jHvCnM]poK L ⊆ X ∗. Æ M]KqLbHS}\MP_QH ∼ V.M X ∗ anHV.M]pQ^RUÝT R GbÄ 8QjVFZ=à MSYÄ O=MIK5HIO*jO*<[à T=GIC%A%à HbA CbM]pQoKUM L, K7~oKDBd}lYR Ý ∀α, β ∈ X ∗ ßQÝ α ∼ β ⇔ Ý ∀γ ∈ X ∗ ßQÝ αγ ∈ L ⇔ βγ ∈ L ßbß . ìå abH®V.M]pQ^RT VFZÃ=MSÄYO=MIK5HIO*jO*<JÃ%T=GIC[A7Ã%HbA CbMpoKUM L, K~o7KPBd}\YxR Ý ∀α, β ∈ X ∗ ßQÝ α ∼ β ⇔ Ý ∀γ, δ ∈ X ∗ ßQÝ δαγ ∈ L ⇔ δβγ ∈ L ßbß . æÐsêÐ F%J%KS3S3Nu}?BAEG1</UL<E8JÄù8JÂbMSÄ Æ LbBKUM]wk~^CnM]poK L V.MP~ M]eJHk_QHk~`BDc X C'anBdcV.TPab}lHk~`cPC'Wl_kWIJB7~`jWlV7KUoHKdR`YxRMP}HSV G V`Wmk Ç ß C'H¸L+Hîdc`}\T]L+V.Wt ¯Dß LÆ LNMRTano7V G M]K G Y\_+KUTKPBdV7îDL+c`HkV`_QHvCbMpoKUM L jTKDBdV7HkOV`jV7Bd@7B G z+W\~t ì ß · o7V G MK G Yl_NKdTKPBdV`îPLNc7HkV`_HvCnM]pQoKUM L jTKDBdV7HkOkV7jV7Bd@`B G z+W\~t æÐsëÐo CÁ R K[à Tt35A7ÁmÁmÄ R G1<wG1APTQC%35jYG]Là 6/>(Ä g F[OQF ¿ H;KUM]wk~7kjcLbHîdc`}sTLNV`WljcACnM]poKc L Hñ7Y\a G c]C2H n ∈ N G M]KDBSRdDEPwHvI`LbBR7[[email protected]+}BSRM α ∈ L ~7k}lKdoMP}lHkanIB HQñ`Yla G c]C'W a+}BSRM α ¶ , α· , αê G M]KDBSRUT7E`wH α· 6 , |α ¶ α· | ≤ n, α α ¶ α· αê MÝ ∀k ∈ ?®ë ßQÝ α ¶ αk· αê ∈ L ß . n ± i KdM]p k u nC'jH M]KD_HI G BDL A Ý Q, X, δ, qÙ , F ßI`z+Y C'WljMCnWl_W CbM]pQoK L MÍV`Hk_N@dÔ α a ¶ . . . ah ∈ L Ý A ß . )Hk_F@DÔ h > |Q|. ³PHpkzbHnC'jDE wHI`z+Y CnWljM]_kW RU^IBOH G V.MP~mab}lBSRDHSj α jc`a+WV`K G HLn^`jY>a G MRoÍI`LbBDC'W G R`Wl_QHkKULNT |α| G tyHS_N@DÔ qÙ , . . . , qi, . . . , qj , . . . , qh C2H G HkV G BR^IJB7OQH G t Æ M]KHQñ`Yla G c]C'W OW\ab}sM i, j G M]KDBSRUT7EwH i < j M Ø pSV.MPOjH α ¶ a ¶ . . . ai , α· ai ¶ . . . aj M αê aj ¶ . . . ah. Æ B G Bdj qi qj . é Ýé ß q δ∗ qÙ , α ¶ i ß q q Ý δ ∗ qi , α · ß qj ∈ Fi Ý δ ∗ qj , α ê h Æ B G BdjÖpSMI.zbHk~7IJBDK7}\MP~`c n |Q| C2H~ i KUM]p®@`B G BSRt Á K%à K5VM1K5HIOQ: YÄ O*HbA R M1<*G æФÏí Ð ?BAEULA M1APG]t )Hk~`H G HL+jY\V`Y\a G Yl_NKd^M]Kd_QHI G BDL>C2H®IJ G Yl_QHÝ Q, X, δ, I, F ß , K~7H C'H¸KDBdV7HkOkV.TjV7BDwkYlVMa G MR i Q C2H¸R7a c`I.V`WZM]eJHS_QHk~.M G Xk Ý Q ßC2H®I`zbHk_F@7B7~7BSRTr{c.V7Kd_QH δ Q ×C2H Xj→ P 7 V D B k w \ Y V.MIJB7OkT G HkOV.Wl_F@a G MkR i I ⊆ Q C2HjV`BPwSYlV.MKPBdV`_QBRU^7_F@a MR t G i F ⊆Q æФÏÏÐ : R </abAbM æ HKV`HkjHDEJwHab}lBSRDB >A R pIK >d6w Á j.%à < V7Hk~`H G HL+jY\VtM]Kd_QHI G BDLbHkj A ÞÝ Q, X, δ, I, F ß , IJBDK7c`~HQñ7Y\a G c]C'H¸IJBda+}αBdc7IV7aBd¶ a G. .a .G aMkR i ∈rXÙ , ∗. . . , r ∈ Q G M]KDBSRUT7E`wH Æ B7~7BDe.V`¸LbHS}\MP_QH ∼ VM X∗ k Ý ð Ç ßFÝ rÙ ∈ I ∀i ∈ h , k − i ri é rk ∈ F. ¶ Ý ∈ δ r i , ai é ¶ ßbß V.M]pQRdHkjHR pIK >d6ÁmÄ(HP6Á 8;: R </aZM1AÁ M]KD_QHkI G BDL+c V.MP~ ab}lBSRdHkj Æ Bdab}lBdc7I.V`Bda G a+}Bdc7IV7Bda G rÙ , r. Ù . ,. ., .r. , rankI}UcPC2HM]}lHkabIJBbI`LnR`V`WZ~Rd®IJB7~`jW\V7KUodEj}lc7R7W\jH®BV`AW`CnM]KPBB 8;: R α. Æ BDKc`~ IJB V.MP~ < aZMIC / A α. U& ¬Q¢P¢¢W5¬Y^£WSS¡Wk«XWW¹¨I«Z¡1¢/ÊZÍØ Õ1¢W`¢L=¦¢5¤WÚ5/®[¤7¢Z¬=Z =¦¢¡W°DbZÝbˬQÖ«Z Ð^«Z¨£WʨZ®7ØݨÙ/I«1 ¨bª7Z®IÎZ¬YÚ ®7¯/bªdS飢PÖ5¤7¢©«Z¨7Õ7+W°D©¬YS¡W°/¨Z ¨ Ü¢W~¬QÖ7± Z®IÔ¤d¢=¦ ¤d¨ ÊIÛ(¤d¢R^~9¨ ¢£/Dì¤d¢P¢W¬z®7¯}/bª1¢ U ®Z¢Þ£Ï1£W~ P¢¢WÍ^¬Y^£WSm¡«XW°D¨I«Z¡1¢×QÊZ&Z¥=¦ ¤Ú5ݨ¤WÚm¡Úm± Z 7 o <=g [j wO Uà Á ÄÅ ¿ M]wk~^~7H G HL+jY\V`Yla G Yl_NKd^M]Kd_QHI G BDL>C2H¸pT]LbBSRDH V`Hk~7H G HL+jYlV.Yla G Y\_+KU^dt æФÏ7ÓÐ b MSÄ )Hk~`H G HL+jY\V`Y\a G Yl_NKPM]Kd_QHI G BDLnoI`z+Y C'W\jM]C'WI`LNTRd®LbHîdc`}sTLNV`W7CnM]pQo7Kdodt ± i KdM]p k ³D~`HB G B.E1M]eUo7_F@7Bdj KDHKUMwS~7kjcV7Hk~7H G HL+jY\V`Yla G Yl_NKPkjcôMKd_QHkI G BDL+c Ý X, δ, I, F ßpKDBdV a G L+c7BSRM]}\Y~7H G HL+jY\V`Yla G Yl_NKd^dESC2HkV`w>C'HAa"V.WljòHKdR`YxRMP}HSV G V`W¤t ± H G HL+jYlV`Y\a G Y\_+Kd^qM]KD_HAI G BDL"eQ, c`~7HAjW G ¯ a G MkR i E K G HLbe.c`~`BdcB7~7IJBSR`Wl~.M G IJB7~`jV7BDwkYlVTPj P Ý Qß . u V7BDwkY\VUca G MR i EP~7B¸V`Y\_N@7wyM]KD_HI G BDL I`zbHbC'~7HdE]V.MP@`|Q| LNMP~`WljH1C'W B7~7IJBSR`Wl~MCnWl_W\jòa G MRdHkjt u V7BDwkY\V.M¸IJB7OkT G HkOV.Wl_N@a G MR i ec`~7H)VM]@`LNM]pHkV.M¸B7~7IJBSR`Wl~MCnWl_W\jòa G MRdHkj KPBdV`_BSRD a G MRUoqe.c.~7BdcI`LNTRd G odE7wkHARCnYljÖB7~7IJBSR`Wl~MC'W\_W\_N@jV7BDwSYlV.TP_F@a G MR i V7HS~7H G HL+jYlV`Y\a G Y\_+KDk@7BM]Kd_QHI G BDL+cedo`} MP}lHkanIJbB C2HS~7HkVa G MRqKPBdV`_BSRU^dt BDL+jTP}lV` k7HKdR`YxRMP}HSV G V`W ~`H G HL+jY\V`Y\a G Yl_NKd^M]KD_HI G BDL;KqpSMP~.MPV7kjcV`Hk~7H G HL jYlV`Y\a G Y\_+KDkjcC2H A0 Ý Q0, X, δ0, I, F 0 ß , K~7H Ý Qß Q0Ý P8 ß Ý ßQÝ Ý ßbß δ 0 A, x {q ∈ Q ∃r ∈ A q ∈ δ r, x } Ý ß ð F 0 {B ⊆ P Q B ∩ F 6 }. Ñdð U ¨Z`7©W¦¢5¤W`Öc®7¯1£WÜ¢ Z¬*¯P¢¢WÍ^¬Y^£WSm¡W«7¯¥¨I«Z¡1¢×QÊZ9¬Q¢7§W(P¢[=ȨZ®IPÖ×/bbP§W¬QÖ9ÍÚ5/ʨI«Í¬=I°Dh£WʨZ®7ØPÛb= Ê7Õ1¢ ¤7¢5¤m¡W°®Z¢ «ZΪ7ÎI£9¬Q¢7§W(E¢bI£¨7ÕS¢Ð¬=ÎP± Z æФÏ× Ð 35APA7Ã[<D8JÄz8 MÄ óyHîdc`}sTLNV`WPCnM]pQo7Kdo G RdBDz+W.V`HnC'jHSV`[bW G z+W\~`c¸CnM]pQo7K i EdK G HLNT¸BDe.a+MP@c]C2HvR7[[email protected]KPBdV`HkOV7>CnM]poKdoMC2H)c7pMRzbHSV.M VMKPBdV7HSOV.Ta¤C2Hk~.V7B7_QHkV`W¤E`KDBdV7KUM G HSV.MP_YZMY G HLNMP_Y U ®7©Íãb±í2îkZb± æФÏUÜZÐ APT=CL35jYG]Là 6f8;:;GYÄ g C'H®~`H.V7BSRTPVYlV`~.c7Kd_SW k Ç ßð MKUMwS~^pkV.M]KC'abBdcLbHkîDc.}\T]L+V`WR^LNM]po ¯Dß IJ,BD Kc`~C'abBdc α, β LbHkîDc.}\T]L+V`WR^LNM]podEPC'anBdcY α β, α · β, α∗ LbHîdc`}sT]L+V`WRU^7LNM]pQo ì ßÒC'YlV`¸LbHkîdc`}\T]L+V.WRU^LFMpoV7HnCnanBdct Ø IJHLNMP_eY B7~7IBSR7W\~.TôaC'Hk~`V`B_HkV`WE KDBdV7KUM G HSV.MP_QHöݤOkMPa G B anH G HkV G B ano7jeJBd})[email protected]RTdßM ∗ Y G HLNMP_QHDt ¿ }HHSV7BSRMRd G MR`}\MPa G V7®z+WKUT7E`wH®LbHîdc.· }\T]L+V`WRU^7LNM]pQoCnanBdcqRe.Y C2HKd_YZa;LbHkîDc.}\T]L+V.WljY7CbM]pQoKUodt æФÏ7áÐ éï 8=</HPK5A7=à MF>(Ä g F[O ³danBdc }\Y L ¶ E L· CnM]pQo7KdoV.MP~ M]eJHk_QHS~7Bdc X E`IM]K IJB7~`}H V.M]pQRdHkjHvCnM]pQo7K Ý ∈ L ¶ ßQÝ vu ∈ L· ß } 35Ab8/:Á OQ8=<;HPK5A= à M7A7Á L · {u ∈ X ∗ ∃v Ý ßFÝ ß R GP Ä 8/:Á O/8=</HPK5A7=à M7AÁ L· L· IJB7~`}LH ¶L ¶ V.M]pQRdHkjHvCnM]pQo7KL ¶L\· /L {u ∈ X ∗ ∃v ∈ L ¶ uv ∈ L · } ¶ æФÏæ Ð égdbÄ 8[p1A%à <*VWMßO/8=</HPK5A7*à M ³DH }lY LbHîdc`}sT]L+V`WPCnM]pQo7KV.MP~ X EPIM]KI`LbB®KdM]wk~7^Ý G Hk~7oY`V`HLbHîdc`}sT]L+V`W{ßJCnM]pQoK L0 V.MP~ X CnanBdc L/L0 M L0 \ L LbHkîdc`}\LT]L+V.W7CnM]pQoKUodt ·U9* ¶h& .'[* &E%/ $ *-0/1P! ê;:=8;: ¨ f æФÏ`çÐ ?BAEULA M1APG]ÁtKÃ%K5VM1K5HIOQ:gbjYVd<*e ÃL65O*<E8;: Ä*C;M7<JÁmÄDM C'H®abHk~`jYl_QHÝ Q, X, ð , δ, qÙ , rÙ , F ß , K7~7H C'H¸KDBdV7HkOkV.TjV7BDwkYlVMa G MR i Q C2H¸R7a c`I.V`WZM]eJHS_QHk~.M G X C2H®pSTPanBDe.V.WKDBSRUTM]eJHk_QHk~M ð k Ý X ∪ { }ß × ð → P Ý Q × ð ∗ ßC2H¸I.zbHk_N@`B~`BSRUTr{c`V`KD_QH δ Q × C'H¸ IJB7OkT G HkOV.Wa G MR q Ù ∈ Q C2H®IJB7OkT HkOV`WpSTPabBDe.V`WlKPBSR^a'o`jeJBd} G r Ù ∈ ð C2HjV`BPwSYlV.MI`z+Y CnWljM]_kWl_F@a MR G i F ⊆Q à HPK R aPKÃ%à <=VWM1Kcgbj(Vd<*e Là 65O*<E8QqEJ%<m*Ä C;M7<JÁmEÄ MIC o GIK% ?õ C2HLbBDpS[bWz+HkV`W M]KD_HI G BDL+c BV`HKPBdV`HkOVd^ pSTPanBDe.V.WKEV.MV7kjw)C2HV.MIJB7OkT G Kc pM]I.a+TPV6ano7jeJBd} rÙ . KUM]wk~7Sj KUL+BPK7c õ ? V.MR`Wl_yjc`abW`I`zbHkOW\a G M¸a+jM]pSM G C'Hk~7HkVa'o`jeJBd}.V.MAR7L+_N@7Bd}\cpSTPanBDe.V.WKc ÝC2H }lY`pSTPabBPeV`WKI.LNT]pk~`VD^UE õ ?úabH pSMPa G MR`Wsß MV.M)R7L+_N@`BD}7pSTPabBDe.V`WlKcpSM]I.aNM G V7bCnM]KDvab}lBSRdBݤjBDwkV7B¸I`LNT]pk~.V7ßFtDf MKD C'HvjBDwkV`;IJBDpSMPa G MR`Y G I`z+Y C'W\jTPV`W a'o`jeJBd} i pkH)R7a G c7IV`WITPabKdo @.}\MRMV.M®R7a G c7I.V.WITPab_QHV`Y\_AV7HkO G H¸MV7HS@D^7eTanHDt g ñ`Yla G cPC'W G Hk~7oI`zbHk_F@7B7~oI`zbHSa I`LNT]pS~`V7ab}lBSRDBRDHr{c.V7KD_kY δ ݲR7[+YljV`Y abY>Ý X ∪ { }ß"RC2HnCnWlj#~7HV`YlOkV`WljÛBDeJBDL+cJß G pQRt u R p1AEHIJ%<;U[F Ð æФÏê Ð <J[à T=C%G(Ä HbAÀ ] C'H G LbBDC'Y\_QH6Ý q, α, β ß , K~7H q ∈ Q, α ∈ X ∗, β ∈ ð ∗. A [email protected]]pkW RKPBdV7.îdc7LNMP_YyÝ q, α, β ß , IJBDK7c`~C2HRdH a G MR7c V.MR7a G c7I.V`WITPab_Hped^RUTI`z+HkOWla G a+}BSRdB α MV.MpSTPanBDe.WlKcC'Hc`}lBPwkHkV7Bab}lBSRDB β Ý G pkV tJV.MRL+_F@7Bd}lc pSTPabBDe.V`q,WlKcC2H®I`LnR`V`WI.W\abjHSV7Bab}lBSRM β ßFt æФÏë Ð À ] R p1A>U%A R pI6 Á < R pIAW>ULA p®KPBdV``îdc7LNMP_QHÝ q, α, β ß"~`BKDBdV7`îdc7LNMP_HÝ q0, α0, β 0 ßÝpSM]I.W\[nHSjH þ `DßFE7IJBDK7c`~I.}\M G W A Ý q0, γ ß ∈ δ Ý q, a, b ß , α aα0 , β bβ 00 , β 0 γβ 00 , K7~7H β, β 0, β 00, γ ∈ ð ∗, b ∈ ð , α, α0 ∈ X ∗, a ∈ X ∪ { }. A R p1AW>ULA p Ý qÙ , αÙ , βÙ ß~7B Ý q , α , β ß n n n ÝpSM]I.W\[nHSjH þ ` DßFE7IJBDK7c`~HQñ7Y\a G c]C'H¸IJBda+}Bdc7IV7Bda G ∗ Ý qÙ , αÙ , βÙ ß ` . . . ` Ý q , α , β ß . n n n ÑÇ æÐ{Ó.í Ð : R </abAbM Æ Bdab}lBdc7I.V`Bda G KPBdV``îdc7LNMP_WV.M]pRDHkjH 8/: R </aZM1AÁ õ ? V.MP~R`a G c7I.V.WljÒab}lBSRDHkj IJBDKc`~I`LnR`V`W.KDBDV``îdc7LNMP_QH C'H®Ý qÙ , α, rÙ ß MAIJBdab}HS~`V`W`jT G RUM]LyÝ q, , β ß , K7~7H q ∈ Q, β ∈ ð ∗ EDM)RKUM]wk~7vKDBDα,V``îdc7LNMP_Y G G B¸IJBdab}lBdc7I.V7Bda G Y MPc G BdjM G I`zbHnCn~7H~7BV.TPa+}Hk~.c]C'W\_WKDBdV7`îdc`LNMP_QHDt Á j æÐ{ÓÏÐ À ] R pIK >d6w u T]jH }\Y α ∈ X ∗, IM]KzbHkKV7HSjHDEwH õ ? A òÝ Q, X, ð , δ, qÙ , rÙ , F ßR pIK >6¤Áj α V R G1jYgbU1ÃQ:ZÁ gbjYVd<*e[u ß Ý ß)I`LbB6V7nCbMKD q ∈ Q. ³dM]pQoK6R`[nHk_F@mab}lBSRµI.z+Y CnWljM]Vd^7_F@ma¸I.LNT]pk~`Vd^7j à 65O*A7 L Á ü K7~ow6Ý ß Ý pSTPabBDe.V`WlKPHSjÖBDpkVqMPÙ O, Wlα,jH rÙ N `Ý A∗ ß . q,õ ? , A R pIK >d6w ß Á j R pIK >d6ÁYÄ HP6Á VWMSPÄ 8=AÁ E`IJBDK7c`~mÝ I.LbBV7nCbMKD q ∈ F, β ∈ ð ∗ . ³dM]pQo7KR`[nHk_F@a+}BSRI.z+αY CnWljMPVd^7_F@I`z+Y CnWljM]_kWlj#a G MRdHkjÖBDpkVqMPÙ O, Wlα,jH rÙ L Ý `A∗ß . q, , β æÐ{ÓÓÐ b MSÄ Æ LbBKUM]wk~^pSTPabBPeV`WlKPBSR^MPc G BdjM G A HQñ`Yla G c]C2H õ ? B G M]KDBSRU^UE`wH N Ý A8ß L Ý B ß . ± i KdM]p k M]a G WlV`W\jH"~7H.V.Yl_YUMPc G BdjM G c G HSVI.LNMP_c]C2H"abKPBDLbBya G HnC'V7 CbM]KPB ¿ A I`z+Y\~.TPjH"V7BSRU^¸IJB7OkT G HkOV`W a G MRMI.z+YI.zbHk_N@`B~.cpV7bC1C2HVM~.V7BBpSTP anBDeV`WK7c~7BDI.}\V7kV V7BSR^anIJHk_YsTPA. }lV.W ano7jeJBd}>ÝI`zbHka+V7nCnSY kDC2HabjM]pSTPV I i RDB7~`V.W1IJB7OkT G HkOV`W a'o`jeJBd}MC2HI`z+Yl~TPVµanIHk_Y\TP}\V`W ano7jeJBd}1abIJBd}lcÍaAI i RDB7~`V`W\jßFt Æ MK I.LbBDe.Wl@TRU^7IJBOH G CbMKDBR A MK~o7wanKDBdV`OWZRU^7IJBOH G A ayI.LNT]pk~`Vd^7j°pSTPabBPeV`WlKPHkj Ý=M G HS~o V.MpSTPanBDeV`WK7c B peUo7}1anIJHk_kY\TP}\V`W ano7jeJBd}sßFE`I`zbHnCn~7H B I.LbB¸CnM]Kd^7KPBd}\Y a G MR I`zbHk_F@7B7~7Hkj#~7BV7BSRdk@7BI`z+Y C'WljMP_Wl@`Ba G MR`ct æÐ{Ó.× Ð b MSÄ Æ LbBKUM]wk~^pSTPabBPeV`WlKPBSR^MPc G BdjM G A HQñ`Yla G c]C2H õ ? B G M]KDBSRU^UE`wH L Ý A ß N Ý B ß . ± i KdM]p k B ec`~7HBDIJ G V7HIJM G L+V`c7I`LFMRDHkVd^ôMPc G BdjM G A. Æ z+Yl~TPjH I`z+Hk_N@7B7~opKPBdV`_BSRU^`_N@ôa G MR i ~7B V`BSRDk@`B a G MR`c MpMC'Y\a G W\jHDEvM]eUo MPc G BdjM G EB_Y G V7H }\YabH6R G Bdj G B a G MR7c E"R V7Sj C'YlwÍp i a G MP}¸M abjM]pSMP} ÝIJBdjB7_W I`zbHS_N@7B7~ i ß3pSTPanBDeV`WKt Á K%à KSVWM1K5HIOQ:úÀ ] æÐ{Ó`ÜZÐ 2 A M1APG]t Á KLà K5VWM1K5HIO/:(ü IJBDKc.~ Ø õ ?%zbHK7V7HkjHdE`wH;C2H ULA M1APG]t I`z+YzFMpSc]C2H®KUM]wk~7kjcI.LnRK7c~7H.V.YlOV.Wl@7BBDeJBDL+cjMñ7Y\jTP}lV`;C2HS~7HkVI`LnRdHKqBDeJBDL+c@`B~.V7B G δHQñ7Y\a c]C'H }lY.I`LbB~.MPVd^a MRMARL+_F@7Bd}`pSTPanBDeV`WK7c I`zbHS_N@7B7~EdV7HkHQñ7Y\a G c]C'HyI`LbBV7yI`zbHS_N@7B7~I`zbHka CnM]KPkKPBd}\Y G G I.Wla+jHkV`BpHR`a G c7I.V.WZM]eJHk_QHk~7o HQñ`Yla G c]C2H }lYDI`LbB)~.MPVD^¸a G MR¸M3R7L+_N@`Bd}PpSTPanBDe.V.WK7c¸I`zbHk_F@7B7~I.zbHkaZV7nCbM]KP>IWla+jHkV7B;R`a G c7IV`WdM]eJHS_QHk~oUEkV7HHQñ`Yla G c]C2H I.LbBV7 I`zbHk_F@7B7~t o <*gU%à j.w Á OÄÅ õ ~7L+c`@`k@7BM G zbH G W\@7BeB~.cI.}o7V`HDEwH I.zbHk_N@`B~C2HI`zbHk_F@7B7~7HkjEK~o V`HB~.a G LNZM UcPC'Y V`Y\_pkHR`a G c7Ict æÐ{ÓáÐ b MSÄ õ TPabBPeV`WKDBSRdM]c G BDjM G oI`z+Y CnWljMC'WZayI`LNT]pk~`Vd^7j#pSTPanBDe.V.WKDHkjÛI.LNTRDeJHpKDBdV G HQñ G BSRDyCbMpoKUo"U ®7Ü©«Z¨=5Ê ~ °DZ£}«XW°DÝ°PÊ¢W ¨Z ¡W°P^Zb± æÐ{Ó.æ Ð [ AEgbO*<J=à M1AbnQM1<E8/:XULA M1APG]ÁtKÃLK5VWM1K5HIO/:>Ä(g F;O ³UMpoKVM]pQ^URTPjH efAPgbO=<JÃ=M7APnQM7<D8/:ZÁ U%AbM7AEG]ÁwKÃLK5VWMIK5HIOQ:ZÁ > Ä(g F[O*AÁü IJBDK7c`~HQñ`Yla G cPC2H;~7H G HkL+jY\V`Yla G Yl_NKd^ õ ?E`K G HLn^@7BI`z+Y CnWljTt * &! ·d`,7*g 5 ê;S: ½y: ëÝ$ ,.$'& v>% Á K%à KSVWM1K5HIOQ:>AEU [à < R jYVdO*<E8;: c C%GIKÃ[T`;8XVWM7G1<(> æÐ{ÓJçÐ2 A M1APG]t C'H®abHk~`jYl_QHÝ Q, X, Y, δ, qÙ , B, F ß , K7~7H C'H¸KDBdV7HkOkV.TjV7BDwkYlVMa G MR i Q R7a c7I.V.W M]eJHS_QHk~.M G X I`LNMP_QBSR`V`WZM]eJHk_QHS~.M Yk⊇X Ç ð Ç I`zbHk_F@7B7~7BSRUTr{c`V`KD_H δ IJ QB7× YHkO→ Q ×R Y × {− , , } k O T . V W a M G G qÙ I`LNT]pk~.VD^a'o`jeJBd}>Ýe.}sM]V`K`ß B ∈ Y, B 6∈ XMP_W a MRo ` I + z Y ' C \ W j G F ⊆Q à HPK R aPKÃ%à <=VWM1K c C[GIK%à T*<D8J Ä VWM7G1<(>A o GIK% f)t at`jTz+W\~`Wl_kWC'Hk~`V7B G K7cE7K G HLNTj i wkH¸VM]ed^URM G KPBdV7HSOV7j[email protected] G MR i EMp;C'Hk~`V7a G LNMPVDoV`HKPBdV`HkOV7BdcITPanK7c a@`}sMRdBdct1MpSMPOkT G KcmI.LNTP_QHqabHz+W\~`Wl_kW C'Hk~`V`B G KUM f)t a[email protected]]pkW>RIBOST G HkOkV`Wlj a G MR7c M @.}\MRMC2HV.MI`LnR`V`W\j IJBd}lW\O+K7cµIJTPanKdoUt C2HS~`V7BdjKULbBDK7cÍf)t atI`zbHSO G HpSV.M]K IJB7~Í@`}\MRdBdcMIB~.}HV7nCMqIJB7~`}Ha G MR7cµpSM]I.W\[nHVM G B G B ѯ jW\a G BÍpkVMKE@.}\MRMÍanHIJBdabc.V7HBC2Hk~.V7BIJBd}lW\O+KDBmV7HeJBp i a G M]V`Ha G T G M6z+W\~`Wl_W C'Hk~`V7B G KUM6I.zbHnC'~`H~7B ÝBDeJHk_kV7ß C'Y\V7k@`Ba G MkR7ct æÐ{Ó.ê Ð <J[à T=C%GÄ(HbA c Ð V Ð ¿ BdV7`îdc7LNMP_QH¸fAt akt T Ý Q, X, Y, δ, qÙ , B, F ß C2H G LbBDC'Y\_QHÝ α, q, β ß , K~7H α, β ∈ Y ∗ , q ∈ Q. æ HK7V7HkjHDEwH T VdAµÃ( Ä HZJ%jYgP6f8XO*<;à T=C%GYÄ HPK Ý α, q, β ß , I`LFTRD®K~7ow V.M i G kj IJBd}lW\O+K7côR`a G c7I.V.W;ITPabKdoµC2H i G I.W\abjHSV7Bmab}lBSRM αβ, IJBDKc`~ i ≤ |αβ|, V7HeJB B, IJBDKc.~ i >C2H¸|αβ| RDHa G MR`c q M@.}\MRMVMR7a G c`I.V`WIJT]a+_QH®O G H¸IJBDpkY\_Y |α|. T Ý ¿ BdV``îdc7LNMP_QH}lY\[bW\_W abH¸IJBdc7pkH¸IJB7O G Hkj B V.MKDBdV`_YIBSRUM]wkcPC2HkjH¸pSMHkKdR`YxRMP}HkV G V`Wtxß æÐ{Ó.ë Ð 2 AbLà K5HbA f)t ak=t R pIK >d6w Á jtV735<E8Q<;ü IBPK7c`~C2HIBqabKPBdV`OHkV`WZRU^IBO G cR`a G c7IV`WZIJT]abKdM_QHS}\TabjM]pSMPVT ݲI.zbHI.aNMPV.TVM ßNE O G HS_W"@`}sMRMC'HVMI`LnR`V`W\jIBD}\WlONKcITPanKUoMf)t at[email protected]]pSWRI`z+Y C'W\jMP_W\j a G MR7ct3Ý ± HV`Y\_QHI`z+Y C'W\jBMP_W KDBdV7`îdc7LFM]_H®}lpHV.MP}kp G YB7~`}\Yl[bV`Dtxß Â V R </abAbMQà :r>QYÄ g F;O æÐs×í Ð APO[C[G1gPK^8à ³UMpoKV.M]pQRdHkjH G1APO[C%G1gPK^8ZÃr  V R </abA M]Qà :Z Á ü IJBDK7c`~C2H®I`z+Y C'W\jTPVV7bCnM]Kd^`j#fc`L+YlV`îPBSR^7j#a G LbBDC2Hkjt Á K%à K5VM1K5HIOQ: c Ð V Ð æÐs× ÏÐ ?BAEULA M1APG]t C'H®~`H.V7BSRTPVCnM]KPB~7H G HL+jYlV.Yla G Y\_+KU^dE`LbBDpk~.Wl}7C'H¸IJBdc7pH¸R k Ý Ç ð Ç ß δ Q × Y → P Q × Y × {− , , } . æÐs×JÓÐ b MSÄ )Hk~`H G HL+jY\V`Y\a G Yl_NKPf)t akt7I.z+Y CnWljM]C'WI`LFTRD®LbHK7c7LbpkYR7V`®abIJB7OQH G V7vCnM]pQo7Kdodt æÐs×× Ð d K%à APjYG]Ã%6 c Ð V Ð f)t aktFC2H 3SK%à APjYG]Là 6ü IJBDKc.~V`Hkj i wH;I`zbHkKULbB7OY G ~7k}lKcR`a G c7I.V.Wl@7Bab}BRUM7tDfB¸pkV.MPjHSV.T7E]wHvI`LbBR`[nHk_F@`V.M q ∈ Q ec`´ δ Ý q, B ßV7HkV.W ~7H.V`BSRUTPV7B6ÝC2H®I`LNT]pk~`VTjV7BDwkY\V.MdßV7HkeJB δ Ý q, B ß Ý q0, B, − Ç ß . æÐs×.ÜZÐ 2 AbLà K5HbA f)t akt G1<*gPJ%</UCD>A CnM]pQo7K VM]~ K~o7wabHRU^7IJBOH G I`LbBqKdM]wk~`ab}lBSRdBpMPa G MR7W M L Ý T uß L. ³dM]pQoK L C'H G1AETO;C%G1gPK^8ZLà 6ü IJBDKc.~Hñ7YlLa G c]C2Hf)X, t aktlE`K G HLn^@`BLbBDpk@7B7~`c]C'HDt æÐs×JáÐ b MSÄ C'H¸LbHkKc7LbpSYxR`V`WE.I`LNTRd®K~o7w L à M Lñ C'anBdcLbHK7c7LbpkYR7V7abIJB7OQH G V7Dt L ê;: Å: ã ,7/>-0/ `$23! æÐs×æ Ð o p1A R K5Vd<D8J(Ä HP6cVdF;VWM7q7Á ± RdBPCnYl_YÝ ß®VMpRDHkjHR pIA R K5Vd<E8JÄYHP6VF;VWM1qÁü IJBDK7c`~ C2H M]eJHS_QHk~.MµM ∗ v u, v ∈ X }H KDBdV7HkOVT7t X,± RdPBPCnYl_kY u → v V.M]pQRdHkjHwR GÄP8[K5U35< Ð Æ LbB pKULNTP_HkXV`W®jW\a G B u →P v⊆¶ , .{u. . ,→ . I \ W n [ k H j u → v n ab}lBSRDB Æ zbHkI.YlabBSRUMP_kWano7a G SjÞÝ ß[R pI6Áw<</U%8=<=gPCD>WA pH;ab}lBSRUM u | . . . |v IJBD→K7c`v~6¶ |vÝ u· → ßv ∈n .P. Æ Bdab}lBdc7I.V7Bda G I`z+W\j®^`X,_N@PB~7RDBDpHkV.WVMp^URTPjH U%AEGIK^8JÄYHP6αü I`zbHkaI.¶YlabuaBSR· M]_kWano7a G βkj°ÝaX,¶ vaP· ß , a+}BSRdB β, Hñ7Y\a G c]C2H }lYZ~7HL+YRM]_H β p α RÝ X, P ß . <;U[8Q<*gPCD>A pHa+}BSRM α æÐs×çÐ ò GÄÁDÄ M1K5OÄ øLNMPjM G YKDBdcV.M]pQRdHkjH®KdM]wk~`BdcO G RdHz+Y\_Y>Ý V , V , S, P ß"K7~7H k T N 2 C ® H ` V H H + L j \ Y . V P T l } . V Z W ] M J e k H Q _ k H ~ M G VN C'H HkL+jYlVTP}lV`WZM]eJHS_QHk~.M G VT C2HY\V`Yl_kY\TP}lV.W ano7jeJBd} S Ý V∈ V∪NV , P ßC2H¸I.zbHI.Y\anBSRMP_W a'o`a G kjE7I.LbBK G HLn^I.}sM G W N T Ý u → v ß ∈ P ⇒ Ý ∃A ∈ V ßQÝ A ∈ u ß N U ®«Z¨7Õd<W,= ¨Z®7S(Ü¢¤7¢Þ¬=¨ Ü¢W®I¨ ¢£/Dì¤7¢P¢W¬r¬Q¢¢W5¬=Î Zb± Ñì æÐs×ê gÐ ÄYg F;OT*AÃ%AEG1<E8JÄÃ=:XT*GÄÁÄDM1K5O=<=C øLNMPjM G YKUM G 0Ý V , V , S, P ß T=AÃ%APGICD>AÍ>Ä(g F[O N T Ý 8ß {α ∈ V ∗ S ⇒ ó V ∪V ,P ô α}. LG ∗ T Ý u W\a G B α ⇒ ó V ∪V ,P ô β I.W\[nHSjH α ⇒G β. ß ∗ ∗ æÐs×ë Ð o pI65O[3²(Ä U øLNMPjM G YKUMÝ {<L+HSTP}lV7 OWla+}B >, <_QHk}sT OkTPa G >, <~7HkabH G YlV.V.T OkTPa G >, <HñIJBdV7HSV G >, <pkV.MPjkV7KDBSRD OW\ab}lB >, pkV.MPjSV7KPB >, <eJHppSV.MPjkV`KPBSRd OkWlab}lB >}, {ð , Ç , ¯ , ì , Ñ , ÷ , Õ , Ú , à , å , ., , −,g }, <LbHSTP}lV` OW\ab}lB >, P ßFEPK~7H < C'H P LbHSTP}\V7 OW\ab}lB >→<_QHk}sT OST]a G ><~`HkanH G Y\V`V.T OkTPa G ><HQñ7IJBdV7HkV G >, < _QHk}sT OkTPa pkVM]jkV7KDBSRd OkWlab}lB >, G < ~7HkabH YlV.V.T >→< k O P T a t eJHkppkV.MPjkV7KDBSRD OW\ab}lB > | , G G <HQñ7IJBdV7HkV g >→pkV.MP<jkV7KDBSRD OW\ab}B G <pkV.MPjkV7KDBS>→ > eJ| Hp, pSV.MPjkV`KPBSRd OW\ab}lB RD OW\ab}<B >→<pSV.MPjkV`KPB >< <pkV.MPjkV7KDB >, <eJHppSV.MPjkV`>→ | − | , KPBSRd OkWla+}B >→ ð | Ç |¯ |ì |Ñ | ÷ |Õ |Ú |à |å , < îDHkV`HL+c]C'H;CbMpoKqpST]I.Y\abcLbHSTP}\VD^`_N@OW\anHk} BDedRUo7K}^qRdHRo7[+[bW\_N@I`LbBDîDLNMPjBSRUMP_W\_N@CbM]pQo7_kWl_N@ t - · L)v* )A$ 5 ,7/(, '*)A$ 5 ê;Ê: ê;: õ )y*3¹ û @7BdjanKDk@7B@`YlHLNM][email protected]pSMP@7L+Vc G oV7K G HLbV7HnC'~ i }HkwkY G nCn[bW G zNWl~oîDLNMPjM G YlKJt Ç ß Ø }lYleJBSRDBd}\V7DE <*efAPHU%à q îDLNMPjM G Y\_QH®I`LbBd@`}sTPabWljHDE.wHvC2H G oI.c ð7tf;z+W\~.MCnM]pQo7K i îDHkV7HLbBSRMPVD^`_N@ G MKDBSRdBdcîDLNM jM G YlKPBdcanH®BPpSV.MPOc]C'H LÙ . ¯Dß <J=à M1AbnQM1<E8=qrT*GÄÁDÄ M1K5O/F ÝîDLNMPjM G YKUo G oI.c Ç ßC'abBdcîDLNMPjM G YlKdoabI.Ü} Uc]CnWl_WZV.TPa+}Hk~.c]C'W\_WI.LNMR7Y\~`}lYB k Ý ∀ Ý u → v ß ∈ P ßQÝ ∃X ∈ V ßQÝ ∃y ∈ Ý V ∪ V ß é ßQÝ ∃α ¶ , α· ∈ Ý V ∪ V ß ∗ ßQÝ u α ¶ Xα· ∧ v α ¶ yα· ß . N N T T N N T N T U «Z¨7Õ7+ WÝ= ¨Z®7S(tÝή1¢W®It¬Q¢×¢Í^¬QÎ PöP§d¨ Ü ¢W¬Y¯2öB£Z®7Ï U = Î7©7Z¬Y¯ZZz©r¬Q¢¢W5¬=Î ~Ø ¨¢W5¬=Î Ð ØEÛ ® = ¨Z®I`/¨I«Ë¤7¢ß¬Q¢×= Î7©dZ¬OWÝ£W Z®I马Q¢¢WÍ^¬=Î ~ Øwh¢W5¬=Î ~ ØP§d¨ Ü¢W¬`WÝ£W¢5¤W¬Y¯IÍ£W Z®7Ϥ¨I«Zr®1Ü¢W®IkZ ± K7c`~mV7HkV`W S V.MI`LFMRDa G LNMPV7wSTP~`V7S@7BI`LFMR7Y\~`}\M7Ej i wkHHQñ`Yla G BSRM G C'Hk[ G I`LNMR7Y\~`}lB îDLNMPjM G YlKdoqîDHSV7HL+c]CnW G z+W\~`c L ¶ O*<JÃ=M7APnQM1<E8/:[HZJz>QÄYg F;O9 Ð ì ß [ APgbO=<J=à M7APnQM7<D8=qT=GÄ.ÁmÄEMIK5OQF ÝîDLNMPjM G YKUo G o7I.c6¯DßanI.}ÜUc]CnWI`LNMR`Yl~.}B Ý ∀ Ý u → v ß ∈ P ßFÝ u ∈ V , v ∈ Ý V ∪ V ß ∗ ß N N S → T U = «Z¨7Õd+W= ¨Z®7S(`ά=¨ ¢W®I¤7¢P¢W¬i¬Q¢¢W5¬=Î ¥¨¬=¨= ¨Z®1XÐʧdZ®I Ь`Wr£WZ®IkZb± efAEgbO*< =M7APnQM1<E8/:[HIJz> Yg F;O JÃ Ä Ð Ñß AET=CL35j(G]ÃL6cT*GÄÁÄDMIK5OQF ÝîDLNMPjM G YKUo G oIc ì ßabI.}c]C'W Ý ∀ Ý u → v ß ∈ P ßQÝbÝ u ∈ V ß ∧ Ý v αX, α ∈ V ∗, X ∈ V N T N ∪ { } ÆB ¿. BdV G HQñ G BSRd øHkV7HL+cPC'W G z+Wl~.c L· ßbß U ¤7¢P¢¬ù¬/¢W×¢W5¬=Î /£d¢Ô=¦¢×=ÚNèd¢¬=¨ß£WZ®IÝ©Í¢W5¬=Î ~Ø U ; =ÈÎ7©7Z¬`WZ1Û9«I¢W§WØ Õ1¢Ý§W¯ c¬=ÎI£W¢bZ®IÎZ¬=h¤d¢Z¬YÚ5 G1APTQC%35jYG L65HZJr> Yg F;9 O ¬Q¢¢WÍ^¬=ΠܢW÷Zb± øHkV7HL+cPC'W G z+Wl~.c Lê ]Ã Ä Ð æÐ\ÜJí Ð b MSÄ f;z+W\~oCnM]pQo7K i û @`BdjanKDk@7B@`YlHLNM]L+_F@`YHvCnanBdcc.anIJBDzNTP~.MPV`®YlV`K}\c7pkW Lê ⊂ L· ⊂ L ¶ ⊂ LÙ . æÐ\ÜZÏÐ b MSÄ ³UMpoKUo G z+W\~o Lê C'anBdcLbHîdc`}sT]L+V`WRdH®a+j®o`ab}lc~7HV`Yl_H®LbHîdc`}sTLNV`Wl_F@CnM]pQo7K i I`zbHSayMPc G BdjM G oUt æÐ\ÜÓÐ ?BAEgbO/GYÄ HPCD>d65HP6cT*GÄ.ÁmÄDM1K5OÄ Ø îDLNMPjM G Yl_H G Ý VT , VN , S, P ß"zbHK7V7HkjHdE7wkH;C'H Ã%APgbO;GÄ(HPCD>d65HP6ü IJBDKc.~ Ç ß V7HkV`W VMI`LNMRd®a G LNMPV7¸wSTP~.V7k@7BI.LNMR7Y\~`}sM ¯DßãSÝ α → β ß ∈ P ⇒ ÝbÝ α S ∧ β ß ∨ Ý |α| ≤ |β| ßnß . 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Æ L+YlV._YI U%FZÃÄÁwK5HIO*qDJ%< R G1<*T*GÄÁ<E8Qj.ÃL6 C2HIJB7~7BDe.Vd^CnM]KPBqcjH G B7~o þ LbBDpk~7k}MIMPVUcPC ézbHk[bHkV`WZ`}lBd@DoC2H anHSa G MRdHkV7Bqp)CnYwpkV.TPj^7_N@6zbHk[bHkV`W1~`W\}lOkWl_N@µIJB~.`}Bd@ tJóyBDpk~`W\}C2HR7[+M]KR G BdjEwHR6~o`V.MPjY\_+KDkj°I.LbBDîDLNMPjBSRTPV`W anHÍzbHk[bWyR`[nHk_F@`VdoöIB~.`}Bd@doöKUM]wk~77LbBSR`V7ÍVMC2HS~`V7Bdc aRo7c7wSY G W\j C'YlwµpkVTPj®^`_N@öR^7ab}lHk~7K i IJB7~``}lBd@ V`Ylwk[bW\_N@ 7LbBSR`V`W IJBda G c7I.c]C'H®anH¸B7~V7HnC'V.Ywk[+W 7LbBSR7V`DEMw®abH¸~`Bda G MPV7HkjHKz+Hk[nHkV.W`}lBd@DoV7HnCRo7[+[bW 7LbBSR`V7DE G CFt`@.}Hk~M]V`kjc zbHk[bHkV`W¤t ± o`V.MPjY\_+KDI`LbBDîDLNMPjBSRTPV`W }lpHIJBdc7wkW G K zbHk[nHSV`W `}lBd@EK G HLbanHpk~MC'W ed^ G zbHS[bY G HS}lV7IJBdc7pHIJBdjMP}^7j eMP_NK G LNMP_+K7YlV7îDHSjtD?A}lîDBDL+Y G jc`a ± Æ C2HvR7[NM]KRU^7LNM]pkV7vLbo7_N@.}HnCn[bW¤EdjTAIJBd}o7V7BdjY\TP}lV.W`OSM]abBSRDBdcab}lBPwSY G Bda G ÝV`HnC'OSM]a G nC'Y zNTP~`c O Ý N ê ßFE"IJM]jQÔ+BSRTmV.T]LbB7OV7Bda G C2H G o7I.Y\_+Kdo O Ý N · ßFt õ Lno`_N@.}HkV.WvR^IJB7O G cúabHµ~7Bda+TP@`V`H pMm_QHSVUcöIJBdc`wkY G W IJBdjB7_V`¸IMPj G YKqc`K}sTP~.TPV`WBDIM]KDBSRM]V`¸RUo`c7wkWRUMPVd^7_N@ jHpSYxR^7ab}lHk~7K i V.MV`YwS[bWl_F@7LbBSR`V`Wl_F@t Ä <%à j(Vd<=eA7Là 6ÁDÄ M1K5H çJÐ{Ó.æ Ð 35<=J }lBD@D M kP³PH;~T]V`B N BDe~7k}\V`WlKPBSR^7_F@jM G Yl_ A ¶ E A· E . . . E A E]_F@`_QHSjH;anIJB7OW G M G C2HnCnYl_F@abBdc`OY\V A ¶ A· . . . A E pkVTPjH;C'HnC'Y\_N@LbBDpkjkLno pÙ E p ¶ E p· E . . . E p t KDBd}HSj C'H¸R7@7NB7~`Vd^7j#c7pSTkRDBDLbKDBSRUTPV.Wlj G Bd@7B G BabBDc.OYlVcjY\V`NY jMP}lYpkBSRUM G IJB7OQH G V.TPanBDeJHkV.W7C2Hk~`V`B G }\YxR^7_F@NI`LnR7K i jM G Y\_Pt æ Hk[nHSV`SW k ± H.Vc]C2HSjH@`B~.V7B G o CnM]KPBqjYlV.YljTP}\V`W IBOQH G V.TPabBDeJHkV`WZI`LnRK i Vc G VD^I`LbBqc7L+OHkV`WanBdc`OY\VUc M I,J J I B n a D B J e ; ' C 7 ~ d B . c _ l W F _ @ j M l Y _ J I 7 B O \ W . V M ' C H G G Hk~o J M]w AJ I− ¶ . s c.~7HkjH¸IBDa G c7I.V`¸IJBOkW G M G MI,J IJB7~`}H ILbBda BDc._Wl@`B AHJ c7, K}sTP~.M A~7 ) ¶ B . ~ 7 V B o . e ` c ` ~ k H j G G G BjM G Y\_Qé H Ô Ç ..N, Ç ..N Õt Æ LnR`V`WzNTP~7HKBDe.a+MP~.WljHVc }sMPjY"ÝpnC'HQR7V`I. 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anBDe E`CbM]K6pkHa G L+BDjca®L i pkVd^7jIJBO G HSja'o`V i c7pS} i c`~7k}sM G eYlV.T]L+V.WSk KUM]wk~^mc7pHk}ec`~7HBDe.a+MP@`BSRUM G c`KdM]pSM G Hk} V.MI.LnR7V.Wl@7Ba'o`V.MMV.Ma'Rdk@7Be.LNM G LNM7t U ZR WÎZÛ¥Õ1¢zS ©Þ°E¨Z®7Ïb± Z 3: !9\ : ¬Q¢W¬YÚÞ`b¡¡W°PÏb§7± ¢W®IÖW¦Wעͬ=¨ hÛÔ= Ê7Õ1¢ùZWS^®IZ ¤ äbä ª7ÎI£WWÊt«Z¨=5 ÐÏ`¤£¢W *£¨ $׶¸*3&y/f'/'$)y* v) /9¸×ìy! u B G YxRMP_QH k"K HSrsHK G YR7V.WyY\jI.}lHkjHkV G MP_Y ± Y C2K7a G LbBSRMmMP}lîPBDL+Y G jc eUo7_F@7Bdjè_F@ G k}\Yy~.M G BSRdBdc a G LNc7K G c7L+cöa}HkI.[bW\jY MPjBDL G YlpBSRUMPVd^7jY7_QHkVMPjYBDIJHkLNMP_W`V7HwvjT)BDeUo7OQHbC'V.T¸@.MP}l~.M¸V7HeJB¸IJBd}lH k ULAPHbG1AÄ(VdA O=AbF ݤabV`WlwHkV`W`@`B~.V7B G oK}lW\OQH I`LnR7Kc E7R ± tM]}lî.t7Rpk~TP}HkV`Bda G ß"R O Ý Ç ß;M Abn/M7GÄYHZM ÁtKà ݲRoC'jc G WI`LnR7KcavV`HnC'jHkV`[bW\jÖK7}lW\OQHkjß3R O ݤ}lBDî nßFt çJÐs×.ÜZÐ 2 AbÃLK5HbA C2H¸~`H.V7BRUTPVCbM]KPBa G LbBdjÖanHka G TRM]C'Wl_kWJpKDBPz+HkV7H®M)C2Hk@7B~` G W ÝIJB7~ à <Jt Á K5jY3Là 6VWM1G1<JÁ [ K% a G LbBdj i ßFt ¿ M]wk~7^me.Y\V7BdBjiYsTP}lV`Wa G 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H, BC2HSi−@7Bµ¶ ano7V i t Ý=³DY\VD^IJBd@.}Hk;~ k B anHka G TRUTpH~RdBdcY\V`a G MPV._W B ¶ MpkW\anKUTanH®p®V`Y\_N@BDIJHkLNMP_Wa+}xo G Wtxß Æ }\M G mW k i i− |Bi | ï¯ i C2H®IJB7OQH G C2HS@7Bano7V i E p1jYU VWM7G1<JÁùC C2H®zNTP~KDBDzbHkV7Hdt çJÐs×JáÐ[ KÃ%<ÁwK5j*3%à 6cJ*Ä 35UÄ s YlV`BdjY\TP}\V`W@.MP}l~MC'H)jV`BPwSYlV.M¸e.Y\V7BdjYsTP}lV`W\_N@a G LbBdj i L i pSVD^`_N@zFT]~ i M¸c7KUM]pSM G Hk} u â c7KdM]pSc]C'W\_WV.M¸KPBDzbHkV ayV7HnCnjHkV.[bWljÛK}\WlOQHkjÖR@.MP}\~7Dt u V7BDwkY\V.Ma G LbBdj i anH®LbHI`LbHkpHkV G cPC2H®IJBd}HSjÛYlV.~7HQñ7BSRUMPVd^7jÛzFT]~`Hkjt Ä eK%à <Jw Á K5j*3Là 6cJYÄ 35U1 çJÐs×æ Ð ´ R APGYÄ HbAµÃZ ÁYÄ O*A J%AUÄ R x kÅ o G RDBDz+W [email protected]}l~.cBDe.a+MP@c]C'W\_WIJBdc7pH¸I`LbRDHK x t · }lBDwkY G Bda G C'HI.zbHKdRM]I.YRD O Ý Ç ßFt Á AEG1T*AQ SÅ · }Bdc`OWv~Rd@.MP}l~7oô~7BC2Hk~`V`Dt c.V7îdc]C2Ha G HbC'V7CnM]KDBÍeYlVTLNV`W;a+OW G TPV`mW k BDe.aNM]@c]C'W }\Y @.MP}l~oͯHa G ¶Lb,BdHj·oa G HnC'V`k@7BqzNTP~`c i E G M]KanHa+}lY C'W1~7B Ç a G LbBdjc zNTP~`c i Ç Ý²IBDa G c7I.c]C'HanHB7~6V7HbC'jHkV [bWl@`BzNTP~`cµK6V7HnCRd G [bW\jcJßFt u â òanHV.MPa G MkR7W V.MqjHkV`[bW1pKPBDzbHSV i BDeJBdcµ@.MP}\~t · }BDwkY G BDa G C2H ݤ}BDî ßNt g ñ`Yla G cPC2H)Y`}\WlVTARM]L+Y\MPV G MI`LNMP_cPC'Wl_kW7R Ý Ç ß kPIJBRDBd}\W`abH;R`Wl_Hya G LbBdj i a G HnCnV7k@7B®zFT]~.cݤc7w)c7K}sTP~.OM]C'W.anH)n~7B anHpkVMPjcEV7H)IBD}lHß"MjB7~`Yl`K7c]C2HanH APOnQM1G(Ä HZM t Á Kà G M]KJE7M]eUoKDBdV7pBd}\Yl~`BSRUMP}sM@MP}l~`cq~7Ba G MR`cEUK~o®C2H KdM]wk~7^qzFT]~pSMPa G Bdc7IHkVV7HbCRU^`[nHvC'Hk~`V`W\j#a G LbBdjHkjݤ}pH¸R O Ý}lBDî nßFE`IJBdjB7_WIJBdjB7_V7S@7BIJBd}HßFt AbnQM1G( ÄHM w Á KÙà SÅ o]C'jH¸p®@.MP}\~oI`LnRdHKayV7HnC'jHkV`[+WljÖK7}lW\OQHkjt õ H®a G LbBdjc E.V.MK G HLn^c7KdM]pSc]C2H u â ïanH)B7~ G [email protected])KDBDzbHkVEOW\jwyR7pkV`YlKV`BDcV7BSRdAa G LbBdjo BÙ , . . . , Bj− ¶ t õ V`Y\_N@qanBH)jRUo G RdBDz+WJV7BSRT@.MP}\~.M Mc`~7k}sTabH w }BDî t Á APG1T*A Ð · }lBDwkY G Bda G C2H ݤ}lBPî ßFE`I`LbB G BDwH K[ à VdAEGdME H, x SÅ }lBDwkWD~`[email protected]}\~o¸V`BSORU^¸I`LnRdnHK x t â jI.}lHkjj HS≤V G c]C2H"· abnH>I`z+WKUM]pHkj ߢWYb¢ U H Û*`¨I« ¢}°Y¢ ¨ U xZtZb± ?)jBDL G YpBSRMPV.Tab}lBDwkY G Bda G C'H O Ý Ç ßFt ÷ì { jYUÀC%gP3SC çJÐs×çÐv K5ef<JÃÄ(HbHPKSJ%<tJÄY35U1Ä YleJBdV.MP__Y\@[email protected]}\~.MvC2H)e.Y\V7BdjYsTP}lV`[email protected]}\~.M®IJBdc7wkWRUM]C'W\_WJ}lW\VD^ ÁwAPG1T*A EDRdH)K G HLbAabHAjBd@7BdcRo7abKdo G BSRM G YDCnYlV7 V`Hwe.YlV`BdjY\TP}\V`W a G LbBdj®odtMR7W\_AC2HI`z+Y\~.TPV.MqBPIHLNMP_QH U%AEHbG1AUÄYVdA O*APF9 H, x, δ EK G HkLNTqabV.WwkW K}\WlOI.LnRK7c x B@`B~.V7B G c δ t³PHYljI}HkjHkV G BSRTPV.M G M]K G YB k Ç ß · V`WlwkWljH¸K7}lW\O¸I`LnR7Kc B t ¯Dß Æ B7~`a G LbBdj aKPBDzbHSV7Hkj x x δB7~7z+WlpkV7HkjHMCnM]KDBa+MPjBda G M G Vd^6a G LbBdj@7BI`z+Y\~.TPjHK Bda G M G V`Wlja G LbBdj i j @.MP}l~oÝIJBdc7wdt.anH®}\WlVTRM]L+Y\MPV G M7E G M]KwH®V7HRUMP~`W¤E`K7~o7w®c`w G MPjÛa G LbBdjÛa G HbC'V7k@`BzNTP~`cC2HßFt ì ß Ø ~ÍKUM]wk~7S@7BR7L+_N@`Bd}lc v jBd@7BdcÍeU^ G B7~7z+WlpkVUc G oV7HnCR^7[bH~RMa'o`V7BSRdDt Æ BB7~7z+WlpkVUc G W>~7LNc`@7k@`B a'o`V.M B~`z+WpkV`HkjH"IJB7~`a G LbBdj|aZKDBDzbHkV7Hkj v B7~vC2HS@7B)LbB~.YlOQHdt OHk}Hkj G Bd@7B G ByBDIJM G zbHSV`WkC2H"pSM]C'Y\a G Y G ~7Bda G M G HSOV7Bdc Á KÃ Ð Æ }sM G WE`wH¸I`z+Y~7B7~7LbwkHkV`W þ [+WzbK7*c a G LbBdj i E7K G HkLNTV.TPjÖpSMCnYla G W}lBDîUM]L+Y G jY\_+KDBdcab}lBPwSY G Bda G APnQM1G(Ä HZM w G Bd@`B G BI.LNMR7Y\~`}sMjTqKUM]wk~^a G LbBdjzFT]~.c i RDH YeJBdV.MP__kYl@7B @MP}l~7RDHS}lYlKPBda G MP}lHkanIB β i I`LbB V7nCbM]KP Çt β> à jw Á OÄÅÆ zbHSa G BDwH U%AEHbG1AUYÄ VdA O*APF j i wkH)RoURdBD}sM G KUMPanKUTP~`cqB7~7zbHpTRUTPV.WEC'HC2HnC'W MPjBDL G YpBRUMPV.T_HkV.M o <=gU[ Ý F ß t Ç O 3: !f! : " h+¥¸'&y9* ·d çJÐs×ê Ð 35<=JÄ û W\}Hkj#`}lBd@DoC'H¸I.LbBR7a G c`I I ݤYlV.a G MPV`_Y .}Bd@Doß"Ro7~M G `}lBD@`BdcabIJHk_Yl`KDBSRUMPVd^qR^7a G c7I J f Ý I ßFt <*gPJ%<(u UL<E8JY Ä HP6 R G1<*e35qÁ C2H`}[email protected]'W\jw¸RU^`a G c7IJHSj C2H?A ظä g t çJÐs×ë Ð õ/UL<E8=jLà 6f8[VWM1C R ¿ M]wk~7BdcYlV.a G MPV`_YI`LbBDe.}lkjc pSM]ZK 7~`cPC2HkjHCbM]KPBab}lBSRDBp®M]eJHk_QHS~o ð Ç ∗ t Ø pSV.MPOjH Ý ßZCnM]pQoKR7[bHk_N@ K 7~ i Y\V`a G MPV`_W.I`LbBDe.}lkjc Q M¸Q~.TP}lH L Ý Qß CnM]pQo7KR7[bHk_N@KZ7~ i Y\V`a G MPV.{_W., a>}B7~7IJBSRdk~.W.?A LØ QM L Ý Qß CbM]pQoK N R`[nHk_F@K 7~ i YlV.a G MPV`_W avB~`IJBSRDS~`W g t Y Æ B G Bdj#C'HqLbBDpk@7B7~7BSRMP_W"I.LbBDe.}lkj G B G wCnM]KDBµLbBDpk@7B7~`V`BDc G I`LbBÍ~.MPVd^mK ~ Y\V`a G MPV`_H x Epk~.M x ∈ L Ý Q ß Y V`HeJB Ý ß Ý Æ zbHk~7IBPK7}\TP~`HnC'jHdEJwkHc`jW\jHLbBDpk@7B7~`V`Bdc G EJpk~.M x ∈ L Ý QßFE G CFtpk~.MK 7~`c]C'HV7nCbM]KPBdc Y\V`a G MPV`x_kY∈E7RLIJQBd}xo`NV7Bd. jYsTP}lV.Wlj#OkMPanH¸Rpk@.}Hk~`HkjÛK |x| txß Á CfüadYÄ Vd<E8QjV735<*ÿPKNM1<*VWM çJÐ\ÜJí Ð { AP4dA7%à 6 R G1<=eL35q7z ± H G HkL+jYlV.Yla G Y\_+KU^f · a®I.LbBDîPLFM]jHkj M p1AE476 R G1<=eL35q7Á Q EZI`LNTRdK~7owR^IJB7OQH G M abKPBdV`OkWI`L+BKUM]wk~^ R`a G c7I x ∈ ð ∗ MI}\M G W L Ý Qß L Ý M ßF2t _;MPabBSRUTa+}BDwkY G Bda G u C'H®~TPV.Mr{c.V7KD_kW Y Ý ß jMSñ {m| Ý ∃x ∈ ð ∗ ß |x| n, RU^7IJB7OQH G M V.MR`a G c7Ic x abKPBdV`OkWIJB m KULbB7_W\_N@ }. TM n g ñ7Y\a G c]C'H }\YIJBd}o7V7Bdj G M]KDBSRU^dE wkH Ý ß Ý ß Ý ßNE IJMKÍabH V.M]pQ^RUB T R <=3^FZ%à <Jt Á K5j*3%à 6 ± f · I.LbB p ∀n TM n ≤ p n M îDLNMPjt Æ LbBµV7HS~7H G HL+jYlV`Y\a G Y\_+KDf · ~`H.Vc]C2HkjHMPVM]}lBDîdYl_NKd/o k e.c`~`HIJB7OQH G KULbBDK i R ¬Q¢5¤«1 ¨ 5èÚ^ I.z+Y CnWljMC'W\_W\j R^IJB7O G c6MIJBd}lBDwkWljH T Ý nß Ç RI`z+WlIMP~7DEwHV7HHQñ`mYla G c]C2HwSTP~`V`ab}lBSRdB x ~`k}KUo n EK G HkLbyC2HI`z+Y C'WljTPV7B ÝIJBDpkV t k.V7HkIJBDwSMP~`c]C'HkjHDMEM]eUoR^IJB7OQH G anKDBdV`OY\} YI`LbBV7HkI`z+Y C'WljMPV7YlV.a G MPV`_QHßFt Ä ? o çJÐ\ÜZÏÐ c pZ65U[F o Æ LbBDe.}lkj C2H®RdH G z+W\~7 Æ EI`LNTRd®K7~o7wHQñ7Y\a G c]C'HIJBd}o7V7BdjYsTP}lV.W ± f · I`L+BPîDLNMPj M zbHS[bW\_W Q. Æ LbBDe.}Sj C2H®RDH G z+W\~7® Æ E`I`LNTkRD®K~7ow®HQñ`Yla G cPC2H®IJBd}xo`V7BdjYsTP}lV`W Af · I`LbBDîDLNMPj M zbHS[bW\_W Q. çJÐ\ÜÓÐ ] 3NM7AEG]ÃZDÄ M1K^8Là 69ULAP Là K5HbA? o Æ LbB I`LNM]K G Y\_+KD.OQHk}xoC2HR`@7B7~`V7bC'[bW>HKUR7YRUMP}lHkV G V`W3jB7~7Hk}>Af · k I`z+Y\~.TPjH~.MP}\[bW>ITPanK7c BDLNT]Kc.}lc`j Ma G LbBDC I.LNMP_c]C2HRdH¯r²T]pSWl_N;@ k V7HnC2I.LnRDHV7Hk~7H G HkL+jY\V`Yla G Yl_+KUoÍ@.TP~.TµÝpSM]IWl[nHa+}BSRdBp {ð , Ç }∗ ~`BBDLNT]Kc`}sMdßAMRÍ~7L+c`@7 rTpSY P¢¢WÍ^¬Y^£WSm¡«1Ï BSRdz+WBDe.a+MP@ BDLNT]Kc.}\M6Ý G CQt ± f · anHR`a G c7IJHSj#I i RdB7~`V`WZR`a G c7I6I.}\c`a)BDe.aNMP@BDLNT]K7c`}\MdßFt }lBD@M®C'H G Hk~7o6 Æ EJIJBDKc`~qC'abjHR IJBd}o7V7BdjY\TP}\V`WljOkMPabHa+_N@`BPIV`YLbBDpS@7B7~`V7Bdc G EUC'Hka G }lY ~.MPVD^ þ _QHL G Y.KdT G ÝBDe.aNMP@BDLNT]Kc`}sMdßC2H®I.}\M G Vd^7jÛzbHk[nHSV`Wlj#`}lBD@dodt Á K5j*3Là 6 R p1Ab8=<;ULKNM1AE3%à <*VM çJÐ\ÜJ× Ð o <=3^F[à <w k ð Ç ∗ ð Ç ∗ C'HIJBd}o7V`BDjY\TP}\V7RUo7OkWla+}lY G HS}lV.T7E1HQñ`Yla G cPC2H }\Y"IJBd}o7V7Bdj M6MP}îDBDL+Y G jc`a c`V`KD_QH G M]KDBSRU^dESwkFH3I`Lb{B)KU, MwS}~^¸→R7a G {c7I , x}∈ {ð , Ç }∗ ~TRUTvRU^7a G c7I f Ý xßROkMPanHV7HnC2RU^`[nH f Ý |x| ßNt æ HkKV7pHSjHDESwHCnM]pQo7K LA¶ C'¥H R <=3^FZ%à <Jt Á K5jY3àR p1AP8=</UKNM1AE3Qà : V.MyCnM]pQo7K L· Ý L ¶ ∝ L· ßFEUIJBDK7c`~HQñ`Yla G cPC2HAIBD}o7V`BdjY\TP}\V7)Ro7OkWlab}\Y G Hk}\V.T r²c`V7Kd_QH G M]KPBSRT7E`wH Ý ∀x ∈ {ð , Ç }∗ ßQÝ x ∈ L ¶ ≡ f Ý x ß ∈ L· ß . ÷Ñ çJÐ\ÜÜZÐ ? o uÈMSÂEÿbO*q R G1<*e35qÁrF Æ bL BDe.}lkj Q C'H® Æ G wKU^dE`I`LNTRd®K~o7wÝ ∀Q0 ∈ N P ß L Ý Q0 ß ∝ L Ý Q ß . Y Y çJÐ\ÜáÐ ? o uta R 3Ã%<=VWM Æ bL BDe.}lkj Q C'H® Æ 7I.}\VD^UE`I`LNTkRD®K~7ow Q ∈ N P M Q C2H Æ G kwKd^Ut çÐÏJÏ.ФÏ.Ð o pI65O;3(Ä U%F? o uka R 3ÃQ:;HZJ"aL35<=J çJÐ\ÜJæ Ð 3SK5OÄ ³DH~.TPVV7HBDL+YlHkV G BSRMPVD^îDLNMPr G Ý V, E ß3MOWla+}B k ∈ õ t Ø ea+MP@UcPC2H G K}\YK7cÍݤ7I}lVd^IJB7~7îDLNMPr+ß RdHk}\YKDBda G Y k Ä çJÐ\ÜçÐ ;] c ÈV R 3Là KNM7AE3¤[à <=VWMZ ³DHv~.TPV.M¸rsBDL+jc.}H V.MAI`L+BDjV7kVd^7_F@ RKDBdV]Cnc`V7K G YR7V.W`V`BDL+jTP}lV.W7r{BDL+jDt g ñ7Y\a G c]C'H;I.LNMR7~`YRdBDa G V`W Bd@7B7~`V`B_HkV`WI`LbBdjFV7kVd^7_N@ E`I`LbBK G HkLb xF¶ ,Ý .x.¶ .,,.x. n. , x 8ß Ç Ä n çJÐ\ÜJê Ð o G1<*e35q7Á <*efHZJ%</U Là 6SJ%<HbAEVWM1CD>d65HP6SJ%< ³DH~.TPVµ7I.}\VD^µV7HBDL+YlHkV G BSRMPVD^6îDLNMPr a@7LNMPVMPjYZBd@`B~`V`B_HkVD^`jY1V7HkpST]IJBDL+VD^`jYZRM]@MPjY MOW\ab}lB w ∈ ó®t g ñ7Y\a G c]C'H¸R ¶MPjY\} G BdV7BSR`anKUTKUL+c7wSGV`Yl_H¸RUTP@doV`HnCR^7[bH Ä G w çJÐ\ÜJë Ð <=C%abA M R <;U1Á%à <*ÿPKQà F ³DH¸~TPV.MjV7BDwkY\V.MI.z+YLbBDpHSVD^`_N@OkWlanHS} S {a ¶ , . . . , a } MI`zNYLbBDpHSV7®OWla+}B b t g ñ7Y\a G c]C'H G MKDBSRT S 0 ⊆ S E7wkH P ai ∈S 0 ai b n Ä ÷D÷ ®frnmýAn ÐWB÷ ± c.MP}\Y G MMC'HnC'W~ i a+}Hk~`Kdodt ML+KdMPanBRDB}HkjjM7t · Y\jI.}lHQñBSRd)jH G B7~o}lY\V7HST]L+V`W\@7BI`L+BPîDLNMPjBSRUTPV.WU KUL+Y G kL+Y\M7E G RM]L G M]e.c`}lKdodEJMP}îDBDL+Y G jc`ayMAC'Hk@7BKPBdV7HSOV7Bda G E`IJBDI.Y\avjV7BDwkY\VDoBDI G YljTP}lV`W\_N@zbHk[bHkV`W¤t ± BDI`LNMR`V`WI`LbBDe}kjt U ¨Í/¨ m¦}SrbBݨ ¢W`¨ SN«1ÏkZb± ¦}Ú5®ZÖ5¤è}Úm¡W°zÜ¢¢¡W°w§W¯I®I¨ B~^¬Q¢ÎZ¬YÚL= &YZ ¨ZÝZ®IÎZ¬YÚc£¨Z`I£¨ S¬Y¯I Z I«1E°(¢W ¨I«ISYΠЬYÚm¡W°/7Õ7¨bb¨Z®I¡Úm¡W°¤d¢Ê`£Z(ª7ÎI£WÙI«1P°P YbZ5SÍϨԤ7¢5¤m¡W°£W 7ÕSÊI£WRW±O¨Z®7Úm¡Ý§WÏZ; 7©£¨I°/7Õ7¨bbZ®I¨D^ ¬Y¯b¡W°©¬=¨ I£WSÚ©¬=¨bª¬QÖÞ©¢ZP«ZZ®IÎZ¬Q± i ¦¢£WÊ£¢Í®Ý£Z*§dZ}«ZZ®7¯ ¡W°B«ZZ^£}Úm¡W°¬=¨¤dbZ¤d¢Z5¬=¡^Û9«I¢W¦Ú©W«ZZEè¢5¤WÚ*¤d¢W¬ ~^¬Q¢ÎZ}«Z¨ß¬YS¡9¤5` ¬ W°DP± i ÊSDÝ«Z¨=5 Щ7¨Z¦ ¨7©W¤W¬Q¢©ßÖ¬/Ö¬QZÝ ¤d±Y/bY¢Ë£WʨZ¯b¡W°/7Õ7¨bb¨Z®d«7Ø*± êФÏ.Ðo <Q35< R G1<*VWM1<*G I`LbBV`nCnM]KD w~ ∈ Rn, t ∈ R C'H {x ∈ Rn k wx ~ ≤ t} êÐ{ÓÐ <JÃQ8=APnZÃL6 R <=3^F=AEULG C'H¸I.L i V`YlKqKPBdV7HSOV7jV`[email protected]}BDI`LbBda G BDL i t êÐs×Ð <JQà 8=APnZÃL6 R <=3^F/M7< R C'H¸BdjHpHkVd^qIJBd}oDHS~7Lkt êÐ\Ü Ð Â MÄ C'H¸IJBd}o G BDII.LNTRd¸K7~owvC'H¸KDBdVDRdHQñ7V.WljÛBDeJM]}lHkjÛV`nCnM]KD®KPBdV7HSOV7jV`BDwkYlVdoqeJB7~ i t P & ' ×$ +#ì $ f/ ¸n$=]! ;: ! : ,.$'h Á jYG]Là 63 Ä ULC%j*3Là 6aL35<=J Ä 3SK%à AEj(G]Là 6SJ%< R G1<=T*GÄ Á <E8=jLà 6 êÐ{áÐ o GIK u T]jH®OW\ab}\M c , a , b Ý α Ç , . . . , n r Ç , . . . , mßc`abIJBDzNTP~.MPV.T~7BV.TPa+}Hk~.c]C'W\_W\@7Bab_F@7kjM G c α rα r c¶ a ¶§¶ ... ... am ¶ . . . amn ttt Á ]à ZÄ Ã x∈M ß {x ∈ En | ttt b¶ . bm R G1<*T*G jMñ ttt ÄÁw<E8=jÃ%6 ݲRV`BPLNjTP}lV.Wlj G RM]L+cßC2H®LbBSR7V.Yl_QH ]à o GIK jYG L6wa%35<QJ w3SK %APjYG L6SJ[< M¶ cn a¶ n n X Ý ß K7~7H f Ý xß {f x }, n X cα x α , α ¶ ð arα xα ≤ br , xα ≥ Ý α Ç , . . . , n r Ç , . . . , m ß }. Ýf xßanHVM]pQ^URT a[abAD35<E8=j l CαÃ% O*HPA t õ M G W\j_QB UC%jY3ÃL6NaL35<=JÄX3SKÃ%AEj(G]ÃL6SJ%< _F@7BSRT]V.WpkV.MPOHkV`W{ß`}[email protected] m jYlV {g Ý y ß }, K~7H g Ý y ß X b y , ¶ y∈M ú M· {y ∈ Em | m X arα yr ≥ cα , yr ≥ r ð Ä.Áw<E8=jÃL6 C'HÝI`zNY pSM R G1<*T=G r r ¶ Ý α Ç , . . . , n r Ç , . . . , m ß }. u H pkYBPI G YljTP}\V`W\jY3zbHS[nHkV`W\jYr I`L+YljT]L+V`W;Mµ~`c.TP}\V`W;`}Bd@do }\YlV`HST]L+V`W\@7BÍI`LbBDîDLNMPjBSRUTPV`W3Hñ7Y\a G c]C2HanBdcR`Yla+}Bda G E K G HLNTanHV.M]pQ^RUTÝR GIKÃ%HPK R UCÄ*3SKNMF Ð Á OÄ êÐsæÐo <=gU[à jw }lBD@doÍ}pkHpM]I.a+M G Ya G LNc`OV7bC'Y1RdHK G BDLbBSRd kI.L+YljTLNV`WjMñ K7~7H M ¶ {~x ∈ Rn|A~x ≤ ~b, ~x ≥ ð }, c~x, ß ~ ~.c.TP}lV`WZjY\V ~b~y, K7~7H M· {y ∈ Rm |AT ~y ≥ ~c, ~y ≥ ð M }. Mú êвçJÐ o GIK[à HPK R UCZ*Ä 3SKNMF )Hk_F@DÔ®jV7BDwSYlVdo CnanBdcµ~7Hk.V7BSRTPVDoµa G HbC'V7ACnM]KDBqR B~.a G tà7tx÷MC'anBdcµV`HI`LNT]pk~.V7Dt Æ B G Bdj HQñ`Yla G cPC'W M · M]KJE`wH eJB7~o xÙ ∈ M ¶ , yMÙ ∈¶ , M G · Ý ß ãjMñ {f Ý xß }, g Ý yÙ ß jY\V {g Ý y ß }, f Ý xÙ ß g Ý yÙ ß . f xÙ ¶ x∈M ß ÷PÕ y∈M ú êÐsêÐ2 %V735APULAEO ÝLbHkabI t ßBDI G YljTP}lV`W\jzbHk[nHkV.WljI.L+YljTLNV`WEZLbHkanIZtZ~.c.TP}lV`W"`}lBd@Dom}lY\V7HST]L+V.Wl@`B ³DH }lY>eJB7~ I.LbBDîPLFM]jBSRUxTPÙ V.∈WEUIJMB G ¶BdjòHQñ`Yla G ycPÙC2H ∈G M wABD· I G Y\jTP}lV.WzbHk[nHSV`W yÙ `}lBd@Doq~`c.TP}\V`WELbHkabI t xÙ `}lBd@DoI`L+Y\jT]L+V`W G M]KJEwH Ý ß g Ý yÙ ß . f xÙ êÐsëÐ 2 %V735APULAEO ³DH }lY ð ð.Ý Ç ß IJB G BdjÒHQñ`Yla G c]C'WBDI G YljTP}\V`WJzbHk[bHkV`W xÙ M yÙ I`L+Y\jT]L+V`WM Ç ~.c.TP}lV`bWZr `≥}Bd@d,oa}lrαY\Vt`≥I.LbBDîDrLNMPjBS,R. TP. .V`,W mM Iα}\M G W f .Ý x. .Ù ,ß n , g Ý yÙ ß . êФÏí Ð 2 [V135APULAPO ³DHka G }\YwH)r²c`V7Kd_QH Ý ß LbHSanI t Ý ßJC2HAV.M®jV7BDwkY\V7 M· , LbHSanI t M ¶ pk~7Bd}sMÝLbHkanIZtDpk@7BDLNMdßV7HBdjHpkHkV.T7EdIJB G Bdj C'H®jV7BDwkYlVM M ¶ g, LbyHkab,I t M· fI`xLFTpS~`V.T7t ;: : />,`/ ·U%* &"* ¸ 5 -ò-0/ b¨ èÚ5 ¢ S¤£Z7©¬=¨bª7Z®IÎZ¬YϧdbZÏ® 7©`ÖW¬`WW = I£WÊZ¤d¨I«Z®Z¢«IÊZÏP±$¢¬*Ú[ÊÔ=¦Ú5~^èhb®ZÖ ¡^Û;«ZZÏdÕ n− D®1Î1ÕWÚ5`¢/ZßÖW¬QÖª7¨I£WW;¢W ¨b¡1¢Þ¬=ÎI£P§7¢W¬YÚ`¨ Sm¡7±ËS¡qWW¬QÖ¬Q¢W¬YÚfÊ`¬Ym¡®7Úm¡WÛf¬Q¢Õf¤7¢W¬`= ÎZ®ZÖ§dbZÏ n ∈R . êФÏÏÐ b MSÄ v (Ä G1OYÄ Vd<E8JÄ ³DHka G }\YwHV7HkLbBSR7V7Bda G PN ð ÝLbHkanIZt PN ðUß1C'HanI.}\V7kVMI.LbBR7[[email protected]~7o x ∈ E , xα ≥ I.LbBK G HLbI.}sM G W PN αc ¶ xarα≤xαð6≤ݲLbHSanI t PN cα x¶ arα U ð ß IJB G Bdj#HQñ7Y\a G c]C'HeJB7~y ∈ En Ç ≥ , r , . . . , m, m α ¶ α α α ¶ α α G M]KJE`wkH¸I.}sM G W M y ≥ ð , X c Ý α Ç , . . . , n r Ç , . . . , mß . a y r rα r α ¶ Ý ß ¬=¨Z®7Úm¡ «I¢W Îz£ÊQ¦ìY¤ÚÔ£ZP£WʨZ®7¬Q¢W Z®d¬QI£mÚ ~x, ð A~x ≤ ~o A ∈ Rn×m , ð ¨I«7ÛLÕ7¢ Z ~c~x ≤ , ~y ≥ ~c AT ~y . êФÏ7ÓÐò AP<ÁAbM7GIK5HIO/:VSÁF[V73 XZHwkW }lY`C'Hk@`}sMPV Rc`pSMRzbHSV7kj#pST]IJBDL+V7SjÛIJBd}BDI`LbBda G BPLNc {~x|~c~x ≤ ð }, IJB G Bdj ~c }HkwkWRC2Hk@.}\MPVUc x ≤ ~o} îDHkV`HLbBSRMPV7kj a{~x¶ ,|A~ ...,a . ± i KdM]p k ± H.Vc]C2HkjH K m≡ {~x ∈ Rm |~x AT ~y, ~y ≥ ð }. Ø G T]pKUMpSV`WE.C2HSa G }lY ~c ∈ K k ± BDKdT]wHkjHDE wH K C'HKPBdVdRDHñ7V`W"jV7BDwkY\V.M7E`C2H G BC2Hk@`}sMPVma¸RLN_N@7Bd}lHkj RÍIJB7OkT G K7cmMC2Hc`pSMRzbHSV.TmÝIJB~.}H~7Hk.V`Y\_QHa®KUM]wk~^`jY ~7RDkjMeJB7~o6BPea+MP@UcPC2HYCnYljY1c7L+OHkV7Bdcµ`abHkO+K7cEC2HS@`}\MPVÍaAKdM]wk~7^7j eJB7~7Hkj ∗ BDe.a+MP@c]C2HY1IJBd}BDI`z+W\jK7c6p R7L+_N@7Bd}\cI`z+Hka G HkV G BµeJB7~Í G HS~o p ≡ {~x ∈ Rn|~x ~x∗t, t ≥ ð }, c`pSMRz+Hk~xV.T6jV tBDe.a+MP@c]C2HaKUM]wk~7Bdc KDBdVDRdHLbîDHkV G V`WIJBda+}Bdc7IV7Bda G W Y7C2HnCnW}\YljY G cßFt Æ LbB~ i KUM]pyabIJBDLbHkj I.zbHk~7IJBDK7}\TP~7HbC'jHdEPwkH ~c 6∈ K. fHk~oRpk~TP}HkV`BDa G d Ý ~c, K ß > ð . Æ LbB G BPwkH d Ý ~c, ~xß ≥ ð , ~x ∈ M C2Hc7pSMR7zbHkV.T7EjTPjH K K r U& ¢«IÊZ Z®ZÖ& LQ ¨ mÚ ^ Ðf= z®dèd¢¡W°P¬=¨ /bZÍÚ^¬(«Z¨ ÊZ / ¢ Z^£m}¤7¢ Ý d ~c, K ß8ïjY\V Ý ~c, ~xß x∈K Ý ≡ d ~c, x~Ù ß Ù k~c − ~x k > ð.Ý ~xÙ ß ∈K ⇒ Ý ð Ý ∗ß Ù ßQÝ Ù ß ~c − ~x > . C'H6c7LNOQHkVmC2Hk~`V`BDpkV.MPOV7dt ¿ ~o7edo G Bdjc G B G Ylw G MK V7HeUo7}lB.E"IM]K ± BDKUT]wHkjHdE>wkH Ù G M]KE ∈RUo7K, wH d Ý ~c, ~x٠߸ dx~Ý ~x, ∈x ßnK°jYlV d Ý ~c, ~xß . Æ B G Bdj eJB~7o.anHkONKdo u Ý ~xÙ , xß ∈ K ÝwkHC2HR ∃x . I } U ^ R T p KDBdVDRdHQñ7V`Bda G YsßjMCnW"R7}sMPa G V7Bda G x∈K Ýd ~c, u Ý ~xÙ , xßbß < d Ý ~c, ~xÙ ß , _QBDwV`HkV`W;jBDwkV7dE1I`LbB G BDwHqR ~7HkK, .V`Y\_Y ~xÙ eUo7}lB jYlV`Y\jc.jÒýR7Yp®BDe.Lkt fHk~7o ~xÙ C2HvC2HS~`YlVd^aycRDHS~7HkV7BdcR`}\MPa G V`Bda G Wt yo`V`WDC2H G zbHkeM®~7BDKUT]pSM G EdwHÝ ~c − ~xÙ ßQÝ ~xÙ − ðUß Ý ~c − ~xÙ ß ð . )HbC2I`LnRdHAcRM]wkc]C'jHDEUwH ~xÙ 6 ð . ± Hk.VUcPC2HkjH IJBd}lBDI`z+W\jKc ÷ ð Ý ~xÙ − ðUß t t ≥ ð } ⊂ K. p ≡ {x ∈ Rn |x Ý G HkV G BRDHkK G BDLyC2HKDBd}lj^V.M u T]jHL+BSR7Y\VUcmc7LNOQHkV7Bdc MeJB7~7HSj pS~.TP}HSV7Bda G B7~ k"Ý Ù ß I.z+WljKcMyC2H G BAC2HS@7BRpk~pT]}lHkV7Bda G EUI.LbB ~cG .BPwkH)R7WljHDEwH x~cÙ C2HAK p c V7~HncC'−e.}lWlxw~HßFt ⊥± TPp}lHjTPjHÝ ~c − ~xÙ ß ⊥ Ý ~xÙ − ðUß M G Hk~7oÝ ~c − ~xÙ ß ð . ³PH }\Y ~xÙ , I.}\M G W G M]KP Ý ~c − ~xÙ ß ~xÙ ð . Ý ∗∗ß ÷DÚ ⇒ ~c − ~x Ä yo`V`WanHka G L+BPCnWljH¸V.MP~7LbBSR`YlVcc7L+OQHkV`BdcRdHK G BDLbHkj Ý ~c − ~xÙ ß3M~7BDKUT]wHkjHdEwH K ⊂ H − ÝI.z+Wla+}lc`[+VD^qpST]IJBDL+Vd^ IJBd}lBDI`LbBda G BDLFßk Ý Ù ßQÝ Ù ß ðUß A ≡ {~x ∈ Rn | ~x − ~x ~c − ~x } ÝI`zNY G BdjÞR7W\jHDE`wkH ~c − ~xÙ ß K ~c ∈ H é , ~7BDKUT]wHkjHdE7wkH K ⊂ H − ≡ {~x ∈ Rn| Ý ~x − ~xÙ ßQÝ ~c − ~xÙ ß ≤ ð }. Æ LbB~ i KUM]panIJBDLbHkjÛI`zbHk~7IBPK7}\T ~`HnC'jHdE`wH ∃~x∗ ∈ K, ~x∗ ∈ H é . Æ B G BdjÝ ~x∗ − ~xÙ ßQÝ ~c − ~xÙ ß > ð . u nC'jHq`abHkO+K7c u Ý ~xÙ , ~x∗ ß ∈ K, RmjV7BDwkYlV`BSRDSjpST]IYlabc u {~x|~x ~xÙ t Ý ~x∗ − ~xÙ ß , t ∈ hð , Ç i} Æ L+B Ý Ù ß3I}\M G W ~x ∈ u ~x , ~x∗ Ý ~x − ~cßQÝ ~x − ~x8ß Ý ~xÙ t Ý ~x∗ − ~xÙ − ~cßQÝ ~xÙ t Ý ~x∗ − ~xÙ − ~c8ß Ý ~xÙ − ~cßQÝ ~xÙ − ~cß ¯7Ý ~xÙ − ~cß t Ý ~x∗ − ~xÙ ß t· Ý ~x∗ − ~xÙ ßQÝ ~x∗ − ~xÙ ß Æ LnR`V`WO}lHkVIJBda+}Hk~.V`Wl@`BRU^7LNM]pkcC2H®jYlV`Y\jHkjE`~7L+c`@d^C2H ð G zbH G WC'H jYlV.Yljc`jt Æ LbB G BI.}sM G W¤E`wH®_QHk}lHK C'H < Ý ~x∗ − ~xÙ ßFÝ ~x∗ − ~xÙ ß3I`L+B~7Bda G M G HkOV7jMP}l t > ð . f<B¸C2H, abIJBDLkE u Ý>~xÙ , ~x∗ ß ∈ K M ~xÙ ~TRUTjYlV.YljT]}\V`W R7pk~.TP}lHkV7Bda G B~ ~c. fZHS~o K ⊂ H − , G Hk~7oI`LbBR7[[email protected] ~x ∈ K I.}\M G W>Ý ~x − ~xÙ ßFÝ ~c − ~xÙ ß ≤ ð . Æ LbBRdBd}e.c ~y Ý e ¶ , . . . , e ß~`Bda G MPV7HkjH ~a ¶ , . . . , ~a ∈ K. · IHk_Y\TP}\V7 a ∈ H − , G Hk~oI.}sM G W n m i Ý ~a − ~xÙ ßQÝ ~c − ~xÙ ß ≤ ð`Ý ∀i Ç , . . . , m ß Ý ∗ ∗ ∗ß i Ý ∗ ß ∧ Ý ∗∗ ß ∧ Ý ∗ ∗ ∗ ß"RdHk~7H®KPHanIJBDL+c t H x ≡ ~c − ~xÙ , Ç ß õ Ý ∗∗ß ⇒ Ý ∗ ∗ ∗ßy~7Bda G MPV7HkjH ~ai Ý ~c − ~xÙ ß ≤ ð ∀i, G CQt A Ý ~c − ~xÙ ß ≤ ð . Æ BDKc.~BDpSV.MPOWlj ~7Bda G TRTPjHDE7wkH Ax ≤ ~o ¯Dß õ Ý ∗∗ß ⇒ Ý ∗ß~7Bda G MPV`HkjH ~c Ý ~c − ~xÙ ß > ð , G CFt ~cx > ð ⇒ anIJBDLyaÝ Ç ßFt ! É=¢W¬ZØP«Z¨7©Í§WÏ``Ö%§W¯ f®/bI£Wʨ ÖbP§W¦¢Û9¨ Ü¢¤7¢S b¡W°PB¬Q¢£ 7©ES¢~¬Y¯b±O¢¡°(¡7¢×¢Ë°D`¬QÖ«ZbË=¦¢×*£¨ " ¸ /f·7$×'. )ì *9+A,7/;&)&h.+A,7*9¶¥¸1- ;:=8;: RU^7LbBDe_YRoLNT]eJnCnWl_W`C2Hk~`HkVRU^7LbBDeJHK v RjV7BDwka G R7Wl_F@ a ¶ , . . . , a ý éabIJB G zbHke.Y G HS}DE`K G Hz+WIJBDwSMP~`c]CnW v Rc7L+O G ^`_N@jV`BPwSa G R7W\_N@ h ¶ , . . .n, h m VT]K}sM]~7oV.M~`BPI.LNMR7cC2HS~`V7B G KdoqR^LbBDe.Kc v p®jWla G M V ~7B S i j O=<=3Å û Hk}lKPBSRdV.T]K}sMP~oVM~7BDI`LNMR`cjMCnWed^ G jY\V`Y\jTP}lV.Wt Ä U"Å AT]K7}\MP~oVM~7BDI`LNMkR7cL+BDa G Bdc}lY\V7HST]L+V7ayjV`BDwka G R7W\jÛ~7BDI`LNMRdBSRMPV7k@7BpeJBDwkW¤t o p1APU R <*O;3²Y pØ kV.MPOW\jH x V7HpSV.TPj®I`zbHI`LFMRDBSRMPV7jV`BPwSa G R7WRU^7LbBDe`Kc v p V ~7B S . ij Ç , . . . , n U ¡7Ý£d¢Þ®7ÏZ®Z¢©7¢© Vi ¦ iÎbP¢«§Z j xi · . . . xim , i ai x i ¶ V ¶ , . . . , Vn S ¶ , . . . , Sm cij bi x¶ x· i i ... xn ¶ U ¡7Ý£d¢bZ®I¢©1¢b n X ai £W Z1;¢¡¥Z Si m X i ¶ j Ý ∗ß bj ¶ óyBSR7V`Y\_QHÝ ßyabHV.M]p^UR T R </U t Á 6[à OJ Ä APO*<[à <w Á K5HIO*qwG1<D8ZÃ%<E8=j*J=F Ð Æ BDKc.~µV`HI.}sM G W¤EpMRUTP~`W\jH`K G YR7V.Wl@7B RU^7LbBDe_QHDE.I`z+WlIMP∗~`V7anIJB G zbHke.Y G Hk}lHýI`zNWlab}\c`[+V.T_QHSV.M c C2H¸Rwk~7o > ð . û W\}Hkj#`}lBd@DoC'H®VMC'W G jY\V`Y\jc`j#r{c`V7Kd_QH Pn Pijm c x V.M i ¶ M ;: y: S½ {xij ∈ Rn×m | m X j ¶ j xij ¶ ij ij bj , n X i ¶ xij ð ai , xij ≥ }. $'-¹+¥¸ 5O *[&9- 5 *ìy!#¸'$'& 5 >,.&h.)y* )+ ,7*Ev",7/>-0*%&">&. ê ÐÏ7×Ðc 6S35<E8=j@ a%abAE35<D8=j= l CÃ%O=HbA Pn pH¸pM]~TPV`WI`L+Y\jT]L+V`W `}lBd@Do}\YlV t`I`LbBDîDLNMPjBSRTPV`W¤t c.V7KD_H cx α ¶ cα x α ÷Pà ê ÐÏÜ Ð [à <=ÿPKÃÄ R pI6 R C%VWM]Ã=:[HZJXp1AE4dAÃL6 C2HjV7BDwkYlVM pHpSMP~.TPV`WI`L+Y\jT]L+V`W>`}lBd@Do}lY\Vt I.LbBDîDLNMPjBSRT]V.Wt ¿ M]wk~^ÍeJB7~ G G B jV7BDwkY\VDoC2HI`z+W Ic`a G Vd^7jÖz+Hk[nHkV.W.M }Bd@DoUt Á jY3Là 6cp1AP4dA7Ã%6 ê ÐÏ`áÐ ´ R M1Kw I`LbBAK G HLb^®I.}\M G W cxBDI G ≤ cx ∀x ∈ M, V.M]pQ^RUTPjH < R MIKÁj*3ÃL6Áçp1AP4dA7ÃL6Á <*efAPHUÃ%q s B7~ xBDI G ∈ M, aL35<=JQFX3SKà РR G1<*T=GÄ.w Á <E8=jLà 6 Ð ê ÐÏ7æÐ 35<=JÄ d o 8XG1<E8ZLà K5Hb<E8QqÁ M78JYÄ GIC jYlV K7~7H M {x ∈ RnkAx b, x ≥ ð }, A ∈ Rm×n, Ç ≤ m < n, b ≥ ~o, b ∈ Rm x∈M cx, ê ÐÏ.çJÐ ?YÄ ULG1<E8[KÃÄ Æ B7~7I.LbBda G BDLy~`Y\jHkV7pkH n − Ç V.M]pQ^RUTPjH Ã(Ä ULG1<E8[K%à <QC R Rn. ê ÐÏ7êÐ <JQà 8=Abn%à 6Á%à <*ÿPKÃÄ u V7BDwkY\VUc ⊂ Rn V.M]pQRdHkjH O*<JQà 8=APnZLà 6ü C2Hka G }lYlwH G MPjÛavKdM]wk~7^7jYZ~RdkjMeB~7oqIJM G zNWY KdM]wk~7^eJB7~ .anHkONKdo G o G BeJBM ~7oabIJBPCnc]C'W\_Wt ê ÐÏ7ëÐo <=35< R G1<=VWM7<*G Æ LbBKUM]wk~7BdcV.MP~`LbBSR7Y\VUc R ¶ {~x ∈ Rn|~a · ~x b, ~a 6 ~o} V.M]pQ^URTPjHjV`BPwSYlVc n− H é ≡ {~x ∈ Rn |~a · ~x ≥ b} K7}\MP~`Vd^7jÖݲI.LNMRU^`jß c`pSMRzbHSVD^7j%IBD}lBDI`LbBda G BDLbHSj Rn U /I«1Y§WÏ¥¬Q¢W Z®7¬=I£W[§WÏZ¨ÞI£WS ÎIÛQ¬Q¢7§WÏ D§WÏ¥b©7¨Z®7¦ ¢W¬Y¯IÛ /I«1Y§WϧWÏZ¨/¨bª¬QÖÛf¬Q¢7§WÏZ%§WÏÝ«I ¨bZ¬Y¯kZb± RUo]CnMP~7z+cPC2H anKUMP}\T]L+V`WZabBDc.OYlV tóvBSR`V`Yl_H ~a · ~x ≥ b îDLNM]_+KdoRoCnMP~`z+c]C2H à j.w Á OÄÅ H®RU^7LNM]pH o <*gU% LbBDpkz+WpkVc G W V.M~Rd®IJBd}BR7YlVdopQRdBd~a}HS· V7~xBdcV.MP~7LbBSR`YlV`·BDc t ê ÐsÓíÐ <JQà 8=Abn%à 6 R <Q3^F=APULG u V7BDwkY\V.MR Rn, K G HLFT abHq~.T pSM]I.aNM G CbMKDBµI`L i V.YKmKPBdV7HSOV7k@`BµIJBO G c c`pSMRzbHSVD^`_N@ IJBd}BDI`L+BDa G BDL i M VM]~`LbBSR7Y\Vt ê ÐsÓ Ï.Ð MSÂ7=à F R <=3^F=AEULGIC Æ Bd}oDHS~7LyC'HBdjHpkHkVma G kV.MPjYt u T }lY"a G SV.M~.YljHkV7pkY Ç EZV.M]p^URTanH J%GÄÃZ/Ä ü jT }\Y>~`Y\jHkV`pkY>ð`E.C2H G B 8[G1HZJ[<Q3 Ð ê ÐsÓJÓÐ b MSÄ · G kVqR`[nHk_F@~`Y\jHkV7pSWKPBdVDRdHQñ`V`W\@7BIJBd}xodHk~7L+cC'H¸KDBdV7HkOkVD^IJB7OQH G t ± i KdM]bp k oI.}^URTp~`H.V.Yl_QHKDBdVDRdHQñ`V`Wl@`BIJBd}xodHk~7LNc a G kVMR7pkV`YlKV`HACnM]KDBqI`L i V`YlKIJBd}BDI.LbBda G BDL i M VM]~`LbBSR7Y\VE`K G HLn^7_F@C'H¸KDBdV7HkOkVD^IJB7OQH G t ê ÐsÓ×Ð b MSÄ u V7BDwkY\V.M I`z+WIc`a G Vd^7_N@ zbHk[nHSV`W3`}lBD@doX Æ C2HRwk~7omKPBdVdRDHñ7V`W3IJBd}oDHk~`Lkt ¿ MwS~^meJB7~pqjV7BDwkYlVdomI`z+W Ic`a G Vd^7_N@µzbHk[nHSV`W1j i wHeU^ G V.M]I.aNT]VCbMKDB}lY\V7HST]L+V.WKDBdje.Y\V.MP_QHR7L+_N@`Bd} i t g ñ7Y\a G c]C2H }lY zbHk[nHSV`W1`}lBd@DoµX Æ EUC2H @`B~7Bda+M]wHSV7BMP}HkabIJbB qRC'Hk~`V7BdjÖRL+_F@7Bd}lcjV`BPwSYlVdoI`z+WIc`a G Vd^7_N@z+Hk[nHkV.Wt ê ÐsÓ.Ü Ð 2 AbLà K5HbA anBdc7zNMP~`V.Yl_ L+BSR7Vd^7_N@mVc`}lHMpeU^URMC'W\_W"anBdc7zNMP~.V`Yl_QH C'abBdc ¿ M]wk~^ÍeJB7~Íp n K G HLn^jT C'Hk~`V7BDpkVMPOVD^`jòz+Hk[nHkRV.WljÞ, anBdc`a G MRoLbnBSR7−V`Y\m_ P a x xb j Ý r Ç , . . . , mß , x diÙ , V.M]pQ^RUTPjH e%jYgPxK5HIi OQ:Á p1AE4dAL à 6Á Ð Æ }sM G W }\Y diÙ ≥ ð , j}lc7R7W\jH3B R pI6 R C%iVWM]ri%à qiç Á eLjYrgPK5HIO*qç Á p1AE4dALà 6 Ð Æ i BDK7c`~ i ð j}lcR`WljH"B %à Abu ULAPT=A% à APG1<D8JÄ.%à q7Á R pI6 R C%VWM%à q7Á p1AP4dA7%à 6ü C'Y\V.M]K¸Cn~7HAB ULAET*A%à AEG1<E8JÄ[à q R pI6 R C[VWM]d%à ٠q>p1AE4d,ALà 6 Ð Æ LbBdjSV`V7 V.M]pQ^URTPjH e%jYgPK5HIO*q*ü I.LbBdjkV`V` x %à APeLjYgPK5HIO*q ÝLbBSR`V7®ðUßFt xi j ê ÐsÓJáÐ b MSÄ ¿ M]wk~7SjcR7L+_N@`BD}\c B7~7IJBSR`Wl~.T®I.LNTRd"C2Hk~.V7BV7Hk~`HîDHkV7HL+BSRUMPV7AI.z+WI.c.a G V7)eJT]pkYl_NKPAzbHk[bHkV`WJ`}lBd@DoX Æ RLbBSR`V`Y\_QBSRDSj G RM]L+ct M ê ÐsÓæÐ o p1AP8=</UÀ<*efAPHU%à qÝaL35<=JQF d o ÃÄ%à <*G]ÁmYÄ 3SK5gb<D8JÄ.%à <=C d o Ø eJHk_VDT kI`LFMRDa G LNMPVdoôÝ ßAjBd@7Bdcµed^ G pT]IJBDL+V7DEjWla G BjYlV.YljMr{c`V`KD_QHanH@`}lHk~.TC2HbC'W jMñ7Y\jc`jE IJB7~`jWlV7KUoj i wBdced^ G }\YlV7HTLNV7bi®pSTR7Y\ab}lDE..}[email protected]~.MPV.TanBdc.a G MRdBDcV7HLbBR7V`Y\_Pt Æ Bda G c`;I k I`LbBpST]IJBDL+VT Ro7VT]abBDe.W\jH®I`z+Wla+}lc.[bV7BdcV7HLbBR7V`Y\_Y Ç RUo7[bKUL G TPjH®pSTbR7iY\ab}l®IJB~.jW\V7Kdo ÷På IJBDKc`~|jTPjHm@`}lHk~.M G jMñ7Y\jc.jE;RUo`V.TPanBDe.W\jH`OQHk}lBSRdBdc|r{c.V7Kd_Y Ç M @`}lHk~.TPjHjYlV.Yljc`jýV7BSRD RpkV`YlK}lr{c.V7Kd_QH V7HLbBSR`V`Yl_H®I`zbHQRdHk~7HSjHV.MLbBSR7V.Yl_QH®IJBdjB7_W ~7BDI.}Ü7KDBSRU^`_N@I`LbBdjkV.VD^`_N@/k I`LbBµKUM]wk~7BdcôV7HLbBSR`V`Y\_YaL+Hk}\MP_W ≥ B~ôV7HL+BSR7V`Y\_QHB7~7HkO G HkjH~7BDI.}Ü7KDBSRDBdc ݤV`YlK~`HV`HIJBdc7wkY G Bdcß I`LbBdjSV`V7BdcMLbHS}\MP_YI`z+HI.W\[nHkjH®V.qM I`LbBKUM]wk~7BdcV7HkLbBSR7V.Yl_Y aLbHS}\MP_W ≤ KqV7HkLbBSR7V`Y\_YI`z+YlO G HkjH®~7BDI.Ü} 7KPBSRdBdcݤV.YK~`H®V7HIJBdc7wSY G Bdcß"I.LbB jkV.V7BdcMLbHk}sMP_YI`z+HI.W\[nHkjH®V.Mq Á jY3Là 6ceLjYgP6 ê ÐsÓçJÐ] 35T*<*GIKNM]ÁzC%VÝV7KÁ R 35APn;<E8Qq6ÁAbM7<;U[F R G1<ÞaL35<=JQF d o VÝ<*G7M7<J%à <*G]w Æ Bdc`wkWxRT abHRI`zNWIMP~`DEC2Hka G }\YwkHqabHpLbBSR`V`Yl_q~.M]C'WRoe.LNM G ab}Bdc`I_QHDEK G HkLb G RDBDz+W"BDL G BdV7BDL+jTP}\V`W>eT]pkY U = ß«Z¨7Õ7Z¯¦ ÎbP¢«¢Z^£WS¤d¢£WZ7;¢¡WÛ9«I¢W¯ß`Î ¤ = ÎZ®ZÖ®Z¬=Z#¦ ÎbI«1ù¨¤5¬=P¢¬Y(ÐÏkZb± Æ BDK7c`~6anH G M]KPBSRT eJTpkH®V.M]C'W G V7Hk~T7E.}pH®IJBdc7wkW G jH G B~7oc`jk}®eT]pHýR7Ylp®V.WwHdt.?A}îDBDL+Y G jc`ak Ç ßAMP}lHpkV7HSjH®}\YeBSRDBd}\VD^KLNM]C'V`WeJB7~jV7BDwkY\VDoI`z+WlI.c`a G VD^`_N@zbHk[bHkV`W¤t ¯Dß õ HQñ`Yla G cPC'W\_Wl@`BKULNM]C'V.Wl@7BeJB7~`cE K G HLn^c7wjTPjHDEI.zbHnC'~7HSjHKC'Y\V7kjcÍKULFMC'V.WljcÍeJB7~`cERÍV7kjwC2H @7B7~`V7B G Mc`OQHk}lBSRDr{c`V`KD_QHjHkV`[+WV`HwRI i RdB7~`V`W\jt Á C ê ÐsÓêÐ <J%à APaU%à <*VWM*Ä 35T*<*GIKNM]z æ Hk[bHkV`WZabH~7BdaNM]@c]C2HRDHRL+_F@7Bd}HS_N@ KPBdVdRDHQñ`V`W\@7BqIJBd}xodHk~7L+c EJM G k_F@C2HKPBdV7HSOVD^IJB7OQH G t û Wl}lBSRUTr²c`V7Kd_QH C'Hvpk~7Bd}sMBdjHpHSV.T®M)RKdM]wk~`kj0KLbBDKcanHvIJBdabc.V7HkjHy~`BR7L+_N@`Bd}lca>V`Ylwk[bW.@7B7~`V`B G Bdc_Wl}lBSRD)r{c.V7Kd_QHDt Æ LbB G BDwH G M]KDBSRU^`_N@C2HKDBdV7HkOVd^IJB7OQH G E.C2HMP}lîDBPLNY G jc.a®KDBdV7HkOkVD^öÝI`z+WlIMP~`VTV7HkBDjHpHkV`Bda G C2HBd[nH G zbHSV.MRI`L i eJk@Uc MP}lîDBPLNY G jcJßFt ê ÐsÓëÐ o G78ZLà 6ÙO/G1<*O Å>ÃYÄ 35AEgbALà 6cO/GEÄ >kLà 6SJ[<tef</UC u TPjH¸`}lBd@UcX Æ a;BDL G BdV7BDL+jTP}\V`WJeT]pkmW k [nHk_F@`VDoqI.LbBdjkV.V7DE7K G HLb®V7HnCnanBdcabBdc`OkTPa G WeT]pHݤab}Bdc`I_QHDE K G HLbRV`W V`HnC'abBdcpSMP@`L+VUc G oß3IJBd}lBDwkWljH¸LbBSR`VDoð`t õ edo G HkKabVM]~.V7BRUo7IJB7O G HkjHdt oCn~7HV.TPjÖI.LnR7V.WKLNM]C'V`W eJB7~t Á CXef</UC ê Ð\×JíÐ 2 GICLJ=:XO/G1<=O1Å o p1AEHZJ%</U OU*Ä 35476ù ± Bqa G TRUM]C'W\_WZeT]pHanHpSMRDHS~7HV7BSRU^RdHK G BDLkEK G HLn^VMP@7LNMP~`WV7kK G HLn^pI i RDB7~`V.Wl_F@ G M]KEJM]eUopkWlabKdMPV7 zbHS[nHkV.WeUo7}lBI`zNWI.c.a G V7ݤjk}lBV`HpST]IJBDL+V7a+}BDwKUo.ßFt Æ LbBSRUTP~`WZanH¸IBDjB7_W G M]e.c`}lKdoUt ê Ð\×ZÏ.Ð c (Ä eCL35OÄ R G1<wO=<J%à O/G1qbMLà 6 R pI6 R (Ä U u nC'jH¸pSM`KPBd} jY\V`Y\jMP}lYlpBSRM G r{c.V7KD_kY Ý ß x· − ì xê ¯ x# , x ≥ ð , Ý j Ç , . . . , Õdß f x j pSMIJB~.jWlV`HK ì ¯ ïÚ x¶ x · − xê x# ¯ Ñ xê x$ Ç ¯ . − x· Ñ ì xê ôà x# x% Ç ð − x· H3ab}lBDc`I_Y B ÝeT]pH]ßC'abBdc®BDpkV.MPOQHkV.WDRDHK G BDL i E G RdBDz+Wl_kWl_F@®BDL G BdV7BDL+jT]}\V`WDeJTpSYE]M G B G M]KEkwkH"BDpkV.MPOQHkV.WPRdHK G BDL+c peJT]pH;C2HR G Bdj G w¸zNTP~7K7cE7K7~7H®jT G HkV G BRdHK G BDL Ç t H®ab}lBdc7I_Y C'anBdcOW\anHk}\V7@7B7~`V7B G oqKDBUHk._YlHkV GNi P .OQjHk}BRDr{c`V`KD_QHB7~7IBSR7W\~.MCnWl_WRdHK G BDL i j P , C'HnC'Y\[email protected]`WJC'abBdc CR6a+}Bdc7I_Y B RdHa G HbC'V7kj zNTP~`Kct H a+}Bdc7I_kWl_F@ P ¶ , . . . , P CnanBdcRUo7I.aNT]VdoOW\anHS}lV7j @`B~.V7B G oKDBUHk._YHSV GNi BdjHpkc]CnWl_W\_N@IB~.jWlV`HKJt zNTP~7K7cqV.MP~ BDpkVMPOQHkV`W\j P ¶ , . . . , Pn C'abBDcOW\anHk}\V7@7B7~`V`B G oKDBUHk._YlHkV GNi .OQHk}lBSRDr²c`V7Kd_QHDt n ð Ç ì ð ¯ ð s û P Ù P ¶ P · P ê P$ P # P % ð Ú Ç ì Ç ð ¯ ð P¶ ð ǯ ð ¯ Ñ Ç ð ð P$ ð Çð ð Ñ ì ð à Ç P% ¿ RU^7eJL+cRdHK G BDL+c K G HLn^e.c`~`HkjHypSMRTP~7 G ~`B¸eJT]pHDEUM]eUo7_N@`Bdj0pkW\anKUMP}lY`KLNM]C'V`W`eJB7~a"jHkV.[bW`@`B~.V7B G Bdc `OQHS}BSRdr{c`V`KD_HDE`IJBdc`wkY C'HkPjjH, ab}lBdc7I_QBSRd®KUL+Y G kL+Ylc.jt ê Ð\×ÓÐ 35<=C R Hb<E8=qO;GIKNM7qEGIKSCÁ ¿ M]wk~^RdHK G BDL P , K G HLn^ [à A7Là 6 ReT]pSYE7abKdMP}sT]L+V7)Ro7VT]abBDe.W\jHabHab}lBdc7I_QHSj C M®RU^`ab}HS~7HKBDpkVMPOWljH TP}HRUo7IJB7OW G TPjjHLbBDpk~.Wl} Z − c MIJB7~`}Hab}lBdc7I_QBRDk@`B6KL+Y G L+YsMpSMRdHk~`HkV`W\j }lYleJBSRDBd}\V7k@7B6RdHK G BDL+c ± Zj . j j ÕPð C2HSjc7w¸B7~7IJBSR`Wl~T O;3²YÄ U =à : LbBDpk~`W\} ~7BeT]pH¸I`zbHbC'~7HkjHKDH¸KULFMC'V.WljcqeJB7~`cavjHkV.[bW@`B~.V7B G Bdc .OQHk}BRDAr{c.V7Kd_QHDEdpkI`LNMR7Y\~`}sM®abHvRUo7e.WlLNT®Zab}ljBdc7−IJcHkj_), a"V`HnCRd G [bW\j LbBDpS~`Wl}lHkjt Æ BDK7c`~®C'anBdcR`[nHS_N@`VdoLbBDpk~`W\}xojHkV`[bW V`HeJBLbBSR`VDoVc`}HdE.V7HHñ7Yla G c]C2H®eJB7~avjHSV`[bW @7B7~`V7B G Bdc.OQHk}lBSRDr²c`V7Kd_QHDt ê Ð\×J×Ð { j(ULO*<E8QqrO/GIKNM1qPGIKSC1Á Æ BDIYla+c]C2HpSMRTP~7kV.W Roe`LNMPV`k@7BRdHK G BDL+c6~`BeT]pHDt Æ LbBqKdM]wk~^ O;3²YÄ U1Qà : KPBH._kYHkV G pMRUTP~7SV7k@7BRdHK G BDL+cµanIJB7OW G TPjH)C2Hk@`BqIB~.Wl}1aAB7~7IJBSR`Wl~.M]C'W\_W1I`LNMRdBdcµa G LNMPV7BdcE G Hk~7o bi . éG1aPCD>d65HP6 R G78=AEO RDHK G BDL+cµ}HkwkWZR zNTP~`KcaV7HnCnjHkV.[bWlj K}sMP~`VD^`j R^7a+}Hk~.VD^7j IJB7~`W\}HSjt Æ BDKc.~ÍRdHRoe.LNMPV7kj a+}Bdc7I_Y"V7HkV.W3MPV`Y C2Hk~7HSVI.L RdHKK7}\MP~`Vd^dEUC2HjV7BDwSYlV.MI.z+WI.c.a G VD^`_N@6zbHk[nHkV.WV7HBdjHpHkVT ÝKdM]wk~`kjc zbHk[bHkV`WZB7~7IBSR7Wl~T¸C'Y\V7}lHI.[+WsßFt ± TP}lHDE M]eUo7_N@`Bdj pSMRdHk~`}\Yab}lBDc`IJHk_y~`B®eJTpkHDEDI.LbBSRUTP~.WljHAjM G Yl_QBSRdyzNTP~7KDBSRd)7I`LNMRo G M]KEUM]edoV.M®jW\a G )c7L+OcPC'W\_Wl@`B I.LnRK7côp i a G MP}\M Ç M R`[bc`~7HC'YlV.~7H ð Ý G Hk~oôI`zbHk~`HQR7[+WljãRUo7~`k}lW\jHzNTP~7HKôac7L+Okc]C'W\_Wlj I`LnRKDHkjè@7B7~`V7B G Bdc G Bd@7B G BµI.LnRK7cE IM]KB~ Bda G M G V`W\_N@ zFT]~`K i B7~7HkOkW G TPjHqR`@7B7~`V7}lY\V7HST]L+V`WKDBdje.Y\V.MPV`_HBda G M G V`W\_N@ . . . ßFt M pSTkRDLyBDI`LNMR7W\jHR G M]e.c`}\_QH~7B7~.M G HkOV7®Y\V`r{BPLNjMP_QH k.V.MP@7LNMP~.WljH¸RqzNTP~7K7c B a G M]Ln^qeT]pSYl_+KU^qRdHK G BDLyV`BSRU^`j MI.zbHI.W\[nHkjH¸KDBUHk._YlHkV G RDHa+}Bdc7I_kY C. à jw Á OÄÅ zNWl~7KU^7_F@I`zNWIMP~7HS_N@j i wkHy~`BPCnW G KpSMP_Fo7K}lHkV`W¤EdK~7oabHvIBD@doec]C2HkjHvRDHAabjo7O_QHAjHpkY`eB~7o o <=gU[ anHa G HnCnV7BdcݤjY\V`Y\jTP}lV.Wsß@7B7~`V`B G Bdc`OQHk}lBSRdr{c`V7Kd_QHDt Ä C1ÁD 35qeLj(gbA ê Ð\×Ü Ð A M1</U1w Æ Bdc`wkWxRTanH)RBDeJHS_V7kjÒI`zNWIMP~`DEUK7~oRpSMP~.TPV`WJV`HkV`WjBDwkV7BV.MP}p G BDL G BdV7BDL+jTP}lV`WeJTpSYt I`L+Y\V`_YlI.c .}Bd@UcBBDL G BdV7BDL+jTP}lV`WeT]pkYLbBDpk[+Wz+W\jH k7pMRDHk~`HkjH¸IJBdjB7_V`I`LbBdjkV.V7Ýa+}Bdc7I_QHßFE7K G HLb®~7BDI.}\V`WOkYpk_QHk}sM Ro G RdBPzNWBDL G BdV7BDL+jTP}\V`WeT]pkYt `OHk}BSRdr{c`V7Kd_Y I`z+Y\~.TPjH®K G M]KPBSR^7jÛI`LbBdjkV`Vd^7jÛIM]LNMPjH G L w, K G HLn^C2H þ @7B7~`V`RdHk}KU^MK7}\MP~`Vd^d~t ü I`LNMkRDHkV`¸LbBSR`V`Y\_QH®e.c`~`Bdc G Hk~7oRoIMP~M G ݲRV`HnC'@`BPLN[bWljÛI`z+WlIMP~7ß G M]K G (B k Ý ß c ¶ x ¶ . . . c x wx ¶ . . . wx f x Pj , n n a ¶¶ x ¶ am ¶ x ¶ ... ... n a ¶ n xn amn xn n m é é xn ¶ é ... xn m b¶ bn abH G Hk´®e.c.~7H3anK7}\TP~M G pH3~RdBdc®OST]a G W] p3V7nCnM]KD[email protected] M;KPBdV`a G MPV G odt õ G Bd@7B)I.}xo`V7HDESwH"LbBDpk~.Wl} Æ LbB G BDwH w C2H@7B7~`V`RDHkZ}lKPjd−cE I`jz+Y>ab}lBDc`I_QBSRdkj KULNY G L+Y\cV7HnCn~7z+WR6RoeWLNTPjHIJB~.}Ha G c`I.V7VwT]abBDe`Kc w, M]w IJB G BdjÖIJB7~`}lH¸KDBdV`a G MPV G odt Á OÄ ê Ð\×áÐ o <*gU%à j I.LNMRUM`OHk}BSRdÍr{c`V`KD_HµVTPjpSMCnYl[nÔ+cPC2HDE3wHqC2Hk~`V`Bdc Ro7}lBdc`OQHkVd^úc`jS}x^ RDHK G BDLc7wÍV7He.c.~7H6pSV7BSR7c pSM]zFMpkHkV~`BeT]pHDt Æ LbB G BabY j i wHkjH~7BSRDBd}\Y G RUo`}Bdc`OHkVD^ C1ÁD 3^: Ý=MAC2HkV`BDj#c`jk}^.ß3RDHkK G BDL;RUo`[nKL G V7Bdc G t Ä >AW>d6c<;U%VWM1GÄÃZÂ7Là 6 ê Ð\×JæÐ 2 APT*A7%à APGYÄ HbA6ß ± HîDHkV7HLNMP_Hyj i wH)V.MPa G M G e.c`´V`HnC2Hk~.V7BDpkV.MPOV`Bda G W7RU^7eJL+cK7}lW\OQBSRdk@7BzNTP~7K7cEdV`HeJB G WljEDwH>C2HypSMP~.MPV.T .}[email protected]c7w~`HîDHkV7HkLbBSRUMPV.T7t õ M]e`LNTPV`Y G anHACnW ~.Tqe.c`´µIJBdjB7_W −BRDjB7~`Yl`KUMP_QHݲK b abHI.z+YlO G BdcÍjB7_V.YlVdo jMP}k@7B®OkWlab}sDM k ßFEPI`z+WIJMP~`V7 s }sMPV`~7BSR^7j0I`LNMR`Yl~`}lHkj#ÝpSMAK}\WlOQBSR^ab}lBdc7IJHk_RUo7eJHL>iI`LnR7V.WK7}\MP~.VD^ Z −c , j j pSMK}lW\OQBSR^zNTP~7aHkijKRUi oeHLvI.LnR7V`W Y\V`~7HñI`z+YlIMP~.M]C'W\_WRRMP@UcßFt Á OÄ ê Ð\×çJÐ o <*gU%à j g ñ`Yla G cPC'W3~.MP}\[bW"LbHQR7Y\~7BSRMPV7RDHL+pHqabY\jI}HQñ7BSRDjH G B7~oµ V.M]I`zStV7HI.LNMP_c]C'W3a)C2Hk~`V`B G KDBSRdBdcjM G Y\_WE KUM]IMP_Y G V.W abY\jI}HQñ7BSRUTjH G B7~.MݤjkV`W anH®I`LNMR`Yl~`}lBI.LbBRU^7IJB7OQH G IYxRdB G Mdß;M G I t ÕÇ é & nrý ('Ý*) Ë y +]f 8ÐoÙ Ð Æ zbHkj^7[+}Hk}UCnanHkjÒR®CbM]KPSjÞr{BDL+jT G cedoeUo7}lBBDI G YljTP}lV`WJIBDabKdo G V7Bdc G BDI`LFMRUodt7)Hk_F@ G k}lBanH¸jYRL G M G I`zNWljB 7~ B pk~`LbBPCbT]K i EZI`LbB G BDwHjBDC2HIJBDpkV.TPjKdomanH G ^7KdM]C'W G cM G MPj V7nCbM]KPRD G oI`L i zbHkpBSRDI`zbHSa¸RDHk}lKDBDcOkTPa G abBdc eJBDLbKDBSRU^`_N@ G HQñ GNi t7M]KPBdV`Hk_"C'abHkjÒpQRdBd}lY\}JI`z+Y\~.TPV`WJKdM]IY G Bd}xoqa3BDI`LNMkRUMPjY¤EUI.LbB G BDwH G W\jÒI i RdB7~`V`W G HQñ G op i a G MPV7Bdc V7Hk~`B G OHkVDoUEZMP}lHIJBDK7c`~C2HBDI`LFMRDBdcÍI`zNYl~.TPV.W_Hk}Rd G odE I i Cn~7H G M]K G BabVMP~}kIJHR`}BDwkY G a G o`}Hkj _c G MPV`~ÍIJMPa G H V7Hw®[email protected]]I.aNMP}C'HkV G Hñ G BSRU^abBdc7eJBDLya;IBPIYlabHkjÛ_F@Do7e t - +)/3`&y9* ·d.Ù$ +A,7@ * &wy,7*">[* &"* $ ¸E* v3$2 $  R : *ì·d/;& 5 ' <;: ! : " ìNfh·D¸ 5 ìA $ &9P!%*ú>*3¹ -;.×·D¸* Å: à )HeUo7}lBjY~7Bda G ~`}lBdc`@7B¸CnMPabV`Ý=MV7Hedo`}C'abHkjÖa+TPjqßFEI`LbB7O3C2H G BR`}\MPa G V7¸~ i ab}lHk~7HKRD G oqBKDBdjIM]K G V7Bda G Yt Æ LbB G BeUo7_F@K G Bdjc G B~`BDI.}lV.Yl}ZjMP}x^@`YlV G E`K G HLb^7j C'H ë ÐÏÐ d A7ÁmÁmÄ I`LFTRD®K~7ow T ∪ {¬A} V`HkV`W abI.}lV.Y G Hk}\V.T7t T | A ± i KdM]bp k õ zbHnCnj¸p~7H.V.Yl_QH |t <;: : " ì -5 , &A×$ ' $ +A,7// &ÔìÊ$ &"c* ·d`$  R : * ì·d;/ & 5 ' -;.×·D¸* Å:¤8 ! à RI`LbR7V`W\jÖzNTP~`KceUojW\a G B C2H Ý ß;MÝ t ¶ Ô eÕ , . . . , t Ô eÕ²ß ∈ M A p t ¶ , . . . , tn n jS}BeU^ G C2H Ý ß;MÝ t ¶ Ô eÕ , . . . , t Ô eÕß ∈ p A p t¶ , . . . , t n n M <;:=8;: " · $ ¶·d`$= $ %* &"/ 5 ¸'&y9* ·d.$ Æ zbHk~IJBSR`Wl~T]V.W7B®abc`e.a G Y G c7BSRM G Hk}\V7Bda G YZÝ G CQtPI`zbHk~B~.a G MRdHk_vOWla+}B÷Ut ìDì ßedo G B®_F@ G k}lBR`}BDwkY G ~`H.V`Y\_Y7RDBd}\VD^7_F@ MRT]pSMPVD^`_N@RU^`anKUo GNi t æ HK7V7kjbH k Ä 8=jYgdÄ.%à q8;:;VdOQF/MF R G1<JÁmÂÃ1Qà :;HZJ ë ÐsÓÐ <=3%à q ù yHS_N@DÔ A C2Hr{BDL+jc`}lH3I`LbHk~`YlKUT G BSRd}lBDîdYKUo®BDe.aNM]@c]C'W\_WdRU^`anKdo G I`LbBdjkV.V7 x t æ HK7V7HkjHDESwH G HkV G B)RU^7abKdo G C'H 8Qj(gdÄ=à : EPC2H }\Y abBDc.OkTPa G WIJB7~`rsBDL+jc`}H ∀xB t BDIMPOV`kjÖI.z+WIMP~` G HkV G BRU^7abKdo G V.M]pQ^RUTPjH 8Q<=3ÃQ:ZÁ t <;S: ½y: " / $*- fA- +A, 5 ì$2 %* &E ¸8* v3$23!  : * ìh·d7;/ & 5 ' -/.·D¸* Å:=8fê à · _N@7kjM G MMñ`YBdj i I`LbBLbBR7V7Bda G C'anBdc G zNYV.YKDBD}\YZ~RDÝ=MPanIJbB IJB7~`}lH ¾ G ITPV7KDBSRdBI.zbHk~`V.TP[bHK`ß;MjMCnW G RUM]L ë Ð\× Ð HZJ%qÁmDÄ MSÄ R G1<wG1<E8%à <*VWM Ý? Ç ß BDL+jc`}lH x x C2HMSñ`YBdjt Ý?¸¯Dß Æ LbB r²c`V7KdOV`W¸a'o`jeJBd} f OQH G V7Bda G Y n C2HrsBDL+jc`}lH x ¶ y ¶ → x· y· → · · · → x y → n n Ý ß Ý ß;MSñ`YBdjt Ý? ì ß fÆ LbxBq¶ I., .Lb.Hk.~`,YlKdxT nG BSR^6fa'o`yj¶ ,eJ. Bd. }. ,Ýyj ni wHed^ G Y ¸ß p OH G V7Bda G Y n C2HrsBDL+jc`}H x ¶ y ¶ → x· y· → · · · → Ý Ý ß Ý ßbß;Mñ7YBdjt x n yn → p x ¶ , . . . , x n → p y ¶ , . . . , y n à j.w Á OÄÅ A → B → C C'H¸pkKULNM G KUMpSM A → Ý B → C ß o <*gU% / +A, 5 & 5 & .E &"/>,  : * ì·d;/ & 5 ' -;.×·D¸* Å5: ½ à <;: Å: " +ºY.2 ¸/ ì $ +º 5 &"* ì $ &v¹ ¿ pM]~TPV`W1eUo G B_F@ G k}lBI`LbB`I.}lV`Bda G IBPpSV.MPjHkVM G EwkH B BDe.a+MP@c]C2H x RdBD}\V7MqwH y C'HV`BSRUTqI`LbBdjkV`V.T7E G Hk~oV7HkBDe.a+M]wHSV.TR B MPV.Y C t - +)/>".&y9* ·d +A,7* +), 5 ìA$'17[* &"* $ ¸E* v3$2 $ <;Ê: ê;: " *3¹ pk@.}Hk~`HkjÖK G Bdjc EwkHC'Hk~`VMp¸B G T]pHKp¸IJBDwSMP~.MR7K i KqanBdc7eBPLN_QHpkV.W þ G oqBKPBdjIM]K G V7Bda G Y M7I.}\V7Bda G Y RU^7LbBDKPBRDMI`L+Hk~`YlKdT G BSRd®}lBDîdYKUYo edo G B_N@ G k}B~7BDI.Ü} `Y G V.MKDBdV7Hk_¸IT G ¸KUM]I.Y G Bd}o Õd¯ ;: ! ê ë ÐlÜZÐ ÂbMSÄ<wO=<JÁ R YÄ O=M]%à <*VWM1K R G1< R G1APUK5O*jDM7<D8=<=C 35<*T=K5O[C fZHkBPLNYH jTjB7~7Hk}¤E7I.LNTRD®K7~ow®KUM]wk~.TKPBdV7HSOV.T T 0 E T 0 ⊆ T jTjB~`Hk}t ± i KdM]bp k T Æ z+Wlj^~ i ab}lHk~7HkKRD G oB7I.}\V7Bda G Y¤t <;: 3: " & 5 ì 5 5 ,.-ò$n&)×$ ·d.×$ '. 1- $ f ·U9* ¶& .2%* &E- $ / $ *3-0/ $  : *ì·d/;& 5 à * 'z-;.×·D¸ Æ zbHk_F@7B7~7BSRTr²c`V7Kd_QH6edo jS}\MmjW\a G B P Ý Q × ð ∗ ßjW G @`B~.V7B G oôR PF IN Ý Q × ð ∗ ßFE"_BPwCnanBdc R7[[email protected] KDBDV`HkOV7®IB~.jV7BDwkY\VDo Q × ð ∗ t <;: ;: ¿ f/ ·d 5 , Y) 5 *", 5 )HQR`WljENC'Hka G }\YedoIB¸O}BRDK7ccanBdc7eJBDLbKUo G c.@`}HRd G YlONKc_N@ G k}\YEDjvanHBdabBDe.V7;pk~.T_QHk}KDHkj0~ i }HkwkY G T7E G M]KwH j G [email protected]KdRM]I.Y\}B.EwH)RanBdc`eJBDLbKPBSR^7_F@ G HQñ G Hk_F@[email protected]¤t Æ BPK7c`~IJBRUM]wkcPC2Hk[3pMabjo7a+}lc7I}lV73CnYJ~7BDI}lV`Y G E~MP}B edoabH®V.MKDBdV7Hk_¸KUM]I.Y G Bd}oóvBDpS~7k}ZMIMPVUcPC¸ÝKdM]I.Y G Bd}\MÚt Õdß"I.z+Yl~M GyG zbHeMÝI.}\c`avBDI`LNMR7Y G ~7RUMB7~7KUM]pQoß ë ÐsáÐ YÄ VWM1APG`M1J%AE<*G1AÁ yHS_N@DÔ E E C'anBdcÍ_QHk}sTqOkWla+}\M G M]KPBSRT7EwH ð`E ¯t)Hk_N@dÔ T k ? → ? C2HV`HK}lHka+M]C'W\_W ÇE r²c`V7Kd_QHMV7Hka_F@DÔ)c I`dLbBKUM]wk~7 n G RM]L+c ck I.}sM G W d ≥ a ≥ c ≥ Ý ß aT Ý n/cß F Ý nß , T n K7~7H F k ? → ? C2H G RUM]L+c F Ý n8ß .Ý nd ßNt Æ B G Bdj Ç ß ca < d ⇒ T Ý n8ß .Ý nd ß ¯Dß log Ý 8ß .Ý nlog a ß d ⇒ T Ý n8 ca > ß .Ý N d log n ß ì ß log logc a d ⇒ T n c ë Ð\æ Ð o pI65O;3²YÄ U%F u MPa G HL G @7HBDLbHSjãanHIJBdc7wkWRUTµI`LbBÍzbHk[bHkV`WLbHK7c7LbHSV G V`W\_N@ôLbBSR`V`Y\_PE K G HL+I`L+BMP}lîDBDL+Y G jo G o7I.c L+BPpS~7k} MqIMPVUc]C G o7I.Y\_+KUoµ~`BDa G TRUTPjHI`LbBOkMPanBSRdBdcµa+}BDwkY G Bda G t ³dM]KDBI`zNWK}sMP~Íj i wHkjHcRdka G jHLbîDHSanBDL G Ýf Ø ± Ø k ~`BPI}lV`Y G B7~7KdM]pVMjHkLbîDHkanBDL G B7~`a G MRdHk_Útx¯ÑUßFt Æ Bdab}lBdc7I.V`BDa G R7wk~o6~7k}\WljHV.M~7RDOkTPa G Y3ݤV.MK G HLbIJM]K RdBd}\TPjH G z+W\~`W\_W.MP}îDBDL+Y G jc`a LbHK7c7LbpkYR7V`ßFEPI`LbB G B a |¯E G o G B®OkTPa G Y`jMCnWIJBd}BSR`YlOV.WRDHS}lYlKPBda G Rpk@.}Hk~`Hkj KRDH }\YKDBda G YJI i RDB7~`V.Wl@7BR7a G c`I.cE G M]KUwH ï¯t HS[nKDHLbBdcI`LNTP_YJKLbBdjALbHkKc7L+pkYxR`V`Wl@`BRdBd}\TPV`Wa G [email protected]¸MP}lîDBDL+Y G jc`a I.LbBSRDSa G R}\YlV`HST]L+V`W\j OkMPanHDE G M]KwH cd Ç t Æ }sM G W G HS~o log a d M G c`~`WlwjHkLbîDHkanBDL G jTOkMPanBSRdBdcmab}lBDwkY G Bda G Ý nd lognßFtÝ õ T]K}sMP~ }lBPîUM]L+Y G jc V7HkV.W"I.z+YMPano7jI G B G cY\_+KDab}lBPwSY G Bda G Y3IJB~.a G M G VD^dE1I`zbHk_F@7B7~KCnYlV`kjc pST]K7}\MP~`cÍC2HC'HkV jc`} G YI.}\YKUM G YxR`V`W;KDBdV`a G M]V G M7t ß ± MP}l[+WI.z+WK7}\MP~ÍC2HeYlV.T]L+V.W3Ro7@`}lHk~.TkRUTPV`WÝf Ø ± Ø k>~7BDI}lV`Y G B7~7KUM]p B~.a G MRdHk_Útx¯ Ç ßFE7K~`[email protected]]pkW a Ç E c |¯E d ð`E.OYl}\Y OkMPanBRUTa+}BDwkY G BDa G C2/H Ý logn ßFt <;:=<;: $'h& ì / Æ h& · 5 , $ ¶$'&y>,.& .×'*) &;Ô! )¸ 5 ìy; &"f/ ';.×'*)#·d7,7*- f  : * ì·d;/ & 5 ' -;.×·D¸* ÅS: ½ Ã Ø IJHLNMP_QH YlV`~ M â V`abHL G I`LbBe.Y\V.T]L+V`WvRo7@`}lHk~.TRMP_WAa G LbBdj®oÍCnanBdcú~7Bda G C2Hk~`V`B~.c`_N@`ÍMCbMPabV7 R KUM]wk~7Sj I`z+WlIMP~7dEMP}lHC2HkV I`L+BµIJBDzNTP~`HKJt Æ BDK7c`~ôa G LbBdjã@7B7~`V7B G c BDe.aNM]@c]C2HdEJC'HIJBDI.a+MPVd^IJBda G c7IôBDIJHLNMP_QH Y\V`~ Ø ¿ t Æ BDKc.~@7B7~`V`B G cmV7BDe.a+MP@c]C2HdEZV7Hkjc`abWed^ G VUc G V`I`LNMR`~.M7E wH@`}HS~.TPV`W>anKDBdV`OW R}lY\a G ct ¿ ~ow@`}lHk~.TPjEMC'abHkj Rc`pk}lc EK G HLn^qjT¸Rd G [bW@7B7~`V`B G cV7Hw@`}lHk~.TPjE7MP}lHV7HkjT}lHQRD[email protected]@`}lHk~.TPV`WabKPBdV`OkWJYJI`zbHka G B.EUwHAI.LNMRU^qa'o`V j i wH;HQñ`Yla G BSRUM G t Æ }\M G W G B®a+MPjBPpkzbHnC'j;Y`a'o`jH G L+Y\_+KUodt Æ BPK7c`~ G Bd@`}HvBDI`LNMR`Wl[kE G M]KyC'H G zbHeJM"C'Hk[ G ;I.LbBKDBdV7pkY\a G HkV._Y c7I.LNMR7Y G IJBDI.Y\a â V`anHL G E`K7~7H®abH¸IWl[nHdE`wH¸I.LbBSRdHk~`c YlV`~ MabKDBDV.OWljÖR}lY\a G ct <;: !9\ : " 5 ¸2/ ·7×$ '. 1- $ ì)9* +A,7;/ &)& .'- $ +),7c* ¶¸- $ : / +$=7c* ¸/ ;:¤8 à H®~`L+c`@7kjÛzNTP~7KcC2H®BDpkV.MPOHkV`W h ¶ , . . . , hm RDHS}ljYIB~.YxR`V7Dt u k}Bedo G MPjÖed^ G b ¶ , . . . , bm t <;: !f! : " ¸f/ ·7×$ '. ì)9* +A,7;/ &)& .+A,79* ¶¥¸1- +¸* ìA, $ ) MKDBdV`_YJR~7Hk.V`Y\_YjV7BDwkY\VDo anH®abc`jc]C'HI`z+Hka;[bIM G V7¸Y\V`~7HñUodt Æ LbR7V`W abc`jMI.LbB b jTed^ G I.zbHka i B7~ j ~7B m t Ç ~7B n [email protected]`LbB ai I`zbHka j B~ Ç M <;: ! : " ¸*> 5 &°,7[* &)&A×$ '%* &E- P &3/, $ R : * ì·d;/ & 5 ' -;.×·D¸* ;: ! ê à [email protected] G Yl}¤E`I.LbB G BPwkHRB~.a G MRU_YBI`zbHQRdB7~`cBDeJHk_V7`}lBd@DoX Æ VMV7BDL+jM]}\YpkBSRUMPV`BDc Æ B7~`jWlV7K7c ÝB7~`a G MRdHk_;OW\ab}Bà7btx¯P≥Õdß~oanH;z+WKUT7E]wkH;I`LNMRdva G LNMPVdo b jBd@`BDceU^ G BDeJHk_V7;pTIBPLNV7yM"CbMKpvV`Yl_F@c`~`k}\M G V7HpT]IJBDL+V7Dt i f>o7IJHkanH GnG Y\V7îeUo1X 0 2 354 Õì c
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