Publicações do PESC Generating all the Acyclic Orientations of an Undirected Graph
8
0
0
Texto
(2)
(3)
(4) !
(5) "#%$ "'&( ) %*+
(6) , !-* ./ '0 132547658 9:,;<138=>@?A1CB F D H E J G L I N K P M Q O S G H R U T V R X K H W K V R N K Y M [ T \ Z V R < ] _ ^ ` G ' ] a R K L b T H E N K J G c M ] d TG`vwd_T ef fg]xfgOyhjoYT[Z{i zAf |UMc}V]A~UkU~AMP@Tla~NT [xh } EHi kHm_ nLGS^_OQocG`]'KNl#RVTAKO bLK T[Ewd KN]UG`Ml<]HpHqH^oYbHTsHtAr ,Tu ] MPTUOyGJZ IUT[ZJl<G`M t ]LOmqVMmHM \1HC4 : !V138Aa UV8 DFEHGJIL¡5EKNMPOQocOQGSGJocRHqHTUoRV]'KXRVWHKKRV¢KNMYT[T[ocZ\K l7RV]<T[£ o^_G G`T]'KRaK¤ bLd Th EHKNGJMc] d TG`vwT f ]LOyoYT[Z!A¥U[H¦TNA§a Ul< A aKA~ i E Kxm¨^_qVG`]MSm¨RVtwKM bLT[EHK G`Mc]w^FbHw,MPTUOyG`Z t © hCª(«7e ^F¬n®T t § t Z`G t ]AMG`KNEaoPTocGJ]AEOHT[ZJkA]UMcG`o¯Hl OVkAMYT[pH¯®O ° ;±!² ³ ° 9² oYo´3G`T[K l<ooG`K]Aµ¶E®ÀOmÁÁ5K« ¸T[ÂKERVºqHKE®OÃÄtRV¼ÅMG`ÃÅG`MK T[Kt EocRTKE RRVT[KNkAZJZÆMYkATNT[§]UpHMc¯G`o]A¯H·_l<l¾GJpwoc¯¹Z`KN]Ava¸MgG`oQ¿IL§EK McRVÀocGJG Á5EHt ¸{k KÁ5O¸ TVZ`º»ZÂocº¯wKKRVÃcOykUÃYKKmC]AOFÇ,MTG`¯HKNEKÈEaRoPOyTp¼½ocT G`T]UKtE§ OCMct KG`Z`ÉE'G tqH]GJ]AILMcMcKKNGJR MPKNTE GSZ`OiZ t t ÀÁʸ#Â/ºÃYm ÐäÐÖËQÌwçUèsÍÏÎÖQÐÎÑÓéÒÄÖQÑÕÔAÝÙÖQÍPêNÐçUÖc×â3ë ÑÙØçAÐì{Ú[åNÑÕÛ@ë ÎÖQÛÖcÍPÎÊÒÚÜ@ÚÑÙÝ Ö!ÞNÑÙÛÑÙÐÑÕØ[ß ÐÚÖgàSØNÐÖQÎØUÍPÐÑÙáØUÍÏÝwâ3áãFÔäÐÖQÎ\å[Ò5ÑÙÖQØUÒ5Ö,àSØÛÐѨæ.
(7) # C,"*+
(8) "# Tµ ERRVÁQµKNEHà ]UÁQ Ùm µXocKFÃCO_TE TMcK_¿EHGJoPGJO@ocK ILKNqwMc EoKNRVvG`M½T[K Et ][oRKRKµ RakUkAMPGSKTO pHOyT±K ¯oPRaO·_G`UkAGJMcocMYK¯ T[OQpHpsEH¯%K ] t ]AocZ`GJw]LIL]UoPKNT[pZ`GJ§O_EH·_KEHR]AG`oM_¯'Vl'§¹¸ qHRV Z`GJoMcG`K pH
(9) ZJocK_ÁQG`EwµXKRVk<à kU ocKT¯HOEK mR -KºRVÁykAµXK ÃO ]]UXMcGJKNµEVmoYT[Ç,oG`¯H]AE®K<O3]U][Mc¦G`K T_EVkAoYT[MYT[ocGJpH]A¯ E ¯GÆTN O IL KC "!#KN %K $&E & ±]UG E OyG`GÆo RVKNt Mc]AKEaRÈoPTGJE)G`E(OXHEH}"]%*ÊNRV·_G`M¯HK KNt MoK KRGJo@¯tt § TAtO{Z`sKOK m'KNE Oyt ¯H§ ]t ·_Z`G E t okU¯MPTT[pHo¯@ocm ¯HK « G`M K t T[]AMYERVOQG`GSE®RVT[K Z`M_GJoQ§oc¯HGSKO pHt McZ`]U]LHOQKNZ`KNZ`§¹l Mct ][KNZÆ!T[kAoKNKEHR+K ocMP]¹T[oocG`EH¯HkK T[t ZJ¯HZ@Mcoc]U¯Hl KT[T oG t§ pZ`G]AZJ§V]AEHMc]UGJKNl<EaoPGSTT[ZgoG`][]UEO oc¯w]K oRa¯HKKO qHMG`E®RVKG`MT[K Et oct T[KZJRkA]UkAMcMPG`To¯HpHl¯µ·_mg¯H´3G KN¯o_¿¼E®RHO,KTocZ`¯HZHK o¯Hoc]AKoY¼T[Z¦]UEVMcqHGJKNl'EVoYT[KNoMCG`]A]E®!O OyqtG`E't ¯<t ]IL]At KNMMPG`KNTEaZ`Z oPT]AocGJl<]AEpwOZ`KNm va« G`oQ§K ÀÀÁÁʸ#Á5t ¸ Â/ ººÃYm ÃļÅÃT[E®R RVKNZSTN§ tt ]Al<pwZ`KNvaG`oQ§½ÀÁʸ Áʸ/ºÃcÃYm¾Ç,¯HK Oyp®T t KtMKÉqwG`McKR GSO Çl,¯w]AKocGJpHIUT[Mc]UocKHR+Z`K lV§/][T{kARVK GSEHOQocKNMcMPGJTHocqHGJEHoKk'R½T[ZJO Zso¯H¯HKKXRVqHT ZJt G`§ EHt k¹Z`G l<t ]UK McGJ¯KNT[EVEwoYT[GSOyol G`]AE®·_O GJ][oc¯!TXT[kApwMYpHT[Z`pHG ¯T[oµ7G`]AE®¯OTAO,oc]%KNMcK K E i OQOQ]A§HqHOQocM KNt l#K%+O Oy¯®( T[~UMcFGJEH" k*Êm»T[E¡5E R OQocq]½¯o¯HKT[pwppHT[tZ`GMYT[T[ZJZ`oKNG`]AZ E®OyOGJlXTqHZÆT[ILot K G`Mc]AocEK vj][][ l<µ ]aRVK MZSKNO pHMc][K'OyKNOQtEa]AoPl<O K T t pw]AlMc] pHKZ`KNOv O oM¯K T[KNo GJILl'KR±qOyo'Mc]Ul Mc]Al ]Uoc¯HoK G`l<MK¹ILKNt ocM]½ocG ocKGJl<Om¹K Ç,t t ¯H]AK<l<KpHRaqwkAocKKOX]A][E7µ»Z`] t T[T[MZXK G`EVOyq ]UMc¯ l oT¯ocT[GJ]Ao E7pwMcT[] E®R KO]AOyKEOXRHoct ¯T[oYTT o l'o¯Hqt KOQOQoKt T]ApHlpHZJlG qHTEwocG`G ]Ut ET[ocO K¯·_TNILG`oK<¯+G`EKt T t ¯%]Ul<]Al<o¯H]AKNEM t GSO]UMcocMc¯®KOyT[po']AocE¯HR K opH]M] TUR[Kt OcT OQt KKNO EVo]AILMKNMcKMcoOQGpst t ]UKEOmRVGJ« EHk ¯Toc] o T]UEVM §%K oQ·,oc¯H]GÆO TAR[]UtET Oyt oKNMPEaT[oGJEVILo K LMcTocG OQt qHKOOyl'K t oCq][Oy¦opHEwM]A] o Kt Oc]UOQl<KO pHGÆqHO oTK Z`Z`]t · ]AE Kt RqHoMct ] MKNEV]AolZ`§LpHm t qH¡5ocE%K ]A]UMYE RVKNqHM MocMc]¹KNEaKNocE ZJ§ i ]URaEHGSOyZ`to§¹McGJGH qHococ¯wKKNtRG`M O t ¯H]AKMRVMcKqHOQZ`pGJEH]AkXERVl<GJEHK k ¯ILT[KNEwMcGSoOyG l t KOFOQoPt TT[McMK'oPO OyT[GJE o,wT[OFEaG`§'E%T OQ]A§ l<ZJKG ]At ]UMcMcGJKNG`K EaEVoPoYT[T[oocG`]UGJt]AEE'][][t.g-µm@HÇ,TE¯wR K K o¯l<T[pHo Z`]]U§wMcO3MT_KOyILpKN]AMct E®§ ROyGJocl<]-pHOyZJG`KE/,HMqHOCZ`G`KgE t oco]¯HkAK K EHqHKNMcMPMTKNocEaK ogT[TEH]U§ oc¯HZJKNG M{]A]AMMG`G`KNtKNEaEaoPtoPTTococt GJGJ]A]AE@E ¯]ATNE ILt K_K ¿o¯HEHKgGSOQpH¯HMcK] R t Koc¯HOcOQK KG`OM ]t Al<pHt qwoPT[oG`]UE@mCÇ,¯HKEHKN·7]AMG`KNEaoPToct G`]UE GSO,kAq®T[t MPTt EVot KNKR oc] K T t § t Z`G t m W]HCM]Aµ7l»TocMc¯HKKXpT[pMKNocMYGÆOyT[pZ`ZJK §t o]UG`MPILRVKXKN][MKgR o¯HVGS§-OTÈO t l¯HKKRaTAqHOQqHZ`GJMcEHK k ][l< K ]At E¯T[qwEwMcGSMcOylK E Aoc§L¯H1m K-0FT ]t ·,§ KNt ILZJG KNt M []UEwMcG`]K EV3K oY2 T[ocGJGJ]AKNEEaOo TGÆOCZ`kUT ]AMcGJKNocEa¯Hocl MYT[ZHGSO GÆOcZJOyG4qw,LK_KNZJ·_§¯Ho] KNE'KNvVOyK GÆOyZ`Kogo]AG`M_EHk oc¯wocK¯HK_pwMcGJEH]AG`woZ`GSKNT[l ZwtT ][§!t ]AZJpHG oG`]Al<McGJG6t KN5NEaG`EwoPkT[ot G`]U]AE@E 7mt qH-McMKNKNEHE K tMP§xT[VoG`·_EHt kȯHG T[t Z`¯ Z oGJEV¯HoK] Tt ¯Ht KN§ qHt ZJMG GSt OQoc]AG MG`KNOyEaocMYoPT[ToocKNGJ]AkAEGJKO O,]oc¦]'Mct KNoc¯HZÆT[GÆocO,GJIL]AKNpHZ`o§ÈG`l<Oyl G65TT[Z`oZLG`kA]UMYE<t T[pHpHt ¯®Mc]UOÅt HGÆZ`O K KNlvampK t ocKRoc] §VGJKNZSRXG`EOQG`kA¯aoPO t . ~.
(10) ,Ç KX¯wK'TURVT[IUpHT[pHEaMoP]LTT kAt KN¯]Uq]O,,G`q®E'OyG`McEwKNkZÆT[oOyG`GJ]AE E',HOoc]][ KNl<T t pH§ ZJt ]ZJ§VG t GJEH]AkFMG`]UKNocEa¯HoPK TM ocG`p]U]xEOcOFOyGJ]HFZ`K µ G`E¯RVTUK OFpsK EKNKNRVE%KNEaOyog¯wOy][qw·_E%OyKNocoY] O ]gILKNMocG t KOC][ µ ( ~ *Êm ´3TUR[K o±T µ KNEVo Koc] T[E GJqHE±EµRVGJm McK ´3t KNocoKR kA
(11) MY
(12) T[ pH ¯\ m X,sK§ T%OyKÁ HÉLÃXqHKN·,E KKFM]KN{pHMocK¯HOyKKNEaILo K Mcococ¯wG KKO OyK ]o ,][µmgIL¬FKNK McoEHG ]At oKK O a§ µt Hoc¯HK OyqHwkAMPTpH¯ G`E®RVq t KRXG`E'µ½V§
(13)
(14)
(15) t LLTER]AMt ÁyµXÃY ÊÁÃ %Á Ã !
(16)
(17)
(18)
(19) " Lm E+]UMcG`K EVoYT[ocGJ]AE%][Xµ GSOMcKNpwMcKOQKNEVoKRV$ § µ# m¹W®]U%M & '( -)Á µ# ÃP@G * µ # t ]AEaoPTG`EOT<pT[o¯+Mc]U+l ±oc,] '¾oc¯HK -E GÆOTE / %/. ]0 '¾G`+E µ# m 1 Á Ã{RVK EH]AoKO o¯HK_OQKNo{][\T[E t KOyo]AMPO{][2 GJ3 E µ # m!´3KN5o 476 -)Á µ# ÃPm &8 $&9& % $ :# &)9<][;4%G`E<µ# GSO_T OQKÉqwKNE t K>= ]{oc¯HKXILKNMocG t KO ][;4 HOQq t ¯ o¯T[oTZ`Z3KRVkAKO ]· KXµ l<# KT[KNEoQ·,ocKN¯HK KXE+RapG`kATMYG`T[MYOÈpH¯¹]]AHILKNoYT[McoGJEHG t KKRO ]Mc> ]Ul 47T[µ¶# MK V§M]AMclKNl<Z`]KIaoG`EHoCk ]'MG`T[kAE¯aR¹oT[GJ?E ZJZ@=KRVkAm<K,O,§KNEVAµo# KNMc@BGJEHk ]Uo¯HMXKZ`KGÆTNOy]UIaZSG`T[EHok'KRG`o mILKNnLMG`oclKNDv G`ZSTMcmZJ§LW G`E®µ7# T[Z`ÂBZJ§LH·,GSOFK oq®¯HOyK'KRVoGJ¯HkAK'MPTOcpHT¯%l<KX·_¯HEHG]At oY¯T[oMcG`K]AOQEqHZ`Á oY&OF a'§Ã TA RwRVG`EHÁyµXk¹Ãoc]TEµ R # EÁ F "'È;à 'Á µX# ÃPoc¯wKl<KTEHG`Ewk Á5T[E®R±p]LOOyG`wZ`K'RVGJMcK t oG`]UE±]goc¯wKKRVkUKAÃgKNG`Ewk t Z`KT[M M]Al o¯HK t ]AEaocK vVo m ¡®5E TAOynLKKR3t m,ocGJÇ,]A¯wE%K<TZ`·,kUK-]AMcRVGJocK¯HO lt McG`G`oPK OQKNoZ ¯H{K GÆO,t kA]AGJE ILt KNKNE pHG`oYEOT[nLEK RoG`pH]UME ]L][¥VÊm OGJE·_¯HG t ¯oc¯wK'T[Z`kU]AMG`oc¯wl GSO t " , $g$ ´3T K § oIZ`G
(20) ]U
(21) McGJ KN EVoYT[oG`]AKET[E]T[µ MHLJ G`o[MP!T[~IM§MOOyKNÉLP¾qHKN¸{E m t K<Q][X: &o¯H K "IL&K McocG t RK.
(22) OX. ][9 TµS _ TEVR U µ # WKJ µ# KT[J E GÆO_t T-t qwt E t ocGJ]AE X KJ Y EÁ [Ã X Z / N~ X ¡^# # LXJ [·_EÁ ¯H\ KNÃE ¶X KJ Á ]A M\ Ã T[ZJ]Z ~U\C® ]UM T Z`Á TZ Ã \ oc-¯HK >E 5Á KSJ ÃPm GS O t RVT[G`ZJMZ`K KR ocGJ_]AE¹^#$TA$QmOOynxGJkAG`l<EHl<GJZSK T[EVMZ`o §LGS O X $KJ/9 GSO $ t ·_¯wKNE X X
(23) \ `;a Á Ã T[EbR `5 1 KJ NEÁ \N]Ã c G KJ Á `YÃ ¶~o¯HKNE KJ Á
(24) \NÃ ¶~Um G. H. .
(25) ,oÇ ¯¯wT[K o ). & U µ # KJ &):T^# % : ! X LJ GSOXT[E ]AMcGJKNEaoPT[oG`]UE µ # ]Xµ COQq t ¯ µ # KJ µ # @ HTER X Á E \ . à 5. T Á µ # " Ã. G \0a EÁ ]à c EÁ \ 5à ÁTµ # Ã" ]Aoc¯wKKNJ McN·_ÁGÆ
(26) Oy\NKLÃ m 7 Ç,¯wKZJKNl<l TsK Z`]· McK ZST[oKO,T t § t Z`G t ]AMG`KNEaoPTocG`]UEO,][ µ o]o¯H]LOQK],µ KJ m K EV oYS T[ocSGJ]AE (O µ #< Ç,]¯w<KNMcµ K< K TvVEGÆOyR oPOpTTG`MY]AOEHK TÁ i µ o# ] KiJ ]AEH KX KJ t ]UÃYMcMcK·_Oyp¯H]AKNEMcKRaKNXE Kt J K GÆKNO oQ·,T/KNZJK KNE kLTT Zt § RVtG`MZ`GK t t oc]AGJ]AMG E i TUOcOQG`kAEwl<KNEao ]AMoc¯wKT t § t Z`G t ]UMcG`K EVoYT[ocGJ]A<E µ # KJ F]_µ KJ Nm X
(27) \ ¬FK¿®EHK<T<qHE t oG`]U E /M]Al oc¯wK OyKNoX] T[Z`ZgX pTG`MYOTÁ µ # KJ LJ Ão]oc¯®T[o] TZ`ZgT t § t Z`G t ]UMcGJKNEVoYT[oG`]AE®OOµ # TUOFX ]AZ`ZJ]·O1( ÁTµ # LJ
(28) KJ Nà * µ # 3·_¯HKNMK µ # GÆOFoc¯wK K vVoKNEOyGJ]AE ][ µ # KJ FGJERVq t KR<V§ KJ m X W{G`MPOQoNL·,K EHKNKX R oc] pHM]ILKFo¯T[ o ( Á µ # KJ KJ à *3GSOgT t § t Z`G t m ,§'¯a§Vp]Ao¯HKOQGSO µ # KJ GSO TÇ,t ¯w§ KNt E Z`G t µ # TLEJ R ]AKJEaoPT[GÆGJOFEOTT ZJKNkLT§ ZCZJTUKOcOQ-G`kAm%Ewl<,KNK Eao,T[q®]AOyK M µµ ## LKJJ mXGSOnLqHT[pHE½pG`]xE®OyRVK q oc¯wKK'R TAOyOcqHOQ¦KNMcRVoGJG`kA]UMPETpHÊT[¯jZSOQ]KL m µ # QgG`o]UZ`Z`]·t Oo¯T[o »lt q®t Oyo t ]AEaoPT[GJE t 5m nLGJE t K<KNILK Mc§%KRVkAK t ] µ FGÆO TAOcOQG`kUEHKR oRa] GSOyoKNG`vHE T t oocZJILX§ K Mc]AocEHG K'KO>RVGJMcK\ t oc G`` ]UEOGJE>X Qµ Á# QS ÃYCKN¯EVoTAKNOXMcGJTEHok¹ZJKT[TAEOQR oX¥<ZJKTNILIVKNGJMcEHokaG t KO,.m G`E0KN E t K MK OyptK ]AEaocG`oPILTK G`Z`E§LO m Ç,¯®T[otGÆO KJ Á t
(29) \NÃ 'T[ER KJ NÁ `PÃ ~Am FZÆOyX ]w @ GÆOFTp®T[oc¯ Mc]Ul t ` oI]
(30) \ GJE µ # KJ G5m¨Kxm ` X 1 LJ NÁ
(31) \ÃPm d ]UEOyKÉqHK EVoZ`§L KJ ÈGÆOFEH]UoZ`KNkxT[ZÊ3T t ]AEaocMPTURVG t ocG`]UE@m 0KNE t K 1( TÁ µ # LJ
(32) KJ Nà *@GÆO_T t § t ZJG t m Tdµ # E ]U EVT ILt K 1§ MPt(OyÁ Z`K µG Z`#t §LKAJ ]AZJ MKN G`o KNX EaµL#J oP3TÃoc*ÊGJKmg]AE ¬FT[E Kµ ¿# T LEHt J K§ t µ Z`#T[G KtEJ R7]A MG`T KNEaµZ`oPKN# T_kxocT[@ GJZ]AE'TA@O][TOygGJEkAµ R EH5l<Xm KK « J EV oKFocpw]'X McKJ]ILKK_TU]UocO ¯M±T]UGJo,oNZ`ZJo][¯H·OyKNq OMctmK_¯ K vVocGƯOyToPoO X \0a EÁ ]à c KJ Á
(33) \NÃ ~ GG ÁÁ
(34) \
(35) \N ;ÃÃ;++'')ÁÁ)µµ ## ÃÃ X «
(36) \K `¯®T ILK o ]½Á OyïH]Oyq·»¯oc¯®oT[¯o T[o KX J L<J [GSÁEO \ Z`KNà kx T[ZÊm V nxX qHKJ pH[pÁE]L OQ`cKà G`o'~-GSO T[EHE]ARao m ` Ç, ¯HKN1 ELJ oc¯HÁEK \McKÃPmXK Ç,vVGƯwOyK o t ¥.
(37) ZÆT[oocKNMG`l<pwZ`G`KO5 ` 1 ÁE\ ÃPmX¡5Eo¯HGSO t TAOyKx3Tp®T[oc¯M]Al `_oc]D
(38) \XG`E µ o]AkAK oc¯HKNM ·_GJoc¯¹oc¯HX KKRVkAKOÁ
(39) \ Ã" NÁ `cà ÁTµ # Ã,]UMcl O_T t § t ZJKXG`E µ # 3T t ]AEaocMPTURVG t ocG`]UE@m 0KNE t K KJ <GÆOT+ZJKNkLTZTUOcOQG`kAEwl<KNEao]AM'oc¯HKT t § t Z`G t ]AMcGJKNEaoPT[X oG`]UE µ # KJ <]['µ KJ Nm Ç,1(¯®Á T[µ # o_LJ GSO
(40) V Xµ # KJ NGÆO Ã *ÊpHm MK t GÆOyKNZJ§oc¯wKKNvaocKNEOQG`]UE]-µ # KJ ,GJERVq t KRa§ KJ Vl<KTEHG`Ewk µ # ´@TUOyo · K pHMc]ILKX oc¯To X GÆOFG`EAQK t ocGJILKLm´3KNo µ # KJ µ # KJ sK'T t § t Z`G t ]UMcGJKNEVoYT[oG`]AE®OÈ] µ KJ [#m FZÆOy]HZ`K o X KJ
(41) KJ K,Z`K kLT[ZaTUOcOQG`kAEwl<X KNEaoPOs]AM µ # KJ µ # KJ McKOQpK t ocGJILKNX Z`§xm3´3KNo µ # X ( Á µ # KJ KJ Ã *!T[ER µ # ( Á µ # KJ KJ Ã *5m,§<¯a§Vp]Uoc¯HKOQGSOCÁ µ # KJ
(42) KJ Nà Á µ # KJ KJ ÃYm+¡ µ # KJ µ # KJ o¯HKNE µ # µ # CK t TqOyK µ # _GSOT[EjK vVoKNEOyGJ]AE ] µoX # ]+KJ K [vHTTl<EG`R EHK'µ # X GS O TXELJ KNvaocKN E®OyX G`]UE m][ ¡5µo # Kl<J KT[G`E®l<OpHocZJ¯§VTGJEHokXo¯Hoc¯HKNK-McK TAGÆO%O OyKNM\ocG`]UQE@m_ Ç, Á¯H K- ÃPOy K Oyt q ]AE¯½R oct ¯TATOQKo KJ LJ NÁ
(43) \Ã LJ ÁE\ ÃPm 0FK E t K oc¯HK KRakAK ÁE\ ÃX]['µ GÆOTUOcOyGJkAEHKR oc]%]At pwps]xOyGJocK RaG`McK t ocGJ]AEOgG`E µ # TER µ # mgÇ,¯ToFGÆOI µ # µ # t ]Ul<pHZ`K ocG`Ewko¯HKXpHMc]L]m ¬KXKNEHT]AOyoKKÉLaqH§ KNE µ t # K LJ = T]E%{T oc¯Ht § Kt ILZ`G K t McXoc]AG Mt G`KKNO Ea]oPT oc GJ]A EÁ ] ÃPmgµ ¬FLJK EH[m]Ao´3KKNV0o § 'X
(44) L
(45) J
(46)
(47) !X K' J Y
(48) oQ ·,]- X RV G` MK t Á ocGJ ]AÃ E Ù TUOc OQG` kAEwl< KN=EaoPO ,·_]UM ¯HK µ # EjKJ ocN¯wXm KNd McK¹T[Z`KNZ vVGÆKOyJ oY O $&T[ EX #&G` %E®&RV9 KNv 8½ #OQq % ¯$&$ !Doc¯.
(49) X TS o X K$&J$NEÁ '[\ #à X KJ EÁ '[$&\N ÃP KJ t « ~Á X KPJ  M ~[à o¯H·_K¯HG`RVZJKGJMcK t KocJ G`N]UÁ E ' TUà OcOyGJM kAEHlKKNJ EV Áo ' ·_ ÃP¯wm G t ¯ ¯H]AZJKNZ`E ]·O LJ X KJ < G`E¸ ocN ¯HK¹XRVG`E KNtEHM]UKocTAK%OQG`VEH§k ZJW{KNG`vaEG Tt Z`]UZ`kA§xMPLTRVpHKN¯HEHG ]Ut ocT[KZ¦V]A§MPRa "KN!$Mc#&GJ%EH(k '*Mc)UKNX Á ZÆX T[KoJ G`ILNÃ{Kococ¯HI] K = RVGJVMcK ]goTG`]UZ`Z{E<RVTUGJOcMcOyK GJt kAoEHG`]UlE KNEVTAOo!Oy]AG`kUHEHoYl<T[G`EwKNX EaKRoPOCMc]A]UBM l µ # X KKJ J N m a]U§¹M OyTKNZ`o;Z ocGJEH\k o`%] ~ TX Z`Z@Á IU T[ ÃPZJmqHK¡5O oK]AJ ZJZ`N]Á·\Oà oOy¯q T[t +o ¯¹ ,oct!$¯#T%&o>('* )U`Á X KJ 1 KÃFJ GÆNOÁEH\ K ÃT[KE®OcOR T[MG`Z`K§¹J NZ`ÁKNkx`ÏT[à ZÊ ]A~AM t TEV§#TAOcOQG`kUEHl<KNEao KJ [m ÇoY,T[¯woG`K]AE\EHKNHvaG`E o_Z`G`K E l<Mcl KTUTXOyG`RVEwKk O t Z`KNMcGJvasG K]UO kAoMY¯HT[KpH¯HZJKNG kLT[TZ¦Z{]ARVMYG`RVMK KNt McocGJEHGJ]AkHE¹m TAOOyGJkAEHl<K EVoYO ]AMXT kAGJILKNE ]AMcGJKNE i t t t S S -3{´3KN, o µ # KJ K,TET t § t Z`G t X]AMG`KNEaoPTocGJ]AE]@µ KJ NmC´3K o =K T,oc]Ap]UZ`]AkUG t TZ ]UMPRVK McG`Ewk ] Á ÃGJE µ # KJ FTER KJ . ¸ N 'T Z`KNkxT[ZXRVGJMcK ocG`]UE7TAOOyG`kUEHl<KNEao ]U]UMM µ µ # # KKJ J mX Mc¡5KNEZÆT[oo¯HG`ILK KG`E oc]t McK= TUOyFG`Ewock<¯wKZ`KNvaTUG Oct Oy]AGJkAkAEHMYT[lpHKN¯wEVG toTZ·_]U¯HMPG RV¯ KNMG`GJEHl<kl<][K RaT[G`ZJTZCocZJZ`t §+KNkxT[]AZgZJZ`TU]Oc·OQG`O kAEwX l<KJ KNEaoPGSOO t "!$#&%('*) ( Á LJ Å ~[/à *5m .
(50) X X X X oc¯wK TAOOyGJkAEHl<K EVoÁ KJ Â7X ~[Ã/ TER ,!$#%&('*)UX Á ÃYm´3KNo È _ F ¬ N K H E U ] c o. K a § ½ X Koc¯HKMG`kU¯Vol<]LOQoGJEX RVKNvG`EO= Oyq t ¯ X oc¯To KJ Á' à Vm Ç,¯HKNE ÁE'[\NÃ+ X LJ NÁ '[\ÃY ~DP 7M Á' Ã. ~TER ÁE'`ÏÃ. V(-M P X Um FZÆOy]w X K t T[qOQK LJ GSOZ`K kLT[Z T[ER = T±o]Ap]AZJ]AkAG t T[Z ]AMYRVKNMcGJEHkGJo]AZ`ZJ]·Ooc¯®T[o Á'[\à ÁE'[\NÃP TUXT~aEOcOQP G`G`kAEEwBRal<KNPv KNEao mX nL qH½pH]ApM OT[]Lµ ocOQ# GÆK KOÄJ X oc§aN¯HG`gEHK<Oyk q ZJKNt X l<¯½ Ál oc'[¯T \T'à o EH]U X o KJ ocX b]ÁM '[K<\X ÃYo McqHM~ KxmP X Ç, m ¯HKNd M E ]UEoOy¯H KKNÉX MqHK K EÁ 'KNEVvaoGSZ`à §LOQoP{ Ooc¯HT±~KNZ`MK TK<kLET[GSR O Z ]tT A ocEÁE]U't pZJ5q]Aà Z`RV7]UKkA] aoc¯m TT0FZgo]]Aoc·,MP¯HRaKNK KNILMcMcKKNGJM EHK kHvVGÆ OyÁEG`oP'o_O 5'Ã7]AZJ` Z`] · VmgO 1 Ç,KJ ¯aM qÁ O'wm 5T[ÃY0FpH3pHKNOQqE ZJ§Vt GJ¯K EHkX oc¯ oÁ T¯H'o K `cX ÃRV KÁ ¿'EH`P~AGJà ocGJl<]AE<K~UT[]mEw G`nLEHt G`Z`kE ]xt OyocVK qH¯MT= KFo · X GSKO t GÆO,EH]AoZ`K kLT[ZÊt HT t ]AEaocMYTARVG t ocGJ]AE@m "'
(51) . Ç,nxqH¯wpHK pT[]LZJOQkAK+]AMoG`¯Ho¯HKl l<GSKNOXo¯H]aTAR OQKR+]UMcqHMpK ]AEocZJ§½´3KNKNlEVqwl l<TAKNOMPT~ocKT[O ER TZ`ZXVCT a§ §%Z`T[G E½]UG`EMcGJRaKNq EVt oYocT[GJoILG`K ]AE®TO MckAµ qw# l<KJ ±KNEa]oN m µµ # KKJJ [[mCGJE,RV§ q ´3KKNR+lVl § T T ~A]Ut EVKTILtKN¯ EwtG`KNT Eat o§ t Z`ZJK G kLt T[Z]UMcTAGJKNOOyEVG`oYkUT[EHol<G`]AKNE Eao µ # t X LtJGSON,t T[TE7ERKNvVoKN]AEEaOQILG`KN]AMYE OyKN]ZJ§L'mOQ]AÇ,l<¯wKK T]UZ`kUM]AKMcT GJoc¯H¯ l Z`KNpHkxt MT[X ] Z t TAKNOKOyRHG`kUO_EHTUl<t O KN]AEaZJo Z`]X ·KJOmg WH]A]AMM_Kµ # T Lt J ¯ T t ]A§ E®t OyZJocG Mt q ]AMcoGJKNocEa¯HoPK<T[oK G`vV]UEoKNEµ#t OyKGJJ ]A E ][µ # _µ ][LJ µ # TKEJ R GJT ERV§ q Z`t G Kt R ]UMcVG`§K EVoYT[LJ ocGJ]AmjEO_Ç,][¯w K±µ]UQMcm GJKNEVoYT[oG`]AE®O Oy]%]AHt oYT[G`EwKR/t ]UMclKNvwT t ocZ`§%oc¯wKOQKNo'][ÈT[Z`Z tt t Ç]U,Mc¯wGJKNK±EVpwoYT[Mco]AG`w]AZ`E KNlµ # KoJ ¯T[mo Ç,MKN¯wl GSOTpHG`EMc]UOXHGSZ`OK l oc]%GÆkAOÈK KEHÉKNqHMPGJTIUocT[K¹Z`K T[EVZJoZ,ZJoKN]kLTo¯ZT[TAoOcOQ][G`kUEH¿l<EKNRVEaGJEHoPkO X TKZ`J Z RVGSOQ]UocM'GJE T[E o ·OQ] TN§Hoc¯O,T]oCEHZÆT[] KNRVZ`KZJOG`EHKNkXE®oRH¯HT[KXEaILoKN][Mc oG T<t KILOCKN]MgocKNTv<EZÆT T[t§ KNt ZJZ`Z`KG t R%RV~GJkA¯MYTAT[OpH¯@ZÆT[Hq®KNOyZgG`Ew ak m oc ¯HKOyZÆ]AT[ZJqHKNocGJZÆ]AO_E ]T[_EG`Rot ~AGSO kU]UG`HILoPKNTE¹G`E½V§¹oc¯w´3K<KNZ`lKNkxl T[t Z T TAVOcmXOQG`kU´3EHKNl<oC=KNEaoPOK'G`E TG`oE ]ApM]AKTAZJ]AOQkAG`EHG t k¹T[Z!Z`KN]AvaMPG Ra]AKNMckAGJMYEHT[k<pH¯w][G T Z Á]U MP RVÃ_K GJMcE G`Ewµk# KMcJ KNNZÆm T[oc« GJILKK oZÆTA] OQo = TAOm OyGJkA¡C EHl< K ÁEV oY Oà T[
(52) MK< %oc¯HocK¯wKN¸ Mc K! ! T[McT[K¹ER EH]½t s¸ TUN OcOy@GJkAMcEHKlOQpsKNK EVoYoct OGJILm KNZ`e §Lm-oc¯H´3K t KNMco·_GSX OQKKLJ ,o¯H XK¿¸_MPN OQo<TK ER T ZJZJKNKNkLvaTG Z_]UTUkAOcMPOyTGJpHkA¯HEHGlT[KNZ¦EV]AoXMPRa]AKNM McGJµEH# k LJ GS[O m% "!Ç,#¯H%(K '*ZJ)%KN( kLÁ XTZ_KJ TAÅO OyGJkA~[EH à l< t K *5m EVoX·_¯HG t ¯+]UZ`ZJ][·O LJ GJE oc¯wK t t Ç,¯wKMcK t qHMPOQG`ILK<]AMlqwZST[oG`]UE KNZJ]·»RVKO t McGJsKO o¯HKpHM] t KOOm Ç,¯wK t qHMMcKNEao Z`K kLT[Z }
(53) .
(54) UILT OcK OQMcG`ockAG EwKl<OCKN][Ea o3µGSO@m,Mc,K pH§ McKOQ]UKNEVEaILocKNKEaRFocaGJ]A§ E@X %µ# ·_¯H G`ZJK; a mg Ç,
(55) ¯H
(56) KX
(57) KNva,ocKNGÆO@MET[T[E Z TMcT[HZJZ3GJocGÆMYO T[Mc1 §OQK ÉqwKNE t KC]Á~ oc L¯wÃYK m t t t 8# 1 Á N µ # KJ Ïà U5N ¸ +KNEaqHl<K MPT[oKT t § t Z`G t ]AMG`KNEaoPTocG`]UE µ # $ . ' U; ÁE Ã7 # 1 ÁEN®Â ~ ;µ # KJ  à $. IX = oc]Ups]UZ`]UkAG t T[Z{]AMPRaKNMcGJEHk ][; EÁ ÃgGJE µ # LJ ¶¸ ! ! (!
(58) %" OU $ . X /8 Oµ # K vVoKNEOyGJ]AE ][ µ # KJ FGJERVq t KR<V§ 1 X Á NHÂ ~ µ # Ã U X ¸ N ! X %" ^ $. ,!$#%
(59) '*) ( Á  ~[Ã/ * ^ $. ! %". ^ . ,¿®Ç E¯wRVK G`Ewt ]Ukl<TpHE+qHK oYvVT[ooG`KN]AX EE'OyGJ][]A!E%TX][oc ]UT#ps]UkUXZ`G`]UILkAKNG Et T[]UZ3Mc]UGJKNMPRVEVK oYT[McG`oEwG`]AkE MKÉLT[qHE%G`MsKKO,ÀRV]UÁÊEH¸ÈK¹GJEºÃÅÀOyÁ5oc¸ K ÃÈpO.Oyo(KN¥ p*5LO·_m'¯HWHGJ]AZ`KM TOQocEKNp®TUOOcmOyGJkAÇ,EHl¯HKKNEV· o ]AM , "ps!$#&K %My(]A'*M) l<( Á KR½Â ·_~G`à oc ¯wG`* E t TKET ¯KG`Koct TAK OyMPGJT[Z`o§'G`]U]AE HoY][T[ GJEHoK¯HRKTZSOQ ]8 GJE ÀwÁʸ#Z`] Â/,jºGSOà to¯H¯KTMct kA]AKl<R+pHocZJ]KNvaoG`¯HoQ§_K<pMcKNK M t qHt MPT[OQZ`G`ZLIL]K ¦oct ¯HTK Z`Z pH·_Mc] ¯Ht G tK¯+RVqH] Mct K t tGSqHOCMPÀOÁ5GJ¸ E Â-oc¯wºGSOÃ@TGJocEKNRMYT[oco¯HG`]AK E\RVm KNZÆdT§ ]UEt ]AOyKl<ÉLpwqHZ`KNKNt EavaocG`ZJoQ§L§ ]goc¯wKTZ`kU]AMcGJoc¯Hl GSOFÀÁ5¸{Á5¸<½ºÃcÃYm 0][· KNILKNM so¯HK<TNILKNMYT[kUK t ]Ul<pHZJKNvVGJoQ§<][ oc¯HKT[ZJkA]AMG`o¯Hl GSOKNocoKNMNm'Ç,¯HK'McK t qHMPOQG`]UE RZJaKKTO t MG`]AMKMcO'KOQT+p]AocEMKNRHK OXoc ]G`T[E E ·_T ¯H§ G t ¯Z`G T[ZJ]AZFMG`oKN¯HEaKoPTZ`ocKG`T]UILE+KO ]T[McµKm T[Ç,o<¯HoK'¯HKoc]UOoPT[T[l<Z K¹EVqwZ`lKNILK KNZ_M¸ ][m OQh ocTKNtp¯ O po¯HKNKMQ]AZJt KMl<TNILKKR+O]a §½ oc¯H·_K¹GJT[oc¯jZJkA]UoMc¯G`T[ot ¯Ho l t ]Ut Mct McT[KE½Oyp]AKERa]UG`HEHoPk TG`oEH]+KR o¯HaK §½G`EaTAocRHKNRaMG`EEHT[k Z_oEw¯H]aK RVK·,O]Um7M ,Ç,¯HRVK¹]AEwocK]UoPT[T[o Z t]]A l<GJEVpHoqwKNoPMcT[EoTG`ZF]UEEw]aTRVoFKoO¯Hm KXZ`Ç,K¯HTNILK%KO,OyK Mo t KÉL qH#G`M]KO EHÀ]aÁcRVÁÊK¸#O Â/·_ºG`oc¯ ÃQ¼CK Ã_vHOQT octKNocpZJO§jm_]AÇ,Ew¯HK KNMt K¯HG`T[ZÆMcR KKoQT·,t ]¯\F,aG`TEERHR O o¯H]A]LMcMOQKK Oyp·_]UG`Eoc¯½RHOl<oc]]UMcK<T o¯]AT[lEpH]AqHEHoPTK ocGJt ]A¯HE%G`ZÆR3][ 1 ]AMl< G`EwkOy K -o ÁN ]mµ # KhJ ÏT Ãt ¯½GJE+G`Ea·_oc¯wKNMG E¯ T[Z EH ]aÁRV K¹Ã][
(60) a m t¡5E¹oc¯HGÆOFOQG`ocq®T[ocGJ]AE@¦oct ¯HKpHMc] t KRVqHMcK GÆO t ]Al<pHqwocKR<G`ET t ]UEOyoYT[EaoEVqwt lKNM ][ OyoKNpOm ZSOy]wL·,.K ,aEH]·jo¯T[o
(61) M ¸3¼gmgÇ,¯T[o_GÆOLoc¯HKoc]UoPTZ t ]Ul<pHqHoYT[ocGJ]AET[o oc¯HKGJEVoKNMcE®T[Z Ew] ]aRVOyoKKNO_p][O,EH
(62) K _KRVGSOFKRÀÁÊT[¸3o¼CKÃPT m ¯ e EEH]aoRV¯HKKX][]A o¯H,KNMGSOF¯ÀT[EÁ5R¦¸<7½ º /ÃPM m Ç,¼g¯Hm_KN¡5ME¹KTA]ARHMRVKXGJococ¯HGJ]AKXE@ocH]UooP¯HTKZ EaEaqHqHl'l'ssK K MM ] OyoKNpO,o]KNEaqHl<K MPT[oKt TZ`Z\¼ T t § t Z`G t ]AMG`KNEaoPTocG`]UEO,][ µ¶GSOFÀÁÁ5¸<½ºÃQ¼CÃPm z.
(63) &LX -%$ ( 3~ *-m d m _T[Ms]xOcT T[E®R h m -TNEHG5 d ]AE t qwMcMcK E t § GJE ¯HKTIaG`ZJ§ Z`]xTARVKR Ew KN G`
(64) kU ¯V ]A"M! ¯H#]L]a R
(65) %i $'t ]A&)E®( Oyoc*MY!T[GJEH KR<¹OQ§HÁcOQ~ ocAKN|Al LÃPO¦}AzU,+a }U|[ w m
(66)
(67)
(68)
(69) (¨ *-m d mg_T[Mc]xOcTV- . /0/!12( 3 1414!15 6$"!17 8 :9) ;
(70) V h Z`ZJGSO0F]UM i · ]L]aR3 d ¯HG t ¯HKOQocKNM HD© 3~ AU¥Vm (¨¥ *¬m h m{©EVqwoc¯@< >=?!@ A :9) B!
(71) CED F@GH "
(72) %$ '!I
(73) " 1JK1ML N4=O RHRVGÆOy]UE i« KOQZ`KN§Lw^ KTARVGJEHkH¢Tam`3~ AzUÁ5OQK t ]AE®R#KRVG`oG`]AE%~ ¥LÃPm ( *^Xm f m nxoPT[EwZ`KN§L t § t ZJG t ]UMcGJKNEVoYT[oG`]AE®O][kAMYT[pH¯®O@ PQ !B!R. S=?! ;IUT Á~NL¥ÃYC~[xI~ +®~[|am (¨} *© m i5f g]H -MPTpH¯ t ]AZJ]AqHMG`EHkxOT[ER%T t § t ZJG t ]AMG`KNEaoPTocGJ]AEO J
(74) ?!
(75) %$V. 1M;4L 1W
(76) X! YK1Z 