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Transcript of Calculus
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Sblobj^ ab rkf`fa^a m^o^ i^ b`r^`fŽk afcbobk`f^i j^qof`f^iD%&p'< ?D&p'Kbv ab bumlkbkqbp m^o^ bumlkbk`f^ibp ab j^qof`bpSblobj^p ab bufpqbk`f^ v rkf`fa^a m^o^ pfpqbj^p ifkb^ibp el,jld‹kblp `lk `lbcf`fbkqbp `lkpq^kqbpDi mol_ibj^ ab `^i`ri^o an?
Sblobj^ ab B^vibv,G^jfiqlkDgbo`f`flpL‹qlal ab Orqwbom^o^`^i`ri^o ap?
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@ 0/ i^odl ab i^ L^qbjŠqf`^ pb bk`rbkqo^k jr`elp bgbjmilp ab l_gbqlp j^qb,jŠqf`lp nrb mrbabk prj^opb rklp `lk lqolp v jriqfmif`^opb mlo k•jbolp ob^ibp-@kqbqlal+ ilp k•jbolp ob^ibp plk l_gbqlp ab q^i k^qro^ibw^+Nqolp bgbjmilp plki^p crk`flkbp sb`qlof^ibp+ ilp k•jbolp `ljmibglp+ i^p pbofbpv ilp sb`qlobp bk bibpm^`fl j,`eiajoekj]h- Dk bpqb`^mŒqrilqo^q^jlp rk `lk`bmql j^qbjŠqf`l dbkbo^i+ii^j^al aol]_ek heja]h+nrb fk`irvb qlalp bplp bgbjmilp v jr`elp lqolp `ljl`^plp m^oqf`ri^obp-
Aobsbjbkqb+ rk bpm^`fl ifkb^i bp rk `lkgrkql ab bibjbkqlp ab k^qro^ibw^`r^inrfbo^ pl_ob bi nrb mrbabk ob^ifw^opbfboq^plmbo^`flkbp ii^j^a^p ]`e_e‰j viqhpelhe_]_e‰j lkn jŠianko- @i abcfkfo rk bpm^`fl ifkb^i kl bpmb`fcf`^jlp i^k^qro^ibw^ ab ilp bibjbkqlp kf ab`fkflp `Žjl pb ob^ifw^k i^p lmbo^`flkbp bkqobbiilp- Dk `^j_fl+ bufdfjlp nrb i^p lmbo^`flkbp qbkd^k `fboq^p molmfba^abp nrbqlj^jlp `ljl ^uflj^p ab rk bpm^`fl ifkb^i- U^jlp ^elo^ ^ e^`bo `lk abq^iib rk^abp`ofm`fŽkab bplp ^uflj^p-
0-1 Cbcfkf`fŽkab bpm^`flifkb^i
Rb^ T rk `lkgrkql kl s^`Œl ab l_gbqlp+ii^j^alp ahaiajpko- Di `lkgrkql Tpb ii^j^ bpm^`fl ifkb^i pf p^qfpc^`bilp afbw ^uflj^p pfdrfbkqbp nrb pb bkrk`f^kbk qobpdormlp-
?teki]o `a _h]qoqn]
@WHNL@ 0- BK@TRTQ@ QDRODBSN CD K@ @CHBHˆM- ? pk`k l]n ]a ahaiajpkoy a v `a T _knnaolkj`a qj ahaiajpk Šje_k `a T hh]i]`k oqi] `a t a v+ `aoecj]`klkn t * v-
2
3 Col]_eko heja]hao
@WHNL@ 1- BK@TRTQ@ QDRODBSN CD K@ LTKSHOKHB@BHˆM ONQ M‰LDQNR QD@,
KDR- ? pk`k t `a T u pk`k jŠiank na]h] _knnaolkj`a qj ahaiajpk `a T hh]i]`klnk`q_pk `a ] lkn t+ `aoecj]`k lkn ]t-
?teki]o l]n] h] ]`e_e‰j
@WHNL@ 2- KDX BNMLTS@SHU@- N]n] pk`k t u pk`k u `a T+ pajaikot * u < u * t-
@WHNL@ 3- KDX @RNBH@SHU@- Aq]haomqean]mqa oa]j t+ u+w `a T+ pajaiko&t * u' * w < t * &u * v',
@WHNL@ 4- DWHRSDMBH@CD DKDLDMSN BDQN- Cteopa qj ahaiajpk aj T+ `a,oecj]`k _kj ah o‡i^khk N+ p]h mqa
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@WHNL@ 6- KDX @RNBH@SHU@- N]n] pk`k t `e T W pk`k l]n `a jŠiankona]hao] u ^+ pajaiko
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@WHNL@ 7- KDX CHRSQHATSHU@ O@Q@ K@ @CHBHˆM DM T- N]n] pk`k t u pk`ku `a T u pk`k jŠiank na]h]+ pajaiko
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@WHNL@ 8- KDX CHRSQHATSHU@ O@Q@ K@ @CHBHˆM CD M‰LDQNR- N]n] pk`kt `a T v pk`k l]n `a jŠianko na]hao] u ^+ pajaiko
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Klp bpm^`flp ifkb^ibp ^pŒabcfkfalp+pb ii^j^k+ ^ sb`bp+bpm^`flp HŒkb^ibpna]haom^o^ obp^iq^obi eb`el ab nrb pb jriqfmif`^k ilp bibjbkqlp ab T mlo k•jbolpob^ibp+ Rf bk ilp ^uflj^p 1+ 6+7 X 8 pb obbjmi^w^ jŠiank na]hmlo jŠiank _ki,lhafk+ i^ bpqor`qro^ nrb obpriq^ pb ii^j^ aol]_ek heja]h _kilhafk- @idrk^p sb`bprk bpm^`fl ifkb^i pb ii^j^ q^j_f‹k aol]_ek ra_pkne]hheja]h l pfjmibjbkqb aol]_ekra_pkne]h:ilp k•jbolp rqfifw^alp `ljl jriqfmif`^alobp pb ii^j^k ao_]h]nao-Tkbpm^`fl ifkb^i ob^i qfbkb k•jbolp ob^ibp `ljl bp`^i^obp: rk bpm^`fl ifkb^i `lj,mibgl qfbkb `ljl bp`^i^obp k•jbolp `ljmibglp- Rf _fbk `lkpfabo^objlp mofk`fm^i,jbkqb bgbjmilp ab bpm^`flp ifkb^ibp ob^ibp+qlalp ilp qblobj^p plk sŠifalp m^o^bpm^`flpifkb^ibp `ljmibglp- Br^kal afd^jlp bpm^`fl ifkb^i pfk jŠp+ pb pl_obkqbk,aboŠ nrb bi bpm^`fl mrbab pbo ob^i l `ljmibgl-
0-2 Dgbjmilpab bpm^`flpifkb^ibp
Rf mob`fp^jlp bi `lkgrkql T v ab`fjlp `Žjl pb prj^k prp bibjbkqlp v `Žjlpb jriqfmif`^k mlo k•jbolp+ l_qbkbjlp rk bgbjmil `lk`obql ab bpm^`fl ifkb^i-Di ib`qlo cŠ`fijbkqb mrbab `ljmol_^o nrb `^a^ rkl ab ilp bgbjmilp pfdrfbkqbpp^qfpc^`bqlalp ilp ^uflj^p m^o^ rk bpm^`fl ifkb^i ob^i-
DIDLOKN 0- Rb^ T < Q+ bi `lkgrkql ab qlalp ilp k•jbolp ob^ibp+v pb^kt * v v ]t i^ ^af`fŽk v i^ jriqfmif`^`fŽk loafk^of^p ab k•jbolp ob^ibp-
DIDLOKN 1- Rb^ T < b bi `lkgrkql ab qlalp ilp k•jbolp `ljmibglp+ abcf,kfjlp t * v `ljl i^ ^af`fŽk loafk^of^ ab k•jbolp `ljmibglp+ v ]t `ljl i^ jri,qfmif`^`fŽkabi k•jbol `ljmibgl t mlo bi k•jbol ob^i ]- @rknrb ilp bibjbkqlp abT pb^k k•jbolp `ljmibglp+ ‹pqb bp rk bpm^`fl ifkb^i ob^i mlonrb ilp bp`^i^obpplk ob^ibp-
DIDLOKN 2- Rb^ T < TŒŒ+bi bpm^`fl sb`qlof^i ab qla^p i^p k,mi^p ab k•jb,olp ob^ibp+ lk i^ ^af`fŽk v i^ jriqfmif`^`fŽk mlo bp`^i^obp abcfkfa^p bk i^ cloj^loafk^of^ bk crk`fŽk ab ilp `ljmlkbkqbp-
DIDLOKN 3- Rb^ T bi `lkgrkql ab qlalp il{c-,sb`qlobpTj loqldlk^ibp ^ rksb`qlo kl kril a^al L, Rf j < 1+ bpqbbpm^`fl ifkb^i bp rk^ ob`q^ nrb m^p^mlo N`lk L `ljl sb`qlo kloj^i- Rf j < 2+ bp rk mi^kl nrb m^p^mlo N `lk L `ljlsb`qlo kloj^i-
Klp pfdrfbkqbpbgbjmilp pb ii^j^k aol]_eko bqj_ekj]hao- Klp bibjbkqlp ab Tplk crk`flkbp sb`qlof^ibp+ `lk i^ prj^ ab alp crk`flkbp b v c abcfkfa^p bk i^-cloj^ loafk^of^9
'b * c'&t' < z&t' * c&t'
5 Col]_eko heja]hao
m^o^qlal ob^i t bk i^ fkqbopb``fŽkab ilp aljfkflp ab G!v c, K^ jriqfmif`^`fŽk abrk^ crk`fŽk Gmlo rk bp`^i^o ob^i ] pb abcfkb ^pŒ9]h bp ^nrbii^ crk`fŽk `rvl s^ilobk `^a^ t abi aljfkfl ab Gbp ]h't(- Di bibjbkql `bol bp i^ crk`fŽk `rvlp s^ilobpplk krilp m^o^ qlal t- Di ib`qlo mrbab `ljmol_^o cŠ`fijbkqb nrb `^a^ rkl abilp `lkgrkqlp pfdrfbkqbpbp rk bpm^`fl crk`flk^i-
DIDLOKN 4- Di `lkgrkql ab qla^p i^p crk`flkbp abcfkfa^p bk rk fkqbos^ila^al-
DIDLOKN 5- Di `lkgrkql ab qlalp ilp mlifkljflp-
DIDLOKN 6- Di `lkgrkql ab&qlalp ilp mlifkljflp ab do^al z j+ pfbkal jcfgl- 'Rfbjmob nrb `lkpfabobjlp bpqb`lkgrkql+ pb pl_obkqbkaboŠ nrb pfbjmob bpqŠfk`irfal bi mlifkljfl kril-( Di `lkgrkql ab qlalp ilp mlifkljflp ab do^al ecq]h^ j kl bp rk^ bpm^`fl ifkb^i mlonrb kl pb p^qfpc^`bkilp ^uflj^p ab `i^rpro^- Olobgbjmil+ i^ prj^ ab alp mlifkljflp ab do^al j mrbab kl pbo ab do^al j-
DIDLOKN 7- Di `lkgrkql ab qla^p i^p crk`flkbp `lkqfkr^p bk rk fkqbos^ila^al- Rf bi fkqbos^il bp Y]+^[- abpfdk^jlp bpqbbpm^`fl `lk A']+ ^(-
DIDLOKN 8- Di `lkgrkql ab qla^p i^p crk`flkbp abofs^_ibp bk rk mrkql a^al-
DIDLOKN 0/- Di `lkgrkql ab qla^p i^p crk`flkbp fkqbdo^_ibpbk rk fkqbos^ila^al-
DIDLOKN 00- Di `lkgrkql ab qla^p i^p crk`flkbp Gabcfkfa^p bk bi mrkql 0pfbkal G' 0( < N-Di k•jbol N bp bpbk`f^i bk bpqbbgbjmil- Rf obbjmi^w^jlp N mlork k•jbol kl kril b+sfli^jlp bi ^uflj^ ab `i^rpro^-
DIDLOKN 01- Di `lkgrkql ab qla^p i^p plir`flkbp ab rk^ b`r^`fŽk afcbobk`f^iifkb^i eljld‹kb^ v! * ]u&* ^u < N+alkab ] v ^ plk `lkpq^kqbp a^a^p- S^j_f‹k^nrŒbp bpbk`f^i bi N- Di `lkgrkql ab plir`flkbp ab rk^ b`r^`fŽk afcbobk`f^i kleljld‹kb^ kl p^qfpc^`bilp ^uflj^p ab `i^rpro^-
Dpqlp bgbjmilp v jr`elp lqolp e^`bk m^qbkqb Žjl bi `lk`bmql ab bpm^`flifkb^i bpqŠbuqbkafal mlo bi …idb_o^+i^ FbljbqoŒ^ v bi @kŠifpfp-Br^kal pb abar`brk qblobj^ ab ilp ^uflj^p ab rk bpm^`fl ifkb^i+ l_qbkbjlp rk obpriq^al sŠifalm^o^ `^a^ bgbjmil `lk`obql- Tkfcf`^kal s^oflp bgbjmilp ab bpqbjlal+ `lkpbdrf,jlp rk `lkl`fjfbkql jŠp molcrkal bk `^a^ rkl- Dk l`^pflkbp bi `lkl`fjfbkqlab rk abqbojfk^al bgbjmil ^vra^ m^o^^kqf`fm^ol fkqbomobq^oobpriq^alp sŠifalpm^o^ lqolp bgbjmilp v mlkb bk bsfabk`f^ obi^`flkbp nrb ab lqol jlal mlaoŒ^km^p^ofk^asboqfa^p-
Akjoa_qaj_e]o ahaiajp]hao `a hko]teki]o 6
)', 6XW\NLr NWLRJ\NUNVNW]JUN\MNUX\JaRXVJ\
Klp qblobj^p nrb pfdrbk pb abar`bk cŠ`fijbkqb ab ilp ^uflj^p ab rk bpm^`flifkb^i-
SDNQDL@ 0-0- TMHBHC@C CDK DKDLDMSN BDQN- Cj _q]hmqeanaol]_ek heja]hateopaqj ahaiajpk _ank v o‰hkqjk-
Baikopn]_e‰j- Di ^uflj^ 4 klp ^pbdro^ nrb bufpqbmlo il jbklp rk bibjbkql`bol- Rrmlkd^jlp nrb bufpq^kalp+ pb^k /0 v M1+ G^`fbkal t < /0 X N < N1 bkbi ^uflj^ 4+ l_qbkbjlp /0 * N1 < //* @kŠild^jbkqb+ e^`fbkal t < N1 XN < N! bk`lkqo^jlp N1 * /0 < M1+ Obol /0 * N1 < N1 * /0 mlo i^ ibv `lk,jrq^qfs^+ ^pŒnrb /0 < M1+
SDNQDL@ 0-1- TMHBHC@C CD DKDLDMSNR NOTDRSNR- Cj _q]hmqeanaol]_ekheja]h pk`k ahaiajpk peaja at]_p]iajpa qj klqaopk- Copk ao+l]n] pk`k t ateopaqj u+v o‰hkqjk p]hmqa t * v < N-
Baikopn]_e‰j- Di ^uflj^ 5 klp af`b nrb `^a^ t qfbkb mlo il jbklp rklmrbpql+ ^ p^_bo ',0 't, Rrmlkd^jlp nrb t qbkd^ alp lmrbpqlp+pb^k W0 b W1&Dk,qlk`bp t * W0 < N X t * W1 < N- Rrj^kal X1 ^ ilp alp jfbj_olp ab i^ mofjbo^fdr^ia^a v ^mif`^kal ilp ^uflj^p 4+ 3 v 2+ l_qbkbjlp nrb
v
W1* &t * Wh(< 'W1 * t' * Xq < M * Wh< Wh* M < Wh-
Olo `lkpfdrfbkqb X0 < W1+`lk il nrb t qfbkb bu^`q^jbkqb rk lmrbpql+ bi bibjbk,ql &+h't,
Lkp]_e‰j- Di lmrbpql ab t pb abpfdk^ mlo ,t- K^ afcbobk`f^ u , t pb abcfkb`ljl i^ prj^ u * ', u(-
Di qblobj^ pfdrfbkqb jrbpqo^ rk `lkgrkql ab molmfba^abp nrb ofdbk ilp`Ši`rilp ^idb_o^f`lp bibjbkq^ibp bk rk bpm^`fl ifkb^i-
SDNQDL@ 0-2- Cj qj aol]_ek heja]h+aoecjaiko _kj t a u `ko ahaiajpko_q]haomqean]u _kj ] v ^ `ko ao_]h]nao_q]haomqean-Œ-Rajaiko ajpkj_ao h]o lnk,lea`]`ao oecqeajpao9
^( Mt < M,_( ]M < N-
7 Col]_eko heja]hao
b( 'y](t < , ']t( < ]' , t(-a( Qe ]t < N+ajpkj_ao ] < N& k t < N+ k hko `ko-b( Qe ]t < ]u v ] <0<N ajpkj_ao t < v-c( Qe ]t < ^t v t <0<N+ ajpkj_ao ] < ^-d( , 't * v( < ' , t( * ' , v( < , t,u-e( t * t < 1t+ t* t *t < 2t+ v aj cajan]h+ Kz<i t < jt-
Cbjlpqo^objlp ^(- _( v b( v abg^jlp `ljl bgbo`f`flp i^p abjlpqo^`flkbp ab i^plqo^p molmfba^abp-
Baikopn]_e‰j `a ^(- Rb^ w< Mt- Cbpb^jlp abjlpqo^o nrb w< N- Rr,j^kal w ^ pŒjfpjl v ^mif`^kal bi ^uflj^ 8+bk`lkqo^jlp nrb
w* w < Mt * Mt < 'N * M(t < Mt < w-
Rrjbjlp ^elo^ , w ^ ^j_lp jfbj_olp v l_qbkbjlp w< N-
Baikopn]_e‰j ab _(- Rb^ w< ]M+ prj^o w^ pŒjfpjl+ v ^mif`^obi ^uflj^ 7-
Baikopn]_e‰j ab b(+ Rb^ w< ',](t- Rrj^kal w ^ ]t v ^mif`^kal bi ^ufl,j^ 8+ bk`lkqo^jlp nrb
w* ]t < ',](t * ]t < ',] * ](t < Mt < N +
^pŒnrb w bp bi lmrbpql ab ]t+ w< ,']t(- @kŠild^jbkqb+ pf prj^jlp ]' ,t( ^]t v ^mif`^jlp bi ^uflj^ 7 v i^ molmfba^a _(+ bk`lkqo^jlp nrb ]' ,t( < ,']t(-
)'- 8SN[LRLRX\
Dk ilp bgbo`f`flp abi 0 ^i 17+ abqbojfk^o pf `^a^ rkl ab ilp `lkgrkqlp a^alp bp rkbpm^`fl ifkb^i ob^i+ pf i^ ^af`fŽk v jriqfmif`^`fŽk mlo bp`^i^obp ob^ibp bpqŠ abcfkfa^ bki^ cloj^ rpr^i- O^o^ ^nrbiilp bk ilp nrb kl bp ^pŒ+ab`fo `rŠibp plk ilp ^uflj^p nrb kl pb`rjmibk- K^p crk`flkbp ab ilp bgbo`f`flp 0 ^i 06 plk ob^ibp- Dk ilp bgbo`f`flp 2+ 3 X 4+ `^a^crk`fŽk qfbkb rk aljfkfl nrb `lkqfbkb N v 0- Dk ilp bgbo`f`flp 6 ^i 01+ `^a^ aljfkfl `lk,qfbkb qlalp ilp k•jbolp ob^ibp-
0- Sla^p i^p crk`flkbp o^`flk^ibp-1- Sla^p i^p crk`flkbp o^`flk^ibp ppa-lk bi do^al ab /3 nrb bi do^al ab d 'fk`irvbk,
al /;.',2- Sla^p i^p G `lk /&.' < /&/',3- Sla^p i^p G`lk 0-&.' ;/%&/',4- Sla^p i^p G `lk /&/' < 0 * /&.',5- Sla^p i^p crk`flkbp bp`^ilk^a^p abcfkfa^p bk ZN+0\-6- Sla^p i^p G bk i^p nrb G&t',y N `r^kal t y * __,7- Sla^p i^p crk`flkbp m^obp-8- Sla^p i^p crk`flkbp fjm^obp-
Qq^aol]_eko `a qj aol]_ek heja]h 8
0/- Sla^p i^p crk`flkbp ^`lq^a^p-00- Sla^p i^p crk`flkbp `ob`fbkqbp-01- Sla^p i^p crk`flkbp `lk mboŒlal 1&hR-
02- Sla^p i^p G fkqbdo^_ibp bk Z/+0\ `lk j G't(`t < N-
03- Sla^p i^p G fkqbdo^_ibp bk Z/+0\ _kjjh't(`t y N-04- Sla^p i^p G nrb p^qfpc^`bk G't( < i'i , t( m^o^ qlal t+05- Slalp ilp mlifkljflp ab S^vilo ab do^al R::j m^o^ rk j cfgl 'fk`irvbkal bi mlifkl,
jfl `bol(-06- Sla^p i^p plir`flkbp ab rk^ b`r^`fŽk afcbobk`f^i ifkb^i eljld‹kb^ ab pbdrkal loabk
v! * N't(u& * O't(u < N+pfbkal N v P crk`flkbp a^a^p+ `lkqfkr^p m^o^ qlal t-07- Sla^p i^p pr`bpflkbp ob^ibp ^`lq^a^p-08- Sla^p i^p pr`bpflkbp ob^ibp `lksbodbkqbp-1/- Sla^p i^p pbofbp ob^ibp `lksbodbkqbp-10- Sla^p i^p pbofbp ob^ibp ^_plirq^jbkqb `lksbodbkqbp-11- Slalp ilp sb`qlobp &t* v+w( ab Ty `lk w < N-12- Slalp ilp sb`qlobp &t* v+ w( ab Ty `lk t < N l v < N-13- Slalp ilp sb`qlobp 't+ v+ w( ab Ty `lk v < 4t-14- Slalp ilp sb`qlobp 't+u+v( ab U^ `lk 2t*3u< 0+ w<N-15- Slalp ilp sb`qlobp &t* v+w( ab Ty nrb plk molar`qlp ab 'i+ 1+ 2( mlo bp`^i^obp-16- Slalp ilp sb`qlobp &t* v+w( ab U^ `rvlp `ljmlkbkqbp p^qfpc^`bk rk pfpqbj^ ab qobpb`r^,
`flkbp ifkb^ibp ab i^ cloj^
17- Slalp ilp sb`qlobp ab Tj nrb plk `lj_fk^`flkbp ifkb^ibp ab alp sb`qlobp a^alp ? v @,18- Rb^ T < Q*+ bi `lkgrkql ab ilp k•jbolp ob^ibp mlpfqfslp- Cbcfk^jlp i^ ~prj^ƒ ab alp
bibjbkqlp t b v ab T `ljl pr molar`ql t --u 'bk bi pbkqfal loafk^ofl(+ v abcfk^jlp i^~jriqfmif`^`fŽkƒ ab rk bibjbkql t ab T mlo rk bp`^i^o a mlkfbkal t€, Cbjlpqo^o nrbT bp rk bpm^`fl ifkb^i ob^i `lk bi bibjbkql `bol-
2/- ^( Cbjlpqo^o nrb bi ^uflj^ 0/ mrbab abar`fopb ab ilp lqolp ^uflj^p-_( Cbjlpqo^o nrb bi ^uflj^ 0/ kl mrbab abar`fopb ab ilp lqolp ^uflj^p pf bi ^uflj^5 bp obbjmi^w^al mlo bi ^uflj^ 5&9 O^o^ qlal t ab +T v qlal v ab T qbkbjlp nrbt*u<M-
2Œ- Rb^ R bi `lkgrkql ab qlalp ilp m^obp loabk^alp &t* *t=' ab k•jbolp ob^ibp- Dk `^a^ `^pbabqbojfk^o pf R bp l kl rk bpm^`fl ifkb^i `lk i^p lmbo^`flkbp ab ^af`fŽk v jriqfmif`^,`fŽk mlo bp`^i^obp abcfkfa^p `ljl pb fkaf`^- Rf bi `lkgrkql kl bp rk bpm^`fl ifkb^i+fkaf`^o `rŠibp plk ilp ^uflj^p nrb kl pb `rjmibk-
^( 'Wi&V1( * 'Xi+ W1( < 'Vh * Xi +V1 * W1(+ ]'Vh+ V1( < ']Vh& M',
_( 'Vh& V1( * 'Xi +W1( < 'Vh * Xi +N(+ ]'Vh +V1( < ']Vh +]t1(•
`( 'Vh& V1( * 'Xi +W1( < 'Vh& V1 * W1(+ ]'Vh& V1( < ']Vh+ ]t1(•a( 'Vh& V1( * 'Xi *W0' < 'Hui * t1/* Hv{* X10(+ ]'Vh& V1( < 'H]thh+ ]t10(•
21- Cbjlpqo^o i^p m^oqbp ab i^ a( ^ i^ e( abi qblobj^ 00-2-
)'. D^KN\YJLRX\MN WN\YJLRXURWNJU
C^al OL bpm^`fl ifkb^i T pb^ Q rk pr_`lkgrkql kl s^`Œl ab T- Rf R bp q^j,_f‹k rk bpm^`fl ifkb^i+bkqlk`bp R pb ii^j^ oq^aol]_ek ab T- Di qblobj^ nrb pfdrb
0/ Col]_eko heja]hao
a^ rk pbk`fiil `ofqbofl m^o^ abqbojfk^o pf rk pr_`lkgrkql ab rk bpm^`fl ifkb^ibp l kl rk pr_bpm^`fl-
SDNQDL@ 0-3- Qa] R qj oq^_kjfqjpk jk r]_‡k `a qj aol]_ek heja]h T-R]h oq^_kjfqjpk R ao qj oq^aol]_ek oev o50/ oeo]peob]_ahko]teki]o `a _h]qoqn]-
Baikopn]_e‰j- Rf R bp rk pr_bpm^`fl+ p^qfpc^`bqlalp ilp ^uflj^p ab rkbpm^`fl ifkb^i+v mlo q^kql+bk m^oqf`ri^o+ilp ^uflj^p ab `i^rpro^-
Cbjlpqobjlp ^elo^ nrb pf R p^qfpc^`bilp ^uflj^p ab `i^rpro^+ p^qfpc^`bq^j_f‹k ilp lqolp- K^p ibvbp `lkjrq^qfs^ v ^pl`f^qfs^ m^o^ i^ ^af`fŽk '^uflj^p2 v 3( v ilp ^uflj^p m^o^ i^ jriqfmif`^`fŽk mlo bp`^i^obp '^uflj^p abi 6 ^i 0/(pb p^qfpc^`bk^rqljŠqf`^jbkqb bk R mlonrb plk sŠifalp m^o^ qlalp ilp bibjbkqlpab T- E^iq^ `ljmol_^o ilp ^uflj^p 4 v 5+ i^ bufpqbk`f^ abi bibjbkql `bol bk R+v i^ bufpqbk`f^ab rk lmrbpql m^o^`^a^ bibjbkql ab R-
Rb^ t rk bibjbkql `r^inrfbo^ ab R- 'R qfbkbmlo il jbklp rk bibjbkql v^ nrbkl bp s^`Œl-( Rbd•k bi ^uflj^ 1+]t bpqŠbk R m^o^qlal bp`^i^o ]- Slj^kal ] < N+obpriq^ nrb Mt bpqŠbk R- Obol Mt < N+ bk sfoqra abi qblobj^ 0-2 ^(+ `lk il`r^i N D R+v pb p^qfpc^`bbi ^uflj^ 4- Slj^kal ] < , 0+sbjlp nrb &+/'t
bpqŠbk R- Obol t * ', h(t < N v^ nrb t v ', h(t bpqŠk^j_lp bk T+ ^pŒnrb bi^uflj^ 5 pb p^qfpc^`bbk R- Olo `lkpfdrfbkqb R bp rk pr_bpm^`fl ab T,
CDEHMHBHˆM- Qa] R qj oq^_kjfqjpk jk r]_‡k `a qj aol]_ek heja]h T- Sjahaiajpk t `a T `a h] bkni]
g
V <1 AeVe*QcT
aj `kj`a Vh& ŒŒŒ+t+ lanpaja_aj pk`ko ] R u _h+ ŒŒŒ+_e okj ao_]h]nao+oa `ajkiej]_ki^ej]_e‰j heja]h `a ahaiajpko `a R- Ch _kjfqjpk, `a pk`]o h]o _ki^ej]_ekjaoheja]haobejep]o`a ahaiajpko `a R o]peob]_ahko ]teki]o `a _h]qoqn] u lkn p]jpkao qj oq^aol]_ek `a T- Ba_eiko `a aoa oq^aol]_ek mqa aop…cajan]`k lkn R+ kp]i^e†j ha hh]i]iko h] ajrkhrajpa heja]h `a R+ u hk `aoecj]iko lkn J'Q(- Qe Rao r]_‡k+`abejeiko J'Q( _kik w]x* ah_kjfqjpk _kjop] o50/ `ah ahaiajpk _ank-
Blkgrkqlp afpqfkqlpmrbabk dbkbo^obi jfpjl pr_bpm^`fl- Olo bgbjmil+ bi bp,m^`fl T1 bpqŠdbkbo^al mlo `^a^ rkl ab ilp pfdrfbkqbp `lkgrkqlp ab sb`qlobp9we*fx* we*g+e* fx* w]* e*+ e*g+, g+e* fx, Di bpm^`fl ab qlalp ilp mlifkljflp j l&p'ab do^al 94j bpqŠdbkbo^al mlo bi `lkgrkql ab j * 0 mlifkljflp x0+p+p!+--- +pjx-
S^j_f‹k bpqŠdbkbo^al mlo bi `lkgrkql x0+p.1+ p1.2+ --- +p!-&j * 0(y v mlox0+'0 * p( +'0 * p(1+--- +'0 * p(jx- Di bpm^`fl ab qlalp ilp mlifkljflp bpqŠdb,kbo^al mlo bi `lkgrkql fkcfkfql ab ilp mlifkljflp x0+p+p!+--- x-
@i iibd^o ^nrŒ prodbk ab jlal k^qro^i krjbolp^p mobdrkq^p-Olo bgbjmil+„nr‹ bpm^`flpmrbabk dbkbo^opbmlork k•jbol cfkfql ab bibjbkqlp> Rf rk bpm^`flbpqŠdbkbo^al mlo rk k•jbol cfkfql ab bibjbkqlp+ „`rŠi bp bi jbklo k•jbol abbibjbkqlp kb`bp^oflp> O^o^afp`rqfo bpq^p`rbpqflkbp v lqo^p `lk bii^p obi^`flk^a^p
Akjfqjpko `alaj`eajpao a ej`alaj`eajpao aj qj aol]_ek heja]h 00
fkqolar`fjlp ilp `lk`bmqlp ab `alaj`aj_e]+ ej`alaj`aj_e]+ ^]oao v `eiajoe‰j-X^ bk bi slirjbk H-bk`lkqo^jlp bp^p fab^p ^i bpqraf^o bi bpm^`fl sb`qlof^i T j
@elo^ s^jlp ^ buqbkaboi^p^ bpm^`flp ifkb^ibp ab qfml dbkbo^i-
0-6 Blkgrkqlp abmbkafbkqbpb fkabmbkafbkqbpbk rk bpm^`fl ifkb^i
CDEHMHBHˆM- Sj _kjfqjpk R `a ahaiajpko `a qj aol]_ek heja]h T oa hh]i]`alaj`eajpa oe ateopa qj _kjfqjpk bejepk `a ahaiajpko `eopejpko `a R+Wi= ’’’ + te+u qj _knnaolkj`eajpa _kjfqjpk `† ao_]h]nao _0+ ŒŒŒ + ao+jk pk`ko _ank+ p]hao mqa
g
H_,tz < M,e;h
Ch _kjfqjpk R oa hh]i] ej`alaj`eajpa oe jk ao `alaj`eajpa- Cj p]h _]ok+ _q]hao,mqean] mqa oa]j hko ahaiajpko `eopejpko Vz* ,‹‹ * t| `a R v hko ao_]h]nao `-+--- +_e+
eilhe_] A0 < A1 < --- < Ag < N-
Rf _fbk i^ abmbkabk`f^ v i^ fkabmbkabk`f^ plk molmfba^abpab ilp `lkgrkqlpab bibjbkqlp+ mlabjlp q^j_f‹k ^mif`^o bp^p abkljfk^`flkbp ^ ilp bibjbkqlpjfpjlp- Olo bgbjmil+ ilp bibjbkqlp ab rk `lkgrkql fkabmbkafbkqbpb ii^j^k bib,jbkqlp fkabmbkafbkqbp-
Rf R bp rk `lkgrkql cfkfql+i^ abcfkf`fŽk ^kqboflo bpqŠab ^`rboal `lk i^ a^a^bk bi Ulirjbk 0 m^o^bi bpm^`fl TjŒ Ml l_pq^kqb+i^ abcfkf`fŽk a^a^ ^nrŒkl bpqŠobpqofkdfa^ `lkgrkqlp cfkfqlp-
DIDLOKN 0- Rf rk pr_`lkgrkql R ab rk `lkgrkql R bp abmbkafbkqb+bi jfpjlR bp abmbkafbkqb-Dpql bp iŽdf`^jbkqb bnrfs^ibkqb ^ i^ ^cfoj^`fŽk ab nrb qlalpr_`lkgrkql ab rk `lkgrkql fkabmbkafbkqbbp fkabmbkafbkqb-
DIDLOKN 1- Rf rk bibjbkql ab R bp bi molar`ql ab lqol mlo rk bp`^i^o+Rbp abmbkafbkqb-
DIDLOKN 2- Rf N D R- bkqlk`bp R bp abmbkafbkqb
DIDLOKN 3- Di `lkgrkql s^`Œl bp fkabmbkafbkqb-
Dk bi Ulirjbk 0 crbolk afp`rqfalp jr`elp bgbjmilp ab `lkgrkqlp abmbkafbk,qbpb fkabmbkafbkqbp-Klp bgbjmilp nrb ^ `lkqfkr^`fŽk pb `ljbkq^k+ firpqo^k bplp`lk`bmqlp bk bpm^`flp crk`flk^ibp- Dk `^a^ `^pl bi bpm^`fl ifkb^i crka^jbkq^i Tbp bi `lkgrkql ab qla^p i^p crk`flkbp ob^ibpabcfkfa^p bk i^ ob`q^ ob^i-
f1 Col]_eko heja]hao
DIDLOKN 4- Rb^k q*&p' < `bp! p+ q1&p' < pbk! p+q**&p'< 0 m^o^ qlal k•jb,ol ob^i p-K^ fabkqfa^a mfq^dŽof`^ morb_^ nrb q+* S1 , S2 < N+ ^pŒnrb i^p qobpcrk`flkbp q++S1+ q! plk abmbkafbkqbp-
DIDLOKN 5- Rb^ Sg&p' < pG, m^o^ g < N+ ($ 1+ --- + v p ob^i- Di `lkgrkqlR < xrk+ S** S1+ ŒŒŒ x bp fkabmbkafbkqb- O^o^ abjlpqo^o bpql+ _^pq^ abjlpqo^o nrbm^o^ `^a^ j ilp j * 0 mlifkljflp Tk+ S** ‹‹‹ * Sj plk fkabmbkafbkqbp- Tk^ obi^,`fŽk ab i^ cloj^ HAgSg < N pfdkfcf`^ nrb
'0-0(j
G_gpg < N
R`?
m^o^ qlal ob^i p- Br^kal p < N+ bk`lkqo^jlp nrb Bl < N- Qbmfqfbkal bi mol`bpl+bk`lkqo^jlp nrb `^a^ `lbcf`fbkqb Ag bp `bol-
DIDLOKN 6- Rf ^! --- + ]: plk k•jbolp ob^ibp afpqfkqlp+ i^p j crk`flkbpbumlkbk`f^ibp
plk fkabmbkafbkqbp- Olabjlp abjlpqo^o bpql mlo fkar``fŽk pl_ob j- Di obpriq^albp qofsf^i `r^kal j < 0- Olo `lkpfdrfbkqb+ prmlkd^jlp nrb bp sŠifa^ m^o^ j , 0crk`flkbp bumlkbk`f^ibp v `lkpfabobjlp ilp bp`^i^obp `-+ --- + BHi q^ibp nrb
'0-1(j
G&_ga]gt < N-
gyh&
Rb^ ]K bi j^vlo ab ilp j k•jbolp ^! --- + ]jk Lriqfmif`^kal ^j_lp jfbj_olp ab'0-1( mlo n]-:9+ l_qbkbjlp
'0-2(j
H_ga']g,]K(t < N-/,;/
Rf g ;/; L+ bi k•jbol ]e + ]K bp kbd^qfsl- Olo `lkpfdrfbkqb+ `r^kal t y * // bki^ b`r^`fŽk '0-2(+ `^a^ q‹ojfkl `lk g ;/; L qfbkab ^ `bol v bk`lkqo^jlp nrb AK < N-Rrmofjfbkal bi q‹ojfkl L,‹pfjl ab '0-1( X ^mif`^kal i^ efmŽqbpfpab fkar``fŽk+bk`lkqo^jlp nrb `^a^ rkl ab ilp j , 0 obpq^kqbp `lbcf`fbkqbp _e bp `bol-
SDNQDL@ 0-4- Qa] Q<wVh+ --- +ua qj _kjfqjpk ej`alaj`eajpa mqa _kjop]`a g ahaiajpko `a qj aol]_ek heja]h T u oa] J'Q( ah oq^aol]_ek cajan]`k lkn R-Cjpkj_ao pk`k _kjfqjpk `a g* 0 ahaiajpko nh• SQ( ao `alaj`eajpa-
Akjfqjpko `alaj`eajpao a ej`alaj`eajpao aj qj aol]_ek heja]h 02
Baikopn]_e‰j- K^ abjlpqo^`fŽk bp mlo fkar``fŽk pl_ob g+k•jbol ab bib,jbkqlp ab R- Rrmlkd^jlp mofjbol nrb g; 0- Dkqlk`bp+mlo efmŽqbpfp+R `lkqfbkbrk plil bibjbkql VG pfbkal Wi<0< N mrbpql nrb R bp fkabmbkafbkqb-@elo^ qljb,jlp bk J&Q' alp bibjbkqlp afpqfkqlpIHb H1&Dkqlk`bp+`^a^ rkl ab bpqlpbibjbkqlpbp rk bp`^i^o jriqfmif`^al mlo Vh+ pb^ IH< AGVG b I1 < A1Vh+ bk alkab BH X A1 klplk ^j_lp `bol- Lriqfmif`^kal Ii mlo A1 b I1 mlo BH X obpq^kal+l_qbkbjlp
Olo 0/ q^kql I&i b I1 plk abmbkafbkqbp+nrba^kal ^pŒabjlpqo^al bi qblobj^`r^kal g< 0-
Rrmlkd^jlp ^elo^ nrb bi qblobj^ bp `fboql m^o^ g , 0 X abjlpqobjlp nrbq^j_f‹k 0/ bp m^o^ g- Sljbjlp rk `lkgrkql ab g* 0 bibjbkqlp bk J'Q(+ pb^R < xXH +W0 * ‹,‹ * Wg* 0 y- Prbobjlp mol_^o nrb R bp abmbkafbkqb-Orbpql nrb `^a^bibjbkql XfbpqŠ`lkqbkfal bk J&Q'* mlabjlp bp`of_fo
'0-3(g
We< %J]efVff;/
m^o^ `^a^ e< 0+1++--- +g * 0- Du^jfkbjlp qlalp ilp bp`^i^obp ]eh nrb jriqfmif,`^k ^ Vh v+m^o^biil+ `lkpfabobjlp alp `^plp bk i^ abjlpqo^`fŽk-
A?QM 0- ^fi<N l]n] pk`k e<0+1+--- +g*0- Dk bpqb`^pl i^ prj^ 'i-3(kl fk`irvb ^ u+: ^pŒ`^a^ He bk R bpqŠ bk i^ bkslisbkqb ifkb^i abi `lkgrkqlQ&< wt1+ ŒŒŒ +t`- Obol Q&bp fkabmbkafbkqbv `lkqfbkb g,0 bibjbkqlp- Olo fkar`,`fŽk v m^o^g+/* bi qblobj^ bp `fboql+pfbkal mlo 0/ q^kql+R abmbkafbkqb-Dpqlabjrbpqo^ bi B^pl 0-
A?QM 1- Lk okj _ank pk`ko hko ao_]h]nao]|- Rrmlkbjlp nrb ]-+ <0< N-Slj^kal e< 0 bk i^ b`r^`fŽk 'i-3( X jr 0qfmif`^kal ilp alp jfbj_olp mlo _e*pfbkal _e<]ezb]hh+ l_qbkbjlp9
g
AeW/< ]e/t/ * &K_e]/ftf,fy0
Rf ab bpq^b`r^`fŽk obpq^jlp i^ 'i-3(+ obpriq^9
g
AeW/ + We< %J&_e]/f + ]ef'tf*fy0
m^o^ e<1+--- +g * 0- Dpq^b`r^`flk bumobp `^a^ rkl ab ilp bibjbkqlp AeWG+ Xf`ljl rk^ `lj_fk^`fŽk ifkb^i ab ilp h , 0 bibjbkqlp fkabmbkafbkqbpV1+ ŒŒŒ+te-
03 Col]_eko heja]hao
Olo fkar``fŽk+ilp g bibjbkqlp AzWh,Xf ab_bk pbo abmbkafbkqbp-Dk `lkpb`rbk`f^+m^o^`r^inrfbo bib``fŽk ab bp`^i^obp p|, ,,, * pg)h* kl qlalp `bol+ qbkbjlp
g*h
y p:'AzWh , We( < N+ey1
v ab ^nrŒ abar`fjlp
Dpq^bp rk^ `lj_fk^`fŽk ab Wh*,,, * Wg)h* nrb obmobpbkqbi sb`qlo `bol+ ab bpq^j^kbo^ ilp bibjbkqlp Wh*! , * Wg)h ab_bk pbo abmbkafbkqbp+ ljmibq^kal ^pŒi^abjlpqo^`fŽk-
0 +7 5J\N\ b MRVNW\RmW
CDEHMHBHˆM- Sj _kjfqjpk bejepk R `a ahaiajpko `a qj aol]_ek heja]h T oahh]i] ^]oa bejep] `a T oe R ao ej`alaj`eajpa v cajan] T- Ch aol]_ek T ao `a`eiajoe‰j bejep] oe peaja qj] ^]oa bejep]- Ba kpnk ik`k+ T ao `a ejbejep]o `eiaj,oekjao-
SDNQDL@ 0 -5- Qa] T qj aol]_ek heja]h `a `eiajoe‰j bejep]- Cjpkj_ao pk`]^]oa bejep] `a T peaja ah ieoik jŠiank `a ahaiajpko-
Baikopn]_e‰j- Rb^k R v R alp _^pbp cfkfq^pab T- Rrmlkd^jlp nrb R v R`lkpq^k obpmb`qfs^jbkqbab g v i bibjbkqlp- Orbpql nrb R bp fkabmbkafbkqbv bk,dbkao^ T* bi qblobj^ 0-4 klp af`b nrb qlal `lkgrkql ab g * 0 bibjbkqlp ab Tbp abmbkafbkqb-Olo `lkpfdrfbkqb+ qlal `lkgrkql ab jŠp ab g bibjbkqlp ab T bpabmbkafbkqb-X^ nrb R bp rk `lkgrkql fkabmbkafbkqb+ab_b pbo i 999::g, Di jfpjlo^wlk^jfbkql `lk R v R fkqbo`^j_f^a^p morb_^ nrb g 999::i- Olo il q^kql g < i-
CDEHMHBHˆM- Qe qj aol]_ek heja]h T peaja qj] ^]oa `a j ahaiajpko+ ah aj,pank j oa hh]i] `eiajoe‰j `a T- Co_ne^eiko j < afj T-
DIDLOKN 0- Di bpm^`fl T! qfbkb afjbkpfŽk j- Tk^ _^pb bp bi `lkgrkql abilp j sb`qlobp `lloabk^alp rkfq^oflp-
DIDLOKN 1- Di bpm^`fl ab qlalp ilp mlifkljflp l&p' ab do^al 999::j qfbkbafjbkpfŽk j * 0- Tk^ _^pb bp bi `lkgrkql ab j * 0 mlifkljflp x0+p+p!+--- +p!x-Slal mlifkljfl ab do^al 999::pebp rk^ `lj_fk^`fŽk ifkb^i ab bplp j * 0 mlif,kljflp-
DID L OKN 2- Di bpm^`fl ab i^p plir`flkbp ab i^ b`r^`flk afcbobk`f^iu! , 1u&, 2u < N qfbkb afjbkpfŽk 1- Tk^ _^pb bpqŠcloj^a^ mlo i^p alp crk,`flkbp qz&t' < |=- q8v&t' < a!* Sla^ plir`fŽk bp rk^ `lj_fk^`fŽk ifkb^i abbp^p alp-
Akilkjajpao 04
DIDLOKN 3- Di bpm^`fl ab qlalp ilp mlifkljflp l&p' bp ab fkcfkfq^pafjbk,pflkbp- Di `lkgrkql fkcfkfql x0+ p+p!+--- x dbkbo^ bpqbbpm^`fl v kfkd•k `lkgrkqlbejepk ab mlifkljflp dbkbo^ bi bpm^`fl-
SDNQDL@ 0-6- Qa] T qj aol]_ek heja]h`a `eiajoe‰j bejep]_kj afj T < j-Qa peaja9
^( Aq]hmqean_kjfqjpk `a ahaiajpko ej`alaj`eajpa `a T ao qj oq^_kjfqjpk`a qj] _eanp]^]oa l]n] T-
_( Aq]hmqean_kjfqjpk `a j ahaiajpko ej`alaj`eajpao ao qj] ^]oa l]n] T-
Baikopn]_e‰j- O^o^ abjlpqo^o '^(+ `lkpfabobjlp bi `lkgrkql fkabmbkafbkqbR<xWi&--- +Vgx `lkpqfqrfal mlo bibjbkqlp bk T, Rf J&Q'<T* bkqlk`bp R bp rk^_^pb- Rf kl+ bkqlk`bp e^v ^id•k bibjbkql u bk T nrb kl bpqŠbk J&Q', @•^a^jlpbpbbibjbkql ^ R v `lkpfabobjlp bi krbsl `lkgrkql R&<wVh&--- +t| * ux- Rf bk bpqb`lkgrkql abmbkafbkqb jriqfmif`^jlp prp bibjbkqlp mlo bp`^i^obp `H+ ŠŠŠ+Ag*h
pfbkal ^idrkl afcbobkqbab `bol+ bpq^_ib`bobjlp nrb
g
-1 _-t‚ * Ag*hW < N -fzi
Obol Ag*h<h< N mrbpql nrb Vh +ŒŒŒ+Vg plk fkabmbkafbkqbp-Cb ^nrŒ nrb mla^jlpobplisbo bpq^b`r^`fŽk obpmb`ql^ u iibd^kal ^ i^ `lk`irpfŽk nrb vD J&Q'* il nrb`lkqo^af`b bi prmrbpql ab nrb v kl mboqbkb`b J&Q',Olo il q^kql bi `lkgrkql R&bpfkabmbkafbkqbv `lkqfbkb g* 0 bibjbkqlp- Rf J'Q&(<T+bkqlk`bp R&bp rk^ _^pb v+pfbkal R rk pr_`lkgrkql ab Q&+i^ m^oqb'^( nrba^ abjlpqo^a^- Rf R&kl bp rk^ _^pb+bkqlk`bp mlabjlp mol`babo `lk R&ab fdr^i j^kbo^ nrb mol`bafjlp `lk R v `lkpf,abo^o lqol krbsl `lkgrkql R! nrb `lkqfbkb g*1 bibjbkqlp v bp fkabmbkafbkqb-Rf R! bp rk^ _^pb+'^( nrba^ abjlpqo^al- Rf kl+ obmbqfjlp bi mol`bpl- Cb_bjlpiibd^o ^ rk^ _^pb abpmr‹p ab rk k•jbol cfkfql ab bq^m^p+v^ nrb ab lqo^ j^kbo^l_qbkaoŒ^jlp rk `lkgrkql fkabmbkafbkqb `lk j* 0 bibjbkqlp+ `lkqo^af`fbkal biqblobj^ '0-4(- Olo bpl+i^ m^oqb'^( abi qblobj^ '0-6( nrba^ abjlpqo^a^-
O^o^ abjlpqo^o i^ m^oqb'_( `lkpfabobjlp rk `lkgrkql fkabmbkafbkqbR `lkj bibjbkqlp- Olo i^ m^oqb'^(+ R bp rk pr_`lkgrkql ab _^pb @, Obol mlo bi qblob,j^ 0-5+i^ _^pb @ qfbkb bu^`q^jbkqb j bibjbkqlp+ mlo q^kql+R<@-
0-8 Bljmlkbkqbp
Rb^ T rk bpm^`fl ifkb^i ab afjbkpfŽk j v `lkpfabobjlp rk^ _^pb `rvlpbibjbkqlp a+Œ--- +aj pb qlj^k bk rk `fboql loabk- Tk^ q^i _^pb loabk^a^ i^ `lk,pfabo^jlp `ljl rk^ k,mi^ 'a! ---Œ aj(- Rf V D T+ mlabjlp bumobp^oV `ljl rk^`lj_fk^`fŽk ifkb^i ab bplp bibjbkqlp _^pb9
'i-R(j
V < J _-a-+fzi
05 Col]_eko heja]hao
Klp `lbcf`fbkqbp bk bpq^ b`r^`fŽk abqbojfk^k rk^ k,mi^ ab k•jbolp 'b+ --- + `k(
nrb bpqŠ rkŒsl`^jbkqb abqbojfk^a^ mlo t- Dk bcb`ql+ pf qbkbjlp lqo^ obmobpbk,q^`fŽk ab t `ljl `lj_fk^`fŽk ifkb^i ab a! --- + aj+ mlo bgbjmil t <K:zi`eae+obpq^kal ab ' 0 +4( bk`lkqo^jlp nrb KziAAe, `e(ae < N- Obol v^ nrb ilp bib,jbkqlp _^pb plk fkabmbkafbkqbp+ bpl fjmif`^ nrb _e<`e m^o^ `^a^ e*`lk il `r^i'b! --- + _j( < 'af+&! +`j(-
Klp `ljmlkbkqbp ab i^ k,mi^ loabk^a^ '`-+ --- + Aj( abqbojfk^a^ mlo '0&-4(pb ii^j^k _kilkjajpao `a t naola_pk ] h] ^]oa kn`aj]`] 'a! --- +aj(-
i-qA 8SN[LRLRX\
Dk `^a^ rkl ab ilp bgboBHBHNRabi 0 ^i 0/+ R bp bi `lkgrkql ab qlalp ilp sb`qlobp&t* u+w( ab Tk `rvlp `ljmlkbkqbp p^qfpc^`bk i^ `lkaf`fŽk nrb pb a^- Cbqbojfk^o pf R bprk pr_bpm^`fl ab Tk& Rf il bp+ `^i`ri^o afj R-
0- t < N-
1- t * u < N-2- t * u * v < N-2, t <u-4- t < u < v+
4, t < uk t < v-6- t1 , u1 < N-7- t * u < 0-
8- W < 1t v v < 2t-/., t * T * v < N v t , u , v < N-
Rb^ N* bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ab do^al 999::j+ pfbkal j cfgl- Dk `^a^bgbo`f`fl abi 00 ^i 1/+ pb^ R bi `lkgrkql ab qlalp ilp mlifkljflp Gab N, nrb p^qfpc^`bk i^`lkaf`fŽk a^a^- Cbqbojfk^o pf R bp rk pr_bpm^`fl ab N‹, Rf il bp+`^i`ri^o afj R-//, /&.' < N-01- .&'/( < N-
02- .!'/( < N-/2, /&.' * .&'/( < N-/3, /&.' < 0/(-/4, /&.' < /&0',/5, Gbp m^o-/6, Gbp fjm^o-08- Gbp ab do^al p: g+ pfbkal g ; j+ l G< N-1/- Gbp ab do^al g+ pfbkal g ; j+ l G< N-10- Dk bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ob^ibp l&p'* abp`of_fo bi pr_bpm^`fl bkdbk,
ao^al mlo `^a^ rkl ab ilp pfdrfbkqbp `lkgrkqlp ab mlifkljflp v abqbojfk^o pr afjbkpfŽk-
^( xi+ p1+p
3x: _( wp+p2+p4x: b( wp+p1x: a( xi * p+'0 * p(1x-
11- Dk bpqb bgbo`f`fl+ J'Q( bp bi pr_bpm^`fl dbkbo^al mlo rk pr_`lkgrkql R ab rk bpm^`flifkb^i T- Cbjlpqo^o i^p molmlpf`flkbp ab i^ ^( ^ i^ c(-^( R R:J&Q',
_( Rf R R: RQ: Tu pf R bp rk pr_bpm^`fl ab T- bkqlk`bp J&Q'R: R- Dpq^ molmfba^a pbbumobp^ af`fbkal nrb J&Q' bp bi iajkn pr_bpm^`fl ab T nrb `lkqfbkb R-b( Tk pr_`lkgrkql R ab T bp rk pr_bpm^`fl ab T pf v pŽil pf J&Q' < R-a( Rf R R: R R: T* bkqlk`bp J&Q'R: J&R',b( Rf R X R plk pr_bpm^`flp ab T* q^j_f‹k il bp R ‡[ R,c( Rf R X R plk pr_`lkgrkqlp ab T, bkqlk`bp J&Qk R' Q9J&Q'‡[ J&R',d( C^o rk bgbjmil bk bi nrb J&Q‡[ R' ", J&Q' ‡[ J&R',
12- Rb^ U bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbp ob^ibp abcfkfa^p bk i^ ob`q^ ob^i- Cbqbo,jfk^o pf `^a^ rkl ab ilp pfdrfbkqbp pr_`lkgrkqlp ab T bp abmbkafbkqb l fkabmbkafbkqb -
- B^i`ri^o i^ afjbkpfŽk abi pr_bpm^`fl dbkbo^al mlo `^a^ `lkgrkql-
Nnk`q_pko ejpaneknao+aol]_eko aq_h‡`ako- Lkni]o 06
^( xH+a!&t+a^Vx* ] :‹ ^, c( oblpt+ pbktx-_( wa!&t+ta!&Vx- d( x`lp! V+oaj 1 tx-
b( xH+a]t+ ta]tx- e( xH+blp 1t+oaj0 tx-a( wa!&t+ta&!+t0a]Vx- f( xpbkt+ pbk 1tx-b( waV+a,t+ blpeuy- g( waVblp t+ a,V pbktx-
13- Rb^k T rk bpm^`fl ifkb^i ab afjbkpfŽk cfkfq^+v R rk pr_bpm^`fl ab T, Cbjlpqo^o `^a^rk^ ab i^p molmlpf`flkbp pfdrfbkqbp-^( R bp ab afjbkpfŽk cfkfq^ v afj R z afj T,_( afj R < afj T pf v pŽil pf R < T-b( Sla^ _^pb ab R bp m^oqb ab rk^ _^pb ab T,a( Tk^ _^pb ab T kl `lkqfbkb kb`bp^of^jbkqb rk^ _^pb ab R-
)')) B[XM^L]X\RW]N[RX[N\%N\YJLRX\N^LUlMNX\'@X[VJ\
Dk i^ FbljbqoŒ^ br`iŒab^ loafk^of^+ ^nrbii^p molmfba^abpnrb `rbkq^k `lki^ mlpf_fifa^a ab jbafo ilkdfqrabp ab pbdjbkqlp ob`qfiŒkblpv Škdrilp cloj^alp mloob`q^p pb ii^j^k molmfba^abp i†pne_]o- Dk krbpqol bpqrafl ab Tj+ abcfkfjlp i^pilkdfqrabp v ilp Škdrilp bk crk`fŽk abi molar`ql bp`^i^o- Prbobjlp ^elo^ buqbk,abo bp^p fab^p ^ bpm^`flp ifkb^ibp jŠp dbkbo^ibp-Oofjbol fkqolar`fobjlp rk^ db,kbo^ifw^`fŽk abi molar`ql bp`^i^o+ nrb ii^j^objlp lnk`q_pk ejpanekn+ v irbdlabcfkfobjlp i^ ilkdfqra v bi @kdrilbk crk`fŽk ab bpqbmolar`ql fkqboflo-
Di molar`ql bp`^i^o t - v ab alp sb`qlobp t < 'Vh& -Œ- + tj( b v < 'Xi+ - ! Wj(ab Tj pb abcfkfŽ bk bi Ulirjbk 0 mlo i^ cŽojri^
'0-5(j
t• W < GVeWe&fzi
Dk rk bpm^`fl ifkb^i dbkbo^i+bp`of_fjlp 'u+ v( bk ird^o ab V% v m^o^ilp molar`qlpfkqboflobp+v abcfkfjlp bi molar`ql ^ufljŠqf`^jbkqb v kl jbaf^kqb rk^ cŽojri^-Dpql bp+bpq^_ib`bjlp rk^p `fboq^pmolmfba^abpnrb nrbobjlp nrb p^qfpc^d^kilpmolar`qlp fkqboflobpv i^p `lkpfabo^jlp `ljl ]teki]o-
CDEHMHBHˆM- Sj aol]_ek heja]h na]h T peaja qj lnk`q_pk ejpanekn oe ] _]`]l]n `a ahaiajpko t a u `a T _knnaolkj`a qj jŠiank na]h Šje_k 't+ v( mqa o]peo,b]_a hko oecqeajpao ]teki]o _q]haomqean] mqa oa]j t+ u+ w `a T v l]n] pk`ko hkoao_]h]nao na]hao _-
0( &t*u' < &u*t'1( &t*u * w( < &t*u' * &t* v'1' a&t*u' < &at*u'2' &t* t' = N oe t ocN
p_kjiqp]pere`]`+ k oeiapn‡](-p`eopne^qpere`]`+ k heja]he`]`(-']ok_e]pere`]`+ q dkikcajae`]`(-'lkoepere`]`(-
Tk bpm^`fl ifkb^i `lk rk molar`ql fkqboflo pb ii^j^ aol]_ek na]h aq_h‡`ak-
07 Col]_eko heja]hao
M^oanr]_e‰j9 G^`fbkal b < N bk '2(+ bk`lkqo^jlp nrb 'M+v( < N m^o^ qlal v-
Dk rk bpm^`fl ifkb^i `ljmibgl+ rk molar`ql fkqboflo &t* v( bp rk k•jbol`ljmibgl nrb p^qfpc^`bilp jfpjlp ^uflj^p nrb ilp abi molar`ql fkqboflo ob^i+bu`bmql bi ab i^ pfjbqoŒ nrb pb obbjmi^w^ mlo i^ obi^`fŽk
'0.( 't+ u' < &u*t( + 'Qepjapn‡] daniepe]j]p&z
pfbkal &u*t' bi `ljmibgl `lkgrd^al ab &u*t', Dk bi ^uflj^ ab eljldbkbfa^a+ bijriqfmif`^alo bp`^i^o a mrbab pbo `r^inrfbo k•jbol `ljmibgl- Cbi ^uflj^ ab i^eljldbkbfa^a v '0&(+iibd^jlp ^ i^ obi^`fŽk
'2.( &t* au' < &au*t' < …&u*t' < …&t*u' ,
Tk bpm^`fl ifkb^i `ljmibgl `lk rk molar`ql fkqboflopb ii^j^ aol]_ek aq_h‡`ak_kilhafk- '@ sb`bp pb rp^ q^j_f‹k i^ abkljfk^`fŽk ab aol]_ek qjep]nek-( Tkbgbjmil bp bi bpm^`fl sb`qlof^i `ljmibgl rjAA' _obsbjbkqb afp`rqfal bk i^ pb`,`fŽk 01-05 abi Ulirjbk H-
@rknrb klp fkqbobp^kmofk`fm^ijbkqb ilp bgbjmilp ab bpm^`flp br`iŒablp ob^,ibp+ilp qblobj^p ab bpqb`^mŒqrilplk sŠifalp m^o^ bpm^`flp br`iŒablp `ljmibglp-Br^kal ab`fjlp bpm^`fl br`iŒabl+pfk jŠp+ bkqbkabobjlp nrb mrbab pbo ob^i l`ljmibgl-
Di ib`qlo ab_fbo^ `ljmol_^o nrb `^a^ bgbjmil nrb pfdrb p^qfpc^`bqlalp ilp^uflj^p abi molar`ql fkqboflo-
DIDLOKN i- Dk Tj pb^ &t* v( < t , v+ bi molar`ql bp`^i^o loafk^ofl ab t b v-
DIDLOKN 1- Rf t < &t* * t1( b X < &u* * W1( plk alp sb`qlobp ab T1+ abcfkf,jlp &t* v( jbaf^kqb i^ cŽojri^
Dpqbbgbjmil mlkb ab j^kfcfbpql nrb mrbabk bufpqfojŠp ab rk molar`ql fkqboflobk rk bpm^`fl ifkb^i a^al-
DIDLOKN 2- Rb^ A&]* ^' bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbp ob^ibp`lk,
q Dk elklo ab Be^oibp Gbojfqb '0711,08/0( j^qbjŠqf`l co^k`‹p nrb `lkqof_rvŽ jr`el^i abp^ooliil abi Šidb_o^ v abi ^kŠifpfp-
Nnk`q_pko ejpaneknao+aol]_eko aq_h‡`ako- Lkni]o- 08
qfkr^p bk rk fkqbos^il Y]* ^[, Cbcfk^jlp rk molar`ql fkqboflo ab alp crk`flkbp
b v d `lk i^ cŽojri^
'g+d( < H8b'p(c'p( `p -
Dpq^ cŽojri^ bp ^kŠild^ ^ i^ b`r^`fŽk '0-5(- nrb abcfkb bi molar`ql bp`^i^o ab alpsb`qlobp bk T j- Klp s^ilobp ab i^p crk`flkbp b&p' v c&p' abpbjmb•^k bi m^mbi abilp `ljmlkbkqbp t+ b u,: v i^ fkqbdo^`fŽk bi ab i^ prj^-
DIDLOKN 3- Dk bi bpm^`fl A&]* ^'* abcfkfjlp
'g+d( < H8s'p(b'p(c'p( `p +
alkab t bp rk^ crk`fŽk mlpfqfs^ cfg^ab A']+ ^-(- S^i crk`fŽk pb ii^j^ bqj_e‰j laok-Dk bi bgbjmil 2 qbkbjlp s&p' < 0 m^o^ qlal p-
DIDLOKN 4- Dk bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ob^ibp+ abcfkfjlp
'g+d( < cl&W(a,pz'p(c'p( `p -
Cb_fal ^i c^`qlo bumlkbk`f^i+ bpq^ fkqbdo^i fjmolmf^ `lksbodb m^o^ qlal m^o abmlifkljflp b v d-
SDNQDL@ 0-7- Cj qj aol]_ek aq_h‡`ak T+ pk`k lnk`q_pk ejpanekn o]peob]_ah] `aoecq]h`]` `a A]q_du,Q_ds]nv9
G't+u(00y 't+ t('u+ u( l]n] pk`k t u &pk`k uaj T-
?`ai…o+ ah oecjk `a ecq]h`]` ao r…he`k oe u o‰hkoe t a u QMj `alaj`eajpao-
Baikopn]_e‰j- Rf l`roob nrb l _fbk t<M l v<N i^ abjlpqo^`fŽk bpqofsf^i- Rrmlkd^jlp nrb t b v kl plk ^j_^p `bol- Rb^ v<]t*^u bk alkab ] v ^plk bp`^i^obp nrb bpmb`fcf`^objlp abpmr‹p- Sbkbjlp i^ abpfdr^ia^a 'w+w(z N m^o^qlal ] v ^, Br^kal bumobp^jlp bpq^ abpfdr^ia^a bk crk`fŽk ab t b v `lk rk^bib``fŽk ^molmf^a^ ab ] v ^+l_qbkbjlp i^ abpfdr^ia^a ab B^r`ev,R`et^ow-
O^o^ bumobp^o &v*v' bk crk`fŽk ab t b v rp^objlp i^p molmfba^abp 'H!(+ '1(
X '2&(+l_qbkfbkal
'w: w( < ']h, * ^u+ ]t * ^u( < ']t+ ]t( * ']t+ ^u( * '^u+ ]t( * '^u+ ^u(
< ]ee't+ t( * ]d't+u( * ^ee'u+t( * ^^'u+u( 1 l-
1/- Col]_eko heja]hao
Slj^kal ];&u*u' v prmofjfbkal bk i^ abpfdr^ia^a bi c^`qlo mlpfqfsl &u*u'*obpriq^
&u*u'&t* t'%* ^et+u' * ^&u* t' * ^^ y N-
@elo^+ e^d^jlp ^< +&t*u', Dkqlk`bp+^< +&u*t' v i^ •iqfj^ abpfdr^ia^a+rk^ sbw pfjmifcf`^a^+ qlj^ i^ cloj^
&u*u'&t* t' y &t*u'&u* t' < i'u+v(01-
Dpql abjrbpqo^ i^ abpfdr^ia^a ab B^r`ev,R`et^ow- Di pfdkl ab fdr^ia^a bp sŠifalpf v pŽil pf w<N- Dpql l`roob pf v pŽil pf t b v plk abmbkafbkqbp-
DIDLOKN- @mif`^kal bi qblobj^ 0-7 ^i bpm^`fl A&]* ^' `lk bi molar`qlfkqboflo 'g+d( < byb'p(c'p( `p+bk`lkqo^jlp nrb i^ abpfdr^ia^a ab B^r`ev,R`et^owpb qo^kpcloj^ bk
Di molar`ql fkqboflo mrbab rqfifw^opbm^o^ fkqolar`fo bi `lk`bmql j‹qof`l abilkdfqra bk `r^inrfbo bpm^`fl br`iŒabl-
CDEHMHBHˆM- Cj qj aol]_ek aq_h‡`ak T+ah jŠiank jk jac]perk Hiuii abeje`klkn h] a_q]_e‰j
Hiuii< &t* V(0.1
oa `ajkiej] jkni] `ah ahaiajpk t-
Br^kal i^ abpfdr^ia^a ab B^r`ev,R`et^ow pb bumobp bk crk`fŽk ab i^p klo,j^p+ qlj^ i^ cloj^
G&t*u'- y Zu\ GGuhh,
Orbpql nrb bp mlpf_ib abcfkfo rk molar`ql fkqboflo ab jr`e^p j^kbo^p+ i^kloj^ ab rk bibjbkql abmbkaboŠabi molar`ql fkqboflo bibdfal- Dpq^c^iq^ ab rkf,`fa^a bo^ ab bpmbo^o-Dpqbeb`el bp ^kŠildl ^i ab nrb mlabjlp ^pfdk^o k•jbolpafpqfkqlp ^ i^ jbafa^ ab i^ ilkdfqra ab rk pbdjbkql ob`qfiŒkbla^al+ pbd•k i^bib``fŽk ab bp`^i^ l rkfa^a ab jbafa^- Di qblobj^ nrb pfdrb a^ i^p molmfba^abpcrka^jbkq^ibp ab i^p kloj^p nrb kl abmbkabk ab i^ bib``fŽk ab molar`ql fkqboflo-
Mnpkckj]he`]` aj qj aol]_ek aq_h‡`ak 10
SDNQDL@ 0-8- Cj qj aol]_ek aq_h‡`ak+ pk`] jkni] peaja h]o lnklea`]`aooecqeajpao l]n] pk`ko hko ahaiajpko t a u+ u pk`ko hko ao_]h]nao `9
^( Zu\ < N pf t < N-_( Zu\ = N pf t l{‹ N 'lkoepere`]`(-b( Zbu\ < Zb\ Hiuii 'dkikcajae`]`(-a( HHu* vii z Zu\ * H.vii '`aoecq]h`]` pne]jcqh]n(-
Ch oecjk `a ecq]h`]` ao r…he`k aj h] `aoecq]h`]` pne]jcqh]n oe u o‰hkoe t a u okj`alaj`eajpao-
Baikopn]_e‰j- K^p molmfba^abp ^(+ _( v b( pb abar`bk fkjbaf^q^jbkqb abilp ^uflj^p abi molar`ql fkqboflo- O^o^ abjlpqo^o a( l_pbosbjlp nrb
Zu* uh/0 < &t * u* t * u' < &t* t' * &u*u' * &t*u' * &u* t' ;
< HHui01* HHvi01* &t*u' * &t*u' ,
K^ prj^ &t* u' * 'u+ u' bp ob^i- K^ abpfdr^ia^a ab B^r`ev,R`et^ow morb_^ nrb
z&t*v(0 z Hiuii Hivii v nrb h&t*u'/ y Hiuii i_ii- ^pŒnrb qbkbjlp
Zu* uhh1 y HHui01* HHvi01* 100uii Hivii < '00uii * iHv00(1-Dpql abjrbpqo^ a(- Di pfdkl ab fdr^ia^a bk a( bp sŠifal pfbjmob nrb il pb^ bk i^abpfdr^ia^a ab B^r`ev,R`et^ow- Br^kal u < at+ pfbkal a = N+ qbkbjlp
Ght * vii < Zu * bu\ < '0 * _' Huii< HZuii* Zbu\ < Hiuii * Hivi -
CDEHMHBHˆM- Cj qj aol]_ek aq_h‡`ak na]h T+ ah …jcqhk bkni]`k lkn `ko aha,iajpko jk jqhko t a u oa `abeja _kik ah jŠiank a `ah ejpanr]hk N z a y pn mqao]peob]_a h] a_q]_e‰j
'0- 6( nko a < 't+ u( -Hiuiiiivii
M^oanr]_e‰j9 K^ abpfdr^ia^a ab B^r`ev,R`et^ow morb_^ nrb bi `l`fbkqb abi pb,drkal jfbj_ol ab '0-6( bpqŠ bk bi fkqbos^il Z,0+ 0\+ ^pŒnrb bufpqb pŽil rk '( bkZN+6S\ `rvl `lpbkl bp fdr^i ^i ab bpqb `l`fbkqb-
>')* A[]XPXWJURMJMNW WN\YJLRXN^LUlMNX
CDEHMHBHˆM- Cj qj aol]_ek aq_h‡`ak T+ `ko ahaiajpko t a u oa hh]i]j knpk,ckj]hao oe oq lnk`q_pk ejpanekn ao _ank- Sj oq^_kjfqjpk R `a T ao qj _kjfqjpkknpkckj]h oe 't+ v( < N l]n] pk`k l]n `a ahaiajpko `eopejpko t a u `a R- Sj _kj,fqjpk knpkckj]h oa hh]i] knpkjkni]h oe _]`] qjk `a oqo ahaiajpko peaja jkni] 0-
-- Col]_eko heja]hao
Di bibjbkql `bol bp loqldlk^i ^ qlal bibjbkql ab T: bp bi •kf`l bibjbkqlloqldlk^i ^ pŒjfpjl- Di pfdrfbkqbqblobj^ abjrbpqo^ rk^ obi^`fŽk bkqobloqldlk^,ifa^a v abmbkabk`f^-
SDNQDL@ 0-0/- Cj qj aol]_ek aq_h‡`ak T+ pk`k _kjfqjpk knpkckj]h `aahaiajpko jk jqhko ao ej`alaj`eajpa- Cj l]npe_qh]n+aj qj aol]_ek aq_h‡`ak `a`eojajoe…j bejep] _kj afj T < j+ pk`k _kjfqjpk knpkckj]h mqa _kjopa `a j aha,iajpko jk jqhko ao qj] ^]oa l]n] T-
Baikopn]_e‰j- Rb^ R rk `lkgrkql loqldlk^i ab bibjbkqlp kl krilp ab T+v prmlkd^jlp nrb rk^ `fboq^ `lj_fk^`fŽk ifkb^i cfkfq^ab bibjbkqlp ab R bp `bol+#BMI
g
AeVe < N+f<i
alkab `^a^ t+D R- Eloj^kal bi molar`ql bp`^i^o ab `^a^ jfbj_ol mlo Wi vqbkfbkal bk `rbkq^ nrb 'Wi& Ve( < N pf e <0< 0+ bk`lkqo^jlp nrb `+'Wi& Wi( < N-Obol 'WH&Wi( <0< N v^ nrb Wi <0< N `lk il `r^i _+< N- Qbmfqfbkalbi o^wlk^jfbkql`^j_f^kal u+mlo t-+ bk`lkqo^jlp nrb `^a^ az < N-Dpql morb_^ nrb R bp fkabmbk,afbkqb- Rf afj T < j v pf R `lkpq^ ab j bibjbkqlp+ bi qblobj^ 0-6 _( abjrbpqo^nrb R bp rk^ _^pb m^o^ T,
DIDLOKN- Dk bi bpm^`fl ifkb^i ob^i B'N+ 166!( `lk bi molar`ql fkqboflo&b*c' < IziSf&t'c&t' `t* pb^ R bi `lkgrkql ab i^p crk`flkbp qofdlklj‹qof`^p xrl+
ri+ S0* ,,‹ x a^a^p mlo
qk'V( < 0+ S1j\0'V( < `lp jt+ S0j'V( <pbk jt + m^o^ j < 0+1+----
Qe i <0< j+ qbkbjlp i^p obi^`flkbp ab loqldlk^ifa^a
^pŒnrb R bp rk `lkgrkql loqldlk^i- Orbpql nrb kfkd•k bibjbkql ab R bp bi bib,jbkql `bol+ R bp fkabmbkafbkqb-K^ kloj^ ab `^a^ bibjbkql ab R pb `^i`ri^ cŠ`fi,jbkqb- Sbkbjlp 'rl + rl( < byhR `t < 166! v+ m^o^ j y 0+qbkbjlp
H! 1'S1j,h& S1j,0( < l `lp jt `t < 6R+- x1iS 1
'S1j+ S1j( <Il pbk jt `t < 6R-
Mnpkckj]he`]` aj qj aol]_ek aq_h‡`ak 12
Olo `lkpfdrfbkqb+ Hirlii < Ui: v .0 Sj 00 < v9::9m^o^ j y 0- Cfsfafbkal `^a^ Sj mlopr kloj^+ l_qbkbjlp rk `lkgrkql loqlkloj^i x8& N+8& i+8& 1+-+- y alkab b-’<qj.hhqjhh-@pŒmrbp+qbkbjlp
07% k&t'< -., +
&U106
pbkku8& 1ŒŒ'V( < U: + m^o^ j y 0-
Dk i^ pb``fŽk 0-03 abjlpqo^objlp nrb qlal bpm^`fl br`iŒabl ab afjbkpfŽkcfkfq^qfbkb rk^ _^pb loqldlk^i- Di qblobj^ nrb pfdrb jrbpqo^ `Žjl pb `^i`ri^kilp `ljmlkbkqbp ab rk bibjbkql obi^qfslp ^ rk^ q^i _^pb-
SDNQDL@ 0 -00- Qa] T qj aol]_ek aq_h‡`ak`a `eiajoe‰j bejep] j+ u oqlkj,c]iko mqa Q < wah&--- +aŒŒx ao qj] ^]oa knpkckj]h l]n] T- Qeqj ahaiajpk t aop…atlnao]`k _kik qj] _ki^ej]_e‰j heja]h`a hkoahaiajpko `a h] ^]oa+oa] †op]
'0-7( ’’t < 1_eae&
e<h
ajpkj_ao oqo _kilkjajpao nah]perko] h] ^]oa kn`aj]`] 'ah=--- +aj( reajaj `]`kolkn h]o b‰niqh]o
'0-8('u+ af'
Bg < ,' ,,( l]n] g< 0+1+--- +j-a-+af
Cj l]npe_qh]n+oeQ ao qj] ^]oa knpkjkni]h+ _]`] az reaja `]`] lkn
'0-0/(
Baikopn]_e‰j- Eloj^kal bi molar`ql fkqboflo ab `^a^ jfbj_ol ab '0+7(`lk af* l_qbkbjlp
j
't+ af( < 1_:'ae+ a( < _f'af+ a(e<h
mrbpql nrb 'az+af( < N pf e<0<f, Dpql fjmif`^ '0-8(+ v `r^kal &az* az( < 0+l_qb,kbjlp '0-0/(-
Rf xbi&--- +ajx bp rk^ _^pb loqlkloj^i+ i^ b`r^`fŽk '0 -8( mrbab bp`of_fopbbk i^ cloj^ -
'0-00(j
V < 1't+ ae(ae•e<h
13 Col]_eko heja]hao
Di pfdrfbkqb qblobj^ morb_^ nrb bk rk bpm^`fl br`iŒabl ob^i ab afjbkpfŽkcfkfq^`lk rk^ _^pb loql kloj^i bi molar`ql fkqbofloab alp bibjbkqlp bp fdr^i ^ i^prj^ ab ilp molar`qlp ab prp `ljmlkbkqbp-
SDNQDL@ 0-01- Qa] T qj aol]_ek aq_h‡`ak na]h `a `eiajoe‰j bejep] j+u oqlkjc]iko hHqawah=--- +ajx ao qj] ^]oa knpkjkni]h l]n] T- N]n] pk`k l]n `aahaiajpko t a u `a T+ pajaiko
'0-01(j
'u+ u( < J 't+ ae('u+ ae( 'D‰niqh] `a N]noar]h(-e;h
Cj l]npe_qh]n+_q]j`k t < u+ pajaiko
'0-02(j
HHui01< J G&t*az'/1Œe;h
Baikopn]_e‰j- Eloj^kal- bi molar`ql fkqboflo ab ^j_lp jfbj_olp ab i^b`r^`fŽk '0-00( `lk u+v ^mif`^kal i^ molmfba^a ab ifkb^ifa^a abi molar`ql fkqb,oflo+l_qbkbjlp '0-01(- Br^kal t < v+ i^ b`r^`fŽk '0-01( pb obar`b ^ '0-02(-
M^oanr]_e‰j9 K^ b`r^`flk '0-01( pb abkljfk^ `ljl pb fkaf`^ bk elklo& abL- @- O^opbs^i '^molufj^a^jbkqb 0665,0725(+ nrb l_qrsl bpqb qfml ab cŽojri^ bk TC
bpm^`fl crk`flk^i bpmb`f^i- K^ b`r^`fŽk '0-02( bp rk^ dbkbo^ifw^`fŽk abi qblobj^ abOfqŠdlo^p-
0-02 Dgbo`f`flp
0- Rb^k t < &VG!%! tj( b v < 'XH!&! Wj( sb`qlobp ^o_fqo^oflp ab Tj- Cbqbojfk^o bk `^a^`^pl+ pf &t* v( bp rk molar`ql fkqboflo bk Tj+ pf &t* v( bpqŠ abcfkfal mlo i^ cŽojri^ nrb pba^- Dk bi `^pl bk nrb &t*v( kl pb^ rk molar`ql fkqboflo+ ab`fo `rŠibp plk ilp ^uflj^pnrb kl pb p^qfpc^`bk-
j
^( 't+ u( <JVe .We.&e;h
'
j (0.1a( 't+ u( < ey0 tzuz
j j j
b( 't+u( < J'te * We(1 , JVy , JWz&e;h e;h e;h
V V
b( 'V+u( <JVe JWe -ey0 ey0
1- Rrmlkd^jlp nrb j^kqbkbjlp ilp qobp mofjbolp ^uflj^p abi molar`ql fkqboflo ob^i'pfjbqoŒ^+ifkb^ifa^a v eljldbkbfa^a( mbol obbjmi^w^jlp bi `r^oql ^uflj^ mlo rkl krb,sl '3&(9 &t* t' < N pf v pŽil pf t < N- Cbjlpqo^o nrb l 'u+ t' = N m^o^ qlal t9… Nl _fbk &t* t' ; N m^o^ qlal t :‹ N-
Cfan_e_eko 14
YGj`e_]_eˆj% Rrmlkbo &t* t' = N m^o^ rk `fboql t +‹ N X &u*v( ; N m^o^ rk `fboqlv +‹ N- Dk bi bpm^`fl dbkbo^al mlo wt* ux+ e^ii^o rk bibjbkql w +‹ N blk 'w+w( < N-\
Cbjlpqo^o nrb bk ilp bgbo`f`flp abi 2 ^i 6 `^a^ rk^ ab i^p molmlpf`flkbp bp sŠifa^ m^o^qlal m^o ab bibjbkqlp t b v ab rk bpm^`fl br`iŒabl ob^i-
2- &t*u' < N pf v pŽil pf Zu* vii < Zu , vii-2, &t*u' < N pf v pŽil pf Hiu * vi01 < HHui01* Hiv001-4- &t*u' < N pf v pŽil pf Zu * `vii 91 Zu\ m^o^ qlal b ob^i4, &t * u+t , u(< N pf v pŽil pf Zu\ < Hivii-6- Rf t b v plk bibjbkqlp kl krilp nrb cloj^k rk Škdril '(+ bkqlk`bp
Hiu , vi01 < HHui01* iHvi01, 1 Hiuii iHvii `lp '(-
7- Dk bi bpm^`fl ifkb^i ob^i B'i+ a'* abcfkfjlp rk molar`ql fkqboflo mlo
'b+c( <b8'ild t(b't(c't( `t-
^( Rf G&t' < T-:+^i`ri^o 00.00-_( G^ii^o rk mlifkljfl ab mofjbo do^al c&t' < ] * ^t nrb pb^ loqldlk^i ^ i^ crk`fŽk`lkpq^kqb G&t'< 0-
8- Dk bi bpm^`fl ifkb^i ob^i B' ,[+ 0(+ pb^ &H*d( <c<,i b'p(c'p(`p- Blkpfabo^o i^p qobp crk,`flkbp S! q1 q2 a^a^p mlo
S2'p( < 0 * p -
Cbjlpqo^o nrb alp ab bii^p plk loqldlk^ibp+ alp cloj^k bkqob pŒrk Škdril &hR.2+v alpcloj^k bkqob pŒrk Škdril &hR.5-
0/- Dk bi bpm^`fl ifkb^i N, ab qlalp ilp mlifkljflp ob^ibp ab do^al z j+ abcfkfjlp
^( Cbjlpqo^o nrb &H*d( bp rk molar`ql fkqboflo m^o^ N‹,_( B^i`ri^o &H*d( `r^kal h&p'< p X c&p' < ]p * ^-b( Rf G&p'< p+e^ii^o qlalp ilp mlifkljflp d loqldlk^ibp ^ h,
((& Dk bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ob^ibp+abcfkfjlp &H*d( < Q::a,pz'p(c'p( `p-^( Cbjlpqo^o nrb bp^ fkqbdo^i fjmolmf^ `lksbodb ^_plirq^jbkqb m^o^ qlalp ilp mlifkl,jflp Gv d-_( Rf t,&p' < p! m^o^ j < N+ 0+ 1+ --- + abjlpqo^o nrb &V,* ti( < &i * j' ,b( B^i`ri^o &H*d( `r^kal h&p'< &p* 0(1 v c&p' < p1 * 0-a( G^ii^o [ qlalp ilp mlifkljflp ab mofjbo do^al c'p( < ] * ^p loqldlk^ibp ^ G'p(< 0* p-
01- Dk bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ob^ibp+ abqbojfk^o pf '.+ d( bp l kl ro:molar`ql fkqboflo `r^kal pb abcfkb &H*d( `lk i^ cŽojri^ nrb pb a^- Dk bi `^pl bk nrb&H*d( kl bp rk molar`ql fkqboflo+ fkaf`^o nr‹ ^uflj^p kl plk obpmbq^alp- Dk b(+ b%vd& fkaf`^k abofs^a^p-
-1 Col]_eko heja]hao
^( 'b+c( <G'h(c'h(•
_( 'b+c( < HH8G'p(c'p( `p h•b( 'h-c( <H8b&'p(c&'p(p+
a( 'b+c( < S9G'p( `p(S9c'p( `p(-
02- T bpqŠ cloj^al `lk qla^p i^p pr`bpflkbp fkabcfkfa^p ab k•jbolp ob^ibp wt,x m^o^ ilp`r^ibp i^p pbofbp 09V1 `lksbodbk- Rf t < wt,x b v < wu-x plk alp bibjbkqlp ab T+abcfkfjlp !
PN
't+++(< 09t+-u!- 2)
^( Cbjlpqo^o nrb bpq^ pbofb `lksbodb ^_plirq^jbkqb-YGj`e_]_e‰j9 Tp^o i^ abpfdr^ia^a ab B^r`ev,R`et^ow m^o^ ^molufj^o i^ prj^
09z<0 Hu+-v!H-i:_( Cbjlpqo^o nrb T bp rk bpm^`fl ifkb^i `lk &t* u' `ljl molar`ql fkqboflo-b( B^i`ri^o 't+ v( pf t: < h.j b v- < h.'j * 0( m^o^ j y 0-a( B^i`ri^o 't+W( pf t: < 1! b v- <h.j m^o^ j y 0-
03- Rb^ T bi `lkgrkql ab qla^p i^p crk`flkbp ob^ibp G lkqfkr^p bk ZN+* //( v q^ibp nrb i^fkqbdo^i Q9&a+pG1&p'`p lksbodb- Cbcfk^jlp &H*d( < Q9&a+ph&p'c&p'`p,^( Cbjlpqo^o nrb i^ fkqbdo^i nrb a^ '.+ d( `lksbodb ^_plirq^jbkqb m^o^ `^a^ m^o abcrk`flkbp Gv d ab T-
YGj`e_]_e‰j9 @mif`^o i^ abpfdr^ia^a ab B^r`ev,R`et^ow m^o^ ^molufj^o i^ fkqb,do^i Ic a+ph-&p'c&p'h`p,[
_( Cbjlpqo^o nrb T bp rk bpm^`fl ifkb^i `lk &f*d( `ljl molar`ql fkqboflo-b( B^i`ri^o &f*d( pf G&p'< a,p v d'q( ;p%*alkab j < /+ 0+ 1+ ----
04- Dk rk bpm^`fl br`iŒabl `ljmibgl+ abjlpqo^o nrb bi molar`ql fkqboflo qfbkb i^p pfdrfbkqbpmolmfba^abp m^o^ qlalp ilp bibjbkqlp t+v+ w v qlalp ilp `ljmibglp ] v ^-
^( &]t* ^u' < ]ˆ&t* u', _( &t* ]u * ^v' < ]&t* u' * ˆ&t* v',05- Cbjlpqo^o nrb bk qlal bpm^`fl br`iŒabl plk sŠifa^p i^p fabkqfa^abp pfdrfbkqbp-
^( Hiu* viii < HHui01* iHv.i1* &t*u' * &u,t',_( Zu * uhh1 , .Hu, vi01 < 0&t* u( * 0&u*t',b( Hiu * vi01 * Hiu , viii < 1 Hiuiii * 1 Hiv001-
06- Cbjlpqo^o nrb bi bpm^`fl ab qla^p i^p crk`flkbp `ljmibg^p `lkqfkr^p bk rk fkqbos^ilY]* ^[ pb qo^kpcloj^ bk rk bpm^`fl rkfq^ofl pf abcfkfjlp rk molar`ql fkqboflo mlo i^cŽojri^
'b+c( <H8s'p(.'p(c'p( `p +
alkab s bp rk^ crk`fŽk mlpfqfs^ cfg^+ lkqfkr^ bk Y]* ^[,
)'), 6XW\][^LLRmWMNLXWS^W]X\X[]XPXWJUN\'?k]XMXMNFo^j,R`ejfaq
Slal bpm^`fl ifkb^i ab afjbkpfŽk cfkfq^qfbkbrk^ _^pb cfkfq^-Rf bi bpm^`fl bpbr`iŒabl+mlabjlp `lkpqorfo pfbjmob rk^ _^pb knpkckj]h- Dpqbobpriq^al pb abar,
Akjopnq__e‰j `a _kjfqjpko knpkckj]hao- K†pk`k `a En]i,Q_die`p 05
`foŠ `ljl `lkpb`rbk`f^ ab rk qblobj^ `rv^ abjlpqo^`fŽk bkpb•^ ^ `lkpqorfo`lkgrkqlp loqldlk^ibp bk `r^inrfbo bpm^`fl br`iŒabl- ab afjbkpfŽk cfkfq^ l abfkcfkfq^pafjbkpflkbp- K^ `lkpqor``fŽk pb ii^j^ i†pk`k `a En]i,Q_die`p+ bk jb,jlof^ ab I- O- Fo^j '074/,0805( v D- R`ejfaq '0734,0810(-
SDNQDL@ 0-02- SDNQDL@ CD NQSNFNM@KHY@BHˆM- Qa] Vz+V1+--- +qj] oq,_aoe‰j bejep] k ej`abeje`] `a ahaiajpko `a qj aol]_ek aq_h‡`ak T+ v `aoecjaiko_kj J'th* ‹‹‹ * Vg( ah oq^aol]_ek cajan]`k lkn hko g lneianko `a aoko ahaiajpko-Cteopa qj] oq_aoe‰j_knnaolkj`eajpa `a ahaiajpko XH= W1Œ--- +`a T mqa peaja h]ooecqeajpao lnklea`]`ao l]n] _]`] ajpank g9
^( Ch ahaiajpk Wgao knpkckj]h ] pk`k ahaiajpk `ah oq^ aol]_ek J'WG=--- Wg,y(-_( Ch oq^ aol]_ek cajan]`k lkn XH= ’’’ + Wg ao ah ieoik mqa ah cajan]`k
lkn Wi&-’’’ te9
b( J] oq_aopkj XH- W1Œ---Œ ao Šje_]+ o]hrk b]_pknao ao_]h]nao- Copk ao+pfu: +W1+&-- +ao kpn] oq_aoe‰j`a ahaiajpko `a T mqa o]peob]_aj h]o lnklea`]`ao ^(v _(+ajpkj_ao l]n] _]`] g ateopa qj ao_]h]n Ag p]hmqa Wy< _hpWhp•
Baikopn]_e‰j- Blkpqorv^jlp ilp bibjbkqlp X0= W1+--- +mlo fkar``fŽk- O^o^fkf`f^o bi mol`bpl+ qlj^jlp XH < Wi& Rrmlkd^jlp ^elo^ nrb ebjlp `lkpqorfalXH+ ’’’ + Xo ab jlal nrb ^( v _( pb p^qfpc^`bk`r^kal g < n- Cbcfk^jlp Xo*0 jb,af^kqb i^ b`r^`fŽk
'0-03(n
Wn*h< tn*0 , ][email protected]
alkab ilp bp`^i^obp ]h%,,, * ]+ qfbkbk nrb abqbojfk^opb- O^o^ f 8899n* bi molar`qlfkqboflo ab Xo*i `lk Xf sfbkb a^al mlo
+'W!&z,0+We(< &V*) * We(, ]z'ue +We(< &V*) * We(, ]z'We &We(&
* e;/
mrbpql nrb 'We+We(< N pf f" f- Rf We-<G<M+ mlabjlp e^`bo Xo*i loqldlk^i ^ Xfqlj^kal
'0-04( ]e
< &t*) * We(-
'We&W:(
Rf Xf < N+ bkqlk`bp Xo*i bp loqldlk^i ^ Xf m^o^`r^inrfbo ]z nrb pb bifg^+bk bpqb`^pl bibdfjlp ]z < N- @pŒmrbp+bi bibjbkql Xo*i bpqŠ_fbk abcfkfal v bp loqldlk^i
-3 Col]_eko heja]hao
^ `^a^ rkl ab ilp ^kqboflobpbibjbkqlp v! --- + Wn&Olo `lkpfdrfbkqb+ bp loqldlk^i^ qlal bibjbkql abi pr_bpm^`fl &
Dpql abjrbpqo^ ^( `r^kal g < n * 0-O^o^ abjlpqo^o _( `r^kal g < n * 0 + qbkbjlp nrb mol_^o nrb
J&W/*%! *Wn)h' < J&t/*•••* tn)/'* a^al nrb J&W/*%! *Wn' < J&t/*•••* u-(-Klp n mofjbolp bibjbkqlp XG ’’- + v+ mboqbkb`bk
v mlo q^kql bpqŠkbk bi pr_bpm^`fl jŠp ^jmifl J&t/* ,,, * tn)h'% Di krbsl bibjbk,ql W&*0 a^al mlo '0-03( bp rk^ afcbobk`f^ ab alp bibjbkqlp ab J&t0+ ŒŒŒŒV&*0(
^pŒnrb q^j_f‹k bpqŠbk J&V/ ‹,,, %tn)h'% Dpql abjrbpqo^ nrb
K^ b`r^`fŽk '0 -03( morb_^ nrb tn)/ bp i^ prj^ ab alp bibjbkqlp `aJ&W/ * ,,, *Wn)/'`lk il nrb rk o^wlk^jfbkql ^kŠildl a^ i^ fk`irpfŽk bk bi lqol pbkqfal9
Dpql abjrbpqo^ _( `r^kal g < n * i- Olo il q^kql ^( v _( e^k pfal abjlpqo^alpmlo fkar``fŽk obpmb`qlab g,
Efk^ijbkqb abjlpqo^jlp b( mlo fkar``fŽk obpmb`qlab g, Di `^pl e_ < 0 bpqofsf^i-Olo `lkpfdrfbkqb+ prmlkd^jlp nrb b( bp `fboql m^o^g < n v `lkpfabobjlpbi bibjbkql W9)h, Dk sfoqra ab _(+ bpqbbibjbkql mboqbkb`b
J&W/*%! *Wn)h'%
^pŒnrb mlabjlp bp`of_fo
n)/W9)h< AeWe< v: * An)hWn)h%
e;/
alkab Y+ D J&uz* ,,,‹ u*', Prbobjlp abjlpqo^o nrb w+< N- Olo i^ molmfba^a^(+W9)h v _n)hWn)h plk ^j_lp loqldlk^ibp ^ v,- Olo `lkpfdrfbkqb+ pr afcbobk`f^+ v-+bp loqldlk^i ^ v-- Cf`el ab lqol jlal+ v: bp loqldlk^i ^ pŒjfpjl+ ^pŒnrbv: < N- Dpql `ljmibq^ i^ abjlpqo^`fŽk abi qblobj^ ab loqldlk^ifa^a-
Dk i^ `lkpqor``fŽk ^kqboflo+mrbab pr`babo nrb Wn)h < N m^o^^id•k n,Dkqlk,`bp '0 -03( morb_^ nrb Vn*0 bp rk^ `lj_fk^`fŽk ifkb^i ab W0 ŒŒŒŒŒv! v mlo q^kql
Akjopnq__e‰j a _kjfqjpko knpkckj]hao- K†pk`k `a En]i,Q_die`p 18
ab W! ’’’ + t! ^pŒnrb ilp bibjbkqlp W0I ’’’ + Vn*h plk abmbkafbkqbp-Dk lqo^p m^,i^_o^p+pf ilp Remofjbolp bibjbkqlp W0I ’’’ + Vg plk fkabmbkafbkqbp+ilp bibjbkqlp`loobpmlkafbkqbpX0I ’’’ + Wg plk jk jqhko- Dk bpqb`^pl ilp `lbcf`fbkqbp ]e ab '0-03(sfbkbk a^alp mlo '0-04(+ v i^p cŽojri^p nrb abcfkbk X! --- +Wg pb `lksfboqbk bk
&/,/4' Wh < Vh +w%&t*) * We( 0 1 g 0
Wn*h < tn* , K'- -(We m^o^ n < + +---+ , -fzi u! u+
Dpq^pcŽojri^p `lkpqfqrvbk bi j‹qlal ab Fo^j,R`ejfaq m^o^`lkpqorfo rk `lkgrkqlloqldlk^i ab bibjbkqlp kl krilp X0I ’’’ + Wg nrb dbkbo^k bi jfpjl pr_bpm^`fl nrbbi `lkgrkql fkabmbkafbkqba^al W! &! to- Dk m^oqf`ri^o+pf W! ’’’ + t| bp rk^_^pb m^o^rk bpm^`fl br`iŒabl ab afjbkpfŽk cfkfq^+bkqlk`bp X! --- +Wg ao rk^ _^pbloqldlk^i m^o^ bi jfpjl bpm^`fl- S^j_f‹k mlabjlp `lksboqfo ‹pq^ bk rk^ _^pbloqlkloj^i jkni]hev]j`k `^a^ rkl ab ilp bibjbkqlp We+bpql bp+afsfaf‹kalil mlopr kloj^- Olo `lkpfdrfbkqb+ `ljl `loli^ofl abi qblobj^ 0-02 qbkbjlp bi pf,drfbkqb-
SDNQDL@ 0-03- Rk`k _kjfqjpk aq_h‡`ak`a `eiajoe‰j bejep]peaja qj] ^]oaknpkjkni]h-
Rf V b u plk bibjbkqlp bk rk bpm^`fl br`iŒabl+`lk u <0< N+ bi bibjbkql
'V+ u' u
&u* u'
W1 < V1 + OpW* + O W O, + y1 1& H, 'uz+Wz(
EHFTQ@ 0-0 Ch i†pk`k `a En]i,Q_die`p aj T]& Sj _kjfqjpk knpkckj]h xX! W1&W2x
oa _kjopnqua ] l]npen `a qj _kjfqjpk ej`alaj`eajpa xu-+ t1& t]x-
2/ Col]_eko heja]hao
pb ii^j^ i^ lnkua__e‰j `a t ok^na v- Dk bi j‹qlal ab Fo^j,R`ejfaq '0-05(+`lkpqorfjlp bi bibjbkql Wn*h obpq^kal ab Wo*ii^ molvb``fŽk ab Wo*ipl_ob `^a^rkl ab ilp ^kqboflobp bibjbkqlp XH= -’- + Wn- K^ cfdro^ 0-0 obmobpbkq^i^ `lkpqor`,`fŽk dblj‹qof`^ bk bi bpm^`fl sb`qlof^i T2Œ
DIDLOKN 0- Dk T,* e^ii^o rk^ _^pb loqlkloj^i m^o^ bi pr_bpm^`fl dbkbo^almlo ilp qobp sb`qlobp Wi < '0+ ,0+ 0+,0(+ V1 < '4+ 0+0+0+(+X V2 < ',2+ ,2+0+,2(-
Qkhq_e‰j- @mif`^kal bi j‹qlal ab Fo^j,R`ejfaq+ bk`lkqo^jlp
Xf< Wi < '0+,0+ 0+,0( +
'V1+ XH( '3 1 N 1(W1 < V1 , XH < V1 , XH < + ! +'XH+v{(
'u^+ XH( 'u^+ W1( * 'N N N N(X^ < W , ,,, XH , W1 < V2 , XH W1 < + ! -'v{ +XH( 'W1+ W1(
Orbpql nrb X2 < N+ ilp qobp sb`qlobp Vz* V1+ V2 ab_bk pbo abmbkafbkqbp- Obol v^nrb Xi b X1 plk kl krilp+ ilp sb`qlobp Wi v z1 plk fkabmbkafbkqbp- Olo `lkpfdrfbkqbJ'th+ V1+ t2( bp rk pr_bpm^`fl ab afjbkpfŽk 1- Di `lkgrkql xXH= W1x bp rk^ _^pbloqldlk^i m^o^ bpb pr_bpm^`fl- Cfsfafbkal XH b X1 `^a^ rkl mlo pr kloj^ iibd^jlp^ rk^ _^pb loqlkloj^i nrb `lkpq^ ab alp sb`qlobp
XH 0 (,,,, < ,'0 ,0 0 ,0HHXHHH 1& !
v W1 0 0 (,,,, < ,/5&0* +/+0 -HHX100 s 5
DIDLOKN 1- Nkhejkieko `a Jacaj`na- Dk bi bpm^`fl ifkb^i ab qlalp ilp ml,ifkljflp+ `lk bi molar`ql fkqboflo &t* v( <c<,i t&p' u&p' `p+`lkpfabo^jlp i^ pr`bpfŽkfkabcfkfa^ t!* VG< t0* ‹‹‹ * alkab tj&p' < p!- Br^kal pb ^mif`^ ^ bp^ pr`bpfŽk biqblobj^ ab loqldlk^ifw^`fŽk pb qo^kpcloj^ bk lqo^ pr`bpfŽk ab mlifkljflpWk+ XH= W1& --- + nrb bi j^qbjŠqf`l co^k`‹p @- L- Kbdbkaob '0641,0722( crb bimofjbol bk bk`lkqo^o bk pr qo^_^gl pl_ob i^ qbloŒ^abi mlqbk`f^i- Klp mofjbolp abbplp mlifkljflp pb `^i`ri^k cŠ`fijbkqb `lk bi j‹qlal ab Fo^j,R`ejfaq- @kqbqlal+ qbkbjlp uk&p' < t**&p' < 0- Orbpql nrb
'Wk+ Wk( <ci `p < 1,0
v 'Wi+Wk( <ci p`p < N+,0
bk`lkqo^jlp nrb
Akilhaiajpko knpkckj]hao- Nnkua__ekjao 20
@ `lkqfkr^`fŽk+ rqfifw^jlp i^p obi^`flkbp
HG 1 1't1 +Wk( < p `p < , +
,0 .'t1 +Wh( <Hh p1 `p < N+
,0 HG 1 1'uz +Wz( < p `p < ,
,0 .
m^o^ l_qbkbo
W1'p( < t1'p( , 't1 +Wk( Wk'p( \ 't1 +Wh( uz'p( < p1 \ -'Xl + Wk( 'Wh +Wh( 2
Cbi jfpjl jlal+ bk`lkqo^jlp nrb
2 2W2'p( < p + 4 p +
3 5 1 2W3'p( < p , , p * , +
- 6 24- - 4 0/ 2 4
Wo'p( < p , , p * , p -8 10
Dk bi `^mŒqril5 bk`lkqo^objlp ab krbsl bplp mlifkljflp bk bi bpqrafl ab i^pb`r^`flkbp afcbobk`f^ibp+v mol_^objlp nrb
j `j'1 h•jW 'p( < , , p , ( -
j '1j( `p!
Klp mlifkljflp N: a^alp mlo
&0j' 0 ]9 ' 1 (jNjAp( < 1j'j (1 Wj'p( < 1jj `pj p , 0
pb `lkl`bk `lk bi klj_ob ab lkhejkieko `a Jacaj`na- Klp mlifkljflp ab i^ pr,`bpfŽk loqlkloj^i `loobpmlkafbkqb oml+ 'x f+ om1! -’ + a^alp mlo nlj< Xk.HHXkii pbii^j^k lkhejkieko `a Jacaj`na jkni]hev]`ko- Cb i^p cŽojri^p m^o^ Wk+ --- + W4a^a^p ^kqbp+bk`lkqo^jlp nrb
H+
H 2'w k'p( < sf& 'w z'p( < 1 p +
/i'x p'q( < 7z 1! '52p4
, 6/p2 * 04p( -
)')- 6XVYUNVNW]X\X[]XPXWJUN\'B[XbNLLRXWN\
Rb^k T rk bpm^`fl br`iŒabl v R rk pr_ bpm^`fl ab afjbkpfŽk cfkfq^-U^jlp^ `lkpfabo^o bi pfdrfbkqb mol_ibj^ ab ^molufj^`fŽk9 B]`k qj ahaiajpk t `a
21 Col]_eko heja]hao
T+ `apaniej]n qj ahaiajpk aj R _qu] `eop]j_e] ] t oa] hk i…o lamqaˆ] lkoe^ha-K^ afpq^k`f^ bkqobalp bibjbkqlp t b u pb abcfkb `ljl i^ kloj^ Hiu, W*,
@kqbpab afp`rqfo bpqbmol_ibj^ bk pr cloj^ dbkbo^i+`lkpfabobjlp rk `^plm^oqf`ri^o+obmobpbkq^albk i^ cfdro^ 0-1- @nrŒT bp bi bpm^`fl sb`qlof^i T! v R bprk pr_bpm^`fl ab afjbkpfŽk alp+ rk mi^kl nrb m^p^mlo bi lofdbk- C^al t ab T*bi mol_ibj^ `lkpfpqb bk bk`lkqo^o+bk bi mi^kl R+bi mrkql o jŠp moŽufjl ^ t-
Rf t D R+bsfabkqbjbkqb i^ plir`fŽk bp o < t- Rf t kl mboqbkb`b R+bi mrkqljŠp moŽufjl o pb l_qfbkb qo^w^kal rk^ mbombkaf`ri^oabpab t ^i mi^kl- Dpqbpbk,`fiil bgbjmil prdfbob rk^ fkqolar``fŽk ^i mol_ibj^ dbkbo^i ab ^molufj^`fŽk v a^lofdbk ^ i^ afp`rpfŽk nrb pfdrb-
CDEHMHBHˆM- Qa] R qj oq^_kjfqjpk `a qj aol]_ek aq_h‡`ak T- Qa `e_a mqa qjahaiajpk `a T ao knpkckj]h ] R oe ao knpkckj]h ] pk`k ahaiajpk `a R-Ch _kjfqjpk`a pk`ko hko ahaiajpko knpkckj]hao ] R oa `aoecj] _kj Rf, u ao ah |lanlaj`e_qh]n] Q€,
Dp rk bgboBHBHNpbk`fiil `ljmol_^o nrb Rf, bp rk pr_bpm^`fl ab T* q^kql+pf R il bp `ljl pfkl ilbp- Dk bi `^pl bk nrb R pb^ rk pr_bpm^`fl+ bkqlk`bp Rf, pbii^j^ _kilhaiajpk knpkckj]h ab R-
DIDLOKN- Rf R bp rk {mi^kl nrb m^p^mlo bi lofdbk+ `ljl pb sb bk i^ cfdr,o^ 0-1- bkqlk`bp Rf, bp rk^ ob`q^ mlo bi lofdbk mbombkaf`ri^o ^ bpb mi^kl- Dpqbbgbjmil a^ q^j_f‹k rk^ fkqbomobq^`fŽkdblj‹qof`^ m^o^ bi qblobj^ pfdrfbkqb-
pI--
EHFTQ@ 0-1 Gjpanlnap]_e‰j caki†pne_] `ah paknai] `a `ao_kilkoe_e‰j knpkckj]h aj T2Œ
Akilhaiajpko knpkckj]hao- Nnkua__ekjao ..
SDNQDL@ 0-04- SDNQDL@ CD K@ CDRBNLONRHBHNM NQSNFNM@K- Qa]j T qjaol]_ek aq_h‡`ak v R qj oq^aol]_ek `a T `a `eiajoe‰j bejep]- Rk`k ahaiajpk t`a T lqa`a nalnaoajp]noaaj bkni] Šje_] _kik qj] oqi] `a `ko ahaiajpko+ qjk`a R v kpnk `a Q,h+,Copk ao+pajaiko
'0-06( t < o * o-h,+ `kj`a o D R
?`ai…o+ h] jkni] `a t reaja `]`] lkn h] b‰niqh] lep]c‰ne_]
'0-07(
Baikopn]_e‰j- Cbjlpqobjlp mofjbol nrb bufpqb bk ob^ifa^a rk^ abp`lj,mlpf`fŽk loqldlk^i '0-06(- Orbpql nrb R bp ab afjbkpfŽk cfkfq^+qfbkb rk^ _^pbloqlkloj^i cfkfq^+pb^ ‹pq^ wah&--- +ajx- C^al t+ abcfkfjlp ilp bibjbkqlp p v p-i,^pŒ9
'0-08(j
R < J 'u+ ae(ae +eyh
-KR <t,o-
N_pbosbjlp nrb `^a^ q‹ojfkl &t* ae'ae bp i^ molvb``fŽk ab t pl_ob ap, Di bibjbk,ql p bp i^ prj^ ab i^p molvb```flkbp ab t pl_ob `^a^ bibjbkql ab i^ _^pb- Orbpqlnrb p bp rk^ `lj_fk^`fŽk ifkb^i ab ilp bibjbkqlp ab i^ _^pb+p bpqŠbk R- K^ abcf,kf`fŽk ab pli morb_^ nrb i^ b`r^`fŽk '0 -06( bp sŠifa^- O^o^ abjlpqo^o nrb okh
bpqŠbk Q,/* `lkpfabobjlp bi molar`ql fkqboflo ab o,/, v `r^inrfbo bibjbkql az ab i^_^pb- Sbkbjlp
Obol ab '0-08:(+ bk`lkqo^jlp nrb &o* az' < &t* az'* ^pŒnrb o,/, bp loqldlk^i ^ af,
Olo `lkpfdrfbkqb oebp loqldlk^i ^ qlal bibjbkql ab R+ il `r^i pfdkfcf`^ nrbo-0-D Q-0--
Ool_^jlp ^ `lkqfkr^`fŽk nrb i^ abp`ljmlpf`fŽk loqldlk^i '0-06( bp •kf`^-Rrmlkd^jlp nrb t qrsfbo^ alp abp`ljmlpf`flkbp+ pb^k ‹pq^p
'0-1/( H t<o*oh v t < '* &,h,*
alkab p v p bpqŠkbk R+v oGX '0 bpqŠkbk Q0k- Prbobjlp abjlpqo^o nrb p < p Xp,K,< &h,,Cb '0-1-/(+ qbkbjlp p , p < '0- , p-K+^pŒnrb pŽil kb`bpfq^jlp abjlp,qo^onrb o , p < N- Obol p , p D R X '0- , p,KD R0-- `lk il nrb p , p bp loql,dlk^i ^ '0-- , o-J b fdr^i ^ p--h--, oh,- Orbpql nrb bi bibjbkql `bol bp bi •kf`l bib,jbkql loqldlk^i ^ pŒjfpjl+ ab_b pbop , p < N- Dpql abjrbpqo^ nrb i^ abp`lj,mlpf`fŽk bp •kf`^-
23 Col]_eko heja]hao
Efk^ijbkqb+ abjlpqobjlp nrb i^ kloj^ ab t sfbkb a^a^ mlo i^ cŽojri^ mfq^,dŽof`^- Sbkbjlp
HHui01< &t* t' < 'p * pz+ p * RK( < 'p+ p( * 'Rz+ RI(+
pfbkal krilp ilp obpq^kqbp q‹ojfklp v^ nrb p v pz plk loqldlk^ibp- Dpql abjrbp,qo^ '0{-07(-
CDEHMHBHˆM- Qa] R qj oq^ aol]_ek `a `eiajoe‰j bejep] `a qj aol]_ek aq_h‡`akT+ u oa] wah=--- +ajx qj] ^]oa knpkjkni]h l]n] R- Qe t D T+ ah ahaiajpk p `abe,je`k lkn h] a_q]_e‰j
j
Q < 1 't+ ae(aef<i
oa `ajkiej] lnkua__e‰j `a t ok^na ah oq^aol]_ek R-
Cbjlpqo^jlp pbdrfa^jbkqb nrb i^ molvb``fŽk ab t pl_ob R bp i^ plir`fŽkabi mol_ibj^ ab ^molufj^`fŽk bpq^_ib`fal ^i `ljfbkwl ab bpq^ pb``fŽk-
0-05& 4Y[XaRVJLRmWmY]RVJMNNUNVNW]X\MN WN\YJLRXN^LUlMNXYX[NUNVNW]X\MN W\^KN\YJLRXMNMRVNW\RmWORWR]J
[
SDNQDL@ 0-05- SDNQDL@ CD @OQNWHL@BHˆM- Qa] R+qj oq^aol]_ek `a `e,iajoe‰j bejep] `a qj aol]_ek aq_h‡`ak T+ u oa] t qj ahaiajpk `a T- J] lnkua__e‰j`a t ok^na R ao i…o ln‰tei] ] t mqa _q]hmqean kpnk ahaiajpk `a R- Copk ao+oe pao h] lnkua__e‰j `a t ok^na R+ pajaiko
Zu , pfi z Zu , qgi
l]n] pk`k p `a R: ao r…he`k ah oecjk `a ecq]h`]` oe u o‰hkoe p < p-
Baikopn]_e‰j- Dk sfoqra abi qblobj^ 0-04 mlabjlp bp`of_fo t < o * pz+alkab o D R X oy D Qy- Dkqlk`bp+ m^o^ `r^inrfbo p ab R+ qbkbjlp
t + p < &t + o' * &o+ p( -
Orbpql nrb p , pD R X t , p < oy D Qy* ‹pq^ bp rk^ abp`ljmlpf`fŽk loqldlk^iab t + p+pŒnrb pr kloj^ sfbkb a^a^ mlo i^ cŽojri^ mfq^dŽof`^
Hiu , ph00 < HHu,+pH01 * ifp , q001-
?lnktei]_e‰j ‰lpei] `a ahaiajpko `a qj aol]_ek aq_h‡`ak 24
Obol ifp , qi01 „ /+ `lk il nrb Hiu, pU „ Hiu, oU+ s^ifbkal bi pfdkl fdr^i pfv pŽil pf p < p-Dpql `ljmibq^ i^ abjlpqo^`fŽk-
DIDLOKN 0- ?lnktei]_e‰j `a bqj_ekjao _kjpejq]o aj ZN+106[+lknlkhejk,ieko pneckjki†pne_ko- Rb^ T < A'M+106(+ bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbpob^ibp `lkqfkr^p bk bi fkqbos^il Z/+166\+ v abcfk^jlp rk molar`ql fkqboflo jbaf^kqbi^ b`r^`fŽk &/*c( < k! b't(c't( `V-Cj i^ pb``fŽk 0-01 sfjlp rk `lkgrkql loql,kloj^i ab crk`flkbp qofdlklj‹qof`^p ADk+ BEH+AD1+ ŒŒŒ + alkab
'0-10(0
BEl'W( < ] ., +U 106
`lp gtAD1g,h'V( < v: + pbk gt
AN1g'V( < v:&m^o^ g „ 0 -
Klp 0j * 0 bibjbkqlp alk+ bmH&--- + al1j dbkbo^k rk pr_bpm^`fl R ab afjbkpfŽk1j * 0- Klp bibjbkqlp ab R pb ii^j^k lkhejkieko pneckjki†pne_ko-
Rf b D B'/+16S(+ pb^ h| i^ molvb``fŽk ab b pl_ob bi pr_ bpm^`fl R- Sbkbjlpbkqlk`bp
'0-11(0j
G9<h9M;b+ alg(alg + alkab &H*alg( < H9!b'V(alg'V( `t -
Klp k•jbolp &/*oma pb ii^j^k _kabe_eajpaoa Dkqneanab b- @mif`^kal i^p cŽojr,i^p '0-10(+ mlabjlp mlkbo '0-11( bk i^ cloj^
'0-12(j
bj't( < f^l * 09&]g `lp gt * ^goaj gt(+ScT
alkab
/ e0
!]g < , b't( `lp gt `t +,2 V
0 h^^g;+ b't(oajgt`t,2 V
m^o^ g < /+ 0+ 1+ --- + j- Di qblobj^ ab ^molufj^`fŽk klp af`b nrb bi mlifkljflqofdlklj‹qof`l '0 -12( ^molufj^ b jbglo nrb `r^inrfbo lqol mlifkljfl qofdlkl,j‹qof`l ab R+ bk bi pbkqfal ab nrb i^ kloj^ Hic, ckii bp i^ jŠp mbnrb•^ mlpf_ib-
DIDLOKN 1- ?lnktei]_e‰j `a bqj_ekjao _kjpejq]o aj Z,0+ 0\ lkn lkhejk,ieko `a cn]`k y j- Rb^ T < B' ,0+ 0(+bi bpm^`fl ab i^p crk`flkbp ob^ibp `lk,qfkr^p bk Z,0+ 0\+ X pb^ &G*c'<Qyhb't(c't(`t- Klp j * 0 mlifkljflp ab Kb,dbkaob kloj^ifw^alp oml+al! --- +nlj+ fkqolar`falp bk i^ pb``fŽk 0-03+ dbkbo^k rkpr_bpm^`fl R ab afjbkpfŽk j * 0 nrb `lkpq^ ab qlalp ilp mlifkljflp ab do^al
25 Col]_eko heja]hao
y j- Rf G D B' ,0+ 0(+ abpfdkbjlp `lk Gj i^ molvb``fŽk ab G pl_ob R- Sbkbjlpbkqlk`bp
j
G*<H&H*b& g'b& g*Sc=
alkab 'H+b& g'<J8b&p'b& ep' `p ,
Dpqb bp bi mlifkljfl ab do^al z j m^o^ bi nrb i^ kloj^ 0HH, Gjhh bp i^ jbklo-Olo bgbjmil+ `r^kal G&t'< pbk jt* ilp `lbcf`fbkqbp :/* b& g'sfbkbk a^alp mlo
Dk m^oqf`ri^o+ qbkbjlp :/* c' l( < N X
H, ,
0 2 21'H+c' i( <Ki 1-p pbk jp `p < H1-,: -
Olo `lkpfdrfbkqb bi mlifkljfl ab mofjbo do^al bp'p( jŠp moŽufjl ^ pbk pnp bkZ,0+0\ bp
Orbpql nrb :/* b& 0' < N+bpqb bp q^j_f‹k i^ jbglo ^molufj^`fŽk `r^aoŠqf`^-
) ')/ 8SN[LRLRX\
0- Dk `^a^ `^pl+ e^ii^o rk^ _^pb loqlkloj^i m^o^ bi pr_bpm^`fl ab T 2 dbkbo^al mlo ilpsb`qlobp a^alp-^( Vh < '0+ 0+0(+ V1 < '0+ /+0(+ t2 < '2+ 1+2(-_( Vh < '0+0+0(+ V1 < ',0+0+ ,0(+ V2 < '0+ /+0(-
1- Dk `^a^ `^pl+ e^ii^o rk^ _^pb loqlkloj^i m^o^ bi pr_bpm^`fl ab T3
dbkbo^al mlo ilpsb`qlobp a^alp-^( Vh < '0 0+N+N(+ V1 < 'N+ 0+0+N(+ t2 < 'N+/+0+0(+ t
3< '0+ N+/+0(-
_( Vh < '0+0+ /+0(+ V1 < '0+ N+1+0(+ t2 < '0+1+ ,1+0(-
2- Dk bi bpm^`fl ifkb^i ob^i B'N+ &iS( `lk molar`ql fkqboflo 'u+ v( < bc t&p'u&p'`p* pb^t!&p' < `lp jp m^o^ j < N+0+ 1+ ---- Cbjlpqo^o nrb i^p crk`flkbp Xl& XH&W1&--- + a^a^pmlo
0uk'p( < sf: v Wj'p( <Hylp jp m^o^ j 1 0 +
cloj^k rk `lkgrkql loqlkloj^i nrb dbkbo^ bi jfpjl pr_bpm^`fl nrb tk& Vh& t1& ŒŒŒ
Cfan_e_eko .2
3- Dk bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ob^ibp+ `lk molar`ql fkqboflo &t* v( <b?t&p'u&p'`p* pb^ t,&p' < p! m^o^ j < /+ 0+ 1+ &! - Cbjlpqo^o nrb i^p crk`flkbp
Wk&p' < 0 + WG'p(< U2 '1p , 0( + 01'0( < s4 '5p0 + 5p * (!
cloj^k rk `lkgrkql loqlkloj^i nrb dbkbo^ bi jfpjl pr_bpm^`fl nrb wVM& Wi&V1x-
4- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbp ob^ibp / `lkqfkr^p bk ZN+* % H'v q^ibpnrb i^ fkqbdo^i Iz a+pb0&p'`p `lksbodb- Cbcfk^jlp 'b+ d( < Iz a+ph&p'c&p'`p* v pb^ Xl+ XH&W1& ŒŒŒ+ bi `lkgrkql l_qbkfal ^mif`^kal bi j‹qlal ab Fo^j,R`ejfaq ^ VM& Vh& t1& ŒŒŒ+
alkab t,&p' < p! m^o^ j 988N- Cbjlpqo^o nrb uk&p' < 0+ WG&p'< p + ($ u1&p' < p0 + 2p * 1+
X &p' < p2 , 8p1 * 07q , 5-5- Dz bi bpm^`fl ifkb^i ob^i A&/* 2( `lk molar`ql fkqboflo 'b+ d( <GG&t'c&t'`t* pb^
G&t' < h-t v abjlpqo^o nrb bi mlifkljfl `lkpq^kqb d jŠp moŽufjl ^ / bp d < fild 2-B^i`ri^o iip , ci01m^o^ bpqb d-
6- Dk bi bpm^`fl ifkb^i ob^i B'N+ 1( `lk molar`ql fkqboflo &b*d( < GG&t'c&t'`t* pb^G&t' < a! v abjlpqo^o nrb bi mlifkljfl `lkpq^kqb d jŠp moŽufjl ^ / bp d < f&a1 , 0(-B^i`ri^o HHd, 0001 m^o^ bpqb d-
7- Dk bi bpm^`fl&ifkb^i ob^i B' ,0+ 0( `lk molar`ql fkqboflo &b*d( ;Hyh-&t'c&t'`t* pb^G't( < a! v e^ii^o bi mlifkljfl d jŠp moŽufjl ^ h- B^i`ri^o Hid , 00.1 m^o^ bpqb d-
8- Dk bi bpm^`fl ifkb^i ob^i B'N+ 0%/R' `lk molar`ql fkqboflo &b* d( < Gr G&t'c&t'`t* pb^G&t' < t, Dk bi pr_bpm^`fl dbkbo^al mlo qk&t' < 0+ qh&t' < `lp t* q
1&t' < pbk t* e^ii^o
bi mlifkljfl qofdlklj‹qof`l jŠp moŽufjl ^ b,0/- Dk bi bpm^`fl ifkb^i T abi bgbo`f`fl 4+ mlkbo G&t' < a+V v e^ii^o bi mlifkljfl ab mofjbo
do^al jŠp moŽufjl ^ b,
1
EC4@DOAC?46<A@8D><@84>8D H ?4EC<68D
*') E[JW\OXWWJLRXWN\URWNJUN\
Tkl ab ilp jlaboklp l_gbqfslp abi @kŠifpfpbp rk bpqrafl ^jmifl ab crk`fl,kbp `rvlp aljfkflp v ob`loofalp plk pr_`lkgrkqlp ab bpm^`flp ifkb^ibp- S^ibp crk,`flkbp pb ii^j^k pn]jobkni]_ekjao+ ]lhe_]_ekjao+r klan]`knao- Dpqb`^mŒqrilqo^q^ab ilp bgbjmilp jŠp pbk`fiilp+ ii^j^alp qo^kpcloj^`flkbp heja]hao+nrb pb mobpbk,q^k bk qla^p i^p o^j^p ab i^ L^qbjŠqf`^- K^p molmfba^abpab qo^kpcloj^`flkbpjŠp dbkbo^ibp pb l_qfbkbk ^ jbkral ^molufjŠkali^p jbaf^kqb qo^kpcloj^`fl,kbp ifkb^ibp-
Hkqolar`fjlp mofjbol i^ klq^`fŽk v i^ qbojfklildŒ^ jŠp `loofbkqb obi^qfs^ ^crk`flkbp `r^ibpnrfbo^- Rb^k T v U alp `lkgrkqlp- Di pŒj_lil
R9 T,, U
pb rp^oŠ m^o^ fkaf`^o nrb R bp rk^ crk`fŽk `rvl aljfkfl bp T v `rvlp s^ilobpbpqŠkbk U- O^o^ `^a^ t ab T+ bi bibjbkql R't( ab U pb ii^j^ ei]caj `a t] pn]r†o `a R+v ab`fjlp nrb R ]lhe_] t aj R't(- Rf ? bp rk pr_`lkgrkql `r^i,nrfbo^ ab T+bi `lkgrkql ab qla^p i^p fjŠdbkbp R't( m^o^t ab ? pb ii^j^ h] ei],caj `a ? ] pn]r†o`a R v pb obmobpbkqmlo R'?(- K^ fj^dbk abi aljfkfl T+R'T(+bp bi ob`loofal ab R,
Rrmlkd^jlp ^elo^ nrb T v U plk bpm^`flp ifkb^ibp nrb qfbkbkbi jfpjl `lk,grkql ab bp`^i^obp+v abcfk^jlp rk^ qo^kpcloj^`fŽk ifkb^i `ljl pfdrb-
CDEHMHBHˆM- QeT WU okj `ko aol]_eko heja]hao+qj] bqj_e‰j R9T y U oahh]i] pn]jobkni]_e‰j heja]h `a T aj U+ pf peaja h]o lnklea`]`ao oecqeajpao9
^( R't * u' < R't( * R'u(_( R'_t( < _R't(
_q]haomqean]mqa oa]j t a u `a T+l]n] pk`k t `a T u _q]hmqeanao_]h]n_-
.4
3/ Rn]jobkni]_ekjao heja]hao u i]pne_ao
Dpql pfdkfcf`^ nrb R `lkpbos^ i^ ^af`fŽk v i^ jriqfmif`^`fŽk mlo bp`^i^obp-K^p alp molmfba^abpmrbabk `lj_fk^opb bk rk^ cŽojri^ nrb bpq^_ib`b nrb
R']t * ^u( < ]R't( * ^R'u(
m^o^ qlal t v qlal u ab T v qlalp ilp bp`^i^obp ] v ^- Olo fkar``fŽk+ qbkbjlpq^j_f‹k i^ obi^`fŽk jŠp dbkbo^i
m^o^ j bibjbkqlp `r^ibpnrfbo^ Vh!%! t| ab T+v j bp`^i^obp `r^ibpnrfbo^]h! ŒŒ+]jk
Di ib`qlo mrbab `ljmol_^o cŠ`fijbkqb nrb ilp bgbjmilp pfdrfbkqbpplk qo^kp,cloj^`flkbp ifkb^ibp-
DIDLOKN 0- Rn]jobkni]_e‰j e`†jpe_]- K^ qo^kpcloj^`fŽk R9T y T+ alkabR&t' < V m^o^ qlal t ab T* pb abkljfk^ qo^kpcloj^`fŽk fa‹kqf`^ v pb abpfdk^mlo 0 l mlo hr-
DIDLOKN 1- Rn]jobkni]_e‰j _ank- K^ qo^kpcloj^`fŽk R9 T y T nrb ^mif`^`^a^ bibjbkql ab T bk N pb ii^j^ qo^kpcloj^`fŽk `bol v pb abpfdk^ mlo l-
DIDLOKN 2- Kqhpelhe_]_e‰j lkn qj ao_]h]n befk _- Sbkbjlp ^nrŒR9 T y T+
alkab R&t' < at m^o^qlal t ab T, Br^kal a < 0+pb qo^q^ab i^ qo^kpcloj^`fŽkfa‹kqf`^- Br^kal a < /+ bp i^ qo^kpcloj^`fŽk `bol-
DIDLOKN 3- C_q]_ekjao heja]hao- Rb^k T < Tj v U < T i- C^alp ijk•jbolp ob^ibp]q+`lk e < 0+1+--- +i v g < 0+1+ --- +j+ abcfk^jlp R9 Tj y T i
`ljl pfdrb9 R ^mif`^ `^a^ sb`qlo t < 'Vh& ŒŒŒ+tj( ab Tj bk bi sb`qlo u < 'X0I--- +Wi( ab T i ab ^`rboal `lk i^p b`r^`flkbp
j
We< K ]egtg m^o^ † < 0+1+--- +i ,ScT
DIDLOKN 4- Nnk`q_pk ejpanekn _kj qj ahaiajpk befk- Rb^ T rk bpm^`fl ob^ibr`iŒabl- O^o^ rk bibjbkql cfgl w ab T+ abcfk^jlp R9 T y Q ^pŒ9Rf t D T+R&t' < &t* v'* bi molar`ql fkqboflo ab t mlo v+
DIDLOKN 5- Nnkua__e‰j ok^na qj oq^aol]_ek- Rb^k T rk bpm^`fl br`iŒablv R rk pr_bpm^`fl ab T ab afjbkpfŽk cfkfq^-Cbcfk^jlp R9 T y R ^pŒ9Rf t D T+R&t' bp i^ molvb``fŽk ab t pl_ob R-
LŠ_hak v na_knne`k 30
DIDLOKN 6- Ch klan]`kn `aner]_e‰j- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^pcrk`flkbp ob^ibp b abofs^_ibp bk rk fkqbos^il ^_fboql &]* ^', K^ qo^kpcloj^`fŽkifkb^i nrb ^mif`^ `^a^ crk`fŽk b ab T bk pr abofs^a^ p%pb ii^j^ lmbo^alo abofs^,`fŽk v pb abpfdk^ mlo B- @pŒmrbp+ qbkbjlp B9 T y U+ alkab B'b(<p& m^o^ `^a^b ab T- Di bpm^`fl U `lkqfbkb qla^p i^p abofs^a^p b%,
DIDLOKN 7- Ch klan]`kn ejpacn]_ekj- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^pcrk`flkbp ob^ibp `lkqfkr^p bk rk fkqbos^il Y]* ^[, Rf b D T* abcfk^jlp d < R&b'`ljl i^ crk`fŽk T a^a^ mlo
c&t' <b&b'p( `p pf ]88899t Q GH‹
Dpq^ qo^kpcloj^`fŽk R pb ii^j^ lmbo^alo fkqbdo^`fŽk-
1-1- @nLUNXb [NLX[[RMX
Dk bpq^ pb``fŽk+ R obmobpbkq^rk^ qo^kpcloj^`fŽk ifkb^i ab rk bpm^`fl ifkb^iT bk rk bpm^`fl ifkb^i U,
SDNQDL@ 1-0- Ch _kjfqjpk R'T( 'na_knne`k `a S( ao qj oq^ aol]_ek `a U-?`ai…o+ R ]lhe_] ah ahaiajpk _ank `a T aj ah ahaiajpk _ank `a U-
Baikopn]_e‰j- O^o^ abjlpqo^o nrb R'T( bp rk pr_bpm^`fl ab U+ q^k pŽilkb`bpfq^jlp `ljmol_^o ilp ^uflj^p ab `i^rpro^- Sljbjlp alp bibjbkqlp `r^ibp,nrfbo^ ab R'T(+ pb^k R't( v R'u(- Dkqlk`bp R't( * R'u( < R't * u(+ ^pŒnrbR't( * R'u( mboqbkb`b ^ R'T(- @pfjfpjl+ m^o^ `r^inrfbo bp`^i^o a qbkbjlp_R't( < R'_t(+ `lk il nrb _R't( mboqbkb`b ^ R'T(- Olo `lkpfdrfbkqb+ R'T( bp rkpr_bpm^`fl ab U- Slj^kal a < N bk i^ obi^`fŽk R'_t( < _R't(+ bk`lkqo^jlp nrbR&M' < N-
CDEHMHBHˆM- Ch _kjfqjpk `a pk`ko hko ahaiajpko `a T mqa R ]lhe_] aj N oahh]i] jŠ_hak `a R v oa `aoecj] lkn L'R(- ?o‡ lqao+ pajaiko
L&R' < wt Ht D T W R&t' < Ny -
SDNQDL@ 1-1- Ch jŠ_hak `a R ao qj oq^ aol]_ek `a T-
Baikopn]_e‰j- Rf t b v bpqŠk bk L'R(+ il jfpjl ibp l`roob ^ t * v v ^ atm^o^ qlalp ilp bp`^i^obp a+v^ nrb
R't * u( < R't( * R'u( < N v R'_t( < _R't( < N-
31 Rn]jobkni]_ekjao heja]haov i]pne_ao
Klp bgbjmilp nrb pfdrbk abp`of_bk ilp k•`iblp ab i^p qo^kpcloj^`flkbp ifkb^,ibp a^a^p bk i^ pb``fŽk 1-0-
DIDLOKN 0- Rn]jobkni]_e‰j e`†jpe_]- Di k•`ibl bp wMx+ bi pr_bpm^`fl`lkpqfqrfal q^k pŽil mlo bi bibjbkql `bol-
DIDLOKN 1- Rn]jobkni]_e‰j _ank- Orbpql nrb qlal bibjbkql ab T pb ^mif`^bk `bol+ bi k•`ibl bp bi jfpjl T-
DIDLOKN 2- Kqhpelhe_]_e‰jlkn qj ao_]h]nbefk _- Rf a <0< N+bi k•`ibl pŽil`lkqfbkb bi bibjbkql N- Rf a < N+bi k•`ibl bp T,
DIDLOKN 3- C_q]_ekjao heja]hao- Di k•`ibl bpqŠ`lkpqfqrfal mlo qlalp ilpsb`qlobp 'u+ --- +tj( ab T j m^o^ilp `r^ibp
j
H]egtg < N m^o^ e < 0+1+--- +i ,ScT
DIDLOKN 4- Nnk`q_pk ejpaneknlkn qj ahaiajpk befk w- Di k•`ibl `lkpq^ab qlalp ilp bibjbkqlp ab T loqldlk^ibp ^ w-
DIDLOKN 5- Nnkua__e‰jok^na qj oq^aol]_ek R- Rf t D T+ qbkbjlp i^•kf`^ abp`ljmlpf`fŽk loqldlk^i t < p * p0, 'pbd•k bi qblobj^ 0-04(- Orbpql nrbR&t' < o* qbkbjlp R&t' < N pf v pŽil pf t < o/+, Olo `lkpfdrfbkqb+ bi k•`ibl bpQ0,+bi `ljmibjbkql loqldlk^i ab R-
DIDLOKN 6- Mlan]`kn `aner]_e‰j- Di k•`ibl bpqŠ cloj^al mlo qla^p i^pcrk`flkbp `lkpq^kqbp bk bi fkqbos^il a^al-
DIDLOKN 7- Mlan]`kn ejpacn]_e‰j- Di k•`ibl `lkqfbkb pli^jbkqb i^ crk,`fŽk `bol-
1-2 7RVNW\RmWMNUWnLUNXb [JWPXMNUJ][JW\OX[VJLRmW
S^j_f‹k bk bpq^pb``fŽk R obmobpbkqrk^ qo^kpcloj^`fŽk ab rk bpm^`fl ifkb^iT bk rk bpm^`fl ifkb^i U- Mlp fkqbobp i^ obi^`fŽk bkqobi^p afjbkpflkbp ab T+abik•`ibl L'R( v abi ob`loofal R'T(- Rf T bp ab afjbkpfŽk cfkfq^+bi k•`ibl q^j_f‹kil pboŠmlo pbo rk pr_bpm^`fl ab T- Dk bi qblobj^ nrb pfdrb+ abjlpqo^jlp nrbbi ob`loofal RaT( q^j_f‹k bp ab afjbkpfŽk cfkfq^: pr afjbkpfŽk pb ii^j^ n]jckab R,
Beiajoe‰j `ah jŠ_hak v n]jck `a h] pn]jobkni]_e‰j 32
SDNQDL@ 1-2- QeT ao `a `eiajoe‰j bejep]+p]i^e†j hk ao R'T(+ v pajaiko
'1-0( afj L&R' * afj R&T' < afj T,
Be_dk `a kpnk ik`k+ h] `eiajoe‰j `ah jŠ_hak i…o ah n]jck `a qj] pn]jobkni]_e‰jheja]hao ecq]h ] h] `eiajoe‰j `a oq `kiejek-
Baikopn]_e‰j- Rb^k j < afj T v a! --- +a• rk^ _^pb m^o^ L'R(+ alkabg < afj L&R' y j- Rbd•k bi qblobj^ 0-6: bplp bibjbkqlp cloj^k m^oqbab rk^•`fboq^_^pb ab T* mlo bgbjmil ab i^ _^pb
'1-1(
alkab g * o < j- Cbjlpqo^objlp nrb ilp o bibjbkqlp
'1-2(
cloj^k rk^ _^pb ab R'T(+ abjlpqo^kal ^pŒnrb afj R'T(<n- Orbpql nrb g*n<j+q^j_f‹k bpl abjrbpqo^ '1-0(-
Cbjlpqo^jlp mofjbol nrb ilp n bibjbkqlp ab '1-2( dbkbo^k R&T', Rfv D R'T(+ bp v < R't( m^o^ rk `fboql t ab T+ v mlabjlp bp`of_fo t < _hah** ---* Ag*-ag*n&Krbdl+ qbkbjlp
mrbpql nrb R'ah( < --- <R'ag(< N- Dpql abjrbpqo^ nrb ilp bibjbkqlp '1-2(dbkbo^k R&T',
Cbjlpqobjlp ^elo^ nrb bplp bibjbkqlp plk fkabmbkafbkqbp-Rrmlkd^jlp nrbbufpqfbo^kbp`^i^obpAg*! --- +Ag*nq^ibpnrb
g+Gn
J _:R'a:( < M-68R&S
Dpql fjmif`^oŒ^nrb
// Rn]jobkni]_ekjao heja]haov i]pne_ao
mlo il nrb bi bibjbkql t < Ag)hag)h * --- * Ag)*ag)n pboŒabi k•`ibl L&R', Rfd,kfcf`^ bpql nrb bufpqfoŒ^kbp`^i^obpAh* ‹‹‹ * Ag q^ibpnrb t < biah * --- * _ea|* `lkil nrb qbkaoŒ^jlp
g g*n
V + V < J a-a+, J a-a+< N -eyh f<h*i
Obol `ljl ilp bibjbkqlp '1-1( plk fkabmbkafbkqbp+qlalp ilp bp`^i^obp a+e^k abpbo `bol- Olo `lkpfdrfbkqb+ ilp bibjbkqlp '1-2( plk fkabmbkafbkqbp-
Lkp]8 Rf T bp ab afjbkpfŽk fkcfkfq^ mlo il jbklp rkl ab ilp alp L&R' l R&T' bpab afjbkpfŽk fkcfkfq^- Dk bi bgbo`f`fl 2/ ab i^ Rb``fŽk 1-3 pb bp_lw^ rk^ abjlpqo^`fŽkab bpqb eb`el-
*', 8SN[LRLRX\
Dk `^a^ rkl ab ilp bgbo`f`flp abi 0 ^i 0/+ pb abcfkb rk^ qo^kpcloj^`fŽk R9T 1 z T 1
jbaf^kqb i^ cŽojri^ a^a^ m^o^ R&t*u'* alkab &t*v( bp rk mrkql `r^inrfbo^ ab T1Œ Cbqbo,jfk^o bk `^a^ `^pl pf R bp ifkb^i- Rf R bp ifkb^i+ ab`fo `rŠibp plk bi k•`ibl v bi ob`loofal+ v`^i`ri^o prp afjbkpflkbp
0- R&t*u' < 'v+ t',0, R&t*u' < &t* +u',1, R&t* u' < &t* M',2, R&t*u' < &t* t',3, R&t*u' < 'V0*u0',
4, R&t*u' < &aV*aF',5, R&t*u' < &t* /',6, R&t*u' < &t * h*u * 0(-7, R&t*u' < &t + u* t * u',
/., R&t* u' < &0t + u* t * u',
G^`bo 0/ jfpjl bk `^a^ rkl ab ilp bgbo`f`flp abi 00 ^i 04- Rf i^ qo^kpcloj^`fŽkR9T 1 z T1 bp i^ nrb pb fkaf`^-00- R e^`b dfo^o `r^inrfbo mrkql bi jfpjl Škdril -m ^iobabalo abi lofdbk- Dpql bp+R ^mif`^
rk mrkql ab `lloabk^a^p mli^obp &n*M' bk bi mrkql ab `lloabk^a^p mli^obp &n*.) ,l'*alkab -m bp cfgl- @abjŠp+ R ^mif`^ N bk pŒjfpjl-
01- R ^mif`^ `^a^ mrkql bk pr pfj‹qof`l obpmb`ql ^ rk^ ob`q^ cfg^ nrb m^p^ mlo bi lofdbk-02+R ^mif`^ qlal mrkql bk bi mrkql '0+ 0(-/2, R ^mif`^ `^a^ mrkql ab `lloabk^a^p mli^obp &n*'f( bk bi mrkql ab `lloabk^a^p &0n*M',
@abjŠp+ R ^mif`^ N bk pŒjfpjl-/3, R ^mif`^ `^a^ mrkql ab `lloabk^a^p mli^obp &n*M' bk bi mrkql ab `lloabk^a^p 'o+ 0.',
@abjŠp+ R ^mif`^ N bk pŒjfpjl-
G^`bo 0/ jfpjl bk `^a^ rkl ab ilp bgbo`f`flp 05 ^i 12 pf i^ qo^kpcloj^`fŽk R9T2yT2bpqŠ abcfkfa^ mlo i^ cŽojri^ nrb pb a^ m^o^ R&t* v+ w(+alkab &t* v+ w( bp rk mrkql ^o_fqo^oflab T2Œ
/4, R&t*u* w( < &v*u*t',/5, R&t*u* w( < &t* u* M',/6, R&t*u* w( < &t* 0u* 1v',/7, R&t* u* w( < &t* u* /',
0., R&t*u*v' ;&t * i+v* i+w ,0(-0/, R&t*u* w( < &t * h*u * 1+w * 2(-00, R&t*u* v' < &t* u0*X2(-
12- Rptnu* v( < 't * v+N+t * u',
Cfan_e_eko 34
Dk `^a^ rkl ab ilp bgbo`f`flp abi 13 ^i 16+ i^ qo^kpcloj^`fŽk R9T y T bp i^ nrb pbfkaf`^- Cbqbojfk^o+ bk `^a^ `^pl+ pf R bp ifkb^i- Rf 0/ bp+ ab`fo `rŠibp plk bi k•`ibl v biob`loofal v `^i`ri^o prp afjbkpflkbp `r^kal pb^k cfkfq^p-13- Rb^ T bi aol]_ek ifkb^i ab qlalp ilp mlifkljflp ob^ibp l&t' ab do^al z j* Rf l C T*
o m< R&l'/ pfdkfcf`^ nrb m&t' < l&t * 0( m^o^ qlal ob^i t,14- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbp ob^ibp abofs^_ibp bk bi fkqbos^il ^_fboql
',0+ 0(- Rf GC T* d < R&b'pfdkfcf`^ nrb c&t' < tf%&t' m^o^ qlal t ab ',0+ 0(-15- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbp ob^ibp `lkqfkr^p bk Y]*^[, Rf GC T*
d < R&b' pfdkfcf`^ nrb
c't( <pb'p( pbk 't , p( `p m^o^ ] y t y ^ -
17-
Rb^ T bi bpm^`fl ab qla^p i^p crk`flkbp ob^ibp abofs^_ibp alp sb`bp bk rk fkqbos^il^_fboql &]* ^', Rf X C T* abcfkfo R&u' < v! * Nu%* Pv pfbkal N v P alp `lkpq^kqbp-Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p pr`bpflkbp ob^ibp `lksbodbkqbp wt,x, Cbcfkfjlp rk^qo^kpcloj^`fŽk R8TyT ^pŒ9Rf t;wt,x bp rk^ pr`bpfŽk `lksbodbkqb `lk iŒjfqb ]*mlkbjlp R&t' < wu,x* alkab v- < ]+t, m^o^ j „ 0- Cbjlpqo^o nrb R bp ifkb^i v ab`fo`rŠibp plk bi k•`ibl v bi ob`loofal ab S-Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbp `lkqfkr^p bk bi fkqbos^il Z,6S+ 6SI- Rb^ Rbi pr_`lkgrkql ab T nrb `lkpq^ ab qla^p i^p crk`flkbp Gnrb p^qfpc^`bk i^p qobpb`r^`flkbp
16-
18-
pH'p(`p < N+ pqb'p(_kop`p < N+ pqb'p(oajp`p < N-
^( Cbjlpqo^o nrb R bp rk pr_bpm^`fl ab T,_( Cbjlpqo^o nrb R `lkqfbkb i^p crk`flkbp G&t'< `lp jt v G&t'< pbk jt m^o^ `^a^j < 1+ 2+ ---
b( Cbjlpqo^o nrb R bp ab afjbkpfŽk fkcfkfq^-Rb^ R8T y T i^ qo^kpcloj^`fŽk ifkb^i abcfkfa^ ^pŒ9Rf GC T* d < R&-' pfdkfcf`^ nrb
c't( <qrxi * `lp 't , p(xb'p(`p -
2/-
a( Cbjlpqo^o nrb R&T'* bi ob`loofal ab R* bp ab afjbkpfŽk cfkfq^ v e^i0^o rk^ _^pbm^o^ R&T',b( Cbqbojfk^o bi k•`ibl ab R,
c( G^i0^o qlalp lp k•jbolp ob^ibp a :l‹ N X qla^p i^p crk`flkbp Gkl kri^p ab T q^ibp nrbR&b'< _b, 'N_pbosbpb nrb rk^ q^i Gmboqbkb`b ^i ob`loofal ab R,'Rb^ z9 T y U rk^ qo^kpcloj^`fŽk ifkb^i ab rk bpm^`fl ifkb^i T bk rk bpm^`fl ifkb^iU, RHT bp ab afjbkpfŽk fkcfkfq^+abjlpqo^o nrb mlo il jbklp rkl ab ilp alp R&T'l L&R' bp ab afjbkpfŽk fkcfkfq^-
YGj`e_]_eˆj8 RrmŽkd^pb afj L&R' < g* afj R&T' < n* pb^ ah%,,, * a* rk^ _^pbm^o^ L&R' v pb^k bi- --- +ae* ag)h, , ,‹ ag), bibjbkqlp fkabmbkafbkqbp ab T* pfbkalj< n, Klp bibjbkqlp R&ag)h'* ,,, * R&ag),' plk abmbkafbkqbp v^ nrb j = o- Tqfifw^obpqb eb`el m^o^ l_qbkbo rk^ `lkqo^af``fŽk-\
35 Rn]jobkni]_ekjao heja]haov i]pne_ao
*'- AYN[JLRXWN\JUPNK[JRLJ\LXW][JW\OX[VJLRXWN\URWNJUN\
K^p crk`flkbp `rvlp s^ilobp mboqbkb`bk ^ rk bpm^`fl ifkb^i a^al U mrbabkprj^opb rk^p `lk lqo^p v mrbabk jriqfmif`^opb mlo bp`^i^obp ab U ab ^`rboal`lk i^ abcfkf`fŽk pfdrfbkqb-
CDEHMHBHˆM- Qa]j R9T y U v R9T y U `ko bqj_ekjao _kj qj `kiejek_kiŠj T u _kj r]hknao lanpaja_eajpao ] qj aol]_ek heja]h U- Rf a ao qj ao_]h]n_q]hmqean] a U+ `abejeiko h] oqi] R * R v ah lnk`q_pk _R lkn h]o a_q]_ekjao
'1-3( 'R * R('t( < Q't( * R't( + '_R('t( < _R't(
l]n] pk`k t `a T-
Mlp fkqbobp^ bpmb`f^ijbkqb bi `^pl bk bi nrb T bp q^j_f‹k rk bpm^`fl ifkb^i`lk ilp jfpjlp bp`^i^obp nrb U- Dk bpqb `^pl abpfdk^jlp `lk 1&' T+U( bi `lk,grkql ab qla^p i^p qo^kpcloj^`flkbp ifkb^ibp ab T bk U-
Rf R X R plk alp qo^kpcloj^`flkbp ifkb^ibp ab 1&' T* U'* bp rk pbk`fiil bgbo`f,`fl `ljmol_^o nrb R* R v _R q^j_f‹k plk qo^kpcloj^`flkbp ifkb^ibp ab 1&' T+U',
@•k jŠp- Blk i^p lmbo^`flkbp nrb ^`^_^jlp ab abcfkfo+ bi jfpjl `lkgrkql0%&T* U' pb qo^kpcloj^ bk rk krbsl bpm^`fl ifkb^i- K^ qo^kpcloj^`fŽk `bol pfosbab bibjbkql `bol bk bpb bpm^`fl+ v i^ qo^kpcloj^`fŽk ',i(S bp i^ lmrbpq^ ab R,Rb `ljmorb_^ nrb pb p^qfpc^`bk ilp afbw ^uflj^p ab rk bpm^`fl ifkb^i- Olo `lk,pfdrfbkqb+ qbkbjlp bi pfdrfbkqb-
SDNQDL@ 1-3- Ch _kjfqjpk 1&'T+U( `a pk`]o h]o pn]jobkni]_ekjao heja],hao`a T aj U ao qj aol]_ek heja]h _kj h]o klan]_ekjao `a ]`e_e‰j v iqhpelhe_],_e‰jlkn ao_]h]nao abeje`]o aj &0,2',
Tk^ lmbo^`fŽk ^idb_o^f`^ jŠp fkqbobp^kqb nrb pb bcb`q•^ `lk i^p qo^kpclo,j^`flkbp ifkb^ibp bp i^ _kilkoe_e‰j k iqhpelhe_]_e‰jab qo^kpcloj^`flkbp- Dpq^lmbo^`fŽk kl rqfifw^ i^ bpqor`qro^ ^idb_o^f`^ ab rk bpm^`fl ifkb^i v mrbab abcfkfopb`lk bkqbo^ dbkbo^ifa^a abi pfdrfbkqb jlal-
CDEHMHBHˆM- B]`ko hko_kjfqjpko S+ T+ U- Qa]j R9S y T qj] bqj_e‰j_kj`kiejek S v r]hknao aj T+v R9T y U kpn] bqj_e‰j _kj `kiejek T v r]hknao ajV- J] _kilkoe_e‰j QR ao h] bqj_e‰j QR9S y U `abeje`] lkn
'QR('t( < QYR't([ l]n] pk`k t aj S-
@pŒmrbp+ m^o^ ^mif`^o t jbaf^kqb i^ `ljmlpf`fŽk QR* ^mif`^jlp mofjbol tjbaf^kqb R v irbdl ^mif`^jlp R't( mlo jbafl ab R- Dpql pb obmobpbkq^bk i^ cfdr,o^ 1-0-
Mlan]_ekjao ]hca^n]e_]o _kj pn]jobkni]_ekjao heja]hao 36
AB2C (D
EHFTQ@ 1-0 En…be_k `a h] _kilkoe_e‰j `a `ko pn]jobkni]_ekjao-
K^ `ljmlpf`fŽk ab crk`flkbp ob^ibp pb e^ bk`lkqo^al obmbqfa^p sb`bp bkkrbpqol bpqrafl abi BŠi`ril+ v ebjlp sfpql nrb i^ lmbo^`fŽk+ bk dbkbo^i+ kl bp`lkjrq^qfs^- Ml l_pq^kqb+ `ljl bk bi `^pl ab i^p crk`flkbp ob^ibp+ i^ `ljmlpf,`fŽk p^qfpc^`b i^ ibv ^pl`f^qfs^-
SDNQDL@ 1-4- QeR8S y T* R9T y U* v P8V z W okj pnaobqj_ekjao* pa+jaiko
P&QR' < &PQ'R,
Baikopn]_eˆj, K^p crk`flkbp P&QR' v &PQ'R qfbkbk ^j_^p aljfkfl S vs^ilobp bk W- O^o^ `^a^ t ab S* qbkbjlp
YP&QR'H&t'< PY&QR'&t'[ < PYQYR&t'[[ v Y&PQ'RH&t'< &PQ'YR&t'[< PYQYR&t'[[*
0/ nrb abjrbpqo^ nrb P&QR' < &PQ'R,
CDEHMHBHˆM- Rb^ R8T y T qj] bqj_eˆj mqa ]lhe_] T aj o† ieoik, Babeje+iko -ej`q_per]iajpa h]o lkpaj_e]o ajpan]o `a R _kik oecqa8
RM< h- R! < RR€< l]n] j9988i-
@nrŒ / obmobpbkq^i^ qo^kpcloj^`fŽk fa‹kqf`^- Di ib`qlo mrbab `ljmol_^o nrbi^ ibv ^pl`f^qfs^ fjmif`^ i^ ibv ab bumlkbkqbp 0!!Rj < 0!!*6/ m^o^ qlalp ilp bkqb,olp kl kbd^qfslp i v j-
Di qblobj^ nrb pfdrb morb_^ nrb i^ `ljmlpf`fŽk ab qo^kpcloj^`flkbp heja]haobp ifkb^i-
37 Rn]jobkni]_ekjao heja]hao v i]pne_ao
SDNQDL@ 1-5- Qe S+ T+ U okj aol]_eko heja]hao _kj hko ieoiko ao_]h]nao+v oe R9 S y T X R9T y U okj pn]jobkni]_ekjao heja]hao+h] _kilkoe_e‰j QR9S y Uao heja]h-
Baikopn]_e‰j- O^o^ qlal t v qlal u ab S v qlalp ilp bp`^i^obp ] v ^+ qb,kbjlp
'QR(']t * ^u( < QYR']t * ^u([ < QY]R't( * ^R'u([ < ]QR't( * ^QR'u( -
K^ `ljmlpf`fŽk mrbab `lj_fk^opb `lk i^p lmbo^`flkbp ^idb_o^f`^p ab ^af`fŽkv jriqfmif`^`fŽk mlo bp`^i^obpbk 1&'T* U' iibd^kal ^i pfdrfbkqb
SDNQDL@ 1-6- Qa]j S+ T+ U aol]_eko heja]hao _kj hko ieoiko ao_]h]nao+oqlkjc]iko mqa R u R lanpaja_aj ] 1!' T+ U(+ v oa] a qj ao_]h]n _q]hmqean]-
^( N]n] _q]hmqean bqj_e‰j P _kj r]hknao aj T+ pajaiko
'R * R(P < QP * RP v '_Q(P < _'QP( -
_( N]n] _q]hmqean pn]jobkni]_e‰j heja]h P9 U y S+ pajaiko
P'Q * R( < PQ * PR v P'_Q( < _'PQ( -
K^ abjlpqo^`fŽk bp rk^ `lkpb`rbk`f^ fkjbaf^q^ ab i^ abcfkf`fŽk ab `ljml,pf`fŽk v pb abg^ `ljl bgbo`f`fl-
1-5 <W_N[\J\
@i bpqraf^o i^p crk`flkbp ob^ibp^mobkafjlp `Žjl `lkpqorfo krbs^p crk`flkbpjbaf^kqb i^ fksbopfŽk ab crk`flkbp jlkŽqlk^p- Prbobjlp ^elo^ buqbkabo bi j‹,qlal ab fksbopfŽk^ rk^ `i^pb jŠp dbkbo^i ab crk`flkbp-
C^a^ rk^ crk`fŽk R*krbpqol l_gbqfsl bp bk`lkqo^o+pf bp mlpf_ib+lqo^ crk`fŽkR `rv^ `ljmlpf`fŽk `lk R pb^ i^ qo^kpcloj^`fŽk fa‹kqf`^- Orbpql nrb i^ `ljml,pf`fŽk+bk dbkbo^i+kl bp `lkjrq^qfs^+ qbkbjlp nrb afpqfkdrfo QR ab RQ- Olo ilq^kql fkqolar`fjlp alp qfmlpab fksbop^p nrb ii^j^jlp fksbop^ mlo i^ abob`e^ bfksbop^ mlo i^ fwnrfboa^-
CDEHMHBHˆM- B]`ko `ko _kjfqjpko T u U u qj] bqj_e‰j R9 T y U- Qa `e_amqa qj] bqj_e‰j Q9R'T( y T ao ejrano] `a R lkn h] evmqean`] oe QYR't([ < tl]n] pk`k t `a T+ aopk ao+oe
QR< Gr+
Gjrano]o /4
`kj`a G• ao h] pn]jobkni]_e‰j e`†jpe_] ok^na T, Sj] bqj_e‰j P9 R&T' y T oahh]i] ejrano] `a R lkn h] `ana_d] oe RYP&u'[ < X l]n] pk`k v `a R&T'* aopk ao+oe
RP < GRs'*
`kj`a Gn'T( ao h] pn]jobkni]_e‰j e`†jpe_] ok^na R&T',
DIDLOKN- Sj] bqj_e‰j oej ejrano] lkn h] evmqean`] lank _kj `ko ejrano]olkn h] `ana_d]- Rb^k T < x0+ 1y X U < xNy- Cbcfkfjlp R9T y U `ljl pfdrb9R&0( < R&0' < N- Dpq^ crk`fŽk qfbkb alp fksbop^p mlo i^ abob`e^ P8 U y T XP&9U y T a^a^p mlo
P&M' < 0 + P%&M'< 1-
Ml mrbab qbkbofksbop^ mlo i^ fwnrfboa^ Q v^ nrb biil bufdfoŒ^
0 < QYR&G'[< RbN( v 1 < QYR&0'[ < RbN( -
Dpqbpbk`fiil bgbjmil mlkb ab j^kfcfbpql nrb kl qfbkb nrb bufpqfokb`bp^of^jbkqbfksbop^ mlo i^ fwnrfboa^ v nrb i^ fksbop^ mlo i^ abob`e^ kl qfbkb nrb pbo kb`bp^,of^jbkqb •kf`^-
Sla^ crk`fŽk R9T y U qfbkbmlo il jbklp rk^ fksbop^ ^ i^ abob`e^- Dk bcb`,ql+`^a^ v ab R&T' qfbkbi^ cloj^ v < R&t' m^o^^i jbklp rk t ab T, Rf bibdfjlprkl ab bplp s^ilobp t v abcfkfjlp P&u' < t* bkqlk`bp RYP&u'[ ;R&t' < u m^o^`^a^ u ab R&T'* ^pŒnrb P bp rk^ fksbop^mlo i^ abob`e^- K^ kl rkf`fa^a mrbab mob,pbkq^opbab_fal ^ nrb mrbab e^_bo jŠp ab rk t ab T nrb pb ^mifnrb bk rk v abR&T', Cbkqol ab ml`l abjlpqo^objlp 'qblobj^ 1-8( nrb pf `^a^ u ab R&T' bpi^ fj^dbk ab qj o‰hkt ab T* i^ fksbop^ mlo i^ abob`e^ bp •kf`^-@kqbpabjlpqo^objlp nrb pf bufpqbfksbop^ mlo i^ fwnrfboa^ bp •kf`^ v+ ^i jfpjlqfbjml+ bp fksbop^ ^ i^ abob`e^-
SDNQDL@ 1-7- Sj] R9T y U lqa`a pajan ] hk i…o qj] ejrano] lkn h]evmqean`]- Qe R peaja ejrano] lkn h] evmqean`] Q+ajpkj_ao Q ao p]i^e†j ejrano]lkn h] `ana_d]-
Baikopn]_e‰j- Rrmlkd^jlp nrb R qbkd^ alp fksbop^p mlo i^ fwnrfboa^+Q8R&T' y T X Q%8R&T' y T, Difg^jlp `r^inrfbo u bk R&T', Cbjlpqo^objlp nrbQ&u' < Q%&u',Bljl v < R&t' m^o^rk `fboql t ab T* qbkbjlp
QYR&t'[ < t v Q-YR&t'[ < t*
YV Rn]jobkni]_ekjao heja]hao u i]pne_ao
mrbpql nrb R v Q&plk ^j_^p fksbop^p mlo i^ fwnrfboa^- Olo `lkpfdrfbkqb Q'u( < tv Q&'u(< t+ `lk il nrb Q'u( < Q&'u( m^o^ qlal u ab R'T(- Olo il q^kql R < R&0/ nrb abjrbpqo^ nrb i^p fksbop^p mlo i^ fwnrfboa^ `lfk`fabk-
Cbjlpqobjlp ^elo^ nrb qla^ fksbop^ mlo i^ fwnrfboa^ R bp q^j_f‹k fksbop^mlo i^ abob`e^- Difg^jlp rk bibjbkql `r^inrfbo^ u bk R&T', Cbjlpqo^objlp nrbRYQ'u([ < v- Orbpql nrb v D R'T(+ qbkbjlp u < R't( m^o^ rk `fboql t ab T- ObolR bp fksbop^ mlo i^ fwnrfboa^+ ^pŒnrb
t < QYR&t'[ < Q&u',
@mif`^kal R+iibd^jlp ^ R't( < RYQ'u([- Obol u < R't(+ `lk 0/ nrb v < RYQ'u([+il `r^i `ljmibq^ i^ abjlpqo^`fŽk-
Di qblobj^ nrb pfdrb `^o^`qbofw^ qla^p i^p crk`flkbp nrb qfbkbk fksbop^ mloi^ fwnrfboa^-
SDNQDL@ 1-8- Sj] bqj_e‰j R9 T y U peaja ejrano] lkn h] evmqean`] oe uo‰hkoe R ]lhe_] ahaiajpko `eopejpko `a T aj ahaiajpko `eopejpko `a U: aopk ao+oe u o‰hkoe+l]n] _q]haomqean] t a u `a T+
'1-4( _23["` eilhe_] R&t' 9:q&R&u',
Lkp]9 K^ `lkaf`fŽk '1-4( bp bnrfs^ibkqb ^ i^ ^cfoj^`fŽk
'1-5( R&t' < R&u' Œokmif`^ t < u -
Tk^ crk`fŽk R nrb p^qfpc^`b '1-4( l '1-5( m^o^ `r^ibpnrfbo^ t b v ab T pb abkljfk^qjk ] qjk bk T,
Baikopn]_e‰j- Rrmlkd^jlp nrb R bp i^ fksbop^ mlo i^ fwnrfboa^ ab R+ v nrbR't(<R'u(- Prbobjlp abjlpqo^o nrb t<u- @mif`^kal R+bk`lkqo^jlp QYR't([ <QYR'u([- Orbpql nrb QYR't([ < t v QYR'u([ < v+ bpql fjmif`^ t < v- Blk biilnrba^ abjlpqo^al nrb rk^ crk`fŽk `lk fksbop^ mlo i^ fwnrfboa^ bp rkl ^ rkl bkpr aljfkfl-
Cbjlpqobjlp ^elo^ bi ob`Œmol`l- Rrmlkd^jlp nrb R bp rkl ^ rkl bk T,Dk`lkqo^objlp rk^ crk`fŽk R9R'T( y T nrb bp fksbop^ ab R mlo i^ fwnrfboa^-Rf u D R'T(+ bkqlk`bp v < R't( m^o^ rk `fboql t ab T- Dk sfoqra ab '1-5(+ bufp,qb at]_p]iajpa qj t bk T m^o^ bi `r^i u < R't(- Cbcfk^jlp Q'u( `ljl bpb t- Dpqlbp+ abcfk^jlp R bk R&T' `ljl pfdrb9
Q&u'< t fjmif`^ nrb R&t' < u,
Sbkbjlp bkqlk`bp QYR't([ < t m^o^ `^a^ t ab T+ ^pŒnrb QR < Gr- Olo `lkpf,drfbkqb+ i^ crk`fŽk R ^pŒabcfkfa^ bp fksbop^ ab R mlo i^ fwnrfboa^-
Rn]jobkni]_ekjao heja]haoqjk ] qjk 40
CDEHMHBHˆM- Qa] R9T ,* U qjk ] qjk aj T- J] Šje_] ejrano] `a R lkn h]evmqean`] 'h] _q]h o]^aiko mqa p]i^e†j ao ejrano] lkn h] `ana_d]( oa `aoecj]lkn R,0- Ba_eiko mqa R ao ej ranpe^ha+v hh]i]iko ] R,0 h] ejrano] `a R-
Klp obpriq^alp ab bpq^pb``fŽk pb obcfbobk crk`flkbp `r^ibpnrfbo^- Rbdrfa^,jbkqb ^mif`^jlp bp^p fab^p ^ i^p qo^kpcloj^`flkbp ifkb^ibp-
*'/ E[JW\OX[VJLRXWN\URWNJUN\^WXJ ^WX
Dk bpq^ pb``fŽk+ T v U obmobpbkq^kbpm^`flp ifkb^ibp `lk ilp jfpjlp bp`^,i^obp+v R9T ,* U bp rk^ qo^kpcloj^`fŽk ifkb^i ab - h&'T+U(- K^ ifkb^ifa^a ab Rklp mbojfqb bumobp^oab s^of^p j^kbo^p i^ molmfba^a ab nrb rk^ qo^kpcloj^`fŽkifkb^i pb^ rkl ^ rkl-
SDNQDL@ 1-0/- Qa] R9T ,* U qj] pn]jobkni]_e‰j heja]h `a - h&'T+U(-Qkj amqer]hajpaoh]o oecqeajpaolnklkoe_ekjao-
^( R ao qjk ] qjk aj T-_( R ao ej ranpe^hav oq ejrano] R,09R'T( ,* T ao heja]h-b( N]n] pk`k t `a T+R't( < N eilhe_] t < N- Copk ao+ahjŠ_hak L'R( _kj,
peaja okh]iajpa ah ahaiajpk _ank `a T-
Baikopn]_e‰j- Cbjlpqo^objlp nrb ^( fjmif`^ _(+ _( fjmif`^ b(+v b( fjmif,`^ ^(- Rrmlkd^jlp mofjbol nrb ^( bp `fboq^- R qfbkb bkqlk`bp fksbop^ 'pbd•k biqblobj^ 1-8(+v qbkbjlp nrb abjlpqo^o nrb R,/ bp ifkb^i- Sljbjlp alp bibjbk,qlp `r^ibpnrfbo^ q v r ab R'T(- Dkqlk`bp q < R't( v r < R'u( m^o^ ^id•k t v^id•k v ab T, O^o^ alp bp`^i^obp`r^ibpnrfbo^ ] v ^* qbkbjlp
]q * ^r < ]R't( * ^R'u( < R']t * ^u( +
v^ nrb R bp ifkb^i- Krbdl+ ^mif`^kal R+0+ qbkbjlp
R,h']q * ^r( < ]t * ^u < ]R,h'q( * ^R,h'T(+
^pŒnrb R,/ bp ifkb^i- Olo `lkpfdrfbkqb ^( fjmif`^ _(+Rrmlkd^jlp pbdrfa^jbkqb nrb _( bp `fboq^-Sljbjlp rk t `r^inrfbo^ ab T
m^o^bi `r^i R't( < N- @mif`^kal R,0+bk`lkqo^jlp nrb t < R,0'M( < N+mrbpqlnrb R,/ bp ifkb^i- Olo `lkpfdrfbkqb+ _( fjmif`^ `(-
Olo •iqfjl+ prmlkd^jlp `fboq^ b(+ Sljbjlp alp bibjbkqlp `r^ibpnrfbo^ qv r ab T pfbkal R'q(<R'r(- Olo i^ ifkb^ifa^a+ qbkbjlp R'q,r( < R'q(,R'r(<< N+ ^pŒnrb q , r < N- Olo `lkpfdrfbkqb+ R bp rkl ^ rkl bk T+Xnrba^ `ljmib,q^a^ i^ abjlpqo^`fŽk abi qblobj^-
0- Rn]jobkni]_ekjao heja]haov] i]pne_ao
Br^kal T bp ab afjbkpfŽk cfkfq^+i^ molmfba^a ab pbo rkl ^ rkl mrbab clo,jri^opb bk crk`fŽk ab i^ abmbkabk`f^ v ab i^ afjbkpflk^ifa^a+ `ljl pb fkaf`^bk bi qblobj^ nrb pfdrb-
SDNQDL@ 1-00- Qa] R9T y U qj] pn]jobkni]_e‰j heja]h `a W'T+ U' voqlkjc]iko mqa T ao `a `eiajoe‰j bejep]+afj T < j- Cjpkj_ao okj amqer]hajpaoh]o lnklkoe_ekjao oecqeajpao-
^( R ao qjk ] qjk aj T-_( Qe ah&--- +al okj ahaiajpko ej`alaj`eajpao `a T+ R'a/'* ‹‹‹ * R'al( okj
ahaiajpko ej`alaj`eajpao `a R'T(-`( afj R&T' < j-a( Qe xbi!&! ajx ao qj] ^]oa l]n] T+ wR'a+(+--- +R'aj(x ao qj] ^]oa
l]n] R'T(-
Baikopn]_e‰j- Ool_^objlp nrb ^( fjmif`^ _(+ _( fjmif`^ b(+ b( fjmif`^ a(+v a( fjmif`^ ^(- Rrmlkd^jlp nrb ^( bp `fboq^- Rb^k bi +--- +al bibjbkqlp fkabmbk,afbkqbp ab T v `lkpfabobjlp ilp bibjbkqlp Rpa-(+--- +R'al' ab R'T(- Rrmlkd^,jlp nrb
l
J _eR'ae( < Ne;h
m^o^ `fboqlp bp`^i^obp bi +--- +_l‹ Dk sfoqra ab i^ ifkb^ifa^a+ l_qbkbjlp
RAy _eae( < N+ X mlo q^kqll
J_eae < Neyh
v^ nrb R bp rkl ^ rkl- Obol ah * ,,, * al plk fkabmbkafbkqbp+ ^pŒnrb Bi < --- <Al < N- Olo `lkpfdrfbkqb ^( gokmif`^ _(-
Rrmlkd^jlp ^elo^ nrb bp `fboq^ _(- Rb^ xbi! -- +ajx rk^ _^pb m^o^ T- Rbd•k_(+ ilp j bibjbkqlp R'ah(+--- +R'aj( ab R'T( plk fkabmbkafbkqbp- Olo `lkpfdrfbk,qb+ afj R'T( „ j- Obol+ pbd•k bi qblobj^ 1-2+ qbkbjlp afj R'T( y j- Krbdlafj R&T' < j+ `lk il `r^i _( fjmif`^ b(+
Rrmlkd^jlp+ pbdrfa^jbkqb+ nrb bp `fboq^ b( v pb^ xbi&--- +ajx rk^ _^pb m^o^T- Sljbjlp rk bibjbkql `r^inrfbo^ v bk R'T(- Dkqlk`bp v < R't( m^o^ ^id•kt bk T* ^pŒnrb qbkbjlp
j
V < J _eae+ X mlo q^kqlf<i
j
u < R't( < J _eR'ae(-eyh
Olo `lkpfdrfbkqb wR'ah(+--- +R'aj'x dbkbo^ R'T(- Obol ebjlp prmrbpql nrbafj R'T( < j+ ^pŒnrb wR'ah(+--- +R'aj'x bp rk^ _^pb m^o^ R'T(- Olo `lkpf,drfbkqb b( fjmif`^ a(-
Cfan_e_eko 0.
Olo •iqfjl+ prmlkd^jlp `fboq^ a(+ Cbjlpqo^objlp nrb R&t' < N fjmif`^t < N- Rb^ xbi! -- +ajx rk^ _^pb m^o^T, Rf t D T* mlabjlp bp`of_fo
j
V < z _:a:+ v mlo q^kql68,
j
R&t' < z _:R'a:(-e;h
Rf R&t' < N+bkqlk`bp BH<---< aj < N+mrbpql nrb ilp bibjbkqlp Rpa,'* ,,, * R&aj(
plk fkabmbkafbkqbp-Olo il q^kql t < N+ `lk il `r^i R bp rkl ^ rkl bk T- @pŒmrbp+a( fjmif`^ ^( v bi qblobj^ nrba^ abjlpqo^al-
1-7 Dgbo`f`flp
0- Rb^ T < xN+0y- Cbp`of_fo qla^p i^p crk`flkbp R8T ,* T, Dk qlq^i plk `r^qol- CbpŒd,kbkpb `lk RG%R
1+ R
2+ R
3X `lkpqorfo rk^ q^_i^ ab jriqfmif`^`fŽk nrb jrbpqob i^ `lj,
mlpf`fŽk ab `^a^ m^o-Hkaf`^o `rŠibp plk rkl ^ rkl bk T v a^o prp fksbop^p-1- Rb^ T < xN+0+ 1y- Cbp`of_fo qla^p i^p crk`flkbp R8T ,,* T m^o^ i^p `r^ibp R&T' < T,
Dk qlq^i plk pbfp-CbpŒdkbkpb`lk RG%R1+ ŒŒ+ R5 X `lkpqorfo rk^ q^_i^ ab jriqfmif`^`fŽknrb jrbpqob i^ `ljmlpf`fŽk ab `^a^ m^o- Hkaf`^o `rŠibp plk rkl ^ rkl bk T* v a^o prpfksbop^p-
Dk `^a^ rkl ab ilp bgbo`f`flp abi+ 2 ^i 01+ rk^ crk`fŽk R8T1
,,* T1
pb abcfkb `lk i^cŽojri^ nrb pb a^ m^o^ R&t*u'* pfbkal &t*v( rk mrkql `r^inrfbo^ -ab T
1Œ Cbqbojfk^o bk
`^a^ `^pl pf R bp rkl ^ rkl bk T1Œ Rf bp ^pŒ+abp`of_fo pr ob`loofal R&T
1(: m^o^ `^a^ mrkql
&q*r' ab R&T0'* mlkbo &t* v( < W+G&S*r' v a^o cŽojri^p m^o^ abqbojfk^o t b v bk crk`fŽkab S v r-
1, R&t*u' < &u*t',2, R&t*u' < &t* +u',3, R&t*u' < &t* M',4, R&t*u' ;%&t* t',5, R&t*u' < 'V0*u0',
6, R&t*u' < 'aV+ aW(-
7, R&t* u' < &t* /',/., R&t*u' < &t * i+v * 0(-//, R&t*u' < &t + u* t * u',/0, R&t* u' < &0t + u* t * u',
Dk `^a^ rkl ab ilp bgbo`f`flp abi 02 ^i 1/+ pb abcfkb rk^ crk`fŽk R9T2
,,* T2
`lk i^cŽojri^ nrb pb a^ m^o^ Rpt* v+w(+pfbkal &t*v+w( rk mrkql `r^inrfbo^ ab T
2Œ Dk `^a^ `^pl+
abqbojfk^o pf R bp rkl ^ rkl bk T2Œ Rf bp ^pŒ+abp`of_fo pr ob`loofal R&T2(: m^o^ `^a^ mrkql
&q*r*s' ab R&T1'* mŽkd^pb &t*u*v' < W+G&S*T*V( v a^o cŽojri^p m^o^-i^ abqbojfk^`fŽk abt+v+w bk crk`fŽk ab q+r+v t-
/1, R&t*u* w( < &v*u* t',/2, R&t*u* w( < &t*u* M',/3, R&t*u* w( < &t* 0u* 1v',/4, R&t*u* w( < &t*u* t * u * w(+
/5, R&t*u* w( < &t * i+v * 0+w , 0(-
/6, R&t* u* w( < &t * 0+W * 1+w * 2(-/7, R&t*u*v' ;&t*t * u*t * u )v',0., R&t*u* w( < &t * u*u * w+t * v',
10- Rb^ R8T ,,* T rk^ crk`fŽk nrb ^mif`^ T bk pŒjfpjl- Olo fkar``fŽk pb abcfkbk i^pmlqbk`f^p `lk i^p cŽojri^p RM < 0+ R• < RRj
+0 m^o^ j:99 0- -Cbjlpqo^o nrb i^ ibv^pl`f^qfs^ m^o^ i^ `ljmlpf`fŽk fjmif`^ i^ ibv ab bumlkbkqb9 RiR• < Ri*j- Rf R bp fk,sboqf_ib+abjlpqo^o nrb R! q^j_f‹k bp fksboqf_ib v nrb &Rj'+h < &R+G'j,
43 Rn]jobkni]_ekjao heja]haov i]pne_ao
Dk ilp bgbo`f`flp abi 11 ^i 14+ R X R obmobpbkq^k crk`flkbp `lk aljfkfl T v s^ilobpbk T, Dk dbkbo^i QR<!* RQ, Rf QR < RQ* ab`fjlp nrb R v R _kjiqp]j,
11- Rf R X R `lkjrq^k+ abjlpqo^o nrb &QR'! < QjRj m^o^ `r^inrfbo bkqbol j 9888T-
12- Rf R X R plk fksboqf_ibp+ abjlpqo^o nrb QR q^j_f‹k il bp v nrb 'RS(,i < //Q+y Cf`elab lqol jlal+ i^ fksbop^ ab QR bp i^ `ljmlpf`fŽk ab i^p fksbop^p+ qlj^a^p bk loabkfksbopl-
13- Rf R X R plk fksboqf_ibp v `lkjrq^k+ abjlpqo^o nrb prp fksbop^p q^j_f‹k `lkjrq^k-14- Rb^ T rk bpm^`fl ifkb^i- Rf R X R `lkjrq^k+ abjlpqo^o nrb
'R * R(1 < R1 * 1QR * R1 v
Hkaf`^o `Žjl ab_bk jlafcf`^opb bp^p cŽojri^p pf QR =&! RQ,15- Rb^k R v R i^p qo^kpcloj^`flkbp ifkb^ibp ab T 2 bk T 2 abcfkfa^p mlo i^p cŽojri^p
Q&t*v+w( < &v*v+t' v R&t* v+w( < &t* t * v+ t * v * w(+pfbkal 'u+ v+ w( rk mrkql `r^i,nrfbo^ ab T
2^( Cbqbojfk^o i^ fj^dbk ab 'u+ v+ w( ^ qo^s‹p ab `^a^ rk^ ab i^p qo^kpcloj^`flkbp pf,drfbkqbp9 QR* RQ* QR + RQ* Q0* O+&QR'0*&RQ'0* &QR+ RQ'0,_( Cbjlpqo^o nrb R v R plk rkl ^ rkl bk T2 v e^ii^o i^ fj^dbk ab &q* r* t( ^ qo^s‹pab `^a^ rk^ ab i^p qo^kpcloj^`flkbp9 Q+/* R+G*&QR'+/* &RQ'+G,b( G^ii^o i^ fj^dbk ab &t* v+ w( ^ qo^s‹p ab 'R , 0(j m^o^ `^a^ j y 0-
16- Rb^ T bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ob^ibp l&t', Rb^k C bi lmbo^alo abofs^,`fŽk v R bi lmbo^alo fkqbdo^`fŽk nrb ^mif`^ `^a^ mlifkljfl l bk rk mlifkljfl m a^almlo m&t' < k l&p'`p, Cbjlpqo^o nrb BR <Hsmbol nrb RB <!%Gr-Cbp`of_fo bi k•`ibl vbi ob`loofal ab RB,
17- Rb^ T bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ob^ibp l&t', Rb^k C bi lmbo^alo abof,s^`fŽk v R i^ qo^kpcloj^`fŽk ifkb^i nrb ^mif`^ l&t' bk tl%&t',^( Olkbo l&t' < 1 * 1t + t0 * 2t2 v abqbojfk^o i^ fj^dbk ab l ^ qo^s‹p ab `^a^ rk^ab i^p qo^kpcloj^`flkbp pfdrfbkqbp9 C+R* BR* RB* BR + RB* R0B0 + C1O-_( Cbqbojfk^o ilp mlifkljflp l ab T• m^o^ ilp `r^ibp R&l' < l,b( Cbqbojfk^o ilp mlifkljflp l ab T m^o^ ilp `r^ibp &BR + 0B'&l' < N-a( Cbqbojfk^o ilp mlifkljflp l ab T m^o^ ilp `r^ibp &BR + RB'j&l' < Bj&l',
18- Rb^k T v C `ljl bk bi bgbo`f`fl 17 mbol R bp i^ qo^kpcloj^`fŽk ifkb^i nrb ^mif`^ l&t' bktl&t', Cbjlpqo^o nrb BR + RB < / X nrb BRj + RjB < jRj+h m^o^ qlal j y 1-
2/- Rb^k R v R+alp qo^kpcloj^`flkbp ifkb^ibp ab - K&&T* T' X prmlkd^jlp nrb QR + RQ < h,Cbjlpqo^o nrb QRj + RjQ < |p€< m^o^ qlal j „ 0-
20- Rb^ T bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp l&t', Rb^k P* R+ R crk`flkbp nrb ^mif,`^k rk mlifkljfl `r^inrfbo^ l&t' < Bl * _/t * ---o* _jt%`a U.bk ilp mlifkljflp n&t'*o&t' v p&t' obpmb`qfs^jbkqb+ pfbkal
n&t' < l&M' *j
o&t' < 0AgVg,0 +R`S
jp&t' < 0Ayg*G Œ
R8?
^( Olkbo l&t' < 1 * 1t + t0 * t2 v abqbojfk^o i^ fj^dbk ab l ^ qo^s‹p ab `^a^ rk^ab i^p qo^kpcloj^`flkbp pfdrfbkqbp9 P* R+R* QR* RQ* &RQ'0* OR1+R1O+RPQ* PQR,_( Cbjlpqo^o nrb P+ R X R plk ifkb^ibp v abqbojfk^o bi k•`ibl v bi ob`loofal ab `^a^rk^-b( Cbjlpqo^o nrb R bp rkl ^ rkl bk T v abqbojfk^o pr fksbop^-a( Qe j y 0+ bumobp^o &RQ'j v o+e€bk crk`fŽk ab / v P,
21- Dk obi^`fŽk `lk bi bgbo`f`fl 17 ab i^ Rb``fŽk 1-3- Cbqbojfk^o pf R bp rkl ^ rkl bk T-Rf il bp+ab`fo `rŠi bp i^ fksbop^-
Rn]jobkni]_ekjao heja]hao _kj r]hknao ]oecj]`ko 44
1-8 So^kpcloj^`flkbp ifkb^ibp `lk s^ilobp ^pfdk^alp
Rf T bp ab afjbkpfŽk cfkfq^+pfbjmob mlabjlp `lkpqorfo rk^ qo^kpcloj^`fŽkifkb^i R9T ,* U `lk s^ilobp ^pfdk^alp ^ ilp bibjbkqlp _^pb ab T+ `ljl pb bumif`^bk bi qblobj^ pfdrfbkqb-
SDNQDL@ 1-01- Qa] ah&--- -a: qj] ^]oa l]n] qj aol]_ek heja]h j,`eiaj,oekj]h T- Qa]j Ti +ŠŠŠ-q‚ j ahaiajpko ]n^epn]neko `a qj aol]_ek heja]h U- Cteopaajpkj_ao qj] v o‰hkqj] pn]jobkni]_e‰j R9T ,* U p]h mqa
'1-6( R'ag( < Sg l]n] g < 0+1+--- +j-
Cop] pn]jobkni]_e‰j, R ]lhe_] qj ahaiajpk _q]hmqean] t `a T `ah ik`k oecqeajpa9
'1-7(V V
Qe t < Gtgag+ ajpkj_ao R't( < GVgSgŒ
hzi hzi
Baikopn]_e‰j- Slal t ab T mrbab bumobp^opbbk cloj^ •kf`^ `ljl `lj_f,k^`fŽk ifkb^i ab ah +--- +aj+pfbkal ilp jriqfmif`^alobp Vh +--- -t: ilp `ljmlkbk,qbp ab t obpmb`ql ^ i^ _^pb loabk^a^ 'ah& --- +aj(- Rf abcfkfjlp R jbaf^kqb '1-7(+`lksfbkb `ljmol_^o nrb R bp ifkb^i- Rf t < ag m^o^ rk `fboql g+ bkqlk`bp qlalpilp `ljmlkbkqbp ab t plk N bu`bmql bi g,†oeik+ nrb bp 0+ `lk 0/ nrb '1-7( a^R&ag' < qo* `ljl nrboŒ^jlp-
O^o^ abjlpqo^o nrb pŽil bufpqb rk^ qo^kpcloj^`fŽk ifkb^i nrb p^qfpc^`b '1-6(+pb^ R& lqo^ v `^i`ribjlp R&'t(- Dk`lkqo^jlp nrb
Orbpql nrb R&'t( < R't( m^o^ qlal t ab T+ qbkbjlp R&< o+0/ `r^i `ljmibq^ i^abjlpqo^`fŽk-
DIDLOKN- Cbqbojfk^o i^ qo^kpcloj^`fŽk ifkb^i R9T1 ,* T1 nrb ^mifnrb ilpbibjbkqlp _^pb e < '0+ N( X f < 'N+ 0( abi jlal pfdrfbkqb
R&e'< e* f* R&f' < 0e+ f-
Qkhq_e‰j- Rf t < the * t1f bp rk bibjbkql ^o_fqo^ofl ab T1+ bkqlk`bp R't(sfbkb a^al mlo
45 Rn]jobkni]_ekjao heja]hao v i]pne_ao
*')( CNY[N\NW]JLRmWVJ][RLRJUMNUJ\][JW\OX[VJLRXWN\URWNJUN\
Di qblobj^ 1-01 abjrbpqo^ nrb rk^ qo^kpcloj^`fŽk ifkb^i R9T ,* U ab rkbpm^`fl ifkb^i ab afjbkpfŽk cfkfq^ T bpqŠ abqbojfk^a^ mlo pr ^``fŽk pl_ob rk`lkgrkql a^al ab bibjbkqlp _^pb a++--- +aj- Rrmlkd^jlp ^elo^ nrb bi bpm^`fl Uq^j_f‹k ao ab afjbkpfŽk cfkfq^+mlo bgbjmil afj U < i+ v pb^ t+ +--- +Uj rk^_^pb m^o^ U, 'K^p afjbkpflkbp j v i mrbabk pbo l kl fdr^ibp-( Orbpql nrb Rqfbkbilp s^ilobp bk U* `^a^ bibjbkql R&a` mrbab bumobp^opb+lk rkf`fa^a+ `ljlrk^ `lj_fk^`fŽk ifkb^i ab ilp bibjbkqlp ab i^ _^pb t+ +--- +Ui+ mlo bgbjmil
j
R'ag' < pegUe *
e;/
alkab p] *,,, *pig plk ilp `ljmlkbkqbp ab R'ag( obpmb`ql ^ i^ _^pb loabk^a^'t+ +--- +si(- Cfpmlkaobjlp sboqf`^ijbkqb i^ i,lh] 'p+g+--- +pig(+ `ljl ^ `lk,qfkr^`fŽk pb fkaf`^9
'1-8(
Dpql pb ii^j^ ra_pkn _khqij] l i]pnev _khqij]- Sbkbjlp rk^ q^i `lirjk^ m^o^`^a^ rkl ab ilp j bibjbkqlp R'a+( +--- +R'a ŒŒ(- Blil`Škali^p rk^ grkql ^ lqo^ vbk`booŠkali^p bk rk m^o ab `lo`ebqbp l_qbkbjlp i^ afpmlpf`fŽk ob`q^kdri^o pf,drfbkqb9
pq p01 p0j
p10 p11 p1j
Dpqb r^aol pb ii^j^ i]pnev v `lkpq^ ab i cfi^pv j `lirjk^p- K^ ii^j^jlp j^qofwi W j- K^ mofjbo^ cfi^ bp i^ j^qofw 0 W j &p// * p%0* ,,, * p+j(- K^ j^qofw i W 0'1-8( bp i^ h,‹pfj^ `lirjk^- Klp bp`^i^obp peg s^k ^cb`q^alp `lk alp Œkaf`bp+bi
Palnaoajp]_e‰j i]pne_e]h `a h]o pn]jobkni]_ekjao heja]hao 46
mofjbol e fkaf`^ i^ peh] v bi pbdrkal g fkaf`^ i^ _khqij] bk i^p `r^ibp ^m^ob`b peg--@ pegib ii^j^jlp bi ahaiajpk eg ab i^ j^qofw- S^j_f‹k pb rqfifw^ i^ klq^`fŽk ^_ob,sf^a^
l
m^o^ abpfdk^o i^ j^qofw `rvl bibjbkql eg bp pq+@pŒmrbp+ qla^ qo^kpcloj^`fŽk ifkb^i R ab rk bpm^`fl k,afjbkpflk^i T bk rk
bpm^`fl j,afjbkpflk^i U a^ lofdbk ^ rk^ j^qofw j W j &peg' `rv^p `lirjk^p plkilp `ljmlkbkqbp ab R&aG'* ‹‹‹ * R&aj( obi^qfslp ^ i^ _^pb 't0+ ’’’ +si(- K^ ii^,j^jlp nalnaoajp]_e‰j i]pne_e]h ab R obi^qfs^ ^ rk^p _^pbp loabk^a^p 'ah& --- +aj'ab T v 'Vi +ŠŠŠ*Ui( m^o^ U- Tk^ sbw `lkl`fa^ i^ j^qofw &peg'*ilp `ljmlkbkqbpab rk bibjbkql `r^inrfbo^ R&t' `lk obi^`fŽk ^ i^ _^pb 'ti +ŠŠŠ+si( mrbabk abqbo,jfk^opb `ljl pb bumif`^ bk bi qblobj^ nrb pfdrb-
SDNQDL@ 1-02- Qa] R qj] pn]jobkni]_e‰j heja]h lanpaja_eajpa ] N'T+ U(+`kj`a afj T < j v afj U < j- Qa]j 'ah!&! aj( v 'V0 + ’’’ +si' ^]oao kn`a,j]`]o `a T v U+naola_per]iajpa+ v 'peg( h] i]pnev j W j _quko ahaiajpko aop…j`apaniej]`ko lkn h]o a_q]_ekjao
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R'ag( < KpegUe+ l]n] g < 0+1+--- +j -f<i
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R't( < JWeUef<0
aj V _kj _kilkjajpao 'XH!&! Wi( nah]perko ] 'ti+ ŠŠŠ+si(- Jko Xf aop…jhec]`ko ] hko _kilkjajpao `a V ia`e]jpa h]o a_q]_ekjao heja]hao
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We< Kpegtg l]n] g< 0+1+ --- +j -g<0
47 Rn]jobkni]_ekjao heja]haov i]pne_ao
Baikopn]_e‰j- @mif`^kal R ^ `^a^ rkl ab ilp jfbj_olp ab '1-00( v rqf,ifw^kal H'1-0/(+ l_qbkbjlp
bk alkab `^a^ Wesfbkb a^a^ mlo '1-02(- Dpql `ljmibq^ i^ abjlpqo^`fŽk-
G^_fbkal bibdfal rk m^oab _^pbp ib0 +’’’ *aj' v 'V0 +’’’ +si( m^o^T v U+obpmb`qfs^jbkqb+qla^ qo^kpcloj^`fŽk ifkb^i R8T y U qfbkb rk^ obmobpbkq^`fŽkj^qof`f^i &peg',Qb`Œmol`^jbkqb+pf afpmlkbjlp ab ij bp`^i^obp`lil`^alp cloj^kalrk^ j^qofw ob`q^kdri^o &pzg' v bibdfjlp rk m^oab _^pbp loabk^a^p m^o^ T v U+bp cŠ`fi abjlpqo^o nrb bufpqbbu^`q^jbkqb rk^ qo^kpcloj^`fŽk ifkb^i R9T y Unrb qfbkbbp^ obmobpbkq^`fŽkj^qof`f^i- Cbcfkfjlp R pfjmibjbkqb `lk ilp bibjbkqlp_^pb ab T mlo jbafl ab i^p b`r^`flkbp '1-0/(- Dkqlk`bp+pbd•k bi qblobj^ 1-01+bufpqbrk^ v pŽil rk^ qo^kpcloj^`fŽk R9T y U `lk bplp s^ilobp ^pfdk^alp- K^ fj^,dbk R't( ab rk mrkql t ab T sfbkb bkqlk`bp a^a^ mlo i^p b`r^`flkbp '1-01( v'1-02(-
DIDLOKN 0- Akjopnq__e‰j a qj] pn]jobkni]_e‰j heja]h] l]npen `a qj] i],pnev`]`]- Rrmlkd^jlp nrb afpmlkbjlp ab i^ j^qofw 1 W 2-
Difg^jlp i^p _^pbp rpr^ibp ab sb`qlobp `lloabk^alp rkfq^oflp m^o^ T2 v T ^, Dk,qlk`bp i^ j^qofw a^a^ obmobpbkqrk^ qo^kpcloj^`fŽk ifkb^i R9T2 y T- nrb ^mif`^rk sb`qlo `r^inrfbo^ &tz* y* t2( ab T2 bk bi sb`qlo &uz*W-(ab T- ab ^`rboal `lki^p b`r^`flkbp ifkb^ibp
DIDLOKN 1- Akjopnq__e‰j a qj] nalnaoajp]_e‰ji]pne_e]h `a qj] pn]jobkn,i]_e‰j heja]h `]`]- Rb^ T bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ob^ibp l't(ab do^al g:2- Dpqbbpm^`fl qfbkb afjbkpfŽk 3+ v bibdfjlp i^ _^pb N+t+t•+u!(-Rb^ C bi lmbo^alo abofs^`fŽk nrb ^mif`^ `^a^ mlifkljfl l&t' ab T bk pr abof,s^a^ l%&t', Olabjlp `lkpfabo^o C `ljl rk^ qo^kpcloj^`fŽk ifkb^i ab T bk U+alkab U bp bi bpm^`fl qofafjbkpflk^i ab qlalp ilp mlifkljflp ob^ibpab do^al g:1-Dk U bibdfjlp i^ _^pb N+t+t•(- O^o^ bk`lkqo^o i^ obmobpbkq^`fŽkj^qof`f^i ab Cobi^qfs^ ^ bp^ bib``fŽk ab _^pbp+qo^kpcloj^jlp 'abofs^jlp( `^a^ bibjbkql _^pb
Palnaoajp]_e‰ji]pne_e]h `a h]o pn]jobkni]_ekjao heja]hao 48
ab T X il bumobp^jlp `ljl rk^ `lj_fk^`fŽk ifkb^i ab ilp bibjbkqlp _^pb ab U,@pŒmrbp+bk`lkqo^jlp nrb
B&h' < N < N * Mt * Mt1 + B&t' < 0 < 0 * Mt * Mt1+
B&t1( < 0t < N * 0t * Mt1+ B&t2( < 1t1 < N * Mt * 1t1 Œ
Klp `lbcf`fbkqbp ab bplp mlifkljflp abqbojfk^k i^p _khqij]o ab i^ obmobpbkq^`fŽkj^qof`f^i ab B, Olo `lkpfdrfbkqb+ i^ obmobpbkq^`fŽkmbafa^ sfbkb a^a^ mlo i^ pf,drfbkqb j^qofw 2 W 3-
O^o^e^`bo klq^o bi eb`el ab nrb i^ obmobpbkq^`fŽkj^qof`f^i abmbkab kl pli^,jbkqb ab ilp bibjbkqlp _^pb pfkl q^j_f‹k ab pr loabk+ fksfoq^jlp bi loabk ab ilpbibjbkqlp _^pb bk U v rqfif`bjlp+ bk pr ird^o+ i^ _^pb loabk^a^ 'u!+ t+ 0(- Dkqlk,`bp ilp bibjbkqlp _^pb ab T pb qo^kpcloj^k bk ilp jfpjlp mlifkljflp l_qbkfalp^kqbp+mbol ilp `ljmlkbkqbp ab ‹pqlp obi^qfslp ^ i^ krbs^ _^pb &t1
+ t* 0( ^m^ob`bkbk loabk fksbopl- Olo `lkpfdrfbkqb+ i^ obmobpbkq^`fŽkj^qof`f^i ab B ^elo^ bp
B^i`ribjlp rk^ qbo`bo^ obmobpbkq^`fŽkj^qof`f^i ab B* rp^kal i^ _^pb'0+ 0 * t+ 0 * t * t&+ 0 * t *-e1 * u!( m^o^ T+ v i^ _^pb '0+t+t1
( m^o^ U-Klp bibjbkqlp _^pb ab T pb qo^kpcloj^k ^pŒ9
B&h' < N+ C'i * t' < 0+ B&h * t * t0' < 0 * 0t *
C'i * t * t1 * t2( < 0 * 0t * 1t1+
`lk il nrb i^ obmobpbkq^`fŽkj^qof`f^i bk bpqb`^pl bp
5/ Rn]jobkni]_ekjao heja]haov i]pne_ao
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X^ nrb bp mlpf_ib l_qbkbo afpqfkq^p obmobpbkq^`flkbp j^qof`f^ibp ab rk^ qo^kp,cloj^`fŽk ifkb^i a^a^ jbaf^kqb i^ bib``fŽk ab _^pbp afpqfkq^p+ m^ob`b k^qro^ifkqbkq^o bibdfo _^pbp ab jlal nrb i^ j^qofw obpriq^kqb qbkd^ rk^ cloj^ il jŠppbk`fii^ mlpf_ib- Di qblobj^ nrb pfdrb morb_^ nrb mlabjlp e^`bo qlalp ilp bib,jbkqlp N bu`bmql ilp ab i^ af^dlk^i nrb s^ abpab bi s‹oqf`b prmboflo fwnrfboal ^ifkcboflo abob`el- @ il i^odl ab bp^ af^dlk^i e^_oŠ rk^ efibo^ ab rklp pbdrfalpab `bolp+ pfbkal bi k•jbol ab rklp fdr^i ^i o^kdl ab i^ qo^kpcloj^`fŽk- Tk^j^qofw &pzg' `lk qlalp ilp bibjbkqlp pq-< N `r^kal e<0<g pb ii^j^ i]pnev `e],ckj]h-
SDNQDL@ 1-03- Qa]j T v U aol]_eko heja]hao`a `eiajoe‰j bejep]+_kjafj T < j v afj U < i- Qqlkjc]iko mqa R C h> 'X+ U( v mqa n < afj R'T(nalnaoajpa ah n]jck `a R- Cteopaj ajpkj_ao qj] ^]oa 'a++--- +aj( l]n] T v kpn]&s* * ,,, * sj( l]n] U p]haomqa
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v
'1-04( R'ae( < M l]n] e < n * 0+--- +j-
Nkn _kjoecqeajpa+h] i]pnev &pzg' `a R nah]per]] ao]o ^]oao peaja pk`ko hkoahaiajpko_ank at_alpk hko n ahaiajpko `a h] `e]ckj]h mqa r]haj
Hk< /11 < --- < Gnn< 0 -
Baikopn]_e‰j- Blkpqorfjlp mofjbol rk^ _^pb m^o^ U- Orbpql nrb R'T(bp rk pr_bpm^`fl ab U `lk afj R'T( < n+bi bpm^`fl R'T( qfbkb rk^ _^pb ab nbibjbkqlp bk U* pb^k ‹pqlp t+ +--- +Un- Rbd•k bi qblobj^ 0-6+ bplp bibjbkqlpcloj^k rk pr_`lkgrkql ab rk^ `fboq^ _^pb m^o^ U- Olo `lkpfdrfbkqb mlabjlp ^a,grkq^o rklp bibjbkqlp Un)* * ,,‹ *Ui ab jlal nrb
'1-05(
pb^ rk^ _^pb m^o^ U-Rbdrfa^jbkqb `lkpqorfjlp rk^ _^pb m^o^ T, B^a^ rkl ab ilp n mofjbolp
bibjbkqlp Ue ab '1-05( bp i^ fj^dbk mlo il jbklp ab rk bibjbkql ab T, Difg^jlp-rkl ab q^ibp bibjbkqlp ab T v ii^j‹jlpib ae8 Dkqlk`bp R&az'< V{ m^o^ e < 0+1+ --- +n ^pŒnrb '1-03( pb p^qfpc^`b- Rb^ ^elo^ g i^ afjbkpfŽk abi k•`ibl L&R',Rbd•k bi qblobj^ 1-2 qbkbjlp j < g * n- Orbpql nrb L&R' < g* bi bpm^`fl L&R'
Akjopnq__e‰j `a qj] nalnaoajp]_e‰j i]pne_e]h aj bkni] `e]ckj]h 50
qfbkbrk^ _^pb nrb `lkpq^ ab g bibjbkqlp ab T nrb abpfdk^jlp mlo an)/ * ‹‹‹ * a-:•-O^o^ `^a^ rkl ab bplp bibjbkqlp+ i^ b`r^`fŽk '1-04( pb p^qfpc^`b-Olo il q^kql+m^o^`ljmibq^o i^ abjlpqo^`fŽk+ qbkbjlp nrb abjlpqo^o nrb bi `lkgrkql loabk^al
'1-06(
bp rk^ _^pb m^o^ T, X^ nrb afj T < j < n * g* pŽil qbkbjlp nrb abjlpqo^onrb bplp bibjbkqlp plk fkabmbkafbkqbp-Rrmlkd^jlp nrb rk^ `fboq^ `lj_fk^`fŽkifkb^i ab biilp pb^ `bol+ mlo bgbjmil
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@mif`^kal R X e^`fbkal rpl ab i^p b`r^`flkbp '1-03( X '1-04(+ bk`lkqo^jlp nrb
n*g n
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Obol Vi +ŠŠŠ+t, plk fkabmbkafbkqbp+v mlo q^kql Bi < --- < a+< N- Olo `lkpf,drfbkqb+ilp n mofjbolp q‹ojfklp ab '1-07( plk `bol+ mlo il `r^i '1-07( pb ob,ar`b ^
n*g
0 a,az < l-e<n*h
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DIDLOKN- Mlp obcbofjlp ^i bgbjmil 1 ab i^ pb``fŽk 1-0/+ alkab B bp bilmbo^alo abofs^`fŽk nrb ^mif`^ bi bpm^`fl T ab ilp mlifkljflp ab do^al 9p: 2bk bi bpm^`fl U ab ilp mlifkljflp ab do^al 9p:1- Dk bpqbbgbjmil+ bi ob`loofalR&T' < U* ^pŒnrb R qfbkbo^kdl 2- @mif`^kal bi j‹qlal pbdrfal bk bi qblobj^1-03+ bibdfjlp `r^inrfbo _^pb m^o^ U* mlo bgbjmil i^ _^pb &h*t*t1
(- Tk `lk,grkql ab mlifkljflp ab T nrb pb ^mif`^ pl_ob bplp bibjbkqlp bp &t* qu1
+ xt1',
@jmif^jlp bpqb`lkgrkql m^o^ ildo^o rk^ _^pb m^o^ T ^agrkq^kal bi mlifkljfl`lkpq^kqb 0+nrb bp rk^ _^pb m^o^bi k•`ibl ab B, Olo `lkpfdrfbkqb+ pf bjmib^jlpi^ _^pb &t* yV1+ t2
+ 0( m^o^ T v i^ _^pb '0+ t* t1( m^o^ U* i^ `loobpmlkafbkqb
obmobpbkq^`fŽkj^qof`f^i m^o^B qfbkb i^ cloj^ af^dlk^i
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Dk qlalp ilp bgbo`f`flp bk ilp nrb pb `lkpfabob bi bpm^`fl sb`qlof^i Tj+ i^ _^pb nrb pbrqfifw^oŠ pboŠ i^ ab ilp sb`qlobp `lloabk^alp rkfq^oflp pf kl pb af`b il `lkqo^ofl- Dk ilp bgbo,`f`flp obi^qfslp ^ i^ j^qofw ab rk^ qo^kpcloj^`fŽk ifkb^i R9T y U pfbkal T << V+ pf kl pbfkaf`^ il `lkqo^ofl qlj^objlp i^ jfpj^ _^pb bk T v bk U,
0- Cbqbojfk^o i^ j^qofw ab `^a^ rk^ ab i^p pfdrfbkqbp qo^kpcloj^`flkbp ifkb^ibp ab Tj bk Tj9^( i^ qo^kpcloj^`fŽk fa‹kqf`^+_( i^ qo^kpcloj^`fŽk `bol+b( jriqfmif`^`fŽk mlo rk bp`^i^o cfgl _-
1- Cbqbojfk^o i^ j^qofw m^o^ `^a^ rk^ ab i^p pfdrfbkqbp molvb``flkbp-
^( R9 T1 ,,* T0*
_( R9 T2++) T1+
b( R8 Up ,,* T1 *
alkab R'th+ V1 +t2( < 'Wi&V1(&alkab R'th+ V1 +V2( < 't1+ V2(&
alkab R'VG& V1+ t2+ V3& to( < 'V1& V2& t3(•
2- Tk^ qo^kpcloj^`fŽk ifkb^i R9T1
y T1
^mif`^ ilp sb`qlobp _^pb e v g`ljl pfdrb9
R&e'< e * e+ R&f' < 0e + e-
^( B^i`ri^o R&1e+ 2f' v N&1e+ 2f' bk crk`fŽk ab e v g-_( Cbqbojfk^o i^ j^qofw ab R v ab O-b( Qbplisbo i^ m^oqb_( pf i^ _^pb &e*f'pb obbjmi^w^ mlo 'b! a0'* pfbkal bi < e , e+a0
<< 2e * g-
3- Tk^ qo^kpcloj^`fŽk ifkb^i R9T1
y T1 pb abcfkb ^pŒ9B^a^ sb`qlo 'u+ v( pb qo^kpcloj^ bkpr pfj‹qof`l obpmb`ql ^i bgb v v irbdl pb armif`^ pr ilkdfqra m^o^ l_qbkbo R&t*u', Cb,qbojfk^o i^ j^qofw ab R v i^ ab R1-
4- Rb^ R9U^ z U^ rk^ qo^kpcloj^`fŽk ifkb^i q^i nrb
R'g( < 1e * 2g* 4g + S'g * g' < e+ R&e* g* g' <g, g,
^( B^i`ri^o R&e* 1g* 1g' v abqbojfk^o i^ afjbkpfŽk abi k•`ibl v bi o^kdl ab R,_( Cbqbojfk^o i^ j^qofw ab R,
5- O^o^ i^ qo^kpcloj^`fŽk ifkb^i abi bgbo`f`fl 4+ pb `lkpfabo^k i^p alp _^pbp `lfk`fabkqbp`lk 'bi& a1+ b^(&pfbkal bi << '1+ 2+ 4(+ a1 << '0+ N+N(+b^ << 'N+ 0+ ,0( v abqbojfk^o i^j^qofw R obi^qfs^ ^ i^p krbs^p _^pbp-
6- Tk^ qo^kpcloj^`fŽk ifkb^i R8U^ z T1 ^mif`^ ilp sb`qlobp _^pb `ljl pfdrb9 R&e'<< 'N+ N(+R&f' << '0+ 0(+R&g' << '0+ ,0(-
^( B^i`ri^o R&2e+ g* g' v abqbojfk^o i^ afjbkpfŽk abi k•`ibl v bi o^kdl ab R,_( Cbqbojfk^o i^ j^qofw ab R,b( Tqfifw^kal i^ _^pb ee-e+g' bk U^ v i^ 't-+ t1( bk T
1+ pfbkal VH < '0+0(+t < '0+1(+
abqbojfk^o i^ j^qofw ab R obi^qfs^ ^ bp^p _^pbp- 1
a( G^ii^o i^p _^pbp 'b-+ a1+ b^( m^o^ U^ X 'tf- t1( m^o^ T
1m^o^ i^p `r^ibp i^ j^qofw ab
R qbkd^ i^ cloj^ af^dlk^i-7- Tk^ qo^kpcloj^`fŽk ifkb^i R8T1 y U^ ^mif`^ ilp sb`qlobp _^pb `ljl pfdrb9 R&e'<
'0+ /+ 0(+R&f' << ',0+ /+ 0(-^( B^i`ri^o R&0e+ 1f' v abqbojfk^o i^ afjbkpfŽk abi k•`ibl v bi o^kdl ab R,_( Cbqbojfk^o i^ j^qofw ab R-b( G^ii^o _^pbp &a**a1( m^o^ T1 v 't{ -V1& V2( m^o^ U^ m^o^ i^p `r^ibp i^ j^qofw ab Rqfbkb cloj^ af^dlk^i-
8- Qbplisbo bi bgbo`f`fl 7 pf R&e'<'0+ /+ 0( v RO( << '0+ 0+ 0(-
Col]_eko heja]hao `a i]pne_ao 52
0/- Rb^k T v U alp bpm^`flp ifkb^ibp+ ^j_lp ab afjbkpfŽk 1 v `lk i^ jfpj^ _^pb 'ah&a1(-
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R'az * a1( < 2az * ca1+ R'2az * 1a1( < 6az * 12a1&
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1bi
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01- '0+ t* aV', 05- &oajt*_kot*toajt*t_kot',
02- '0+ 0 * t* 0 * t * aV', 06- &aVpbk t* aV `lp t',
03- &aV*ta!%', 07- &a08h8pbk 2t+ a0t `lp 2t(-08- Dibdfo i^ _^pb '0+ t+ t1+ t2( -bk bi bpm^`fl ifkb^i T ab qlalp ilp mlifkljflp ob^ibp ab
do^al 999:2- Rb^k B bi lmbo^alo abofs^`fŽk v R8T y T i^ qo^kpcloj^`fŽk ifkb^i nrb^mif`^ l&t' bk tl%&t', Blk obi^`fŽk ^ i^ _^pb a^a^+ abqbojfk^o i^ j^qofw ab `^a^ rk^ab i^p qo^kpcloj^`flkbp pfdrfbkqbp9 ^( R: _( BR: b( RB: a( RB , BR: b( R1:
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Rb^k j v j alp bkqbolp mlpfqfslp v pb^ 0i‹j bi `lkgrkql ab qlalp ilp m^obpabbkqbolp 'f+:( q^ibpnrb 099::f 99::i+ 0 99::: 99::j- Br^inrfbo crk`fŽk ? `rvl aljfkflpb^ J: -ŒŒpb abkljfk^ i]pnev j W j- Di s^ilo ab i^ crk`fŽk @'f+:( pb ii^j^ ahaiaj,pk f: ab i^ j^qofw v pb abpfdk^oŠ q^j_f‹k mlo ]ef, Noafk^of^jbkqb pb afpmlkbkqlalp ilp s^ilobp ab i^ crk`fŽk bk rk ob`qŠkdril nrb `lkpq^ ab j cfi^p v j `l,irjk^p+ abi jlal pfdrfbkqb
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Clp crk`flkbp plk fdr^ibp pf v pŽil pf qfbkbk bi jfpjl aljfkfl v qlj^k ilpjfpjlp s^ilobp bk `^a^ bibjbkql abi aljfkfl- Orbpql nrb i^p j^qof`bp plk crk,`flkbp+ alp j^qof`bp ? < ']zz( v @ < '^:z( plk fdr^ibp pf v pŽil pf qfbkbk bi jfpjlk•jbol ab cfi^p+bi jfpjl k•jbol ab `lirjk^p+ b fdr^ibp bibjbkqlp ]-+< ^,* m^o^`^a^ m^o &e*f',
Rrmlkd^jlp ^elo^ nrb ilp bibjbkqlp plk k•jbolp 'ob^ibp l `ljmibglp( vabcfk^jlp i^ ^af`fŽk ab j^qof`bp v i^ jriqfmif`^`fŽk mlo bp`^i^obp pfdrfbkal bijfpjl j‹qlal nrb m^o^ crk`flkbp ob^ibp l `ljmibg^p `r^ibpnrfbo^-
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Gokiknbeoik ajpna pn]jobkni]_ekjao heja]haov i]pne_ao 54
nrb bpqb bpm^`fl bp ab afjbkpfŽk i W j- Dk bcb`ql+ rk^ _^pb m^o^ Ki+j `lkpq^ab ij j^qof`bp nrb qfbkbk rk bibjbkql fdr^i ^ 0 v qlalp ilp abjŠp fdr^ibp ^ N-Olo bgbjmil+ i^p pbfp j^qof`bp
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cloj^k rk^ _^pb m^o^ bi `lkgrkql ab qla^p i^p j^qof`bp 1 W 2-
1-03 Hpljlocfpjl bkqob qo^kpcloj^`flkbp ifkb^ibp v j^qof`bp
Ulis^jlp ^elo^ ^ i^ obi^`fŽk bkqob j^qof`bp v qo^kpcloj^`flkbp ifkb^ibp-Rb^k T v U alp bpm^`flp ifkb^ibp ab afjbkpfŽk cfkfq^ `lk afj T < j v afj U < i-Difg^jlp rk^ _^pb &ah* ,,, * aj' m^o^ T v lqo^ 'tf ’ --- +Ui( m^o^ U- Dk bpq^afp`rpfŽk bp^p _^pbp pb j^kqfbkbk cfg^p-Cbpfdkbjlp`lk HppT*U' bi bpm^`fl ifkb^i&abqla^p i^p qo^kpcloj^`flkbp ifkb^ibp ab T bk U- Rf RCe1&'T+U(+ pb^ i'R( i^j^qofw ab R obi^qfs^ ^ i^p _^pbp a^a^p- Qb`loabjlp nrb i'R( pb abcfkb `ljl pfdrb-
K^ fj^dbk ab `^a^ bibjbkql _^pb ag pb bumobp^ `ljl rk^ `lj_fk^`fŽk ifkb^iab ilp bibjbkqlp _^pb ab U9
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K^ b`r^`fŽk '1-1/( abcfkb rk^ krbs^ crk`fŽk i `rvl aljfkfl bp 1&'T+ U( v`rvlp s^ilobp plk j^qof`bp ab Ki+j- Orbpql nrb qla^ j^qofw i W j bp i^ j^qofwi'R( m^o^ rk^ `fboq^ R ab 1&'T+U'* bi ob`loofal ab i bp Ki-jŒ Di qblobj^ pf,drfbkqb morb_^ nrb i^ qo^kpcloj^`fŽk i8 1&'T+ U( ,,* Ki+j bp ifkb^i v rkl ^ rklbk 0%&T*U',
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11 Rn]jobkni]_ekjao heja]hao v i]pne_ao
Baikopn]_eˆj, K^ j^qofw i&R' bpqŠ cloj^a^ `lk ilp c^`qlobp pq- ab '1-08(-Cbi jfpjl jlal+ i^ j^qofw i&Q' bpqŠ `lkpqfqrfa^ `lk ilp c^`qlobp Qeg ab i^p b`r^,`flkbp
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Dpql abjrbpqo^ nrb i bp ifkb^i-O^o^ abjlpqo^o nrb i bp rkl ^ rkl+ prmlkd^jlp nrb i&Q' < i&R'* pfbkal
R < &Qeg'v R < &peg',K^p b`r^`flkbp '1-08( v '1-10( abjrbpqo^k nrb Q&ag' ;; R&ag' m^o^ `^a^ bibjbkql _^pb ao* ^pŒnrb Q&t' < R&t' m^o^ qlal t ab T* v mloq^kql R < R,
M^oanr]_e‰j9 K^ crk`fŽk i bp rk eokiknbeoik- Dibdfa^p rk^p _^pbp+ i bpq^_ib`brk^ `loobpmlkabk`f^ rkl ^ rkl bkqob bi `lkgrkql ab i^p qo^kpcloj^`flkbp-9q& &T* U' vbi `lkgrkql K ‹‹‹,‹ab i^p j^qof`bp i W j- K^p lmbo^`flkbp ab ^af`fŽk v jriqfmif`^`fŽk mlobp`^i^obp pb `lkpbos^k ^ qo^s‹p ab bp^ `loobpmlkabk`f^- Klp bpm^`flp ifkb^ibp-9q&&T*U'v K|: pb af`b nrb plk eokiknbko Hk`fabkq^ijbkqb+ bi qblobj^ 1-00 abjrbpqo^ nrb bialjfkfl ab rk^ qo^kpcloj^`fŽk ifkb^i rkl ^ rkl qfbkb i^ afjbkpfŽk fdr^i ^ pr ob`loofal-Olo `lkpfdrfbkqb+ afj ,8p%&T,U' < afj K ‹‹‹,‹< ij-
Rf T < U v bibdfjlp i^ jfpj^ _^pb m^o^ ^j_lp+ i^ j^qofw i&h' `loobpmlk,afbkqb ^ i^ qo^kpcloj^`fŽk fa‹kqf`^ 09T y T bp rk^ j^qofw af^dlk^i `lk ilp bib,jbkqlp ab i^ af^dlk^i fdr^ibp ^ 0 v qlalp ilp abjŠp fdr^ibp ^ N- Dpq^ pb ii^j^e`ajpe`]` l i]pnev qje`]` v pb abpfdk^ `lk / l `lk Gj-
1-04 ?^U]RYURLJLRmWMNj^qof`bp
@idrk^p qo^kpcloj^`flkbp ifkb^ibp mrbabk jriqfmif`^opb mlo jbafl ab i^ `lj,mlpf`fŽk- Cbcfkfobjlp ^elo^ i^ jriqfmif`^`fŽk ab j^qof`bp ab j^kbo^ nrb bi mol,ar`ql ab alp j^qof`bp `loobpmlka^ ^ i^ `ljmlpf`fŽk ab i^p qo^kpcloj^`flkbp ifkb^,ibp nrb biilp obmobpbkq^k-
Qb`loabjlp nrb pf R8S y T X Q8T y U plk qo^kpcloj^`flkbp ifkb^ibp+ pr`ljmlpf`fŽk QR8S y U bp rk^ qo^kpcloj^`fŽk ifkb^i a^a^ mlo
QR&t' < QYR&t'[ m^o^ qlal t ab S,
Rrmlkd^jlp nrb S* T* X U plk ab afjbkpfŽk cfkfq^+mlo bgbjmil
afj S; j+ afj T<l+ afj s< i-
Kqhpelhe_]_e‰j `a i]pne_ao 56
Difg^jlp _^pbp m^o^ S* T* X U, Blk obi^`fŽk ^ bp^p _^pbp i&Q' bp rk^ j^qofwi W l+ R bp rk^ j^qofw l W j+ v QR bp rk^ j^qofw i W j - K^ pf,drfbkqb abcfkf`fŽk ab jriqfmif`^`fŽk ab j^qof`bp klp mbojfqb abar`fo i^ obi^`fŽki'QR( < i'Q(i'R(- Dpql buqfbkab ^ ilp molar`qlp i^ molmfba^a ab fpljlocfpjl-
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Kqhpelhe_]_e‰ja i]pne_ao 14
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61 Rn]jobkni]_ekjao heja]hao u i]pne_ao
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kl plk `fboq^p m^o^ i^p j^qof`bp 1 W 1+ ? < Zz ,z\ v @< Z9 zi_( Llafcf`^o bi pbdrkal jfbj_ol ab bp^p fabkqfa^abp m^o^ l_qbkbo cŽojri^p sŠifa^pm^o^ qla^p i^p j^qof`bp `r^ao^a^p ? v @-b( „O^o^ nr‹ j^qof`bp ? v @ plk sŠifa^p i^p fabkqfa^abp bpq^_ib`fa^p bk ^(>
*')/ DR\]NVJ\MNNL^JLRXWN\URWNJUN\
Rb^ ? < &]ef' rk^ j^qofw i W j ab k•jbolp a^a^+ v pb^k AG * ‹‹‹ ,_| lqolpi k•jbolp- Tk `lkgrkql ab i b`r^`flkbp ab i^ cloj^
'1-12(j
-v]egVg < a+ m^o^ e < 0+1+--- +i+g<h
pb A^ok^ pfpqbj^ ab i b`r^`flkbp ifkb^ibp `lk j fk`Ždkfq^p- Blkpfabo^jlpWH+ --- + t-: `ljl fk`Ždkfq^p- Tk^ okhq_e‰j abi pfpqbj^ bp rk^ k,mi^ `r^inrfbo^ abk•jbolp 'WH+ --- +Vj( m^o^ ilp nrb pb p^qfpc^`bk qla^p i^p b`r^`flkbp- K^ j^qofw ?pb A^ok^ i]pnev `a hko _kabe_eajpao abi pfpqbj^-
Klp pfpqbj^p ifkb^ibp mrbabk bpqraf^opb mlo jbafl ab i^p qo^kpcloj^`flkbpifkb^ibp- Dibdfjlp i^p _^pbp rpr^ibp ab sb`qlobp `lloabk^alp rkfq^oflp bk Tj v T i-
K^ j^qofw ab ilp `lbcf`fbkqbp ? abqbojfk^ rk^ qo^kpcloj^`fŽk ifkb^i+ R9 Tj y T i+
nrb ^mif`^ rk sb`qlo ^o_fqo^ofl t < &t* * ,,, * tj( ab T j bk bi sb`qlo u < &WG* ,,, *Wi( ab T i a^al mlo i^p b`r^`flkbp ifkb^ibp
j
We< G]egtg m^o^ f< 0+1+--- +i-0_<0
Qeopai]o `a a_q]_ekjao heja]hao 2.
Rb^ a < '`i +ŠŠŠ+Ai( bi sb`qlo ab T i `rvlp `ljmlkbkqbp plk ilp k•jbolp nrb^m^ob`bk bk bi pfpqbj^ '1-12(- Dpqb pfpqbj^ mrbab bp`of_fopbjŠp pbk`fii^jbkqbmlkfbkal
R&t' < _,
Di pfpqbj^ qfbkb rk^ plir`fŽk pf v pŽil pf a bpqŠbk bi ob`loofal ab R, Rf rk plilu ab Tj pb ^mif`^ bk a+ bi pfpqbj^ qfbkb rk^ pli^ plir`fŽk- Rf jŠp ab rk t pb^mif`^ bk a+bi pfpqbj^ ^ajfqb jŠp ab rk^ plir`fŽk-
DIDLOKN 0- Sj oeopai] oej okhq_e‰j- Di pfpqbj^ t * u < 0+ t * u < 1kl qfbkb plir`fŽk- K^ prj^ ab alp k•jbolp kl mrbab pbo ^ i^ sbw 0 v 1-
DIDLOKN 1- Sj oeopai] _kj okhq_e‰j Šje_]- Di pfpqbj^ t * u < 0+t + u < N qfbkb bu^`q^jbkqb rk^ plir`fŽk9 &t* v( < 'i+ q(•
DIDLOKN 2- Sj oeopai] _kj i…o `a qj] okhq_e‰j- Di pfpqbj^ t * v < 0+nrb `lkpq^ ab rk^ b`r^`fŽk `lk alp fk`Ždkfq^p+qfbkb jŠp ab rk^ plir`fŽk- Clpk•jbolp `r^ibpnrfbo^ `rv^ prj^ pb^ 0 a^k rk^ plir`fŽk-
@ `^a^ pfpqbj^ ifkb^i '1-12(+ mlabjlp ^pl`f^o lqol pfpqbj^
j
H]egtg < N m^o^ f< 0+1+--- +i *h_<h
l_qbkfal obbjmi^w^kal `^a^ az bk '1-12( mlo l- †pqb pb ii^j^ bi oeopai] dkik,c†jak `loobpmlkafbkqb ^i '1-12(- Rf a <0<N+ bi pfpqbj^ '1-12( pb ii^j^ jk dk,ikc†jak- Tk sb`qlo t ab Tj p^qfpc^oŠbi pfpqbj^ eljld‹kbl pf v pŽil pf
R&t' < M*
alkab R bp i^ qo^kpcloj^`fŽk ifkb^i abqbojfk^a^ mlo i^ j^qofw ab ilp `lbcf`fbkqbp-Di pfpqbj^ eljld‹kbl qfbkb pfbjmob i^ plir`fŽk t < N+ mbol mrbab qbkbo lqo^p-Di `lkgrkql ab plir`flkbp abi pfpqbj^ eljld‹kbl bp bi k•`ibl ab R- Di qblobj^pfdrfbkqb bumlkb i^ obi^`fŽk bkqobi^p plir`flkbp abi pfpqbj^ eljld‹kbl v i^p abipfpqbj^ kl eljld‹kbl-
SDNQDL@ 1-07- Qqlkjc]iko mqa ah oeopai] jk dkikc†jak '1-12( pajc]qj] okhq_e‰j+lkn afailhk ^-
^( Qe qj ra_pkn t ao qj] okhq_e‰j `ah oeopai] jk dkikc†jak+ ajpkj_ao ahra_pkn r < t , ^ ao qj] okhq_e‰j `ah _knnaolkj`eajpa oeopai] dkik,c†jak-
2/ Rn]jobkni]_ekjao heja]hao v i]pne_ao
_( Rf qj ra_pkn r ao qj] okhq_e‰j `ah oeopai] dkikc†jak+ ah ra_pkn t < r * ^ao qj] okhq_e‰j `ah oeopai] jk dkikc†jak-
Baikopn]_e‰j- Rb^ R9 T j y T i i^ qo^kpcloj^`fŽk ifkb^i abqbojfk^a^ mlo i^j^qofw ab ilp `lbcf`fbkqbp+`ljl ^kqbppb e^ af`el- Orbpql nrb ^ bp rk^ plir`fŽkabi pfpqbj^ kl eljld‹kbl qbkbjlp R&^' < _- Rb^k t v r alp sb`qlobp ab Tj q^ibpnrb r < t,^- Dkqlk`bp qbkbjlp
R'r( < R't , ^( < R't( , R' 9&(< R't( , b
Olo `lkpfdrfbkqb R't( < a pf v pŽil pf R'r( < N- Dpql abjrbpqo^ ^ i^ sbw ^( v _(-
Dpqbqblobj^ morb_^ nrb bi mol_ibj^ ab e^ii^o qla^p i^p plir`flkbp ab rkpfpqbj^ kl eljld‹kbl pb bp`fkab bk alp m^oqbp90( G^ii^o qla^p i^p plir`flkbpr abi pfpqbj^ eljld‹kbl+ bpql bp+abqbojfk^kal bi k•`ibl ab R: v 1( e^ii^o rk^plir`fŽk m^oqf`ri^o ^ abi pfpqbj^ kl eljld‹kbl- Rrj^kal ^] `^a^ rkl ab ilpsb`qlobp r abi k•`ibl R* pb l_qfbkbk qla^p i^p plir`flkbp t < r * ^ abi pfpqbj^kl eljld‹kbl-
Rb^ g i^ afjbkpfŽk ab L'R(- Rf mlabjlp bk`lkqo^o g plir`flkbp ej`alaj`eaj,pao Th +ŒŒŒ+Tg abi pfpqbj^ eljld‹kbl+ bii^p cloj^oŠk rk^ _^pb m^o^L'R(+ v ml,abjlp l_qbkbo `r^inrfbo r ab L&R' cloj^kal qla^p i^p `lj_fk^`flkbp ifkb^ibp
alkab p**,,, *pg plk bp`^i^obp ^o_fqo^oflp-Dpq^`lj_fk^`fŽk ifkb^i pb ii^j^ okhq,_e‰j cajan]h `ah oeopai] dkikc†jak- Rf ^ bp rk^ plir`fŽk m^oqf`ri^oabi pfpqbj^ kleljld‹kbl+ bkqlk`bp qla^p i^p plir`flkbp t sfbkbk a^a^p mlo
Dpq^ `lj_fk^`fŽk ifkb^i pb ii^j^ okhq_e‰j cajan]h `ah oeopai] jk dkikc†jak-Di qblobj^ 1-07 mrbab mlkbopb bk bpq^ lqo^ cloj^9
SDNQDL@ 1-08- Qa] R9Tj y Ti h] pn]jobkni]_e‰j heja]h p]h mqa R't( < v+`kj`a t < 'Vh& ŒŒŒ+Vj(+ u < 'Xi +--- +Wi(+a
j
We<-h]egtg l]n] e<0+1+ --- +i-S4T
R†_je_]o `a _…h_qhk 64
Qa] g h] `eiajoe‰j `ah jŠ_hak `a R- Rf q 0 + ’’’ +0&gokj g okhq_ekjao ej`alaj`eaj,pao `ah oeopai] dkikc†jak R't( < /+ v pf ^ ao qj] okhq_e‰j l]npe_qh]n `ah oeopai]jk dkikc†jak R't( < a+ajpkj_ao h] okhq_e‰j cajan]h `ah oeopai] jk dkikc†jak ao
t < ^ * phqh * --- * pgqg*
oeaj`k p,- --- +pe,ao_]h]nao _q]haomqean]-
Dpqb qblobj^ kl klp af`b `Žjl bk`lkqo^o rk^ plir`fŽk m^oqf`ri^o ^ abi pfp,qbj^ kl eljld‹kbl+ kf i^p plir`flkbp q+ +--- *Tg abi pfpqbj^ eljld‹kbl- Mlp af`bq^k pŽil il nrb mrbab l_qbkbopb `r^kal bi pfpqbj^ kl eljld‹kbl qbkd^ rk^ pl,ir`fŽk- Di pfdrfbkqb bgbjmil+ ^rknrb jrv pbk`fiil+ firpqo^ bi qblobj^-
DIDLOKN- Di pfpqbj^ t * v < 1 qfbkb `ljl pfpqbj^ eljld‹kbl ^pl`f^al i^b`r^`fŽk t * v < N- Olo `lkpfdrfbkqb+ bi k•`ibl `lkpq^ ab qlalp ilp sb`qlobp abT1 ab i^ cloj^ &p*,p(+ pfbkal &po_fqo^ofl- Orbpql nrb &p*,p( < p'0+ ,0(+‹pqb bprk pr_bpm^`fl rkf afjbkpflk^i ab T 1 `lk _^pb&'0+ , 0(- Tk^ plir`fŽk m^oqf`ri^oabi pfpqbj^ kl eljld‹kbl bp '/+1(- Olo q^kql+i^ plir`fŽk dbkbo^i abi pfpqbj^ kleljld‹kbl sfbkb a^a^ mlo
&t*u' < '/+1( * p&h*+/' l t < p+ u<1,p+
pfbkal p ^o_fqo^ofl-
*')0 EkLWRLJ\MNLjUL^UX
Ulis^jlp ^i mol_ibj^ abi `Ši`ril bcb`qfsl ab i^p plir`flkbp ab rk pfpqbj^ifkb^i kl eljld‹kbl- @rknrb pb e^k abp^oolii^al jr`elp j‹qlalp m^o^ ^q^`^obpqb mol_ibj^+ qlalp bufdbk `Ši`rilp `lkpfabo^_ibp pf bi pfpqbj^ bp ab do^k q^j^,•l- Olo bgbjmil+ m^o^ obplisbo rk pfpqbj^ ab afbw b`r^`flkbp `lk bi jfpjl k•jbolab fk`Ždkfq^p mrbabk pbo kb`bp^of^p s^of^p elo^p ab `Ši`rilp+ fk`irpl `lk i^ ^vra^ab rk `^i`ri^alo j^kr^i-
U^jlp ^ `ljbkq^o rk j‹qlal jrv rqfifw^al+ nrb pb ii^j^ i†pk`k `a aheie,j]_e‰j `a E]qoo,hkn`]j+ nrb bp obi^qfs^jbkqb pbk`fiil v mrbab moldo^j^opb cŠ`fi,jbkqb m^o^ `^i`ri^alobp bib`qoŽkf`lp ab ^iq^ sbil`fa^a- Di j‹qlal `lkpfpqb bk i^^mif`^`fŽk ab qobplmbo^`flkbp crka^jbkq^ibp ^ i^p b`r^`flkbp ifkb^ibp abi pfpqbj^9
0( Gjpan_]i^ek `a `ko a_q]_ekjao-1( Kqhpelhe_]_e‰j `a pk`ko hko p†niejko `a qj] a_q]_e‰j lkn qj ao_]h]n jk
jqhk-2( Qqi] `a qj] a_q]_e‰j ] kpn] iqhpelhe_]`] lkn qj ao_]h]n-
21 Rn]jobkni]_ekjao heja]haou i]pne_ao
B^a^ sbw nrb bcb`qr^jlp rk^ ab bp^p lmbo^`flkbp bk bi pfpqbj^ l_qbkbjlp rkkrbsl pfpqbj^ `lk i^p jfpj^p plir`flkbp- Clp pfpqbj^p `lk i^p jfpj^p plir`flkbppb ii^j^k amqer]hajpao-Dcb`qr^kal bp^p lmbo^`flkbp rk^ qo^p lqo^ ab jlal pfpqb,jŠqf`l iibd^jlp mlo cfk ^ rk pfpqbj^ bnrfs^ibkqb nrb mrbab obplisbopb ^ pfjmibsfpq^-
Hirpqo^objlp bi j‹qlal `lk ^idrklp bgbjmilp m^oqf`ri^obp- Rb sboŠ bkqlk`bp`Žjl pb ^mif`^ bi j‹qlal bk dbkbo^i-
DIDLOKN 0- Qeopai] _kj okhq_e‰jŠje_]- Blkpfabobjlp bi pfpqbj^
1t , 4u * 3w< ,2
t , 0u * w < 4
t , 2u * 5w < 0/-
Dpqb pfpqbj^ qfbkb plir`fŽk •kf`^+ t <0013+u<64+w < 20+ nrb l_qbkaobjlp mlo bij‹qlal ab bifjfk^`fŽk ab F^rpp,Hloa^k- O^o^ bsfq^o qo^_^gl kl `lmf^jlp i^p ib,qo^p t+ u+w kf ilp pfdklp ab fdr^ia^a+ pfkl nrb qo^_^g^objlp `lk i^ i]pnev ]ilhe]`]
'1-13(
,4 3
(- ,
(/ 1
,z\0/
l_qbkfa^ ^i ^agrkq^o ilp pbdrkalp jfbj_olp abi pfpqbj^ ^ i^ j^qofw abilp `lbcf`fbkqbp- K^p qobp lmbo^`flkbp _Špf`^p ^kqbp jbk`flk^a^p pb bcb`q•^k `lki^p cfi^p ab i^ j^qofw ^jmif^a^ v pb ii^j^k klan]_ekjao beh]-Dk `r^inrfbo c^pb abimol`bpl mlabjlp mlkbo i^p ibqo^p t+ v+ w b fkqbo`^i^o ilp pfdklp ab fdr^ia^a bk i^psboqf`^ibp `loobpmlkafbkqbp l_qbkfbkal b`r^`flkbp- Mrbpqol l_gbqfsl bp iibd^o ^
'1-14( -,-/G64
20
i^ j^qofw ^jmif^a^ abpmr‹p ab rk^ pr`bpfŽk ab lmbo^`flkbp cfi^- Di `loobpmlkafbkqbpfpqbj^ ab b`r^`flkbp bp t; 013+ v < 64+ w < 20+ nrb klp a^ i^ plir`fŽkabpb^a^-
R†_je_]o `a _…h_qhk 66
Di mofjbo m^pl bp l_qbkbo rk 0 bk bi s‹oqf`b prmboflo fwnrfboal ab i^ j^qofw-Olabjlp e^`boil fkqbo`^j_f^kal i^ mofjbo^ cfi^ ab i^ j^qofw a^a^ '1-13( `lki^ pbdrka^ l `lk i^ qbo`bo^-N _fbk+ mlabjlp jriqfmif`^o i^ mofjbo^ cfi^mloTy,Hkqbo`^j_f^kal i^p cfi^pmofjbo^ v pbdrka^+ l_qbkbjlp
]-z\0/
Di m^pl pfdrfbkqb `lkpfpqb bk `lksboqfo qlalp ilp obpq^kqbpbibjbkqlp ab i^mofjbo^ `lirjk^ bk `bolp+ abg^kal bi mofjbol fkq^`ql- A^pq^m^o^biil jriqfmif`^oi^ mofjbo^ cfi^ mlo , 1 X prj^o bi obpriq^al ^ i^ pbdrka^ cfi^- Krbdl jriqfmif`^,jlp i^ mofjbo^ cfi^ mlo , 0 X prj^jlp bi obpriq^al ^ i^ qbo`bo^-Cbpmr‹p ab bp^palp lmbo^`flkbp+l_qbkbjlp
'1-15( Zz <zz ,0zI-N ,1 4 4
Qbmbqfjlp ^elo^ bi mol`bpl bk i^ j^qofw obar`fa^ Z<z zH,0z\ nrb
^m^ob`bgrkql ^ ilp alp `bolp- Olabjlp l_qbkbo 0 bk oq s‹oqf`b prmboflo fwnrfboaljriqfmif`^kal i^ pbdrka^ cfi^ ab H'1-15( mlo ,0- Dpql klp a^ i^ j^qofw
Z
0 ,1 0
N 0,1
N ,1 4
Lriqfmif`^kal i^ pbdrka^ cfi^ mlo 1 v prj^kal bi obpriq^al ^ i^ qbo`bo^+ lkpb,drfjlp
'1-16( Zz ,z ,z
? ? ,0z\-20
@i iibd^o ^nrŒ+bi `loobpmlkafbkqb pfpqbj^ ab b`r^`flkbp sfbkb a^al mlo
t + 0u * v < 4
u,1v<02
v < 20-
23 Rn]jobkni]_ekjao heja]haou i]pne_ao
Dpq^p b`r^`flkbp mrbabk obplisbopb pr`bpfs^jbkqb m^oqfbkal ab i^ qbo`bo^ v qo^,_^g^kal e^`f^ ^qoŠp+aŠkalklp
w< 20+ W < 02 * 1w< 02 * 51 < 64+ t < 4 * 1u , w< 4 * 04/ , 20 < 013-
l _fbk+ mlabjlp `lkqfkr^o bi mol`bpl ab F^rpp,Hloa^k `lksfoqfbkal bk `bolpqlalp ilp bibjbkqlp pfqr^alp mlo bk`fj^ ab i^ af^dlk^i ab rklp bk i^ pbdrka^v bk i^ qbo`bo^ `lirjk^p- Lriqfmif`^kal i^ pbdrka^ cfi^ ab '1-16( mlo 1 v pr,j^kal bi obpriq^al ^ i^ mofjbo^+ l_qbkbjlp
Z
0 N ,2N 0 ,1? ? ,
20\02-
20
Olo •iqfjl+ jriqfmif`^jlp i^ qbo`bo^ cfi^ mlo 2 v prj^jlp bi obpriq^al ^ i^ mofjbo^cfi^+ v irbdl jriqfmif`^jlp i^ qbo`bo^ cfi^ mlo 1 v prj^jlp bi obpriq^al ^ i^ pb,drka^ `lk il nrb iibd^jlp ^ i^ j^qofw '1-14(-
DIDLOKN 1- Qeopai] _kj i…o `a qj] okhq_e‰j- Blkpfabobjlp bi pfdrfbkqbpfpqbj^ ab 2 b`r^`flkbp `lk 4 fk`Ždkfq^p9
'1-17(
1t , 4u * 3w* q , r < ,2
t , 0u * w , q * r < 4
t , 2u * 5w * 1q , r < 0/-
K^ `loobpmlkafbkqb j^qofw ^jmif^a^ bp
Z
1 ,4 3 0,00 ,1 0 ,0 0
0 ,3 5 1,0
,2\4 -
0/
Klp `lbcf`fbkqbp ab t+u+w v ilp pbdrkalp jfbj_olp plk ilp jfpjlp nrb ilp abibgbjmil 0- Rf bcb`qr^jlp i^p jfpj^p lmbo^`flkbp cfi^ nrb bk bi bgbjmil 0+ iibd^,jlp ^ i^ j^qofw ^jmif^a^
Zzz z? ? ,
,05 08,8 00,2 3
013\64 -
20
R†_je_]o `a _…h_qhk 68
Di `loobpmlkafbkqb pfpqbj^ ab b`r^`flkbp mrbab obplisbopb obpmb`ql ^ t+ v+ w bkcrk`fŽk ab q v r aŠkalklp
t < 013 * /4q + /7r
u < 64 * 8q , hhr
v < 20 * 2q , 3r-
Rf e^`bjlp q < p+X r < p|* pfbkal p+v p1 k•jbolp ob^ibp ^o_fqo^oflp+ v abqbojf,jfk^jlp t* v+ w jbaf^kqb bp^p b`r^`flkbp+ bi sb`qlo &t* v+Y+ J-* r' ab r-- a^al mlo
'u+ u* w+q* r' < '013 * /4b0 , /7b1+ 64 * 7b0 , hhb1+ 20 * 1b0 , 2b1+ b0+ '1(
bp rk^ plir`fŽk- Rbm^o^kal ilp q‹ojfklp nrb `lkqfbkbk p*v p--qbkaobjlp9
&t*u* w+q* r' < '013+64+20+ N+N( * bhh4* 8+2+0+N( * b1&+/7* ,00+ ,3+ /+0(-
Dpq^ b`r^`fŽk klp a^ i^ plir`fŽk dbkbo^i abi pfpqbj^- Di sb`qlo '013+ 64+ 20+ N+N(bp rk^ plir`fŽk m^oqf`ri^o abi pfpqbj^ kl eljld‹kbl '1-17(- Klp alp sb`qlobp (-$/$*$($ N( X ',08+ ,00+,3+ /+0( plk plir`flkbp abi `loobpmlkafbkqb pfp,qbj^ eljld‹kbl- Orbpql nrb plk fkabmbkafbkqbp+ `lkpqfqrvbk rk^ _^pb m^o^ bibpm^`fl ab qla^p i^p plir`flkbp abi pfpqbj^ eljld‹kbl-
DIDLOKN 2- Qeopai] oej okhq_e‰j- Blkpfabobjlp bi pfpqbj^
'1-18(
1t , 4u * 3v < ,2
t , 0u * w < 4
t , 2u * 4v < 0/-
Dp fa‹kqf`l ^i abi bgbjmil 0 bu`bmql nrb bk bi `lbcf`fbkqb ab v bk, i^ qbo`bo^ b`r^,`fŽk e^ pfal `^j_f^al bi 5 mlo rk 4- K^ j^qofw ^jmif^a^ `loobpmlkafbkqb bp
Z
1 ,4 30 ,1 00 ,3 4
,2\4 -
0/
@mif`^kal i^p jfpj^p lmbo^`flkbp cfi^ rp^a^p bk bi bgbjmil 0 m^o^ qo^kpcloj^o'1-13( bk '1-16(+ iibd^jlp ^ i^ j^qofw ^jmif^a^
'1-2/(0
(-
N0z\-20
7/ Rn]jobkni]_ekjao heja]hao v i]pne_ao
Br^kal i^ •iqfj^ cfi^ pb bumobp^ `ljl b`r^`fŽk+ iibd^jlp ^ N < 20- Olo `lkpf,drfbkqb bi pfpqbj^ lofdfk^i kl qfbkb plir`fŽk mrbpql nrb ilp alp pfpqbj^p '1-18(X '1-2/( plk bnrfs^ibkqbp-
Dk `^a^ rkl ab ilp bgbjmilp ^kqboflobp+ bi k•jbol ab b`r^`flkbp kl bu`baŒ^^i ab fk`Ždkfq^p- Rf e^v jŠp b`r^`flkbp nrb fk`Ždkfq^p+ bi mol`bpl ab F^rpp,Iloa^k mrbab ^•k ^mif`^opb- Olo bgbjmil+ `lkpfabobjlp bi pfpqbj^ abi bgbjmil 0+nrb qfbkb i^ plir`fŽk t < 013+ X < 64+ Y < 20- Rf ^agrkq^jlp rk^ krbs^ b`r^,`fŽk ^ bpqb pfpqbj^ nrb pb^ p^qfpcb`e^ mlo i^ jfpj^ qbok^+ mlo bgbjmil+ i^ b`r^,`fŽk 0t + 1u * Y < 43+ bkqlk`bp bi mol`bpl ab bifjfk^`fŽk klp iibs^ ^ i^ j^qofw
^jmif^a^
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Dibdfa^ i^ _^pb rpr^i ab ilp sb`qlobp `lloabk^alp rkfq^oflp ab Tj+ pb^R9 Tj y Tj i^ qo^kpcloj^`fŽk ifkb^i `lk j^qofw i'R( < ?- Sbkbjlp bkqlk`bp bipfdrfbkqb
Gjrano]o `a i]pne_ao _q]`n]`]o 70
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Baikopn]_e‰j- Rrmlkd^jlp nrb ? bp kl pfkdri^o v nrb @? < b, Cbjlpqo^,objlp nrb R&t' < N fjmif`^ t < N- C^al t q^i nrb R&t' < /+ pb^ W i^ j^qofw`lirjk^ j W 0 cloj^a^ ^ m^oqfoab ilp `ljmlkbkqbp ab t, Orbpql nrb R&t' < /+i^ j^qofw molar`ql ?V bp rk^ j^qofw `lirjk^ j W 0 cloj^a^ mlo `bolp+ ^pŒnrb@'?V( bp q^j_f‹k rk^ j^qofw `lirjk^ ab `bolp- Obol @'?V( < '@?(V < GV < W+mlo 0/ nrb qlal `ljmlkbkqb ab t bp N- Olo `lkpfdrfbkqb+ R bp fksboqf_ib+ v i^b`r^`fŽk RR,/ < b fjmif`^ nrb i'R(i'R,h( < 0 l ?i'R,/
' < h- Lriqfmif`^kal^ i^ fwnrfboa^ mlo @+bk`lkqo^jlp i'R,/
' < @- Qb`Œmol`^jbkqb+ pf R bp fksboqf_ibbkqlk`bp R,0R bp i^ qo^kpcloj^`fŽk fa‹kqf`^ ^pŒnrb i'R,/(i'R( bp i^ j^qofwfabkqfa^a- Olo `lkpfdrfbkqb ? bp kl pfkdri^o v i'R,0(? < h-
Sla^p i^p molmfba^abp ab i^p qo^kpcloj^`flkbp ifkb^ibp fksboqf_ibp qfbkbk pr`lkqo^m^oqfa^ m^o^ i^p j^qof`bp kl pfkdri^obp- Dk m^oqf`ri^o+ i^p fksbop^p mlo i^fwnrfboa^ 'pf bufpqbk( plk •kf`^p+ v qla^ fksbop^ mlo i^ fwnrfboa^ bp q^j_f‹k fk,sbop^ mlo i^ abob`e^- Cf`el ab lqol jlal+ pf ? bp kl pfkdri^o v @? < /* bkqlk,`bp ?@ < h-Ki^j^jlp ^ @ i^ ejrano] ab ? v i^ abpfdk^jlp mlo ?,h- K^ fksbo,p^ ? ,0 q^j_f‹k bp kl pfkdri^o v oq fksbop^ bp ?,
Rbdrfa^jbkqb abjlpqo^jlp nrb bi mol_ibj^ ab i^ abqbojfk^`fŽk bcb`qfs^ abilp bibjbkqlp ab i^ fksbop^ ab rk^ j^qofw kl pfkdri^o bp bnrfs^ibkqb ^ i^ obplir,`fŽk ab j pfpqbj^p ifkb^ibp kl eljld‹kblp-
Rb^ ? < ']ef( kl pfkdri^o v pb^ ? ,0 < '^ef( pr fksbop^- Klp bibjbkqlp ab ?v ? ,0 bpqŠk ifd^alp mlo i^p j1 b`r^`flkbp-
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71 Rn]jobkni]_ekjao heja]hao v i]pne_ao
Rf ^mif`^jlp bi mol`bpl ab F^rpp,Iloa^k+ iibd^jlp ^ i^p obpmb`qfs^pj^qof`bp ^j,mif^a^p
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Di mol`bpl ab bifjfk^`fŽk klp iibs^ ^
K^ j^qofw ab i^ m^oqbabob`e^ ab i^ _^oo^ sboqf`^i bp i^ fksbop^ abpb^a^- K^ ab i^fwnrfboa^ bp i^ j^qofw fabkqfa^a 2 W 2-
Ml bp mob`fpl`lkl`bo ab ^kqbj^kl pf ? bp kl pfkdri^o- Rf? bp oejcqh]n+ mlab,jlp ^•k ^mif`^o bi j‹qlal ab F^rpp,Hloa^k+ mbol l`roob nrb bk bi mol`bpl rklab ilp bibjbkqlp ab i^ af^dlk^i pb `lksfboqb bk `bol+ v kl pboŠmlpf_ib qo^kpcloj^o? bk i^ j^qofw fabkqfa^a-
Tk pfpqbj^ ab j b`r^`flkbp ifkb^ibp `lk j fk`Ždkfq^p+bpqŠobmobpbkq^almlo
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@mif`^kal bi mol`bpl ab F^rpp,Hloa^k ^ `^a^ rkl ab ilp pfpqbj^p pfdrfbkqbp+ abqbojfk^oi^ plir`fŽk dbkbo^i+ pf bufpqb-
0- V * u * 2v < 4
1t , u * 3v < 00,u * v < 2-
1- 2t * 1u * v < 04t * 2u * 2v < 1t* u, w<i-
2- 2t * 1u * v < 04t * 2u * 2v < 16t * 2u * 4v < 2-
3- 2t * 0u * v < 04t * 2u * 2v < 1
6t * 2u * 4v < 2t * u , v < N-
4- 2t , 1u * 4v * q < 0- t * u , 2v * 1q < 15t * u , 3v * 2q < 6-
5- t * u , 2v * q < 41t , u * v , 1q < 16t * u , 6v * 2q < 2-
6- t * u * 1v * 2q * 3r < N1t * 0u * 6v * hhq * 03r < N2t * 2u * 5v * iNr * 04r < N-
7- t , 1u * v * 1q < ,11t * 2u , v , 4q < 83t , u * v , q < 4
4t , 2u * 1v * q < 2-
8- Cbjlpqo^o nrb bi pfpqbj^ t * v * 1v < 1+ 1t , v * 2w < 1+ 4t , v * ]v < 5+ qfbkb pl,ir`fŽk •kf`^ pf ] :< 7- G^ii^o qla^p i^p plir`flkbp `r^kal ] < 7-
0/- ^( Cbqbojfk^o qla^p i^p plir`flkbp abi pfpqbj^
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t , u * v , q < ,1-
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00- Dpqb bgbo`f`fl klp fkaf`^ `Žjl pb abqbojfk^k qla^p i^p j^qof`bp kl pfkdri^obp 1 W 1-Cbjlpqo^o nrb
73 Rn]jobkni]_ekjao heja]haou i]pne_ao
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0- Rf rk^ j^qofw `r^ao^a^ qfbkb rk^ `lirjk^ ab `bolp l rk^ cfi^ ab `bolp+ abjlpqo^o nrbbp pfkdri^o-
Cfan_e_ekor]neko ok^na i]pne_ao 74
1- O^o^ `^a^ rk^ ab i^p molmlpf`flkbp pfdrfbkqbp obi^qfs^p ^ j^qof`bp j W j+ a^o rk^ ab,jlpqo^`fŽk l rk `lkqo^bgbjmil-^( Rf ?@ * @? < N+ bkqlk`bp ?0@1 < @1?0,_( Rf ? X @ plk kl pfkdri^obp+ bkqlk`bp ? * @ bp kl pfkdri^o-`( RI ? v @ plk kl pfkdri^obp+ bkqlk`bp ?@ bp kl pfkdri^o-a( Rf ?* @* X ? * @ plk kl pfkdri^obp+ bkqlk`bp ? + @ bp kl pfkdri^o-b( Rf ?1 < N+ bkqlk`bp ? + h bp kl pfkdri^o-c( Rf bi molar`ql ab g j^qof`bp ?h%,, ?g bp kl pfkdri^o+ `^a^ rk^ ab i^p j^qof`bp ?+ bp
kl pfkdri^o-
2- Rf ? < F zI+e^ii^o rk^ j^qofw kl pfkdri^o N q^i nrb N+/?N < Zz ] zI-Y
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molmfba^a ab nrb ?0 < ?, Cbp`of_fo bk cloj^ `ljmibq^ qla^p i^p j^qof`bp ?* 1 W 1+`lk bibjbkqlp `ljmibglp q^ibp nrb @1 < ?,
4- Rf ?0 < ?* abjlpqo^o nrb &? * h(g < h * '1g , h'?,5- K^ qbloŒ^ab i^ obi^qfsfa^a rqfifw^ rk `lkgrkql ab b`r^`flkbp ab i^ cloj^ t%< ]&t 8+re'*
v&< v+ v&< Y+ p&< ]'p , rt.a1(- @nrŒ r obmobpbkq^i^ sbil`fa^a ab rk l_gbql nrb pb
jrbsb+ a i^ sbil`fa^a ab i^ irw+ v ] < a.Ta1 , r1+ alkab Hsi; a- K^ qo^kpcloj^`fŽknrb ^mif`^ bi sb`qlo _f afjbkpflk^i &t* p' bk 'u&+p%'pb ii^j^ pn]jobkni]_eˆj `a Jknajpv,Rr j^qofw obi^qfs^ ^ i^p _^pbp rpr^ibp pb abpfdk^ `lk J&r' v sfbkb a^a^ mlo
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6- Rf `^j_f^jlp i^p cfi^p mlo i^p `lirjk^p bk rk^ j^qofw ob`q^kdri^o ?* i^ krbs^ j^qofw^pŒl_qbkfa^ pb ii^j^ i^ pn]jolqaop] ab ? v pb abpfdk^ mlo ? q- Olo bgbjmil+ pf qbkbjlp
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8- O^o^ `^a^ rk^ ab i^p molmlpf`flkbp pfdrfbkqbp ^`bo`^ ab i^p j^qof`bp j W j+ a^o rk^abjlpqo^`fŽk l bk pr ird^o rk `lkqo^bgbjmil-^( Rf ? X @ plk loqldlk^ibp+ ? * @ bp loqldlk^i-
31 Rn]jobkni]_ekjao heja]haou i]pne_ao
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0/- K]pne_ao `a F]`]i]n`+ ii^j^a^p ^pŒmlo Z^lnrbp G^a^j^oa '0754,0852(+ plk ^nrbii^pj^qof`bp& j W j `lk i^p molmfba^abp pfdrfbkqbp9
0- B^a^ bibjbkql bp 0 Ž , 0- ]00- B^a^ cfi^+`lkpfabo^a^ `ljl rk sb`qlo ab T,* qfbkb ilkdfqra fdr^i ^ Tj-
00H-Di molar`ql bp`^i^o ab alp cfi^p afpqfkq^p `r^ibpnrfbo^ bp N-K^p j^qof`bp ab G^a^j^oa pb mobpbkq^k bk `fboqlp mol_ibj^p ab dbljbqoŒ^ v bk i^qbloŒ^ab k•jbolp+ v e^k pfal ^mif`^a^p ob`fbkqbjbkqb bk i^ `lafcf`^`fŽk Žmqfj^ m^o^ i^`ljrkf`^`fŽk bpm^`f^i- @ mbp^o ab pr ^m^obkqb pfjmif`fa^a+ mobpbkq^k jr`elp mol_ibj^ppfk obplisbo- Di mofk`fm^i mol_ibj^ kl obprbiql bk bpqbjljbkql bp bi ab abqbojfk^o qlalpilp s^ilobp ab j m^o^ ilp nrb bufpqb rk^ j^qofw ab G^a^j^oa j W j- Dpqb bgbo`f`fl a^fab^ ab rk^ plir`fŽk m^o`f^i-^( Cbqbojfk^o qla^p i^p j^qof`bp ab G^a^j^oa 1 W 1 'e^v bu^`q^jbkqb 7(-_( Dpq^ m^oqb abi bgbo`f`fl bp_lw^ rk^ abjlpqo^`fŽk pbk`fii^ abi pfdrfbkqb qblobj^9Rf ? ao qj] i]pnev `a F]`]i]n` j W j+ oeaj`k j = 1+ ajpkj_ao j ao qj iŠhpelhk `a 3-K^ abjlpqo^`fŽk pb _^p^ bk alp ibj^p jrv pbk`fiilp obi^qfslp ^ ilp sb`qlobp bk bi bpm^,`fl ab afjbkpfŽk j- Cbjlpqo^o `^a^ rkl ab bplp ibj^p v ^mif`^oilp ^ i^p cfi^p ab i^j^qofw ab G^a^j^oa m^o^ abjlpqo^o bi qblobj^-
KDL@ 0- Rf W+W+Y okj ra_pknaoknpkckj]hao `a Tj* oa peaja
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Dk bi Ulirjbk 0 pb fkqolargbolk ilp abqbojfk^kqbp ab pbdrkal v qbo`boloabk`ljl rk^ klq^`fŽk •qfi m^o^ bumobp^o fboq^p cŽojri^p bk cloj^ `ljm^`q^- Qb,`loabjlp nrb bi abqbojfk^kqb ab pbdrkal loabk pb abcfkfŽ jbaf^kqb i^ cŽojri^
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alp `lo`ebqbp(- Di abqbojfk^kqb bp rk jŠiank ^pfdk^al ^ i^ j^qofw v nrb pb`^i`ri^ `lk i^ cŽojri^ '2-0(- O^o^ ^`bkqr^o bpq^`lkbufŽk q^j_f‹k bp`of_fjlp
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Klp abqbojfk^kqbp ab qbo`boloabk pb abcfkfbolk bk bi Ulirjbk 0 bk crk`fŽkab abqbojfk^kqbp ab pbdrkal loabk jbaf^kqb i^ cŽojri^
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Dpqb`^mŒqril`lkpfabo^ bi `^pl jŠp dbkbo^i+bi abqbojfk^kqb ab rk^ j^qofw `r^,ao^a^ ab loabk j m^o^`r^inrfbo bkqbol j 1&90- Mrbpqol mrkql ab sfpq^ `lkpfpqb bkqo^q^obi abqbojfk^kqb `ljl rk^ crk`fŽk nrb ^pfdk^ ^ `^a^ j^qofw `r^ao^a^ ?rk k•jbol ii^j^al abqbojfk^kqb ab ? v nrb pb fkaf`^ mlo abq?- Rb mrbab abcfkfobp^ crk`fŽk mlo jbafl ab rk^ cŽojri^ nrb dbkbo^ifw^'2-0( v '2-1(- S^i cŽojri^bp rk^ prj^ nrb `lkqfbkb j molar`qlp ab bibjbkqlp ab ?, O^o^ s^ilobp do^kabpab j bp^ cŽojri^ bp ab afcŒ`fij^kbgl v pb rp^ ml`l bk i^ moŠ`qf`^-Dp mobcbof_ibbpqraf^o ilp abqbojfk^kqbp abpab lqol mrkql ab sfpq^ nrb mlkd^ ab j^kfcfbpql `lkj^vlo `i^ofa^a prp molmfba^abp bpbk`f^ibp- S^ibp molmfba^abp+fjmloq^kqbp bki^p ^mif`^`flkbp+pb qlj^oŠk `ljl ]teki]o m^o^abcfkfork^ crk`fŽk abqbojfk^kqb-Dk mofk`fmfl+krbpqol mi^k `lkpq^oŠ ab qobpm^oqbp90( Irpqfcf`^o,i^ bib``fŽk ab ilp^uflj^p- 1( Cbar`fo lqo^p molmfba^abpab ilp abqbojfk^kqbp ^ m^oqfoab ilp ^ufl,j^p- 2( Cbjlpqo^o nrb bufpqb rk^ crk`fŽk v pŽil rk^ nrb p^qfpc^d^^ q^ibp^uflj^p-
+'* =^\]RORLJLRmWMNUJNUNLLRmWMNUX\JaRXVJ\YJ[J ^WJO^WLRmWMN]N[VRWJW]N
Dk bi Ulirjbk 0 pb abjlpqoŽ nrb bi molar`ql jfuql ab qobp sb`qlobp?h +?1 +?2 bk C2 mrbab bumobp^opbljl bi abqbojfk^kqb ab rk^ j^qofw `rv^pcfi^pplk ilp sb`qlobp a^alp- @pŒqbkbjlp
alkab ?h < ']00+ ]01+ ]02(& ?1 < ']10+ ]11+ ]12(& f X ?2 < ']20+ ]21+ ]22(&Rf i^p cfi^p plk ifkb^ijbkqb fkabmbkafbkqbpbi molar`ql jfuql kl bp kril:
bi s^ilo ^_plirql abi molar`ql bp fdr^i ^i slirjbk abi m^o^ibibmŒmbalabqbojfk^almlo ilp zobpsb`qlobp ?h +?1 + ?2 Œ Rf i^p cfi^pplk ifkb^ijbkqb abmbkafbkqbpbi mol,ar`ql jfuql bp kril- Dk q^i `^pl ?h +?1 +?2 plk `lmi^k^oflp v bi m^o^ibibmŒmbalabdbkbo^ bk rk^ cfdro^ mi^k^ ab slirjbk kril-
@idrk^p ab i^p molmfba^abpabi molar`ql jfuql grpqfcf`^ki^ bib``fŽk ab ilp^uflj^p m^o^rk^ crk`fŽk abqbojfk^kqb bk bi `^pl k,afjbkpflk^i- O^o^ bpq^_ib`bobpzp molmfba^abpbk czzj^ ^mq^m^o^i^ dbkbo^ifw^`fŽk+lkpfabo^jlp bi molar`qljHuqz+`ljl rk^ crk`fŽk ab ilp qobpsb`qlobp cfi^ ?h +?1 + ?2Œ Cbpfdk^jlp bpq^crk`fŽk mlo `: ^pŒmrbp+
Hqopebe_]_e‰j`a h] aha__e‰ja hko ]teki]o l]n] qj] bqj_e‰j `apaniej]jpa 78
Bbkqobjlp krbpqo^ ^qbk`fŽk bk i^p molmfba^abppfdrfbkqbp9^( Fkikcajae`]` aj _]`] beh]-Olo bgbjmil+ i^ eljldbkbfa^a bk i^ mofjbo^
cfi^ bpq^_ib`bnrb
_( ?`epere`]` aj _]`] beh]-Olo bgbjmil+ i^ ^afqfsfa^a bk i^ pbdrka^ cfi^Rfdkfcf`^nrb
m^o^qlal sb`qlo B-b( Ch lnk`q_pk ietpk ao jqhk pf `ko `a h]o beh]ookj ecq]hao-a( Lkni]hev]_e‰j9
`&e*f*g' < 0+ alkab e< '0+/+ N(+ f < '/+0+ N(+ g < '/+/+0(
B^a^ rk^ ab bp^pmolmfba^abpmrbab `ljmol_^opb cŠ`fijbkqb ^ m^oqfoab i^pmolmfba^abpab ilp molar`qlp bp`^i^o v sb`qlof^i- @idrk^p plk prdbofa^p mlo i^obi^`fŽk dblj‹qof`^ bkqobbi molar`ql jfuql v bi slirjbk abi m^o^ibibmŒmbalab,qbojfk^al mlo ilp sb`qlobp dblj‹qof`lp @i+?1 +?]- Di pfdkfcf`^al dblj‹qof`lab i^ molmfba^a ^afqfs^ _( bk rk `^pl m^oqf`ri^obp ab bpmb`f^ifkqbo‹p-Rf qlj^,jlp b < @i bk _( bi pbdrkal q‹ojfkl abi pbdrkal jfbj_ol bp `bol bk sfoqraab b(+v i^ obi^`fŽk _( pb qo^kpcloj^ bk
'2-2(
Ulirjbk < `&?*, ?*, @I Ulirjbk < `&?*,?* * ?!?**'
EHFTQ@ 2-0Gjpanlnap]_e‰jcaki†pne_] `a h] lnklea`]` `'?+ ?! @i( < `'?! ?+ * -?! @i(&Jko `ko
l]n]hahal‡la`ko peajaj rkhŠiajao ecq]hao-
4+ Bapaniej]jpao
Dpq^molmfba^a pb mlkb ab j^kfcfbpql bk i^ cfdro^ 2-0 nrb obmobpbkqrk m^o^ibib,mŒmbalabqbojfk^al mlo ?h&@1 +?]+ X lqol abqbojfk^al mlo @i+?h * ?1 +?]-K^ fdr^ia^a '2-2( bpq^_ib`bnrb bplp alp m^o^ibibmŒmbalpqfbkbksli•jbkbp fdr^ibp-Fblj‹qof`^jbkqb biil bp bsfabkqb v^ nrb ilp m^o^ibibmŒmbalpqfbkbk ^iqro^p fdr^ibpv _^pbp ab fdr^i Šob^-
2-2 Blkgrkql ab ^uflj^p nrb abcfkbk rk^ crk`fŽk abqbojfk^kqb
K^p molmfba^abp abi molar`ql jfuql jbk`flk^a^p bk i^ pb``fŽk ^kqboflomrbabk dbkbo^ifw^opblk c^`fifa^a v rqfifw^opb ljl ^uflj^p m^o^ abqbojfk^kqbpab loabk j, Rf ? < &]ez'bp rk^ j^qofw j W j `lk bibjbkqlp ob^ibp l `ljmibglp&+abpfdkbjlp prp cfi^pmlo @i +--- +?j ‹ @pŒ+i^ cfi^ f,‹pfj^ ab ? bp rk sb`qlo bk Cja^al mlo
Blkpfabobjlp bi abqbojfk^kqb `ljl rk^ crk`fŽk ab i^p j cfi^p@i +--- *?j v ab,pfdkbjlp pr s^ilo mlo `'?h+ --- +?j( l mlo abq?-
CDEHMHBHˆM @WHNL…SHB@ CD TM@ ETMBHˆM CDSDQLHM@MSD- Sj] bqj_e‰j _kjr]hknao na]haok _kilhafko `+ `abeje`] l]n] _]`] j _kilkjajpao kn`aj]`]o `ahko ra_pknao ?h* ,,, * @k aj Cj+ oa `ajkiej] bqj_e‰j `apaniej]jpa `a kn`aj joe o]peob]_ahko oecqeajpao]teki]o _q]haomqean]mqa oa]j hko ra_pknao?h* ,,, *?j
v b aj Cj9@WHNL@ 0- GNLNFDMDHC@C DM B@C@ EHK@- Qe oa iqhpelhe_] h] g,†oei] beh]
?g lkn qj ao_]h]np+ah `apaniej]jpa mqa`] p]i^e†j iqhpelhe_]`k lkn p9
`' --- +p?g+ ŒŒŒ( < p`' --- +?g+ ŒŒŒ(-
@WHNL@ 1- @CHSHUHC@C DM B@C@ EHK@- N]n] _]`] r]hkn `a g pajaiko
@WHNL@ 2- DK CDSDQLHM@MSD RD @MTK@ RH CNR EHK@R BT@KDRPTHDQ@ RNM
HFT@KDR9
`&?h, * ,,, *?j' < N oe ?e < ?h 'l]n] _eanpkoe v f p]haomqa e<0<f,'
@WHNL@ 3- DK CDSDQLHM@MSD CD K@ L@SQHY HCDMSHC@C DR HFT@K ?h9
`'0h +--- +Gj( < 0+ oeaj`k 0g ah g,†oeik ra_pkn _kkn`aj]`k qje`]` -
Akjfqjpko `a ]teki]o mqa `abejaj qj] bqj_e‰j `apaniej]jpa 80
Klp alp mofjbolp ^uflj^p bpq^_ib`bk nrb bi abqbojfk^kqb ab rk^ j^qofw bprk^ crk`fŽk ifkb^i ab `^a^ rk^ ab prp cfi^p- Blk cob`rbk`f^ bpql pb bumobp^af,`fbkal nrb bi abqbojfk^kqb bp rk^ crk`fŽk iqhpeheja]h ab prp cfi^p- @mif`^kalobfqbo^a^jbkqb i^ ifkb^ifa^a ^ i^ mofjbo^ cfi^ mlabjlp bp`of_fo
pfbkal p**,,, *pl bp`^i^obp v B0 +’’’ +Al sb`qlobp `r^ibpnrfbo^ ab Cj-@ sb`bp pb rqfifw^ rk^ sbopfŽk m^oqf`ri^o abi ^uflj^ 29
@WHNL@ 2&- DK CDSDQLHM@MSD RD @MTK@ RH CNR EHK@R BNMRDBTSHU@R RNM
HFT@KDR9
pf ?g < ?g*0 m^o^rk `fboql g < 0+1+--- +j , 0-
Rb abjrbpqo^ jŠp ^abi^kqb nrb m^o^rk j a^al bufpqbrk^ v pŽil rk^ crk`fŽk` nrb p^qfpc^`bilp ^uflj^p 0+1+ 2&X 3- Di qblobj^ nrb pfdrb a^ •kf`^jbkqb i^pmolmfba^abpab ilp abqbojfk^kqbp abar`fa^p ^ m^oqfoab ilp ^uflj^p 0+ 1+ X 2&-Tk^ ab bp^p molmfba^abpbp bi ^uflj^ 2- Rb l_pbos^oŠ nrb bi ^uflj^ 3 kl pbrqfifw^ bk i^ abjlpqo^`fŽk ab bpqbqblobj^- S^i l_pbos^`fŽk pboŠab rqfifa^a jŠp^abi^kqb `r^kal abjlpqobjlp i^ rkf`fa^a ab i^ crk`fŽk abqbojfk^kqb-
SDNQDL@ 2-0- Sj] bqj_e‰j `apaniej]jpa mqa o]peob]c]hko ]teki]o 0+1+X2&peaja ]`ai…o h]o oecqeajpaolnklea`]`ao9
^( Ch `apaniej]jpa oa ]jqh] oe ]hcqj] beh]ao k8
oe ?g < M l]n] ]hcŠj g-
_( Ch`apaniej]jpa _]i^e] `a oecjk oeoa ejpan_]i^e]j `ko beh]o_kjoa_qper]o9
`&,,, * ?g+ ?g*0& ŒŒŒ( < +`& ,,, * ?g*0& ?g+ ŒŒŒ(-
b( Ch `apaniej]jpa _]i^e] `a oecjk oe `ko beh]o_q]haomqean]?e v ?z _kje <0< f oa ejpan_]i^e]j-
a( Ch `apaniej]jpa oa ]jqh] oe okj ecq]hao`ko beh]o_q]haomqean]9
oe ?e < ?z l]n] qj l]n e*{+_kj e <Nf -
b( Ch `apaniej]jpa oa ]jqh] oe oqo beh]ookj heja]hiajpa `alaj`eajpao-
4- Bapaniej]jpao
Baikopn]_e‰j- O^o^ abjlpqo^o ^( qljbjlp pfjmibjbkqb p < N bk bi ^ufl,j^ 0- O^o^ abjlpqo^o _(+ pb^ @ rk^ j^qofw nrb qbkd^ i^p jfpj^p cfi^p nrb ?bu`bmql i^p cfi^pg v g * 0- Rb^k i^p cfi^p@* v @g)h fdr^ibp ^ ?g * ?g)h% Dkqlk,`bp pbd•k bi ^uflj^ 2&abo P < N - @pŒmlabjlp bp`of_fo
@mif`^kal i^ molmfba^a ^afqfs^ ^ i^p cfi^pg v g * 0 mlabjlp bp`of_fobp^ fdr^ia^abk i^ cloj^9
`& ,,, * ?g* ?g* ,,, ' * `& ,,, * ?g* ?g)/* ,,, ' * `& * ?g) < ?g* '
) `& * ?g)/* ?g) < ' < N-
Klp q‹ojfklp mofjbol v `r^oql plk krilp bk sfoqra abi ^uflj^ 2&-Krbdl bi pbdrkal v qbo`boq‹ojfklp plk lmrbpqlp+il nrb abjrbpqo^ _(+
O^o^ abjlpqo^o b( mlabjlp prmlkbo nrb e ; :- Rb mrbabk fkqbo`^j_f^o i^pcfi^p@v ?z bcb`qr^kal rk k•jbol fjm^o ab qo^kpmlpf`flkbpab cfi^p_kjoa_qper]o-Oofjbol qo^kpmlkbjlp i^ cfi^ ?z pr`bpfs^jbkqb `lk i^p cfi^p?z+h * ?z+0 * ,,, * ?e Œ
Dpql bufdb : , e qo^kpmlpf`flkbp-Krbdl i^ cfi^ ?e i^ qo^kpmlkbjlp pr`bpfs^jbkqb`lk i^p cfi^p?e)/ * ?e)1 + ŒŒŒ + ?z+h , Dpql prmlkb: , e + 0 qo^kpmlpf`flkbp-B^a^qo^kpmlpf`fŽkl fkqbo`^j_fl ab cfi^p `lkpb`rqfs^p fksfboqb bi pfdkl abi abqbojf,k^kqb- Di k•jbol qlq^i ab `^j_flp ab pfdkl bp mrbp &9+e')&f+e+/';0&f+e'+/nrb bp rk k•jbol eil]n+ il nrb abjrbpqo^ `(-
O^o^ abjlpqo^o a(+ pb^ @ i^ j^qofw l_qbkfa^ fksfoqfbkal bk ? i^p cfi^p ?zv ?z, Orbpql nrb ?e < ?z* pb qfbkb @ < ? X mlo q^kql abq@ < abq?, Obol+pbd•k b( abq@< , abq? , Olo `lkpfdrfbkqb abq? < N-
O^o^abjlpqo^o b( prmlkd^jlp nrb bufpqbkilp bp`^i^obp ./ * ‹‹‹ * aj +kl qlalpkrilp+ q^ibp nrb Jy;/ _g?g < M, Dkqlk`bp qla^ cfi^ ?g `lk _e,;/; N mrbab bumob,p^opb`ljl `lj_fk^`fŽk ifkb^i ab lqo^p cfi^p- O^o^ j^vlo pbk`fiibw+prmlkd^jlpnrb ?h bp `lj_fk^`fŽk ifkb^i ab i^p lqo^p+mlo bgbjmil ?h < Jy<1pyg% Dk sfoqraab i^ ifkb^ifa^a ab i^ mofjbo^ cfi^ qbkbjlp
Obol `^a^ q‹ojfkl `&?g * ?0 * ,,, * @k( ab i^ •iqfj^ prj^ bp `bol v^ nrb ?g bpfdr^i mlo il jbklp ^ rk^ ab i^p cfi^p ?1 +ŒŒŒ+?j‹ Krbdl qla^ i^ prj^ bp `bol-Rf i^ cfi^ ?e bp rk^ `lj_fk^`fŽk ifkb^i ab i^p lqo^p cfi^p+o^wlk^jlp bk cloj^^kŠild^+ rqfifw^kal i^ ifkb^ifa^a bk i^ cfi^ e- Dpql abjrbpqo^ b(-
A…h_qhka `apaniej]jpao 4.
+', 6jUL^UXMNMN]N[VRWJW]N\
@i iibd^o ^nrŒmrbab pbofkpqor`qfsl `^i`ri^o ^idrklp abqbojfk^kqbp+rqfifw^k,al q^k pŽil ilp ^uflj^p v i^p molmfba^abpabi qblobj^ 2-0+ prmlkfbkal pfbjmobnrb i^p crk`flkbp abqbojfk^kqbp bufpqbk-Dk `^a^ rkl ab ilp bgbjmilp nrb pfdrbkkl ^mif`^jlp bi ^uflj^ 3 e^pq^ bf cfk^i abi `Ši`ril-
DIDLOKN 0- Bapaniej]jpa `a qj] i]pnev 1 W1- Prbobjlp abjlpqo^o nrb
Dp`of_^jlp ilp sb`qlobp cfi^ `ljl `lj_fk^`flkbp ifkb^ibp ab ilp sb`qlobp `lloab,k^alp rkfq^oflp e < '0+ N( Xg< 'N+0( 9
Tqfifw^kal i^ ifkb^ifa^a bk i^ mofjbo^ cfi^ qbkbjlp
TqfifwŠkali^ krbs^jbkqb bk i^ pbdrka^ cfi^ pb l_qfbkb
`&e* ?0' < `&e* ]0/e * ]00f' < ]0/ `&e* e' * ]00 `&e*f' < ]00 `&e*f'*
mrbpql nrb ` &e*e' <N- Cbi jfpjl jlal bk`lkqo^jlp
Olo q^kql l_qbkbjlp
Obol ` &e*f' < 0 pbd•k bi ^uflj^ 3+ `lk il nrb `&?/* ?0' < ]//]00 + ]/0]0/ `ljlpb ^cfojŽ-
Dpqbo^wlk^jfbkql abjrbpqo^ nrb pf rk^ crk`fŽk abqbojfk^kqb bufpqbm^o^i^p j^qof`bp 1 W1+ ab_b qbkbo kb`bp^of^jbkqb i^ cloj^ '2-3(- Qb`Œmol`^jbkqb+bp cŠ`fi `ljmol_^o nrb bp^ cŽojri^ abcfkb+bcb`qfs^jbkqb+ rk^ crk`fŽk abqbojf,k^kqb ab loabk 1- Olo `lkpfdrfbkqb ebjlp abjlpqo^al nrb bufpqbrk^ v pŽil rk^crk`fŽk abqbojfk^kqb ab loabk 1-
83 Bapaniej]jpao
DIDLOKN 1- Bapaniej]jpa `a qj] i]pnev `e]ckj]h- Tk^ j^qofw `r^ao^a^ab i^ cloj^
54
pb abkljfk^ i]pnev `e]ckj]h- B^a^ bibjbkql ]ef kl mboqbkb`fbkqb i^ af^dlk^imofk`fm^i+&e;/; g( bp `bol- U^jlp ^ abjlpqo^o nrb i^ abqbojfk^kqb ab ? bp fdr^i^i molar`ql ab ilp bibjbkqlp mboqbkb`fbkqbp i^ af^dlk^i
'2-4(
K^ cfi^ g ab ? bp bi molar`ql ab rk bp`^i^o mlo bi g,†oeik sb`qlo `lloabk^alrkfa^a+ ?g < ]gg e-@mif`^kal obmbqfa^jbkqb i^ molmfba^a ab eljldbkbfa^a iibd^jlp ^
Dpq^ cŽojri^ mrbab bp`of_fopbbk i^ cloj^
abq ? < ^k --- ]jj abq 0+
bk alkab / bp i^ j^qofw fabkqfa^a- Di ^uflj^ 3 klp af`b nrb abq / < 0+`lk il nrbl_qbkbjlp '2-4(-
DIDLOKN 2- Bapaniej]jpa `a qj] i]pnev pne]jcqh]n oqlanekn- Tk^ j^qofw`r^ao^a^ ab i^ cloj^
!k !01 !Hk
N !11 !1j
q<
pb ii^j^ j^qofw qof^kdri^o prmboflo- Slalp ilp bibjbkqlp pfqr^alp mlo ab_^gl ab
A…h_qhka `apaniej]jpao 40
i^ af^dlk^i mofk`fm^iplk krilp- U^jlp ^ abjlpqo^o nrb bi abqbojfk^kqb ab rk^q^i j^qofw bp fdr^i ^i molar`ql ab ilp bibjbkqlp ab i^ af^dlk^i mofk`fm^i+
abq S < Tk S11 ŒŒŒSjj ‹
Cbjlpqo^jlp mofjbol nrb abq S < N pf ^id•k bibjbkql q| ab i^ af^dlk^imofk`fm^ibp Szz < N- Rf bi •iqfjl bibjbkql ab bp^ af^dlk^i q!! bp `bol+ i^ •iqfj^cfi^ bp N v abq T < N bk sfoqra abi qblobj^ 2-0 ^(- Rrmlkd^jlp+ ^elo^+ nrb pb^kril ^id•k bibjbkql Szz 'kl mob`fp^jbkqb bi Sjj', Rb^ mlo bgbjmil S1-1 < N- Dkqlk,`bp `^a^ rkl ab ilp j , 0 sb`qlobp cfi^ T1 + ŒŒŒ + Sj qfbkbk prp alp mofjbolp `ljlmlkbkqbp krilp- Olo q^kql bplp sb`qlobp dbkbo^k rk pr_bpm^`fl `rv^ afjbkpfŽkbp mlo il jbklp j , 1- Cb ^eŒnrb bp^p j , 0 cfi^p'v mlo q^kql pk`]o i^p cfi^p(pb^kifkb^ijbkqb abmbkafbkqbp-Rbd•k bi qblobj^ 2-0 b(+ abq S < N- Cbi jfpjl jlalpb abjrbpqo^ nrb abq S < N+pf bp `bol `r^inrfbo bibjbkql ab i^ af^dlk^i mofk,`fm^i-
U^jlp ^ abjlpqo^o ^elo^ bi `^pl dbkbo^i-Dp`of_^jlp i^ mofjbo^ cfi^ TG`ljlrk^ prj^ ab alp sb`qlobp,cfi^+
pfbkal TG < ZTii + N+--- +N\ X TG < ZN+T01 + ’’’ + S/j[, Dk sfoqra ab i^ ifkb^,ifa^a bk i^ mofjbo^ cfi^ qbkbjlp
abq S < abq'UH+S1+ ŒŒŒ+ Sj( * `ap'Tw+ S1+ ŒŒŒ+ Sj(-
Obol abq'Uz+ S1 + ŒŒŒ + Sj( < N v^ nrb ‹pqb bp bi abqbojfk^kqb ab rk^ j^qofwqof^kdri^o prmboflo `lk rk bibjbkql kril bk i^ af^dlk^i mofk`fm^i-Krbdl qbkbjlp
'2-5( abq S < abq &TG%S1+ ŒŒŒ+ Sy(-
So^qbjlp ^elo^ bi sb`qlo,cfi^ T1 bk cloj^ ^kŠild^+ bumobpŠkalil `ljl rk^ prj^+
pfbkal
T1 < ZN+S11+ N+--- +N\ v T y < ZN+N+S01% ‹‹‹ * q0j[ ‹
G^d^jlp bpql bk bi pbdrkal jfbj_ol ab '2-5( v ^mifnrbjlp i^ ifkb^ifa^a bk i^pbdrka^ cfi^ `lk il nrb l_qbkbjlp
'2-6( abq S < abq 'UH&T1+ S2+ ŒŒŒ+ Sj(+
41 Bapaniej]jpao
v^ nrb `ap'T+ +Ty +S2 + ŒŒŒ+ Sj( < N- Qbmfqfbkal bi o^wlk^jfbkql m^o^ `^a^ rk^ab i^p cfi^p nrb pfdrbk bk bi pbdrkal jfbj_ol ab '2-6( l_qbkboklp cfk^ijbkqb
alkab 'T+ +T1 + ŒŒŒ + Tj( bp rk^ j^qofw af^dlk^i `lk ilp jfpjlp bibjbkqlp nrb Sbk i^ af^dlk^i mofk`fm^i- Olo `lkpfdrfbkqb+ pbd•k bi bgbjmil 1+qbkboklp
abq S < SjS11&! Sjj+
`lokl abpbŠ_^jlp abjlpqo^o-DIDLOKN 3- A…h_qhklkn ah i†pk`k `a E]qoo,hkn`]j- Di j‹qlal ab bifjf,
k^`fŽk ab F^rpp, I ^oa^k m^o^ obplisbo pfpqbj^p ab b`r^`flkbp ifkb^ibp bp q^j_f‹krkl ab ilp jbglobp j‹qlalp m^o^ bi `Ši`ril ab abqbojfk^kqbp- Qb`loabjlp nrbbi j‹qlal `lkpfpqb bk i^ ^mif`^`fŽk ab qobp qfmlp ab lmbo^`flkbp ^ i^p cfi^p ab i^j^qofw9
0( Rn]jolkoe_e‰j `a `ko beh]o-1( Kqhpelhe_]_e‰j `a pk`ko hko ahaiajpko `a qj] beh] lkn qj ao_]h]n jk jqhk-2( ?`e_e‰j ] qj] beh] `ah lnk`q_pk `a kpn] lkn qj ao_]h]n-
Dcb`qr^kal rk^ v lqo^ sbw bp^p lmbo^`flkbp ab j^kbo^ pfpqbjŠqf`^ mlaboklp qo^kp,cloj^o `r^inrfbo j^qofw `r^ao^a^ ? bk rk^ j^qofw qof^kdri^o prmboflo S `rvlabqbojfk^kqb p^_boklp v^ `^i`ri^o- Dp cŠ`fi abqbojfk^o i^ obi^`fŽk bkqob abq ?v abq S, B^a^ sbw nrb pb ob^ifw^ i^ lmbo^`fŽk 0( bi abqbojfk^kqb `^j_f^ ab pfdkl-B^a^ sbw nrb pb bcb`q•^ 1( `lk rk bp`^i^o a ;b%; N+ bi abqbojfk^kqb pb jriqfmif`^mlo _- Rf pb bcb`q•^ 2( bi abqbojfk^kqb kl s^oŒ^-Olo `lkpfdrfbkqb+ pf i^ lmbo^`fŽk 0(pb bcb`q•^ m sb`bp v pf Ah * ‹‹‹ * _m plk ilp c^`qlobp bp`^i^obp nrb pb rqfifw^k bki^ lmbo^`fŽk 1(+ pb qfbkb
'2-7(
N_pbosbjlp krbs^jbkqb nrb bpq^ cŽojri^ bp `lkpb`rbk`f^ q^k pŽil ab ilp qobpmofjbolp ^uflj^p- Rr abjlpqo^`fŽk kl abmbkab abi ^uflj^ 3-
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Dk bi bgbjmil 2 ab i^ pb``fŽk ^kqboflo pb abjlpqoŽ nrb ilp ^uflj^p 0+ 1+ X 2fjmif`^k i^ cŽojri^ abq S < SjSvv ‹‹‹ Sjj abq h, Blj_fk^kal ‹pq^ `lk '2-7( sbjlpnrb m^o^ qla^ j^qofw ?+jtj+ bufpqb rk bp`^i^o a 'nrb abmbkab ab ?( q^i nrb
'2-8(
Cfan_e_eko 42
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SDNQDL@ 2-1- SDNQDL@ CD TMHBHC@C O@Q@ KNR CDSDQLHM@MSDR- Qa] `qj] bqj_e‰j mqa o]peob]c] hko _q]pnk ]teki]o mqa _]n]_panev]j qj] bqj_e‰j `apan,iej]jpa `a kn`aj j+ u oa] b kpn] bqj_e‰j mqa o]peob]c] hko ]teki]o 0+1 W 2- Cj,pkj_ao+ ahace`k qj oeopai] _q]hmqean] `a ra_pknao @i +--- +?! `ah aol]_ek j,`e,iajoekj]h pajaiko
'2-0/(
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Nnk`q_pk `a `apaniej]jpao- 44
5- Rb^k p+.! c! d+ `r^qol crk`flkbp abofs^_ibp bk rk fkqbos^il &]*^', Rb abcfkb
m^o^ `^a^ t ab &]* ^', Cbjlpqo^o nrb
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8- Rb^k S v T alp j^qof`bp qof^kdri^obp prmboflobp j Wj-^( Cbjlpqo^o nrb S * T v ST plk j^qof`bp qof^kdri^obp prmboflobp-_( Cbjlpqo^o nrb abq &ST' < 'abq T('abq T',b( Rf abq SzN abjlpqo^o nrb bufpqb rk^ j^qofw qof^kdri^o prmboflo S+%q^i nrb SS+%;h*v abar`fo nrb abq &S+%'< i.abq S,
0/- B^i`ri^o abq ?* abq &?+%'*W? ,0 m^o^ i^ pfdrfbkqb j^qofw qof^kdri^o prmboflo9
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0// Bapaniej]jpao
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Dk i^ abjlpqo^`fŽk ab i^ cŽojri^ m^o^ bi molar`ql pb e^`b rpl ab rk^pbk`fii^ obi^`fŽk nrb bufpqbbkqobi^p cfi^pab ?@ v i^p ab ?, K^ bpq^_ib`bjlp `ljlrk ibj^- Bljl ab `lpqrj_ob+ abpfdk^jlp `lk ?e i^ cfi^ e ab i^ j^qofw ?,
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Olo q^kql i^ cfi^ f+Ae+bp i^ j^qofw cfi^
Obol ‹pq^ bp q^j_f‹k bi obpriq^al ab i^ jriqfmif`^`fŽk ab i^ j^qofw cfi^ ?e mlo @*v^ nrb
Olo `lkpfdrfbkqb Az < ?@* il nrb abjrbpqo^ bi ibj^
Bapaniej]jpa `a h] i]pnev ejrano] `a qj] i]pnev jk oejcqh]n /./
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L^kqbkd^jlp @ cfg^b fkqolarw`^jlp rk^ crk`fŽk b abcfkfa^ mlo i^ cŽojri^
K^ fdr^ia^a nrb abpb^jlp abjlpqo^o bpq^_ib`b nrb
'2-02(
Dp ^elo^ ^prkql cŠ`fi `ljmol_^o nrb b p^qfpc^`bilp ^uflj^p 0+1 X 2 obi^qfslp ^rk^ crk`fŽk abqbojfk^kqb+ `lk il nrb+ bk sfoqra abi qblobj^ ab rkf`fa^a+ i^fdr^ia^a '2-02( bp sŠifa^ m^o^`r^inrfbo j^qofw ?- Dpql `ljmibq^ i^ abjlpqo^`fŽk-
Dk i^p alp pb```flkbp nrb pfdrbk pb bumlkbk ^mif`^`flkbp ab i^ cŽojri^ abimolar`ql-
2-7 Cbqbojfk^kqb ab i^ j^qofw fksbop^ ab rk^ j^qofw kl pfkdri^o
Qb`loabjlp nrb rk^ j^qofw `r^ao^a^ ? pb ii^j^ kl pfkdri^o pf qfbkb rk^fksbop^ @mlo i^ fwnrfboa^ q^i nrb @? < H-Rf bufpqbrk^ fksbop^ mlo i^ fwnrfboa^bp •kf`^ v bp q^j_f‹k fksbop^ mlo i^ abob`e^+ ?@ < h- Cbpfdkbjlp i^ fksbop^ mlo@,i- K^ obi^`fŽk bkqobabq? v abq@,i bp i^ nrb mlaŒ bpmbo^opb-
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'2-03( abq@,0< ]0]-abq ?
0/1 Bapaniej]jpao
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2-8 Cbqbojfk^kqbpb fkabmbkabk`f^ab sb`qlobp
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SDNQDL@ 2-5- Sj _kjfqjpk `a j ra_pknao@i+ --- +?j `a qj aol]_ek j,`e,iajoekj]h ao heja]hiajpa ej`alaj`eajpa oe v o‰hkoe `'?h * ‹‹‹ *?j' ;/; N-
Baikopn]_e‰j- X^ abjlpqo^jlp bk bi qblobj^ 2-1 b( nrb i^ abmbkabk`f^ifkb^i fjmif`^ `'?h* ‹‹‹ * ?j( < N- O^o^ abjlpqo^o bi ob`Œmol`l+pb prmlkb nrb@i +--- +? ŒŒplk ifkb^ijbkqb fkabmbkafbkqbpv pb morb_^ nrb `'?h * ‹‹, * ?j( ;/; N-
Cbpfdkbjlp `lk Tj bi bpm^`fl ifkb^i ab i^p k,mHp ab bp`^i^obp- Orbpql nrb@i +--- +? ŒŒplk j bibjbkqlp fkabmbkafbkqbpbk rk bpm^`fl k,afjbkpflk^i+ cloj^,oŠk rk^ _^pb m^o^ Tj‹ Rbd•k bi qblobj^ 1-01 bufpqbrk^ qo^kpcloj^`fŽk ifkb^iR9Tj y Tj nrb ^mif`^ bplp j sb`qlobp bk ilp sb`qlobp `lloabk^a^p rkfa^a+
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I-qN Cbqbojfk^kqb ab rk^ j^qofw af^dlk^i bk _ilnrbp
Tk^ j^qofw `r^ao^a^ b ab i^ cloj^
Bapaniej]jpa `a qj] i]pnev `e]ckj]h aj ^hkmqao 0/2
bk i^ nrb ? v A plk j^qof`bp `r^ao^a^p v `^a^ N obmobpbkq^rk^ j^qofw ab `bolp+pb abkljfk^ i]pnev `e]ckj]h aj ^hkmqao`lk alp _ilnrbp ? v @-Bljl bgbjmilpb^ i^ j^qofw 4 W4-
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'2-04( abq Zz z\ < 'abq ?'& abq @' ,
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Y? M[ < Y? M[Yhj /HM @ M n9 M @
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'2-05( Y? M[ Y? M[ YGj M[abq < abq abq ’M @ M n: M @
0/3 Bapaniej]jpao
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D‰niqh]ol]n] `ao]nnkhh]n `apaniej]jpao 0/4
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alkab @*b+C plk j^qof`bp `r^ao^a^p v N bp rk^ j^qofw ab `bolp-6- @mif`^obi qblobj^ 2-5 m^o^abqbojfk^o pf ilp pfdrfbkqbp lkgrkqlp ab sb`qlobp plk ifkb^i,
jbkqb abmbkafbkqbpl fkabmbkafbkqbp-
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2-01 EŽojri^p m^o^abp^oolii^o abqbojfk^kqbp- Lbklobp v `lc^`qlobp
Ml ebjlp abjlpqo^al qla^sŒ^ i^ bufpqbk`f^ ab rk^ crk`fŽk abqbojfk^kqb+bu`bmql bk bi `^pl 1 W1- Dk bpq^pb``fŽk rqfifw^jlp i^ ifkb^ifa^a v bi qblobj^ abrkf`fa^a m^o^abjlpqo^o nrb+ pf bufpqbkabqbojfk^kqbp+mrbabk `^i`ri^opb jbaf^kqbrk^ cŽojri^ nrb bumobp `r^inrfbo abqbojfk^kqb ab loabk j `ljl rk^ `lj_f,k^`fŽk ifkb^i ab abqbojfk^kqbp ab loabk j+h, K^ fdr^ia^a '2-1( ab i^ pb``fŽk 2-0bp rk bgbjmil ab bp^ cŽojri^ bk bi `^pl 2 W2- K^ cŽojri^ dbkbo^i prdbofoŠ rkj‹qlal m^o^ abjlpqo^o mlo fkar``fŽk i^ bufpqbk`f^ ab crk`flkbp abqbojfk^kqbp-
Sla^ cfi^ ab rk^ j^qofw ?* j Wj+mrbab bumobp^opbljl rk^ `lj_fk^`fŽkifkb^i ab ilp j sb`qlobp `lloabk^alp rkfa^a 0/ * ‹‹‹ * Gj- Olo bgbjmil+ i^ mofjbo^cfi^ ?h mrbab bp`of_fopb`ljl pfdrb9
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0/5 Bapaniej]jpao
Olo `lkpfdrfbkqb m^o^ `^i`ri^o abq? _^pq^ `^i`ri^o `'Gz +?1 + ŒŒŒ + ?j( m^o^ `^a^sb`qlo `lloabk^al rkfa^a Hz,
Tqfif`bjlp i^ klq^`fŽk ?yz m^o^obmobpbkq^oi^ j^qofw l_qbkfa^ ab ? obbjmi^,w^kal i^ mofjbo^ cfi^ ?h mlo bi sb`qlo rkfq^ofl Hz, Olo bgbjmil+ pf j < 2 bufpqbkqobpj^qof`bp ab bpb qfml9
Z0 N /g
?y0 < ]10 ]11 ]12 +
]20 ]21 ]2
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?y1 < ]10 ]11 ]12 +
]20 ]21 ]2
N
N_pbosbjlp nrb abq?yz < `e[z *?1 + ŒŒŒ+?j(- K^ fdr^ia^a '2-06( mrbab ^elo^bp`of_fopbbk i^ cloj^
'2-07(j
abq ? < y]/e abq?ye&fy/
Dpq^ bp rk^ b‰niqh] `a `ao]nnkhhk: v bk bii^ pb bumobp^bi abqbojfk^kqb ab ?`ljl rk^ `lj_fk^`fŽk ifkb^i ab ilp bibjbkqlp ab pr mofjbo^ cfi^-
Di o^wlk^jfbkql rqfifw^al m^o^abar`fo '2-07( mrbab ^mif`^opb^ i^ cfi^ g bkird^o ab e^`boil `lk i^ mofjbo^- Di obpriq^al bp rk^ cŽojri^ ab abp^ooliil bkcrk`fŽk ab ilp bibjbkqlp ab i^ cfi^ g,
SDNQDL@ 2-7- CDR@QQNKKN ONQ BNE@BSNQDR- Qa] ?&gzh] i]pnev k^paje`]`a h] i]pnev ? ]h oqopepqenh] beh]g `a ?g lkn ah ra_pkn _kkn`aj]`k qje`]` Hz-Qa k^peaja ajpkj_ao h] b‰niqh] `a `ao]nnkhhk
'2-08(j
abq ? < z ]ge abq ?yefy/
mqa atlnao] ah `apaniej]jpa `a ? _kik _ki^ej]_e‰j heja]h `a hko ahaiajpko `ah] beh]g- Ch jŠiank abq?ye oa hh]i] _ke]_pkn k ]`fqjpk `ah ahaiajpk ]gz-
Dk bi qblobj^ nrb pfdrb abjlpqo^objlp nrb `^a^ `lc^`qlo bp+p^isl bi pfdkl+fdr^i ^i abqbojfk^kqb ab rk^ j^qofw ab loabk j , 0 - Dp^p j^qof`bp pb ii^j^kiajknao-
CDEHMHBHˆM- B]`] qj] i]pnev _q]`n]`] ? `a kn`aj j :991+ h] i]pnev _q],`n]`] `a kn`aj j,0 k^paje`] oqlneieaj`k h] beh]g v h] _khqij]f `a ? oa hh]i]iajkn g+f`a ? v oa `aoecj] lkn ?gz -
DSDLOKN- Tk^ j^qofw ? < ']gz( ab loabk 2 qfbkb krbsb jbklobp- Sobp abbii^p plk
D‰niqh]ol]n] `ao]nnkhh]n`apaniej]jpao 0/6
K^ fdr^ia^a '2-1( bumobp^bi abqbojfk^kqb ab rk^ j^qofw 2 W2 `ljl rk^`lj_fk^`fŽk ifkb^i ab ilp abqbojfk^kqbp ab bp^p qobpjbklobp- K^ cŽojri^ mrbabbp`of_fopb ljl pfdrb9
abq? < ^k abq@r , ^01 abq @i1* ]02 abq?02Œ
Di pfdrfbkqbqblobj^ buqfbkab bp^ cŽojri^ ^i `^pl j Wj m^o^`r^inrfbo j y 1-
SDNQDL@ 2-8- CDR@QQNKKN ONQ K@R LDMNQDR BNQQDRONMCHDMSDR @ K@ EHK@
g, N]n] _q]hmqeani]pnev ?+ jr:j+ j y 1+ah_kf]_pkn `a ]g:aop…nah]_ekj]`k _kjh] iajkn ?g: lkn h] b‰niqh]
'2-1/(
Nkn _kjoecqeajpa+ah `ao]nnkhhk`ah abq? aj bqj_e‰j `a hko ahaiajpko `a h] beh]greaja `]`k lkn h] b‰niqh]
'2-10(j
abq ? < 0&+/'g)e]ge abq ?ge,f<i
Baikopn]_e‰j- Blkpfabobjlp mofjbol bi `^pl m^oqf`ri^og < e < 0 - K^ j^,qofw?%h/qfbkb i^ cloj^
,++ ?
?yh <
@mif`^kal i^p lmbo^`flkbp bibjbkq^ibp abi qfml '2( ^ i^p cfi^p+mlabjlp `lksboqfobk `bolp qlalp ilp bibjbkqlp pfqr^alp ab_^gl abi 0 bk i^ mofjbo^ `lirjk^+ abg^kalfks^of^_ibp ilp abjŠp bibjbkqlp- Olo bgbjmil+ pf jriqfmiq`^jlp i^ mofjbo^ cfi^ ab?9hmlo ,z&i v prj^jlp bi obpriq^al ^ i^ pbdrka^ cfi^+i^ krbs^ pbdrka^ cfi^ pboŠ'M+]11 + ]12 + ŒŒŒ+ ]1b0h(- Olo jbafl ab rk^ pr`bpfŽk ab bp^plmbo^`flkbp bibjbkq^ibp
0/7 Bapaniej]jpao
`lk i^p cfi^p l_qbkbjlp rk^ krbs^ j^qofw nrb abpfdk^objlp `lk ?yh v nrb qfbkbi^ cloj^
0 NN ]11N ]21
?yh ;
N ]j1
N
Orbpql nrb i^p lmbo^`flkbp `lk i^p cfi^pabi qfml '2( kl jlafcf`^k bi abqbojfk^kqbqbkbjlp
'2-11(
Obol ?yh bp rk j^qofw af^dlk^i bk _ilnrbp+ ^pŒnrb+ bk sfoqra abi qblobj^ 2-6+qbkbjlp
abq ?yh < abq @k+
pfbkal ?j i^ jbklo 0+0ab ?*
Olo `lkpfdrfbkqb abq ?yh < abq ?hh*0/ nrb abjrbpqo^ '2-1/( m^o^g < f < 0-Blkpfabobjlp pbdrfa^jbkqb bi `^pl m^oqf`ri^og < 0+f `r^inrfbo^+ v abjlp,
qobjlp nrb
'2-12(
Tk^ sbw abjlpqo^a^ '2-12( i^ cŽojri^ '2-1/( jŠp dbkbo^i obpriq^ fkjbaf^q^jbkqb+ab_fal ^ nrb i^ j^qofw ?ye mrbab qo^kpcloj^opb bk rk^ j^qofw ab i^ cloj^ @e
ejbaf^kqb h,i fkqbo`^j_flp pr`bpfslp ab cfi^p ^av^`bkqbp- Di9abqbojfk^kqb `^j,_f^ ab pfdkl bk `^a^ qo^kpmlpf`fŽk+ pŒnrb
'2-13(
D‰niqh]ol]n] `ao]nnkhh]n`apaniej]jpao 0/8
pfbkal @ rk^ j^qofw j Wj `rv^ mofjbo^ cfi^ bp H: v `rv^ jbklo /*e* Ai:+bp ?g: -Rbd•k '2-12(+ qbkbjlp
`lk il nrb '2-13( klp a^
Olo il q^kql pf abjlpqo^jlp '2-12( q^j_f‹k abjlpqo^jlp '2-1/(-U^jlp ^elo^ ^ abjlpqo^o '2-12(- K^ j^qofw ?yf qfbkbi^ cloj^
l 0 l
Lbaf^kqb lmbo^`flkbp bibjbkq^ibp `lk i^p cfi^p abi qfml '2( fkqolarw`^jlp rk^`lirjk^ ab `bolp ab_^gl abi 0 v i^ qo^kpcloj^jlp bk
l N 0 N N^-, ]1+f,h N ]1+e*h ]1j
?ye ;
Bljl ^kqbp+bi abqbojfk^kqb kl s^oŒ^+pŒnrb abq ?yf < abq?ye%K^ j^qofw jbklo?h9qfbkbi^ cloj^
Blkpfabobjlp pbdrfa^jbkqb bi abq?bf `ljl rk^ crk`fŽk ab i^p j , 0 cfi^pab ?0‡ +
mlkd^jlp abq ?bf < &?h9'‹ K^ crk`fŽk p^qfpc^`bilp qobpmofjbolp ^uflj^p ab
00/ Bapaniej]jpao
rk^ crk`fŽk abqbojfk^kqb ab loabk j , 0 - Olo `lkpfdrfbkqb+ pbd•k bi qblobj^ abrkf`fa^a mlabjlp bp`of_fo
'2-14( b'?/e' <b'H( abq?/e *
bk alkab / bp i^ j^qofw fabkqfa^a ab loabk k,i- Dk `lkpb`rbk`f^+ m^o^abjlp,qo^o'2-12( ab_bjlp abjlpqo^o nrb b&H'< &\/'e+0
Œ Olo abcfkf`fŽk b&j bp,bi abqbo,jfk^kqb ab i^ j^qofw
l --- N 0 N N
0 N N N N
-z-- -- -
K8 N 0 N N N z Efi^ g
N N N 0 N
-z-- -- -
N N N N --- 0
fBlirjk^ g
Klp bibjbkqlp pfqr^alp bk i^p iŒkb^pl_if`r^p plk qlalp fdr^ibp ^ 0- Klp obp,q^kqbpbibjbkqlp kl bp`ofqlp plk qlalp N- Hkqbo`^j_f^kal i^ mofjbo^ cfi^ ab Bpr`bpfs^jbkqb `lk i^p cfi^p 1+2+--- ,e iibd^jlp ^ i^ j^qofw fabkqfa^a 0 ab loabkj Wj abpmr‹p ab g, 0 qo^kpmlpf`flkbp-Di abqbojfk^kqb `^j_f^ ab pfdkl bk `^a^qo^kpmlpf`fŽk+ pŒnrb abqB < &\/'e+0
ŒKrbdl b&-' < &\/'e+0&+ il nrb abjrbp,
qo^ '2-12( v mlo q^kql '2-1/(-
2-02 Dufpqbk`f^ab i^ crk`fŽk abqbojfk^kqb
Dk bpq^pb``fŽk rqfifw^jlp i^ fkar``fŽk obpmb`qlab j+ nrb bp bi loabk ab i^j^qofw+m^o^abjlpqo^o i^ bufpqbk`f^ ab i^p crk`flkbp abqbojfk^kqbp ab `r^inrfboloabk- O^o^ j < 1 v^ ebjlp abjlpqo^al nrb bufpqbrk^ crk`fŽk abqbojfk^kqb- O^o^bi `^pl j; 0 ^`bmq^jlp mlo abcfkf`fŽk nrb abq Y]F[ < ]hh ,
Rrmlkfbkal nrb bufpqbrk^ crk`fŽk abqbojfk^kqb ab loabk j , 0+m^ob`b iŽ,df`l nrb rk^ crk`fŽk abqbojfk^kqb ab loabk j crbo^ rk^ ab i^p cŽojri^p ababp^ooliil abi qblobj^ 2-8+mlo bgbjmil+ bi abp^ooliil jbaf^kqb i^p jbklobp ab i^mofjbo^ cfi^-Ml l_pq^kqb+obpriq^ jŠp pbk`fiil `ljmol_^o ilp ^uflj^p pf rqfifw^jlprk^ cŽojri^ ^kŠild^ bumobp^a bk crk`fŽk ab i^p jbklobp ab i^ mofjbo^ `lirjk^-
Cteopaj_e] `a h] bqj_e‰j `apaniej]jpa 000
SDNQDL@ 2-0/- Qqlkjc]iko h] ateopaj_e] `a `apaniej]jpao `a kn`aj j+h,N]n] qj] i]pnev j Wj _q]hmqean]? < ']eg(+oa] b h] bqj_e‰j `abeje`] lkn h]
'2-15(!
z&?h%,,, *?**' < ' +/'F/]// abq ?//‹68,
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Baikopn]_e‰j- Blkpfabobjlp `^a^ q‹ojfkl ab i^ prj^ '2-15( `ljl rk^crk`fŽk ab i^p cfi^pab ? v bp`of_^jlp
Rf `ljmol_^jlp nrb `^a^ ezp^qfpc^`bilp ^uflj^p 0 v 1 q^j_f‹k b ilp p^qfpc^oŠ-Lriqfmifnrbjlp i^ mofjbo^ cfi^ ab ? mlo rk bp`^i^o p-S^i jriqfmif`^`fŽk kl
^cb`q^ ^ i^ jbklo ?j mrbpql nrb ‹pq^ kl fk`irvb i^ mofjbo^ cfi^- Di `lbcf`fbkqb]// bpqŠjriqfmif`^al mlo p+pŒnrb qbkbjlp
Rf f = 0 i^ mofjbo^ cfi^ab `^a^ jbklo ?d nrba^ jriqfmif`^a^ mlo pv bi `lbcf`fbkqb]d kl nrba^ ^cb`q^al+ mlo il nrb lqo^ sbw qbkbjlp
Olo il q^kql+^a^ bzbp eljld‹kb^ bk i^ mofjbo^ cfi^-Rf pb jriqfmif`^ mlo p i^ cfi^ g ab ?* pfbkal g = 0+i^ jbklo ?gh kl pb jlaf,
cf`^ mbol ]d nrba^ jriqfmif`^al mlo p+mlo il nrb bg bp eljld‹kb^ bk i^ cfi^ g,Rf f !" g* bi `lbcf`fbkqb ]d kl pb ^cb`q^ mbol ^idrk^ cfi^ ab ?zh nrba^ jriqfmif`^a^mlo p-Krbdl qla^ bz bp eljld‹kb^ bk i^ cfi^ g,
Tk o^wlk^jfbkql m^ob`fal abjrbpqo^ nrb `^a^ bzbp ^afqfs^ obpmb`ql^ `r^i,nrfbo cfi^+mlo il `r^i b p^qfpc^`bilp ^uflj^p 0 v 1- Rbdrfa^jbkqb abjlpqo^jlpnrb b p^qfpc^`bbi ^uflj^ 2&+i^ sbopfŽk m^oqf`ri^oabi ^uflj^ 2- Cbi qblobj^ 2-0+pb abar`b bkqlk`bp nrb b p^qfpc^`bbi ^uflj^ 2-
O^o^ `ljmol_^o nrb b p^qfpc^`bbi ^uflj^ 2&+prmlkd^jlp nrb pb^k fdr^ibpalp cfi^p`lkpb`rqfs^p ab ?* pb^k ?g < ?g) 0 ’ Dkqlk`bp+ bu`bmql i^p jbklobp ?g/v ?g)h*y * `^a^ jbklo @{i qfbkbalp cfi^pfdr^ibp ab jlal nrb abq?e/ < N - Olo ilq^kql i^ prj^ '2-15( `lkpq^ q^k pŽil ab ilp alp q‹ojfklp `loobpmlkafbkqbp ^f<guf<g*h+
'2-16(
001 Bapaniej]jpao
Obol,@p+ < ?g)h,h o ]| < ]g)/,/ v^ nrb ?g < ?g)/% Olo `lkpfdrfbkqb+ ilp alpq‹ojfklp ab '2-16( afcfbobk q^k pŽil bk bi pfdkl+ mlo il nrb H'@0+’’’ *?**';M,@pŒmrbp+Gp^qfpc^`bbi ^uflj^ 2&-
Olo •iqfjl+ `ljmol_^jlp nrb Gp^qfpc^`bbi ^uflj^ 3- Br^kal ? < 0 qbkb,jlp ^k < 0 X ]d < N m^o^g= 0- @pfjfpjl+ @k bp i^ j^qofw fabkqfa^a abloabk j+h * mlo il `r^i `^a^ q‹ojfkl ab '2-15( bp `bol p^isl bi mofjbol+ nrbbp fdr^i ^i- Krbdl G'HG + Œ-Œ+0++(< 0 mlo il nrb G p^qfpc^`bbi ^uflj^ 3-&
Dk i^ abjlpqo^`fŽk ^kqboflomlaoŒ e^_bopb jrv _fbk rqfifw^al rk^ crk`fŽk Gabcfkfa^ bk crk`fŽk ab i^p jbklobp ?fg ab i^ `lirjk^ g bk ird^o ab i^p jbklobp@:i ab i^ mofjbo^ `lirjk^- Dk bcb`ql+ pf mlkbjlp
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bu^`q^jbkqb bi jfpjl qfml ab abjlpqo^`fŽk e^`b sbo nrb bp^ Gp^qfpc^`bilp `r^,,qol ^uflj^p ab rk^ crk`fŽk abqbojfk^kqb- Orbpql nrb i^p crk`flkbp abqbojfk^kqbpplk •kf`^p+ i^p cŽojri^p ab abp^ooliil '2-17( v i^p ab '2-10( plk qla^p fdr^ibp^ `ap?-
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Di qblobj^ 2-4 mrpl ab j^kfcfbpql nrb pf? bp kl pŒkdri^o-abq? ;/; N-Di qblob,j^ pfdrfbkqb abjrbpqo^ bi ob`Œmol`l-Dpql bp+pf abq? ;/; @$bufpqb?,h- @abjŠp+a^ rk^ cŽojri^ m^o^ bumobp^o? ,0 bk crk`fŽk ab rk^ j^qofw cloj^a^ `lk ilp`lc^`qlobp ab ilp bibjbkqlp ab ?,
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I 03 Bapaniej]jpao
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DIDLOKN 1- Ch ]qpkaol]_ek C'?( mqa _kjop] `a pk`ko hko t p]hao mqaR&t' < ?V, Rb^ R8 R z T rk^ qo^kpcloj^`fŽk ifkb^i nrb qfbkb rk ^rqls^ilo @+
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DIDLOKN 2- Cteopaj_e] `a ]qpkr]hknao _ank- Rf bufpqb rk ^rqlsb`qlo klmrbab pbo `bol+ mlo abcfkf`fŽk- Rfk bj_^odl+ bi bp`^i^o `bol lqa`a pbo rk ^rql,s^ilo- Dk bcb`ql+pf N bp rk ^rqls^ilo m^o^t bkqlk`bp R't( < Mt < N+mlo 0/ nrbt bp abi k•`ibl& ab R, Qb`Œmol`^jbkqb+pf bi k•`ibl ab R `lkqfbkb bibjbkqlp klkrilp `^a^ rkl ab ‹plp bp rk ^rqlsb`qlo `lk ^rqls^ilo N- Dk dbkbo^i+C&?' bpbi k•`ibl ab R , @i -
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DIDLOKN 5- Ch klan]`kn `aner]`]- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p crk,`flkbp ob^ibpp nrb ^ajfqbk abofs^a^p ab `r^inrfbo loabk bk rk fkqbos^il ^_fboqla^al- Rb^ C i^ qo^kpcloj^`fŽk ifkb^i nrb ^mif`^ `^a^ pbk pr abofs^a^+ B&b' < b%,Klp ^rqlsb`qlobp ab C plk ^nrbii^p crk`flkbp . kl kri^p nrb p^qfpc^`bkrk^ b`r^,`fŽk ab i^ cloj^
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l < ?b']( < ?_bb.(&-
Orbpql nrb a].t krk`^ bp `bol+sbjlp nrb i^ b`r^`fŽk R&G'< ?b kl mrbab p^qfpc^`bopb `lk rk^ b kl kri^+ ^pŒnrb R kl qfbkb^rqlcrk`flkbp kf ^rqls^ilobp-
DIDLOKN 7- Qq^ aol]_ek ajcaj`n]`k lkn qj ]qpkra_pkn- Rb^ R9 R z T rk^qo^kpcloj^`fŽk ifkb^i nrb qfbkbrk ^rqls^ilo @- Rb^ t rk ^rqlsb`qlo mboqbkb`fbkqb^ @ v pb^ J&t' bi pr_bpm^`fl bkdbkao^al mlo t, Dpql bp+J&t' bp bi `lkgrkql abqlalp ilp molar`qlp ab t mlo bp`^i^obp-Dp cŠ`fi abjlpqo^o nrb R ^mif`^ J&t' bk pŒjfpjl- Dk bcb`ql+pf v < at qbkbjlp
R'u( < R'_t( < _R't( < A'?V( < ?'AV( < ?u-
Rf a <0<, N bkqlk`bp v <0<, N mlo il nrb qlal bibjbkql kl kril v ab J't( bp q^j_f‹krk ^rqlsb`qlo mboqbkb`fbkqb @-
Rb af`b nrb rk pr_bpm^`fl S ab R bp ejr]ne]jpa bk i^ qo^kpcloj^`fŽk R+ pf‹pq^ ^mif`^ `^a^ bibjbkql ab S bk lqol bibjbkql ab S, @`^_^jlp ab abjlpqo^onrb bi pr_ bpm^`fl bkdbkao^al mlo rk ^rqlsb`qlo bp fks^of^kqb bk R,
3-2 Hkabmbkabk`f^ifkb^i ab ^rqlsb`qlobp `loobpmlkafbkqbp^ ^rqls^ilobp afpqfkqlp
Tk^ ab i^p molmfba^abp jŠp fjmloq^kqbp ab ilp ^rqls^ilobp bp i^ nrb pbbumlkb bk bi qblobj^ pfdrfbkqb- Bljl ^kqbp+R obmobpbkqrk pr_bpm^`fl ab rkbpm^`fl ifkb^i T,
013 ?qpkr]hknao v yqpkra_pknao
SDNQDL@ 3-1- Qe Sp* ‹‹‹ * Sg okj ]qpkra_pknao`a qj] pn]jobkni]_e‰j heja]hR9Q y T+ X hko ]qpkr]hknao @{+ --- +?g okj `eopejpko+ajpkj_ao hko ]qpkra_pknao&,hz+ ŒŒŒ+ Sg okj ej`alaj`eajpao
Baikopn]_e‰j- K^ abjlpqo^`fŽk bp mlo fkar``fŽk bk g- Di obpriq^al bpqofsf^i `r^kal g < 0- Rrmlkd^jlp+ bkqlk`bp+ nrb e^ pfal abjlpqo^al m^o^`r^i,nrfbo `lkgrkql ab g,0 ^rqlsb`qlobp- Rb^k Sz * ‹‹‹ * qe-g^rqlsb`qlobp mboqbkb`fbk,qbp^ ^rqls^ilobp afpqfkqlp+v prmlkd^jlp nrb bufpqbkbp`^i^obpaz q^ibpnrb
g
y AeSe < N-f<i
@mif`^kal R ^ ilp alp jfbj_olp ab '3-3( v rqfifw^kal bi eb`el ab nrbR&qz' < ?zSz bk`lkqo^jlp
'3-4(g
Ae?eSe < N -f<i
Lriqfmif`^kal '3-3( mlo ?g v obpq^kal ab '3-4( l_qbkbjlp i^ b`r^`fŽk
R(S
Ae'?e , ?g(Se < N-f<i
Obol v^ nrb qz * ‹‹‹ * Sg+z plk fkabmbkafbkqbp+ab_b pbo Az&?z+ ?g' < N m^o^`^a^e < 0+ 1+ &! *g + 0- Orbpql nrb ilp ^rqls^ilobp plk afpqfkqlp qbkbjlp @{", ?gm^o^e", g ^pŒnrb az << N m^o^ e < 0+1+ --- +g , 0- Dk sfoqra ab '3-3( sbjlpnrb _a bp q^j_f‹k N+ mlo 0/ nrb ilp ^rqlsb`qlobp Sz * ‹‹‹ -q• plk fkabmbkafbkqbp
N_p‹osbpb nrb bi qblobj^ 3-1 kl pboŒ^fboql pf bi bibjbkql `bol mrafbo^ pbork ^rqlsb`qlo- Dpq^bp lqo^ o^wŽkm^o^bu`irfo N `ljl ^rqlsb`qlo-
?`ranpaj_e]9 Di ob`Œmol`l abi qblobj^ 3-1 kl bp `fboql- Dpql bp+ pf R qfbkb^rqlsb`qlobp fkabmbkafbkqbp TH+ ’’’ +qe+ bkqlk`bp ilp `loobpmlkafbkqbp ^rqls^ilobp@i + ’’’ *?g kl plk kb`bp^of^jbkqb afpqfkqlp- Olo bgbjmil+ pf R bp i^ qo^kpcloj^`fŽkfa‹kqf`^+ R&t' < t m^o^ qlal t* bkqlk`bp qlal V!D, N bp rk ^rqlsb`qlo+ mbol bufpqbpŽil rk ^rqls^ilo+ @< 0-
Di qblobj^ 3-1 qfbkb `lkpb`rbk`f^p fjmloq^kqbp bk bi `^pl ab afjbkpfŽkcfkfq^-
SDNQDL@ 3-2- Qe afj T < j+ pk`] pn]jobkni]_e‰j heja]h R9 T y T peajalkn hk iajko j ]qpkr]hknao `eopejpko-QeR peaja at]_p]iajpa j ]qpkr]hknao `eopej,pko+ajpkj_ao hko ]qpkra_pknao _knnaolkj`eajpao bkni]j qj] ^]oa r]n] T X &h]
Cfan_e_eko 014
i]pnev `a R nah]per]] ao] ^]oa ao qj] i]pnev `e]ckj]h _kj hko ]qpkr]hknao _kikahaiajpko `e]ckj]hao-
Baikopn]_e…j- Rf bufpqfbo^kj * 0 ^rqls^ilobp afpqfkqlp-bkqlk`bp+ pbd•k biqblobj^ 3-1+ T `lkqbkaoŒ^ j * 0 bibjbkqlp fkabmbkafbkqbp-Dpql kl bp mlpf_ibmrbpql nrb afj T < j- K^ pbdrka^ ^cfoj^`fŽk pb abar`b ab ilp qblobj^p 3-0 v/)-)
M^oanr]_eˆj8 Di qblobj^ 3-2 klp af`b nrb i^ bufpqbk`f^ ab j ^rqls^ilobp afpqfkqlpbp rk^ `lkaf`fŽk oqbe_eajpa m^o^ nrb R qbkd^ rk^ obmobpbkq^`fŽk bk j^qofw af^dlk^i-Dpq^ `lkaf`fŽk kl bp kb`bp^of^- Dufpqbk qo^kpcloj^`flkbp ifkb^ibp `lk jbklp ab j ^rql,s^ilobp afpqfkqlp nrb mrbabk obmobpbkq^opbjbaf^kqb j^qof`bp af^dlk^ibp- K^ qo^kpclo,j^`fŽk fabkqfa^a bp rk bgbjmil- Slalp prp ^rqls^ilobp plk fdr^ibp ^ 0 mbol mrbab ob,mobpbkq^opbmlo i^ j^qofw fabkqfa^a- Di qblobj^ 3-0 klp af`b nrb i^ bufpqbk`f^ ab j^rqls^ilobp fkabmbkafbkqbp bp ja_ao]ne] v oqbe_eajpa m^o^ nrb R ^ajfq^ rk^ obmobpbkq^,`fŽk bk j^qofw af^dlk^i-
,', 8SN[LRLRX\
0- ^( Rf R qfbkb rk ^rqls^ilo W+abjlpqo^o nrb ]R qfbkb bi ^rqls^ilo ]V,_( Qe t bp rk ^rqlsb`qlo m^o^ R* v R* abjlpqo^o nrb q^j_f‹k il bp m^o^ ]R, * ^%G%|,„BŽjl bpqŠk obi^`flk^alp ilp ^rqls^ilobp>
1- Rrmlkd^jlp nrb R9 T y T qfbkb rk ^rqlsb`qlo t mboqbkb`fbkqb ^ rk ^rqls^ilo W-Cb,jlpqo^o nrb t bp rk ^rqlsb`qlo ab R&mboqbkb`fbkqb ^ u&v+ `lk j^vlo dbkbo^ifa^a+ t bprk ^rqlsb`qlo ab R! mboqbkb`fbkqb ^ W!- Tqfifw^o irbdl bi obpriq^al abi bgbo`f`fl 0 m^o^abjlpqo^o nrb pf O bp rk mlifkljfl+ bkqlk`bp t bp rk ^rqlsb`qlo ab N&R' mboqbkb`fbkqb^ O'W(-
2- Blkpfabobjlp bi mi^kl `ljl rk bpm^`fl ifkb^i ob^i+ T < U+'Q(+ v pb^ R rk dfol ab Tab &hR.1 o^af^kbp- Rf _fbk R kl qfbkb ^rqlsb`qlobp+ abjlpqo^o nrb qlal sb`qlo kl krilbp rk ^rqlsb`qlo ab R&-
3- Rf R9 T y T qfbkb i^ molmfba^a ab nrb R&qfbkb rk ^rqls^ilo kl kbd^qfsl W&+abjlpqo^onrb mlo il jbklp rkl ab ilp alp s^ilobp W l , W bp rk ^rqls^ilo m^o^ R,
YGj`e_]_eˆj8 R%+ V%G< &R * ?h'&R + VG',[4- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbp ob^ibp abofs^_ibp bk 'N+0(- Rf b D T* abcf,
k^jlp d < R&b' mlkfbkal c&p' < pb%&p'm^o^ qlal p bk 'N+0(- Cbjlpqo^o nrb qlal Wob^ibp rk ^rqls^ilo ab R* v abqbojfk^o i^p ^rqlcrk`flkbp `loobpmlkafbkqbp ^ W-
5- Rb^ T bi bpm^`fl ifkb^i ab qlalp ilp mlifkljflp ob^ibp l&t' ab do^al z j, Rf l D T* abcf,k^jlp m< R&l' mlkfbkal m&p'< l&p * 0( m^o^ qlal p ob^i- Cbjlpqo^o nrb R qfbkb pli^,jbkqb bi ^rqls^ilo 0- „BrŠibp plk i^p ^rqlcrk`flkbp mboqbkb`fbkqbp^ bpb ^rqls^ilo>
6- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbp `lkqfkr^p bk ', //+ * //( v q^ibp nrb i^fkqbdo^i I9&;WI b&p'`p bufpqb m^o^ qlal t ob^i- Rf b D T abcfk^jlp d < R&b' mlkfbkalc&t' < I9&;WI b&p'`p, Cbjlpqo^o nrb qlal Wmlpfqfsl bp rk ^rqls^ilo m^o^ R v abqbojfk^oi^p ^rqlcrk`flkbp `loobpmlkafbkqbp ^ W-
7- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p crk`flkbp `lkqfkr^p bk ', //+ * //( v q^ibp nrb i^fkqbdo^ig&f+;WI pb&p'`p bufpq^ m^o^ qlal t ob^i- Rf b D T abcfk^jlp d < R&b' mlkfbkalc&t' < I9&;WI pb&p'`p,Cbjlpqo^o nrb qlal W kbd^qfsl bp rk ^rqls^ilo m^o^ R v abqbojfk^oi^p ^rqlcrk`flkbp `loobpmlkafbkqbp ^ W-
015 ?qpkr]hknao u ]qpkra_pknao
8- Rb^ T < B'N+&06!( bi bpm^`fl ifkb^i ob^i ab qla^p i^p crk`flkbp ob^ibp `lkqfkr^p bk bi fk,qbos^il ZN+&06!\- Rb^ R bi pr_bpm^`fl ab qla^p i^p crk`flkbp b nrb ^ajfqbk abofs^a^ pb,drka^ `lkqfkr^ v nrb p^qfpc^`bk q^j_f‹k i^p `lkaf`flkbp ab `lkqlokl /&.' < b'&06!( < N-Rb^ R9 R z T i^ qo^kpcloj^`fŽk ifkb^i nrb ^mif`^ `^a^ Gbk pr abofs^a^ pbdrka^+R&b'< f!+ Cbjlpqo^o nrb ilp ^rqls^ilobp ab R plk ilp k•jbolp ab i^ cloj^ ,j&+alkab j < 0+1+--- +v nrb i^p ^rqlcrk`flkbp `loobpmlkafbkqbp ^ ,j& plk G'p( < _-pbk jp+pfbkal _- :0c N -
0/- Rb^ T bi bpm^`fl ifkb^i ab qla^p i^p pr`bpflkbp `lksbodbkqbp xu-y- Cbcfk^jlp R9 T y Tabi jlal pfdrfbkqb9 Rf t < wt,x bp rk^ pr`bpfŽk `lksbodbkqb `lk iŒjfqb ]* R&t' < wu,x*pfbkal v- < ],t- m^o^ j 99990- Cbjlpqo^o nrb R qfbkb pŽil alp ^rqls^ilobp+ @< N X@< ,0+X abqbojfk^o ilp ^rqlsb`qlobp mboqbkb`fbkqbp^ `^a^ rkl ab bplp @-
00- Rrmlkd^jlp nrb rk^ qo^kpcloj^`fŽk ifkb^i R qfbkb alp ^rqlsb`qlobp t b v mboqbkb`fbk,qbp ^ ^rqls^ilobp afpqfkqlp @ v {-i- Rf ]t * ^u bp rk ^rqlsb`qlo ab R+ abjlpqo^o nrb] < N l ^ < N-
01- Rb^ R9 R z T rk^ qo^kpcloj^`fŽk ifkb^i q^i nrb qlal bibjbkql kl kril ab R bp rk^rqlsb`qlo- Cbjlpqo^o nrb bufpqb rk bp`^i^o a q^i nrb R&t' < at, Cf`el ab lqol jlal+i^ •kf`^ qo^kpcloj^`fŽk `lk bpq^ molmfba^a bp bi molar`ql ab i^ fabkqfa^a mlo rkbp`^i^o- YGj`e_]_e‰j9 G^`bo rpl abi bgbo`f`fl 00-\
3-4 B^pl ab afjbkpfŽk cfkfq^-Olifkljflp `^o^`qboŒpqf`lp
Rf afj T < j+ bi mol_ibj^ ab abqbojfk^o ilp ^rqls^ilobp ab rk^ qo^kpcloj^,`fŽk ifkb^i R9 T y T mrbab obplisbopb `lk i^ ^vra^ ab ilp abqbojfk^kqbp- Cbpb^,jlp e^ii^o ^nrbiilp bp`^i^obp+[q^ibpnrb i^ b`r^`fŽk R&t' < %Ztqbkd^ rk^ plir`fŽkt " N- K^ b`r^`fŽk R&t' < ?V mrbab bp`of_fopbbk i^ cloj^
&?h+ R'&t' < M*
alkab / bp i^ qo^kpcloj^`fŽk fabkqfa^a- Rf mlkbjlp R9,< +[I , R* bkqlk`bp +[bprk ^rql s^ilo pf v pŽil pf i^ b`r^`fŽk
'3-5( R9,&t' < M
qfbkb rk^ plir`fŽk t kl kri^+ bk `rvl `^pl R:- kl bp fksboqf_ib 'bk sfoqra abiqblobj^ 1-0/(- Olo `lkpfdrfbkqb+ pbd•k bi qblobj^ 1-1/+ rk^ plir`fŽk kl kri^ ab'3-5( bufpqbpf v pŽil i^ j^qofw ab R:- bp pfkdri^o- Rf ? bp rk^ obmobpbkq^`fŽkj^,qof`f^i ab R+bkqlk`bp +[I , ? bp rk^ obmobpbkq^`fŽkj^qof`f^i m^o^ R:-- Rbd•k biqblobj^ 2-02+i^ j^qofw +[I , ? bp pfkdri^o pf v pŽil pf abq '?h , ?' < N- @pŒmrbp+pf +[bp rk ^rqls^ilo m^o^R ab_b p^qfpc^`boi^ b`r^`fŽk
'3-6( abq &?h+ ?' < N-
Qb`Œmol`^jbkqb+`r^inrfbo +[ abi _qanlk bqj`]iajp]h `a ao_]h]naonrb p^qfpc^d^'3-6( bp rk ^rqls^ilo- Dpql prdfbob nrb bi abqbojfk^kqb abq &K + ?' ab_boŒ bpqr,af^opb `ljl rk^ crk`fŽk ab @-
A]ok `a `eiajoe‰j bejep] 016
SDNQDL@ 3-3- Qe ? ao qj] i]pnev j Wj _q]hmqean] a 0 ao h] i]pnev e`ajpe,`]` j Wj+ ajpkj_ao h] bqj_e‰j b `abeje`] lkn h] a_q]_e‰j
ba?( < abq '?h , ?(
ao qj lkhejkiek aj +Z-a cn]`k j- ?`ai…o+ ah p†niejk `a i]ukn cn]`k ao +Z-j+ v ahp†niejk ej`alaj`eajpa l _kjop]jpa ao baM(< abq ',?( < ']i(k abq?-
Baikopn]_e‰j- K^ ^cfoj^`fŽk baM(< abq ',?( obpriq^ fkjbaf^q^jbkqb abi^ abcfkf`fŽk ab b, U^jlp ^ abjlpqo^o nrb b bp rk mlifkljfl ab do^al j •kf`^,jbkqb m^o^bi `^pl j 999:2- K^ abjlpqo^`fŽk bk bi `^pl dbkbo^i mrbab e^`bopb mlofkar``fŽk v i^ abg^jlp `ljl bgbo`f`fl- 'Ubo bgbo`f`fl 8 ab i^ pb``fŽk 3-7-(
O^o^ j < 0 bi abqbojfk^kqb bp bi mlifkljfl ifkb^i b&%Z%'< +[-, ]j% O^o^j < 1 qbkbjlp
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< @1 , ']q * ]11(? * ']S]11 , ]h1]10(+
mlifkljfl ab pbdrkal do^al bk +[--O^o^ j<2 qbkbjlp
abq '?h , ?( < ,]10 @, ]11 ,]12
Klp alp •iqfjlp q‹ojfklp plk mlifkljflp ab mofjbo do^aŽ bk &[&-Di mofjbo q‹ojfklbp rk mlifkljfl ab qbo`bodo^al+ pfbkal bi q‹ojfkl ab j^vlo do^al +[-2-
CDEHMHBHˆM- Qe ? ao qj] i]pnev j Wj ah `apaniej]jpa
ba?( < abq '?h , ?'
oa `ajkiej] lkhejkiek _]n]_pan‡ope_k`a ?-
K^p o^Œ`bpabi mlifkljfl `^o^`qboŒpqf`lab ? plk k•jbolp `ljmibglp+ ^idrklab ilp `r^ibp mrbab pbo ob^i- Rf abpfdk^jlp `lk D bi `^jml ob^i Q l bi `^jml`ljmibgl J$qbkbjlp bi qblobj^ pfdrfbkqb-
017 ?qpkr]hknao u ]qpkra_pknao
SDNQDL@ 3-4- Rb^ R9 T y R qj] pn]jobkni]_e‰j heja]h+oeaj`k E ah _]ilk`a ao_]h]nao `a T+ u afj T < j- Qa] ? qj] nalnaoajp]_e‰j i]pne_e]h `a R- Cjpkj_aoah _kjfqjpk `a ]qpkr]hknao `a R _kjop] `a ]mqahh]o n]‡_ao `ah lkhejkiek _]n]_pa,
n‡ope_k`a ? mqa lanpaja_aj ] E-
Baikopn]_p…j- K^ afp`rpfŽk abi qblobj^ 3-3 mlkb ab j^kfcfbpql nrb qlal^rqls^ilo ab R p^qfpc^`bi^ b`r^`fŽk abq &<,,/ + ?' < N X nrb `r^inrfbo o^Œwabimlifkljfl `^o^`qboŒpqf`lab ? nrb mboqbkb`b E bp rk ^rqls^ilo ab R-
K^ j^qofw ? abmbkab ab i^ bib``fŽk ab i^ _^pb m^o^ T* mbol ilp ^rqls^ilobpab R pb abcfkfbolk pfk e^`bo obcbobk`f^^ rk^ _^pb- Olo `lkpfdrfbkqb+ bi _kjfqjpk abo^Œ`bpabi mlifkljfl `^o^`qboŒpqf`lab ? ab_b pbofkabmbkafbkqbab i^ bib``fŽk abi^ _^pb- LŠp ^•k+ bk rk^ pb``fŽk mlpqbofloabjlpqo^objlp nrb bi jfpjl mlifkljfl`^o^`qboŒpqf`lbp fkabmbkafbkqbab i^ bib``fŽk ab _^pb-Ulis^jlp ^elo^ ^i mol_ibj^ab `^i`ri^o ilp ^rqls^ilobp v ^rqlsb`qlobp bk bi `^pl ab afjbkpfŽk cfkfq^-
3-5 BŠi`ril ab ^rqls^ilobp v ^rqlsb`qlobp bk bi `^pl ab afjbkpfŽk cfkfq^
Dk bi `^pl ab afjbkpfŽk cfkfq^ilp ^rqls^ilobp v ^rqlsb`qlobp ab rk^ qo^kp,cloj^`fŽk ifkb^i R pb ii^j^k q^j_f‹k ^rqls^ilobp v ^rqlsb`qlobp ab i^ obmobpbkq^,`fŽk j^qof`f^i ab R, @pŒmrbp+ilp ^rqls^ilobp ab rk^ j^qofw `r^ao^a^ ? plk i^po^Œ`bpabi mlifkljfl `^o^`qboŒpqf`lb'=!( < abq &<,,/ + ?', Klp ^rqlsb`qlobp `loobp,mlkafbkqbp ^ rk ^rqls^ilo =-- plk ^nrbiilp sb`qlobp kl krilp W < 'Vh& --- +tj'`lkpfabo^alp `ljl j^qof`bp `lirjk^ j W 0 nrb p^qfpc^`bki^ b`r^`fŽk j^qof`f^i
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Dpqbbp rk pfpqbj^ ab j b`r^`flkbp ifkb^ibp m^o^ ilp `ljmlkbkqbp Vh!%! VjŒ
Dk `r^kql pb `lkl`b =-- mlabjlp l_qbkbo ilp ^rqlsb`qlobp obplisfbkal bpb pfpqbj^-Rbdrfa^jbkqb lcob`bjlp qobpbgbjmilp nrb mobpbkq^k pmb`ql afpqfkql-
DIDLOKN 0- Sj] i]pnev _kj pk`ko oqo ]qpkr]hknao `eopejpko- K^ j^qofw
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A…h_qhka ]qpkr]hknao v ]qpkra_pknao 018
`lk il nrb bufpqbkqobp^rqls^ilobp afpqfkqlp9 0+ ,0 X 2- O^o^ e^ii^o ilp ^rqlsb`,qlobp `loobpmlkafbkqb ^ =- < 0 obplisbjlp bi pfpqbj^ ?V < W+l
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,0 ,0 ,1 Vo Vo
Dpql klp a^
0tG * V0 * Vo < Vh
0VG * 1V0 * 2to < V0
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nrb mlabjlp bp`of_fobk i^ cloj^Vh * V0 * Vo < N
0tG * 0V0 * 2to < N
,Wi , V1 , 2up < N-
Rrj^kal i^p b`r^`flkbp mofjbo^ v qbo`bo^bk`lkqo^jlp W^ < N+X i^p qobpb`r^,`flkbp pb obar`bk bkqlk`bp ^ Wi * V0 < N- Blk il `r^i+ ilp ^rqlsb`qlobp `loobp,mlkafbkqbp ^ @ < 0plk W < p&/*,0+N(+pfbkal p `r^inrfbo bp`^i^o kl kril-
Lbaf^kqb `Ši`rilp m^ob`falp bk`lkqo^jlp ilp ^rqlsb`qlobp W < p&M*0+,0(
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@rqls^ilo @ @rqlsb`qlobp afj C&<%'
0 /&/* ,0+ N(+ /n %. 0,0 /&.*/* +/'* /n %. 0
2 /&0*1* +/'* /n %. 0
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02/ ?qpkr]hknao u ]qpkra_pknao
qfbkbbi mlifkljfl `^o^`qboŒpqf`l
abq &?h\ ?' < abq Z@ z 1 @ z 2
,1 ,0
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Klp ^rqls^ilobp plk 1+ 1 X 3- 'Bfq^jlp bi ^rqls^ilo 1 alp sb`bp m^o^ abpq^`^onrb bp rk^ o^Œwal_ib abi mlifkljfl `^o^`qboŒpqf`l-(O^o^bk`lkqo^o ilp ^rqlsb`ql,obp `loobpmlkafbkqbp^ @ < 1 obplisbobjlp bi pfpqbj^ ?V < 0V* nrb pb obar`b ^
+V0 * Vo < N
V0 + Vo < N
1tz * V0 * Vo < N-
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afj C&?'
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q',i+i+i(+ pyMp'h+,0+0(+ p y N
DIDLOKN 2- Mpn] i]pnev _kj ]qpkr]hknao nalape`ko- K^ j^qofw
qfbkb bi mlifkljfl `^o^`qboŒpqf`l'@ , i('@ , i('@ , 6(- Br^kal @< 6 bi pŒpqb,j^ ?V < 6W pb&lksfboqb
4t0 , V1 , Vo < N
, 1tz * 3t1 , 1to < N
, 2tz , 2t1 * 2to < N Š
†pqb qfbkb-i^ plir`fŽk V1 < 1uH+V2 < 1tz* ^pŒnrb ilp ^rqlsb`qlobp `loobpmlkafbk,
Rn]v] `a qj] i]pnev 020
qbp ^ +[< 6 plk p&/* 1+2(+ alkab p" N- O^o^ bi ^rqls^iloW < 0+ bi pfpqbj^?V < W `lkpq^ ab i^ b`r^`fŽk
Vh * V1 * V] < N
obmbqfa qobpsb`bp- O^o^ obplisbo bpq^ b`r^`fŽk mlabjlp qlj^o Wi < ]+ V1 < ^*alkab ] v ^ plk ^o_fqo^oflp+v qlj^jlp bkqlk`bp V2 < , ],^- @pŒ+qlal ^rql,sb`qlo `loobpmlkafbkqb ^ +[< 0 qfbkbi^ cloj^
&]* ^* +] + ^' < ]&h* N+,0( * ^&M*0+,0(+
pfbkal ] " N l ^ " N- Dpql pfdkfcf`^ nrb ilp sb`qlobp '0+ N+,0( X 'N+ 0+,0(cloj^k rk^ _^pb m^o^ C& ', Krbdl afj C&%Z'< 1 `r^kal +[< 0- Klp obpriq^alpmrbabk obprjfopb ^pŒ9
@rqls^ilo @r qlsb`qlobp afj C&%Z'
01
60+0
p'h+1+ 2(+ p9zh9-N
]&h* N+,0( * ^&M*0+,0(+ ]* ^jk ^j_lp N-
N_p‹osbpb nrb bk bpqbbgbjmil bufpqbkqobp^rqlsb`qlobp fkabmbkafbkqbpmbol pli^,jbkqb alp ^rqls^ilobp afpqfkqlp-
3-6 E[JcJ MN WJVJ][Rc
Rb^ b&%Z'bi mlifkljfl `^o^`qboŒpqf`lab rk^ j^qofw ?* j Wj- Cbpfdkbjlp i^pj o^Œ`bpab b&%Z'mlo @i + --- +@k+ obmfqfbkal`^a^ o^Œwj•iqfmib i^p sb`bp nrb fkaf,nrb pr loabk ab jriqfmif`fa^a- Sbkbjlp bkqlk`bp i^ c^`qlofw^`fŽk
S^j_f‹k mlabjlp bp`of_fob'?( bk mlqbk`f^p ab`ob`fbkqbp ab @ `ljl pfdrb+
Bljm^oŠkalil `lk i^ cloj^ c^`qlofw^a^ bk`lkqo^jlp nrb bi q‹ojfkl fkabmbkafbk,qb Ak v bi&lbcf`fbkqb ab @k
,0 sfbkbk a^alp mlo i^p cŽojri^p
v
021 ?qpkr]hknao u ]qpkra_pknao
Orbpql nrb q^j_f‹k qbkbjlp Ak < ']0(! abq?* sbjlp nrb
@i --’ ? ‹‹ < abq ? -
Dpql bp+ah lnk`q_pk `a h]o n]e_ao`ah lkhejkiek _]n]_panhope_ka ? ao ecq]h ]h`apaniej]jpa `a ?-
K^ oqi] ab i^p o^Œ`bpab b'?( pb ii^j^ pn]v] `a ?+ v pb abpfdk^ `lk qo?- @pŒmrbp+mlo abcfkf`fŽk
Di `lbcf`fbkqb ab -[00,- sfbkb a^al mlo Aj,0 < ,qo ?, S^j_f‹k mlabjlp `^i`ri^obpqb`lbcf`fbkqb m^oqfbkal ab b'?( bk cloj^ ab abqbojfk^kqb v bk`lkqo^jlp
'Dk bi bgbo`f`fl 01 ab i^ pb``fŽk 3-7 pb mfab rk^ abjlpqo^`fŽk ab bp^ cŽojri^-(K^p alp cŽojri^p ab Bk,0 abjrbpqo^k nrb
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rqfifw^opb ljl rk^ `ljmol_^`fŽk krj‹of`^ bk ilp `Ši`rilp ab ^rqls^ilobp- Dk ilpbgbo`f`flp nrb pfdrbk sbobjlp lqo^p molmfba^abpab i^ qo^w^-
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Cbqbojfk^o ilp ^rqls^ilobp v ilp ^rqlsb`qlobp ab `^a^ rk^ ab i^p j^qof`bp ab ilp bgbo,`f`flp 0 ^i 2- @pfjfpjl+ m^o^ `^a^ ^rqls^ilo W `^i`ri^o i^ afjbkpfŽk abi ^rqlbpm^`fl C&V',
0- ^( Zz zi _( Zz 5S1-+F :i^= l+ ^ = N-
3- K^p j^qof`bp OH< F z\ &
2- cblp M ,oajk[-Kpbk M blp M
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Cfan_e_eko 022
qbloŒ^`rŠkqf`^ abi plfj bib`qo5k v pb abkljfk^k i]pne_ao olej `a N]qhe+bk elklo abicŒpf`lVlicd^kd O^rif '08//,0847(- Bljmol_^o nrb qfbkbk ilp jfpjlp ^rqls^ilobp 0 v ,0-Cbqbojfk^o bkqlk`bp ola^p i^p j^qof`bp 1 W1 `lk bibjbkqlp `ljmibglp nrb qbkd^k ilpalp ^rqls^ilobp 0 v , 0-
4- Cbqbojfk^o qla^p i^p j^qof`bp 1W1 `lk bibjbkqlp ob^ibp `rvlp ^rqls^ilobp pb^k ^( ob^ibpv afpqfkqlp+ _( ob^ibp b fdr^ibp+ b( `ljmibglp `lkgrd^alp-
5- Cbqbojfk^o ]+^* a+ * a+b p^_fbkal nrb ilp sb`qlobp '0+ 0+-0(+ 0+N+,0( X '0+ ,0+N( plk^rqlsb`qlobp ab i^ j^qofw
6- B^i`ri^o ilp ^rqls^ilobp v ^rqlsb`qlobp ab `^a^ rk^ ab i^p j^qof`bp pfdrfbkqbp- S^j_f‹k+`^i`ri^o i^ afjbkpf5k abi ^rqlbpm^`fl C&V' m^o^ `^a^ ^rqls^ilo W-
0 2\1 2+
2 1/
b( Z,9 ,9 ,9\-
2 ,5 ,3
7- B^i`ri^o ilp ^rqls^ilobp ab `^a^ rk^ ab i^p `fk`l j^qof`bp
^( Z9 z 9 z\+ _( Z9 z ]9 z\ + b( Zz 9 z 9\+
N N N N N N ,0 N N N
a( Zz ye y y[ 'y , y y zIN N N ,e& b( N N N -
N N N N N /,0
Dpq^p pb ii^j^k i]pne_ao `a Ben]_ bk elklo ab O^_il @- L- Cfo^` '08/1, (+ cŒpf`lfkdi‹p- Rb mobpbkq^k bk i^ obplir`f5k ab i^ b`r^`f5k ab lka^p obi^qfsfpq^ bk Lb`Škf`^BrŠkqf`^-
7, Qe? X @ plk j^qof`bp j Wj+ pfbkal @ rk^ j^qofw af^dlk^i+ abjlpqo^o 'mlo fkar``f5k(nrb bi abqbojfk^kqb b&V' < abq &V@+ ?' bp rk mlifkljfl bk @ `lk b&M'< ', V abq ?*v `lk bi `lbcf`fbkqb ab Wz fdr^i ^i molar`ql ab ilp bibjbkqlp af^dlk^ibp ab @,
0/- Cbjlpqo^o nrb rk^ j^qofw `r^ao^a^ ? v pr qo^kpmrbpq^ ?& qfbkbk bi jfpjl mlifkljfl`^o^`qboŒpqf`l-
00- Rf ? X @ plk j^qof`bp j Wj pfbkal ? kl pfkdri^o+ abjlpqo^o nrb ?@ v @? qfbkbk bijfpjl `lkgrkql ab ^rqls^ilobp+ fk`irpl pf ? bp pfkdri^o+ mbol kl bp kb`bp^ofl abjlp,qo^o bpql •iqfjl-
023 ?qpkr]hknao v ]qpkra_pknao
01- Rb^ ? rk^ j^qofw j tj `lk mlifkljfl `^o^`qboŒpqf`lb&V', Cbjlpqo^o 'mlo fkar``fŽk(nrb bi `lbcf`fbkqb ab Wcq
,Hbk c'=--( bp ,qo ?,
02- Rb^k ? v @ alp j^qof`bp j Wj q^ibp nrb abq? < abq@ v qo? < qo@, Cbjlpqo^o nrb? v @ qfbkbk bi jfpjl mlifkljfl `^o^`qboŒpqf`lpf j < 1 mbol nrb bpql kl bp pbdrolpf j :• 1-
03- Cbjlpqo^o `^a^ rk^ ab i^p pfdrfbkqbp molmlpf`Œlkbp obi^qfs^p ^ i^ qo^w^-
^( qo&? * @' < qo? * qo@,_( qo'a?( < a qo?-b( qo&?@'< qo&@?',a( qo?p < qo? -
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Dk bpq^ pb``fŽk abjlpqo^jlp nrb alp obmobpbkq^`flkbpj^qof`f^ibp afpqfkq^pab rk^ qo^kpcloj^`fŽk ifkb^i qfbkbk bi jfpjl mlifkljfl `^o^`qboŒpqf`l-O^o^ biilbpqraf^jlp `lk j^vlo `rfa^al i^ obi^`fŽk bkqobi^p j^qof`bp nrb obmobpbkq^ki^jfpj^ qo^kpcloj^`fŽk-
Qb`loabjlp `Žjl pb abcfkbk i^p obmobpbkq^`flkbpj^qof`f^ibp- Rrmlkd^jlpnrb R9 T y U pb^ rk^ ^mif`^`fŽk ab rk bpm^`fl k,afjbkpflk^i T bk rk bpm^`flj,afjbkpflk^i U- Rb^k &ah%,,, *aj' v 'U/ * ‹‹‹ * si( _^pbp loabk^a^p m^o^ T vU obpmb`qfs^jbkqb-K^ obmobpbkq^`fŽkj^qof`f^i ab R obi^qfs^ ^ i^p _^pbp bibdfa^pbp i^ j^qofw i Wj `rv^p `lirjk^p `lkpq^k ab ilp `ljmlkbkqbp ab R&ah'* ‹‹‹ * R&aj(
obpmb`ql^ i^ _^pb &s/ * ‹‹‹ * si(- O^oqfbkal ab _^pbp afpqfkq^ppb l_qfbkbk obmob,pbkq^`flkbp j^qof`f^ibp afpqfkq^p-
Blkpfabobjlp ^elo^ bi `^pl bk bi nrb T < U+v prmlkd^jlp nrb pb rqfifw^i^jfpj^ _^pb &ah%,,, * aj' m^o^T v m^o^U, Rb^ ? < &]eg' i^ j^qofw ab R obi^qfs^^ bpq^_^pb- Dpql pfdkfcf`^Prb
'3-7(’’
R'ag( < ]egae m^o^ g9:< 0+1+--- +j-f<i
Difg^jlp ^elo^ lqo^ _^pb &q+z* ,‹‹ * q,*' m^o^T v U v pb^ @< &^gf' i^ j^qofw ab Robi^qfs^ ^ bpq^krbs^ _^pb- Dkqlk`bp qbkbjlp
'3-8(’’
R&q f( < ^geSg m^o^ g< 0+1+--- +j -g;G
K]pne_ao mqa nalnaoajp]j h] ieoi] pn]jobkni]_e‰j heja]h 024
X^ nrb `^a^ Sf mboqbkb`b i bpm^`fl bkdbkao^al mlo bi +--- +aj mlabjlp bp,`of_fo
'3-0/(j
qf< _gfag m^o^ f<0+1+ --- +j+h<i
m^o^rk `fboql `lkgrkql ab bp`^i^obp Agf, K^ j^qofw j Wj B < &_gf' abqbojfk^a^mlo bplp bp`^i^obpbp kl pfkdri^o mrbpql nrb obmobpbkqrk^ qo^kpcloj^`fŽk ifkb^inrb ^mif`^ rk^ _^pb ab T bk lqo^ _^pb ab T, @mif`^kal R ^ ilp alp jfbj_olp ab'3-0/( q^j_f‹k l_qbkbjlp i^p b`r^`flkbp
' 3-00(’’
R'qf( < _gfR'ag( m^o^ g< 0+1+--- +j-h<i
Klp pfpqbj^p ab b`r^`flkbp abi '3-7( ^i '3-00( mrbabk bp`of_fopb`lk j^vlopfjmif`fa^a bk cloj^ j^qof`f^i fkqolar`fbkal j^qof`bp `rvlp bibjbkqlp pb^k sb`,qlobp- Rb^k
v
j^qof`bp cfi^ 0Wj `rvlp bibjbkqlp plk ilp ab i^ _^pb nrb pb `lkpfabo^- Dkqlk`bpbi `lkgrkql ab b`r^`flkbp '3-0/( mrbab bp`of_fopbjbaf^kqb rk^ b`r^`fŽk j^qof`f^i•kf`^+
'3-01( S<CA-
@kŠild^jbkqb+ pf fkqolar`fjlp
v S%< YR&q/'* ‹‹‹ * R&qj([+
K^p b`r^`flkbp '3-7(+ '3-8( X '3-00( pb `lksfboqbk obpmb`qfs^jbkqb bk
'3-02( C&<C?+ S&< S@+ S&<C&A-
@ m^oqfoab '3-01( q^j_f‹k pb l_qfbkb
C < TB,i-
025 ?qpkr]hknao v ]qpkra_pknao
O^o^e^ii^o i^ obi^`fŽk bkqob? v @bumobp^jlp S%ab alp j^kbo^p bk crk`fŽkab S, Cb '3-02( qbkbjlp
S&< S@v
S&< C&A< C?A < SA,G?A-
Olo il q^kql S@ < SA,h?A- Obol `^a^ bibjbkql bk bpq^b`r^`fŽk j^qof`f^i bp rk^`lj_fk^`fŽk ifkb^i ab ilp sb`qlobp _^pb Ti +ŠŠŠ+i3q- Orbpql nrb ilp qz plk fkab,mbkafbkqbpab_b pbo
@< A,h?A-
Blk biil+ ebjlp abjlpqo^al bi pfdrfbkqb qblobj^-
SDNQDL@ 3-5- Qe `ko i]pne_ao j Wj ? v @ nalnaoajp]j h] ieoi] pn]jobkn,i]_e‰j heja]h R+ateopaqj] i]pnev jk oejcqh]n B p]hmqa
@< A,G?A-
?`ai…o+ oe ? ao h] i]pnev `a R nah]per] ] qj] ^]oa C < Yah&--- +aj[ v @ h]i]pnev `a R nah]per]] h] ^]oa S < ZT{+--- *Sj[* ajpkj_ao _kik B lk`aiko pki]nh] i]pnev jk oejcqh]n mqa nah]_ekj] h]o `ko ^]oao ] pn]r†o`a h] a_q]_e‰ji]pne_e]hS;CA,
S^j_f‹k bp `fboql bi ob`Œmol`labi qblobj^ 3-5-
SDNQDL@ 3-6- Qa]j ? v @`ko i]pne_ao j t-j nah]_ekj]`]o lkn qj] a_q]_e‰j`a h] bkni] @< B,i ?A+ aj h] mqa b ao qj] i]pnev j Wj jk oejcqh]n- Cjpkj_ao? v @ nalnaoajp]j h] ieoi] pn]jobkni]_e‰j heja]h-
Baikopn]_e‰j- Difg^jlp rk^ _^pb C < Yah&--- +aŒŒ[ m^o^ rk bpm^`fl k,af,jbkpflk^i T, Rb^k Ti +ŠŠŠ+Sj ilp sb`qlobp abqbojfk^alp mlo i^p b`r^`flkbp
'3-03(IH
qQ< _gQag m^o^ f<h+1+ ---Œj+CK(S
bk alkab ilp bp`^i^obpAgf plk ilp bibjbkqlp ab B- Orbpql nrb b bp kl pfkdri^o ob,mobpbkq rk^ qo^kpcloj^`fŽk ifkb^i fksboqf_ib+ pŒnrb S < Yqh*‹‹‹ +Sj[ bp q^j,_f‹k rk^ _^pb m^o^T, v qbkbjlp S < CA,
Rb^ R i^ qo^kpcloj^`fŽk ifkb^i nrb qfbkb ? `ljl obmobpbkq^`fŽkj^qof`f^i
K]pne_ao mqa nalnaoajp]j h] ieoi] pn]jobkni]_e‰j heja]h 026
obpmb`ql i^ _^pb C* X pb^ R i^ qo^kpcloj^`fŽk ifkb^i nrb qfbkb@ `ljl obmobpbk,q^`fŽk j^qof`f^i obi^qfs^ ^ i^ _^pb S, Sbkbjlp bkqlk`bp
'3-04(ŠŠ
R'a++(<H]z!az m^o^ g < ($)$ &&&$j{<0
v
'3-05(ŠŠ
Q'qz( <G^!zq++ m^o^ g< )%*%''' %j-009,0
Cbjlpqo^objlp nrb R < R mol_^kal nrb R'qf( < Q'Sf( m^o^ `^a^ f-K^p b`r^`flkbp '3-04( v '3-05( mrbabk bp`of_fopbbk cloj^ j^qof`f^i `ljl
pfdrb+
YR'a0(+ ŒŒŒ+ R'aŒŒ([ < C?+ YQ&q0(+ŒŒŒ+Q&q‹‹'[ < S@,
@mif`^kal R ^ '3-03( pb l_qfbkb q^j_f‹k i^ obi^`fŽk R'qz( < H_gfR'ag(+l
YR&q0(+ŒŒŒ+R&q‹‹'[ < C?A,
Obol qbkbjlp
S@< CA@< CA&A+/?A' < C?A*
nrb abjrbpqo^ nrb R'qz( < Q'Sf( m^o^`^a^ f- Olo `lkpfdrfbkqb+R't( < Q't( m^o^`^a^ t ab T* `lk il nrb R < R- Cf`el ab lqol jlal+ i^p j^qof`bp ? v @ obmob,pbkq^k i^ jfpj^ qo^kpcloj^`fŽk ifkb^i-
CDEHMHBHˆM- Bko i]pne_ao j Wj ? v @ oa hh]i]j oaiaf]jpao oe ateopa qj]i]pnev jk oejcqh]n b p]hmqa @< a+h?a,
Klp qblobj^p 3-5 v 3-6 mrbabk `lj_fk^opb aŠkalklp bi pfdrfbkqb
SDNQDL@ 3-7- Bko i]pne_ao j Wj okj oaiaf]jpao oev o‰hkoe nalnaoajp]j h]ieoi] pn]jobkni]_e‰j heja]h
K^p j^qof`bp pbjbg^kqbp qfbkbk jr`e^p molmfba^abp-Olo bgbjmil+ qfbkbk bijfpjl abqbojfk^kqb mrbpql nrb
abq &A+h?A' < abq 'B,i('abq @('abq B( < abq ?,
Dpq^molmfba^a klp a^ bi qblobj^ pfdrfbkqb-
SDNQDL@ 3-8- J]o i]pne_ao oaiaf]jpao peajaj ah ieoik lkhejkiek _]n]_pa,n‡ope_kv lkn p]jpk hko ieoiko ]qpkr]hknao-
027 ?qpkr]hknao u ]qpkra_pknao
Baikopn]_e‰j- Rf ? X @ plk pbjbg^kqbp bufpqbrk^ j^qofw kl pfkdri^o bq^i nrb @ < a+/?a, Olo `lkpfdrfbkqb+qbkbjlp
?h , @ < ?h , a+/?a < (-B,H.B, A+G?A< B,H'@i, ?'A,
Dpqlmorb_^ nrb @i+@X?h+? plk pbjbg^kqbp+ pŒnrb abq&?h+@' < abq '@i +?',
Klp qblobj^p 3-7 v 3-8 morb_^k nrb qla^p i^p obmobpbkq^`flkbpj^qof`f^ibpab rk^ qo^kpcloj^`fŽk ifkb^i a^a^ R qfbkbk bi jfpjl mlifkljfl `^o^`qboŒpqf`l-Dpqbmlifkljfl q^j_f‹k pb ii^j^ bi mlifkljfl `^o^`qboŒpqf`lab R-
Di qblobj^ nrb pfdrb bp rk^ `lj_fk^`fŽk ab ilp qblobj^p 3-4+ 3-1 X 3-5-Dk bi qblobj^ 3-0/+ E obmobpbkq_fbk bi `rboml ob^i Q l bi `rboml `ljmibgl B-
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Baikopn]_e‰j- Rbd•k bi qblobj^ 3-4 `^a^ o^Œw@{ bp rk ^rqls^ilo- Orbpqlnrb bufpqbkj o^Œ`bpafpqfkq^p+bi qblobj^ 3-1 klp af`b nrb ilp ^rqlsb`qlobp `loobp,mlkafbkqbpq++--- -q: plk fkabmbkafbkqbp-Krbdl cloj^k rk^ _^pb m^o^ T- Dpqlabjrbpqo^ ^(- Bljl R&qz' < ?zSe* i^ j^qofw ab R obi^qfs^^ S bp i^ j^qofw af^dlk^i@+il nrb abjrbpqo^ _(- O^o^ abjlpqo^o b( rqfifw^jlp bi qblobj^ 3-5-
M^oanr]_e‰j9 K^ j^qofw kl pfkdri^o B abi qblobj^ 3-0/ pb ii^j^ i]pnev `e]ckj]he,v]jpa- Rf 'ah!!+ a-( bp i^ _^pb ab ilp sb`qlobp `lloabk^alp rkfq^oflp 'IH+ --- +h,'* bk,qlk`bp i^ b`r^`fŽk S < CA abi qblobj^ 3-0/ abjrbpqo^ nrb i^ `lirjk^ g ab B `lkpq^ab ilp `ljmlkbkqbp ab ilp ^rqlsb`qlobp Sg obi^qfslp ^ &H,*,,, *h,',
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Cfan_e_eko 028
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0- Cbjlpqo^o nrb i^p j^qof`bp Zz 9\ v Zz z\ qfbkbk ilp jfpjlp ^rqls^ilobp mbol kl
plk pbjbg^kqbp-1- G^ii^o bk `^a^ `^pl rk^ j^qofw kl pfkdri^o B q^i nrb A+G?Abp rk^ j^qofw af^dlk^i l
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2- Rb a^k bk bi mi^kl qobp _^pbp- Blk obpmb`ql ^ bp^p _^pbp rk mrkql qfbkb `ljl `ljml,kbkqbp &t! t*'* &u! u*'* v 'w+ v*' obpmb`qfs^jbkqb- Rrmlkd^jlp nrb Yu! u*[ < ZWH+t*[?*Yv!v+[ < Yt!t*[@* v Yv!v+[ < Yu!u+[A pfbkal ?* P* B j^qof`bp 1W1- Dumobp^o B bkcrk`fŽk ab ? v @-
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mbol nrb `^a^ rk^ bp pbjbg^kqb ^ rk^ j^qofw qof^kdri^o ab i^ cloj^ Z@i z\ bk i^ nrb @bp rk ^rqls^ilo- .0+
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7- C^a^ rk^ j^qofw ? j tj blk bibjbkqlp ob^ibp q^i nrb ?&< ,h- Cbjlpqo^o i^p molml,pf`flkbp pfdrfbkqbp obcbobkqbp ?,^( ? bp kl pfkdri^o-_( j bp m^o-b( ? kl qfbkb ^rqls^ilobp ob^ibp-a( `ap? < 0-
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Dpqb`^mŒqrilpb l`rm^ ab ^idrk^p molmfba^abpab ilp ^rqls^ilobp v ^rqlsb`,qlobp ab i^p qo^kpcloj^`flkbp ifkb^ibp nrb lmbo^k bk bpm^`flp br`iŒablp+bpql bp+bk bpm^`flp ifkb^ibp nrb qfbkbk molar`ql fkqboflo l bp`^i^o- Qb`loabjlp i^p molmfb,a^abp crka^jbkq^ibp ab ilp molar`qlp fkqboflobp-
Dk rk bpm^`fl br`iŒabl na]hrk molar`ql fkqboflo 't+u( ab alp bibjbkqlp t b vbp rk k•jbol ob^i nrb p^qfpc^`bi^p molmfba^abppfdrfbkqbp9
'0( &t* u' < &u*t' 'pfjbqoŒ^(&0' &t * v*u' < &t* u' * &v*u' 'ifkb^ifa^a(&1' &at*u' < a&t*u' 'eljldbkbfa^a(&2' &t* t' = N fc t y M 'mlpfqfsfa^a(-Dk rk bpm^`fl br`iŒabl _kilhafk bi molar`ql fkqboflo bp rk k•jbol `ljmibgl
nrb p^qfpc^`bi^p jfpj^p molmfba^abp+lk i^ bu`bm`fŽk ab nrb i^ pfjbqoŒ pb obbj,mi^w^mlo i^ oeiapn‡] `a Faniepa l daniepe]j]+
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bk alkab i^ _^oo^ obmobpbkqbi `ljmibgl `lkgrd^al- Dk 2( bi bp`^i^o a bp `ljmibgl-Cb '0&(v '2( l_qbkbjlp
'2&( &t* _u' < _&t*u'*
nrb klp af`b nrb ilp bp`^i^obpplk `lkgrd^alp `r^kal pb p^`^k abi pbdrkal c^`qlo-G^`fbkal bk+'0&(t < v sbjlp nrb ht+t( bp ob^i+ lk il nrb i^ molmfba^a '3( qfbkbpbkqfal pf bi bpm^`fl bp `ljmibgl-
Br^kal e^_i^jlp ab bpm^`fl br`iŒabl+ pfk jŠp+ pb pl_obbkqfbkab nrb bibpm^`fl mrbab pboob^i l `ljmibgl- Rf _fbk i^ j^vlo m^oqbab krbpqo^p^mif`^`flkbppb e^oŠk bk bpm^`flp ab afjbkpfŽk cfkfq^+kl fjmlkaobjlp bp^ obpqof``fŽk^ moflof-
030
031 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
Di mofjbo qblobj^ abjrbpqo^ nrb ilp ^rqls^ilobp 'pf bufpqbk( mrbabk bumob,p^opb bk crk`fŽk abi molar`ql fkqboflo-
SDNQDL@ 4-0- QeC ao qj aol]_ek aq_h‡`ak+T qj oq^aol]_ek `a C v _kjoe,`an]iko qj] pn]jobkni]_e‰j heja]h R9T y C mqa pajc] qj ]qpkr]hkn @ _kj qj_knnaolkj`eajpa ]qpkra_pkn t+ ajpkj_ao
'4-0( @ < &R&t'* t' ,
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&R&t'* t' < &?V*t' < ?&V*t',
Bljl t ;/; N mlabjlp afsfafo mlo &t* t' l_qbkfbkal '4-0(-
U^of^p molmfba^abp ab ilp ^rqls^ilobp pb abar`bk cŠ`fijbkqb ^ m^oqfo ab i^b`r^`fŽk '4-0(- Olo bgbjmil+ ab i^ pfjbqoŒ^ ebojfqf^k^ abi molar`ql fkqboflo qb,kbjlp i^ cŽojri^ ^kŠild^
'4-1(t < &t* R&t€
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m^o^ bi `ljmibgl `lkgrd^al ab @- Cb '4-0( v '4-1( abar`fjlp nrb @ bp ob^i'@ < V( pf v pŽil pf &R&t'* t' bp fj^dfk^ofl mrol+ bpql bp+pf v pŽil pf
&R&t'* t' < &t* R&t€ m^o^ bi ^rqlsb`qlo t-
'Dpq^ `lkaf`fŽk pb `rjmib bk rk bpm^`fl br`iŒabl ob^i(- S^j_f‹k+ @ bp fj^dfk^oflmrol '@-< +V' pf v pli^jbkqb pf &R&t'* t' bp fj^dfk^ofl mrol+ il nrb bp il jfpjl+pf v pli^jbkqb pf
&R&t'* t' < +&t* R&t€ m^o^ bi ^rqlsb`qlo t-
-'* E[JW\OX[VJLRXWN\QN[VR]RJWJ\b ebjf,ebojfqf^k^p
Dk bpq^ pb``fŽk fkqolar`fjlp alp qfmlp fjmloq^kqbp ab lmbo^alobp ifkb^ibpnrb ^`q•^k bk bpm^`flp br`iŒablp- Dplp lmbo^alobp qfbkbk alp `^qbdloŒ^p ab abkl,jfk^`flkbp+ nrb abmbkabk ab pf bi bpm^`fl br`iŒabl crka^jbkq^i qfbkb molar`qlfkqboflo ob^i l `ljmibgl- Dk bi `^pl ob^i i^p qo^kpcloj^`flkbp pb ii^j^k oei†pne_]ol daie,oei†pne_]o- Dk bi `^pl `ljmibgl pb ii^j^k daniepe]j]o l daie,daniepe]j]o-Dp^p qo^kpcloj^`flkbp pb mobpbkq^k bk jriqfqra ab&^mif`^`flkbp afpqfkq^p- Olo
Rn]jobkni]_ekjao daniepe]j]o v daie,daniepe]j]o 032
bgbjmil+ ilp lmbo^alobp ebookfqf^klp bk bpm^`flp ab afjbkpfŽk fkcfkfq^abpbjmb,•^k rk fjmloq^kqb m^mbibk Lb`Škf`^ BrŠkqf`^- Cfp`rqfobjlp bk mofjbo ird^o bi`^pl `ljmibgl v^ nrb kl mobpbkq krbs^p afcf`riq^abp-
CDEHMHBHˆM- Qa]j C qj aol]_ek aq_h‡`ak v T qj oq^aol]_ek `a C- Sj]pn]jobkni]_e‰j heja]h R9 T y C oa hh]i] daniepe]j] aj Toe
&R&t'*u' < &t* R&u'' l]n] pk`k t v pk`k v `a T-
Ch klan]`kn R oa hh]i] daie,daniepe]jk aj T oe
&R&t'*u' < , &t* R&u,'' l]n] pk`k t v pk`k v `a T-
Cf`el ab lqol jlal+ rk lmbo^alo ebojfqf^kl R mrbab m^p^opbab rk c^`qloab rk molar`ql fkqboflo ^i lqol pfk jlafcf`^o bi s^ilo abi molar`ql- S^i m^pl bkbi `^pl ab rk lmbo^alo ebokf,ebojfqf^kl `^j_f^ bi pfdkl abi molar`ql-
M^oanr]_e‰j9 Bljl v^ pb e^ jbk`flk^al+ pf D bp rk bpm^`fl br`iŒabl na]h+i^p qo^kplcloj^`flkbp ebojfqf^k^p q^j_f‹k pb ii^j^k oei†pne_]o: i^p qo^kpcloj^`flkbp ebjf,ebojf,qf^k^p pb ii^j^k daie,oei†pne_]o-
DIDLOKN 0- Qeiapn‡] v daie,oeiapne] aj ah aol]_ek A']+ ^(- Rb^ A']+ ^(bi bpm^`fl ab qla^p i^p crk`flkbp ob^ibp`lkqfkr^p bk rk fkqbos^il `boo^al Y]* ^[*`lk bi molar`ql fkqboflo ob^i
'I+ d( < qb'p(c'p( `p-
Rb^ T rk pr_bpm^`fl ab A']+ ^(- Qe R9 T y A']+ ^( bp rk^ qo^kpcloj^`fŽk ifkb^i+bkqlk`bp 'f+ R'c• <byb'p(Rc'p(`p+ alkab ebjlp bp`ofql Rc'p( bk ird^o ab R'c('p(Olo `lkpfdrfbkqb+i^p `lkaf`flkbp m^o^ i^ pfjbqoŒ v i^ ebjf,pfjbqoŒ^ pb `lksfbo,qbk bk
'4-2( qwH'p(Rc'p( , c'p(Rb'p(x `p < N pf R bp pfj‹qof`^+
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'4-3( qwH'p(Rc'p( * c'p( Rb'p(x `p < N pf R bp ebjf,pfj‹qof`^-
DIDLOKN 1- Kqhpelhe_]_e‰j lkn qj] bqj_e‰j fee]- Dk bi bpm^`fl A']+ ^( abibgbjmil 0+bifg^jlp rk^ crk`fŽk cfg l v abcfk^jlp R'f( < lb+ molar`ql ab l v b-O^o^ bp^ R* i^ b`r^`fŽk '4-2( pb p^qfpc^`b`r^ibpnrfbo^ nrb pb^k b v d bk B'z+ ^'
033 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h†`ako
mrbpql nrb bi fkqbdo^kal bp `bol- Olo `lkpfdrfbkqb+ i^ jriqfmif`^`fŽk mlo rk^ crk,`fŽk cfg^bp rk lmbo^alo pfj‹qof`l-
DIDLOKN 2- Ch klan]`kn `aner]`], Dk bi bpm^`fl A&]* ^' abi bgbjmil 0+pb^ T bi pr_bpm^`fl ab qla^p i^p crk`flkbp b nrb qfbkbk abofs^a^,`lkqfkr^ bk bifkqbos^il ^_fboql &]* ^' X nrb p^qfpc^`bk q^j_f‹k i^ _kj`e_eˆj `a _kjpknjkba]' < &^', Rb^ C9 T y A&]* ^' bi lmbo^alo abofs^a^ a^al mlo B&b' < c-Qbpriq^pbk`fiil abjlpqo^o nrb C bp ebjf,pfj‹qof`l- Dk bpqb`^pl bi fkqbdo^kal ab '4-3( bpi^ abofs^a^ abi molar`ql pa-mlo 0/ `r^i i^ fkqbdo^ibp fdr^i ^
H8'bc(&'p( `p < b'^(c'^( , b'](c'](-
Orbpql nrb b v d p^qfpc^`bk ^j_^p i^ `lkaf`fŽk ab `lkqlokl+ qbkbjlpb&^'c&^' + b&]'c&]' < N-@pŒmrbp+i^ `lkaf`fŽk ab `lkqlokl fjmif`^ i^ ebjŒ,pfjb,qoŒab C- K^p crk`flkbp `lkpq^kqbp plk i^p •kf`^p ^rqlcrk`flkbp bk bi pr_bpm^,`fl T- Oboqbkb`bk^i ^rqls^ilo N-
DIDLOKN 3- Mlan]`knao `a Qpqni+Jekqrehha, Dpqb bgbjmil bp fjmloq^kqbbk i^ qbloŒ ab i^p b`r^`flkbp afcbobk`f^ibp ifkb^ibp ab pbdrkal loabk- Tqfif`bjlprk^ sbw jŠp bi bpm^`fl A&]* ^' abi bgbjmil 0 v pb^ T bi pr_ bpm^`fl ab qla^p i^pcrk`flkbp b nrb qfbkbk abofs^a^ pbdrka^ `lkqfkr^ bk Y]* ^[ X nrb p^qfpc^`bki^p`lkaf`flkbp ab `lkqlokl
'4-4( l'](b']( < N+ l'^(b'^( < N+
pfbkal l rk^ crk`fŽk cfg^ab A&]* ^' `lk abofs^a^ `lkqfkr^ bk Y]* ^[, Rb^ m lqo^crk`fŽk cfg^bk A&]* ^' v pb^ R8 T y A&]* ^' bi lmbo^alo abcfkfal mlo i^ b`r^`fŽk
R'b( < 'NG&(&* mb•
†pqb pb ii^j^ klan]`kn `a Qpqni+Jekqrehha,O^o^ ^sbofdr^o pr pfjbqoŒ l_pbosbjlpnrb R&c' + cR&b' < b&lc%'%+ c&lb%'*,Tqfifw^kal bpqbobpriq^al bk '4-2( b fkqb,do^kal mlo m^oqbp+bk`lkqo^jlp
H8wbR'c( , cR'b(x `p < blc& 09, H8lc&b&`p , clb& 09* qNG&d&p < N+
v^ nrb q^kql b `ljl d p^qfpc^`bki^p `lkaf`flkbp ab `lkqlokl '4-4(- Olo q^kqlR bp pfj‹qof`l bk T, K^p ^rqlcrk`flkbp ab R plk ^nrbii^p crk`flkbp kl kri^p
Mnpkckj]he`]` `a hko ]qpkra_pknao 034
b nrb p^qfpc^`bk+ m^o^ rk `fboql s^ilo ob^i @+rk^ b`r^`fŽk afcbobk`f^i ab i^ cloj^
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bk Y]* ^[* v i^p `lkaf`flkbp ab `lkqlokl '4-4(-
4-2 @rqls^ilobp v ^rqlsb`qlobp ab ilp lmbo^alobp ebojfqf^klp v ebjf,ebojfqf^klp
Dk `r^kql ^ ilp ^rqls^ilobp qbkbjlp bi pfdrfbkqb qblobj^9
SDNQDL@ 4-1- Rf R peaja qj ]qpkr]hkn @+ajpkj_ao9^( Rf R ao daniepe]jk+ @ ao na]h9@ < V,_( Rf R ao daie,daniepe]jk+ @ ao ei]cej]nek lqnk9 @< ,V-
Baikopn]_e‰j- Rb^ t rk ^rqlsb`qlo `loobpmlkafbkqb ^ @- Sbkbjlp bkqlk`bp
‹ &R&t'* t'Hq< ,,,
&t* t'v p, &t* R&t€
Hq<,,,,-&t* t'
Rf R bp ebojfqf^kl qbkbjlp &R&t'* t' < &t* R&t€ ^pŒnrb @< V, Rf R bp ebjf,ebojfqf^kl qbkbjlp &R&t'* t' < , &t* R&t€ `lk il `r^i @< ,V-
M^oanr]_e‰j9 Rf R bp oei†pne_k+ bi qblobj^ 4-1 k^a^ krbsl klp af`b ^`bo`^ ab ilp^rqls^ilobp ab R mrbpql nrb qlalp ilp ^rqls^ilobp ab_bk pbo ob^ibp pf pr molar`ql fkqboflobp ob^i- Rf R bp daie,oei†pne_k+ ilp ^rqls^ilobp ab R ab_bk pbo ^ rk qfbjml ob^ibp bfj^dfk^oflp mrolp+ irbdl ab_bk pbo `bol 'pf bufpqbk(-
4-3 Noqldlk^ifa^a ab ilp ^rqlsb`qlobp `loobpmlkafbkqbp ^ ^rqls^ilobp afpqfkqlp
Klp ^rqls^ilobp afpqfkqlp ab rk^ qo^kpcloj^`fŽk ifkb^i `r^inrfbo^ `loobpmlk,abk ^ ^rqlsb`qlobp fkabmbkafbkqbp 'pbd•k bi qblobj^ 3-1(- O^o^ i^p qo^kpcloj^,`flkbp ebojfqf^k^p v ebjf,ebojfqf^k^p mlabjlp ab`fo ^•k jŠp-
SDNQDL@ 4-2- Rf R ao qj] pn]jobkni]_e‰j daniepe]j] k daie,daniepe]j]v oe @ u I,q okj ]qpkr]hknao `eopejpko `a R _kj hko ]qpkra_pknao _knnaolkj`eajpaot a u* ajpkj_ao t a u okj knpkckj]hao: aopk ao &t* u';M, ,
Baikopn]_e‰j- Dp`of_^jlp R&t' < ?V* R&u' < H+pWX `ljm^objlp ilp alpmolar`qlp fkqboflobp &R&t'* u' v &t* R&u€, Sbkbjlp
&R&t'*u' < &H,t*u' < ?&V*u' v &t* R&u€'< &t* "u' < N&t*u',
035 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h†`ako
Rf R bp ebojfqf^k^ bpql klp a^ %Z&t*v( < zh&t*u' < l,&t*v( v^ nrb b+h< zh,Olo `lk,pfdrfbkqb &t* v( < N mrbpql nrb +[<G<xJ- Rf R bp ebjf,ebojfqf^k^ l_qbkbjlp%Z&t*v( < +zh&t*u' < l,&t*v( nrb fjmif`^ q^j_f‹k &t*v( < N-
DIDLOKN- @mifnrbjlp bi qblobj^ 4-2 ^ ^nrbii^p crk`flkbp kl kri^p nrbp^qfpc^`bkrk^ b`r^`fŽk afcbobk`f^i ab i^ cloj^
'4-5( 'Nb&(&* mh< (+0
bk rk fkqbos^il Y]* ^[* v nrb p^qfpc^`bk q^j_f‹k i^p `lkaf`flkbp ab `lkqlokll&]'b&]' < l&^'b&^' < N- K^ `lk`irpfŽk bp nrb alp plir`flkbp `r^ibpnrfbo^ b vd`loobpmleafbkqbp ^ alp s^ilobp afpqfkqlp ab +[ plk loqldlk^ibp- Olo bgbjmil+ `lk,pfabobjlp i^ b`r^`fŽk afcbobk`f^i abi jlsfjfbkql ^ojŽkf`l pfjmib
b! * gy< N
bk bi fkqbos^il ZN+6S\+ pfbkal g <0< N- †pq^ qfbkbi^ cloj^ '4-5( `lk l < 0+m < N+X +[< , g1 - Sla^p i^p plir`flkbp sfbkbk a^a^p mlo b&p' < Bi `lp gp * A1 pbk gp -K^ `lkaf`fŽk ab `lkqlokl baM( < N fjmif`^ ah < N- K^ pbdrka^ `lkaf`fŽk ab`lkqlokl+ b'6R( < N+fjmif`^ A1 pbk g6R < N- Orbpql nrb A1 <0< N m^o^ rk^ plir`fŽkkl kri^+ ab_b pbo pbk g6R < N+0/ nrb fkaf`^ nrb g bp bkqbol- Cf`el ab lqoljlal+ i^p plir`flkbp kl kri^p nrb p^qfpc^`bki^p `lkaf`flkbp ab `lkqlokl bufpqbkpfv pŽil pf g bp bkqbol- Dp^pplir`flkbp plk b&p' < pbk jp+j < ,*,0+,*,1+---- K^ `lk,af`fŽk ab loqldlk^ifa^a nrb bi qblobj^ 4-2 fjmif`^+ pb qo^kpcloj^ ^elo^ bk i^obi^`fŽk `lkl`fa^
Hk! pbk jp pbk ip `p < N
pf i! v j1 plk bkqbolp afpqfkqlp-
4-4 Dgbo`f`flp
0- Rb^k C rk bpm^`fl br`iŒabl v T rk pr_bpm^`fl+ v pb^ R9T y C rk^ qo^kpcloj^`fŽkifkb^i a^a^- Rb^k @rk bp`^i^o v t rk bibjbkql kl kril ab T, Cbjlpqo^o nrb @bp rk^rqls^ilo ab R*`lk t `ljl ^rqlsb`qlo+ pf v pŽil pf
&R&t'* u' < ?,&t*u' m^o^ qlal u ab C,
1- Rb^ R't( < at m^o^ qlal t rk bpm^`fl ifkb^i T+ pfbkal b rk bp`^i^o cfg^al- Cbjlpqo^onrb R bp pfj‹qof`l pf T bp rk bpm^`fl br`iŒabl ob^i-
2- Rrmlkd^jlp nrb R8T y T bp rk^ qo^kpcloj^`fŽk ebojfqf^k^-^( Cbjlpqo^o nrb R! bp ebojfqf^k^ m^o^ qlal bkqbol mlpfqfsl j+v nrb R,&bp ebojfqf^k^pf R bp fksboqf_ib-_( „Pr‹ mrbab ab`fopb ab R! v ab R,& pf R bp ebjf,ebojfqf^k^>
Cfan_e_eko 036
3- Rb^k S+9 T y C X R+9T y C alp qo^kpcloj^`flkbp ebojfqf^k^p-^( Cbjlpqo^o nrb ]RG * ^&G&+bp ebojfqf^k^ m^o^ qlal m^o ab bp`^i^obp ob^ibp ] v ^ -_( Cbjlpqo^o nrb bi molar`ql 'i^ `ljmlpf`fŽk( RGR*bp ebojfqf^k^ pf RGv R* plk mbojr,q^_ibp+ bpql bp+ pf RGR*< R*R*,
4- Rb^ T < U+'Q( `lk bi molar`ql bp`^i^o loafk^ofl `ljl molar`ql fkqboflo- Rb^ Srk^pfjbqoŒ^ bk bi mi^kl tu9 bpql bp+R':( < e* RS( < f v R'g( < ,g- Cbjlpqo^o nrb Rbp pfj‹qof`^-
5- Rb^ A&M*0( bi bpm^`fl ifkb^i ob^i ab qla^p i^p crk`flkbp `lkqfkr^p bk Z/+0\ `lk molar`qlfkqboflo '.+ d( <k h&p'c&p'`p,Rb^ U bi pr_bpm^`fl ab qla^p i^p Gq^ibp nrb k h&p'`p< l- Rb^R8 T y A&M*0( bi lmbo^alo fkqbdo^`fŽk abcfkfal mlo RG&t' < Izh&p'`p,Cbjlpqo^o nrb Rbp ebjf,pŒj‹qof`^-
6- Rb^ T bi bpm^`fl br`iŒabl ob^i ab qlalp ilp mlifkljflp `lk bi molar`ql fkqboflo&b*d( ;C,/-&p'c&p'`p, Cbqbojfk^o `rŠibp ab i^p pfdrfbkqbp qo^kpcloj^`flkbp R8T y Tokjpfj‹qof`^p l ebokŒ,pŒj‹qoŒ`^p9 H
^( Rb't( <b' ,t(-_( Rb't( < b't(b' ,t(-
b( Rb't( < b't( * b' ,t(-
a( Rb't( < b't( , b' ,t(-
7- Dk bi bgbjmil 3 ab i^ pb``fŽk 4-1+ jlafcf`^o bi molar`ql fkqboflo ^pŒ9
'b+c( < I9b'p(c'p(s'p( `p+
pfbkal t rk^ crk`fŽk mlpfqfs^ cfg^a^ mboqbkb`fbkqb ^ A&]* ^', Llafcf`^o bi lmbo^alo R abRqroj,Kflrsfiib bp`of_fbkal
R'b( < 'lb&(&* mb-s
Cbjlpqo^o nrb bi lmbo^alo jlafcf`^al bp pfj‹qof`l bk bi pr_bpm^`fl T,8- Rb^ T rk pr_bpm^`fl ab rk bpm^`fl br`iŒabl `ljmibgl C, Rb^ R8 T y C rk^ qo^kpclo,
j^`fŽk ifkb^i v abcfk^jlp rk^ crk`fŽk ab s^ilobp bp`^i^obp P bk T* `ljl pfdrb9
O't( < 'R't(+ t( m^o^ qlal t ab T,
^( Rf R bp ebojfqf^k^ bk T* abjlpqo^o nrb O&t' bp ob^i m^o^ qlal t,_( Rf R bp ebjf,ebojfqŒ^k^+ abjlpqo^o nrb O&t' bp fj^dfk^of^ mro^ m^o^ qlal t,b( Cbjlpqo^o nrb O&pt' < peO&t' m^o^ qlal bp`^i^o p-a( Cbjlpqo^o nrb O&t * v( < O&t' * O&u' * &R&t'* v( * &R&u'*t'* v e^ii^o i^ cŽojri^^kŠild^ m^o^ O&t * pu',b( Rf O&t' < N m^o^ qlal t abjlpqo^o nrb R&t' < N m^o^ qlal t,c( Rf O&t' bp ob^i m^o^ qlal t abjlpqo^o nrb R bp ebojfqf^k^- YGj`e_]_eˆj8 Tqfifw^oi^ molmfba^a ab nrb O&t * pu' bp fdr^i ^ pr `lkgrd^a^ m^o^ qlal bp`^i^o p,[
0/- Dpqb bgbo`f`fl mlkb ab j^kfcfbpql nrb ilp mlifkljflp ab Kbdbkaob 'fkqolar`falp bk i^pb``fŽk 0-03( plk ^rqlcrk`flkbp ab rk lmbo^alo ab Rqroj,Kflrsfiib- Klp mlifkljflp abKbdbkaob pb abcfkbk jbaf^kqb i^ b`r^`fŽk
alkab bj'p( < 'p1 , H(!+
^( Bljmol_^o nrb &p%+ i(g&k'q(< 1jp.-'p( -
037 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
_( Cbofs^o i^ b`r^`f5k abi ^m^oq^al^( j * 0 sb`bp+jbaf^kqb i^ cŽojri^ ab Kbf_kfw'sbo m- abi Ulirjbk 0(- lk 0/ nrb pb l_qfbkb
'p1 , h(byj*1('p( * 1p'j * Obyj*hh'p( * j'j * h(byj('p(
< 1jpby!*h('p( * 1j'j * iUz!('q(-
`( Cbjlpqo^o nrb i^ b`r^`f5k abi ^m^oq^al_( mrbab mlkbopbbk i^ cloj^
'p1 ,h(Ny'p([& < j'j * h(N+-'p(-
Dpql abjrbpqo^ nrb N,&p' bp rk^ ^rqlcrk`f5k abi- lmbo^alo ab Rqroj,Kflrsfiib a^al bkbi fkqbos^il Z,0+0\mlo jbafl ab R&b' < &lb%'%*pfbkal l&p' < b ,,,,90- K^ ^rqlcrk`f5kN,&p' mboqbkb`bi ^rqls^ilo @< j&j * 0(- Dk bpqbbgbjmil i^p `lkaf`flkbp ab `lkqloklm^o i^ pfjbqoŒpbp^qfpc^`bkrqljŠqf`^jbkqb mrbpqlnrb m'q( < l& ,0( < N-
-'. 8aR\]NWLRJMN WLXWS^W]Xloqlkloj^i MNJ^]X_NL]X[N\YJ[J XYN[JMX[N\ebojf,]RJWX\b ebjf,ebojŒqf^klp Z^NJL]nJWNWN\YJLRX\MNMRVNW\RmWORWR]J
Klp alp qblobj^p 4-1 v 4-2 pb crka^jbkq^k bk i^ efmŽqbpfpab nrb R qfbkbrk ^rqls^ilo- Bljl p^_bjlp+ ilp ^rqls^ilobp kl bufpqbkkb`bp^of^jbkqb- Ml l_p,q^kqb pf R ^`q•^ bk rk bpm^`fl _kilhafk ab afjbkpfŽk bejep]+bkqlk`bp bufpqbkpfbjmob ilp ^rqls^ilobp mrbpql nrb plk i^p o^Œ`bpabi mlifkljfl `^o^`qboŒpqf`l-Rf R bp ebojfqf^kl+ qlalp ilp ^rqls^ilobp plk ob^ibp- Rf R bp ebjf,ebojfqf^kl+qlalp ilp ^rqls^ilobp plk fj^dfk^oflp mrolp-
S^j_f‹k p^_bjlp nrb alp ^rqls^ilobp afpqfkqlp mboqbkb`bk^ ^rqlsb`qlobploqldlk^ibp+ pf R bp ebojfqf^kl l ebjf,ebojfqf^kl- Tp^kal bpq^ molmfba^a pbmrbab mol_^o nrb R qfbkbrk `lkgrkql loqlkloj^i ab ^rqlsb`qlobp nrb bkdbkao^kqlal bi bpm^`fl- 'Qb`loabjlp nrb rk `lkgrkql loqldlk^i pb ii^j^ loqlkloj^i pf`^a^ rkl ab prp bibjbkqlp qfbkb kloj^ 0-( -
SDNQDL@ 4-3- Qqlkjc]iko mqa afj T < j v oa] R9 T y T daniepe]jk ldaie,daniepe]jk- Cteopaj ajpkj_ao j ]qpkra_pknao S0+ ŒŒŒ+Sj `a R mqa bkni]jqj] ^]oa knpkjkni]h l]n] T- Nkn p]jpk+h] i]pnev `a R nah]per]] aop] ^]oa ao h]i]pnev `e]ckj]h @< af^d '-[0&--- ++[+-(+aj `kj`a ,Zg ao ah ]qpkr]hkn lanpaja_eajpa] Sg Œ
Baikopn]_e‰j- Tqfif`bjlp bi j‹qlal ab fkar``fŽk obpmb`ql^ i^ afjbkpfŽkj- Rf j < 0+ bkqlk`bp R qfbkb bu^`q^jbkqb rk ^rqls^ilo- Br^inrfbo ^rqlsb`qloS/ ab kloj^ 0 bp rk^ _^pb loqlkloj^i m^o^ T ,
Rrmlkd^jlp ^elo^ bi qblobj^ `fboql m^o^ qlal bpm^`fl br`iŒabl ab afjbk,pfŽk j+h, O^o^ abjlpqo^o nrb bp `fboql m^o^ T bifg^jlp rk ^rqls^ilo z m^o^
Palnaoajp]_e‰ji]pne_e]h l]n] klan]`knao 038
R X rk ^rqlsb`qlo `loobpmlkafbkqb Ti ab kloj^ 0- Dkqlk`bp R&qh' < @0Ti vIiriii < 0 - Rb^ R bi pr_ bpm^`fl bkdbkao^al mlo Sh ‹ @mif`^objlp i^ efmŽqbpfpabfkar``fŽk ^i pr_bpm^`fl R0- nrb `lkpq^ ab qlalp ilp bibjbkqlp ab U nrb plk loql,dlk^ibp ^ T0 +
R0, < wt Ht D T* &t* ri( < Ny-
O^o^ biil kb`bpfq^jlp p^_bo nrb afj R0- < j,0 v nrb R ^mif`^ R0- bk pŒjfpjl-Rbd•k bi qblobj^ 0-6 ^( p^_bjlp nrb q+bp m^oqbab rk^ _^pb m^o^ T* pb^
‹pq^ i^ _^pb 'ri +T1 + ŒŒŒ+rj(- Olabjlp prmlkbo+ pfk m‹oafa^ ab dbkbo^ifa^a+ nrb‹p^ bp rk^ _^pb loqlkloj^H- 'Rf kl 0/ crbo^+ ^mif`^oŒ^jlp bi j‹qlal ab Fo^j,R`ejfaq m^o^ `lksboqfoi^ bk q^i+j^kqbkfbkal T0 `ljl mofjbo bibjbkql ab i^_^p, ( Sljbjlp pbdrfa^jbkqb rk t `r^inrfbo^ bk R0- v bp`of_^jlp
Dkqlk`bp Vh < &t* ri( < N v^ nrb i^ _^pb bp loqlkloj^i+ ^pŒnrb t mboqbkb`b^ibpm^`fl bkdbkao^al mlo T0*!! Tj‹ Krbdl afj R0- < j,h-
Cbjlpqobjlp ^ `lkqfkr^`fŽk nrb R ^mif`^ RI---bk pŒjfpjl- Rrmlkd^jlp nrbR bp ebojfqf^k^- Rf t D R0- qbkbjlp
&R&t'*qh( < &t* R&qh((< &t* @iri( < @i'W+qh( < N+
mlo 0/ nrb R&t' D o/,, Orbpql nrb R bp ebojfqf^k^ bk Q/, mlabjlp ^mif`^o i^ ef,mŽqbpfpab fkar``fŽk bk`lkqo^kal nrb R qfbkb j , 0 ^rglsb`qlobp S1 + ŒŒŒ-q: nrb`lkpqfqrvbk rk^ _^pb loqlkloj^i m^o^ Q0--Olo il q^kql+bi `lkgrkql loqldlk^iSh * ‹‹‹ * Sj bp rk^ _^pb loqlkloj^i m^o^ T, Dpql abjrbpqo^ bi qblobj^ pf R bpebojfqf^k^- @odrjbkql pfjfi^o ^mif`^objlp pf R bp ebjf,ebojfqf^k^-
4-6 Qbmobpbkq^`fŽkj^qof`f^i m^o^lmbo^alobp ebojfqf^klp v ebjf,ebojfqf^klp
Rrmlkbjlp bk bpq^pb``fŽk nrb T bp rk bpm^`fl br`iŒabl ab afjbkpfŽk cfkf,q^l Tk^ qo^kpcloj^`fŽk ebojfqf^k^ l ebjf,ebojfqf^k^ mrbab `^o^`qbofw^opbmlopr ^``fŽk pl_ob ilp bibjbkqlp ab rk^ _^pb `r^inrfbo^-
SDNQDL@ 4-4- Qa]j 'ah&--- +aj( qj] ^]oa l]n] T u R9 T y T qj] pn]jo,bkni]_e‰j heja]h-Rajaiko ajpkj_ao9
^( R ao daniepe]j] oe u o‰hkoe 'R'af(+az( < 'af+R'az• l]n] pk`k l]n e*g-_( Rao daie,daniepe]j] pf u o‰hkpf'R'af(+az(<, 'af+R'az•l]n] pk`k l]n e*f,
Baikopn]_e‰j- Sljbjlp alp bibjbkqlp `r^ibpnrfbo^ t b u ab T v bumob
04/ ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
pbjlp `^a^ rkl bk crk`fŽk ab ilp bibjbkqlp ab i^ _^pb+ pb^k t < t-a+ bv < uzaz- Sbkbjlp bkqlk`bp
Cbi jfpjl jlal bk`lkqo^jlpj j
't+ R'u• < teWe'ae+R'ae((-f<0f<i
K^p molmlpf`flkbp ^( v _( pb abar`bk ^i jljbkql ^ m^oqfoab bp^pb`r^`flkbp-
U^jlp ^ bumobp^obpqlp `lk`bmqlp mlo jbafl ab i^ obmobpbkq^`fŽkj^qof`f^iab R,
SDNQDL@ 4-5- Qa] 'bi&--- *aj' qj] ^]oa knpkjkni]h l]n] T+u oa] ? < ']e(h] nalnaoajp]_e‰ji]pne_e]h `a qj] pn]jobkni]_e‰j heja]hR9 T y T naola_pk`a ao]^]oa- Rajaiko ajpkj_ao9
^( R ao daniepe]j] oeu o‰hkoe ]-+< ]eel]n] pk`k l]n e+e,_( R ao daie,daniepe]j] oeu o‰hkoe]e: < ,]:: l]n] pk`k l]n e*e-Baikopn]_e‰j- Orbpql nrb ? bp i^ j^qofw ab R qbkbjlp R'af( < z<0 ]geag-
Slj^kal bi molar`ql fkqboflo ab R&af' mlo az v qbkfbkal bk `rbkq^ i^ ifkb^ifa^aabi molar`ql fkqboflo l_qbkbjlp
Obol &ag*az' < N p^isl pf g < e* ^pŒ nrb i^ •iqfj^ prj^ pb obar`b ^]ef'az+az( < ]q &v nrb 'b„ ae(< 0 - Krbdl obpriq^
]e: < 'R'ae(+ae( m^o^qlal m^oe*f,
Hkqbo`^j_f^kal e X f* qlj^kal ilp `lkgrd^alp+ v qbkfbkal bk `rbkq^ i^ pfjbqoŒ^ebojfqf^k^ abi molar`ql fkqboflo+bk`lkqo^jlp
]:e << 'a:+R'ae• m^o^qlal m^oe*e-
O^o^ `ljmibq^o- i^ abjlpqo^`fŽk _^pq^ ^mif`^o ^elo^ bi qblobj^ 4-4-
4-7 L^qof`bp ebojfqf^k^p v ebjf,ebojfqf^k^p+ L^qofw ^agrkq^ ab rk^ j^qofw
Di qblobj^ 4+5 klp prdfbob i^ pfdrfbkqb abcfkf`fŽk-
Be]ckj]hev]_e5j `a qj] i]pnev daniepe]j] l daie,daniepe]j] 040
CDEHMHBHˆM- Sj] i]pnev _q]`n]`] ? < ']z.( oa `ajkiej] daniepp]j] -oe]ee< ]ql]n] pk`k l]n e+f- Qa `e_a mqa ? ao daie,daniepe]j] oe]:e < ,]ze l]n]pk`k l]n e*f-
Di qblobj^ 4-5 bpq^_ib`b nrb rk^ qo^kpcloj^`f5k R bk rk bpm^`fl T ab af,jbkpfŽk cfkfq^ bp ebojfqf^k^l ebjf,ebojfqf^k^ pbd•k nrb pr j^qofw obi^qfs^ ^rk^ _^pb loqlkloj^i pb^ ebojfqf^k^ l ebjf,ebojfqf^k^-
Dp^p j^qof`bp mrbabk fkqolar`fopb ab lqo^ j^kbo^- Ki^jbjlp ? i^ j^qofwl_qbkfa^ obbjmi^w^kal `^a^ bibjbkql ab ? mlo pr `ljmibgl `lkgrd^al- K^ j^,qofw? pb ii^j^ i^ _kjfqc]`] ab ?- K^ j^qofw ? bp ebojfqf^k^ pf v pŽil pf bpfdr^i ^ i^ qo^kpmrbpq^ ab pr `lkgrd^a^ ? < ?p- Dp ebjf,ebojfqf^k^ pf ? < , ?p -
K^ qo^kpmrbpq^ ab i^ `lkgrd^a^ ob`f_b rk klj_ob bpmb`f^i-
CDEHMHBHˆM CD L@SQHY @CITMS@ CD TM@ L@SQHY C@C@- B]`] qj] i]pnev_q]hmqean]?+ h] pn]jolqaop] `a h] _kjfqc]`]+ ?p+oa hh]i] p]i^e†j ]`fqjp] `a ?v oa nalnaoajp] lkn ? ) -
@pŒmrbp+ rk^ j^qofw `r^ao^a^ ? bp ebojfqf^k^ pf ? < ? )+ v ebjf,ebojf,qf^k^ pf ? < , ? !- Tk^ j^qofw ebojfqf^k^ pb ii^j^ q^j_f‹k ]qpk,]`fqjp]-
M^oanr]_e‰j9 Fo^k m^oqbab i^ ^kqfdr^ ifqbo^qro obi^qfs^^ j^qof`bp rqfifw i^ abkljf,k^`fŽk ab ]`fqjp] m^o^i^ qo^kpmrbpqab i^ j^qofw `lc^`qlo+ nrb bp rk bkqb `ljmibq^+jbkqb afpqfkql-K^ abcfkf`fŽka^a^ ^nrŒbpqŠab ^`rboal `lk i^ kljbk`i^qro^ ^`qr^i abi^ qbloŒ ab lmbo^alobpifkb^ibp-
4-8 CŒ^dlk^iŒw^`Œ‹kab rk^ j^qofw ebojfqf^k^ l ebjf,ebojfqŒ^k^
SDNQDL@ 4-6- Rk`] i]pnev ?+ j Wj+ daniepe]j] k daie,daniepe]j] ao oa,iaf]jpa ] h] i]pnev `e]ckj]h @< af^d O&i+--- +-[!+(a oqo ]qpkr]hknao- ?`ai…o+pajaiko
@< a+G?A*
aj `kj`a b ao qj] i]pnev jk oejcqh]n _qu] ejrano] ao oq ]`fqjp]+ B,i < A)-
Baikopn]_e‰j- Rb^ T bi bpm^`fl ab i^p j,lh]o ab k•jbolp `ljmibglp+ vpb^ 'bi!&! a**' i^ _^pb loqlkloj^i ab sb`qlobp `lloabk^alp rkfq^oflp- Rft < teaz b v < r+a: `lkpfabobjlp bi molar`ql fkqboflo a^al mlo 'u+ v( << t:u:- O^o^ i^ j^qofw a^a^ ?* pb^ R i^ qo^kpcloj^`fŽk obmobpbkq^a^ mlo ?obi^qfs^ ^ i^ _^pb bibdfa^- Dkqlk`bp bi qblobj^ 4-3 klp af`b nrb T qfbkb rk^ _^pbloqlkloj^i ab ^rqlsb`qlobp 'ri+ ŠŠŠ*q**'* obpmb`ql ^ i^ `r^i R qfbkb rk^ obmob,pbkq^`fŽk bk j^qofw af^dlk^i @ < af^d '@i& --’ +@++(+pfbkal @h bi ^rqls^ilo mbol
041 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
qbkb`fbkqb^ qe - Orbpql nrb q^kql ? `ljl @ obmobpbkq^kR*pboŠkpbjbg^kqbp+^pŒnrb qbkbjlp @< A,0?A+ alkab B < 'Aez( bp i^ j^qofw kl pfkdri^o nrb obi^`flk^i^p alp _^pbp9
Dpq^&b`r^`fŽk jrbpqo^ nrb i^ `lirjk^ f ab B `lkpq^ ab ilp `ljmlkbkqbp abSz obpmb`ql^ 'ah&--- +aj'% Olo `lkpfdrfbkqb+Aez bp bi `ljmlkbkqb e,†oeik ab Sz-
Di molar`ql fkqboflo ab Sz v q+sfbkb a^al mlo
j
'qf* qe( < JAge†geŒg<h
Orbpql nrb xri +ŠŠŠ+Sjx bp rk `lkgrkql loqlkloj^i+ bpl abjrbpqo^ nrb AA) < 0+
`lk 0/ nrb B,i < B) -
M^oanr]_e‰j9 K^ abjlpqo^`fŽk abi qblobj^ 4-6 klp af`b q^j_f‹k i^ j^kbo^ ab abqbo,jfk^o i^ j^qofw af^dlk^ifw^kqb B- Dk`lkqo^jlp rk `lkgrkql loqlkloj^i ab ^rqlsb`qlobpq++--- +Sj v irbdl rqfifw^jlp ilp `ljmlkbkqbp ab Sz 'obi^qfslp ^ i^ _^pb ab sb`qlobp`lloabk^alp rkfq^oflp( `ljl bibjbkqlp ab i^ `lirjk^ e ab B-
DIDLOKN 0- K^ j^qofw ob^i ebojfqf^k^ ? < F 9\ qfbkb ilp ^rqls^ilobp
@i < 0 X @1 < 5- Klp ^rqlsb`qlobp mboqbkb`fbkqbp 0 plk p'1+,0(+ p<0<N- Klpmboqbkb`fbkqbp 5 plk p'h+1(+ p<0<N- Klp alp ^rqlsb`qlobp q| < p'1+,0( Xq < p'h+1( `lk p < 0.--04 `lkpqfqrvbk rk `lkgrkql loqlkloj^i- Olo `lkpfdrfbkqb+i^ j^qofw
B , ]0 Z 1 10\, H4 +/
bp rkz j^qofw af^dlk^ifw^kqb m^o^?- Dk bpqb`^pl A)y A&mrbpql nrb B bp ob^i-
EŠ`fijbkqb pb `ljmorb_^ nrb Ap?A < Z9 z\-
DIDLOKN 1- Rf ? bp v^ rk^ j^qofw af^dlk^i+ i^ j^qofw af^dlk^ifw^kqb B abiqblobj^ 4-6 l _fbk abg^ fks^of^_ib ? l q^k pŽil obloabk^ ilp bibjbkqlp af^dlk^ibp-
-')( ?J][RLN\^WR]J[RJ\'?J][RLN\X[]XPXWJUN\
CDEHMHBHˆM- Sj] i]pnev _q]`n]`] ? oa hh]i] qjep]ne] oe ?? ) < h- Qahh]i] knpkckj]h oe ?? p < 0 -
K]pne_ao qjep]ne]o- K]pne_ao knpkckj]hao 042
M^oanr]_e‰j9 Sla^ j^qofw rkfq^of^ ob^i bp loqldlk^i mrbpql nrb ?• < ?&-
Di qblobj^ 4-6 klp af`b nrb rk^ j^qofw ebojfqf^k^ l ebjf,ebojfqf^k^ pfbj,mobmrbab pbo af^dlk^ifw^a^ mlo jbafl ab rk^ j^qofw rkfq^of^- Tk^ j^qofw ob^iebojfqf^k^ qfbkb ^rqls^ilobp ob^ibp v ilp ^rqlsb`qlobp `loobpmlkafbkqbp mrbabkqlj^opb ob^ibp- Olo `lkpfdrfbkqb- rk^ j^qofw ob^i ebojfqf^k^ mrbab pbo af^dlk^,ifw^a^ mlo rk^ j^qofw ob^i loqldlk^i- Dpql jk bp `fboql m^o^ i^p j^qof`bp ebjf,ebojfqf^k^p ob^ibp- 'Ubo bi bgbo`f`fl 00 ab i^ pb``fŽk 4-00-(
@pfjfpjl qbkbjlp ilp `lk`bmqlp obi^`flk^alp pfdrfbkqbp+
CDEHMHBHˆM- Sj] i]pnev _q]`n]`] ? _kj ahaiajpko na]haok _kilhafko oahh]i] oei†pne_] oe ? < ?p: oa hh]i] daie,oei†pne_] oe ? < \?p-
DIDLOKN 2- Rf ? bp ob^i+pr ^agrkq^ bp fdr^i ^ pr qo^kpmrbpq^+? ) < ?p -@pŒmrbp+qla^ j^qofw ebojfqf^k^ na]h bp pfj‹qof`^+ mbol rk^ j^qofw pfj‹qof`^ klbp kb`bp^of^jbkqb ebojfqf^k^-
Z0 * e 1[
DIDLOKN 3- Rf ? < -2 , e 3e
bkqlk`bp qf! < Z0, e 1\2 * e ,3e &
Z0 * e 2 , e[
1 3e Y/0+ e 2 * eH-
X ?) ;,3e
DIDLOKN 4- K^p alp j^qof`bp Zz z\ v Z1 z e 19 fI plk ebojfqf^k^p-
K^ mofjbo^ bp pfj‹qof`^+ i^ pbdrka^ kl-
DIDLOKN 5- ZN ,1/\ X Y1eK^p alp j^qof`bp 1 ,1\ plk ebjf,ebojfqf^k^p-
2e
K^ mofjbo^ bp ebjf,pfj‹qof`^+ i^ pbdrka^ kl-
DIDLOKN 6- Slalp ilp bibjbkqlp af^dlk^ibp ab rk^ j^qofw ebojfqf^k^ plkob^ibp- Slalp ilp bibjbkqlp af^dlk^ibp ab rk^ j^qofw ebjf,ebojfqf^k^ plk fj^,dfk^oflp mrolp- Slalp ilp bibjbkqlp af^dlk^ibp ab rk^ j^qofw ebjf,pfj‹qof`^ plk`bol-
DIDLOKN 7- O^o^ rk^ j^qofw `r^inrfbo^ ?+ i^ j^qofw @< F? * ?)( bpebojfqf^k^+ v i^ j^qofw b < G@ , ? )( bp ebjf,ebojfqf^k^- Rr prj^ bp ?, @pŒmrbp+qla^ j^qofw `r^ao^a^ ? mrbab bumobp^opbljl rk^ prj^ ? < @* b+pfbk,
043 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
al @ ebojfqf^k^ v b ebjf,ebojfqf^k^- Dp rk bgbo`f`fl pbk`fiil `ljmol_^o nrbbp^ abp`ljmlpf`fŽk bp •kf`^- @pfjfpjl qla^ j^qofw `r^ao^a^ ? mrbab bumob,p^opb ab j^kbo^ •kf`^ `ljl prj^ ab rk^ j^qofw pfj‹qof`^+ G@ * ? %'* X rk^j^qofw ebjf,pfj‹qof`^+ G@ , ? p( -
DIDLOKN 8- Rf ? bp loqldlk^i qbkbjlp 0 < abq &??p' < 'abq @('abq @&(;< 'abq ?'0* ^pŒnrb abq ? < ,*, 0-
-')) Dgbo`f`flp
0- Cbqbojfk^o `rŠibp ab i^p pfdrfbkqbp j^qof`bp plk pfj‹qof`^p+ ebjf,pfj‹qof`^p+ ebojfqŒ^k^pl ebjf,ebojfqf^k^p-
^(
F N 9i _c N 9i. (- (. 3f
b( Yye N 9i a( ZzH N 5G(- (. (- (.
1- ^( Bljmol_^o nrb i^ j^qofw 1W1 @ < oblp apbk a
, pbka[ bp rk^ j^qofw loqldlk^i-blp a
_( Rb^ R i^ qo^kpcloj^`fŽk ifkb^i `lk i^ j^qofw ^kqboflo ? obi^qfs^ ^ i^ _^pb loafk^of^we*fx,Cbjlpqo^o nrb R ^mif`^ `^a^ mrkql abi mi^kl ab `lloabk^a^p mli^obp &n*]' bk bimrkql &n*] * 7(- @pŒmrbp+ R bp rk^ olq^`fŽk abi mi^kl ^iobabalo abi lofdbk+ pfbkal7 bi Škdril ab dfol-
2- Rb^ T bi bpm^`fl ob^i ab afjbkpfŽk 2 `lk i^ _^pb e*g+g- Cbjlpqo^o nrb `^a^ rk^ab i^p j^qof`bp pfdrfbkqbp bp loqldlk^i v obmobpbkq^i^ qo^kpcloj^`fŽk nrb pb fkaf`^-
'pfjbqoŒ^ bk bi mi^kl t+u',
'pfjbqoŒ^ obpmb`ql ^i bgb t',
Cfan_e_eko 044
'pfjbqoŒ obpmb`ql i lofdbk(-
'olq^`f5k ^iobabalo abi bgb t',
'olq^`f5k ^iobabalo abi bgb t pbdrfa^ abpfjbqoŒ obpmb`ql i mi^kl uv',
3- Tk^ j^qofwloqldlk^i ob^i ? pb ii^j^ lnkle] pf abq? < 0+b eilnkle] pf abq? < ,0 -
Z
BNR b^( Rf? bp rk^ j^qofwmolmf 1W1+abjlpqo^o nrb ? < -
- pbk p
k- Dpq^obmobpbkqrk^ olq^`f5k ab Škdril &H,
Z0 N\ Z,0 N\_( Cbjlpqo^o nrb v plk j^qof`bp Hjmolmf^p-K^ mofjbo^obmobpbkq^N ,0 N 0
rk^ pfjbqoŒbk bi mi^kl tu obpmb`ql i bgbt: i^ pbdrka^ obmobpbkq^rk^ pfjbqoŒobpmb`ql^i bgbu- G^ii^o qla^p i^p j^qof`bp fjmolmf^p 1W1-
,pbkb\m^o rk `fboql
`lp b
Dk `^a^ rkl ab ilp bgbo`f`flpabi 4 ^i 7+e^ii^o ^( rk `lkgrkql loqldlk^i ab ^rqlsb`qlobpm^o^?* v _( rk^ j^qofwrkfq^of^B q^i nrb A+G?A pb^rk^ j^qofw af^dlk^i-
3, ? < Z 8 01\,4, ? < F ,z\,
01 05
6- ? y Y9
2
,I 7- ? y Yy
2 zi(-
,0 N
8- Cbqbojfk^o `rŠibp ab i^p pfdrfbkqbpj^qof`bp plk rkfq^of^p+v `rŠibp plk loqldlk^ibp&]*^+&H ob^ibp(-
F++#!N
pbk &\ ZqU1 ,isf y+05\^( Yay] ay^h _( N N + b( N isg iUz -
,pbkb N `lp b re isf ,iU5
045 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_he`ako
0/- K^ qbloŒ bpmb`f^i ab i^ obi^qfsfa^a e^`b rpl ab i^p b`r^`flkbp
t&< ]'t , rp(+ u&<u++
v <v+ p&< ]'p , rtfa1(-
@nrŒr bp i^ sbil`fa^a ab rk l_gbql jŽsfi+ a i^ sbil`fa^a ab i^ irw+ v ] < af!z bi , r0‹
K^ qo^kpcloj^`fŽk ifkb^i nrb ^mif`^ 't+ u+v+p(bk 't&+u&+v&+p&(pb ii^j^ pn]joekni]_e…j`a Jknajpv- ^( Olkd^jlp 'Wi&V 1&up+ V3( < 't+ u+v+eap(u'ty +ty+ ty+ ty( <'t&+u&+v&+e_p&x+Cbjlpqo^o nrb i^p `r^qol b`r^`flkbp mrbabk mlkbopb bk cloj^ ab rk^ b`r^`fŽk j^qk,`f^i `ljl pfdrb+
Hu:+t:+t:+,^ z Yt! t++t! tw y
N N
SiN
N 0
e]k[_ N N
_( Cbjlpqo^o nrb i^ j^qofw 3W3 ab ^( bp loqldlk^i mbol kl rkfq^of^-
00- Rb^k ] rk k•jbol ob^i kl kril v ? i^ j^qofw ebjf,pfj‹qof`^ ? < Yy] 9[-^( G^ii^o rk `lkgrkql loqlkloj^i ab ^rqlsb`qlobp m^o^ ?,_( G^ii^o rk^ j^qofw rkfq^of^ b q^i nrb a+/?a pb^ rk^ j^qofw af^dlk^i-`( Cbjlpqo^o nrb kl bufpqb rk^ j^qofw loqldlk^i ob^i b q^i nrb a+G?a pb^ rk^ j^qofwaf^dlk^i-
01- Rf ilp ^rqls^ilobp ab rk^ j^qofw ebojfqf^k^ l ebjf,ebojfqf^k^ ? plk qlalp fdr^ibp ^ a+abjlpqo^o nrb ? < ah-
02- Rf ? bp rk^ j^qofw ebjf,pfj‹qof`^ ob^i+abjlpqo^o nrb i^p alp j^qof`bp 0 , ? b 0 * ?plk kl pfkdri^obp v nrb &/ + ?'&h * ?'+% bp loqldlk^i-
03- O^o^ `^a^ rk^ ab i^p pfdrfbkqbp molmlpf`flkbp obi^qfs^p ^ i^p j^qof`bp j&t-j+ a^o rk^abjlpqo^`fŽk& l rk `lkqo^bgbjmil-^( Rf ? X @ plk rkfq^of^p+bkqlk`bp ? * @ bp rkfq^of^-_( Rf ? X @ plk rkfq^of^p+?@ bp rkfq^of^-b( Rf ? X ?@ plk rkfq^of^p+@ bp rkfq^of^-a( Rf ? X @ plk rkfq^of^p+? * @ kl bp rkfq^of^-
4-01 Eloj^p `r^aoŠqf`^p
Rb^k T rk bpm^`fl br`iŒabl na]h v R9 T y T rk lmbo^alo pfj‹qof`l- Dpqlpfdkfcf`^nrb R mrbab `^j_f^opb ab rk c^`qlo ^i lqol bk rk molar`ql fkqboflo
&R&t'*u' < &t* R&u'' m^o^ qlal m^o t*u ab T,
C^a^ R* abcfk^jlp rk^ crk`fŽk ab s^ilobp ob^ibp P bk T jbaf^kqb i^ b`r^`fŽk
O&t' < &R&t'* t',
Dkni]o _q]`n…pe_]o 046
K^ crk`fŽk P pb abkljfk^ bkni] _q]`n…pe_]^pl`f^a^ ^ R- K^ m^i^_o^ ~`r^aoŠ,qf`^ƒ bpqŠ prdbofa^ mlo bi qblobj^ pfdrfbkqb nrb jrbpqo^ nrb bk bi `^pl abafjbkpfŽk cfkfq^O&t' bp rk mlifkljfl `r^aoŠqf`l bk ilp `ljmlkbkqbp ab t,
SDNQDL@ 4-7- Qa] 'a++--- +aj( qj] ^]oa knpkjkni]h l]n] qj aol]_ek aq_h‡,`ak T- Qa]j R9T y T qj] pn]jobkni]_e‰j oei†pne_] v ? < ']zf( h] i]pnev `a Rnah]per] ] ao] ^]oa- Cjpkj_ao h] bkni] _q]`n…pe_]O't( < 'R't(+ t( aop…hec]`]] ? `ah ik`k oecqeajpa9
'4-6(j j
O't( < ]eetetee<0e<0
j
pf t < teae-e<0
Baikopn]_e‰j- Dk sfoqra ab i^ ifkb^ifa^a qbkbjlp R't( < teR'a:(- Olo`lkpfdrfbkqb+
Dpql abjrbpqo^ '4-6( v^ nrb ]zf < ]fz < 'R'az(+af( -
K^ prj^ nrb ^m^ob`bbk '4-6( qfbkb pbkqfal fk`irpl pf i^ j^qofw ? kl bp pf,j‹qof`^-
CDEHMHBHˆM- Qa] T qj aol]_ek aq_h‡`ak na]h _q]hmqean]_kj qj] ^]oa knpk,jkni]h 'a++--- +aj(+v oa] ? < ']zf( _q]hmqeani]pnev j Wj `a ao_]h]nao-J] bqj,_e‰j`a r]hknao ao_]h]naoP `abeje`] aj _]`] ahaiajpk t < t-a+ `a T lkn h]oqi] `k^ha
'4-7(V V
O't( < ]eetetee<he<0
oa `ajkiej] h] bkni] _q]`n…pe_]]ok_e]`] ] ?-
Rf ? bp rk^ j^qofw af^dlk^i+ bkqlk`bp ]zf < N pf e <0< f ab jlal nrb i^ prj^'4-7( `lkqfbkb •kf`^jbkqb `r^ao^alp v pb mrbab mlkbo bk i^ cloj^ jŠp pbk`fii^
'4-8(j
O't( < ]eet9-68,
Dk bpqb`^pl i^ cloj^ `r^aoŠqf`^ pb ii^j^ bkni] `e]ckj]h-K^ prj^ al_ib nrb ^m^ob`b bk '4-7( q^j_f‹k pb mrbab bumobp^o ljl rk
molar`ql ab qobpj^qof`bp-
047 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_he`ako
SDNQDL@ 4-8- Qa] W < Yt-+ --- +tj[ qj] i]pnev beh]0•:j+ u oa] ? < ']ef(qj] i]pnev j Wj- Cjpkj_ao V?Vp ao qj] i]pnev 0W 0 _quk ahaiajpk ao
j j
]z:tete‹fzi fzi
Baikopn]_e5j- Di molar`ql V? bp rk^ j^qofw 0Wj+ V? < ZXH+--- +Wj[+bk alkab bi bibjbkql Wzbp bi molar`ql bp`^i^o ab W mlo i^ `lirjk^ e ab ?+
’’r+< te]ef&
f<i
Olo `lkpfdrfbkqb+bi molar`ql V?Vp bp rk^ j^qofw 0W0 `rvl •kf`l bibjbkql bpbi molar`ql bp`^i^o
M^oanr]_e‰j9 Dp -`loofbkqb fabkqfcf`^o i^ j^qofw+ 0W0+ V?V& `lk i^ prj^ '4-8( vii^j^o ^i molar`ql V?V& cloj^ `r^aoŠqf`^- K^ b`r^`fŽk '4-7( pb bp`of_b jŠp pbk`fii^,jbkqb ^pŒ9
O'V( < V?Vp-
DIDLOKN 0- Rb^k ? < Z 0 ,0\+W < q,+t1[- Sbkbjlp bkqlk`bp,2 4
V? < ZWi&W1iZ0 ,0\ < ZWi, 1t0* ,Wi * 4u1i+,2 4
v mlo q^kql
W?Vp < ZWi, 2t1+ , Wi * 3V1w99[ < uz , 2W1Wi , WHW1* 4ty-
DIDLOKN 1- Rb^k @ <Z 0 ,1\+ W< YVh= t1[- Sbkbjlp bkqlk`bp,1 4
V@Vp
< ZWi&V0w \y ,zI Z99I< Wz , 1W1Wi , 1WHW1* 4ty-
Dk ^j_lp bgbjmilp 0 v 1+ ilp q‹ojfklp bk ilp molar`qlp jfuqlp a^k ^i pr,j^oilp& ,3WHW1 ^pŒnrb V?Vp < V@VpŒDpqlp bgbjmilp mlkbk ab j^kfcfbpql nrbj^qof`bp afpqfkq^pmrbabk `lkar`fo ^ i^ jfpj^ cloj^ `r^aoŠqf`^- N_p‹osbpb nrbrk^ ab bp^p j^qof`bp bp pfj‹qof`^- Dpql `lkpqfqrvb rk bgbjmil abi pfdrfbkqbqblobj^-
Pa`q__e…j `a qj] bkni] _q]`n…pe_]na]h] bkni] `e]ckj]h 048
SDNQDL@ 4-0/- N]n] _q]hmqeani]pnev ?+ j t:j+ u _q]hmqeani]pnev beh]W+
0Wj+ pajaiko V?Vp <V@Vp aj `kj`a @ ao h] i]pnev oei†pne_] @< G@ * ? p(-
Baikopn]_e…j+ Orbpql nrb V?Vp bp rk^ j^qofw 0 W 0+ bp fdr^i ^ pr qo^kp,mrbpq^+ V?Vp < 'V?Vp(p- Obol i^ qo^kpmrbpq^ ab rk molar`ql bp bi molar`ql abi^p qo^kpmrbpq^p bk loabk fksbopl+ mlo il nrb 'V?Vp(p < V?pVp- Olo `lkpfdrfbk,qb V?Vp < V?Vp * qV? pV&< V@Vp -
-')+ CNM^LLRmWMN WJOX[VJL^JM[j]RLJ[NJUJ OX[VJMRJPXWJU
Tk^ j^qofw pfj‹qof`^ ob^i ? bp ebojfqf^k^- Olo q^kql+ pbd•k bi qblobj^ 4-6bp pbjbg^kqb ^ i^ j^qofw af^dlk^i @ < af^d '@i+ --- +@++(+ab prp ^rqls^ilobp-@abjŠp+ qbkbjlp @< Ap?A+ pfbkal B rk^ j^qofw loqldlk^i- U^jlp ^elo^ ^abjlpqo^o nrb B mrbab rqfifw^opb m^o^ `lksboqfo i^ cloj^ `r^aoŠqf`^ V?Vp ^ rk^cloj^ af^dlk^i-
SDNQDL@ 4-00- Qa] V?Vp qj] bkni] _q]`n…pe_]]ok_e]`] ] qj] i]pnev oe,i†pne_] na]h?+ v oa] B qj] i]pnev knpkckj]h mqa _kjreanpa ? aj qj] i]pnev `e],ckj]h @ < Ap?A- Rajaiko ajpkj_ao
!V?Vp < W?up < ?-‡W9+
e;h
`kj`a W < ZXi + --- +uj[ ao h] i]pnev beh] W < VA+ W @i + -’’ +?j okj hko ]qpk,r]hknao `a ?-
Baikopn]_e…j- Orbpql nrb B bp loqldlk^i qbkbjlp B,0 < A&+Olo `lkpf,drfbkqb i^ b`r^`fŽk W < WB fjmif`^ W < u_p+v l_qbkbjlp
M^oanr]_e‰j9 Di qblobj^ 4-00 pb bumobp^ af`fbkal nrb i^ qo^kpcloj^`fŽk ifkb^iv < WB obar`b i^ cloj^ `r^aoŠqf`^ V?V& ^ rk^ cloj^ af^dlk^i X?W&-
DIDLOKN 0- K^ cloj^ `r^aoŠqf`^ `loobpmlkafbkqb ^ i^ j^qofw fabkqfa^a bp
!VGVp < t9 < HHWH01
+e;h
nrb bp bi `r^ao^al ab i^ ilkdfqra abi sb`qlo W < 'Wi&--- *Vj', Tk^ qo^kpcloj^,`fŽk ifkb^i W < VA* alkab B bp rk^ j^qofw loqldlk^i+ klp a^ rk^ krbs^ cloj^`r^aoŠqf`^ W?up pfbkal @ < AGAp < AAp < G- Orbpql nrb VGVp < WGup qbkb,jlp HHWfi1<HHXV+mlo il nrb W qfbkb i^ jfpj^ ilkdfqra nrb W- Tk^ qo^kpclo,j^`fŽk ifkb^i nrb `lkpbos^ i^ ilkdfqra ab `^a^ sb`qlo pb abkljfk^ eoknjapn‡]-
05/ ?qpkr]hknao `a klan]`knao aj aol]_eko aq_he`ako
Dk i^ pb``fŽk 4-08 pb bpqraf^k `lk j^vlo abq^iib bp^p qo^kpcloj^`flkbp-
DIDLOKN 1- Cbqbojfk^o rk^ j^qofw loqldlk^i b nrb obarw`^ i^ cloj^ `r^,aoŠqf`^ O't( < 1ty * 3V0V1 * 4ty ^ cloj^ af^dlk^i-
Qkhq_e‰j- Dp`of_^jlp O't( < V?Vp+ pfbkal ? < F z\- Dpq^j^qofw pf,
j‹qof`^ pb af^dlk^ifwŽ bk bi bgbjmil 0 nrb pfdrb ^i qblobj^ 4-6- Sfbkb ilp ^rql,s^ilobp @i < 0+&[1< 5+ X rk `lkgrkql loqlkloj^i ab ^rqlsb`qlobp q0+ q,+ pfbkalSG < p&0*,0(+ S1 < p&h*1(+ p < 0.+-.4- Tk^ j^qofw af^dlk^ifw^kqb loqldlk^i bp
b < pY \ y yI- K^ cloj^ af^dlk^i `loobpmlkafbkqb bp
W?up < :&iXz* :&1Wy< Wy* 5uy-
Di obpriq^al abi bgbjmil 1 qfbkb rk^ fkqbomobq^`fŽkdblj‹qof`^ pbk`fii^+ ob,mobpbkq^a bk i^ cfdro^ 4-0- K^ qo^kpcloj^`fŽk ifkb^i W < WB mrbab `lkpfabo^opb`ljl rk^ olq^`fŽk nrb ^mif`^ i^ _^pb e*gbk i^ krbs^ _^pb qh+ q1Œ Tk mrkqlnrb obpmb`ql^ i^ mofjbo^ _^pb qfbkb`lloabk^a^p 'Vh& t1(- qfbkbi^p krbs^p `lloab,k^a^p 'XH&W1(obpmb`ql^ i^ pbdrka^ _^pb- Orbpql nrb V?Vp < u?up+ bi `lkgrkqlab mrkqlp 'Vh& t1( nrb p^qfpc^`bki^ b`r^`fŽk V?tp < a m^o^rk `fboql a bp fa‹k,qf`l ^i `lkgrkql ab mrkqlp &W/< W0' nrb p^qfpc^`bkW?up < _- K^ pbdrka^ b`r^`fŽk+bp`ofq^ bk i^ cloj^ uy * 5u9 < a+bp i^ b`r^`fŽk `^oqbpf^k^ ab rk^ bifmpb pf_=M- Olo q^kql i^ b`r^`fŽk V?Vp<_+ mrbpq^ bk i^ cloj^ 1ty*3tGV1*4ty<_+obmobpbkq i^ jfpj^ bifmpbbk bi pfpqbj^ `lloabk^al lofdfk^i- K^ cfdro^ 4-0jrbpqo^ i^ bifmpb`loobpmlkafbkqb ^ a < 8-
i 'u+ t1( obpmb`ql ^ i^ _^pb e,[
’ {'W+- W1( obpmb`ql ^ i^ _^pb q++q+
WH
EHFTQ@ 4-0 Pkp]_e‰j`a afao ia`e]jpa qj] i]pnev knpkckj]h- J] aheloa peaja h] a_q]_e‰j_]npaoe]j]V?V& < 8 aj ah oeopai] VGV! u h] a_q]_e‰jW?W&< 8 aj ah oeopai] WGW&-
?lhe_]_ekjao ] h] Eakiapn‡] ?j]h‡pe_] 050
-'=, 4YURLJLRXWN\J UJ:NXVN][lJ 4WJUl]RLJ
K^ obar``fŽk ab rk^ cloj^ `r^aoŠqf`^ ^ cloj^ af^dlk^i mrbab rqfifw^opbm^o^fabkqfcf`^obi `lkgrkql ab qlalp ilp mrkqlp 'u+v( abi mi^kl nrb p^qfpc^`brk^b`r^`fŽk `^oqbpf^k^ ab i^ cloj^
'4-0/( ]thh * ^tu * _uhh* `t * au * b< N-
Dk`lkqo^objlp pfbjmob nrb bpb`lkgrkql bp rk^ pb``fŽk `Žkf`^+ bpql bp+rk^ bifmpb+rk^ efm‹o_li^+ rk^ m^oŠ_li^ l rkl ab ilp `^plp abdbkbo^alp 'bi `lkgrkql s^`Œl+rk plil mrkql+ l rk^ l alp ob`q^p(-Di qfml ab `Žkf`^ sfbkb `^o^`qbofw^al mlo ilpq‹ojfklp ab pbdrkal do^al+ bpql bp+mlo i^ cloj^ `r^aoŠqf`^ ]t& * ^tu * _u! ,S‹kd^pb bk `rbkq^ nrb ^nrŒebjlp mrbpql t bk ird^o ab Vh b v bk ird^o ab V1 Œ
Ulisfbkal ^ i^ klq^`fŽk ^kqboflo v bumobp^kal bp^ cloj^ `r^aoŠqf`^ `ljl mol,ar`ql j^qof`f^i
Y] _.1I
pfbkal W < Yt! t1[ X ? < - Blk i^ olq^`fŽk W < WB obar`fjlp bp^^.1 a
cloj^ `r^aoŠqf`^ ^ rk^ cloj^ af^dlk^i ?-Gx&y* ?-1-Wy+alkab @i+z plk ilp ^rqls^,ilobp ab ?, Tk `lkgrkql loqlkloj^i ab ^rqlsb`qlobp q! S0 abqbojfk^ rk krbsl`lkgrkql ab bgbp`lloabk^alp+ obpmb`ql^ ilp `r^ibp i^ b`r^`fŽk `^oqbpf^k^ '4-0/(pb `lksfboqb bk
'4-00(
`lk krbslp `lbcf`fbkqbp `& v a&bk ilp q‹ojfklp ab mofjbo do^al- Dk bpq^b`r^`fŽkkl bufpqbq‹ojfkl bk bi molar`ql jfuql W0W1+lk il `r^i bi qfml ab `Žkf`^ pbfabkqfcf`^cŠ`fijbkqb bu^jfk^kal ilp ^rqls^ilobp @i v @1’ Rf i^ `Žkf`^ kl bp abdb,kbo^a^+ i^ b`r^`fŽk '4-00( obmobpbkqrk^ aheloa pf z+@1 qfbkbk bi jfpjl pfdkl+rk^ del†n^kh] pf @i+@1 qfbkbk pfdklp `lkqo^oflp+ v rk^ l]n…^kh] pf rkl ab ilpalp bp `bol v bi lqol kl- Klp qobp`^plp `loobpmlkabk ^ @0@1= N+@
0@
1; N+v
zz < N- Rbdrfa^jbkqb a^jlp ^idrklp bgbjmilp-
DIDLOKN 0- 0t%0* 2tu * 3u1 * 2t * /1u + < N- Dp`of_fjlp i^ b`r^,`fŽk ^pŒ
'4-01(
K^ cloj^ `r^aoŠqf`^ 1ty * 2V0V1 * 4ty bp i^ qo^q^a^bk bi bgbjmil 1 ab i^ pb``fŽk
051 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
^kqboflo- Rr j^qofw qfbkb ilp ^rqls^ilobp @i < 0+@1 < 5+ X rk `lkgrkql loqlklo,j^i ab ^rqlsb`qlobp S0 < q'1+ ,0(+ S1 < p&h*1(+ pfbkal p < h.HQ- Tk^ j^qofw
af^dlk^ifw^kqb loqldlk^i bp B < pY 1 0\- †pq^ obar`b i^ m^oqb`r^aoŠqf`^ ab,0 1
'4-01( ^ i^ cloj^ Xf * 4uy, O^o^ abqbojfk^o bi bcb`ql bk i^ m^oqbab mofjbo do^almlkbjlp i^ b`r^`fŽk ab i^ olq^`fŽk X < WB bk i^ cloj^ W < WAp v l_qbkbjlp
0 Z1 ,0\ZWi&V1[ < H4 YWh&W1[ 0 1&
Olo `lkpfdrfbkqb+i^ m^oqbifkb^i 2t0 * /1t1 pb qo^kpcloj^ bk
3 02 ,,H4 '1Wh * X1( * H4 ',Wh * 1W1( < ,H4 Wh* 5H4 X1-
K^ b`r^`fŽk `^oqbpf^k^ qo^kpcloj^a^ pb `lksfboqb bk
We* 5uy , H4 Wh* 5H4 W1, 0, < N-
Bljmibq^kal ilp `r^ao^alp bk X0 b X1 bp`of_fjlp ‹p^ ^pŒ9
'Xi , eH4(1 * 5'W1 * eH4(1 < 8-
†pq^ bp i^ b`r^`fŽk ab rk^ bifmpb lk pr `bkqol bk bi mrkql 'eH4+,qI4( bk bipfpqbj^ `lloabk^al W/W0%K^p afob``flkbp mlpfqfs^pab ilp bgbpXi b X1 bpqŠkabqbo,jfk^a^p mlo ilp ^rqlsb`qlobp T0 X q1+ `ljl pb fkaf`^ bk i^ cfdro^ 4-1-
Olabjlp ^•k pfjmifcf`^o jŠp i^ b`r^`fŽk bp`of_fbkal
Yi <Xi , e-H4-
Fblj‹qof`^jbkqb+ bpql bp 0/ jfpjl nrb fkqolar`fo rk krbsl pfpqbj^ ab bgbp`lloabk^alp m^o^ibilp ^ ilp bgbpXHX1 mbol `lk bi krbsl lofdbk bk bi `bkqol ab i^bifmpb-Dk bi pfpqbj^ XhX1 i^ b`r^`fŽk ab i^ bifmpbbp pbk`fii^
- -
Yi * z < 0-8 2.1
K^ bifmpbv ilp qobppfpqbj^p ab `lloabk^a^p pb e^k af_rg^al bk i^ cfdro^ 4-1-
wf* 5vy < 8+ l
?lhe_]_ekjao ] h] Eakiapn‡] ?j]h‡pe_] 052
EHFTQ@ 4-1 Pkp]_e‰j v- pn]oh]_e‰j`a afao _kkn`aj]`ko- J] nkp]_e‰j X] < WB reajaoacqe`] lkn h] pn]oh]_e‰jvh < X0 , qz4+ X0 < X1 * qz4-
DIDLOKN 1- 0t0 + 2tu + u0 + 2t * iNv , 02 < N- OlkdŠjlpi^ bk i^cloj^
1ty , 3W0W1, uz , 3ui * 0/t1 , 02 < N-
Z 1 ,1\K^ m^oqb r^aoŠqf`^ bp V?Vp+ pfbkal ? < - Dpq^j^qofw qfbkbilp ^rql,,1 ,0
s^ilobp !,0<2+!,1<,1- Tk `lkgrkql loqlkloj^i ab ^rqlsb`qlobp bp q/;p&0* +/'*S1 < p&h*1(+ pfbkal p < 0.z4- Tk^ j^qofw af^dlk^ifw^kqb loqldlk^i bp
B < pY 1 0\- K^ b`r^`fŽk ab i^ olq^`fŽk W < WApklp a^,0 1
0 0Wi < -H2'1Wh * W1(+ W1 < -H4', Wh* 1W1(&
Olo `lkpfdrfbkqb+i^ b`r^`fŽk qo^kpcloj^a^ pb `lksfboqb bk
2uy , 1uy , :p'1Xi * W1( * yy',Wh * 1W1( ,02 < N+
l
2 1 1 07 05Wh , 1W1 , -H4Wh* H4 W1 , 02 < N-
053 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
'^( Gf m‹o_li^92vh , 1vy < 01
EHFTQ@ 4-2 Aqnr]o `a hko afailhko 1 v 2-
'_( O^oŠ_li^9uh * uy ŒŒN
Bljmibq^kal ilp `r^ao^alp bk W/ b W0 l_qbkbjlp i^ b`r^`fŽk
nrb obmobpbkqrk^ efm‹o_li^ `lk `bkqol bk 'z-HQ+p-HQ(bk bi pfpqbj^ W/W0%K^ qo^p,i^`fŽk Yi < XH , z-HQ+X1 < W1 , -IR pfjmifcf`^ i^ b`r^`fŽk iibd^kal ^ -
2vy , 1v9 < 01+ l
K^ efm‹o_li^ bpqŠaf_rg^a^ bk i^ cfdro^4-2x^(- Klp ^rqlsb`qlobp S0 X S1 abqbojfk^ki^p afob``flkbp mlpfqfs^pab ilp bgbpX0 b X1 ’
DIDLOKN 2- 7t1 * 02tu * 05u1, 0.t * 04u99999:N - Olkd^jlp bpq^b`r^`fŽk
^pŒ9
7ty * 02t0V0 * /4ty + 1/u0 * /3t0 < N-
Z 8 01\K^ j^qofw pfj‹qof`^ m^o^i^ m^oqbr^aoŠqf`^ bp ? < -Rrp ^rqls^ilobp plk
01 05
@i < 14+ @1 < N- Tk `lkgrkql loqlkloj^i ab ^rqlsb`qlobp bp S0
< ,0'2+3(+
?lhe_]_ekjao ] h] Eakiapnh] ?j]h‡pe_] 054
, Z32
,32\S1 < •G,3+ 2(- Tk^ j^qofw af^dlk^ifw^kqb loqldlk^i bp B < r ŒK^ ol,
q^`fŽk W < WAp klp a^
Olo `lkpfdrfbkqb+i^ b`r^`fŽk `^oqbpf^k^qo^kpcloj^a^ pb `lksfboqb bk
Rfjmifcf`^kal bp^ b`r^`fŽk pb iibd^ ^ uy * W1 < N+nrb bp i^ b`r^`fŽk ab rk^ m^,oŠ_li^ `lk bi s‹oqf`b bk bi lofdbk- K^ m^oŠ_li^ bpqŠaf_rg^a^ bk i^ cfdro^ f4-2'_(-
DIDLOKN 3- A]oko `acajan]`ko- Di plil `lkl`fjfbkql ab ilp ^rqls^ilobp klobsbi^ pf i^ b`r^`fŽk `^oqbpf^k^obmobpbkqrk^ `Žkf`^ abdbkbo^a^- Olo bgbjmil+ i^pqobpb`r^`flkbp t1 * 1v1 < 0+t1 * 1v1 < N X t1 * 1u1 9999 ,0 qfbkbk ilp jfpjlp^rqls^ilobp9 i^ mofjbo^ obmobpbkqrk^ bifmpbkl abdbkbo^a^+ i^ pbdrka^ pŽil pbp^qfpc^`bm^o^ &t* v( < 'N+N(+X i^ qbo`bo^obmobpbkq bi `lkgrkql s^`Œl+ K^p alp•iqfj^p mrbabk `lkpfabo^opb `^plp abdbkbo^alp ab bifmpb-
K^ doŠcf`^ab i^ b`r^`fŽk v1 < N bp bi bgb t- K^ b`r^`fŽk v1 , 0 < N obmob,pbkq^ i^p alp ob`q^pm^o^ibi^pv 99990 b v < , 0 - Dpqlp mrbabk `lkpfabo^opb `ljl`^plp abdbkbo^alp ab m^oŠ_li^- K^ b`r^`fŽk t1 , 3u1 9999N obmobpbkq alp ob`q^pnrb pb `loq^k v^ nrb pb p^qfpc^`bpf t , 1u < N l pf t * 1v < N - †pqb mrbab`lkpfabo^opb `ljl `^pl abdbkbo^al ab efm‹o_li^-
Rfk bj_^odl+ pf i^ b`r^`fŽk `^oqbpf^k^]t& * ^tu * _u0 * `t * au * b < Nobmobpbkqrk^ `Žkf`^ kl abdbkbo^a^+bkqlk`bp bi pelk ab `Žkf`^ mrbab abqbojf,k^opb `lk- qla^ c^`fifa^a- Di mlifkljfl `^o^`qboŒpqf`lab i^ j^qofw ab i^ cloj^`r^aoŠqf`^ ]t& * ^tu * _u! bp
Y? , ] ,^.1[
abq < ?1, '] * A(? * ']_ , e^1
( < '? , ?0('? , ?1(-
,^.1 ? , a
Olo q^kql+bi molar`ql ab ilp ^rqls^ilobp bp
Orbpql nrb bi qfmlab `Žkf`^ bpqŠabqbojfk^al mlo bi pfdkl ^idb_o^f`l abi molar`ql&[&&[1&sbjlp nrb i^ `Žkf`^ bp aheloa+del†n^kh] l l]n…^kh]+pbd•k nrb 3]_ , ^! pb^lkoeperk+jac]perk l jqhk- Di k•jbol 3]_ , ^! pb ii^j^ `eo_neiej]jpa ab i^ cloj^`r^aoŠqf`^ ]t& * ^tu * _u! - Dk ilp bgbjmilp 0+1 X 2 bi afp`ofjfk^kqb qfbkb ilps^ilobp 23+,13+ X N+obpmb`qfs^jbkqb-
055 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
-')- 8SN[LRLRX\
Dk `^a^ rkl ab ilp bgbo`f`flp 0 ^i 6+ e^ii^o ^( rk^ j^qofw pfj‹qof`^ ? m^o^ i^ cloj^`r^aoŠqf`^: _( ilp ^rqls^ilobp ab ?: b( rk `lkgrkql loqlkloj^0 ab ^rqlsb`qlobp: a( rk^j^qofw af^dlk^ifw^kqb loqldlk^i B-
/, 2ty * 2V/V0 * ty,
0, V/V0%
1, ty * 0V/V0 + ty,
2, 12ty + 02thV0 * 2/ty,
Q, ty * V/V0 * tht] * V0V],
4, 0te * 2Vht] * ty + ty,
6- 1ty * 2V/V0 * 6V/V] * 2t0V] * 1ty,
Dk `^a^ rkl ab ilp bgbo`f`flp 7 ^i 07+fabkqfcf`^oi^ `Žkf`^ obmobpbkq^a mlo i^ b`r^`fŽk`^oqbpf^k^ v e^`bo rk af_rgl-
6, u0 + 0tu * 0t0 + Q < N-7, u0 + 0tu * Qt < N-
/., u0 + 0tu * t0 + Qt < N-//, Qt0 + 2tu * 0u0 + 5 < N-
/0, /7t0 * 2tu * 05v1 , 101u * h.2u < 134,
/1, 7t0 * 02tu * 05v1 , Q0t * /2u < 5-
/2, ot0 * 4tu * Qu0 + 1 < N-/3, t0 * 0tu * u0 + 0t * 0u * 2 < N-05- 1u1 * 2tu * Qu0 + 0t + u + 3 < N-06-u1 )2tu +0u0 ,01 </-
/6, tu * u + 0t + 1 < N-
08- „O^o^ nr‹ s^ilo 'l s^ilobp( ab a i^ doŠcf`^ ab i^ b`r^`fŽk `^oqbpf^k^ 1tu,3t* 6u*_</pboŠ rk m^o ab ob`q^p>
1/- Rf i^ b`r^`fŽk ]t&* ^tu * `v&< 0 obmobpbkq rk^ bifmpb+abjlpqo^o nrb bi Šob^ ab i^obdfŽk nrb ifjfq^ bp 10R s 3]_ \ ^1Œ Dpql a^ rk pfdkfcf`^al dblj‹qof`l ^i afp`ofjfk^kqb3]_,^&-
o -'). ')( 4^]X_JUX[N\ MN WJ ][JW\OX[VJLRmW\RVk][RLJXK]NWRMX\LXVX _JUX[N\MN\^ OX[VJ L^JM[j]RLJ
U^jlp ^ mobp`fkafo^elo^ ab i^ bufdbk`f^ ab nrb T pb^ ab afjbkpfŽk cfkfq^v s^jlp ^ bk`lkqo^o rk^ obi^`fŽk bkqobilp ^rqls^ilobp ab rk lmbo^alo pfj‹qof`lv pr cloj^ `r^aoŠqf`^-
Rrmlkd^jlp nrb t bp rk ^rqlsb`qlo `lk kloj^ 0 mboqbkb`fbkqb rk ^rqls^,ilo @- Dkqlk`bp R&t' < ?V `lk il nrb qbkbjlp
'4-02( O&t' < &R&t'* t' < 'le+ t' < ?&V*t' < ?*
v^ nrb &t* t' < 0- Di `lkgrkql ab qlalp ilp t ab T nrb p^qfpc^`bk&t*t' < 0 pb
')( K^p pb``flkbp pb•^i^a^p `lk ^pqbofp`l mrbabk prmofjfopb l mlpmlkbopb pfk mbogrf`flab i^ `lkqfkrfa^a abi qbj^-
?qpkr]hknao `a qj] pn]jobkni]_e‰j oei†pne_] 056
ii^j^ i^ aoban] qje`]` ab T- K^ b`r^`fŽk '4-02( abjrbpqo^ bi qblobj^ pfdrfbkqb-
SDNQDL@ 4-01- Qa] R9 T y T qj] pn]jobkni]_e‰j oei†pne_] aj qj aol]_ekaq_h‡`ak na]h T+ v oa] O't( < 'R't(+ t(- Cjpkj_ao hko ]qpkr]hknao `a R'oe ateopa]hcqjk( oa aj_qajpn]j ajpna hko r]hknao mqa P pki] aj h] aoban] qje`]` `a T-
DIDLOKN- Rb^ T < T1&P' `lk i^ _^pb &e*f'v `lk bi molar`ql bp`^i^o loaf,k^ofl `ljl molar`ql fkqboflo- Rb^ R i^ qo^kpcloj^`fŽk pfj‹qof`^ `lk j^qofw
?< Y3/ •7I, - Dkqlk`bp i^ cloj^ `r^aoŠqf`^ ab R sfbkb a^a^ mlo
1 1
O't( < 00]::t:t: < 3ty * 7ty-68,68,
Klp ^rqls^ilobp ab R plk @i < 3+ @1 < 7- Dp cŠ`fi sbo nrb bplp ^rqls^ilobp plk+obpmb`qfs^jbkqb+ilp s^ilobp jŒkfjl v jŠufjl nrb qlj^ P bk bi `Œo`ril rkfa^auf * ty < 0 - Dk bcb`ql+bk bpb `Œo`ril qbkbjlp
O't( < 3'ty * ty( * 3ty < 3 * 3ty+ alkab ,0 z V0 y 0-
†pqb^i`^kw^ bi s^ilo jŒkfjl+ 3+`r^kal V1 < N X bi jŠufjl+ 7+`r^kal V1 < ,* 0-
K^ cfdro^ 4-3 jrbpqo^ bi `Œo`ril rkfa^a v alp bifmpbp-K^ bifmpbfkqboflo qfbkb`ljl b`r^`fŽk `^oqbpf^k^3ty * 7ty < 3- Blkpq^ ab qlalp ilp mrkqlp t < 'Vh& t1(
abi mi^kl nrb p^qfpc^`bk O&t' < 3- K^ bifmpb buqboflo bp i^ ab b`r^`fŽk2ty * 6ty < 7 X `lkpq^ ab ilp mrkqlp nrb p^qfpc^`bk O&t' < 7- Klp mrkqlp'~ 0+N( bk ilp nrb i^ bifmpbfkqboflobp q^kdbkqb^i `Œo`ril rkfa^a plk ^rqlsb`qlobp`loobpmlkafbkqbp ^i ^rqls^ilo 3- Klp mrkqlp 'N+,* 0( ab i^ bifmpbbuqboflo plk^rqlsb`qlobp `loobpmlkafbkqbp ^i ^rqls^ilo 7-
Di bgbjmil ^kqboflo firpqo^ molmfba^abpobi^qfs^p^ ilp buqobjlp ab ilp ^rql,s^ilobp nrb plk sŠifalp `lk j^vlo dbkbo^ifa^a- Dk i^ pb``fŽk nrb pfdrb mol_^ob,jlp nrb bi jŒkfjl v bi jŠufjl ^rqls^ilo 'pf bufpqbk(plk pfbjmob bi jŒkfjl v bijŠufjl s^ilo nrb P qlj^ bk i^ bpcbo rkfa^a- Dk i^ afp`rpfŽk nrb s^jlp ^ e^`boab bp^p molmfba^abprqfifw^objlp bi pfdrfbkqb qblobj^ obi^qfsl ^ cloj^p `r^aoŠ,qf`^p- Cb_b l_pbos^opb nrb bpqbqblobj^ kl bufdb nrb T pb^ ab afjbkpfŽk cfkfq^-
SDNQDL@ 4-02- Qa] R9 T y T qj] pn]jobkni]_e‰j oei†pne_] aj qj aol]_ekaq_h‡`ak na]h T _kj bkni] _q]`n…pe_] O't( < 'R't(+ t(- Qqlkjc]iko mqa P jk_]i^e] `a oecjk aj T- Cjpkj_ao oe O't( < N l]n] qj _eanpk t `a T p]i^e†j pa,jaiko R't( < N- Be_dk `a kpnk ik`k+ oe P jk _]i^e] `a oecjk+ ajpkj_ao P oa]jqh] okh]iajpa aj ah jŠ_hak `a R-
Baikopn]_e‰j- Rrmlkd^jlp nrb O't( < N m^o^ rk `fboql t ab T v pb^ v
057 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
@rqlsb`qlo mboqbkb`fbkqb 7
Vh
@rqlsb`qlo mboqbkb`fbkqb ^ 3
O&t' < 3 bk bpq^ bifmpb
EHFTQ@ 4-3 Pah]_e‰jcaki†pne_] ajpna hko ]qpkr]hknao`a R v hko r]hknao `a P aj h]aoban]qje`]`+ ehqopn]`]_kj qj afailhk ^e,`eiajoekj]h-
rk bibjbkql `r^inrfbo^ ab T, Difg^jlp rk p `r^inrfbo^ v `lkpfabobjlp O&t * pu',
Djmib^kal i^ ifkb^ifa^a ab R* i^ ifkb^ifa^a abi molar`ql fkqboflo+v i^ pfjbqoŒ^ab R* qbkbjlp
O&t * pu' < &R&t* pu'* t * pu' < &R&t' * pR&u'*t * pu'
< &R&t'* t' * p&R&t'*u' * p&R&u'*t' * p1&R&u'*u'
< O&t' * 0p&R&t'*u' * p1O&u' < ]p * ^p!*
pfbkal ] < 0&R&t'* v( v ^ < O&u', Rf P bp kl kbd^qfs^ bk T qbkbjlp i^ abp,fdr^ia^a
]p * ^p1 y N m^o^qlal k•jbol ob^i p-
Dk lqo^p m^i^_o^p+bi mlifkljfl `r^aoŠqf`l l&p' < ]p * ^p&qfbkb pr joorjl bkp < N- Krbdl l%&M' < N-Obol l%&M' < ] < 0&R&t'* u'* ^pŒnrb &R&t'* v( < N- Orbp,ql nrb v bp ^o_fqo^ofl+ mlabjlp qlj^o bk m^oqf`ri^o v < R&t'* a^kal&R&t'* R&t''; N- Dpql abjrbpqo^ nrb R&t' < N-
Rf P bp kl mlpfqfs^bk T qbkbjlp l'p( < ]p * ^p&99:N m^o^qlal p+ pŒnrb lqfbkbpr jŠufjl bk p < N+X mlo q^kql zR&M'< N `ljl ^kqbp-
o -')/ B[XYRNMJMN\[NUJ]R_J\J Na][NVX\ MNUX\J^]X_JUX[N\MN WJ][JW\OX[VJLRmW\RVk][RLJ
Cbjlpqo^objlp ^elo^ nrb ilp s^ilobp buqobjlp ab rk^ cloj^ `r^aoŠqf`^ bk i^bpcbo rkfa^a plk ^rqls^ilobp-
SDNQDL@ 4-03- Qa] R9 T y T qj] pn]jobkni]_e‰j heja]hoei†pne_] aj qj ao,
Nnklea`]`ao nah]per]o ] atpnaiko `a hko ]qpkr]hknao 058
l]_†] aq_h†`ak na]h T* v oa] M&t' < &R&t'* t', Cjpna pk`ko hkor]hknao mqa N pki]aj h] aoban] qje`]`* oqlkjc]iko mqa ateopaqj atpnaik ')( &i„teik k i†jeik'aj qj lqjpk q aj ahmqa&q*q' < 0- Cjpkj_ao peao qj ]qpkra_pkn l]n] R9 ah_knnao+lkj`eajpa ]qpkr]hkn ao M&q'* r]hkn atpnaik `a N aj h] aoban] qje`]`,
Baikopn]_eˆj, Rrmlkd^jlp nrb N qfbkb rk jŒkfjl bk q, Sbkbjlp bkqlk`bp
'4-03( O&t' y O&q' m^o^ qlal t nrb `rjmi^ 'u+ t' < 0-
Rb^ W< M&q', Rf &t* t' < 0 qbkbjlp M&q' < ,Z,&t*t' < &,Z,t*t' ^pŒ nrb i^ abp,fdr^ia^a '4-03( mrbab mlkbopb ^pŒ
'4-04( &R&t'* tx y 'e+t'
`lk q^i nrb &t* t' < 0- Cbjlpqobjlp ^elo^ nrb '4-04( bp sŠifal m^o^ pk`k t abT, Rrmlkd^jlp nrb H{uff< ], Dkqlk`bp t < ]u* pfbkal H{XHH< 0- Krbdl
&R&t'* t' < &R&]u'* ]u' < ]0&R&u'* u' v &?,V*t' < ]1&?,u*u',
Obol &R&u'*v( z '-[-v+v( v^ nrb 'v+ v( < 0- Lriqfmif`^kal ^j_lp jfbj_olp ab bpq^abpfdr^ia^a mlo ]1 iibd^jlp ^ '4-04( m^o^ t < ]u,
Orbpql nrb &R&t'* t' + &,Z,t*t' < &R&t' + ot* t'* mlabjlp mlkbo i^ abpfdr^i,a^a '4-04( bk i^ cloj^ &R&t' + ,Z,t*t' y N+ l
'4-05( &Q&t'*t' y N+ alkab R< R , S-
Br^kal t < q qbkbjlp i^ abpfdr^ia^a '4-03( v mlo q^kql q^j_f‹k '4-05(- K^qo^kpcloj^`fŽk ifkb^i Q bp pfj‹qof`^- K^ -abpfdr^ia^a '4-05( bpq^_ib`b nrb i^cloj^ `r^aoŠqf`^ /0 a^a^ mlo ./&V' < &Q&t'* t' bp kl kbd^qfs^ bk T, Br^kalt < q qbkbjlp M*&t' < N- Olo `lkpfdrfbkqb+ pbd•k bi qblobj^ 4-02 ab_b pboQeq' < N- Cf`el ab lqol ljal+ R&q' < oq* ^pŒnrb q bp rk ^rqlsb`qlo m^o^ R*v -[- < M&q' bp bi `loobpmlkafbkqb ^rqls^ilo- Dpql `ljmibq^ i^ abjlpqo^`fŽk pf Nqfbkb rk jŒkfjl bk q-
Rf bufpqb rk jŠufjl bk q qla^p i^p abpfdr^ia^abp ab i^ abjlpqo^`fŽk ^kqboflopb fksfboqbk v ^mif`^jlp bi qblobj^ 4-02 ^ i^ cloj^ `r^aoŠqf`^ kl mlpfqfs^ ./%
')( Rf T bp ab afjbkpfŽk fkcfkfq^+i^ cloj^ `r^aoŠqf`^ P kl qfbkb kb`bp^of^jbkqb rkbuqobjl bk i^ bpcbo^ rkfa^a- Dpqb pboŠ bi `^pl `r^kal R kl qfbkb ^rqls^ilobp- Dk bi `^plab afjbkpfŽk cfkfq^+P qfbkb pfbjmob rk jŠufjl v rk jŒkfjl bk ^id•k mrkql ab i^ bpcbo^rkfa^a- Dpql obpriq^ `ljl rk^ `lkpb`rbk`f^ ab rk qblobj^ jŠp dbkbo^i pl_ob ilp s^ilobpbuqobjlp ab crk`flkbp `lkqfkr^p- Dk i^ pb``fŽk 8-05 mrbab sbopb rk `^pl m^oqf`ri^o ab bpbqblobj^-
06/ ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
) 4-07 B^pl ab afjbkpfŽk cfkfq^
Rrmlkd^jlp ^elo^ nrb afj T < j- Dkqlk`bp R qfbkb j ^rqls^ilobp ob^ibpnrb mrbabk afpmlkbopb bk loabk `ob`fbkqb
Cb ^`rboal `lk bi qblobj^ 4-03+bi jbklo ^rqls^ilo @i bp bi jŒkfjl ab P bk i^ bp,cbo^ rkfa^a+ v bi j^vlo ^rqls^ilo bp bi jŠufjl ab P bk i^ bpcbo^rkfa^a- Cbjlp,qo^objlp pbdrfa^jbkqb nrb ilp ^rqls^ilobp fkqbojbaflp q^j_f‹k pb mobpbkq^k ljls^ilobp buqobjlp ab P+ obpqofkdfalp^ `fboqlp pr_`lkgrkqlp ab i^ bpcbo^rkfa^a-
Rb^ S/ rk ^rqlsb`qlo bk i^ bpcbo^ rkfa^a nrb jfkfjfw^ P- Dkqlk`bp@i < O&q0(- Rf @ bp rk ^rqls^ilo afpqfkql ab @i `r^inrfbo ^rqlsb`qlo `loobpmlk,afbkqb ^ @ ab_b pbo loqldlk^i ^ q/‹ Olo `lkpfdrfbkqb+bp k^qro^i _rp`^o `ljl q^irk ^rqlsb`qlo bk bi `ljmibjbkql loqldlk^i abi pr_bpm^`fl bkdbkao^al mlo q--
Rb^ R bi pr_ bpm^`fl bkdbkao^al mlo q0Œ Di `ljmibjbkql loqldlk^i R0-`lkpq^ ab qlalp ilp bibjbkqlp ab T loqldlk^i ^ q-- Dk m^oqf`ri^o+R0- `lkqfbkbqlalp ilp ^rqlsb`qlobp `loobpmlkafbkqbp ^ ilp ^rqls^ilobp @ <0< @i&Dp cŠ`fi `lj,mol_^o nrb afj R0- < j , 0 X nrb R ^mif`^ R0- bk pŒjfpjl ')(- Cbpfdkbjlpmlo Rk,0 i^ bpcbo^rkfa^a bk bi pr_bpm^`fl R0- ab afjbkpfŽk j , 0- 'K^ bpcbo^rkfa^a Rk,0 bp rk pr_`lkgrkql ab i^ bpcbo^rkfa^a bk T,' @mif`^kal bi qblobj^4-03 ^i pr_bpm^`fl R0- bk`lkqo^jlp nrb @1 < O&q1(+ alkab S1 bp rk mrkql nrbe^`b jŒkfjl P bk Rk,0&
Di pfdrfbkqb ^rqlsb`qlo @2 mrbab l_qbkbopb bk cloj^ m^ob`fa^ `ljl bi s^ilojŒkfjl ab P bk i^ bpcbo^rkfa^a Qj,1 bk bi bpm^`fl ab afjbkpfŽk k , 1 nrb`lkpq^ ab ^nrbiilp bibjbkqlp loqldlk^ibp pfjriqŠkb^jbkqb ^ S/ X q,- Blkqfkr^kalbk bpq^cloj^ bk`lkqo^jlp nrb `^a^ ^rqls^ilo @h bp bi s^ilo jŒkfjl nrb qlj^P bk rk^ bpcbo^rkfa^a Qj,g*0 bk rk pr_bpm^`fl ab afjbkpfŽk j,g * 0- Dij^vlo ab bplp jŒkfjlp+ ?j+ bp q^j_f‹k bi i…teik s^ilo nrb qlj^ P bk `^a^ rk^ab i^p bpcbo^pQj,g*&0& Di `loobpmlkafbkqb `lkgrkql ab ^rqlsb`qlobp q0+ ŒŒŒ+Sj
cloj^ rk^ _^pb loqlkloj^i m^o^ T,
4-08 So^kpcloj^`flkbp rkfq^of^p
Blk`irfjlp bpqb `^mŒqril`lk rk^ _obsb afp`rpfŽk ab lqol qfml fjmloq^kqbab qo^kpcloj^`flkbp ii^j^a^p rkfq^of^p- Dk bi `^pl ab afjbkpfŽk cfkfq^ bpqŠkobmobpbkq^a^pmlo j^qof`bp rkfa^a-
CDEHMHBHˆM- Qa]j C qj aol]_ek aq_h‡`ak u T qj oq^aol]_ek `a C- Sj]pn]jobkni]_e‰j R9 T y C oa hh]i] qjep]ne] aj T oe pajaiko
&R&t'*R&u'' < &t*u' l]n] pk`k l]n t+u `a T- '4-06(
')( Dpql pb efwl bk i^ abjlpqo^`fŽk abi qblobj^ 4-3+pb``fŽk 4-5-
Rn]jobkni]_ekjao qjep]ne]o 060
Aq]j`k C ao qj aol]`k aq_h‡`ak na]h+qj] pn]jobkni]_e‰j qjep]ne] p]i^e†j oa`ajkiej] pn]jobkni]_e‰j knpkckj]h-
K^ b`r^`fŽk '4-06( pb bumobp af`fbkal nrb R `lkpbos^ ilp molar`qlp fkqb,oflobp- Dk `lkpb`rbk`f^+ bp k^qro^i bpmbo^onrb R q^j_f‹k `lkpbosb i^ loqldl,k^ifa^a v i^p kloj^p+ mrbp ‹pq^p pb abofs^k ab ilp molar`qlp fkqboflobp-
SDNQDL@ 4-04- Qe R9 T y C ao qj] pn]jobkni]_e‰j qjep]ne] `a T+ ajpkj,_ao l]n] pk`k l]n t+u `a T pajaiko
^( 't+ u( < N eilhe_] 'R't(+ R'u• < N 'R _kjoanr] h] knpkckj]he`]`(-_( GGR't(00< Hiuii 'R _kjoanr] h]o jkni]o(-b( heR't( , R'u(00< Hiu, vii 'R _kjoanr] h]o `eop]j_e]o(-a( R ao ej ranpe^ha+u R,0 ao qjep]ne] aj R'T(-
Baikopn]_e‰j- K^ m^oqb ( bp `lkpb`rbk`f^ fkjbaf^q^ ab i^ b`r^`fŽk '4-06(-K^ m^oqb_( pb abar`b e^`fbkal t < u bk '4-06(- K^ m^oqbb( obpriq^ ab _( mlonrbR't( , R'u( < R't , u(-
O^o^ abjlpqo^o a( ^mif`^jlp _( il nrb e^`b sbo nrb R't(<M fjmif`^ t<M+^pŒnrb R bp fksboqf_ib- Rf t D R'T( b u D R'T( mlabjlp bp`of_fo t < R'q(+u < R&r', `lk il nrb qbkbjlp
&R+h&V'*R+h&u€< &q*r' < &R&q'*R&r€ < &t*u',
Olo il q^kql R,0 bp rkfq^of^ bk R'T(-
Dk `r^kql ^ ilp ^rqls^ilobp v ^rqlsb`qlobp qbkbjlp bi qblobj^ pfdrfbkqb-
SDNQDL@ 4-05- Qa] R9 T y C qj] pn]jobkni]_e‰j qjep]ne] aj T-^( QeR peaja qj ]qpkr]hkn &Z+ajpkj_ao 0+[0< 0 -_( Qet a u okj ]qpkra_pknao_knnaolkj`eajpao ] ]qpkr]hknao `eopejpko@ u gI-+
ajpkj_ao t a u okj knpkckj]hao-b( QeT < C Wafj T < j+ u oe T ao qj aol]_ek _kilhafk+ ateopaj hko ]qpk,
ra_pknaoS/ * ‹‹‹ +Sj `a R mqa bkni]j qj] ^]oa knpkjkni]h l]n] T- J]i]pnev `a R nah]per]] ao] ^]oa ao h] i]pnev `e]ckj]h @<af^d '@i&--- +@k(+
oeaj`k ?g ah ]qpkr]hkn _knnaolkj`eajpa ] qo-
Baikopn]_e‰j- O^o^ abjlpqo^o ^(+pb^ t rk ^rqlsb`qlo `loobpmlkafbkqb ^ @-
Dkqlk`bp t <0< N X R't( < ?t- G^`fbkal u < t bk i^ b`r^`fŽk '4-06( iibd^jlp ^
'e+ e( < &t* t' l ,,py&t*t' < &t* t',
Orbpql nrb &t* t' = N u @W < 0-0-01+ bpql fjmif`^ H@[ < 0 -
061 ?qpkr]hknao `a klan]`knao aj aol]_eko aq_h‡`ako
O^o^ abjlpqo^o _(+ bp`of_^jlp R&t' < ?V* R&u' < l+u X `^i`ri^objlp bi mol,ar`ql fkqboflo &R&t'* R&u€ ab alp j^kbo^p- Sbkbjlp
&R&t'* R&u'' < &t* u'
v^ nrb Rao rkfq^of^- @pfjfpjl
&R&t'* R&u'' < &?V* G+hW'< ?f/&V* u'
v^ nrb t b u plk ^rqlsb`qlobp- Olo `lkpfdrfbkqb-HkŒu-g&(< 'V+ u'* ^pŒnrb 'u+ u' < Np^isl pf ?+eh< 0- Obol ?(9 < 0 pbd•k ^(+ mlo il nrb pf crbo^ ?+eh< 0 ab_boŒ^ pbo?(9 < ?+eh+(9 < +eh+? < G+h% il nrb `lkqo^af`b i^ efmŽqbpfp ab nrb @ v m- plk afp,qfkqlp- Olo `lkpfdrfbkqb ?+ehy 0 X &t* u' < N -
Di ^m^oq^al b( pb abjrbpqo^ mlo fkar``fŽk obpmb`ql ab j bk cloj^ jrv m^ob,`fa^ ^i qblobj^ 4-3+ nrb a^ bi obpriq^al ^kŠildl m^o^ ilp lmbo^alobp ebojfqf^klp-Di •kf`l `^j_fl kb`bp^ofl ^cb`q^ ^ i^ m^oqb ab i^ abjlpqo^`fŽk nrb ^cfoj^ nrb R^mif`^ R--K bk pŒjfpjl+ alkab
RI- < wt Ht D T* &t* q0( < Ny-
@nrŒ S/ bp rk ^rqlsb`qlo ab R `lk bi ^rqls^ilo ?h% @ m^oqfo ab i^ b`r^`fŽkR&q0( < ?0S0 bk`lkqo^jlp
v^ nrb (&0y90< H@001 < 0- Difg^jlp ^elo^ rk t `r^inrfbo^ bk R--K v l_pbosbjlp nrb
Krbdl R&t' D RI- pf t D o, +mlo il `r^i R ^mif`^ R--K bk pŒjfpjl- Di obpql abi^ abjlpqo^`fŽk bp fa‹kqf`l ^ i^ abi qblobj^ &:-3+mlo il nrb kl 0/ obmbqfobjlp-
Klp alp qblobj^p nrb pfdrbk pb obcfbobk ^ molmfba^abp ab i^p qo^kpcloj^`flkbprkfq^of^p bk bpm^`flp ab afjbkpfŽk cfkfq^- C^jlp q^k pŽil rk _lpnrbgl ab i^pabjlpqo^`flkbp-
SDNQDL@ 4-06- Qqlkjc]iko mqa afj T < j u oa] C < 'ah!! +aj( qj]^]oa l]n] T bef]`]- J] pn]jobkni]_e‰j heja]h R9 T y T ao qjep]ne] oe u o‰hkoe
'4-07( 'R'ae(& R'af'' < 'ae+af' l]n] pk`k l]n e,f -
Rn]jobkni]_ekjao qjep]ne]o 062
Cj l]npe_qh]n+oeC ao knpkjkni]h ajpkj_ao R ao qjep]ne] oev o‰hkoeR ]lhe_] C ajqj] ^]oa knpkjkni]h-
Co^kvk `a h] `aikopn]_e‰j- Olkd^jlp t < tae* v < uzaz- Sbkbjlp bk,qlk`bp
v
@ `lkqfkr^`fŽk pb `ljm^o^ &t* v( `lk &R&t'* R&u'',
SDNQDL@ 4-07- Qqlkjc]iko mqa afj T < j v pb^ 'ah!&! aj( qj] ^]oaknpkjkni]h l]n] T- Qa]? < ']ez( h] nalnaoajp]_e‰ji]pne_e]h`a qj] pn]jobkni]_e‰jheja]hR9 T y T nah]per]] ao] ^]oa- Cjpkj_ao R ao qjep]ne] oev o‰hkoe ? ao qje,p]ne]+aopkao+oeu o‰hkoe
'4-08( ?)? < h-
Co^kvk `a h] `aikopn]_e‰j- Orbpql nrb 'b+ +az( bp bi bibjbkql ef ab i^ j^qofwfabkqfa^a+ i^ b`r^`fŽk '4-08( fjmif`^
'4-1/(V V
'b-+bg( < bege]gf< ]gebegf•g<h g<h
Orbpql nrb ? bp i^ j^qofw ab R qbkbjlp R 'b-( < X<h ]gd* R'af' < z<0]nfan `lk0/ `r^i
Rb `ljm^o^ irbdl `lk '4-1/( v pb ^mif`^ bi qblobj^ 4-06-
SDNQDL@ 4-08- Rk`] i]pnev qjep]ne] ? peaja h]o lnklea`]`ao oecqeajpao9^( ? ao jk oejcqh]n u ?,h < ?)-_( A]`] qj] `a h]o i]pne_ao ? p+? v ? ) ao qjep]ne]-b( Jko ]qpkr]hknao `a ? okj jŠianko _kilhafko `a r]hkn ]^okhqpk 0-a( Zabq?h < 0: oe ? ao na]h+ajpkj_ao abq ? < ,*,0-
K^ abjlpqo^`fŽk abi qblobj^ 4-08 pb abg^ `ljl bgbo`f`fl m^o^ bi ib`qlo-
063 .DC>E7<>A9B89 >?9A78>A9B9= aol]_eko aq_h‡`ako
-'*( 8SN[LRLRX\
0- ^( Rb^ R8T y T i^ qo^kpcloj^`fŽk a^a^ mlo R&t' < at* alkab a bp rk bp`^i^o cfg^al-Cbjlpqo^o nrb R bp rkfq^of^ pf v pŽil pf Zb\< 0 -_( Rf T bp rkfafjbkpflk^i+ abjlpqo^o nrb i^p •kf`^p qo^kpcloj^`flkbp rkfq^of^p bk Tplk i^p abp`ofq^p bk ^(- Dk m^oqf`ri^o+ pf T bp rk bpm^`fl ob^i rkfafjbkpflk^i+ bufpqbkpŽil alp qo^kpcloj^`flkbp loqldlk^ibp+ R&t' < t v R&t' < +t,
1- Cbjlpqo^o `^a^ rk^ ab i^p molmlpf`flkbp+ obi^qfs^p ^ rk^ j^qofw ?* j •:j+ ob^i loql,dlk^i^( Rf @ bp rk ^rqls^ilo ob^i ab ?* bkqlk`bp @ < 0 Ž @< ,0 Š_( Rf @ bp rk ^rqls^ilo `ljmibgl ab ?* bi `ljmibgl `lkgrd^al V q^j_f‹k bp ^rqls^iloab ? - Dp ab`fo+ ilp ^rqls^ilobp ab ? kl ob^ibp plk `lkgrd^alp ^ m^obp-b( Rf j bp fjm^o+ ? qfbkb mlo il jbklp rk ^rqls^ilo ob^i-
2- Rb^ T rk bpm^`fl br`iŒabl ob^i ab afjbkpfŽk j- Tk^ qo^kpcloj^`fŽk loqldlk^i R9 T y T`lk abqbojfk^kqb fdr^i ^ 0 pb iH^j^ nkp]_e‰j- Rf j bp fjm^o+ abjlpqo^o nrb 0 bp ^rql,s^ilo m^o^ R, Dpql morb_^ nrb qla^ olq^`fŽk ab rk bpm^`fl ab afjbkpfŽk fjm^o qfbkbrk bgb cfgl- YGj`e_]_e‰j9 @mif`^o bi bgbo`f`fl 1-\
3- C^a^ rk^ j^qofw ob^i loqldlk^i ? `lk ,0 `ljl ^rqls^ilo ab jriqfmif`fa^a g- Cbjlpqo^onrb abq ? < &\h'g ,
4- Rf R bp ifkb^i v `lkpbos^ i^ kloj^+ abjlpqo^o nrb R bp rkfq^of^-5- Rf R9 T y T bp rkfq^of^ v ebojfqf^k^+ abjlpqo^o nrb R! < h-6- Rb^k &ah* ‹‹‹ * aj' v &q! ,,, * Sj' alp _^pbp loqlkloj^ibp m^o^ rk bpm^`fl br`iŒabl T,
Cbjlpqo^o nrb bufpqb rk^ qo^kpcloj^`fŽk rkfq^of^ R nrb ^mif`^ rk^ ab bp^p _^pbp bki^ lqo^-
7- G^ii^o rk k•jbol ob^i ] q^i nrb i^ pfdrfbkqb j^qofw pb^ rkfq^of^9
Y
] qf ]'1e , 0(\e] N * f( q^N , f( -
] , ‡]'1 , f(
8- Rf ? bp rk^ j^qofw ebjf,ebojfqf^k^+ abjlpqo^o nrb G+ ? b G* ? plk kl pfkdri^obpv nrb &h+ ?'&h * ?'+h bp rkfq^of^-
0/- Rf ? bp rk^ j^qofw rkfq^of^ v pf G* ? bp kl pfkdri^o+ abjlpqo^o nrb &h+ ?'&h * ?'+%bp ebjf,ebojfqf^k^-
00- Rf ? bp ebojfqf^k^+ abjlpqo^o nrb ? + eh bp kl pfkdri^o v nrb &? + eG(,&'?* fH( bprkfq^of^-
01- Cbjlpqo^o nrb `r^inrfbo j^qofw rkfq^of^ mrbab af^dlk^ifw^opb `lk rk^ j^qofw rkfq^of^-02- Tk^ j^qofw `r^ao^a^ pb iH^j^ jkni]h pf ?? ) < ? )?- Cbqbojfk^o `rŠi ab ilp qfmlp
pfdrfbkqbp ab j^qof`bp plk kloj^ibp-^( L^qof`bp ebojfqf^k^p- a( L^qof`bp ebjf,pfj‹qof`^p-_( L^qof`bp ebjf,ebojfqf^k^p- b( L^qof`bp rkfq^of^p-`( L^qof`bp pfj‹qof`^p- c( L^qof`bp loqldlk^ibp-
03- Rf ? bp rk^ j^qofw kloj^i &??) < ?• ?' X pf S bp rk^ j^qofw rkfq^of^+ abjlpqo^o nrbS•?S bp kloj^i-
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SDNQDL@ 5-2- SDNQDL@ CD DWHRSDMBH@ X TMHBHC@C O@Q@ DBT@BHNMDR KH,
MD@KDR CD NQCDM j- Rb^k Nh%N1+ ŒŒŒ-N: bqj_ekjao _kjpejq]o aj qj ejpanr]hk]^eanpk H*v oa] J ah klan]`kn `ebanaj_e]hheja]h
Rf uP D H v oe g,*g-+--- +gj+/ okj j jŠianko na]hao`]`ko+ ateopa ajpkj_ao qj]v o‰hkqj] bqj_e‰j v < b't( mqa o]peob]_ah] a_q]_e‰j `ebanaj_e]h dkikc†ja]J&u' < N aj H v mqa p]i^e†j o]peob]_ah]o _kj`e_ekjao eje_e]hao
M^oanr]_e‰j9 Di sb`qlo abi k,bpm^`fl a^al mlo 'b'tk=-b&'tk= Œ---Œ{b!,ii'ulƒ pb A^ok^ra_pkn,r]hkn eje_e]h ab b bk tk- Di qblobj^ 5-2 klp af`b nrb pf bibdfjlp rk mrkql t|bk H v rk sb`qlo bk bi k,bpm^`fl+ i^ b`r^`fŽk eljld‹kb^ J&u' < N qfbkb bu^`q^,jbkqb rk^ plir`fŽk v ;b&t' bk / `lk ^nrbi sb`qlo `ljl s^ilo fkf`f^i bk t r+ Olobgbjmil+ `r^kal j < 1 bufpqb bu^`q^jbkqb rk^ plir`fŽk `lk s^ilo ^pfdk^al b&tk' vabofs^a^ ^pfdk^a^ f%&t_' bk bi mrkql tk,
K^ abjlpqo^`fŽk abi qblobj^ ab bufpqbk`f^ v rkf`fa^a pb l_qbkaoŠ `ljl`loli^ofl ab ilp qblobj^p ab bufpqbk`f^ v rkf`fa^a jŠp dbkbo^ibp nrb pb bpqraf^kbk bi `^mŒqril 6- Dk i^ pb``fŽk 6-8 pb bpqraf^ lqo^ abjlpqo^`fŽk m^o^ bi `^pl abb`r^`flkbp `lk `lbcf`fbkqbp `lkpq^kqbp-
5-5 CfjbkpfŽk abi bpm^`fl plir`fŽk ab rk^ b`r^`fŽk ifkb^i eljld‹kb^
SDNQDL@ 5-3- SDNQDL@ CD CHLDMRHNM@KHC@C- Qa] J9 h%Aj&H'++++,,h%A&H'qjklan]`kn `ebanaj_e]h heja]h `a kn`aj j `]`k lkn
'5-0/(
071 C_q]_ekjao `ebanaj_e]haoheja]hao
Cjpkj_ao ah aol]_ek okhq_e‰j a h] a_q]_e‰jJ&u' < N peaja `eiajoe‰j j-
Baikopn]_e‰j- Rb^ T k bi bpm^`fl ifkb^i k,afjbkpflk^i ab i^p k,mi^p ab bp`^,i^obp-Rb^ R i^ qo^kpcloj^`fŽk ifkb^i nrb ^mif`^ `^a^ crk`fŽk b abi bpm^`fl plir,`fŽk L&J' bk bi sb`qlo,s^ilo fkf`f^i ab b bk tk+
pfbkal t‚ rk mrkql cfgl bk Z+Di qblobj^ ab rkf`fa^a klp af`b nrb R&b' < Nfjmif`^ nrb b < N- Olo `lkpfdrfbkqb+ pbd•k bi qblobj^ 1-0/+ R bp rkl ^ rklbk L&J', Krbdl Rn! q^j_f‹k bp rkl ^ rkl v ^mif`^ Tj bk L&J'* v bi qblobj^1-00 abjrbpqo^ nrb afj L&J' < afj Tj < j-
Orbpql nrb bi bpm^`fl plir`fŽk qfbkb afjbkpfŽk j+ rk `lkgrkql `r^inrfbo^ab j plir`flkbp fkabmbkafbkqb„pbosfoŠab _^pb- Olo `lkpfdrfbkqb+ `ljl `loli^oflabi qblobj^ ab afjbkpflk^ifa^a qbkbjlp9
SDNQDL@ 5-4- Qa] J9 AAj'H( ,,* AA'H( qj klan]`kn `ebanaj_e]h heja]h `akn`aj j- Qeq++-- +Sj okj j okhq_ekjao ej`alaj`eajpao `a h] a_q]_e‰j`ebanaj_e]hdkikc†ja] J&u' < N aj [+ pk`] okhq_e‰ju < b't( aj [ lqa`a atlnao]noa aj h]bkni]
'5-00(j
b't( < _gqet(+h!!i
oeaj`k `i+ ŠŠŠ+_! `lkpq^kqbp-
M^oanr]_e…j9 Orbpql nrb qla^p i^p plir`flkbp ab i^ b`r^`fŽk afcbobk`f^i J&u' < NbpqŠk `lkqbkfa^p bk i^ cŽojri^ '5-00(+ i^ `lj_fk^`fŽk ifkb^i abi pbdrkal jfbj_ol+`lk i^p `lkpq^kqbp ^o_fqo^of^p BH+’’’ +a: ^ sb`bp pb ii^j^ okhq_e…jcajan]h ab i^b`r^`fŽk afcbobk`f^i-
Di qblobj^ ab afjbkpflk^ifa^a klp af`b nrb bi bpm^`fl plir`fŽk ab rk^b`r^`fŽk afcbobk`f^i ifkb^i eljld‹kb^ ab loabk j qfbkb pfbjmob rk^ _^pb ab jplir`flkbp+ mbol kl klp af`b `Žjl pb abqbojfk^ bp^ _^pb- Dk ob^ifa^a+ kl pb`lkl`b rk j‹qlal pbk`fiil m^o^ abqbojfk^o rk^ _^pb ab plir`flkbp m^o^ qla^b`r^`fŽk ifkb^i- Ml l_pq^kqb+pb e^k fab^al j‹qlalp bpmb`f^ibpm^o^ `^plp m^o,qf`ri^obp-Dkqob‹pqlp `^_b `lkpfabo^o i^p b`r^`flkbp afcbobk`f^ibp`lk `lbcf`fbkqbp`lkpq^kqbp nrb slisbjlp ^elo^ ^ `lkpfabo^o-
5-6 …idb_o ab lmbo^alobp ab `lbcf`fbkqbp`lkpq^kqbp
Tk lmbo^alo ? ab `lbcf`fbkqbp `lkpq^kqbp bp rk lmbo^alo ifkb^i ab i^ cloj^
'5-01(
?hca^n] `a klan]`knao `a _kabe_eajpao_kjop]jpao 072
alkab B bp bi lmbo^alo abofs^a^ v ]|* ^i&--- -]: plk `lkpq^kqbp ob^ibp-Rf ]• <0< Nbi lmbo^alo pb ii^j^ ab loabk j- Di lmbo^alo ? mrbab ^mif`^opb ^ `r^inrfbocrk`fŽk v `lk j abofs^a^p bk rk `fboql fkqbos^il+ pfbkal bi obpriq^al rk^ crk,`fŽk ?&u' a^a^ mlo
?&u' < ]ku:j' * ^0v;k,i( * --- 0, ]j+/u% * ]ju,
Dk bpq^ pb``flk+ ifjfq^jlp krbpqol bpqrafl ^ crk`flkbp nrb qfbkbk abofs^a^p ab`r^inrfbo loabk bk ', //+ * //(- Di `lkgrkql ab q^ibp crk`flkbp pb abpfdk^oŠ`lk zll v pb ib ii^j^oŠ `i^pb ab i^p bqj_ekjao ej`abeje`]iajpa `aner]^hao- Rfv D Bc.ll+ bkqlk`bp ?&u' mboqbkb`bq^j_f‹k ^ zll-
K^p lmbo^`flkbp ^idb_o^f`^p `loofbkqbp `lk i^p qo^kpcloj^`flkbp ifkb^ibp']`e_e‰j+iqhpelhe_]_e‰jlkn ao_]h]nao+v _kilkoe_e‰j l iqhpelhe_]_e‰j( mrbabk^mif`^opb+bk m^oqf`ri^o+ ilp lmbo^alobp `lk `lbcf`fbkqbp `lkpq^kqbp- Rb^k ? v @alp lmbo^alobp `lk `lbcf`fbkqbp `lkpq^kqbp 'kl kb`bp^of^jbkqb abi jfpjl loabk(-Orbpql nrb i^ prj^ ? * @v qlalp ilp molar`qlp ?? plk q^j_f‹k lmbo^alobp `lk`lbcf`fbkqbp `lkpq^kqbp+bi `lkgrkql ab qlalp ilp lmbo^alobp `lk `lbcf`fbkqbp `lkp,q^kqbp bp rk bpm^`fl ifkb^i- Di molar`ql ab ? mlo @ 'bk `r^inrfbo loabk( bpq^j_f‹k rk lmbo^alo `lk `lbcf`fbkqbp `lkpq^kqbp- Olo `lkpfdrfbkqb+ i^p prj^p+molar`qlp v molar`qlp mlo bp`^i^obp ab lmbo^alobp `lk `lbcf`fbkqbp `lkpq^kqbpp^qfpc^`bki^p ibvbp `lkjrq^qfs^+ ^pl`f^qfs^ v afpqof_rqfs^ loafk^of^p nrb `rjmibkqla^p i^p qo^kpcloj^`flkbp ifkb^ibp- @pfjfpjl+ mrbpql nrb B&B7 < B!B& m^o^qlalp ilp bkqbolp mlpfqfslp n v o+alp lmbo^alobp `lk `lbcf`fbkqbp `lkpq^kqbp `r^,ibpnrfbo^ ? v @ plk mbojrq^_ibp: ?@ < @?,
@ `^a^ lmbo^alo `lk `lbcf`fbkqbp `lkpq^kqbp ? ^pl`f^jlp rk mlifkljfl N?ii^j^al mlifkljfl `^o^`qboŒpqf`lab ?, Rf ? sfbkb a^al mlo '5-01(+ N? bp bi mlif,kljfl nrb qfbkb ilp jfpjlp `lbcf`fbkqbp nrb ?, Dpql bp+m^o^qlal n ob^i qbkbjlp
N?'n( < ]knj * ]-n!9> * --- * ]j} Œ
Qb`Œmol`^jbkqb+a^al rk mlifkljfl ob^i `r^inrfbo^ l* bufpqbrk `loobpmlkafbkqblmbo^alo ? `rvlp `lbcf`fbkqbp plk ilp jfpjlp nrb ilp ab l, Di pfdrfbkqb qblobj^jrbpqo^ nrb q^i ^pl`f^`fŽk bkqoblmbo^alobp v mlifkljflp bp rk^ `loobpmlkabk`f^rkl ^ rkl- @abjŠp+ bpq^`loobpmlkabk`f^ ^pl`f^ ^ prj^p+ molar`qlp ab lmbo^alobpv molar`qlp ab bp`^i^obpmlo lmbo^alo i^p obpmb`qfs^pprj^p+ molar`qlp v molar`,qlp mlo bp`^i^obpab prp mlifkljflp `^o^`qboŒpqf`lp-
SDNQDL@ 5-5- Qa]j ? v @ `ko klan]`knao _kj _kabe_eajpao_kjop]jpao _kjlkhejkieko _]n]_paneope_konaola_perkoN? v N@+X @ qj jŠiank na]h-Cjpkj_ao pa,jaiko9
^( ? < @ oe v o‰hkoe N? < N@+_( N?*@ < N? * N@+b( N?@ < N? - N@+a( N(&?< @&N?-
073 C_q]_ekjao `ebanaj_e]hao heja]hao
Baikopn]_eˆj, Blkpfabobjlp mofjbol i^ m^oqb^(- Rrmlkd^jlp N? < N@,Prbobjlp abjlpqo^o nrb ?&u' < @&u' m^o^ qla^ v ab `b // ’ Orbpql nrb N? < N@*^j_lp mlifkljflp qfbkbk bi jfpjl do^al v ilp jfpjlp `lbcf`fbkqbp- Olo `lkpf,drfbkqb ? v @ qfbkbkbi jfpjl loabk v ilp jfpjlp `lbcf`fbkqbp+ pŒnrb ?&u' < @&u'm^o^qla^ v ab `b // ’
Rbdrfa^jbkqb abjlpqo^jlp nrb ? < @ fjmif`^ N? < N@,K^ obi^`fŽk ? < @pfdkfcf`^ nrb ?&u' < @&u', m^o^ qla^ v ab `b // ’ Sljbjlp v < a&!+pfbkal nqj]`lkpq^kqb- Orbpql nrb u&g' < nganpGHm^o^ qlal g y N+qbkbjlp
?&u' <N? &n'anv Œ v @&ux< N@'n(an-n-
K^ b`r^`fŽk ?&u' < @&u' fjmif`^ l?&n' < l@&n', X^ nrb 6 bp `r^inrfbo^+ ab_b pboN? < N@,Dpql `ljmibq^ i^ abjlpqo^`fŽk ab i^ m^oqb (-
K^p m^oqbp_(+ b( v a( pb abar`bk ^i jljbkql ab i^ abcfkf`fŽk ab mlifkljfl`^o^`qboŒpqf`l-
Cbi qblobj^ 5-5 obpriq^ nrb qla^ obi^`fŽk ^idb_o^f`^ nrb fk`irv^ prj^p+ mol,ar`qlp v molar`qlp mlo bp`^i^obp ab ilp mlifkljflp N? v N@plk q^j_f‹k sŠifalpm^o^ilp lmbo^alobp ? v @, Dk m^oqf`ri^o+pf bi mlifkljfl `^o^`qboŒpqf`lN? mrbabc^`qlofw^opbljl molar`ql ab alp l jŠp mlifkljflp+ `^a^ c^`qlo ab_b pbobi mlifkl,jfl `^o^`qboŒpqf`lab rk `fboql lmbo^alo `lk `lbcf`fbkqbp `lkpq^kqbp+ pŒnrb pbd•kbi qblobj^ 5-5 bufpqbrk^ `loobpmlkafbkqb c^`qlofw^`fŽkabi lmbo^alo ?, Olo bgbj,mil+ pf l?&n' < l@&n'l_&n'* bkqlk`bp ? < @a, Rf l?&n' mrbab c^`qlofw^opb`ljlmolar`ql ab j c^`qlobp ifkb^ibp+mlo bgbjmil pb^
'5-02(
i^ `loobpmlkafbkqb c^`qlofw^`fŽkab ? qlj^ i^ cloj^
Di qblobj^ crka^jbkq^i abi Šidb_o^ klp af`b nrb qlal mlifkljfl l?&n' abdo^al j :b9 0 qfbkbrk^ c^`qlofw^`fŽkab i^ cloj^ '5-02(+ alkab n0 +61 + ’’’ + n+plki^p o^Œ`bpab i^ b`r^`fŽk
ii^j^a^ a_q]_eˆj _]n]_pan†ope_] ab ?, B^a^ o^Œwpb bp`of_bq^kq^psb`bp `ljl fkaf`^pr loabk ab jriqfmif`fa^a- K^p o^Œ`bpmrbabk pbo ob^ibp l `ljmibg^p- Orbpql nrbN?&n' qfbkb`lbcf`fbkqbp ob^ibp+i^p o^Œ`bpljmibg^p pb mobpbkq^kbk m^obpab `lk,grd^a^p+ ] * ef1* ] , ef1* pf f1 ", N- Klp alp c^`qlobp ifkb^ibp `loobpmlkafbkqbp ^`^a^ rkl ab q^ibp m^obp mrbab `lj_fk^opb m^o^ a^o rk c^`qlo `r^aoŠqf`l
Bapaniej]_e‰j `a qj] ^]oa `a okhq_ekjao 074
+1,-+Xkn * ]1 * V `rvlp `lbcf`fbkqbp plk ob^ibp- Olo `lkpfdrfbkqb+ qlal mlifkl,jfl l?'n( mrbab c^`qlofw^opb ljl rk molar`ql ab mlifkljflp ifkb^ibp v `r^aoŠ,qf`lp _kj _kabe_eajpaona]hao-Dpql klp molmlo`flk^ rk^ `loobpmlkafbkqb c^`qlofw^,`fŽk abi lmbo^alo ? `ljl rk molar`ql ab lmbo^alobp ab mofjbo v pbdrkal loabk`lk `lbcf`fbkqbp `lkpq^kqbp v ob^ibp-
DIDLOKN 0- Rb^ ? < B1, RC * 5- Orbpql nrb bi mlifkljfl `^o^`qboŒpqf`l
l?'n( qfbkb i^ c^`qlofw^`fŽk n1, Ro* 5 < 'n , 1('n , 2(+ bi lmbo^alo ? qfbkb
i^ c^`qlofw^`fŽk
B1 , 4B * 5 < 'B , 1('B , 2(-
DIDLOKN 1- Rb^ ? < B3, 1B2 * 1B1
, 1B * 0- Di mlifkljfl `^o^`qb,oŒpqf`lN?&n' qfbkbi^ c^`qlofw^`fŽk
n3 , 1n2 * 1n1 , 1n * 0 < 'n , 0('n , 0('n1 * 0(+
^pŒnrb ? qfbkbi^ c^`qlofw^`fŽk? < 'B , 0('B , 0('B1 * 0(-
.'0 7N]N[VRWJLRmWMN WJKJ\NMN\XU^LRXWN\YJ[J NL^JLRXWN\URWNJUN\LXWLXN&ORLRNW]N\LXW\]JW]N\YX[ OJL]X[RcJLRmWMNXYN[JMX[N\
Di qblobj^ nrb pfdrb abjrbpqo^ `ljl i^ c^`qlofw^`fŽk ab lmbo^alobp `lk`lbcf`fbkqbp `lkpq^kqbpklp ^vra^ bk i^ obplir`fŽk ab b`r^`flkbp afcbobk`f^ibpifkb^,ibp `lk `lbcf`fbkqbp `lkpq^kqbp-
SDNQDL@ 5-6- Qa] J qj klan]`kn _kj _kabe_eajpao_kjop]jpao mqa lqa`a Y]_,pknev]noa_kik qj lnk`q_pk `a klan]`knao _kj _kabe_eajpao_kjop]jpao+lkn afailhk
Cjpkj_ao ah aol]_ek okhq_e‰j a h] a_q]_e‰j`ebanaj_e]h heja]h J&u' < N _kjpeajaah aol]_ek okhq_e‰j a _]`] qj] `a h]o a_q]_ekjao `ebanaj_e]hao?z&u' < N- Be_dk`a kpnk ik`k+
'5-03( L'?:( p9: L'J( l]n] _]`] e< 0+1+--- +g-
Baikopn]_e‰j- Rf q bp bi k•`ibl abi •iqfjl c^`qlo ?g qbkbjlp ?g&S' < N+^pŒnrb
075 C_q]_ekjao `ebanaj_e]hao heja]hao
Olo il q^kql+bi k•`ibl ab J `lkqfbkb bi k•`ibl abi •iqfjl c^`qlo ?d Obol v^ nrbilp lmbo^alobp `lk `lbcf`fbkqbp `lkpq^kqbp plk mbojrq^_ibp+ mlabjlp obloabk^oilp c^`qlobp ab jlal nrb rkl `r^inrfbo^ ab biilp pb^ bi •iqfjl c^`qlo- Dpql ab,jrbpqo^ '5-03(-
Rf J'q( < N+pb af`b nrb bi lmbo^alo J ]jqh] q- Di qblobj^ 5-6 klp af`b nrbpf rk c^`qlo ?e ab J ^kri^ q+q^j_f‹k J ^kri^ q-
U^jlp ^ sbo `Žjl mrbab rqfifw^opbbi qblobj^ m^o^ obplisbo i^p b`r^`flkbpafcbobk`f^ibp eljld‹kb^p `lk `lbcf`fbkqbp `lkpq^kqbp- Gbjlp bibdfal bgbjmilpm^o^ firpqo^o afpqfkqlp ^pmb`qlp+nrb abmbkabk ab i^ k^qro^ibw^ ab i^p o^Œ`bpabi^ b`r^`fŽk `^o^`qboŒpqf`^-
A?QM K P]‡_ao na]hao `eopejp]o-
DIDLOKN 0- G^ii^o rk^ _^pb ab plir`flkbp m^o^i^ b`r^`fŽk afcbobk`f^i
'5-04( 'B2 , 6B * 5(u < N-
Qkhq_e‰j- Sfbkb i^ cloj^ J'u( < N `lk
J < B2 , 6B * 5 <'B , 0('B , 1('B * 2(!
Di k•`ibl ab C , 0 `lkqfbkb q0&t' < a!* bi ab C , 1 `lkqfbkb q1&t' < a1e0H+ vbi ab C * 2 `lkqfbkb S2'V( < a,2e0H
Œ Dk bi `^mŒqril 0 'm- 01( pb abjlpqoŽ nrbq-+q,+S1 plk fkabmbkafbkqbp-Orbpql nrb qobpplir`flkbp fkabmbkafbkqbpab rk^b`r^`fŽk ab qbo`boloabk cloj^k rk^ _^pb m^o^ bi bpm^`fl plir`fŽk+ i^ plir`fŽkdbkbo^i ab '5-04( sfbkb a^a^ mlo
Di j‹qlal rqfifw^al m^o^ obplisbo bi bgbjmil 0 klp mbojfqb bk`lkqo^o rk^_^pb m^o^ bi bpm^`fl plir`fŽk ab `r^inrfbo lmbo^alo `lk `lbcf`fbkqbp `lkpq^kqbpnrb! mrba^ abp`ljmlkbopb bk molar`ql ab c^`qlobp ifkb^ibp afpqfkqlp-
SDNQDL@ 5-7- Qa] J qj klan]`kn _kj _kabe_eajpao _kjop]jpao _qu] a_q]_e‰j_]n]_pan‡ope_] lJ'n( < N peaja j n]‡_ao na]hao `eopejp]o n(-=%pql l l + njk Cjpkj_ao h]okhq_e‰j cajan]h `a h] a_q]_e‰j `ebanaj_e]h J'u( < N aj ah ejpanr]hk ', //+ * //(
reaja `]`] lkn h] b‰niqh]
'5-05(j
u < y_gang!-R`S
Bapaniej]_e‰j `a qj] ^]oa `a okhq_ekjao 076
Baikopn]_e‰j- Sbkbjlp i^ c^`qlofw^`fŽk
Orbpql nrb bi k•`ibl ab &B + ng( `lkqfbkb Sg'V( < a&!g!+bi k•`ibl ab J `lkqfbkbi^p j crk`flkbp
Dk bi `^mŒqril0 'm- 01( pb abjlpqoŽ nrb bp^p crk`flkbp plk fkabmbkafbkqbp-Olo`lkpfdrfbkqb `lkpqfqrvbk rk^ _^pb m^o^bi bpm^`fl plir`fŽk ab i^ b`r^`fŽk J&u';;M*^pŒnrb i^ plir`fŽk dbkbo^i sfbkb a^a^ mlo '5-05(-
A?QM IH- P]‡_ao na]haoiŠhpelhao-Rf qla^p i^p o^Œ`bpplk ob^ibp mbol kl afpqfkq^p+i^p crk`flkbp '5-06( kl plk
fkabmbkafbkqbpv mlo q^kql kl cloj^k rk^ _^pb m^o^ bi bpm^`fl plir`fŽk- Rf rk^o^Œwn pb mobpbkq^ lk jriqfmif`fa^a i+ bkqlk`bp &B + n'i bp rk c^`qlo ab J,Di qblobj^ nrb pfdrb klp af`b `Žjl l_qbkbo i plir`flkbp fkabmbkafbkqbpbk bik•`ibl ab bpb c^`qlo-
SDNQDL@ 5-8- J]o i bqj_ekjao
'5-06( Sh'V( < an,!
okj i ahaiajpko ej`alaj`eajpao ]jqh]`ko lkn ah klan]`kn 'B , o(!-
Baikopn]_e‰j- K^ fkabmbkabk`f^ ab bp^p crk`flkbp pb abar`b ab i^ fkab,mbkabk`f^ ab ilp mlifkljflp 0+t+t1
+ ŒŒŒ+ ti+0Œ O^o^abjlpqo^o nrb q0+ q1+ ŒŒŒ-q|
plk ^kri^a^p mlo &B+ n(i 0/ e^objlp mlo fkar``fŽk-Qe i < 0 bufpqbq^k pŽil rk^ crk`fŽk+ q/&t' < an
,! nrb bsfabkqbjbkqb bp^kri^a^ mlo &B + n', Rrmlkd^jlp bkqlk`bp+nrb bi qblobj^ bp `fboql m^o^i + 0-Dpql pfdkfcf`^ nrb i^p crk`flkbp S0+ --Œ +Si,0 plk ^kri^a^p mlo &B + n(\0-Orbpql nrb
'B , n(i < 'B , n('B , n(i,0
i^p crk`flkbp S/ * ‹‹‹ *Si,/ q^j_f‹k plk ^kri^a^p mlo &B+ n(i- O^o^ `ljmibq^oi^ abjlpqo^`fŽk qbkbjlp nrb abjlpqo^o nrb &B + n(i ^kri^ q,9 Blkpfabobjlpmlo q^kql
077 C_q]_ekjao `ebanaj_e]haoheja]hao
Sbkbjlp
; &i + /'ti,0aR%! * ti,0naRk8 + nty+haRk8
< &i + h'ti,1aR&! < &i + /'qi\0'V(-
Br^kal ^mif`^jlp 'C , n'\h ^ ilp alp jfbj_olp ab bpq^•iqfj^ b`r^`fŽk l_qb,kbjlp N bk bi pbdrkal jfbj_ol v^ nrb 'C , n'\/ ^kri^ ^ Si+h% Krbdl'C , n'iqi < N `lk 0/ `r^i q| bp ^kri^a^ mlo 'C , n'i, Dpql `ljmibq^ i^ ab,jlpqo^`fŽk-
DIDLOKN 1- G^ii^o i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk afcbobk`f^i J&u' < N+alkab J < Z(R , C1 , 7C * 01-
Qkhq_e5j- Di lmbo^alo J qfbkb i^ c^`qlofw^`fŽk
J < 'B , 1(1'B * 2(-
Rbd•k bi qblobj^ 5-8+ i^p alp crk`flkbp
q0't( < a1/9+
mboqbkb`bk i k•`ibl ab 'C , 1(1- K^ crk`fŽk qo&t' < nhhHmboqbkb`b i k•`ibl ab'C * 2(- Bljl nrfbo^ nrb S0+ S1& So plk fkabmbkafbkqbp'sbo bgbo`f`fl 06 ab i^pb``fŽk 5-8( cloj^k rk^ _^pb m^o^ bi k•`ibl ab J* ^pŒnrb i^ plir`fŽk dbkbo^iab i^ b`r^`fŽk afcbobk`f^i bp
Di qblobj^ 5-8 klp fkaf`^ `Žjl e^ii^o rk^ _^pb ab plir`flkbp m^o^`r^inrfbob`r^`fŽk ifkb^i ab loabk j `lk `lbcf`fbkqbp `lkpq^kqbp `rv^ b`r^`fŽk `^o^`qboŒpqf`^qbkd^ pŽil o^Œ`bpob^ibp+ idrk^ ab i^p `r^ibp pb obmfq^-Rf i^p o^Œ`bpeopejp]o plkn--n1+ ŒŒŒ -n+v pb mobpbkq^k`lk i^p jriqfmif`fa^abp obpmb`qfs^pi-+ i‚ --- -i|+i^ m^oqbab i^ _^pb nrb `loobpmlkab ^ nl sfbkb a^a^ mlo i^p il crk`flkbp
alkab m < 0+1+--- +iGh ‹
Br^kal l qlj^ ilp s^ilobp 0+1+--- +g l_qbkbjlp bk qlq^i ia * --- * ia crk,`flkbp- Dk bi bgbo`f`fl 06 ab i^ pb``fŽk 5-8 bp_lw^jlp rk^ abjlpqo^`fŽk e^`fbkalsbo&nrb qla^p bp^p crk`flkbp plk fkabmbkafbkqbp-Orbpql nrb i^ prj^ ab i^p jri,
Bapaniej]_eˆj `a qj] ^]oa `a okhq_ekjao 078
qfmif`fa^abpi/ * ---* i€ bp fdr^i ^ j* bi loabk ab i^ b`r^`fŽk+ i^p crk`flkbpSl+m cloj^k rk^ _^pb m^o^bi bpm^`fl plir`fŽk ab i^ b`r^`fŽk-
DIDLOKN 2- Qbplisbo h] b`r^`fŽk 'B5 * 1B4, 1B2 , B1'u < N-
Qkhq_eˆj, Sbkbjlp B5*1B4\1B2\B1<B1'B,0('B* 0(2- K^ m^oqb abi^ _^pb `loobpmlkafbkqb ^i c^`qlo C1 bp q/&t' < 0+q1&t' < t9 i^ m^oqb loobpmlk,afbkqb ^i c^`qlo 'C , 0( bp q]&t' < b!&:Xi^ `loobpmlkafbkqb ^i c^`qlo 'C * 0(2 bpq3&t' < a8!* S4 &t' < ta9!+ q5&t' < t&a9!- K^p pbfpcrk`flkbp T0 +’’’ +S5 plk fk,abmbkafbkqbp+pŒnrb i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk bp
A?QM Ghh,P]†_ao _kilhaf]o,Rf pb bjmib^k bumlkbk`f^ibp `ljmibg^p+ kl e^v kb`bpfa^a ab afpqfkdrfo bkqob
o^Œ`bpob^ibpv `ljmibg^p ab i^ b`r^`fŽk `^o^`qboŒpqf`ab i^ b`r^`fŽk afcbobk`f^iJ'u( < N- Rf pb abpb^k plir`flkbp ab s^ilo ob^i+c^`qlofw^jlp bi lmbo^alo J bk&c^`qlobpifkb^ibp v `r^aoŠqf`lp `lk `lbcf`fbkqbp ob^ibp- B^a^ m^o ab o^Œ`bp lj,mibg^p lkgrd^a^p ] * ew1*] , ew1loobpmlkab ^i c^`qlo `r^aoŠqf`l+
'5-07(
Di k•`ibl ab bpqblmbo^alo ab pbdrkal loabk `lkqfbkb i^p alp crk`flkbp fkabmbk,afbkqbp q&t' < a! `lp w1t v r&t' < a! pbk w1t, Rf bi m^oab o^Œ`bp] ,*, ew1pb mob,pbkq^`lk jriqfmif`fa^a i+ bi c^`qlo `r^aoŠqf`l pb mobpbkq bibs^al ^ i^ mlqbk`f^i,†oei]- Di k•`ibl abi lmbo^alo
`lkqfbkb 0i crk`flkbp fkabmbkafbkqbp+
m< 0+1+--- +i-
Dpql mrbab mol_^opbcŠ`fijbkqb mlo fkar``fŽk obpmb`ql^ i- 'Dk bi bgbo`f`fl 1/ab i^ pb``fŽk 5-8 pb a^ rk bpnrbj^ ab i^p abjlpqo^`flkbp-( Klp bgbjmilp pfdrfbk,qbpfirpqo^k ^idrk^p ab i^p mlpf_fifa^abp-
DIDLOKN 3- v&! , 3u! * 02u&< N- K^ b`r^`fŽk `^o^`qboŒpqf`^++^, 3o ** 02o < N+qfbkbi^p o^Œ`bpN+1 ,*, 2e: i^ plir`fŽk dbkbo^i bp
u < B0 * a1!&'_1`lp 2t * B^ pbk2u(-
/7. C_q]_ekjao `ebanaj_e]haoheja]hao
DIDLOKN 4- v&&&, 1u! * 3u&, 7u < N- K^ b`r^`fŽk `^o^`qboŒpqf`bp
n2, 3n1 * 2n + 7 < &n+ 0'&n1 * 3( < N :
prp o^Œ`bpplk 1+0e*+0e*^pŒnrb i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk afcbobk`f^i bp
DIDLOKN 5- u'4( , 8u'3( * 23u&&&, 55u! * 54u&, 14u < N- K^ b`r^`fŽk`^o^`qboŒpqf`mrbab bp`of_fopb^pŒ
&n+ 0'&n1 , 2n * 4(1 < N :
prp o^Œ`bpplk 0+1 * e*1 * e*mlo il nrb i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk afcb,obk`f^i bp
5-8 Dgbo`f`flp
G^ii^o i^ plir`fŽk dbkbo^i ab `^a^ rk^ ab i^p b`r^`flkbp afcbobk`f^ibp ab ilp bgbo`f`flp0 ^i 01-
0- u%!+ 0u! + 1u%< N-0, uhhh+ u%*< N-
1, u%%%* 2u! * 2u%< N-2, uhhh+ 1u! * 1u%+ W < N-4- uh2' * 2u%%%* 4u! * 2u%* u < N-4, o&!, 05v < N-
6- u&2' * 05v < N-
6, u&&&, W < N-7, uh2' * 2uhhh* 6u! * 6u%* 2u < N-
/., uh2' * 0u! * u < N-00- uh4' * 2uh2' * 2u! < N-/0, uh4' * 6uh2' * 05v! < N-
02- Rf i bp rk^ `lkpq^kqb mlpfqfs^+e^ii^o i^ plir`fŽk m^oqf`ri^o u < b&t' ab i^ b`r^`fŽk af,cbobk`f^i
nrb p^qfpc^d^i^p `lkaf`flkbp b&M'< /%&.' < N+n&M' < 0-03- Tk^ b`r^`fŽk afcbobk`f^i ifkb^i `lk `lbcf`fbkqbp `lkpq^kqbp qfbkb i^ b`r^`fŽk `^o^`qboŒp,
qf`^ b&n' < N- Rf qla^p i^p o^Œ`bpab i^ b`r^`fŽk `^o^`qboŒpqf`plk kbd^qfs^p+abjlpqo^onrb qla^ plir`fŽk ab i^ b`r^`fŽk afcbobk`f^i qfbkab ^ `bol `r^kal t y * b` + „Pr‹ pbmrbab ^pbdro^o ^`bo`^ abi `ljmloq^jfbkql ab qla^p i^p plir`flkbp bk bi fkqbos^ilZN+* //( pf qla^p i^p o^Œ`bpab i^ b`r^`fŽk `^o^`qboŒpqf`plk kl mlpfqfs^p>
Cfan_e_eko 080
04- Dk `^a^ `^pl+ e^ii^o rk^ b`r^`flk afcbobk`f^i ifkb^i `lk `lbcf`fbkqbp `lkpq^kqbp nrb pbp^qfpc^d^ m^o^ qla^p i^p crk`flkbp a^a^p+
^( qz&t' < a!* qv&t' < |€* S1&V' < a0nnH* S2&V' < a+0nnH‹_( qz&t' < a+0nnH* S0&V' < ta+0nnH* S1&V' < t0a+0nnH,b( Sz&t' < 0 + S0&V' < t* S1&V' < a!* q2&t' < ta!+a( qz&t' < t* q0&t' < annH* q]At' < ta!9b( qz&t' < t0* S0&V' < a!* q1&t' < ta!+c( qz&t' < a+0nnH`lp 1t* S0&V' < a+0nnHpbk 1t* S1&V' < a+0nnH* q2&t' < ta+0nnH,d( qz&t' < `lpe t* S0&V' < p`ke t* S1&V' < t `lpe t* S2&V' < t pbkeu-e( qz&t' < `lpe t pbku+ S0&V' < pbke t `lp t* q1&t' < t,
05- Rb^k n* ,,, *n,* j k•jbolp ob^ibp afpqfkqlp+ v M! --- +M-+j mlifkljflp+ kfkdrkl ab ilp`r^ibp bp bi mlifkljfl kril- Cbjlpqo^o nrb i^p j crk`flkbp
plk fkabmbkafbkqbp-@komqafk `a h] `aikopn]_eˆj, Djmib^o i^ fkar``fŽk obpmb`ql ^ j, O^o^ j < 0 X
j < 1 bi obpriq^al bp cŠ`fijbkqb `ljmol_^_ib- Rrmlkd^jlp nrb i^ molmlpf`fŽk bp `fboq^m^o^ j < m v pb^k A! ŒŒŒ+A-*h+ O * 0 bp`^i^obp ob^ibp q^ibp nrb
l*z
K AgOg&t'angnnH< N-g;z
Lriqfmifnrbjlp ilp alp jfbj_olp mlo a+n%)hnnHv abofsbjlp i^ b`r^`fŽk obpriq^kqb- Dj,mib^o bkqlk`bp i^ efmŽqbpfpab fkar``fŽk m^o^ mol_^o nrb qlalp ilp bp`^i^obp _- plk N-Orbab a^opb lqo^ abjlpqo^`fŽk _^p^a^ bk bi loabk ab j^dkfqra `r^kal t ,* * //+ `ljlpb efwl bk bi bgbjmil 6 ab i^ pb``fŽk 0-6 'm- 01(-
06- Rb^k i! i! -io+ g bkqbolp mlpfqfslp+ v n+n+--- +no+g k•jbolp ob^ibp afpqfkqlp+ vpb^ j < ie * * i-- O^o^ `^a^ m^o ab bkqbolp m+m nrb `rjmi^k 0949m 949g*0 949m 949i-+ mlkd^jlp
Olo bgbjmil+ `r^kal m < 0 i^p `loobpmlkafbkqbp crk`flkbp plk
Cbjlpqo^o nrb i^p j crk`flkbp qŒ-ŒpŒabcfkfa^p plk fkabmbkafbkqbp-YGj`e_]_eˆj8 @mif`^o bi bgbo`f`fl 05-\
07- Rb^ J rk lmbo^alo afcbobk`f^i ifkb^i ab loabk j `lk `lbcf`fbkqbp `lkpq^kqbp v mlifkljfl`^o^`qboŒpqf`l l&n', Rb^ J& bi lmbo^alo ab `lbcf`fbkqbp `lkpq^kqbp `rvl mlifkljfl `^o^`,qboŒpqf`lbp i^ abofs^a^ l%&n',Olo bgbjmil+ pf J < 1B& , 2B\* 0 bkqlk`bp J%< 3C , 2-Blk j^vlo dbkbo^ifa^a+ abcfk^jlp i^ abofs^a^ j,‹pfj^ sj0 `ljl bi lmbo^alo `rvl mlif,kljfl `^o^`qboŒpqf`l-bp i^ abofs^a^ j,‹pfj^ m'j0'o(- 'Di lmbo^alo r%! kl ab_b `lkcrk,afopb `lk i^ mlqbk`f^ j,‹pfj^ J j-(
081 C_q]_ekjao `ebanaj_e]haoheja]hao
^( Rf q qfbkb j abofs^a^p+ abjlpqo^o nrb
k &g' 'N(J&q' < J y S&g' ‹
S4=
_( Rf q qfbkb j,i abofs^a^p+ abjlpqo^o nrb
j,i 'g*i('k(J&i'&q' < J N g S&g'
S4=
m^o^ i < N+0+1+ : -- +j +
alkab CNi99999J ,08- Blk i^ klq^`fŽk abi bgbo`f`fl 07- Rf q v r qfbkbk j abofs^a^p+ abjlpqo^o nrb
k J'g('S(J'qr( <J ,,,,{{, T&g',
S4=
YGj`e_]_e‰j9 Djmib^o bi bgbo`f`fl 07 grkql `lk i^ cŽojri^ ab Kbf_kfw m^o^ i^abofs^a^ g,†oei] ab rk molar`ql9
g&Sr'&g' < J &y'q&g+n'r&n' ,[
Y4=
1/- ^( Rb^ l&p' 88888m&p'in&p'* alkab m v n plk mlifkljflp v i bp rk bkqbol mlpfqfsl- Cbjlp,qo^o nrb l%&p'88888m&p'i+Go&p'*alkab p bp rk mlifkljfl-_( Rb^ J rk lmbo^alo `lk `lbcf`fbkqbp `lkpq^kqbp nrb ^kri^ q+pfbkal q rk^ crk`fŽka^a^ ab t- Rb^ L 99999J j+ i^ mlqbk`f^ j,‹pfj^ ab J* alkab i = 0- Cbjlpqo^o nrb `^a^rk^ ab i^p abofs^a^p K&+ K!+ --- +K'i,h( ^kri^k q^j_f‹k q-b( Blk i^ m^oqb _( v bi bgbo`f`fl 08 abjlpqo^o nrb K ^kri^ `^a^ rk^ ab i^p crk`flkbpD%54& ((( -tn9•-a( Blk i^ m^oqb `( abjlpqo^o nrb bi lmbo^alo 'B& , 1]B &*]&* b0&(i ^kri^ `^a^ rk^ab i^p crk`flkbp tma&V pbk b/t v tma&V`lp b/t m^o^ m 999990+1+--- +i , 0-
10- Rb^ J rk lmbo^alo ab loabk j `lk `lbcf`fbkqbp `lkpq^kqbp v mlifkljfl `^o^`qboŒpqf`ll&n', Rf ] bp `lkpq^kqb v q qfbkb j abofs^a^p+ abjlpqo^o nrb
5-0/ Qbi^`fŽk bkqobi^p b`r^`flkbp eljld‹kb^p v kl eljld‹kb^p
Ulis^jlp ^elo^ ^ i^ b`r^`fŽk afcbobk`f^i ifkb^i dbkbo^i ab loabk j `lk `lb,cf`fbkqbpnrb kl pb^k kb`bp^of^jbkqb `lkpq^kqbp- Di qblobj^ nrb pfdrb abp`of_b i^obi^`fŽk bkqob i^p plir`flkbp ab rk^ b`r^`fŽk eljld‹kb^ J&u' < N X i^p ab rk^kl eljld‹kb^ J&u' < P&t',
SDNQDL@ 5-0/- Qa] J 8yj&H'+)y&H' qj klan]`kn `ebanaj_e]hheja]h`a kn`aj
Bapaniej]_e‰j `a qj] okhq_e‰jl]npe_qh]n 082
j- Qa]j qz+--- +Sj+ j okhq_ekjaoej`alaj`eajpao `a h] a_q]_e‰jdkikc†ja] J&u';M*u oa] Xi qj] okhq_e‰jl]npe_qh]n`a h] a_q]_e‰jjk dkikc†ja] J&u' < P* `kj`aP D A'f &H', Cjpkj_ao pk`] okhq_e‰ju < b't( `a h] a_q]_e‰jjk dkikc†ja] peaja h]bkni]
'5-08(j
z't( < Wh'V( * J_gSet(+g<h
`kj`a B0 + ’’’ +Aj plk `lkpq^kqbp-
Baikopn]_e‰j- Olo i^ ifkb^ifa^a qbkbjlp J&b+Wh';J&b'+J&Wh';P+P;M,Olo il q^kql b + Xi mboqbkb`b^i bpm^`fl plir`fŽk ab i^ b`r^`fŽk eljld‹kb^J&u' < N+ ^pŒnrb b + Xi bp rk^ `lj_fk^`fŽk ifkb^i ab T0+ ’’’ +Sj+ bp ab`fo+b + Xi < B0Ti * --- * _jSj- Dpql abjrbpqo^ '5-08(-
Orbpql nrb qla^p i^p plir`flkbp ab J&u' < P pb l_qfbkbk `lk '5-08(+ i^ prj^abi pbdrkal jfbj_ol ab '5-08( '`lk i^p `lkpq^kqbp ^o_fqo^of^p -+A1+ŒŒŒ+_j' pbii^j^ i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk kl eljld‹kb^- Di qblobj^ 5-0/ bpq^_ib`bnrb i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk kl eljld‹kb^ pb l_qfbkb prj^kal ^ Xii^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk eljld‹kb^-
M^oanr]_e‰j9 Di qblobj^ 5-0/ qfbkb rk^ pbk`fii^ ^k^ildŒ^ dblj‹qof`^ nrbklp ^vra^ ^ molcrkafw^o bk pr pfdkfcf`^al- O^o^ abqbojfk^o qlalp ilp mrkqlp ab rkmi^kl bk`lkqo^jlp rk mrkql abi jfpjl v ib prj^jlp qlalp ilp mrkqlp ab rk mi^klm^o^ibil nrb m^p^ mlo bi lofdbk- O^o^ bk`lkqo^o qla^p i^p plir`flkbp ab J&u' < Pbk`lkqo^jlp rk^ plir`fŽk m^oqf`ri^o v ib prj^jlp qla^p i^p plir`flkbp ab i^ b`r^,`fŽk eljld‹kb^ J&u' < N- Di `lkgrkql ab plir`flkbp ab i^ b`r^`fŽk kl eljld‹kb^bp ^kŠildl ^i mi^kl nrb m^p^ mlo rk abqbojfk^al mrkql- Di bpm^`fl plir`fŽk ab i^b`r^`fŽk eljld‹kb^ bp ^kŠildl ^i mi^kl m^o^ibil nrb m^p^ mlo bi lofdbk-
Dk i^ moŠ`qf`^m^o^rqfifw^obi qblobj^ 5-0/ qbkbjlp nrb obplisbo alp mol_ib,j^p9 0( G^ii^o i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk eljld‹kb^ J&u' < N+X1( e^ii^ork^ plir`fŽk m^oqf`ri^oab i^ b`r^`fŽk kl eljld‹kb^ J&u' < P, Dk i^ moŽufj^pb``fŽk abjlpqo^jlp nrb pfbjmob pb mrbab obplisbo bi mol_ibj^ 1( pf mlabjlpobplisbo bi mol_ibj^ 0(-
5-00 Cbqbojfk^`fŽk ab rk^ plir`fŽk m^oqf`ri^o ab i^ b`r^`fŽk kl eljld‹kb^-L‹qlal ab s^of^`fŽk ab `lkpq^kqbp
Ulis^jlp ^ `lkpfabo^o bi mol_ibj^ ab i^ abqbojfk^`fŽk ab rk^ plir`fŽk m^o,qf`ri^o Xi ab i^ b`r^`fŽk kl eljld‹kb^ J&u' < P, Dumlkaobjlp rk j‹qlal ii^,j^al ab r]ne]_e‰j a _kjop]jpao nrb klp fkaf`^ `Žjl abqbojfk^o Xi pf `lkl`bjlpj plir`flkbp fkabmbkafbkqbp T0+ ’’’ + Sj ab i^ b`r^`fŽk eljld‹kb^ J&u' < N-
083 C_q]_ekjao `ebanaj_e]haoheja]hao
Di j‹qlal molmlo`flk^ rk^ plir`fŽk m^oqf`ri^oab i^ cloj^
'5-1/(
alkab UH + -’’ + rj plk crk`flkbp nrb mrbabk `^i`ri^opb bk crk`fŽk ab T0 + ’’’ + Sj
v abi pbdrkal jfbj_ol P- Di j‹qlal klp `lkar`b ^ rk pfpqbj^ ab j b`r^`flkbp^idb_o^f`^p ifkb^ibp nrb pb p^qfpc^`bk`lk i^p abofs^a^p ry+ --- +ry- Dpqbpfpqbj^pfbjmob mrbab obplisbopb ab_fal ^ nrb qfbkb rk^ j^qofw ab `lbcf`fbkqbp kl pfk,dri^o- K^ fkqbdo^`fŽk ab i^p abofs^a^p+ a^ bkqlk`bp i^p crk`flkbp abpb^a^pUH + ’-’ + rj- Di mofjbol nrb rqfifwŽ bi j‹qlal crb Ir^k Aboklriif m^o^ obplisbob`r^`flkbp ifkb^ibp ab mofjbo loabk+ v irbdl K^do^kdbbk 0663 m^o^obplisbo b`r^,`flkbp ifkb^ibp ab pbdrkal loabk-
O^o^ bi `^pl ab loabk j mrbabk pfjmifcf`^opbilp abq^iibprqfifw^kal klq^`fŽksb`qlof^i v j^qof`f^i- Di pbdrkal jfbj_ol ab '5-1/( mrbab bp`of_fopb`ljl rkmolar`ql fkqboflo
'5-10( Wh< &r* q'*
alkab r v q plk crk`flkbp sb`qlof^ibp k,afjbkpflk^ibp a^a^p mlo
Hkqbkq^jlp bibdfo T ab j^kbo^ nrb bi molar`ql fkqboflo nrb abcfkb X+p^qfpc^d i^b`r^`fŽk kl eljld‹kb^ J'u( < P+p^_fbkal nrb J'q( < N+alkab J'q( < 'J'qh' *
,,, *J&qj•-Bljbkw^jlp `^i`ri^kal i^ mofjbo^ abofs^a^ ab XH&Dk`lkqo^jlp
'5-11( We,< &r*q%'* &r%*q',
Bljl qbkbjlp j crk`flkbp T*!%! Tj mlo abqbojfk^o+ ab_bobjlp mob`fp^oj`lkaf`flkbp nrb i^p obi^`flkbk+ Rf fjmlkbjlp i^ `lkaf`fŽk ab nrb bi pbdrkalq‹ojfkl abi pbdrkal jfbj_ol ab '5-11( pb ab_^ ^kri^o+ i^ cŽojri^ m^o^ vc pbpfjmifcf`^ v nrba^
We,< 'r+ q&(+ `lk q^i nrb 'r&+q( < N-
Cbofs^kal i^ obi^`fŽk nrb a^ Wybk`lkqo^jlp
Wy< 'r+ q!( * 'r&+Sb',
Bapaniej]_e‰j `a qj] okhq_e‰jl]npe_qh]n 084
Rf mlabjlp bibdfo r ab jlal nrb 'r&+//' < N bkqlk`bp i^ cŽojri^ nrb a^ u:q^j_f‹k pb pfjmifcf`^ v nrba^
uy < 'q+q!( + lk q^i nrb q^j_f‹k' q&+q&(< N-
Rf pbdrfjlp ab bpqbjlal `lk i^p j , 0 mofjbo^p abofs^a^p ab Wh bk`lkqo^jlp
`lk q^i nrb 'r&+q&j+0€ < N-
G^pq^ ^nrŒ ebjlp bpq^_ib`fal j , 0 `lkaf`flkbp ^ r- Cbofs^kal rk^ sbw jŠpiibd^jlp ^
Hjmlkd^jlp ^elo^ i^ `lkaf`fŽk &r%*q&j+h€ < P&t'* v i^ •iqfj^ b`r^`fŽk pb qo^kp,cloj^ bk
`lk q^i nrb &q%*q'j,M( < P&t',
Rrmlkd^jlp+ mlo bi jljbkql+ nrb pb mrbabk p^qfpc^`boi^p j `lkaf`flkbp fjmrbp,q^p ^ r, Rb^ J < B! * N/&t'Bj+h * --- * Nj&t', Br^kal ^mif`^jlp J ^ Whbk,`lkqo^jlp
J'Wh( < uej( * Nh'V(uyj,M * --- * Nj'V(Wh
< w&q*q&j' * P&t'x * N/&t'&r* q&j+h' * --- * Nj&t'&r* q'
; &q*J&q€ * P&t' < &q*N( * P&t' < P&t',
Dp ab`fo+J'Wh( < P&t'* ^pŒnrb u 0 bp rk^ plir`fŽk ab i^ b`r^`fŽk kl eljld‹kb^-Di j‹qlal qbkaoŠ‹ufql pf pb mrbabk p^qfpc^`boi^p j `lkaf`flkbp nrb ebjlp
fjmrbpql ^ r- Dp^p `lkaf`flkbp bpq^_ib`bk nrb 'r&+S'g• < N m^o^ g < /+0+ -- 0 +
j , 1+ X nrb &r%*q&j+h€; P&t', Olabjlp bp`of_fobp^p j b`r^`flkbp bk rk^ pli^b`r^`fŽk j^qof`f^i+
'5-12( U'V(!'V( , P'Vw:[ +
085 C_q]_ekjao `ebanaj_e]haoheja]hao
alkab r &t' pb `lkpfabo^ `ljl rk^ j^qofw `lirjk^ j •: 0+ v V bp i^ j^qofwj Wj `rv^p cfi^p bpqŠk cloj^a^p mlo ilp `ljmlkbkqbp ab q v prp abofs^a^p pr,`bpfs^p9
Sh S1
qw qy
s<
q&j+hh qyj+z'] 0
K^ j^qofw V pb ii^j^ i]pnev snkjoge]j] ab T0+ ’’’ +Sj+ bk ob`rboal abI- L- G- Volkphf '0667,0742(-
Dk i^ pb``fŽk nrb pfdrb abjlpqo^objlp nrb i^ j^qofw tolkphf^k^ bp klpfkdri^o- Olo `lkpfdrfbkqb+mlabjlp jriqfmif`^o ^j_lp jfbj_olp ab '5-12( mloU&V'+h l_qbkfbkal
+&'t(, P't(s't(,we[-
Difg^jlp alp mrkqlp a v t bk bi fkqbos^il I nrb pb `lkpfabo^+ b fkqbdobjlp bp^b`r^`fŽk sb`qlof^i bk bi fkqbos^il+ abpab a ^ t+ l_qbkfbkal
alkab
K^ cŽojri^ Xi < &q*r' m^o^i^ plir`fŽk m^oqf`ri^oqlj^ ^elo^ bi ^pmb`ql
Hh< &q*r' < &q*r&_' * w( < &q*r&_'' * &q*v',
Bapaniej]_e‰j `a qj] okhq_e‰jl]npe_qh]n 086
Di mofjbo q‹ojfkl &q*r&_€ p^qfpc^`bi^ b`r^`fŽk eljld‹kb^ mrbpql nrb bp rk^`lj_fk^`fŽk ifkb^i ab TH ŠŠŠŠŠSj- Olo `lkpfdrfbkqb mlabjlp ljfqfo bpqbq‹ojfklv rqfifw^obi pbdrkal q‹ojfkl &q,v' `ljl rk^ plir`fŽk m^oqf`ri^o ab i^,b`r^`fŽkkl eljld‹kb^- Dp ab`fo+rk^ plir`fŽk m^oqf`ri^oab J&u' 98988P sfbkb a^a^ mlo bimolar`ql fkqboflo
'r'ui+ v't• y 'T'Wi-cQ'&iV'H(,x:\ `G' ,
N_p‹osbpb nrb kl bp kb`bp^ofl nrb i^ crk`fŽk P pb^ `lkqfkr^ bk bi fkqbos^il H,Slal il nrb pb bufdb bp nrb P pb^ fkqbdo^_ibbk Y_*t[,
Olabjlp obprjfo ilp obpriq^alp ab bpq^pb``fŽk jbaf^kqb bi qblobj^ pfdrfbkqb-
SDNQDL@ 5-00- Qa]j TH + ’’’ + q!+j okhq_ekjaoej`alaj`eajpao `a h] a_q]_e‰j`ebanaj_e]hheja]h `a kn`aj j dkikc†ja] J&u' 98988N aj qj ejpanr]hk H, Cjpkj_aoqj] okhq_e‰jl]npe_qh]nXH `a h] a_q]_e‰jjk dkikc†ja] J&u' 98988P reaja `]`] lknh] b‰niqh]
j
Wh'V( <z Sg'V(Tg'V(+R8S
`kj`a UH! ’’ + r! okj hko ahaiajpko `a h] i]pnev _khqij] r+ jV 0+`apaniej]`]lkn h] a_q]_e‰j
r'V( , oP&G'U'pz,w c\ p -
Cj aop]b‰niqh]+V ao h] i]pnev snkjoge]j] `a S/ I ŠŠŠ + Sj+ Wa ao qj lqjpk _q]h,mqean]`a H,
'5-13(
M^oanr]_e‰j9 K^ fkqbdo^i abcfkfa^ bk '5-13( mrbab obbjmi^w^opb mlo `r^inrfbofkqbdo^i fkabcfkfa^-
DIDLOKN 0- G^ii^o i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk afcbobk`f^i
! 1W+W;++0 * a&!
bk bi fkqbos^il ' , //+ * // (-
087 C_q]_ekjao `ebanaj_e]haoheja]hao
Qkhq_e‰j- K^ b`r^`fŽk eljld‹kb^+ 'B0+ h'u < N qfbkb i^p alp plir`flkbp
fkabmbkafbkqbpq/&t' < a!* qet' < a9;- K^ j^qofw tolkphf^k^ ab Sh v z bp
Ya&! a,t[
U&t' < -aV ,a,V
Orbpql nrb abqU&t' < ,1+i^ j^qofw bp kl pfkdri^o v pr fksbop^ sfbkb a^a^ mlo
Olo `lkpfdrfbkqb+
0Y,a,t ,a,t[U&V'+G< , ,1 -
'M_ a&!
v qbkbjlp
Hkqbdo^kal `^a^ `ljmlkbkqb abi sb`qlo abi pbdrkal jfbj_ol bk`lkqo^jlp
H a,V H& aV (UH'V( < -,, `t < a,V , 0 * ,, `t < \a,t , t * ild '0 * a9H:(0 * aV 0 * "&
v
;ME
r0't( < ,<,, `t < ,i^d '0 * aV',0 * aV
K^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk afcbobk`f^i bp+mlo `lkpfdrfbkqb+
u < BHTH'W(* A1S1'V( * Th'V(Sh't( * T1'V(S1'V(
< _hat * _1a,t , 0 , ta! * 'a&!, a,V( ild '0 * b!(-
5-01 Ml pfkdri^ofa^a ab i^ j^qofw toz+i[0zhf^k ab j plir`flkbp fkabmbkafbkqbpabrk^ b`r^`fŽk ifkb^i eljld‹kb^
Dk bpq^ pb``fŽk abjlpqo^jlp nrb i^ j^qofw tolkphf^k^ U ab j plir`flkbpfkabmbkafbkqbpS0 + ŒŒŒ + Sj ab rk^ b`r^`fŽk eljld‹kb^ J&u' 99888N bp kl pfkdri^o-Kl s^jlp ^ e^`bo abjlpqo^kal nrb bi abqbojfk^kqb ab U bp rk^ crk`fŽk bumlkbk,
Lk oejcqh]ne`]` `a h] i]pnev snkjoge]j] 088
`f^i nrb krk`^ pb ^kri^ bk bi fkqbos^il . nrb pb `lkpfabo^-Rb^ s&t' < abq U&t' m^o^ `^a^ t ab {+v prmlkd^jlp nrb i^ b`r^`fŽk afcb,
obk`f^i nrb pb p^qfpc^`b `lk i^p crk`flkbp T0 +’’’ +Sj qfbkb i^ cloj^
'5-14(
Sbkbjlp bkqlk`bp9
SDNQDL@ 5-01- Ch `apaniej]jpa snkjoge]jk o]peob]_ah] a_q]_e‰j `ebanaj_e]h`a lneian kn`aj
'5-15( s& * Nh't(s < N
aj b, Nkn _kjoecqeajpa+ pf a “ { pajaiko
'5-16( s't( < s'_( bum Z, q&Nh'p( `p[ 'D‰niqh] `a ?^ah(-
?`ai…o+ s't( <0<N l]n] pk`k t `a H,
Baikopn]_e‰j- Rb^ q bi sb`qlo cfi^ q < 'r0 +’’’ +Sj(- X^ nrb `^a^ `ljml,kbkqb ab q p^qfpc^`b i^ b`r^`fŽk afcbobk`f^i '5-14( 0/ jfpjl l`roob m^o^ q- K^pcfi^p ab i^ j^qofw tolkphf^k^ U plk ilp sb`qlobp q+q&+--- -Š!9!+Krbdl mlabjlpbp`of_fo
s < abq U < abq 'q+ q&+--- +q'j,h•-
K^ abofs^a^ ab t bp bi abqbojfk^kqb ab i^ j^qofw l_qbkfa^ abofs^kal i^ •iqfj^ cfi^ab U 'sbo bgbo`f`fl 7 ab i^ pb``fŽk 2-06(- Dpql bp
s& -< abq 'q+q&+--- +T'qGfi+ q&j',
Lriqfmif`^kal i^ •iqfj^ cfi^ ab t mlo N/&t' q^j_f‹k qbkbjlp
Rrj^kal bp^p alp •iqfj^p b`r^`flkbp bk`lkqo^jlp
s& * Nh't(s < abq 'q+ q&+--- +q'j,1(+ q'jh * Nh't(q'j,h(-
Obol i^p cfi^p ab bpqb •iqfjl abqbojfk^kqb plk abmbkafbkqbp mrbpql nrb q p^qfpc^`bi^ b`r^`fŽk afcbobk`f^i '5-14(- Olo q^kql bi abqbojfk^kqb bp `bol+ 0/ nrb pfdkfcf`^nrb t p^qfpc^`b '5-15(- Qbplisfbkal '5-15( l_qbkboklp i^ cŽojri^ ab @_bi '5-16(-
-++ C_q]_ekjao `ebanaj_e]hao heja]hao
Rbdrfa^jbkqb abjlpqo^jlp nrb s&_'88z4 N m^o^rk `fboql a ab Z+Kl e^`bjlpmlo obar``fŽk ^i ^_proal- Rrmlkd^jlp nrb s&p' < N m^o^ qlal p ab h-Difg^jlprk p cfgl bk 0+mlo bgbjmil p < pk+ X `lkpfabobjlp bi pfpqbj^ ifkb^i ab b`r^`flkbp^idb_o^f`^p
alkab W bp rk sb`qlo `lirjk^- X^ nrb abq U&pk' < N+i^ j^qofw U&pk' bp pfkdri^omlo 0/ nrb bpb pfpqbj^ ^ajfqb rk^ plir`fŽk kl kri^+ pb^ ‹pq^ W < 'bi +--- +Aj( 99{5
'N+ --- +N(- Tqfifw^kal ilp `ljmlkbkqbp ab bpqbsb`qlo kl kril+ pb^ b i^ `lj_f,k^`fŽk ifkb^i
K^ crk`fŽk b ^pŒabcfkfa^ p^qfpc^`bJ&b' < N bk / mrbpql nrb bp rk^ `lj_fk^`fŽkifkb^i ab q++--- +Sj- K^ b`r^`fŽk j^qof`f^i U&pk'V < N fjmif`^ nrb
Olo `lkpfdrfbkqb+b qfbkb`ljl s^ilo fkf`f^i bi sb`qlo N bk p < pkŒ pŒnrb+ pbd•k biqblobj^ ab rkf`fa^a+ b bp i^ plir`fŽk `bol- Dpql pfdkfcf`^ Bi < --- < Aj < N+0/0/ `r^i bp rk^ `lkqo^af``fŽk- Olo 0/ q^kql s&p' 99{5N m^o^rk `fboql paj Y+Slj^kalbpb s^ilo ab p `ljl a bk i^ cŽojri^ ab @_bi sbjlp nrb s&t'88z4 N m^o^ qlal t
ab h-Dpql `ljmibq^ i^ abjlpqo^`fŽk abi qblobj^ 5-01-
5-02 L‹qlalp bpmb`f^ibpm^o^abqbojfk^o rk^ plir`fŽk m^oqf`ri^oab i^ b`r^`fŽkkl eljld‹kb^- Qbar``fŽk ^ rk pfpqbj^ ab b`r^`flkbp ifkb^ibp ab mofjboloabk
Rf _fbk bi j‹qlal ab s^of^`fŽk ab `lkpq^kqbp molmlo`flk^ rk j‹qlal dbkbo^im^o^ abqbojfk^o rk^ plir`fŽk m^oqf`ri^oab J&u' < P* bufpqbkj‹qlalp bpmb`f^ibpnrb ^ jbkral plk ab ^mif`^`fŽk jŠp pbk`fii^ `r^kal i^ b`r^`fŽk qfbkb `fboq^pcloj^p bpmb`f^ibp-Olo bgbjmil+ pf i^ b`r^`fŽk qfbkb `lbcf`fbkqbp `lkpq^kqbp mlab,jlp obar`fo bi mol_ibj^ ^i ab obplisbo rk^ pr`bpfŽk ab b`r^`flkbp ifkb^ibp abmofjbo loabk- Di j‹qlal dbkbo^i nrba^ jbglo firpqo^al `lk rk bgbjmil pbk`fiil-
DIDLOKN 0- G^ii^o rk^ plir`fŽk m^oqf`ri^o ab i^ b`r^`fŽk
&4,06' &B + h'&B + 0'u < Va!&*!+1-
Qkhq_e‰j- Olkd^jlp q < 'B , 0'u, Dkqlk`bp i^ b`r^`fŽk pb qo^kpcloj^ bk
'B , h(q < ta!&*!+]-
K†pk`k `ah ]jqh]`kn l]n] `apaniej]n qj] okhq_e‰j l]npe_qh]n 1/0
†pq^ bp rk^ b`r^`fŽk ifkb^i ab mofjbo loabk bk q nrb mrbab obplisbopb `lk biqblobj^ 5-0- Tk^ plir`fŽk m^oqf`ri^o bp
Rrpqfqrv‹kali^ bk i^ b`r^`fŽk q < &B + 0'u l_qbkbjlp
&B + 0'u < qb!&*9i91+
nrb bp rk^ b`r^`fŽk ab mofjbo loabk bk u- Qbplisf‹kali^ `lk bi qblobj^ 5-0 bk-`lkqo^jlp nrb rk^ plir`fŽk m^oqf`ri^o '`lk Wh&M'< N( sfbkb a^a^ mlo
@rknrb i^ fkqbdo^i kl mrbab `^i`ri^opb mlo jbafl ab crk`flkbp bibjbkq^ibp+ `lk,pfabo^jlp i^ b`r^`fŽk `ljl obprbiq^+ mrbpql nrb i^ plir`fŽk pb bumobp^ mlo jbaflab fkqbdo^ibp ab crk`flkbp `loofbkqbp- K^ plir`fŽk dbkbo^i ab '5-17( bp
.'), ?k]XMX MNUJW^UJMX[YJ[J MN]N[VRWJ[WJplir`fŽk YJ[]RL^UJ[MNUJNL^JLRmWWXQXVXPkWNJ
Cbp`of_fjlp ^ `lkqfkr^`fŽk rk j‹qlal nrb pb mrbab rqfifw^o pf i^ b`r^`fŽkJ&u' < P qfbkb `lbcf`fbkqbp `lkpq^kqbp v pf bi pbdrkal jfbj_ol P bp ^kri^al mlork lmbo^alo ab `lbcf`fbkqbp `lkpq^kqbp+ ^ p^_bo ?&P' < N- Dk mofk`fmfl+ bi j‹,qlal bp jrv pbk`fiil- @mif`^jlp bi lmbo^alo ? ^ ilp alp jfbj_olp ab i^ b`r^`fŽkafcbobk`f^i J&u' < P v l_qbkbjlp rk^ krbs^ b`r^`fŽk ?J&u' < N nrb ab_b pbop^qfpcb`e^ mlo qla^p i^p plir`flkbp ab i^ b`r^`fŽk lofdfk^i- Orbpql nrb ?h%bp lqollmbo^alo `lk `lbcf`fbkqbp `lkpq^kqbp mlabjlp abqbojfk^o pr k•`ibl `^i`ri^kali^p o^Œ`bpab i^ b`r^`fŽk `^o^`qboŒpqf`^ab ?J- Di mol_ibj^ pb obar`b bkqlk`bp ^abqbojfk^o+ ^ m^oqfo ab bpb k•`ibl+ rk^ crk`fŽk m^oqf`ri^o Xi nrb p^qfpc^`bJ'Wh( < P, Ub^jlp ^idrklp bgbjmilp-
DIDLOKN 0- G^ii^o rk^ plir`fŽk m^oqf`ri^o ab i^ b`r^`fŽk
'B3 , /4'u < t3 * t * 0-
Qkhq_e‰j- Di pbdrkal jfbj_ol+ rk mlifkljfl ab `r^oql do^al+ bp ^kri^almlo bi lmbo^alo B4
Œ Olo q^kql+`r^inrfbo plir`fŽk ab i^ b`r^`fŽk a^a^ q^j_f‹k 0/bp ab i^ b`r^`fŽk
'5-18( B4'B3 , /4'u < N-
-+- C_q]_ekjao `ebanaj_e]haoheja]hao
K^p o^Œ`bpab i^ b`r^`fŽk `^o^`qboŒpqf`plk N+N+N+N+N+1+ , 1+ 1f+ , 1f+`lk ilnrb qla^p i^p plir`flkbp ab '5-18( pb bk`rbkqo^k bk i^ `lj_fk^`fŽk ifkb^i
Cbpb^jlp bibdfo i^p Az ab jlal nrb J'u( < t3 * t * 0+ alkab J < C3 , 05-Orbpql nrb ilp `r^qol •iqfjlp q‹ojfklp plk ^kri^alp mlo J* mlabjlp qlj^oA4 < A5 < Bp < Bd < N b fkqbkq^jlp bk`lkqo^o B0+ ’’’ +Bp ab jlal nrb
Dp ab`fo+ _rp`^jlp rk^ plir`fŽk m^oqf`ri^o Xi nrb pb^ rk mlifkljfl ab `r^oqldo^al nrb p^qfpc^d J'Wh( < t2 * t * 0- O^o^ pfjmifcf`^o bp`of_^jlp
05Wh< ]t9 * ^t2 * _t1 * `t * a-
Dpql klp a^ 05We3( < 13]+ ^pŒnrb We3
( < 2].1- Rrpqfqrvbkal bk i^ b`r^`fŽk afcb,obk`f^i J'Wh( < t3 * t * 0+qbkbjlp nrb abqbojfk^o ]+ ^* _+`* a nrb p^qfpc^d^k
,h] , ]t3 , ^t2 , _t1 , `t , a < t3 * t * 0 -
Hdr^i^kal ilp `lbcf`fbkqbp ab i^p mlqbk`f^p pbjbg^kqbp ab t l_qbkbjlp
] < ,0+ ^ < B < N+ `; +/* a , \he, 1+
ab j^kbo^ nrb i^ plir`fŽk m^oqf`ri^oXi sfbkb a^a^ mlo
DIDLOKN 1- Qbplisbo i^ b`r^`fŽk afcbobk`f^i u! , 4u&* 5u < ta!+
Qkhq_e‰j- K^ b`r^`fŽk afcbobk`f^i qfbkb i^ cloj^
&4,1.' J&u' < P*
alkab P't( < ta! X J < B1, 4C * 5- K^ `loobpmlkafbkqb b`r^`fŽk eljld‹kb^
mrbab mlkbopb bk i^ cloj^
&B + 0'&B + 1'u < N:
nrb qfbkb i^p plir`flkbp fkabmbkafbkqbpq0&t' < a1 A+ q1&t' < a!8
K†pk`k `ah ]jqh]`kn l]n] `apaniej]n qj] okhq_e‰j l]npe_qh]n 1/2
Arp`^jlp ^elo^ rk^ plir`fŽk m^oqf`ri^o Xi ab i^ b`r^`fŽk kl eljld‹kb^-Bljmol_^jlp nrb i^ crk`fŽk P&t' < ta! bp rk^ plir`fŽk ab i^ b`r^`fŽk eljl,d‹kb^
&B + h'0u < N-
Olo `lkpfdrfbkqb+ pf ^mif`^jlp ^ ilp alp jfbj_olp ab '5-2/( bi lmbo^alo 'C , 0(1
bk`lkqo^jlp nrb `r^inrfbo crk`fŽk nrb p^qfpc^d '5-2/( ab_b q^j_f‹k p^qfpc^`boi^ b`r^`fŽk
&B + /'0&B + 0'&B + 1'u < N-
Dpq^b`r^`fŽk afcbobk`f^i qfbkbi^p o^Œ`bp^o^`qboŒpqf`^p0+0+1+2+ mlo il nrb qla^pprp plir`flkbp pb bk`rbkqo^k bk i^ `lj_fk^`fŽk ifkb^i
u < ]a! * ^ta! * _a0,h * `a1t*
alkab ]+ ^* a+` plk `lkpq^kqbp- Prbobjlp bibdfo ]+ ^* a+`* ab jlal nrb i^ pl,ir`fŽk Xi obpriq^kqbp^qfpc^d J'Wh( < ta!- Orbpql nrb Je_a! * `a1V
' < N `r^ibp,nrfbo^ nrb pb^k ilp a v `* pŽil kb`bpfq^jlp bibdfo ] v ^ ab j^kbo^ nrb-Je]a! * ^ta!( < ta! v qlj^jlp a < ` < N- Rf mlkbjlp
XH < ]a! * ^ta!+qbkbjlp
B'Wh( < &] * ^'nb%* ^ta!*
^pŒnrb i^ b`r^`fŽk &B1, 4C * 4'Wh < ta! pb `lksfboqb bk
'1] , 2^ (aV * X^ta! < ta! -
Rrmofjfbkal bi c^`qlo a! b fdr^i^kal ilp `lbcf`fbkqbp ab i^p mlqbk`f^p pbjbg^kqbpab t bk`lkqo^jlp ] < c+ < q-- Olo il q^kql+Xi < ba%!* ptnb%v i^ plir`fŽkdbkbo^i ab J&u' < P sfbkb a^a^ mlo i^ cŽojri^
Di j‹qlal rqfifw^al bk ilp bgbjmilp ^kqboflobppb ii^j^ i†pk`k `ah ]jqh]`kn-Rb mlaoŠ bjmib^o pf mlabjlp bk`lkqo^o rk lmbo^alo ab `lbcf`fbkqbp `lkpq^kqbp ?nrb ^krib P- @ m^oqfoab krbpqol bpqrafl ab i^p b`r^`flkbp afcbobk`f^ibp ifkb^ibpeljld‹kb^p `lk `lbcf`fbkqbp `lkpq^kqbp+p^_bjlp nrb i^p •kf`^p crk`flkbp ab s^il,
1/3 C_q]_ekjao `ebanaj_e]hao heja]hao
obp ob^ibp ^kri^a^p mlo lmbo^alobp `lk `lbcf`fbkqbp `lkpq^kqbp plk `lj_fk^`flkbpifkb^ibp ab crk`flkbp ab i^ cloj^
alkab i bp rk bkqbol mlpfqfsl v ] v '2 plk `lkpq^kqbp ob^ibp- K^ crk`fŽkv < ti,&a!&! bp rk^ plir`fŽk ab rk^ b`r^`fŽk afcbobk`f^i `lk o^Œw o^`qboŒpqf`]ab jriqfmif`fa^a i- Olo il q^kql+bpq^crk`fŽk qfbkb bi ^kri^alo &B + ](i- B^a^rk^ ab i^p crk`flkbp u < ti,/a!&! `lp &1t b u < ti,/a!&! oaj%&1tbp rk^ plir`fŽk abrk^ b`r^`fŽk afcbobk`f^i `lk o^Œ`bp^o^`qboŒpqf`^pljmibg^p bu ~ ewH*`lk jriqf,mif`fa^a i `^a^ rk^+ ab jlal nrb plk ^kri^a^p mlo bi lmbo^alo YB1
, 1]B )) &]1 * '21([i- O^o^ c^`fifq^o i^ obplir`fŽk ab ^idrklp bgbo`f`flp+ a^jlp rk^ifpq^ab bplp ^kri^alobp bk i^ q^_i^ 5-0+grkql `lk ^idrkl ab prp `^plp m^oqf`ri^obp-
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,0 pbkwHt
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Bi
B,nt-'B , nt-(i
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@rknrb bi j‹qlal abi ^kri^alo bp jrv bcf`^w`r^kal pb mrbab ^mif`^o+pbifjfq^ ^ i^p b`r^`flkbp `rvlp pbdrkalp jfbj_olp P qfbkbk rk ^kri^alo `lk `lb,cf`fbkqbp`lkpq^kqbp- Rf P&t' qfbkb i^ cloj^ at&+ild t* l q^k t* bi j‹qlal kl pbmlaoŠ ^mif`^o: qbkbjlp bkqlk`bp nrb rqfifw^oi^ s^of^`fŽk ab `lkpq^kqbp l ^id•klqol j‹qlal m^o^bk`lkqo^o rk^ plir`fŽk m^oqf`ri^o-
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Dk `^a^ rkl ab ilp bgbo`f`flp 0 ^i iN+ e^ii^o i^ plir`fŽk dbkbo^i bk bi fkqbos^il', //+* //(-
/, u! , . < t0‹
1- u! , 3u < a0t‹
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5- .! , u&< a!:6- u&! , u& < aV * a+t,
7- u&! * 2u! * 2. * u < ta9! -8- u! * u < ta! pbk 1t -
/., o&!, W < t0a,t Œ
Cfan_e_eko 1/4
00- Rf rk lmbo^alo `lk `lbcf`fbkqbp `lkpq^kqbp ? ^kri^ / v pf rk lmbo^alo `lk `lbcf`fbkqbp`lkpq^kqbp @ ^kri^ d- abjlpqo^o nrb bi molar`ql ?@ ^kri^ / * d-
01- Rb^ ? rk lmbo^alo `lk `lbcf`fbkqbp `lkpq^kqbp `lk mlifkljfl `^o^`qboŒpqf`l l Œ-^( @mif`^o bi j‹qlal abi ^kri^alo m^o^ abjlpqo^o nrb i^ b`r^`fŽk afcbobk`f^i?&u' < a09z9 qfbkb rk^ plir`fŽk m^oqf`ri^o ab i^ cloj^
pf ] kl bp rk `bol abi mlifkljfl N?-_( Rf ] bp rk `bol pfjmib ab l, 'jriqfmif`fa^a 0(+ abjlpqo^o nrb i^ b`r^`fŽk@'v( < a]v
qfbkb i^ plir`fŽk m^oqf`ri^o
ta]v
Wh< ly'nt-(-
b( Fbkbo^ifw^o Ilp obpriq^alp ab ^( v _( `r^kal ] bp rk `bol ab m-`lk jriqfmif`fa^a i-02- C^alp alp lmbo^alobp `lk `lbcf`fbkqbp `lkpq^kqbp ? v @ `rvlp mlifkljflp `^o^`qboŒpqf`lp
kl qfbkbk `bolp `ljrkbp- Rb^ B < ?@,^( Cbjlpqo^o nrb qla^ plir`fŽk ab i^ b`r^`fŽk afcbobk`f^i A&u' < N qfbkb i^ cloj^v < Xi * u*, alkab ?&u*' < N X @&u*' < N-_( Cbjlpqo^o nrb i^p crk`flkbp Xi b v+ ab i^ m^oqb ^( bpqŠk abqbojfk^a^p `lk rkf`fa^a-Dpql bp+ m^o^ rk^ v a^a^ nrb p^qfpc^d^ A&u' < N bufpqb pŽil rk m^o Xe v+ `lk i^p mol,mfba^abp ab i^ m^oqb ]',
03- Rf J&u' < v! * ]u% * ^u* alkab ] v ^ plk `lkpq^kqbp+ pb^ / i^ plir`fŽk m^oqf`ri^o abJ&u' < N nrb p^qfpc^`b i^p `lkaf`flkbp /&.' < N X .&'/( < 0- Cbjlpqo^o nrb rk^ plir`fŽkm^oqf`ri^o ab, J&u' < P sfbkb a^a^ mlo i^ cŽojri^
Wh&V' < cb! e&t+ p(P'p( `p
m^o^ `r^inrfbo `- Dk m^oqf`ri^o+ pf i^p o^Œ`bpab i^ b`r^`fŽk `^o^`qboŒpqf`^plk fdr^ibp+mlo bgbjmil /%/ < /%* < i* abjlpqo^o nrb i^ cŽojri^ nrb a^ uz&t' pb `lksfboqb bk
04- Rb^ P bi lmbo^alo ~jriqfmif`^`fŽk mlo uƒ+ Dpql bp+O&u'&t' < t , u&t' m^o^ `^a^ v ab i^`i^pb Bcill v `^a^ t ob^i- Cbpfdkbjlp `lk h bi lmbo^alo fabkqfa^a+ abcfkfal mlo h'u( < vm^o^ `^a^ v ab Abh// ’
^( Cbjlpqo^o nrb CP , PC < h-_( Cbjlpqo^o nrb B%O+ OB%bp rk lmbo^alo ab mofjbo loabk `lk `lbcf`fbkqbp `lkp,q^kqbp+v abqbojfk^o q^i lmbo^alo bumiŒ`fq^jbkqb `ljl rk mlifkljfl ab mofjbo do^albk C-`( Cbjlpqo^o mqa B2O + OB%bp rk lmbo^alo ab pbdrkal loabk `lk `lbcf`fbkqbp `lkp,q^kqbp+ v abqbojfk^o af`el lmbo^alo bumiŒ`fq^jbkqb `ljl rk mlifkljfl ab pbdrkaldo^al bk C-a( Dkrk`f^o i^ dbkbo^ifw^`fŽk prdbofa^ mlo bi lmbo^alo B!O + OB!* v abjlpqo^oi^ mlofkar``fŽk-
-+1 C_q]_ekjao `ebanaj_e]haoheja]hao
Dk `^a^ rkl ab ilp bgbo`f`flp abi 05 ^i 1/+ e^ii^o rk^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk afcb,obk`f^i bk bi fkqbos^il nrb pb fkaf`^-
05-u!,u<h.t+ 'N+ * '/(-
06- u! * 3u < pb` 0t* '6S 6S(,3&3 -
/6, u! \u < pb`! u ] oa_t+ ' 6S 6S(,1&1 -08- u! , 1u& * u < a&!'aV + 0(1+
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0- Tk^ `ros^ fkqbdo^i v < q&t' ab i^ b`r^`flk afcbobk`f^i v! , 2u&, 3v < N `loq^ ^ rk^`ros^ fkqbdo^i v < r&t' ab i^&b`r^`fŽk afcbobk`f^i v! * 3v& , 4v < N bk bi lofdbk- Cb,qbojfk^o i^p crk`flkbp q v r pf i^p alp `ros^p qfbkbk i^ jfpj^ mbkafbkqb bk bi lofdbkv pf
- 'T'V([3 4ej,, <,5&
tykk q&t'
1- Tk^ `ros^ fkqbdo^i v < q&t' ab i^ b`r^`fŽk afcbobk`f^i v! , 3v& * 18v < N `loq^ ^ rk^`ros^ fkqbdo^i v < r&t' ab i^ b`r^`fŽk afcbobk`f^i v! * 3v& * 02v < N bk bi lofdbk- K^palp `ros^p qfbkbk i^ jfpj^ mbkafbkqb bk bi lofdbk- Cbqbojfk^o q v r pf q%&5R-0'< 0-
2- R^_fbkal nrb i^ b`r^`fŽk afcbobk`f^i v! * 2tu% * O&t'u < N qfbkb alp plir`flkbp ab i^cloj^ v+ < q&t' b v+ < tq&t'* alkab q&M' < 0+ abqbojfk^o q&t' v O&t' bumiŒ`fq^jbkqbbk crk`fŽk ab t-
3- Rb^ J&u' < v! * Nru&* N*u, O^o^ obplisbo i^ b`r^`fŽk kl eljld‹kb^ J&u' < P mlo bij‹qlal ab s^of^`fŽk ab `lkpq^kqbp+ kb`bpfq^jlp `lkl`bo alp plir`flkbp ifkb^ijbkqb fkab,mbkafbkqbp ab i^ b`r^`fŽk eljld‹kb^- Dpqb bgbo`f`fl abjrbpqo^ nrb pf pb `lkl`b qj]plir`fŽk q* ab J&u' < N+X pf q* kl pb ^kri^ bk rk fkqbos^il H* rk^ pbdrka^ plir`fŽk q*ab i^ b`r^`fŽk eljld‹kb^ sfbkb a^a^ mlo i^ cŽojri^
alkab O&t' < a+HN*&V'`V* v a bp rk mrkql `r^inrfbo^ ab H, Dpq^p alp plir`flkbp plkfkabmbkafbkqbp bk H,^( Cbjlpqo^o nrb i^ crk`fŽk q+p^qfpc^`b J&u' < N-_( Cbjlpqo^o nrb q+v q+plk fkabmbkafbkqbp bk I-
4- G^ii^o i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk
th& , 1't * i(v&* 't * 1(u < t1a0t
C_q]_ekjao heja]hao`a oacqj`k kn`aj _kj _kabe_eajpao]j]h‡pe_ko 1/6
m^o^ t = l+ p^_fbkal nrb i^ b`r^`fŽk eljld‹kb^ qfbkb rk^ plir`fŽk ab i^ cloj^ u<aitŒ
5- N_qbkbo ^ pfjmib fkpmb``fŽk rk^ plir`fŽk kl kri^ v irbdl bk`lkqo^o i^ plir`fŽk dbkbo^iab i^ b`r^`fŽk afcbobk`f^i
&u! + 2u%' * t1&u% + 2u' < N-
6- G^ii^o i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk afcbobk`f^i
2t1u! * 2tu% + u < N+
p^_fbkal nrb bufpqbrk^ plir`fŽk m^oqf`ri^o ab i^ cloj^ v < t! m^o^ t = N-7- G^ii^o rk^ plir`fŽk ab i^ b`r^`fŽk eljld‹kb^ mlo q^kqbl+v bk`lkqo^o irbdl i^ plir`fŽk
dbkbo^i ab i^ b`r^`fŽk
t&/ + t'u! + '0 , 0t'u% * &t1 , 1t * i(v < '0 , V'1,
8- G^ii^o i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk
&0t + 1t1yu! * 2u%* 4tu < N+
p^_fbkal nrb qfbkb rk^ plir`fŽk nrb bp rk mlifkljfl bk t-0/- G^ii^o i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk
t1&/ + t'u! * 0t&0 + t'u% * 1'0 * t'u < t1+
p^_fbkal nrb i^ b`r^`fŽk eljld‹kb^ qfbkb rk^ plir`fŽk ab i^ cloj^ v < t|,00- Rb^ c&t' < If a%Yp`p pf t = N- 'Ml fkqbkq^obi `Ši`ril ab bpq^ fkqbdo^i-( G^ii^o qlalp ilp
s^ilobp ab i^ `lkpq^kqb ] q^ibp nrb i^ crk`fŽk b abcfkfa^ mlo
0z't( < , a]c'!+(
t
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1/7 C_q]_ekjao `ebanaj_e]haoheja]hao
qfbkbrk abp^ooliil bk pbofbab mlqbk`f^p bk bpb fkqbos^il+
//
b't( < ]j't , tk(j+U8?
`lksbodbkqb m^o^ Gt + Wli ; n, Rf ilp `lbcf`fbkqbp ab rk^ b`r^`fŽk afcbobk`f^iifkb^i eljld‹kb^
u;j( * N0't(u;j,h( * --- * Nj'V(W < N
plk ^k^iŒqf`lpbk rk fkqbos^il 'u+ , n*Vk * n'* mrbab bkqlk`bp abjlpqo^opb nrbbufpqbkj plir`flkbp fkabmbkafbkqbpq++--- +Sj+ `^a^ rk^ ab i^p `r^ibp bp ^k^iŒqf`^bk bi jfpjl fkqbos^il- Cbjlpqo^objlp bpqbqblobj^ m^o^ b`r^`flkbp ab pbdrkalloabk v irbdl afp`rqfobjlp rk fjmloq^kqb bgbjmil nrb pb mobpbkq bk jr`e^p^mif`^`flkbp-
SDNQDL@ 5-02- Qa]j N0- v N1 ]j]h‡pe_]o aj qj ejpanr]hk ]^eanpk 'tk , n+Vk * n(+p]hao_kik
//
N0't( < ^jAt , tkp+U8?
//
Nht( < _j't , tk(j-U8?
Cjpkj_ao h] a_q]_e‰j`ebanaj_e]h
'5-20(
peaja `ko okhq_ekjao ej`alaj`eajpao TI+ v z mqa okj ]j]h‡pe_]oaj ah ieoik ej,panr]hk-
Baikopn]_e5j- Hkqbkqbjlp bk`lkqo^o rk^ pbofbab mlqbk`f^p plir`fŽk ab i^cloj^
//
'5-21( W < ]jAt , tk(j+U8?
`lksbodbkqb bk bi fkqbos^il a^al- O^o^ biil+ prpqfqrfjlp i^p pbofbpa^a^p m^o^N* X N1 bk i^ b`r^`fŽk afcbobk`f^i v abqbojfk^jlp irbdl i^p obi^`flkbp nrb ilp`lbcf`fbkqbp ^-- ab_bk p^qfpc^`bom^o^ nrb i^ crk`fŽk v a^a^ mlo '5-21( p^qfpc^d^i^ b`r^`fŽk-
K^p abofs^a^p v&b v! mrbabk l_qbkbopb abofs^kal i^ pbofbab mlqbk`f^p abv q‹ojfkl ^ q‹ojfkl 'sbo qblobj^ 00-8 abi Ulirjbk 0(- Dpql klp a^
C_q]_ekjao heja]hao `a oacqj`k kn`aj _kj _kabe_eajpao ]j]h†pe_ko 1/8
^l ^l
u&< j]jAt + Wl(k,i < &j * /']j)h&t + Vk'j*U8S V4=
^l ^l
u! < j&j + /']jAt + Vk'j+0 < &j * 0'&j * /']j)0&t + tk'j,j+0 j+M
Klp molar`qlp NG&t'u%v N1&t'u sfbkbk a^alp mlo i^p pbofbpab mlqbk`f^p ')(
v
Br^kal bp^ppbofbppb prpqfqrvbkbk i^ b`r^`fŽk afcbobk`f^i '5-20( bk`lkqo^jlp
Olo `lkpfdrfbkqb+i^ b`r^`fŽk afcbobk`f^i pb p^qfpc^oŠpf bibdfjlp ilp `lbcf`fbkqbp]j ab jlal nrb p^qfpc^d^ki^p cŽojri^p ob`roobkqbp
'5-22(j
&j * 0'&j * /']j)0 < , Y&g* /']g)h^j\g * ]gAj+g[S4=
m^o^ j < N+0+1+---- Dpq^ cŽojri^ bumobp^]j)1 bk crk`fŽk ab ilp `lbcf`fbkqbp^kqboflobp],* ]d% ,, * ^-k*i X ilp `lbcf`fbkqbp ab i^p crk`flkbp a^a^p OHv N0, Difg^,jlp s^ilobp ^o_fqo^oflpab ilp alp mofjbolp `lbcf`fbkqbp ]‚ v ^i v rqfif`bjlp i^cŽojri^ ob`roobkqbm^o^abcfkfoilp obpq^kqbplbcf`fbkqbp ]1+ ]2+ --- + bk crk`fŽk ab]‚ v ]h- Dpql d^o^kqfw nrb i^ pbofbab mlqbk`f^p '5-21( p^qfpc^oŠi^ b`r^`fŽk af,cbobk`f^i '5-20(- Di pfdrfbkqb m^pl ab i^ abjlpqo^`fŽk bp mol_^o nrb i^ pbofb^pŒabcfkfa^ `lksbodb ob^ijbkqb m^o^ qlal t abi fkqbos^il &tk , n*Vk * n', Dpql pbe^`b j^vlo^kal i^ pbofb'5-21( mlo lqo^ pbofbab mlqbk`f^p `lksbodbkqb- Efk^ijbk,qb+abjlpqo^jlp nrb mlabjlp bibdfo ]• v ]h m^o^l_qbkbo alp plir`flkbp fkabmbk,afbkqbp-
Cbjlpqobjlp ^elo^ nrb i^ pbofb'5-21( `rvlp `lbcf`fbkqbp bpqŠkabcfkfalp mlo'5-22( `lksbodb bk bi fkqbos^il fkaf`^al-
')( Klp ib`qlobp kl c^jfif^ofw^alp `lk i^ jriqfmif`^`fŽk ab pbofbp ab mlqbk`f^p mrbabk`lkpriq^o bi bgbo`f`fl 6 ab i^ pb``fŽk 5-10-
10/ C_q]_ekjao `ebanaj_e]haoheja]hao
Difg^jlp rk mrkql cfgl+ Vy ,<0< Wl bk bi fkqbos^il 'u+ , n+ Vk * o( v pb^p < zVh , tkh- Orbpql nrb i^p pbofbpnrb abcfkbk OHv N1 `lksbodbk ^_plirq^jbkqbm^o^V < Wi ilp q‹ojfklp ab bp^ppbofbpbpqŠk^`lq^alp+ mlkd^jlp
v
m^o^ `fboqlp k•jbolp LH = N+L1 = N- Rb^ L bi j^vlo ab ilp alp k•jbolp LHv pK1Œ Sbkbjlp bkqlk`bp
v
K^ cŽojri^ ab ob`roobk`f^ fjmif`^ i^ abpfdr^ia^a
G^d^jlp ^elo^ ?k < h]kh+ @i < i^ii+ v abcfk^jlp ?1+ ?]* ,,, pr`bpfs^jbkqbjbaf^kqb i^ cŽojri^ ab ob`roobk`f^
'5-23(
m^o^ j y N- Dkqlk`bp h]jh y ?! m^o^ qlal j y N+^pŒnrb i^ pbofb ]**&t + tk(!bp j^vlo^a^ mlo i^ pbofb ?jht , uli!- @mif`^jlp ^elo^ bi `ofqbofl abi `l`fbkqbm^o^abjlpqo^o nrb ?!ht , tkh! `lksbodb pf Hu, tkh ; p-
Rrpqfqrvbkal j mlo j , 0 bk '5-23( v obpq^kal bi molar`ql ab i^ b`r^`fŽkmlo n9&ab '5-23( bk`lkqo^jlp nrb 'j * 1('j * h'?!)0 + p,h'j * /'j?!)h <; Kpj * 1(@--*H- Olo `lkpfdrfbkqb
? \ ? aj * 0(j * 'j * 1(Kpj*1 , k*i 'j * 1('j * h(p &
v e^ii^jlp
?j*1ht , tkhj*
1< 'j * h(j * 'j * 1(Kp Zu] uli,* Hu, uli
?j*h Zu, ulik*i 'j * 1('j * h(p p
J] a_q]_e‰j`a Jacaj`na 100
`r^kal j y `l + DpqbiŒjfqbbp jbklo nrb 0 pf Gt , tkh ; p-Krbdl J ]j't ----9VM(P
`lksbodb pf Hu, uli ; p-Obol v^ nrb p< HWi, tkh v nrb Wi bp rk mrkql ^o_fqo^,ofl bk bi fkqbos^il 'u+ , n*Vk, * n'* i^ pbofbJ ]j&t + WN(Q `lksbodb m^o^ qlal tbk 'u+ , n*t• * n',
Klp alp mofjbolp `lbcf`fbkqbp ]• v ]h obmobpbkq^kilp s^ilobp fkf`f^ibp ab uv ab pr abofs^a^ bk bi mrkql VkŒ Rf Sh bp i^ pbofbab mlqbk`f^p plir`fŽk `lk ^l < 0X ]h < N+ab j^kbo^ nrb
v
v S1 i^ plir`fŽk `lk ^l < N X ]h < 0+ab q^i jlal nrb
v
bkqlk`bp i^p plir`flkbp T`0 v S1 pboŠk fkabmbkafbkqbp-Dpql `ljmibq^ i^ abjlpqo^`fŽk+
.')0 >J NL^JLRmWMN>NPNWM[N
Dk bpq^pb``fŽk bk`lkqo^jlp pbofbpab mlqbk`f^p plir`flkbp m^o^i^ b`r^`fŽkab Kbdbkaob+
'5-24( 'i , t1'u! + 0tu%* HW'HW* h'u < N+
alkab ] bp `r^inrfbo `lkpq^kqb ob^i- Dpq^b`r^`fŽk pb mobpbkq bk mol_ibj^p ab^qo^``fŽk v ab cirgl ab `^ilo `lk pfjbqoŒ bpc‹of`^- Br^kal ] bp rk bkqbol mlpfqfslbk`lkqo^objlp nrb i^ b`r^`fŽk qfbkb plir`flkbp mlifkŽjf`^p ii^j^a^p lkhejkieko`a Jacaj`na- Dplp plk ilp jfpjlp mlifkljflp nrb pb bk`lkqo^olk ^i bpqraf^o bimol`bpl ab Fo^j,R`ejfaq '`^mŒqril ($ mŠd- 20(-
K^ b`r^`fŽk ab Kbdbkaob mrbab bp`of_fopb^pŒ9
Y&t1 , h'u%[%< HW'HW* h'u*nrb ,qfbkb i^ cloj^
R'u(9999?u+
bk alkab R bp rk lmbo^alo ab Rqroj,Kflrsfiib+ R& ' < 'lbW+ `lk l't( < t1, 0
X @ < ]'] * 0(- Olo `lkpfdrfbkqb+i^p plir`flkbp kl kri^p ab i^ b`r^`fŽk ab Kb,dbkaob plk ^rqlcrk`flkbp ab R `loobpmlkafbkqbp ^i ^rqls^ilo ]'] * 0(- Orbpqlnrb l&t' p^qfpc^`bi^p `lkaf`flkbp ab `lkqlokl
l&h' < l&+h' < N+
101 C_q]_ekjao `ebanaj_e]haoheja]hao
bi lmbo^alo R bp pfj‹qof`l `lk obpmb`ql^i molar`ql fkqboflo
&f*d( <qHb't(c't( `t -
K^ qbloŒdbkbo^i ab ilp lmbo^alobp pfj‹qof`lp klp af`b nrb i^p ^rqlcrk`flkbp `l,oobpmlkafbkqbp ^rqls^ilobp afpqfkqlp plk loqldlk^ibp 'qblobj^ 4-2(-
Dk i^ b`r^`fŽk afcbobk`f^i qo^q^a^bk bi qblobj^ 5-02 bi `lbcf`fbkqb ab v! bp 0-K^ b`r^`fŽk ab Kbdbkaobmrbab mlkbopbbk bp^ cloj^ pf afsfafjlp mlo 0 , t&+Cb'5-24( l_qbkbjlp
alkab0t
N/&t' < ,,,0, t1
v N &t' < fW'fW * 0(1 0 ] t1 &
pf t1 <:5 0- Orbpql nrb 0.'0 , t1( < z:9lu1k m^o^ Gth; 0+O0 X N1 qfbkbk ^j_lp
abp^ooliilp bk pbofbab mlqbk`f^pbk bi fkqbos^il ^_fboql ' , 0+0( ^pŒnrb bi qblobj^5-02 bp ^mif`^_ib- O^o^ bk`lkqo^o i^ cŽojri^ ab ob`roobk`f^ m^o^ ilp `lbcf`fbkqbpbp jŠp pbk`fiil abg^o i^ b`r^`fŽk bk i^ cloj^ '5-24( b fkqbkq^oe^ii^o rk^ pbofbab mlqbk`f^p plir`fŽk ab i^ cloj^
sŠifa^ bk bi fkqbos^il ^_fboql ',0+ 0(- Cbofs^kal bpq^ pbofb q‹ojfkl ^ q‹ojfkll_qbkbjlp
//
u& < z j]!t0&,0+"c+
Olo 0/ q^kql+qbkbjlp
v//
u! < z j'j , 0(]0&
t0&,1Œ
+"4,
++ ++
1tu& < J 1j]0&t0&< J 1j]0&t0&++"4+ +"4*
v++ ++
'0 , V1
(u! < J j'j , 0(]0&t0&,1, J j'j , h(]0&
tjj<1 j<1
++ ++
; J 'j * 1('j * h(]0&*1tj , y j'j , h(]jtj
+"c= Vc=
//
< z Yaj * 1('j * h(]j*1 , j'j , h(]j[tj-Vc=
J] a_q]_eˆj `a Jacaj`na 102
Rf prpqfqrfjlp bp^ppbofbpbk i^ b`r^`fŽk afcbobk`f^i '5-24(+ sbjlp nrb i^ b`r^`f5kpb p^qfpc^`bpf+v p50/ pf+ilp `lbcf`fbkqbpp^qfpc^`bki^ obi^`f5k
&j * 0'&j * h']j)1 , j&j + h']j , 0j]j * /'/' * h']j < N
m^o^qlal j y -/- Dpq^b`r^`fŽk bp i^ jfpj^ nrb
&j * 0'&j * h']j)0 + &j + l`('k * 0 * M&']j < N+
l
'5-25('l` , k('l` * j * 0(
]j*1 < , 'j * 0('j * 1( ]jŒ
Dpq^obi^`fŽk klp mbojfqb abqbojfk^o ]1+ ]e*]5+ ŒŒŒ+ pr`bpfs^jbkqb bk crk`f5k ab]: @kŠild^jbkqb+ mlabjlp `^i`ri^o ]2+ ]o+],+--- +bk crk`f5k ab /0& O^o^ ilp `lb,cf`fbkqbp`lk Œkaf`bpm^obpqbkbjlp
l`'l` * 0(]1 < , ]k+
0•1
]3
< ] 'l` , 1('/' * 2( ]1
< ']0(1 l`'N' , 1('l` * 0('l` * 2( ]k
2• 3 3 &v+ bk dbkbo^i+
\ j HW'N', 1( --- 'l` , 1j * 1( - 'l` * 0('HW * 2( - , - 'HW* 1j , 0(]1j , ',0( ,,,,,,,,,,,,,,,,,,,,,, ]k,
&0j'
Dpql mrbab abjlpqo^opb mlo fkar``fŽk- O^o^ ilp `lbcf`fbkqbp `lk Œkaf`bpfjm^obpbk`lkqo^jlp
\ &\G'j 'l` , 0('l` , 2( , - , 'l` , 0j * 0( , 'N' * 1('HW * 3( , -- 'HW* 0j']1j)0 , ,,,,,,,,,,,,y,y&,,,,&,,,,&,,,&,,,,! ]
&0j * 0( 0,
Olo `lkpfdrfbkqb+i^ pbofbnrb abcfkb v mrbab bp`of_fopb^pŒ
'5-26(
alkab
'5-27( //
{'u( < 0! * •' \0(j N'HW, 1( --- 'HW, 0j * 1( - 'HW* 0('/' * 2( - , - 'l` * 0j + 0( 1j
j;h &0j' t
103 C_q]_ekjao `ebanaj_e]haoheja]hao
v
'5-28(
\ y&\h'j &GV‹,, /'&GV‹,, 2(&--&GV+ 0j * 0(&&GV* 0'&GV* 3(&-- '/09 * 0j' V0j)0q0&t' + t * z &0j * 0( -
U`S
Di `ofqbofl abi `l`fbkqb abjrbpqo^ nrb `^a^ rk^ ab bp^p pbofbp`lksbodb m^o^Hui; 0- @pfjfpjl+ v^ nrb i^ obi^`fŽk '5-25( pb p^qfpc^`bpbm^o^a^jbkqb mlo ilp`lbcf`fbkqbp m^obpb fjm^obp+ `^a^ rk^ ab i^p crk`flkbp ii\- v z bp rk^ plir`f5kab i^ b`r^`f5k afcbobk`f^i '5-24(- Dp^pplir`flkbp p^qfpc^`bki^p `lkaf`flkbp fkf`f^ibp
T0'/( < 0+ Sy'M( < N+ Sy'M( < 0-
Orbpql nrb S0 X S1 plk fkabmbkafbkqbp+i^ plir`f5k dbkbo^i ab i^ b`r^`f5k ab Kb,dbkaob '5-24( bk bi fkqbos^il ^_fboql ',,0+ 0( sfbkb a^a^ mlo i^ `lj_fk^`f5kifkb^i '5-26( `lk i^p `lkpq^kqbp ^o_fqo^of^p P v '0{-
Br^kal ] bp } l rk bkqbol m^o mlpfqfsl+ mlo bgbjmil ] < 0i* i^ pbofbabq/&t' pb qo^kpcloj^ bk rk mlifkljfl ab do^al 1i nrb p50/ `lkqfbkb mlqbk`f^pm^obpab t- Orbpql nrb qbkbjlp
v
ni&/09'/09 , 1( --- '/09 ’-- 0j * 1( < 0i&0i + 1( --- &0i + 0j * 1( <- -&i + j'
'/09 * 0('/09 * 2( --- '/09 * 0j + 0( < &0i * /'&0i * 2( --- &0i * 0j + 0(
< &0i * 0j' i
0j&0i' &i * j'
i^ c5ojri^ nrb a^ qz&t' bk bpqb`^pl pb qo^kpcloj^ bk
'5-3/( '( 0 &i '0 y&h'g &0i * 0g' 0gT
0 t < * &0i ' 5, &i \ g' &i * g' &0g' t ,
Olo bgbjmil+ `r^kal ] < /+ 1+ 3+ 5 &i < /+ 0+1+ 2( ilp mlifkljflp `loobpmlk,afbkqbp plk
0 , 2t1*
K^ pbofbnrb a^ q1&t' kl bp rk mlifkljfl `r^kal ] bp m^oab_fal ^ nrb bi `lbcf,`fbkqb ab V0j)/ krk`^ bp `bol-
Br^kal ] bp rk bkqbol eil]n+ pb fksfboqbk ilp m^mbibpab T0 X q1: i^ pbofb
Nkhejkieko `a Jacaj`na 104
`loobpmlkafbkqb ^ S1'V( pb `lksfboqb bk rk mlifkljfl v i^ pbofbab qG&t' kl bp rkmlifkljfl- Blk`obq^jbkqb+ pf •] < 0i * ($ qbkbjlp
&4,2/' q0&t' < u * &i '0 x,',0( g &0i * 0g * 0( V0g)/,
&0i * 0( 5 &i + g' &i * g' &0g * 0(
Olo bgbjmil+ `r^kal ]<h+ 2+ 4 'i<M+ ($)!$ ilp mlifkljflp `loobpmlkafbkqbpplk
.')1 BXURWXVRX\MN>NPNWM[N
@idrk^p ab i^p molmfba^abpab i^p plir`flkbp mlifkŽjf`^p ab i^ b`r^`fŽk abKbdbkaob mrbabk abar`fopb afob`q^jbkqb ^ m^oqfoab i^ b`r^`fŽk afcbobk`f^i l abi^p cŽojri^p '5-3/( v '5-30(- Nqo^ppb abar`bk jŠp cŠ`fijbkqb m^oqfbkal ab lqo^cŽojri^ m^o^bplp mlifkljflp nrb abar`fobjlp ^elo^-
N_qbkaobjlp mofjbol rk^ •kf`^ cŽojri^ nrb `lkqfbkb 'p^isl c^`qlobp `lkp,q^kqbp(ilp mlifkljflp '5-3/( v '5-30(- Olkd^jlp
'5-31(0Zk.1i &+/W&0j + 0n' j+0n
l &t'< , !!y+y++++t *j 1j‚n 'j,n( 'j,1n(
Y4=
alkab Yj-0[ obmobpbkqbi j^vlo bkqbol 994k.1- Cbjlpqo^objlp irbdl nrb ‹pb bpbi lkhejkiek `a Jacaj`na ab do^al j fkqolar`fal bk bi `^mŒqril0- Br^kal j bpm^o+bp rk j•iqfmil `lkpq^kqb abi mlifkljfl qG&t' ab i^ b`r^`fŽk '5-3/(: `r^kal jbp fjm^o+ bp rk j•iqfmil `lkpq^kqb abi mlifkljfl q1&t' ab '5-30(- ')( Klp pfbqbmofjbolp mlifkljflp ab Kbdbkaob sfbkbk a^alp mlo i^p cŽojri^p
NM&t' < 0+ NG&t' < t* N1&t' < p&1t1 , 0(+ N2&t' < p&3t2 , 1t'*
N2&t' < +h&13t2+ 1.t1 * 2(+ Nˆ&t' < +h&41t4 , 5.t2 * /3t'*
N4&t' < h4&01/t4 + 1/3t2 * /.3t1 , 4(-
>J cfdro^ 5-0 jrbpqo^ i^p doŠcf`^pab i^p `fk`l mofjbo^p ab bp^p crk`flkbp bk bifkqbos^il Z,0+0\-
')( Br^kal j bp m^o+j < 1i+ mlabjlp obbjmi^w^o bi Œkaf`bab prj^`f5k g bk '5-3/(mlo lqol n* pfbkal o < i + g: bk`lkqo^jlp nrb i^ prj^ '5-3/( bp bi molar`ql ab N,&t' mlork^ `lkpq^kqb- @kŠild^jbkqb+ `r^kal j bp fjm^o- rk `^j_fl ab Œkaf`bqo^kpqloj^ i^ prj^'5-30( bk bi molar`ql ab N,&t' mlo rk^ `lkpq^kqb-
105 C_q]_ekjao `ebanaj_e]haoheja]hao
u
t
EHFTQ@ 5-0 En…be_]oa hko lkhejkieko `a Jacaj`na aj ah ejpanr]hk Z,0- 0\
Olabjlp ^elo^ abjlpqo^o nrb+ p^isl c^`qlobp bp`^i^obp+ilp mlifkljflp abKbdbkaob plk ilp nrb pb l_qfbkbk ^mif`^kal bi mol`bpl ab loqldlk^ifw^`fŽk abFo^j,R`ejfaq ^ i^ pr`bpfŽk ab mlifkljflp 0+u+ t1
+ ŒŒŒ + `lk bi molar`ql fkqboflo
'g+d( < qHb't(c't( `t +
N_pbosbjlp mofjbol nrb pf i <D j Œlpmlifkljflp N: v Ni plk loqldlk^ibpmlonrb plk ^rqlcrk`flkbp ab rk lmbo^alo pfj‹qof`l mboqbkb`fbkqbp ^rqls^ilobpafpqfkqlp- S^j_f‹k+ mrbpql nrb N| qfbkb do^al j v Ol < 0+ ilp mlifkljflpNk&t'* N/&t'* ,‹, *Nj&t' bkdbkao^k bi jfpjl pr_bpm^`fl nrb 0+t+--- -t!- Dk i^pb``fŽk 0-03+ bgbjmil 1+ `lkpqorfjlp lqol `lkgrkql loqldlk^i ab mlifkljflpXl+ Xi *W0 * * q^ibpnrb Wk&t' *Wh&V' * ,,, *Wj&V' bkdbkao^k bi jfpjl pr_bpm^`flnrb 0+t: +tj m^o^`^a^ j- Di qblobj^ ab loqldlk^ifw^`fŽk 'qblobj^ 0-02( klpaf`b nrb+ p^isl c^`qlobp bp`^i^obp+bufpqbrk plil `lkgrkql ab crk`flkbp loqldlk^ibp`lk bp^ molmfba^a-Krbdl ab_b pbo
D‰niqh]`a Pk`necqao l]n] hkolkhejkieko `a Jacaj`na 106
m^o^`fboqlp bp`^i^obpa: Di `lbcf`fbkqb ab t! bk Wj'V( bp 0+^pŒnrb _| bp bi `lbcf,`fbkqb ab t! bk Nj&t', Cb '5-31( sbjlp nrb
'1j( b <,,-,-
! 0!&j '0
5-1/ EŽojri^ ab Qlaofdrbp m^o^ilp mlifkljflp ab Kbdbkaob
Dk i^ prj^ '5-31( nrb abcfkb Nj&t' l_pbos^jlp nrb
'1j , 1n( j,1n `! 1j,1n++++t ;+t'j , 1n( `t!
v 0 0 'j(n 'j , n( < j n &
alkab 'z( bp bi `lbcf`fbkqb _fkljf^i+ v bp`of_fjlp i^ prj^ bk i^ cloj^
0 `j /5/-0/
Net( < ,, !! '\0n'j(t1j,1n-1jj `tj J+ n
X8?
Br^kal Yj-0[ ; o z j* bi q‹ojfkl t0j+0n qfbkb do^al jbklo nrb j* mlo 0/ nrbpr abofs^a^ j,†oei] bp `bol- Olo `lkpfdrfbkqb+kl pb ^iqbo^i^ prj^ pf e^`bjlp nrbo ob`loo^ ilp s^ilobp ab N ^ j- Dpql klp a^
0 `j 5/
Nj't( <,, !!'\hn'j(t1j,1n-1jj `t! J+ n
X8?
Ubjlp ^elo^ nrb i^ prj^ abi pbdrkal jfbj_ol bp bi abp^ooliil abi _fkljfl&t1 , i(!- Olo `lkpfdrfbkqb+qbkbjlp
0 `jNj't( < , , 't1 , 0(!-
1jj `t!
Dpq^pb `lkl`b `lk bi klj_ob ab b‰niqh] `a Pk`necqao+bk elklo ab Nifkab Ql,,aofdrbp '0683,0740(+ b`lkljfpq^ v obcloj^alo co^k`‹p-
Blk i^ cŽojri^ ab Qlaofdrbp v i^ b`r^`fŽk afcbobk`f^i+mlabjlp abar`fo rkk•jbol ab molmfba^abpfjmloq^kqbp ab ilp mlifkljflp ab Kbdbkaob- @idrk^p abbp^p molmfba^abppb `fq^k ^ `lkqfkr^`fŽk- Rrp abjlpqo^`flkbp bpqŠkbp_lw^a^p bkbi `lkgrkql ab bgbo`f`flp nrb pfdrb-
O^o^ `^a^ j >9N qbkbjlp
N**&h'< 0-
107 C_q]_ekjao `ebanaj_e]haoheja]hao
@abjŠp+ Nj&t' bp bi •kf`l mlifkljfl nrb p^qfpc^`b i^ b`r^`fŽk ab Kbdbkaob
'i , t1'u! + 1tu&* j'j * h'u < N
v s^ib 0 `r^kal t < 0-O^o^ `^a^ j y N qbkbjlp
Dpql abjrbpqo^ nrb Nj bp rk^ crk`fŽk m^o `r^kal j bp m^o+v rk^ crk`fŽk fjm^opf j bp fjm^o-
X^ ebjlp jbk`flk^al i^ obi^`fŽk ab loqldlk^ifa^a+
pf i u 9j-
Br^kal i < j qbkbjlp i^ bumobpfŽk ab i^ kloj^
HHOki01< HGYNet([1 `t < ]1]-+/ 0j * 0
Slal mlifkljfl ab do^al j mrbab bumobp^opb`ljl `lj_fk^`fŽk ifkb^i ab ml,ifkljflp ab Kbdbkaob Nk+N +--- +N• Dk bcb`ql+ pf b bp rk mlifkljfl ab do^al jqbkbjlp
alkab
j
b't( < _gNet(+S4=
@ m^oqfoab i^ obi^`fŽk ab loqldlk^ifa^a obpriq^ nrb
qHc&t'N j'V( `t < N
m^o^ qlal mlifkljfl d ab do^al jbklo nrb j- Dpq^ molmfba^a mrbab rp^opb m^o^abjlpqo^o nrb bi mlifkljfl ab Kbdbkaob N j qfbkb j `bolp ob^ibp v afpqfkqlp pfqr^,alp qlalp bk bi fkqbos^il ',0+ 0(-
5-1 q Dgbo`f`flp
0- K^ b`r^`fŽk ab Kbdbkaob '5-24( `lk ! < N qfbkb bi mlifkljfl plir`fŽk qz&t' < 0 X rk^
Cfan_e_eko 108
plir`fŽk kl mlifkŽjf`^+ a^a^ mlo i^ pbofb '5-30(-^( Cbjlpqo^o nrb i^ prj^ ab i^ pbofb nrb a^ q+sfbkb a^a^ mlo
0 0 * tS1'V( < ,ild,,
1 0 , tm^o^ Hui; 0-
_( Bljmol_^o afob`q^jbkqb nrb i^ crk`fŽk q+ab i^ m^oqb- ( bp rk^ plir`fŽk ab i^b`r^`fŽk ab Kbdbkaob `r^kal ] < N-
1- Cbjlpqo^o nrb i^ crk`fŽk b abcfkfa^ mlo i^ b`r^`fŽk
t 0 * tb'tx < 0 , 1!ild 0 ] t
m^o^ Gth; 0 p^qfpc^`b i^ b`r^`fŽk ab Kbdbkaob '5-24( `lk ] < 0- Dumobp^obpq^ crk`fŽk`ljl `lj_fk^`fŽk ifkb^i ab i^p plir`flkbp q+v q+a^a^p mlo i^p b`r^`flkbp '5-27( v'5-28(-
2- K^ b`r^`fŽk ab Kbdbkaob '5-24( mrbab bp`of_fopbbk i^ cloj^
Y&t1 , /'u%[%+ bu' bu * hxu < N-
^( Rf ]+^+a plk `lkpq^kqbp pfbkal ] = ^ v 3_ * 0 = N+abjlpqo^o nrb i^ b`r^`fŽk afcb,obk`f^i abi qfml
Y&t + ]'&t + ^xu&[&, _u < N
mrbab qo^kpcloj^opb bk rk^ b`r^`fŽk ab Kbdbkaob jbaf^kqb rk `^j_fl ab s^of^_ib abi^ cloj^ t < ?p * @+ lk ? = l- Cbqbojfk^o ? v @ bk crk`fŽk ab ] v ^-_( Tqfifw^obi j‹qlal prdbofal bk i^ m^oqb^( m^o^ qo^kpcloj^o i^ b`r^`fŽk
&t1 , t'u! * &0t + iyv& , 0u < N
bk rk^ b`r^`fŽk ab Kbdbkaob+3- G^ii^o alp plir`flkbp fkabmbkafbkqbp+bk cloj^ ab pbofb ab mlqbk`f^p+ ab i^ a_q]_e‰j
`a Faniepa
! -\#W , W * 1atu < N
bk rk fkqbos^il ab i^ cloj^ &+n*n', Cbjlpqo^o nrb rk^ ab bp^p plir`flkbp bp rk mliŒkljfl `r^kal ] bp bkqbol kl kbd^qfsl-
R- G^ii^o rk^ pbofb ab mlqbk`f^p plir`fŽk ab i^ b`r^`fŽk afcbobk`f^i
tu! * '2 * n'u%* 1t1u < N
sŠifa^ m^o^ qlal t- G^ii^o rk^ pbdrka^ plir`fŽk ab i^ cloj^ u < t,&H]!t! sŠifa^ m^o^VyM,
5- G^ii^o rk^ pbofb ab mlqbk`f^p plir`fŽk ab i^ b`r^`fŽk afcbobk`f^i
t1u! * thu& , '`uu * 0'u < N
--+ C_q]_ekjao `ebanaj_e]haoheja]hao
sŠifa^ bk rk fkqbos^il ab i^ cloj^ &+n*n',6- C^a^p alp crk`flkbp ? v @ ^k^iŒqf`^pbk rk fkqbos^il &tk + n*tk * n'*
//
?&t' < ]j&t + tk'j*V4=
//
@&t' < ^j&t + tk'j,V4=
Orbab abjlpqo^opb nrb bi molar`ql A&t' < ?&t'@&t' bp q^j_f‹k ^k^iŒqf`^bk &tk + n*Vk * n', Dpqb bgbo`f`fl abjrbpqo^ nrb B qfbkb bi abp^ooliil bk pbofb ab mlqbk`f^p
//
A&t' < _j&t + Vk'j*V'=
jalkab Aj < ]g^j+g ,
S4*
^( Blk i^ obdi^ ab Kbf_kfw m^o^ i^ abofs^a^ k,‹pfj^ ab rk molar`ql abjlpqo^o nrb i^abofs^a^ k,‹pfj^ ab B sfbkb a^a^ mlo
_&j'&t' < f&j'?&gh &t'@&j+gh &t' *g,M g
_( G^`bo rpl abi eb`el ab nrb ?&gH&tk' < g ]g v @&j+gH&tk'< &j + g( ^-,g m^o^l_qbkbo
j_&jh&tk' < j ]g^j+g%
S4=
Orbpql nrb BH!('ul( < j a: nrba^ abjlpqo^a^ i^ cŽojri^ nrb a^ aŒŒ
Dk ilp bgbo`f`flp abi 7 ^i 03+N,&t' abpfdk^ bi mlifkljfl ab Kbdbkaob ab do^al j* Dplpbgbo`f`flp a^k bi bpnrbj^ ab i^p abjlpqo^`flkbp ab i^p molmfba^abp ab ilp mlifkljfklp abKbdbkaob abp`ofq^p bk i^ pb``fŽk 5-1/-
7- ^( Blk i^ cŽojri^ ab Qlaofdrbp abjlpqo^o nrb
iNj&t' < 0j &t * I(! * &t + h'Oj&t'*
alkab O,&t' bp rk mlifkljfl-_( Cbjlpqo^o nrb O-N( < 0 X nrb N,&+/' < ',0(!+`( Cbjlpqo^o nrb N,&t' bp bi •kf`l mlifkljfl plir`fŽk ab i^ b`r^`fŽk ab Kbdbkaob'`lk HW < j' nrb qfbkb s^ilo 0 `r^kal t < 0-
8- ^( Tqfifw^o i^p b`r^`flkbp afcbobk`f^ibp ^ i^p nrb p^qfpc^`bkO-v Oj m^o^ abjlpqo^o nrb
_( Rf i y j+ fkqbdo^oi^ b`r^`fŽk abi ^m^oq^al ^( abpab ,0 ^ 0 m^o^ a^o lqo^ abjlpqo^`fŽk ab i^ obi^`fŽk ab loqldlk^ifa^a
Cfan_e_eko 110
iN+ ^( Rb^ b&t' < &t%+ 0(!+ Blk i^ fkqbdo^`fŽkmlo m^oqbpabjlpqo^o nrb
@mif`^obpq^ cŽojri^ obfqbo^a^jbkqb m^o^ abar`fo nrb i^ fkqbdo^iabi mofjbo jfbj_olbp fdr^i ^
0&0j' H8'0 , t1(j `t *
_( K^ prpqfqr`fŽk t < `lp p qo^kpcloj^ i^ fkqbdo^i j '0 , t%'j `t bk Qc.1 pbk0j)hp `p+Djmib^o i^ obi^`fŽk
/!-1 0j&0j + 1( --- 1pfk1k* p `p < ,,,,,,,,,,
l &0j * /'&0j + 0( --- 2 - 0
v i^ cŽojri^ ab Qlaofdrbp m^o^ l_qbkbo
>H 1YNj'V([1 `t < 1,,0 -
+/ j )
00+ ^( Cbjlpqo^o nrb
alkab O,&t' bp rk mlifkljfl ab do^al jbklo nrb j-_( Dumobp^obi mlifkljfl b&t' < t% `ljl `lj_fk^`fŽk ifkb^i ab Ol+OH+N1+ N2+ X N*,b( Cbjlpqo^o nrb qlal mlifkljfl b ab do^al j mrbab bumobp^opbljl `lj_fk^`fŽkifkb^i ab ilp mlifkljflp ab KbdbkaobOl+OH+-- +&N-+
01- ^( Rf b bp rk mlifkljfl ab do^al j+ bp`of_fo
j
b't( < 1 AgNg'V(-S4=
ZDpqlbp mlpf_ib pbd•k bi bgbo`f`fl 00 b(-\ O^o^rk i cfgl+N9Ri 9R j+ jriqfmif`^o ^j_lpjfbj_olp ab bp^ b`r^`fŽk mlo Ni&t' b fkqbdo^obkqob ,0 v 0- Sbkfbkal bk `rbkq^ ilpbgbo`f`flp 8 _( X 0/ _( abar`fo i^ obi^`fŽk
0i * iIHAi < ,1, \-&t'N j &t' `t ,
02- Tqfifw^oilp bgbo`f`flp8 v 00 m^o^abjlpqo^o nrb D-Hc&t'N,&t' `t < Nm^o^qlal mlifkljfld ab do^al jbklo nrb j-
--- C_q]_ekjao `ebanaj_e]haoheja]hao
03- ^( Blk bi ^rufifl abi qblobj^ ab Qliib abjlpqo^o nrb N, kl mrbab qbkbo`bolp j•iqfmibpbk bi fkqbos^il ^_fboql ',0+0(- Dp ab`fo+ ilp `bolp ab N, nrb bpqŠk bk ',0+0( ab_bkpbo `bolp pfjmibp-_( Rrmlkd^jlp nrb N, qfbkb i `bolp bk bi fkqbos^il ',0+0(- Rf i < /+ pb^ Ok&t' < 0-Rf i y 0+ pb^
alkab V! V! ŒŒŒ+t: plk i `bolp ab l, bk ',0+ 0(- Cbjlpqo^o nrb+ bk `^a^ mrkql V ab',0+ 0(+Oi'V( qfbkb bi jfpjl pfdkl nrb N,&t',b( Blk bi ^m^oq^al _( v bi bgbo`f`fl 02+abjlpqo^o nrb i^ abpfdr^ia^a i ; j klp iibs^^ rk^ `lkqo^af``fŽk- Dpql abjrbpqo^ nrb N, qfbkb j `bolp ob^ibp afpqfkqlp+qlalp pfqr^alpbk bi fkqbos^il ^_fboql ',0+0(-
04- ^( Cbjlpqo^o nrb bi s^ilo ab i^ fkqbdo^iIzi Nj&V'Ny)h &t' `t bp fkabmbkafbkqb `aj-_( B^i`ri^o i^ fkqbdo^iIzi V Nj&t'Nj\/&t' `t -
.'** ?k]XMXMN9[XKNWR^\
Dk i^ pb``fŽk 5-06 ^mobkafjlp ^ bk`lkqo^o plir`flkbp+ bk cloj^ ab pbofbpabmlqbk`f^p+ab i^ b`r^`fŽk afcbobk`f^i
'5-32(
bk rk bkqlokl abi mrkql Wl bk bi nrb ilp `lbcf`fbkqbp OHv O1 plk ^k^iŒqf`lp-Rf rklab ilp alp OHl N1 kl bp ^k^iŒqf`lbk i^p molufjfa^abp ab tk+ mrbabk l kl bufpqfopbofbpab mlqbk`f^p plir`fŽk bk bi bkqlokl ab tkŒ Olo bgbjmil+ prmlkd^jlp nrb fk,qbkq^jlp bk`lkqo^o rk^ pbofbab mlqbk`f^p plir`fŽk ab i^ b`r^`fŽk afcbobk`f^i
'5-33( t1u! , u&, W < N
bk rk bkqlokl ab Wl < N-Rf prmlkbjlp nrb bufpqbrk^ plir`fŽk u < ]`& v i^prpqfqrfjlp bk i^ b`r^`fŽk afcbobk`f^i+iibd^jlp ^ i^ cŽojri^ ab ob`roobk`f^
j * 0
Rf _fbk bpql klp a^ rk^ pbofbab mlqbk`f^p u < ]gtg nrb cloj^ijbkqb p^qfp,c^`b '5-33(+ bi `ofqboflabi `l`fbkqb mlkb bk bsfabk`f^ nrb bp^ pbofb`lksbodb Šje_],iajpa m^o^t < N-@pŒmrbp+kl bufpqbpbofbab mlqbk`f^p plir`fŽk ab '5-33( sŠifa^bk `r^inrfbo fkqbos^il ^_fboql bk qlokl ^ Wl < N- Dpqbbgbjmil kl `lkqo^af`b biqblobj^ 5-02 mlonrb `r^kal mlkbjlp i^ b`r^`fŽk '5-33( bk i^ cloj^ '5-32( bk`lk,qo^jlp nrb ilp `lbcf`fbkqbp OHv O1 sfbkbk a^alp mlo
0 0N/&t' < , !1 X N1&t' < , , -
V t0
K†pk`k `a Dnk^ajeqo --.
Dpq^pcrk`flkbp kl ^ajfqbk abp^ooliil bk pbofbab mlqbk`f^p bk qlokl ^i lofdbk-K^ afcf`riq^a ^nrŒ o^af`^ bk nrb bi `lbcf`fbkqb ab u! bk '5-33( qfbkb bi s^ilo N`r^kal t < N: bp ab`fo+i^ b`r^`fŽk afcbobk`f^i qfbkbrk mrkql pfkdri^o bk t < N-
O^o^ ^mob`f^o i^p afcf`riq^abp nrb pb mobpbkq^kbk i^ fksbpqfd^`fŽk ab i^pb`r^`flkbp afcbobk`f^ibp bk i^p molufjfa^abp ab rk mrkql pfkdri^o bp kb`bp^ofl`lkl`bo i^ qbloŒ ab crk`flkbp ab s^of^_ib `ljmibg^- Rfk bj_^odl+ ^idrklp `^plpm^oqf`ri^obp ab b`r^`flkbp `lk mrkqlp pfkdri^obp mrbabk qo^q^opb lk j‹qlalpbibjbkq^ibp- Olo bgbjmil+ prmlkd^jlp i^ b`r^`fŽk afcbobk`f^i '5-32( bnrfs^ibkqb^ rk^ b`r^`fŽk ab i^ cloj^
'5-34( &t + VM(1u! * &t + tk'N&t'u% * O&t'u < N+
alkab O v P qfbkbkabp^ooliilp bk pbofbpab mlqbk`f^p bk rk `fboql fkqbos^il ^_fbo,ql 'u+, n+Vk * n(- Dk bpqb`^pl ab`fjlp nrb Vk bp cfk mrkql pfkdri^o nacqh]n abi^ b`r^`fŽk- Rf afsfafjlp ^j_lp jfbj_olp ab '5-34( mlo &t + VM(1 i^ b`r^`fŽk pbqo^kpcloj^ bk
u! * N&t' u&* O&t' u < Nt + Vk &t + VM(1
m^o^ t"+ tkŒ Rf N&tk( ", N l O&tk( ", N+l pf O&tk( < N X O%&tk( ", N+l bi `lbcf,`fbkqb ab u& l bi ab v kl qbkaoŠabp^ooliil bk pbofbab mlqbk`f^p bk qlokl ^i mrkqltk+ ^pŒnrb bi qblobj^ 5-02 kl bp ^mif`^_ib- Dk 0762 bi j^qbjŠqf`l ^ibjŠk IlodbEol_bkfrp '0738,0806( abp^ooliiŽ rk j‹qlal jrv moŠ`qf`l m^o^qo^q^oq^ibp b`r^,`flkbp- Dkrk`f^objlp bi qblobj^ ab Eol_bkfrp mbol kl a^objlp pr abjlpqo^,`fŽk- ')( Dk i^ pb``fŽk pfdrfbkqb a^jlp ilp abq^iibp ab i^ abjlpqo^`fŽk m^o^ rk`^pl m^oqf`ri^ofjmloq^kqb+i^ b`r^`fŽk ab Abppbi-
Di qblobj^ ab Eol_bkfrp pb abpal_i^ bk alp m^oqbp+nrb abmbkabk ab i^k^qro^ibw^ab i^p o^Œ`bpab i^ b`r^`fŽk `r^aoŠqf`^
'5-35( p&p+ 0( * N&tk'p * O&tk' < N-
Dpq^b`r^`fŽk `r^aoŠqf`^ pb ii^j^ i^ a_q]_e‰j `a ‡j`e_ao ab i^ b`r^`fŽk afcbobk`f^ia^a^ '5-34(- Klp `lbcf`fbkqbp N&tk( v O&tk( plk ilp q‹ojfklp `>kpq^kqbpab ilpabp^ooliilp ab O v P bk pbofbpab mlqbk`f^p- Rb^k ]h v ]0 i^p o^Œ`bpab i^ b`r^`fŽkab Œkaf`bp-Di qfml ab plir`fŽk nrb pb l_qfbkb mlo bi j‹qlal ab Eol_bkfrp ab,mbkab ab pf bp^p o^Œ`bpafcfbobkl kl bk rk k•jbol bkqbol-
')( O^o^ i^ abjlpqo^`fŽk s‹^pb D- Gfiib+ ?j]huoeo+Uli- 00+Ai^fpabii Or_ifpefkd Bl-+0855+l D- @- Blaafkdqlk+ ?j Gjpnk`q_pekj pk Mn`ej]nu Beffanajpe]hCmq]pekjo+Oobkqf`b,G^ii+0850-
113 C_q]_ekjao `ebanaj_e]haoheja]hao
SDNQDL@ 5-03- OQHLDQ B@RN CDK SDNQDL@ CD EQNADMHTR- Qa]j ^i u]1 h]on]‡_ao`a h] a_q]_e‰j`a ej`e_ao-u oqlkjc]iko mqa ^i , ]1 jk ao qj ajpank- Cj,pkj_ao h] a_q]_e‰j`ebanaj_e]h '5-34( peaja `ko okhq_ekjao ej`alaj`eajpao q+u S1
`a h] bkni]
`b
'5-36( qz't( < Zu , tkh]z J ]jAt , tk(j+ _kj ]k < 0+jyM
u^l
'5-37( qvAt( < Zu , tkh]ŒJ ^j't , tk(j+ _kj ^‚ < 0-jyM
?i^]o oaneao_kjrancaj aj ah ejpanr]hk Gt + uli ; n+u h] a_q]_e‰j`ebanaj_e]hoao]peob]_al]n] N ; Gt , tkh ; o-
SDNQDL@ 5-04- RDFTMCN B@RN CDK SDNQDL@ CD EQNADMHTR- Qa]j ^i W]1
h]o n]‡_ao a h] a_q]_e‰j`a ej`e_ao v oqlkjc]iko mqa ^i , ]1 < L ao qj ajpankjk jac]perk- Cjpkj_ao h] a_q]_e‰j`ebanaj_e]h '5-34( peaja qj] okhq_e‰jq+`a h]bkni] '5-36( u kpn] okhq_e‰jej`alaj`eajpa S1 `a h] bkni]
^l
q0't( < Zu , tkh]ŒJ ^jAt , tk(j * B qz't( ild Zu , tkh+V4=
`kj`a ^‚ < 0- J] _kjop]jpa B jk ao jqh] oe L < N- Qe L = N+ h] _kjop]jpa Blqa`a k jk oan _ank- Akik aj ah _]ok 0+]i^]o oaneao_kjrancaj aj ah ejpanr]hkHu, tkh ; n+v h]o okhq_ekjao okj r…he`]ol]n] N ; Hu, tkh ; n+
5-12 D`r^`fŽk ab Abppbi
Dk bpq^ pb``fŽk rqfifw^jlp bi j‹qlal prdbofal mlo Eol_bkfrp m^o^ obplisboi^ b`r^`fŽk ab Abppbi
'5-38(
alkab ] bp rk^ `lkpq^kqb kl kbd^qfs^- Dpq^b`r^`fŽk pb bjmib^ bk mol_ibj^p obi^,qfslp ^ sf_o^`flkbp ab jbj_o^k^p+ cirgl ab `^ilo bk `fifkaolp+ v molm^d^`fŽk ab`loofbkqbp bi‹`qof`^p bk `lkar`qlobp `fiŒkaof`lp-@idrk^p ab prp plir`flkbp pb `l,kl`bk `lk bi klj_ob ab bqj_ekjao `a @aooah-S^j_f‹k pb mobpbkq^kbp^pcrk`flkbpbk SbloŒ^ ab M•jbolp- K^ b`r^`fŽk qljŽ bi klj_ob abi ^pqoŽkljl ^ibjŠkE- V- Abppbi'0673,0735(+ pf _fbk v^ ^m^ob`b bk i^p fksbpqfd^`flkbp ab C^kfbiAboklriif '0621( v ab Dribo '0653(-
K^ b`r^`fŽk ab Abppbi qfbkb i^ cloj^ '5-34( `lk t• < N+ N&t' < 0+ X
C_q]_e‰j a @aooah 114
O&t' < t1, |+ ab jlal nrb bi mrkql Wl bp rk mrkql pfkdri^o obdri^o- Orbpql
nrb N v P plk ^k^iŒqf`^pbk qla^ ob`q^ ob^i+fkqbkq^jlp bk`lkqo^o plir`flkbp abi^ cloj^
'5-4/(//
u < Gthp0] ‹‹t!*&’’</
`lk ^l <0< N+sŠifa^ m^o^qlal t ob^i `lk i^ mlpf_ib bu`bm`fŽk ab t < N-Oofjbol j^kqbkbjlp t = N+ab jlal nrb t q < t&+K^ abofs^`fŽk ab '5-4/(
klp a^
// // //
u&< ptp,0 J ] ŒŒu! * uqJ j] ŒŒt!,h < uq
,0 J 'j * p(]ŒŒu! -
’’</ ’’zN ’’</
@kŠild^jbkqb+ l_qbkbjlp
//
u! < tp,10 'j * p('j * p , h(] ŒŒu! -bb8+
RfJ&u' < t1u! * tu%* &t1 , k_1'u* bk`lkqo^jlp
// //
J'u( < tp 1 'j * p('j * p , h(] ŒŒu! * tp J 'j * p(]ŒŒu!’’</ ’’</
++ ++ ++ ++
* uq J ] ‹‹t!*1 , uq 1 l`0^ ’’u! < uq J Yaj * p(1 , k_1[]!t! * tp 1 ] ŒŒt!*1 Œ’’</ ’’</ ’’</ ’’</
Olkd^jlp ^elo^ J&u' < N+prmofj^jlp tp+b fkqbkqbjlp abqbojfk^o ilp ^! ab jlalnrb bi `lbcf`fbkqb ab `^a^ mlqbk`f^ ab t pb ^krib- O^o^ bi q‹ojfkl fkabmbkafbkqbbp kb`bp^ofl nrb 'q1 , ]1']k < N- Bljl nrfbo^ nrb _rp`^jlp rk^ plir`fŽk `lk]• <0< N+bpql bufdb nrb
'5-40( p1 , l`1 < N-
Dpq^bp i^ a_q]_e‰j a ‡j`e_ao- Rrp o^Œ`bp] v ,] plk ilp •kf`lp s^ilobp mlpf_ibpab p nrb klp mrbabk a^o rk^ plir`fŽk abi qfml abpb^al-
Blkpfabobjlp mofjbol p < ]- O^o^ bpq^ p+i^p b`r^`flkbp obpq^kqbpm^o^ i^abqbojfk^`fŽk ab ilp `lbcf`fbkqbp pb qo^kpcloj^k bk
'5-41( Z'0 * NB(1 , l`1\^0 < N v
m^o^j y 1- Orbpql nrb ] w N+i^ mofjbo^ ab bp^pfjmif`^ nrb ^i < N-K^ pbdrka^
115 C_q]_ekjao `ebanaj_e]haoheja]hao
cŽojri^ mrbab bp`of_fopb bk i^ cloj^
'5-42(]j\1
j&j * 10W(+
`lk il nrb ]2 < ]‚ < ]+ < --- < N- O^o^ ilp `lbcf`fbkqbp `lk Œkaf`bp m^obp qb,kbjlp
] , ,]13 , 3'3 * 10W(
] \ ,]3 < &+/'1]k
5 , 5'5 * 10W( 152 '0 * 0W('1 * 0W('2 * HW(+
&+/'0]k
131 '0 * 0W('1 * HW(+
v+ bk dbkbo^i
] \ ',h(j]k1j , 11jj '0 * 0W('1 * HW(--- &j * HW(-
Olo `lkpfdrfbkqb+ i^ bib``fŽk p < ] klp a^ i^ plir`fŽk
Di `ofqbofl abi `l`fbkqb abjrbpqo^ nrb i^ pbofb ab mlqbk`f^p nrb ^m^ob`b bk bpq^cŽojri^ `lksbodb m^o^ qlal t ob^i-
Dk bpq^ afp`rpfŽk ebjlp prmrbpql nrb t = N- Rf t ; N mlabjlp obmbqfoi^obbjmi^w^kal tp mlo '\t(p- Dk`lkqo^jlp krbs^jbkqb nrb p ab_b p^qfpc^`bo i^b`r^`fŽk p1
, ]1 < N- G^`fbkal p< ] l_qbkbjlp i^ jfpj^ plir`fŽk+ p^isl nrb bic^`qlo buqbokl t! nrba^ obbjmi^w^al mlo &+t'!, Olo q^kql i^ crk`fŽk bbu a^a^ mloi^ pbofb
'5-43( q• < ]k Zu\! '0 * ]]z']]yh(\jt\1j (
j<h 11jj '0 * 0W('1 * HW(--- &j * HW(
bp rk^ plir`fŽk ab i^ b`r^`fŽk ab Abppbi sŠifa^ m^o^ qlal ob^i t <0< N- O^o^ ilp s^,
ilobp ab HW m^o^ ilp nrb bufpqbkGy'N( X/9&.'* i^ plir`fŽk q^j_f‹k bp sŠifa^ m^o^t < N-
Blkpfabobjlp ^elo^ i^ o^Œwp < ,] ab i^ b`r^`fŽk ab Œkaf`bp- N_qbkbjlp bkird^o ab '5-41(+ i^p b`r^`flkbp
v
C_q]_e‰j `a @aooah 116
nrb pb `lksfboqbk bk
'i , 10W(^i < N v j&j + 0/V']j * ]j,1 < N-
Rf 1] kl bp bkqbol bp^pb`r^`flkbp klp a^k ]h< N X
m^o^k z 1- Orbpql nrb bpq^cŽojri^ ab ob`roobk`f^ bp i^ jfpj^ nrb '5-42(+ `lk ]
prpqfqrfa^ mlo ,]+ iibd^jlp ^ i^ plir`fŽk
'5-44( b,ht( < ]k iuf,^ '0 * ]- ']]0(\jt\1j (kzi 1•jj '0 , 0W('1 , HW(--- &j + HW(
sŠifa^ m^o^qlal ob^i t <0< N-K^ plir`fŽk b,`u pb l_qrsl bk i^ efmŽqbpfpab nrb 1] kl bp rk bkqbol mlpfqfsl-
Ml l_pq^kqb+i^ pbofbnrb a^ b ,`u qfbkb pbkqfal fk`irpl pf h] bp rk bkqbol ml,pfqfsl- bk q^kql nrb ] kl pb^ bkqbol mlpfqfsl- Orbab `ljmol_^opb nrb b ,`u p^qfpc^`bi^ b`r^`fŽk ab Abppbim^o^q^i s^ilo ]- Olo `lkpfdrfbkqb+ m^o^`^a^ ] y N qbkbjlpi^ pbofbplir`fŽk b`u+ a^a^ mlo '5-43(: X pf ] kl bp rk bkqbol kl kbd^qfsl ebjlp bk,`lkqo^al lqo^ plir`fŽk b,at- a^a^ mlo '5-44(- K^p alp plir`flkbp b `u v f,• plk fkab,mbkafbkqbp+v^ nrb rk^ ab bii^p z // `r^kal t y N+X i^ lqo^ kl- Rbdrfa^jbkqbpfjmifcf`^objlp i^ cloj^ ab i^p plir`flkbp- O^o^biil kb`bpfq^jlp ^idrk^p molmfba^,abp ab i^ crk`fŽk d^jj^ ab Dribo nrb _obsbjbkqb s^jlp ^ ob`loa^o-
O^o^ `^a^ ob^i p = N abcfkfjlp obp( jbaf^kqb i^ fkqbdo^ifjmolmf^
obp(< /!! pQ,0a,p`p ++&
Dpq^fkqbdo^i`lksbodb pf p = N v afsbodb pf o 4 N- K^ fkqbdo^`fŽkmlo m^oqbpklp`lkar`b ^ i^ b`r^`fŽk crk`flk^i
'5-45(
Dpql fjmif`^ nrb
obp* 0( < o obp(-
obp* 1( < 'o * 0(o'p * 0( < 'o * h(o obp(+
obp* 2( < 'o * 1(o'p * 1( < 'o * 1( 'o * h(o obp(+
v+ bk dbkbo^i
'5-46( obp* j( < 'o * j , 0( --- 'o * h(o obp(
--3 C_q]_ekjao `ebanaj_e]haoheja]hao
m^o^ qlal bkqbol mlpfqfsl j- Orbpql nrb o'0(< Q9%an&p < 0+ `r^kal mlkbjlpp < 0 bk '5-46( bk`lkqo^jlp
o'k * 0( < j ,
@pŒmrbp+ i^ crk`fŽk d^jj^ bp rk^ buqbkpfŽk ab i^ crk`fŽk c^`qlof^i ab ilp bkqb,olp ^ ilp k•jbolp ob^ibp mlpfqfslp-
K^ b`r^`fŽk crk`flk^i '5-45( mrbab rp^opb m^o^ buqbkabo i^ abcfkf`fŽk abobp( ^ s^ilobp kbd^qfslp ab o nrb kl pb^k bkqbolp- Dp`of_^jlp '5-45( bk i^ cloj^
'5-47( obp(< obp* 0( -p
Di pbdrkal jfbj_ol qfbkb pbkqfal pf o * 0 = N v o " N- Olo `lkpfdrfbkqb+ mlab,jlp rp^o bp^ b`r^`fŽk m^o^ `abejen o'p( pf ,0 ; o ; N- Di pbdrkal jfbj_ol ab'5-47( qfbkb ^elo^ pbkqfal pf o * 1 = N+ o " ,0+ o " N+ X mlabjlp rp^o bp^b`r^`fŽk m^o^ abcfkfo o'p( m^o^ ,1 ; o ; ,0- Blkqfkr^kal ^pŒ+mlabjlp buqbk,abo i^ abcfkf`fŽk ab o'p( mlo fkar``fŽk ^ `r^inrfbo fkqbos^il ^_fboql ab i^ cloj^,j ; o ; ,j * 0+alkab j bp rk bkqbol mlpfqfsl- K^ b`r^`fŽk crk`flk^i '5-45( vpr buqbkpfŽk '5-46( plk ^elo^ sŠifa^p m^o^ qlal ob^i o m^o^ bi nrb ^j_lp jfbj,_olp qbkd^k pbkqfal-
Ulis^jlp ^elo^ ^ i^ afp`rpfŽk ab i^ b`r^`fŽk ab AbppbH-K^ pbofb nrb a^ b]-bk i^ b`r^`fŽk '5-43( `lkqfbkb bi molar`ql '0 * ]' '1 * ]' ,,, &j * ]', Olabjlpbumobp^o bpqb molar`ql jbaf^kqb i^ crk`fŽk d^jj^ qlj^kal o < 0 * ] bk '5-46(-Dpql klp a^
'0 * 0W('1 * HW(ŠŠ- 'j * HW(< o'k * 0 * HW(ŠH&'H* HW(
Olo `lkpfdrfbkqb+ pf bibdfjlp& // < 1,^-.o'i * HW( bk '5-43( v abpfdk^jlp i^ crk,`fŽk obpriq^kqb b],&t' mlo H],&t' `r^kal t< N+i^ plir`fŽk m^o^ t = N mrbab bp`of,_fopb bk i^ cloj^
Het' < 'y(] ']i(k 'y(1j-1 k<N j H&'k* 0 * HW( 1
K^ crk`fŽk H]- abcfkfa^ mlo bpq^ b`r^`fŽk m^o^ t = N v ] y N pb ii^j^ bqj_e‰j`a@aooaha lneian] aola_ea v `a kn`aj ]- Br^kal ] bp rk bkqbol kl kbd^qfsl+ pb^] < l* i^ crk`fŽk ab Abppbi Hl sfbkb a^a^ mlo i^ pbofb ab mlqbk`f^p
'5-48(
H &t' < ]' ]]0](k]'z(1k*c(c( j<kj 'j * l( 1
'l << /+ 0+1+--- (-
C_q]_e‰j`a @aooah --4
Dpq^bp q^j_f‹k plir`fŽk ab i^ b`r^`fŽk ab Abppbim^o^t ; N- Rb e^k `lkpqorfalq^_i^p ab crk`flkbp ab Abppbi-Dk i^ cfdro^ 5-1 pb e^k af_rg^al i^p doŠcf`^pab i^palp crk`flkbp ab Abppbi./ o p--
u
Hk
t
EHFTQ@ 5-1 En…be_]oa h]o bqj_ekjao `a @aooah&lv I{-
Olabjlp abcfkfo rk^ krbs^ crk`fŽk . ,HW obbjmi^w^kal ] mlo ,] bk i^b`r^`fŽk '5-48(+ pf ] bp q^i nrb /%&j * 0 , ]( qfbkbpbkqfal: bpql bp+pf ] kl bp rkbkqbol mlpfqfsl- Olo `lkpfdrfbkqb+ pf t = N u]= N+ ] <0< 0+1+2+--- +abcfkfjlp
Slj^kal p < 0 , ] bk '5-46( l_qbkbjlp
o'k * 0 , bu( < '0 , bu( '1 , bu( ’’’ &j + bu( o'0 , bu(
v sbjlp nrb i^ pbofbnrb a^ .,HW'W( bp i^ jfpj^ nrb i^ ab b+hV&t' ab i^ b`r^`fŽk'5-44( `lk ]‚ < 1!&.0&'0, ](+V = N- Olo 0/ q^kql+pf ] kl bp bkqbol mlpfqfsl+.,HWbp rk^ plir`fŽk ab i^ b`r^`fŽk ab Abppbim^o^t = N-
Rf ] kl bp bkqbol+i^p alp plir`flkbp .HW&t' v KHW&t' plk ifkb^ijbkqb fkabmbk,afbkqbpbk bi bgbob^i mlpfqfsl 'mrbpql nrb pr `l`fbkqbkl bp `lkpq^kqb( v i^ plir`fŽkdbkbo^i ab i^ b`r^`fŽk ab Abppbim^o^t = N bp
Rf ] bp rk bkqbol kl kbd^qfsl+ pb^ ] < l* ebjlp bk`lkqo^al •kf`^jbkqb i^plir`fŽk h• v prp molar`qlp mlo `lkpq^kqbp sŠifalp m^o^ t = N- Nqo^ plir`fŽk+
12/ C_q]_ekjao `ebanaj_e]haoheja]hao
fkabmbkafbkqbab ‹pq^+mrbab bk`lkqo^opb mlo bi j‹qlal abp`ofql bk bi bgbo`f`fl 3ab i^ pb``fŽk 5-05- bpqb bpq^_ib`b nrb pf S0 bp rk^ plir`fŽk ab u!*N0u&*N1u</nrb krk`^ pb ^kri^ bk rk fkqbos^il /* rk^ pbdrka^ plir`fŽk S1 fkabmbkafbkqbabT0 sfbkb a^a^ mlo i^ fkqbdo^i
S1'V( < Sh'V( c! O'p( 1 `p+Ib Yq0'p•(
,ilkab O&V' < a+GNh&**'`!,O^o^ i^ b`r^`fŽk ab Abppbiqbkbjlp N/&t' < h-t* ^pŒnrb O&t' < h-t v rk^ pbdrka^ plir`fŽk S1 sfbkb a^a^ mlo i^ cŽojri^
'5-5/(
pf a v t mboqbkb`bk^i fkqbos^il 0 bk bi nrb Hl kl pb ^kri^-Dpq^pbdrka^ plir`fŽk mrbab mlkbopb bk lqo^p cloj^p- Olo bgbjmil+ ^ m^oqfo
ab '5-48( mlaboklp bp`of_fo
0 0YHlwp•(1< p1l clwp(+
alkab cl&M' ;/; N- Dk bi fkqbos^il 0 i^ crk`fŽk cl qfbkb rk abp^ooliil bk pbofbabmlqbk`f^p
//
cep( < + ?Œ-p!bb8+
nrb mlaoŒ abqbojfk^opb fdr^i^kal `lbcf`fbkqbp bk i^ fabkqfa^a cl&p'&Hl&p'H0 < p0N,
Rf prmlkbjlp i^ bufpqbk`f^ab q^i abp^ooliil+ bi fkqbdo^kal ab '5-5/( qlj^ i^ cloj^
00++
pYHl'p([1 < q1&O,q0z ? ‹‹n-
Hkqbdo^kalbpq^cŽojri^ q‹ojfkl ^ q‹ojfkl bkqobb v t l_qbkbjlp rk q‹ojfkl ild^,oŒqjf`l ?0N ild t 'ab i^ mlqbk`f^ p+/
' jŠp rk^ pbofb ab i^ cloj^ t,0l + @!tbh,Olo `lkpfdrfbkqb+'5-5/( qlj^ i^ cloj^
//
q1't( < ?1lHet(ildt * Hlwt(t,1N+ @jt! -bb8+
Orbab abjlpqo^opb nrb bi `lbcf`fbkqb ?0N ;/; N-Rf jriqfmif`^jlp S8 &t' mlo 0. @1O i^plir`fŽk nrb obpriq^ pb abpfdk^ `lk Il&t' v qfbkb i^ cloj^
//
Iet( < Het( ild t * t,l+ A ‹‹u! -bb8+
Cfan_e_eko 120
Dpq^bp i^ cloj^ ab i^ plir`fŽk ^krk`f^a^ bk bi pbdrkal `^pl abi qblobj^ abEol_bkfrp-
G^_fbkal iibd^al ^ bpq^cŽojri^+ mlabjlp `ljmol_^o nrb bufpqbob^ijbkqbrk^ plir`fŽk ab bpq^cloj^ prpqŒqrvbkalbk bi pbdrkal jfbj_ol ab i^ b`r^`fŽkab Abppbiv abqbojfk^kal ilp `lbcf`fbkqbp aj ab jlal nrb i^ b`r^`fŽk pb p^qfpc^d^-Klp abq^iibp ab bpqb`Ši`ril plk i^odlp v pboŠkljfqfalp- Di obpriq^al cfk^i mrbabbumobp^opbpŒ
Iet( < Het(hkct \h'y(,NG'N , j+, 0( 'y(1j \ 'y(N ',hp d+j* dj*l+'y(1j+1 1 j;M j - 1 1 1 j;M j- 'j * l', 1
alkab d‚ < NXd: < 0 * q* --- * 00j m^o^j y 0- K^ pbofbabi pbdrkal jfbj,_ol `lksbodb m^o^qlal ob^i t- K^ crk`fŽk I: abcfkfa^ m^o^t= Nmlo bp^ cŽojri^ pbii^j^ bqj_e‰j `a @aooaha oacqj`] aola_ea v `a kn`aj l- Orbpql nrb I: kl bp bimolar`ql ab rk^ `lkpq^kqb mlo Hl* i^ plir`fŽk dbkbo^i ab i^ b`r^`fŽk ab Abppbibkbpqb`^pl m^o^ t = N bp
u < _/Hl&t' * _0Il&t',
Dk ilp bgbo`f`flp nrb pfdrbk pb afp`rqfoŠk lqo^p molmfba^abpab i^p crk`flkbp abAbppbi-
.'*, 8SN[LRLRX\
0- ^( Rb^k b rk^ plir`fŽk `r^inrfbo^ ab i^ b`r^`fŽk ab Abppbi ab loabk ] v c&t' < thdb&t'm^o^ t = N- Cbjlpqo^o nrb d p^qfpc^`b i^ b`r^`fŽk afcbobk`f^i
'0 , 3/'1(
u! * 0 * ,,,-{:1 u < N-
_( Br^kal 3]1 < 0 i^ b`r^`fŽk afcbobk`f^i abi ^m^oq^al ^( pb qo^kpcloj^ bk v! * v < N:pr plir`fŽk dbkbo^i bp v < ? `lp t * @pbk t- Tqfifw^o bp^ fkcloj^`fŽk v i^ fdr^ia^a ')(o'i( < s&:m^o^ abjlpqo^o nrb+ m^o^ t = N+
' 1(zHy&t' < 0RV pbk t v ' 1(z
Jy't( < 0RV `lp t-
')( Di `^j_fl ab s^of^_ib p < q1 klp a^
oj < bk9G,y‡a,pp < 1 qNb,r&q < s&9:-'Dk bi bgbo`f`fl 05 ab i^ pb``fŽk 00-17 mrbab sbopb rk^ abjlpqo^`fŽk ab nrb
1 b9%a,q&`q < s&9:-(
121 C_q]_ekjao `ebanaj_e]haoheja]hao
b( @ m^oqfoab i^p pbofbpnrb a^k H%?,&t' X H ,G &t'* abar`fo afob`q^jbkqb i^p cŽojri^pabi ^m^oq^al_(+
1- Tqfifw^oi^ obmobpbkq^`fŽkbk pbofbpab mlqbk`f^pab i^p crk`flkbp ab Abppbim^o^abjlp,qo^onrb
2- Rb^kD*p:t' < t]H*et' v E]&t' < t+]H] &t' m^o t 9• N- N_p‹osbpbnrb `^a^ `bol mlpfqfslab H] bp rk `bol ab E] v q^j_f‹k il bp ab E|, Blk bi qblobj^ ab Qliib v bi bgbo`f`fl1abjlpqo^o nrb ilp `bolp ab H] v H])/ pb fkqbo`^i^k-Dpql bp+bufpqbrk `bol ab H] bkqob`^a^ m^oab `bolp mlpfqfslpab H])/% X rk `bol ab H])h bkqob`^a^ m^oab `bolp mlpf,qfslp ab ]& 'Ubo cfdro^5-1-(
3- ^( @ m^oqfoab i^p obi^`flkbpabi bgbo`f`fl1 abar`fo i^p obi^`flkbpab ob`roobk`f^
bu+Het' * Hy&t' < H]+/&t't
vbu+Het' +Hy&t' < H])0&t',t
_( Blk i^p obi^`flkbp abi ^m^oq^al^( abar`fo i^p cŽojri^p
v
4- Tqfifw^obi bgbo`f`fl0 _( Xrk^ cŽojri^ ab ob`roobk`f^^ab`r^a^ m^o abjlpqo^o nrb
'1 [G'pbku (
Hy&t' < 6Rth 6 , `lp t ,
G^ii^o rk^ cŽojri^ ^kŠild^ m^o^%+1?wt'* M^oanr]_e‰j9 H]&t' bp rk^ c•oŒ`f‹k bibjbkq^im^o qlal ] nrb pb^ i^ jfq^a ab rk bkqbolfjm^o-
5- Cbjlpqo^o nrb
v
6- ^( Tp^o i^p fabkqfa^abpabi bgbo`f`fl5 m^o^abjlpqo^o nrb
//
Hy&t' * 1 Hy&t' < 0U8S
v//
&0j * h'Hj&V'Hj)h&V' < t,V4=
_( Cbi ^m^oq^al ( abar`fo nrb HIl'u(0 <9: 0 X GHj&t'/ y 0s1 m^o j < 0+1+2+--’ + vqlal t y N-
Cfan_e_eko 122
7- Rb^c]:t' < tH+†Y,,&]V%'m^o^ t= N+alkab ] v ^ plk `lkpq^kqbp kl kri^p- Cbjlpqo^o nrbceh- p^qfpc^`b0! b`r^`fŽk afcbobk`f^i
pf+v pŽil pf+.00- bp rk^ plir`fŽk ab i^ b`r^`fŽk ab Abppbiab loabk ]-8- G^`bo rpl abi bgbo`f`fl 7 m^o^ bumobp^oi^ plir`fŽk dbkbo^i ab `^a^ rk^ ab i^p b`r^`fl,
kbp afcbobk`f^ibp pfdrfbkqbp mlo jbafl ab i^p crk`flkbp ab Abppbim^o^ t = N-
^( u! * tu < N-_( u! * t1u < N-
b( u! * tiu < N-a( t1u! * 'u3 * p(u < l-
0/- Fbkbo^ifw^o bi bgbo`f`fl 7 `r^kal Z-- v ceh, pb obi^`flk^k jbaf^kqb i^ b`r^`fŽkch/,&t' < tAzh/,&]V%'m^o^ t< N- G^ii^o bkqlk`bp i^ plir`fŽk dbkbo^i ab i^p pfdrfbkqbpb`r^`flkbp mlo jbafl ab i^p crk`flkbp ab Abppbi m^o^ t = l-
^( tu! * 4u%* u < N-_( tu! * 5u&* tu < N-
00- C^a^ i^ fabkqfa^a ab i^ cloj^
b( tu! * 4u%* t2u < N-a( teu! , tu& * &t * i(v < N-
H0&t' + Hk&t' < ]H9 &t'*
alkab ] v a plk `lkpq^kqbp- Cbqbojfk^o ] v _-01- Dk`lkqo^o rk^ pbofb ab mlqbk`f^p plir`fŽk ab i^ b`r^`fŽk afcbobk`f^i tu! * v&* v < N
`lksbodbkqb m^o^ , // ; t ; * bb + Cbjlpqo^o nrb m^o^ t = N mrbab bumobp^opbjbaf^k,qb rk^ crk`fŽk ab Abppbi-
02- Blkpfabobjlp rk^ b`r^`fŽk afcbobk`f^i ifkb^i ab pbdrkal loabk ab i^ cloj^
t0?&t'u! * tN&t'u% * O&t'u < N+
bk i^ nrb ?&t'* N&V'*v O&t' ^ajfqbk abp^ooliilp bk pbofbpab mlqbk`f^p+
//
?'t( < 1 ]gtg+g<M
//
N&t' < 1Nyg+g<M
//
O't( < 1 mgtg +g<M
`lk ]- y l+ `lksbodbkqb `^a^ rk^ bk rk fkqbos^il ^_fboql &+n*n', Rf i^ b`r^`fŽk afcb,obk`f^i qfbkb rk^ pbofb plir`fŽk ab i^ cloj^
//
u < Vh 1 _jtj+j<M
sŠifa^ m^o^ N ; t ; o+ abjlpqo^o nrb p p^qfpc^`b rk^ b`r^`fŽk `r^aoŠqf`^ ab i^ cloj^c* ^p * a < N+X abqbojfk^o ^ v a bk crk`fŽk ab ilp `lbcf`fbkqbp ab i^p pbofbp ab?&t'* N&t' v O&t',
03- Blkpfabo^o rk `^pl m^oqf`ri^o abi bgbo`f`fl 02 bk bi nrb ?&t' < 0 , t* N&t' < qvO&t' < +Gt, G^ii^o rk^ pbofb plir`fŽk `lk p kl bkqbol-
04- K^ b`r^`fŽk afcbobk`f^i 1t&u! *'t& , t(u&* v < N qfbkb alp plir`flkbp fkabmbkafbkqbpab i^ cloj^
//
u < th1 _jtj+j<M
123 C_q]_ekjao `efanaj_e]hao heja]hao
sŠifa^ m^o^ t = N- Cbqbojfk^o bp^p plir`flkbp-05- K^ b`r^`fŽk afcbobk`f^i kl ifkb^i v! * v * ]e < N bp ~ifdbo^jbkqbƒ kl ifkb^i Rf&] bp rk^
`lkpq^kqb mbnrb•^ kl kri^- Rrmlkd^jlp nrb bufpqb rk^ plir`fŽk nrb mrbab bumobp^opb`ljl pbofb ab mlqbk`f^p ab ] ab i^ cloj^
//
u < Kqj't(k_j 'sŠifal bk rk `fboql fkqbos^il M;];n(Vc=
v nrb bpq^ plir`fŽk p^qfpc^d^ i^p `lkaf`flkbp fkf`f^ibp v < 0 b v&< N `r^kal t < N-O^o^ ^grpq^opb ^ bp^p `lkaf`flkbp fkf`f^ibp+ fkqbkq^jlp bibdfo ilp `lbcf`fbkqbp Sj'V( abjlal nrb qk&M'< h*qy&M'; N v q,&M' ;qy&M' < N m^o^ j y 0- Rrpqfqrfo bp^ pbofb bk i^b`r^`fŽk afcbobk`f^i+ fdr^i^o i^p mlqbk`f^p ^ab`r^a^p ab ] v abqbojfk^o `lk biil q,&t'v Sh'V(-
6
D<DE8?4D 78 86F46<A@8D 7<98C8@6<4>8D
/') <W][XM^LLRmW
@rknrb bi bpqrafl ab i^p b`r^`flkbp afcbobk`f^ibp `ljbkwŽ bk bi+pfdil WUHH+
kl crb e^pq^ bi WHWnrb ilp j^qbjŠqf`lp pb afbolk `rbkq^ nrb rk k•jbol obi^qfs^,jbkqb mbnrb•l ab b`r^`flkbp afcbobk`f^ibp mlaŒ^obplisbopb `lk jbaflp bibjbk,q^ibp- Klp qo^_^glp ab B^r`ev+ Kflrsfiib v lqolp+ jlpqo^olk i^ fjmloq^k`f^ abbpq^_ib`bo qblobj^p dbkbo^ibp m^o^ d^o^kqfw^oi^ bufpqbk`f^ ab plir`flkbp m^o^`fboq^p `i^pbp bpmb`f^ibpab b`r^`flkbp afcbobk`f^ibp- Di `^mŒqril 5 pb abaf`Ž ^ibjmibl ab rk qblobj^ ab bufpqbk`f^ v rkf`fa^a bk bi bpqrafl ab i^p b`r^`flkbpafcbobk`f^ibp ifkb^ibp- Dk bpqb`^mŒqrilklp fkqbobp^jlp bk rk^ abjlpqo^`fŽk abbpb qblobj^ v bk qbj^p obi^`flk^alp `lk ‹i-
K^ qbloŒab bufpqbk`f^m^o^b`r^`flkbp afcbobk`f^ibpab loabk prmboflo mrbabobar`fopb ^i `^pl ab mofjbo loabk fkqolar`fbkal oeopai]o ab b`r^`flkbp- Olo bgbj,mil+ i^ b`r^`fŽk ab pbdrkal loabk
&5,/' u! * 0pu%+%+W< a&
mrbab qo^kpcloj^opb bk rk pfpqbj^ ab alp b`r^`flkbp ab mofjbo loabk fkqolar,`fbkal alp crk`flkbp fk`Ždkfq^pXi b W1+pfbkal
WG< u+ W1 < ue•
Sbkbjlp bkqlk`bp v&1< v&z< u!+ ^pŒnrb '6-0( mrbab bp`of_fopb`ljl rk pfpqbj^ab alp b`r^`flkbp ab mofjbo loabk9
ue < W1'6-1(
Ml mlabjlp obplisbo i^p b`r^`flkbp pbm^o^a^jbkqb `lk ilp j‹qlalp abi `^mŒqril5mlonrb `^a^ rk^ ab bii^p `lkqfbkb alp crk`flkbp fk`Ždkfq^p-
124
-.1 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
Dk bpqb `^mŒqril `lkpfabo^jlp pfpqbj^p nrb `lkpq^k ab j b`r^`flkbp afcb,obk`f^ibp ifkb^ibp ab mofjbo loabk `lk j crk`flkbp fk`Ždkfq^p XH + -’’ +Xk- Dplppfpqbj^p qfbkbk i^ cloj^
'6-2(
K^p crk`flkbp Neg v mznrb ^m^ob`bkbk '6-2( pb `lkpfabo^k crk`flkbp a^a^p abcfkf,a^p bk rk `fboql fkqbos^il h,K^p crk`flkbp XH + --- + Wj plk i^p crk`flkbp fk`Ždkfq^pnrb e^v nrb abqbojfk^o- Klp pfpqbj^p ab bpqbqfml pb ii^j^k oeopai]o heja]hao`alneian kn`aj- Dk dbkbo^i `^a^ b`r^`fŽk abi pfpqbj^ `lkqfbkb jŠp ab rk^ crk`fŽkfk`Ždkfq^ mlo il `r^i i^p b`r^`flkbp kl mrbabk obplisbopb pbm^o^a^jbkqb-
Tk^ b`r^`fŽk afcbobk`f^i ifkb^i ab loabk j pfbjmob mrbab qo^kpcloj^opb bkrk pfpqbj^- Rrmlkd^jlp nrb i^ b`r^`fŽk ab loabk j a^a^ bp
'6-3( uG!' * ^0vi!,0( * --- * ]!u < P'p(+
alkab ilp `lbcf`fbkqbp ]z plk crk`flkbp a^a^p- O^o^ qo^kpcloj^oi^ bk rk pfpqbj^bp`of_fjlp XH < W b fkqolar`fjlp rk^ krbs^ crk`fŽk fk`Ždkfq^ m^o^`^a^ rk^ abi^p pr`bpfs^p abofs^a^p ab u- Dpql bp+mlkbjlp
WG< u+ W1 < uw* W2< uy+ --- +u! < Wy,h&
v bp`of_fjlp 'z-3( `ljl pfpqbj^
Ww< W1
uy < W2
'6-4(
Wy,h < u!
uy < ,]jWh , ]j,0W1 , --- ,]hWj * P&p',
K^ afp`rpfŽk ab ilp pfpqbj^p mrbab pfjmifcf`^opb`lkpfabo^_ibjbkqb jbaf^kqbi^ klq^`fŽk j^qof`f^i v sb`qlof^i+ Blkpfabobjlp bi pfpqbj^ dbkbo^i '6-2( b fkqol,
Gjpnk`q__e‰j -.2
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Jau `a atlkjajpao l]n] atlkjaj_e]hao `a i]pne_ao 134
Cbofs^kal bpqbmolar`ql l_qbkbjlp
E&'p(< a,p?D&'p( , ?a,p?D'p( < a,p??D'p( , a,pyD'p( < N-
Olo `lkpfdrfbkqb E&p' bp rk^ j^qofw `lkpq^kqb+
E'p( < F'N( < D'M( < @-
Dpab`fo+a+p?D&p' < @,Lriqfmif`^kal mlo ap? v ^mif`^kal '6-03( l_qbkbjlp '6-04(-
M^oanr]_eˆj8 Di jfpjl qfml ab abjlpqo^`fŽk e^`b sbo nrb D&p' < @a!9 bp i^•kf`^ plir`fŽk abi mol_ibj^ ab s^ilo fkf`f^i
D&'p( < D'p(?+ D&M' < @,
6-7 >Nb MNNaYXWNW]N\YJ[J NaYXWNWLRJUN\MNVJ][RLN\
K^ ibv ab bumlkbkqbpa&a! < a? *@ kl pfbjmob bp sŠifa^ m^o^bumlkbk`f^ibp abj^qof`bp- Dk bi bgbo`f`fl 02 ab i^ pb``fŽk 6-01 pb a^ rk `lkqo^bgbjmil- Ml l_pq^kqb+kl bp afcŒ`fiabjlpqo^o nrb i^ cŽojri^ bp sŠifa^ m^o^j^qof`bp mbojrq^_ibp-
SDNQDL@ 6-5- Qa]j ? v @ `ko i]pne_ao j t j laniqp]^hao+ ?@ < @?- Ra,jaiko
Baikopn]_‡‰j- Cb i^ b`r^`fŽk ?@ < @? abar`fjlp nrb
?1@ < ?'@?( < '?@(? < '@?(? < @?1+
ab jlal nrb @bp mbojrq^_ib `lk ? 1- Olo fkar``fŽk+ @ bp mbojrq^_ib `lk `r^i,nrfbo mlqbk`f^ ab ?- Dp`of_fbkal a&!bk cloj^ ab pbofbab mlqbk`f^p bk`lkqo^jlpnrb @ q^j_f‹k bp mbojrq^_ib `lk a&!m^o^qlal p ob^i-
Rb^ ^elo^ E i^ crk`fŽk j^qof`f^i abcfkfa^ mlo i^ b`r^`fŽk
Cbofs^kal D&p' v qbkfbkal bk `rbkq^ nrb @ bp mbojrq^_ib `lk ap? bk`lkqo^jlp
D&'p(< '? * @(ap'?*@h\ ?ap?ap@\ ap?@ap@
< '? * @(†'?*@h , '? * @(ap?-ap@< '? * @(D'p(-
135 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
Rbd•k bi qblobj^ ab rkf`fa^a qbkbjlp
D'p( < ap;?*@hD'M(-
Obol D&M' < N+ ^pŒnrb D&p' < N m^o^ qlal p-Krbdl
Br^kal p < 0 l_qbkbjlp '6-05(-
DIDLOKN- K^p j^qof`bp o? v p? plk mbojrq^_ibp m^o^ qlalp ilp bp`^i^obpp v p- Krbdl qbkbjlp
0-8 Sblobj^p ab bufpqbk`f^ v rkf`fa^a m^o^ pfpqbj^p ifkb^ibp eljld‹kblp `lk`lbcf`fbkqbp `lkpq^kqbp
K^ b`r^`fŽk afcbobk`f^i sb`qlof^i W%&p'< ?W&p'* alkab ? bp rk^ j^qofw`lkpq^kqb j W j b X bp rk^ crk`fŽk sb`qlof^i k,afjbkpflk^i '`lkpfabo^a^ `ljl rk^j^qofw `lirjk^ j W 0( pb abkljfk^ oeopai] heja]h dkikc†jak _kj _kabe_eajpao_kjop]jpao- Tqfifw^objlp i^ bumlkbk`f^i ab rk^ j^qofw m^o^ a^o rk^ cŽojri^ bumiŒ,`fq^ ab i^ plir`fŽk ab rk q^i pfpqbj^-
SDNQDL@ 6-6- Qa]j ? qj] i]pnev _kjop]jpa j Wj `]`] u @ qj ra_pkn j,`e,iajoekj]h- Ch lnk^hai] `a r]hkn eje_e]h
'6-06( W.'p( < ?W&p'* W&M'< @*
peaja okhq_e‰jŠje_] aj ah ejpanr]hk , // ; p ; * ll + Cop] okhq_e‰jreaja `]`]lkn h] b‰niqh]
'6-07(
K…ocajan]h+h] Šje_] okhq_pkj `ah lnk^hai] `a r]hkn eje_e]h
W-&p'< ?W&p'* W&]' < @*
ao W&p' < a'p,](?@-
Baikopn]_e‰j- K^ abofs^`fŽk ab '6-07( klp a^ W%&p'< ?ap?@ < ?W&p', Orbp,
Ch lnk^hai] `a _]h_qh]n ap? -/2
ql nrb W&M' < @* ‹pq^ bp rk^ plir`fŽk abi mol_ibj^ ab s^ilo fkf`f^i '6-06(-O^o^abjlpqo^o nrb bp i^ •kf`^ plir`fŽk+ o^wlk^jlp `ljl bk i^ abjlpqo^`fŽk
abi qblobj^ 6-4- Rb^ X&p' lqo^ crk`fŽk sb`qlof^i nrb p^qfpc^d X%&p'< ?X&p' `lkY'N( < @*X mlkd^jlp E&p' < a+p,hX&p', Bljmol_^jlp bkqlk`bp `lk c^`fifa^a nrbE%&p'< /+ ^pŒnrb E&p' < F'N( < X&M' < @, Dp ab`fo+ a+qX&p' < @* ab jlalnrb X&p' < ap,/@< W&p', Cbi jfpjl jlal pb mrbab afp`rqfo bi `^pl jŠp dbkbo^i`lk s^ilo fkf`f^i W&]' < @,
/')( 8UY[XKUNVJMNLJUL^UJ[ap?
@rknrb bi qblobj^ 6-6 a^ rk^ cŽojri^ bumiŒ`fqm^o^UJplir`fŽk ab rk pfpqb,-k^ eljld‹kbl `lk `lbcf`fbkqbp `lkpq^kqbp+nrba^ qla^sŒ^bi mol_ibj^ ab `^i`ri^obcb`qfs^jbkqb i^ bumlkbk`f^i a&!+Rf pb qo^q^o^ab `^i`ri^o ap? afob`q^jbkqb ^m^oqfoab i^ abcfkf`fŽk ab pbofbqbkaoŒ^jlp nrb `^i`ri^o qla^p i^p mlqbk`f^p ? g
m^o^g < N+ 0+1+--- +v `^i`ri^o irbdl i^ prj^ ab `^a^ pbofb g9kpgA:y(-g * alkaba :y( bp bi bibjbkql eeab ?h*,Dk dbkbo^i ‹pb bp rk qo^_^gl abpbpmbo^kqbp^isl pf ?bp rk^ j^qofw `rv^p mlqbk`f^p mrbabk `^i`ri^opb cŠ`fijbkqb- Olo bgbjmil+ pf? bp rk^ j^qofw af^dlk^i+ pb^
bkqlk`bp qla^ mlqbk`f^ ab ? q^j_f‹k bp rk^ j^qofw af^dlk^i+ mrbp
?g < af^d '?J --- +?y( -
Nkn `lkpfdrfbkqb bk bpqb`^pl ap? bp rk^ j^qofw af^dlk^i a^a^ mlo
++ S ++ S
†? , af^d '&! o9G &! o9 0g( af &k,* p(-j(, 5 g 00-0&’’’ &5g GG,j < i^d a +--- +a -
Nqol `^pl cŠ`fi ab j^kbg^o bp `r^kal ? bp rk^ j^qofw nrb mrbab af^dlk^,kfw^opb-Olo bgbjmil+ pf bufpqbrk^ kl pfkdri^o B q^i nrb B,0@B bp rk^ j^qofw af^,dlk^i+ pb^ B,0 ?A < C+ bkqlk`bp qbkbjlp ? < BCB,f+ ^ m^oqfoab i^ `r^i bk`lklqo^jlp
v+ jŠp dbkbo^i+
137 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
Olo q^kql bk bpqb`^pl qbkbjlp
@nrŒi^ afcf`riq^a bpqŠbk abqbojfk^o B v pr fksbop^- Tk^ sbw ‹p^p plk `lkl`fa^p+ap pb `^i`ri^ `lk c^`fifa^a- M^qro^ijbkqb+ kl qla^ j^qofw mrbab af^dlk^ifw^opbab jlal nrb i^ rqfifa^a ab i^p l_pbos^`flkbp mob`babkqbpbp ifjfq^a^-
DIDLOKN 0- B^i`ri^o a&!m^o^ i^ j^qofw 1 W1+ ? < F 9\-Qkhq_e‰j- Dpq^ j^qofw qfbkb ^rqls^ilobp afpqfkqlp @i < 5+ @1 < 0+ ^pŒnrb
kl pfkdri^o B <Z9 9\ q^i nrb A+%?A< B* alkab
&Z5N\B < af^d '@! @1( < N 0 - O^o^ abqbojfk^o B mlabjlp bp`of_fo ?A < AB* l
bufpqb rk^ j^qofw
Lriqfmif`^kal i^p j^qof`bp+ bk`lkqo^jlp nrb bp^ b`r^`fŽk pb p^qfpc^`b r^ibpnrfbo^nrb pb^k ilp bp`^i^obp]+^* a+ q^ibpnrb ] < 3_+ < ,`- Slj^kal a < ` < 0bibdfjlp
Olo 0/ q^kql
†? < AapBA,h < Z30 ,
,0\ Ya4p /\Z 00\0 N bi ,0 3
DIDLOKN 1- Qbplisbo bi pfpqbj^ ifkb^i
Ww< 4Wh * 3W1
Wy < Wh * 1W1
prgbql ^ i^p `lkaf`flkbp fkf`f^ibp u*&M' < 1+ W0&.' < 2-
Raknai] `a A]uhau,F]iehpkj -/4
Qkhq_e‰j- Dk cloj^ j^qof`f^i bi pfpqbj^ pb mrbab bp`of_fo ^pŒ9
W&'p(< ? W'p(+ W&M'< Z9\+ alkab ? < F 9\-Rbd•k bi qblobj^ 6-6 i^ plir`fŽk bp W&p' < aSW&M', Tp^kal i^ j^qofw ap? `^i`ri^,a^ bk bi bgbjmil 0 bk`lkqo^jlp
ab i^ nrb l_qbkbjlp
Rb `lkl`bk jr`elp j‹qlalp m^o^ `^i`ri^o ap? `r^kal ? kl mrbab af^dlk^,ifw^opb- K^ j^vloŒ^ ab biilp plk jŠp _fbk `ljmif`^alp v bufdbk qo^kpcloj^`flkbpj^qof`f^ibp mobsf^p+ `rv^ k^qro^ibw^ abmbkab ab i^p jriqfmif`fa^abp ab ilp ^rql,s^ilobp ab ?- LŠp ^abi^kqb afp`rqfobjlp rk j‹qlal moŠ`qf`l v pbdrol m^o^ `^i`ri^oap
- nrb pb mrbab rqfifw^o q^kql pf ? mrbab af^dlk^ifw^opb `ljl pf kl- Dp sŠifalm^o^ pk`]o i^p j^qof`bp ? v kl bufdb qo^kpcloj^`flkbp mobsf^p ab kfkd•k qfml-S^i j‹qlal crb abp^oolii^al mlo D- I- Orqwbo bk rk ^oqŒ`ril abi ?iane_]jK]pdai]pe_]h Kkjpdhu+ Uli- 62 '0855(- mŠdp- 1,6- Rb _^p^ bk rk c^jlpl qblobj^^qof_rfal ^ @oqero B^vibv '0710,,0784( X Vfiif^j Qlt^k G^jfiqlk '07/4,07549nrb bpq^_ib`b nrb qla^ j^qofw `r^ao^a^ p^qfpc^`b pr b`r^`fŽk `^o^`qboŒpqf`^-Cb,jlpqo^objlp mofjbol bi qblobj^ ab B^vibv,G^jfiqlk v irbdl il ^mif`^objlp m^o^l_qbkbo i^ cŽojri^ ab Orqwbo m^o^ `^i`ri^o bKi’
/')) ENX[NVJ MN6JbUNb&;JVRU]XW
SDNQDL@ 6-7- SDNQDL@ CD B@XKDX,G@LHKSNM- Qa]j ? qj] i]pnev j•:j v
'6-08( b'(-( < abq &?h+ ?' < (-j * _j\G',!+/ * --- * `i(- * Bl
oq lkhejkiek _]n]_pan‡ope_k-Cjpkj_ao b'?( < N- Co `a_en+? o]peoe]_a h] a_q]_e‰j
'6-1/(
Baikopn]_e‰j- K^ abjlpqo^`fŽk pb _^p^ bk NUqblobj^ 2-01 nrb bpq^_ib`bnrb m^o^ qla^ j^qofw `r^ao^a^ ? pb qfbkb
'6-10( ? '`lc ?(p < 'abq@( -
14/ Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
@mifnrbjlp bpq^ cŽojri^ obbjmi^w^kal ? mlo ?h , ?, Orbpql nrb abq '?h , ?' ;;b&<!'* i^ b`r^`fŽk '6-10( pb `lksfboqb bk
'6-11( '?h , ?(w_kb '?h , ?(xp <b'?(G-
Dpq^ b`r^`fŽk bp sŠifa^ m^o^ qlal ob^i =---K^ fab^ ab i^ abjlpqo^`fŽk `lkpfpqb bke^`bo sbo nrb q^j_f‹k bp sŠifa^ `r^kal=! pb obbjmi^w^ mlo ?-
Klp bibjbkqlp ab i^ j^qofw `lc '?h , ?' plk ilp `lc^`qlobp ab ?h , ?, Du`bm,ql m^o^ rk c^`qlo ~ 0+ `^a^ rkl ab q^ibp `lc^`qlobp bp bi abqbojfk^kqb ab rk^jbklo ab ?h , ? ab loabk j,h- Olo il q^kql `^a^ bibjbkql ab `lc '?h , ?'*X mlo q^kql ab x`lc '?h , ?'xp* bp rk mlifkljfl bk =--ab do^al z j , 0- Olo`lkpfdrfbkqb
U(S
w_kb'?h , ?(xp < G?g@g+Sc=
alkab `^a^ `lbcf`fbkqb @*bp rk^ j^qofw j Wj `lk bibjbkqlp bp`^i^obp- @mif`^kalbpql bk '6-11( l_qbkbjlp i^ obi^`fŽk
'6-12(k,i
'H--G, ?( H?g@g< b'?(GSc=
nrb pb mrbab mlkbo bk i^ cloj^
'6-13(k,i k,i
?j@j\0 * G?g'@g\0 , ?@g( , ?@k < ?jG * G?gAgG * _kh-h<i h<i
Hdr^i^kal ^elo^ ilp `lbcf`fbkqbp ab i^p mlqbk`f^p pbjbg^kqbp ab =--bk '6-13( l_qb,kbjlp i^p b`r^`flkbp
@j\h < 0
@j,1 , ?@j\0 < _j\0G
'6-14(
Al , ?@0 < _-G
,?@k < _kh-
K^ fdr^i^`fŽk ab ilp `lbcf`fbkqbp bp mlpf_ib mlonrb '6-13( bp bnrfs^ibkqb ^ j1
b`r^`flkbp bp`^i^obp+ bk `^a^ rk^ ab i^p `r^ibp mlabjlp fdr^i^o ilp `lbcf`fbkqbpab mlqbk`f^p pbjbg^kqbp ab @- Lriqfmifnrbjlp ^ `lkqfkr^`fŽk i^p b`r^`flkbp '6-14(
Cfan_e_eko 140
pr`bpfs^jbkqb mlo ?!+?!,h+ --- +?+ 0 X prjbjlp ilp obpriq^alp- Klp q‹ojfklp abimofjbo jfbj_ol abp^m^ob`bk v l_qbkbjlp
il `r^i abjrbpqo^ bi qblobj^ ab B^vibv,G^jfiqlk+
M^oanr]_e‰j9 G^jfiqlk abjlpqoŽ bi qblobj^ bk 0742 m^o^ rk qfml bpmb`f^i abj^qof`bp- Ol`lp ^•lp jŠp q^oab+ B^vibv ^krk`fŽ nrb bi qblobj^ bo^ sŠifal m^o^qla^p i^p j^qof`bp+ mbol kl afl i^ abjlpqo^`fl,
DIDLOKN- K^ j^qofw ? < Zz 9 9\ qfbkb `ljl mlifkljfl `^o^`qboŒpqf`l
011
b'(-( < '(-, 0('(&, 1('(& , 5( < (-2 , 8(-1 * 1/(- , 01-
Di qblobj^ ab B^vibv,G^jfiqlk bpq^_ib`b nrb ? p^qfpc^`b i^ b`r^`fŽk
'6-15( ?2 , 8?1 * 1/? , 01. < M-
Dpq^ b`r^`fŽk mrbab rp^opb m^o^ bumobp^o ?2 v qla^p i^p mlqbk`f^p prmboflobp ab? bk crk`fŽk ab /* ? X ?1
Œ Olo bgbjmil+ qbkbjlp
?2 < 8?1 , 1/? * 01.+
?3 < 8?2 , 1/?1 * 01? < 8'8?1 , 1/? * 01.( , 1/?1 * 01?
< 50?1 , 057? * 0/7.-
S^j_f‹k pb mrbab bjmib^o m^o^ bumobp^o?,/ `ljl rk mlifkljfl bk ?- Cb '6-15(obpriq^ q^j_f‹k ?'L , 8? * 1/.( < 01.+ X l_qbkbjlp
/')* 8SN[LRLRX\
Dk `^a^ rkl ab ilp bgbo`f`flp abi 0 ^i 3+ ^( bumobp^o? ,0+ ?& X qla^p i^p mlqbk`f^p prmb,
141 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
oflobp ab ? `ljl `lj_fk^`flkbp ifkb^ibp ab 0 v ?- 'Di qblobj^ ab B^vibv,G^jfiqlk mrbabpbosfo ab ^vra^(- _( B^i`ri^o ab?,,
0- ?<Y9 zi 1- ? < Z9 zi 2- ? < ol 0\- 3- ? < Z,z ziKi •
Z,z z\ +abjlpqo^o nrbZ `lp p pbk p[-4- ^( Rf ? < ap? <
,pbk p `lp p
_( G^ii^o i^ cŽojri^ `loobpmlkafbkqb m^o^ ab?, `r^kal ? < Yy^ 9[+ ]* ^ ob^ibp-
5- Rf D&p' < Zz p y 0\ +abjlpqo^o nrb aDAph < aD'ap,G(-
6- Rf ?&p' bp rk^ crk`fŽk bp`^i^o ab p+i^ abofs^a^ ab b!'i( bp b!'0(@&'q(-B^i`ri^o i^ abofs^a^
ab b!'i( `r^kal ?&p'; Yy y[ v abjlpqo^o nrb bi obpriq^al kl bp fdr^i ^ kfkdrkl ab ilp
alp molar`qlp b!'0(@&'q(l ?%&p'a!hh'‹
Dk `^a^ rkl ab ilp bgbo`f`flp 7+ 8+ iN+ ^( `^i`ri^o ?!+ v bumobp^o @i bk crk`fŽk abH*?+?&-_( B^i`ri^o a&&&-
00- Rf ? y Y
,0
• \ +NW++!+&!%? lljl `lj_fk^`fŽk ifkb^i al 0+?+?&-
ZNiNI
01- Rf ? < 1 } 1
/0/Y
V0
abjlpqo^o nrb a? < 0tu
`,
u1 [1tu +alkab t < `lpe- 0 b
t0 v < pbke 0-tu
02- Dpqb bgbjmil abjrbpqo^ nrb i^ b`r^`fŽk a?*@ < a?a@kl pfbjmob bp sŠifa^ m^o^ i^pbumlkbk`f^ibp ab j^qof`bp- B^i`ri^o `^a^ rk^ ab i^p j^qof`bp a?a@* a@a?‹ a?)@ `r^kal
K†pk`k `a Nqpvan l]n] _]h_qh]n ap? 142
? < Zz z\ v @< Zz ,z\+ v l_pbos^o nrb ilp qobp obpriq^alp plk afpqfkqlp-
6-02 ?k]XMX MNOrqwbo YJ[J LJUL^UJ[ap?
Di qblobj^ ab B^vibv,G^jfiqlk abjrbpqo^ nrb i^ mlqbk`f^ k,bpqj^ ab `r^i,nrfbo j^qofw ?* j Wj+ mrbab bumobp^opb`ljl `lj_fk^`fŽk ifkb^i ab i^p mlqbk`f^pfkcboflobp /* ?+?1
+ ŒŒŒ + ?j,0- Cb ^nrŒ obpriq^ nrb `^a^ rk^ ab i^p mlqbk`f^p pr,mboflobp ? k*q+ ? k*1+ ’’’ + q^j_f‹k mrbab bumobp^opb `ljl `lj_fk^`fŽk ifkb^i ab/* ?+?1
+ ŒŒŒ + ?j,0- Olo il q^kql+ bk i^ pbofb nrb abcfkb a&9&+`^a^ q‹ojfkl p&?!.g `lk g y j bp rk^ `lj_fk^`fŽk ifkb^i ab pgh+pg?+ zg?!+ --- +zg?j,h- Krbdl `^_b mbk,p^o nrb †? mrbab bumobp^opb `ljl rk mlifkljfl bk ? ab i^ cloj^
00,0
a-? < J mg&p'?g*
S4=
alkab ilp `lbcf`fbkqbp bp`^i^obp mg&p' abmbkabk ab p- Orqwboabp^ooliiŽ alp j‹qlalp•qfibp m^o^ bumobp^o a-,h `ljl rk mlifkljfl bk ?, Di qblobj^ nrb pfdrb abp`of_bbi jŠp pbk`fiil ab ilp alp j‹qlalp-
'6-16(
SDNQDL@ 6-8- Qa]j--Zh!&! --Z+jhko ]qpkr]hknao `a qj] i]pnev ?+ j Wj+ v`abej]iko qj] oq_aoe‰j `a lkhejkieko aj ? _kik oecqa9
&5,06' NkA?' < /* !N**&?' < SH&? + ?iG(+ l]n] g < 0+1+--- +j-iyh
Rajaiko ajpkj_ao
'6-18(
j+h
ap? < J ng)h&p'N**&?'*Sc=
`kj`a hko _kabe_eajpao ao_]h]nao nh'p(+--- +nj'p( oa `apaniej]j lkn na_qnnaj_e] ]l]npen `ah oeopai] `a a_q]_ekjao `ebanaj_e]hao heja]hao-
&g < 0+1+--- +j , 0(-
M^oanr]_e‰j9 K^ b`r^`fŽk '6-18( kl bumobp^ a&? afob`q^jbkqb bk mlqbk`f^pab ? `ljl fkaf`^ '6-16(+ pfkl `ljl rk^ `lj_fk^`fŽk ifkb^i ab ilp mlifkljflpNk&?' *N*&?' * ,,, *Nj+*&?', Dpqlp mlifkljflp pb `^i`ri^k cŠ`fijbkqb bk `r^kql pbe^k abqbojfk^al ilp ^rqls^ilobp ab ?, @pfjfpjl plk ab cŠ`fi `Ši`ril ilp jriqfmif,`^alobp n*&p'*,,, * nj&p' ab '6-2/(- @rknrb bpql bufdb obplisbo rk pfpqbj^ ab b`r^`fl,
143 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
kbp afcbobk`f^ibp ifkb^ibp+ bi pfpqbj^ nrb klp l`rm^ qfbkb rk^ j^qofw qof^kdri^o vi^p plir`flkbp mrbabk abqbojfk^opb bk cloj^ pr`bpfs^-
Baikopn]_e‰j- Rb^k nh'p(+--- +nj'p(i^p crk`flkbp bp`^i^obp abqbojfk^a^p mlo'6-2/( X abcfk^jlp rk^ crk`fŽk j^qof`f^i E mlo fkar``fŽk
'6-20(k,i
D'p( < &1ng*h'p(Ne?(-g<M
N_p‹osbpb nrb E'N( < nh&M'Nk&?' < h, Cbjlpqo^objlp nrb D&p'< ab? mol_^kalnrb D p^qfpc^`b i^ jfpj^ b`r^`fŽk afcbobk`f^i nrb a!+bp ab`fo+ D%&p'< ?D&p',
Cbofs^kal '6-20( v rp^kal i^p cŽojri^p ab ob`roobk`f^ '6-2/( l_qbkbjlp
k,i k,i
D&'p( < &1ny*h'p(Ne?( < &1wng'p( * ?g*hng*h'p(x Ng'?(+g<M! g<M
alkab nk&p' bp mlo abcfkf`fŽk N- Ulisbjlp ^ bp`of_fo bp^ cŽojri^ bk i^ cloj^
V', k,i
D&'p( < &1ng*h'p(Ng*h'?( * &1?g*hng*z'p(Ng'?(+g<M g<M
obpq^jlp irbdl ?jD'p( < zz9z?-jng*h'p(Ng'?( m^o^ l_qbkbo i^ obi^`fŽk
V',
&5,10' D&'p( , ?jD'p( < &1ng*h'p(wNg*h'?( * '@h*i , ?j(Ng'?(x-g<M
Obol ab '6-17( sbjlp nrb Ng)h&?' < &? + ?g)`'Ng&?'* mlo il nrb
Ng*/'?( * '@h*i , ?j(Ng'?( < '? , ?g*hG(Ne?( * '@h*i , ?j(Ng'?(
; '? , ?jh(le?(-
Olo `lkpfdrfbkqb i^ b`r^`fŽk '6-21( pb `lksfboqb bk
V',
D&'p( , ?jD'p( < '? , ?jG(&1ng*z'p(Ng'?( < '? , ?H(wD'p( , nj'p(Nj\h'?(xg<M
; '? , ?jG(D'p( , nj'p(N j'?(-
Di qblobj^ ab B^vibv,G^jfiqlk fjmif`^ nrb Nj&?' < /+ ^pŒnrb i^ •iqfj^ b`r^,`fŽk pb `lksfboqb bk
D&'p( , ?jD'p( < '? , ?H(D'p( < ?D'p( , ?jD'p(+
K…pk`k `a Nqpvan l]n] _]h_qh]n ap? 144
ab i^ nrb obpriq^ N%&p'< ?D&p', Orbpql nrb D&M'< *%bi qblobj^ ab rkf`fa^a '6-6(abjrbpqo^ nrb D&p' < a&!+
DIDLOKN 0- Dumobp^oap? `ljl `lj_fk^`fŽk ifkb^i ab 0 v ab ? pf ? bp rk^j^qofw 1 W1 `lk prp ^rqls^ilobp fdr^ibp ^ @-
Qkhq_eˆj, Olkfbkal @+ < @1 < @+ qbkbjlp nrb obplisbo bi pfpqbj^ ab b`r^,`flkbp afcbobk`f^ibp
nw'p( < ?nz'p(+
ny'p( < ?n1'p( * nz'p(+
neAM( < 0+
n1&.' < N-
Qbplisfbkal bp^pb`r^`flkbp ab mofjbo loabk bk cloj^ pr`bpfs^ bk`lkqo^jlp
Orbpql nrb N**&?' < / X N*&?' < ? + ?h+i^ cŽojri^ mbafa^ m^o^ap? bp
DIDLOKN 1- Qbplisbo bi bgbjmil 0 pf ilp ^rqls^ilobp ab ? plk @ v q+q^ibpnrb @ <0< .,h-
Qkhq_eˆj, Dk bpqb`^pl bi pfpqbj^ ab b`r^`flkbp afcbobk`f^ibpbp
nw'p( < ?nz'p(+
ny'p( < U1'p( * nz'p(+
neAM( < 0+
n0&.'* < N-
Rrp plir`flkbp sfbkbk a^a^p mlo
Orbpql nrb N**&?'< / X N*&?' < ? + ?h i^ cŽojri^ mbafa^ m^o^a&!bp
'6-23(
Rf ilp ^rqls^ilobp @v {-q plk k•jbolp `ljmibglp+ i^p bumlkbk`f^ibp aF v a!q^j_f‹k il pboŠk-Obol pf @v {:- plk `ljmibglp `lkgrd^alp i^p bumobpflkbpnrb jri,
145 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
qfmif`^k 0 X ? bk '6-23( pboŠk ob^ibp- Olo bgbjmil+ prmlkd^jlp
? < l` * eb2+ bH*< l` , eb2+ b2<.<M-
Dkqlk`bp @, m- < 0eb1 ^pŒnrb i^ b`r^`fŽk '6-23( pb qo^kpcloj^ bk
']*elhp '],elhp…3
-< a']*eNhpG* a 1yb2a Y? + 'l` * e'2(G[
welp ,elp x
< a]p aelpG* a 9:. '? , |h , eb2G(
< a]pw'`lp b2p* fpbk b2p(G* oa:b2p &? + |G , eb2G(x-
Klp q‹ojfklp nrb `lkqfbkbk e abp^m^ob`bk v nrba^
'6-24(a!
ap-?< pew'b2`lp b2p, l` oajb2p(G * pbk b2p?x ,
6-03 Nqolp j‹qlalp m^o^ `^i`ri^o ap?- bk `^plp bpmb`f^ibp
Di j‹qlal ab Orqwbo m^o^ bumobp^oap? `ljl rk mlifkljfl bk ? bp `ljmibq^,jbkqb dbkbo^i ab_fal ^ nrb bp sŠifal m^o^ qla^p i^p j^qof`bp `r^ao^a^p ?- Tkj‹qlal dbkbo^i kl pfbjmob bp bi jŠp pbk`fiil bk `fboqlp `^plp m^oqf`ri^obp- Dk bpq^pb``fŽk a^jlp j‹qlalp jŠp pbk`fiilp m^o^ `^i`ri^o ap? bk qobp `^plp bpmb`f^ibp9^( Br^kal qlalp ilp ^rqls^ilobp ab ? plk fdr^ibp+ _( `r^kal qlalp ilp ^rqls^ilobpab ? plk afpqfkqlp+ v b( `r^kal ? qfbkb alp ^rqlsŠilobp afpqfkqlp v rkl ab biilpmob`fp^jbkqb ab jriqfmif`fa^a 0-
SDNQDL@ 6-0/- Qe? ao qj] i]pnev j Wj _kj pk`ko oqo ]qpkr]hknao ecq]hao] @+ajpkj_ao pajaiko
Baikopn]_e‰j-qbkbjlp
k,i g
ap-?< a:-pJ ,-f &? + H--Gp-g<M g
Orbpql nrb i^p j^qof`bp KG v p'? , @i( plk mbojrq^_ibp
'6-25(
Mpnko i†pk`ko l]n] _]h_qh]nap? -02
Di qblobj^ ab B^vibv,G^jfiqlk fjmif`^ nrb &? + ?h(g < N m^o^qlal g y j+ ^pŒnrb bi qblobj^ nrba^ abjlpqo^al-
SDNQDL@ 6-00- Qe ? ao qj] i]pnev j Wj _kj j ]qpkr]hknao `eopejpko@i + @1 + ’’’ ++[+++ ajpkj_ao pajaiko
&+-ap? <0…%gJg&?'*
g<h
`kj`a Jg&?' ao qj lkhejkiek `a cn]`k j , 0 `]`k lkn h] b‰niqh]
Jg'?(- < kk ? , ?9b g 0 1l]n] <! --- +j -e;h ?g + ?+e)g &
M^oanr]_e‰j9 Klp mlifkljflp Jg'?( pb ii^j^k _kabe_eajpaoa ejpanlkh]_e‰jaJ]cn]jca-
Baikopn]_e‰j- Cbcfk^jlp rk^ crk`fŽk j^qof`f^i D mlo i^ b`r^`fŽk
j
'6-26( D'p( <0…:gJg&?'g<h
v `ljmol_bjlp nrb E p^qfpc^`bi^ b`r^`fŽk afcbobk`f^i D%&p'< ?D&p' X i^ `lkaf,`fŽk fkf`f^i D&M' < h, Cb '6-26( sbjlp nrb
j
?D&p' + D%&p'< haSg&? + ?gG(Jz.?(-h<i
Rbd•k bi qblobj^ ab B^vibv,G^jfiqlk qbkbjlp &? + ?gh(Jg'?( < N m^o^`^a^ g*ab jlal nrb E p^qfpc^`bi^ b`r^`fŽk afcbobk`f^i D%&p'< ?D&p',
O^o^ `ljmibq^o i^ abjlpqo^`fŽk kb`bpfq^jlp mol_^o nrb E p^qfpc^`bi^ `lk,af`fŽk fkf`f^i D'M( < G+nrb pb `lksfboqb bk
'6-27(
Dk bi bgbo`f`fl 05 ab i^ pb``fŽk 6-04 pb bp_lw^ rk^ abjlpqo^`fŽk ab '6-27(-Di qblobj^ nrb pfdrb qo^q bi `^pl bk bi nrb ? qfbkb alp ^rqls^ilobp afpqfk,
qlp+rkl ab ilp `r^ibp qfbkbmob`fp^jbkqb jriqfmif`fa^a 0-
SDNQDL@ 6-01- Qa] ? qj] i]pnev j t j 'j y 2( _kj `ko ]qpkr]hknao `eopej,pko@v ml+ p]haomqa@ peajaiqhpelhe_e`]` j , 0 X ml peaja iqhpelhe_e`]` 0- Rajaikoajpkj_ao
147 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
jy1 pg wa.hp a! j,1 g xp? ?p + ? \ H,Gg \ ----- ] g \ k,i&
a < a „g & ' * &pe\ @v,i 'zp \ ?(j,h „ g 'zp ?( '? ?h(h<N h<N
Baikopn]_e‰j- Bljl bk bi `^pl abi qblobj^ 6-0/ bjmbw^jlp bp`of_fbkal
// g j,1 g // gap? < a?p %! - --, '? , H-Gh< a! &! ----- '? , H-Gh* a! &! --, '? \ H-G(gK---g K---g K--- g
hzN hzN g<j,h
j,1 pg // pj,h)n; a! &! , '? , ?h(g * a?p %! +++++ '? \ ?h(j,0*n-:Qg y'j,0*n(
B^i`ribjlp ^elo^ bk cloj^ cfkfq^i^ pbofb`lk Œkaf`bn abi pbdrkal q‹ojfkl abi pb,drkal jfbj_ol jbaf^kqb bi qblobj^ ab B^vibv,G^jfiqlk- Orbpql nrb
bk`lkqo^jlp? , zpG< ? , ?-G, 'zp , ?(G
&? + ?-h(j,h'? , zpG(< '? , H-G(j, 'zp , ?('? , ?G(j,h-
Di mofjbo jfbj_ol bp N bk sfoqra abi qblobj^ ab B^vibv,G^jfiqlk ^pŒnrb
'? , ?G(j < 'zp , ?('? , qr+€,
Tp^kal bpq^obi^`fŽk obfqbo^a^jbkqb iibd^jlp ^
Olo `lkpfdrfbkqb i^ pbofb`lk Œkaf`bn pb `lksfboqb bk
y pj,Fn 0 z pg
K--- 'zp , ?n_? , ?-hp,h < ,,, K--- , 'zp , ?(Z? , H-Gp,hozN &j + 0 * n' 'zp , ?p,
hg<j,h g
< 0 wap'.h,:&z\ y -q--- &hh\ ?(gx'? \ H-Gp,h-'zp , ?p+h K---g n9
R8?
Dpql `ljmibq^ i^ abjlpqo^`fŽk-
K^ cŽojri^ bumiŒ`fqabi qblobj^ 6-01 mrbab abar`fopb q^j_f‹k ^mif`^kal bij‹qlal ab Orqwbo+mbol ilp abq^iibp plk jŠp `ljmif`^alp-
K^p cŽojri^p bumiŒ`fq^pab ilp qblobj^p 6-0/+ 6-00 X 6-01 pfosbk m^o^qla^pi^p j^qof`bp ab loabk j3 2- Orbpql nrb bi `^pl 2 W2 bp cob`rbkqb bk i^ moŠ`qf`^+obprjfjlp ^ `lkqfkr^`fŽk i^p cŽojri^p m^o^ j^vlo c^`fifa^a bk pr rqfifw^`fŽk-
Mpnkoi†pk`ko l]n] _]h_qh]nap?
A?QM h- Rf rk^ j^qofw ?+ 2 W2+ qfbkb ^rqls^ilobp u+ &[+&[+bkqlk`bp
148
A?QM h.- Rf rk^ j^qofw ?+ 2 W2+ qfbkb ^rqls^ilobp u+ p,+r+bkqlk`bp
p? q y&?\+y-+h\Gy'&y?\+\rGy' lp &? + %q'&? + rG' * rp \&?\+\?,\G\'&\?\+y-+hh\'a <a *a y,y,,, a -'@- , bh'&?,+ r' &bh+ ?,'&-+h+ r' &r + ?,'&r + -+h'
A?QM GG.- Rf rk^ j^qofw ?+ 2 W2+ qfbkb ^rqls^ilobp &[+&[+m-+ pfbkal+Z<Nl-+ bkqlk`bp
DIDLOKN- B^i`ri^o a! `r^kal ? <Zz l(0 0
Qkhq_e‰j- Klp ^rqls^ilobp ab ? plk 0+ 0+1+ ^pŒnrb i^ cŽojri^ abi `^plfHiHklp a^
G^`fbkal lmbo^`flkbp v loabk^kal l_qbkbjlp
@elo^ v^ mlabjlp `^i`ri^o &? + Gx1 l ? 1 X bcb`qr^o i^p lmbo^`flkbp fkaf`^a^pbk '6-28( l '6-3/( m^o^bp`of_fobi obpriq^al `ljl rk^ j^qofw 2W2-
Y
,1pap * a1p
ap? < ,1'p * h(ap* 1a1p
, 1'p * 1(ap * 3a1p
'2p * 1(ap , 1a1p
'2p * 4(ap , 3a1p
'2p * 7(ap , 7a0p
,'p * h(ap* a
1p[
,'p * 1(ap * 1a1p Œ
, 'p * 2'ab * 2a0p
-1+ Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
/')- 8SN[LRLRX\
O^o^ `^a^ rk^ ab i^p j^qof`bp ab ilp bgbo`f`flp 0 ^i 5+ bumobp^o a&-Œljl rk mlifkljflbk 5(
2 ? y Y9N
9\Z4 ,1\ 0, ? < Z0 1\,/, ? < -3 ,0 1 ,0
N
4- ? y Y: I 5-?wN
z-
N
0,0
z 03?yY N N NN 2
(1 ,00 (1 ,0N N
6- ^( Rb p^_b nrb rk^ j^qofw ?* 2 W2+ qfbkb qlalp prp ^rql s^ilobp fdr^ibp ^ @- Cbjlp,qo^o nrb
_( Dk`lkqo^o rk^ c5ojri^ ^kŠild^ pf ? bp rk^ j^qofw 3 W3 `lk qlalp prp ^rqls^ilobpfdr^ibp ^ W-
Dk `^a^ rkl ab ilp bgbo`f`flp abi 7 ^i 04+ obplisbo bi pfpqbj^ X&<< ?W prgbql ^ i^ `lk,af`f5k fkf`f^i a^a^-
7- ? < F
qT zZ9zz
1\+ X'N( < ZBi\-+/ A0
W&M'< Z9I-
Qeopai]o heja]haojk dkikc†jako 150
05- Dpqb bgbo`f`fl bp_lw^ rk^ abjlpqo^`f5k ab i^ b`r^`f5k '6-27( rqfifw^a^ bk i^ abjlpqo^`f5kabi qblobj^ 6-00- Rb^ Jg&!GZ' bi mlifkljfl bk !0[ ab do^al j , 0 abcfkfal jbaf^kqb
Jg'(-( < fof;he)g
alkab !0[++ ’’’ +!0[- plk j bp`^i^obp afpqfkqlp+^( Cbjlpqo^o nrb
_( Rb^k u! ,,, * o|* j bp`^i^obp ^o_fqo^oflp+ v pb^
j
l&',' < JWgJg'(-(-R`S
Cbjlpqo^o nrb l&!GZ' bp bi •kf`l mlifkljfl ab do^al z j , 0 nrb p^qfpc^`b i^p j b`r^,`flkbp
N'(-g( < Wg m^o^ g < 0+1+ --- +j -
b( Cbjlpqo^o nrb J:<h Jg&!GZ'< 0 m^o^ qlal !0[+v abar`fo +nrb m^o^ qla^ j^qofw `r^ao^a^? qbkbjlp
alkab / bp i^ j^qofw fabkqfa^a-
/'). DR\]NVJ\URWNJUN\WXQXVXPkWNX\LXWLXNORLRNW]N\LXW\]JW]N\
@ `lkqfkr^`fŽk `lkpfabo^jlp bi mol_ibj^ ab s^ilo fkf`f^i kl eljld‹kbl
'6-30( W.'p( < ?W'p( * O'p(+ W&]' < P*
bk rk fkqbos^il b, ? bp rk^ j^qofw `lkpq^kqb j Wj+ P bp rk^ crk`fŽk sb`qlof^ik,afjbkpflk^i '`lkpfabo^al `ljl rk^ j^qofw j WH( `lkqfkr^ bk H* v ] bp rkmrkql a^al bk b, Olabjlp l_qbkbo rk^ cŽojri^ bumiŒ`fqm^o^i^ plir`fŽk ab bpqbmol_ibj^ pfdrfbkal bi jfpjl mol`bpl nrb bk bi `^pl bp`^i^o-
-1- Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
Lriqfmif`^jlp mofjbol ^j_lp jfbj_olp ab '6-30( mlo i^ bumlkbk`f^i j^qof,`f^i a,p? v mlkd^jlp i^ b`r^`fŽk afcbobk`f^i bk i^ cloj^
'6-31( a,p?wW&'p(, ?W'p(x < a,p?O'p(-
Di mofjbo jfbj_ol ab '6-31( bp i^ TBi0s^a^ abi molar`ql a+p?W&p',Olo `lkpf,drfbkqb+pf fkqbdo^jlp ^j_lp jfbj_olp ab '6-31( bkqob] v t- alkab t D Q$l_,qbkbjlp
Lriqfmif`^kal mlo a!? l_qbkbjlp i^ cŽojri^ bumiŒ`fq'6-32( nrb ^m^ob`b bk biqblobj^ pfdrfbkqb-
SDNQDL@ 6-02- Qa]j ? qj] i]pnev _kjop]jpa j t j v P qj] bqj_e‰jra_pkne]hj,`eiajoekj]h _kjpejq] aj qj ejpanr]hk Y- Cjpkj_ao ah lnk^hai] `a r]hkn eje_e]h
W%&p'< ?W&G'* O'p(+ W&]' < @*
peaja qj] okhq_e‰jŠje_] aj 0 `]`] lkn h] b‰niqh]atlh‡_ep]
'6-32(
Bljl bk bi `^pl eljld‹kbl+ i^ afcf`riq^a ^i ^mif`^obpq^cŽojri^ bk ilp `^plpmoŠ`qf`lpo^af`^ bk bi `Ši`ril ab i^p bumlkbk`f^ibp ab j^qof`bp-
N_p‹osbpb nrb bi mofjbo q‹ojfkl+ a:!*+]'?@* bp i^ plir`fŽk abi mol_ibj^ el,jld‹kbl W%&p'< ?W&p'*W&,8+%< @, Di pbdrkal q‹ojfkl bp i^ plir`fŽk abi mol,_ibj^ kl eljld‹kbl
W&'p(< ?W'p( * O'p(+ W&]' < M,
Hirpqo^jlp bi qblobj^ 6-02 `lk rk bgbjmil-
DIDLOKN- Qbplisbo bi mol_ibj^ ab s^ilo fkf`f^i
W&'p(999:9?W&p' * O'p(+ W&M'< @*
Qeopai]o heja]haojk dkikc†jako 152
bk bi fkqbos^il ' , //+ * //(- alkab
Y
a
0p
[O'p( < N +
pa0p
Qkhq_e‰j- Cb ^`rboal `lk bi qblobj^ 6-02+i^ plir`fŽk sfbkb a^a^ mlo
&5,22' W'V( < a!&?cl&! a,p?O'p( `p < 4/&! a'!&,ph?O'p( `p -
Klp ^rqls^ilobp ab ? plk 1+ 1 X 3- O^o^ `^i`ri^o av? rqfifw^jlp i^ cŽojri^ abi`^pl Hii+ pb``fŽk 6-03+ l_qbkfbkal
at? < a1!&wH* t'? , 1G(x * Gb3&! , a1!&('? , 10(1 , eta1!&'? , 10(1
; a0!%wn)t&? + 10( * Fa0V+ 1u , /'&? + 10(1y-
Olabjlp obbjmi^w^o t mlo t + p bk bpq^cŽojri^ m^o^ l_qbkbo a:!%+p'?, Olo `lk,pfdrfbkqb bi fkqbdo^kal bk '6-33( bp
a't,p(?O'p( < a1't,phwH * 'u , p('? , 10( * Gb1'!&,qi , 1't , p( , 0['? , 10(1xO'p(
Z0\ Zu , p [ Y a
1!&a,
1p, 1't , p( , 0\
; a1&!N * '? , 10(a1&! N * z'? , 10(1a1&! N -
p p't , p( a1tpa,1p , 1p't , p( , p
Hkqbdo^kal+bk`lkqo^jlp
Orbpql nrb qbkbjlp
? , 1.< Y9
) -
,0
0 v
153 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
bk`lkqo^jlp
Y
ea1+!, f * t , V1[
< a1+!, ea1+!* f * t * V1 -
fb1&!, f , t * V1
K^p cfi^pab bpq^j^qofw plk i^p crk`flkbp mbafa^p X0I W1+W]-
/')/ 8SN[LRLRX\
0- Rb^ Y rk^ plir`fŽk abi pfpqbj^ kl eljld‹kbl
X%&p'< ?X&p' * O&p'*
bk rk fkqbos^il + `lk s^ilo fkf`f^i X&]', Cbjlpqo^o nrb bufpqbrk^ pli^ plir`fŽk abipfpqbj^ eljld‹kbl
u%&p'< ? W&p'* O&p'
bk + `lk s^ilo fkf`f^i W&]' v nrb sfbkb a^al mlo i^ cŽojri^
W&p'< X&p' * a&p+]'?wW&]' + X&]'x,
@ jbkral pb afpmlkb ab lqolp j‹qlalp m^o^ abqbojfk^o rk^ plir`fŽk m^oqf`ri^oX&p' nrb ^pbjbg^ ^ i^ crk`fŽk a^a^ M&p', Klp bgbo`f`flp 1+ 2+ 4+ X 6 fkaf`^k q^ibpj‹,qlalp m^o^ M&p'< B *M&p' < a]pA *M&p' < pnA* v M&p' < '`lp ]p'A * 'pbk ]p'B* alkabB v C plk sb`qlobp `lkpq^kqbp-Rf i^ plir`fŽk m^oqf`ri^o^pŒl_qbkfa^ X&p' kl qfbkb bis^ilo fkf`f^i mbafal+jlafcf`^jlp X&p' `ljl pb fkaf`^ bk bi bgbo`f`fl 0 m^o^l_qbkbo lqo^plir`fŽk W&p' `lk bi s^ilo fkf`f^i bufdfal-
1- ^( Rb^ ? rk^ j^qofw `lkpq^kqb j&t j+ @ v B pb^k sb`qlobp `lkpq^kqbp k,afjbkpflk^ibp-Cbjlpqo^o nrb i^ plir`fŽk abi pfpqbj^
u%&p'< ?W&p' * b+ W&]' < @*
bk ', //+ * //( sfbkb a^a^ mlo i^ cŽojri^
Cean_e_eko 154
_( Rf ? bp kl pfkdri^o+ abjlpqo^o nrb i^ fkqbdo^i abi ^m^oq^al ^( qfbkb bi s^ilowa&!*++]G?\ Gx?,h-b( B^i`ri^o W&t' bk cloj^ bumiŒ`fq^r^kal
2- Rb^k ? rk^ j^qofw `lkpq^kqb+jr:j+ v @ X B sb`qlobp `lkpq^kqbp k,afjbkpflk^ibp+ v pb^ ]rk bp`^i^o a^al-^( Cbjlpqo^o nrb bi pfpqbj^ kl eljld‹kbl X%&p'< ?X&p' * akp A qfbkb rk^ plir`fŽkab i^ cloj^ X&p' < akp@ pf+v pŽil pf+&]h + ?'@ < B-_( Rf ] kl bp rk ^rqls^ilo ab ?* abjlpqo^o nrb bi sb`qlo @ pfbjmob pb mrbab bibdfoab jlal nrb bi pfpqbj^ abi ^m^oq^al ^( qbkd^ rk^ plir`fŽk ab i^ cloj^ X&p' < a]p @,`( Rf ] kl bp rk ^rqls^ilo ab ?+ abjlpqo^o nrb qla^ plir`fŽk abi pfpqbj^u%&p'< ?W&p'* a!pApeaja i^ cloj^ W&p'< aG?'u'M( , @( * a]p@+alkab @ < 'ntG,+ ?'+hA,
3- Tqfifw^o bi j‹qlal prdbofal mlo bi bgbo`f`fl 2 m^o^ e^ii^o rk^ plir`fŽk abi pfpqbj^ kleljld‹kbl W%&p'< ? W&p'* a0pA `lk
W&M' < FI-4- Rb^k ? rk^ j^qofw `lkpq^kqb j t9j+ @ v B sb`qlobp `lkpq^kqbp w,aijbkpflk^ibp+ v i
rk bkqbol mlpfqfsl-^( Cbjlpqo^o nrb bi pfpqbj^ kl eljld‹kbl W%&p'< ?W&p' * p%!A*X'N( < @*qfbkb rk^plir`fŽk m^oqf`ri^o ab i^ cloj^
bk alkab @,*@** ,,, -@: plk sb`qlobp `lkpq^kqbp+ pf v pŽil pf
0B< \*?bbhF@,
U(
Cbqbojfk^o ilp `lbcf`fbkqbp @,*@** ,,, ,@• m^o^ rk^ q^i plir`fŽk-_( Rf ? bp kl pfkdri^o+ abjlpqo^o nrb bi sb`qlo fkf`f^i @pfbjmob mrbab bibdfopbab j^,kbo^ nrb bi pfpqbj^ abi ^m^oq^al ^( qbkd^ rk^ plir`fŽk ab i^ cloj^ fkaf`^a^-
5- Blkpfa‹obpb bi pfpqbj^ kl eljld‹kbl
uy < 2Wh* W1 * p2
uy < 1Wh * 1W1 * p1‹
^( Dk`lkqo^o rk^ plir`fŽk m^oqf`ri^o ab i^ cloj^ W&p'< @,* p@** b@v* p%@‹,_( Dk`lkqo^o rk^ plir`fŽk abi pfpqbj^ `lk i^ `lkaf`fŽk v+'N( < X1'N( < 0 -
6- Rb^k ? rk^ j^qofw `lkpq^kqb j Wj+ @*B+C sb`qlobp `lkpq^kqbp k,afjbkpflk^ibp v ] rkk•jbol ob^i kl kril a^al- Cbjlpqo^o nrb bi pfpqbj^ kl eljld‹kbl
v&'o( < ? W'p( * '`lp ntp(A * 'pbk ntp(B+ W&M' < @*
-11 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
qfbkb rk^ plir`fŽk m^oqf`ri^o ab i^ cloj^
W'p( < '`lp n9t-p(C* 'oajn9t-p(D+
pfbkal C X E sb`qlobp `lkpq^kqbp+ pf v pŽil pf
'?1 * nz+1G(@< ,'?A * |B(:
Cbqbojfk^o C X E bk crk`fŽk ab ?* @*b m^o^ rk^ q^i plir`fŽk- N_p‹osbpb nrb pf?& * /0&[ bp kl pfkdri^o+ bi sb`qlo+ fkf`f^i @ pfbjmob pb mrbab bibdfo ab jlal nrb bi pfp,qbj^ qbkd^ rk^ plir`fŽk ab i^ cloj^ fkaf`^a^-
7- ^( G^ii^o rk^ plir`fŽk m^oqf`ri^o abi pfpqbj^ kl eljld‹kbl
XŒ< Wh* 2X1 * 3 pbk 1p
_( G^ii^o rk^ plir`fŽk abi pfpqbj^ `lk i^p `lkaf`flkbp u*&M' < u*&M' < 0-
Dk `^a^ rkl ab ilp bgbo`f`flp 8 ^i 01+ obplisbo bi pfpqbj^ kl eljld‹kblW%&p'< ?W&p' * O&p' prgbql ^ i^ `lkaf`fŽk fkf`f^i fkaf`^a^-
7, ? < Z 3 9i O'p( < Z N qi W'M( < Fi,1 ,1a
Z,4 ,ii O'p( < Ya i W'M( < Z99\-/., ? < 0(. a0p
Z,4 ,ii Y 6ap
+ 16\ Z ]‚3/3/16\00-? < 1 O'p( < + W'M( < -(. ,2ap * 01 ,)ZS
110
Z,0,0 ,y O'&(y ZziX'N( z Z,90/0, ? < N ,0
N N ,0
6-07 Rfpqbj^ ifkb^i dbkbo^i W-&p'< N&p'W&p'* O&p'
Di qblobj^ 6-02 a^ rk^ cŽojri^ bumiŒ`fqm^o^i^ plir`fŽk abi pfpqbj^ ifkb^i
W&'p( < ? W'p(* O'p(+ W'](<@+
Qeopai] heja]h cajan]h -12
alkab ? bp rk^ j^qofw `lkpq^kqb j Wj v O&p'* W'p( plk j^qof`bp `lirjk^ j W0-Ulisbjlp ^elo^ ^i `^pl jŠp dbkbo^i
'6-34( W-&p'< N&p'W&p'* O'p(+ W&]' < @*
bk alkab i^ j^qofw N&p'* j Wj+ kl bp kb`bp^of^jbkqb `lkpq^kqb-Rf N X P plk `lkqfkr^p bk rk fkqbos^il ^_fboql H*rk qblobj^ dbkbo^i ab bufp,
qbk`f^ v rkf`fa^a nrb abjlpqo^objlp jŠp ^abi^kqb klp af`b nrb m^o^`^a^ ] ab /v `^a^ sb`qlo fkf`f^i @ bufpqbrk^ pli^ plir`fŽk m^o^bi mol_ibj^ ab s^ilo fkf`f^i'6-34(- Dk bpq^ pb``fŽk rqfifw^jlp bpqbobpriq^al m^o^ l_qbkbo rk^ cŽojri^ m^o^i^ plir`fŽk+ nrb dbkbo^ifw^bi qblobj^ 6-02-
Dk bi `^pl bp`^i^o &j < 0( i^ b`r^`fŽk afcbobk`f^i '6-34( mrbab obplisbopbabi jlal pfdrfbkqb-Rb^?&t' < byN&p'`p*jriqfmifnrbjlp bkqlk`bp ^j_lp jfbj_olpab '6-34( mlo a+?&pxmlkfbkal i^ b`r^`fŽk afcbobk`f^i bk i^ cloj^
'6-35( a,?;phwW&'p(, N'p(W'p(x < a,?'phO'p(-
Di mofjbo -jfbj_ol bp i^ abofs^a^ abi molar`ql a,? &pxW&p',Olo `lkpfdrfbkqb+ ml,abjlp fkqbdo^o^j_lp jfbj_olp bkqob] v t+ pfbkal ] v t mrkqlp ab H* v l_qb,kbjlp
Lriqfmif`^kal mlo a?'!x pb iibd^ ^ i^ cŽojri^ bumiŒ`fq^
'6-36(
K^ •kf`^ m^oqbab bpqbo^wlk^jfbkql nrb kl bp ^mif`^_ib ^ i^p crk`flkbp j^,qof`f^ibpbp i^ ^cfoj^`fŽk ab nrb bi mofjbo jfbj_ol ab '6-35( bp i^ abofs^a^ abimolar`ql a+?&pxu&p',Dk bpqb mrkql rqfifw^jlp bi eb`el ab nrb i^ abofs^a^ aba+?&pxbp +N&p'a+?&px, Dk bi `^pl bp`^i^o bpql bp rk^ `lkpb`rbk`f^ ab i^ cŽojri^pfdrfbkqb m^o^i^ abofs^`fŽk ab i^p crk`flkbp bumlkbk`f^ibp
Rf C'p( < a?;ph+ bkqlk`bp C&'p(< ?&'p(a?'ph-
Cbpdo^`f^a^jbkqb+ bpq^cŽojri^ ab abofs^`fŽk kl pfbjmob bp sŠifa^ `r^kal ? bprk^ crk`fŽk j^qof`f^i- Olo bgbjmil+ bp c^ip^ m^o^ i^ crk`fŽk j^qof`f^i 1 W1
?&p' <Zz9\ 'Ubo bgbo`f`fl 6 ab i^ pb``fŽk 6-01(- Olo q^kql bp kb`bp^ofl rk^
-13 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
jlafcf`^`fŽk abi o^wlk^jfbkql m^o^ buqbkabo i^ b`r^`fŽk '6-36( ^i `^pl ab i^pj^qof`bp-
Rrmlkd^jlp nrb jriqfmif`^jlp `^a^ jfbj_ol ab '6-34( mlo rk^ j^qofwD&p'*j Wj+ kl bpmb`fcf`^a^-Dpql klp a^ i^ obi^`fŽk
D'p( W&'p(< D'p(N'p( W'p( * D'p(O'p(-
Rrjbjlp ^elo^ ^ ilp alp jfbj_olp D&'p(u'p( `lk i^ fab^ ab qo^kpcloj^o bi mofjbojfbj_ol bk i^ abofs^a^ abi molar`ql D'p(W'p(- Rf e^`bjlp bpql+i^ •iqfj^ b`r^,`fŽk klp a^
wD'p(W'p(h&< wD&'p(* D'p(N'p(x W'p( * D'p(O'p(-
Rf mlabjlp bibdfoi^ j^qofw D'p( ab j^kbo^ nrb i^ prj^ wD&'p(* D'p(N'p(x abi pb,drkal jfbj_ol pb^ i^ j^qofw `bol+ i^ •iqfj^ b`r^`fŽk pb pfjmifcf`^ v nrba^
wD'p(W'p(x&< D'p(O'p(-
Hkqbdo^kal ‹pq^ abpab ] ^ t l_qbkbjlp
D't(W't( , D'](W']( <oD'p(O'p( `p-
Rf+^abjŠp+ i^ j^qofw D&t' bp kl pfkdri^o+l_qbkbjlp i^ cŽojri^ bumiŒ`fq^
'6-37( W't( < D't(,hD'](W']( * D'V(,h oG9'p(O'p( p-
†pq^ bp rk^ dbkbo^ifw^`fŽkab i^ cŽojri^ bp`^i^o '6-36(- Di mol`bpl crk`flk^oŠ_fbk pf mlabjlp bk`lkqo^o rk^ crk`fŽk j^qof`f^i D&p'* j Wj+ nrb p^qfpc^d i^ b`r^,`fŽk afcbobk`f^i j^qof`f^i
D&'p(< ,D'p(N'p(
v nrb kl pb^ pfkdri^o-N_p‹osbpb nrb bpq^b`r^`fŽk afcbobk`f^i bp jrv m^ob`fa^ ^ i^ b`r^`fŽk afcb,
obk`f^i lofdfk^i '6-34( `lk O&p' < N+ p^isl nrb i^ crk`fŽk fk`Ždkfq^ D&p' bp rk^j^qofw `r^ao^a^ bk ird^o ab rk^ j^qofw `lirjk^- @pfjfpjl+ i^ crk`fŽk fk`Ždkfq^bpqŠjriqfmif`^a^ ^ i^ abob`e^ mlo , N&p' bk ird^o ab bpq^oil ^ i^ fwnrfboa^ mloN&p',
Rbdrfa^jbkqb abjlpqo^objlp nrb i^ b`r^`fŽk afcbobk`f^i m^o^ E pfbjmobqfbkbrk^ plir`fŽk kl pfkdri^o- K^ abjlpqo^`fŽk abmbkaboŠabi pfdrfbkqb qblobj^ab bufpqbk`f^ m^o^ pfpqbj^p ifkb^ibp eljld‹kblp-
Qeopai] heja]hcajan]h -14
SDNQDL@ 6-03- Qqlkjc]iko mqa ?'p( ao qj] bqj_e‰j i]pne_e]h j t9j _kj,pejq] aj qj ejpanr]hk ]^eanpk b, Qe] D / v @ao qj ra_pkn j,`eiajoekj]h `]`k+ ahoeopai] heja]hdkikc†jak
W&'p(< ?'p( W'p(+ W&]' < /%
peaja aj / qj] okhq_e‰jX mqa ao qj ra_pkn j,`eiajoekj]h
Dk i^ pb``fŽk 6-10 a^jlp rk^ abjlpqo^`fŽk ab bpqbqblobj^- Blk i^ ^vra^ab ‹pqb mlabjlp abjlpqo^o bi pfdrfbkqb-
SDNQDL@ 6-04- B]`] qj] bqj_e‰j i]pne_e]h N+jr:j+ _kjpejq] aj qj ejpan,r]hk ]^eanpk! v `]`k qj lqjpk _q]hmqean]] aj ! ateopaqj] bqj_e‰j i]pne_e]h E+j Wj+ mqa o]peob]_ah] a_q]_e‰j`ebanaj_e]h i]pne_e]h
'6-38( D&'t( < ,D't(N't(
aj / _kj ah r]hkn eje_e]hD']( < h-?`ai…o+ D't( ao jk oejcqh]n l]n] _]`] t aj h,
Baikopn]_e‰j- Rb^ Wg&V' rk^ plir`fŽk sb`qlof^i ab i^ b`r^`fŽk afcbobk`f^i
bk / `lk sb`qlo fkf`f^i Wg&]' < he+alkab e bp i^ `lirjk^ g ab i^ j^qofw fabkqf,a^a J+j Wj- @nrŒN't(p obmobpbkq i^ qo^kpmrbpq ab N't(- Rb^ E't( i^ j^qofwj Wj `rv^ `lirjk^ g bp Wg&V', Dkqlk`bp F p^qfpc^`bi^ b`r^`fŽk afcbobk`f^i j^,qof`f^i
'6-4/( F&'t( < , N't(pE't(
bk / `lk s^ilo fkf`f^i E&]' < h, Sljbjlp ^elo^ i^ qo^kpmrbpq ab `^a^ jfbj_olab '6-4/(- Orbpql nrb i^ qo^kpmrbpq ab rk molar`ql bp bi molar`ql ab i^p qo^kp,mrbpq^pbk loabk fksboqfal+ l_qbkbjlp
wE&'t(N< ,E't(pN't(+
S^j_f‹k+ i^ qo^kpmrbpq ab i^ abofs^a^ F&bp i^ abofs^a^ ab i^ qo^kpmrbpq E&+Olo q^kql i^ j^qofw D't( < E't(p p^qfpc^`b i^ b`r^`fŽk afcbobk`f^i '6-38( `lks^ilo fkf`f^i D&]' < h,
Cbjlpqobjlp ^elo^ nrb D&t' bp kl pfkdri^o `lkpqorvbkal pr fksbop^- Rb^ G -&i^ crk`fŽk j^qof`f^i j Wj `rv^ `lirjk^ g bp i^ plir`fŽk ab i^ b`r^`fŽk afcbobk`f^i&
W&'t(< N't(W't(
-2+ Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
`lk s^ilo fkf`f^i W&]' < Go+i^ `lirjk^ g ab h, Dkqlk`bp G p^qfpc^`b bi mol_ibj^ab s^ilo fkf`f^i
F%&t' < N&t'F&t'* F']( < 0+
bk .- Di molar`ql D&t'F&t' qfbkb abofs^a^
D&t'F%&t' * D%&t'F&t' < D&t'N&t'F&t' + D&t'N&t'F&t' < M
m^o^ `^a^ t ab .- Olo `lkpfdrfbkqb bi molar`ql D&t'F&t' bp `lkpq^kqb+ D&t'F&t' ;; D&]'F&]' < /* ^pŒnrb F&t' bp i^ fksbop^ ab D&t', Dpql `ljmibq^ i^ abjlp,qo^`fŽk-
Dk bi qblobj^ nrb pfdrb nrba^k obprjfalp ilp obpriq^alp ab bpq^ pb``fŽk-
SDNQDL@ 6-05- B]`]o qj] bqj_e‰j i]pne_e]h N+ j o_j+ v qj] bqj_e‰j ra_,pkne]h j,`eiajoekj]h P+ ]i^]o _kjpejq]o aj qj ejpanr]hk ]^eanpk H*h] okhq_e‰j `ahlnk^hai] `a r]hkn eje_e]h
'6-40( W%&t'< N&t' W&t' * O&t'* W&]' < @*
aj H reaja `]`k lkn h] b‰niqh]
'6-41( W't( < D't(,hW']( * D'V(,h q&D'p(O'p( `p-
J] i]pnev D't(+ j Wj+ ao h] pn]jolqaop] `a h] i]pnev _qu] _khqij] g ao h] okhq_e‰j`ah lnk^hai] `a r]hkn eje_e]h
'6-42( W%&t'< +N&t'hW&t'* W']( < Gg+
aj `kj`a 0g ‹ ao h] _khqij] g `a h] i]pnev e`ajpe`]` h-
@rknrb bi qblobj^ 6-05 molmlo`flk^ rk^ cŽojri^ bumiŒ`fq m^o^ i^ obplir`fŽkabi pfpqbj^ ifkb^i dbkbo^i '6-40(+ q^i cŽojri^ kl pfbjmob obpriq^ •qfi m^o^ `^i`ri^oi^ plir`fŽk ab_fal ^ i^ afcf`riq^a nrb prmlkb i^ abqbojfk^`fŽk ab i^ crk`fŽk j^,qof`f^i E- Diil bufdb i^ plir`fŽk ab j pfpqbj^p ifkb^ibp eljld‹kblp '6-42(- Dk i^pfdrfbkqb pb``fŽk pb bumlkb rk j‹qlal `lk pbofbp ab mlqbk`f^p nrb ^ sb`bp pbbjmib^ bk i^ obplir`fŽk ab pfpqbj^p ifkb^ibp eljld‹kblp {- ,
Tk^ sbw jŠp ob`loa^jlp ^i ib`qlo nrb i^ abjlpqo^`fŽk abi qblobj^ 6-05 pb_^pŽ bk bi qblobj^ ab bufpqbk`f^ 6-03+ m^o^ ilp pfpqbj^p ifkb^ibp eljld‹kblp+ nrbqla^sŒ^ kl ebjlp abjlpqo^al-
Paokhq_e‰j a oeopai]o heja]haodkikc†jako 160
6-08 Qbplir`fŽk ab pfpqbj^p ifkb^ibpeljld‹kblp jbaf^kqb pbofbpab mlqbk`f^p
Blkpfabobjlp rk pfpqbj^ ifkb^i eljld‹kbl
'6-43( W%&t'< ?&t' W&t'* W&M'< @*
bk bi nrb i^ j^qofw ?* j Wj+ a^a^ qfbkbrk abp^ooliil bk pbofbab mlqbk`f^p ab t`lksbodbkqb bk rk `fboql fkqbos^il ^_fboql nrb `lkqbkd^ bi lofdbk+ q^i `ljl
?&t' < ?k * t?0 * V>:?1 * --- * tg ?g * --- + m^o^ Zu\; &0&
alkab ilp `lbcf`fbkqbp ?k+ ?y* ?1+ ŒŒŒ plk j^qof`bp j Wj a^a^p- Hkqbkqbjlp bk`lk,qo^ork^ pbofbab mlqbk`f^p plir`fŽk ab i^ cloj^
`lk ilp sb`qlobp @k+@|* @1+ ŒŒŒ `ljl `lbcf`fbkqbp- Orbpql nrb W&M' < @o+ i^ `lkaf`fŽk fkf`f^i pb p^qfpc^oŠqlj^kal @k < @*bi sb`qlo fkf`f^i mobp`ofql-O^o^ abqbo,jfk^o ilp `lbcf`fbkqbp obpq^kqbpprpqfqrfjlp i^ pbofbab mlqbk`f^p nrb a^ W&t' bki^ b`r^`fŽk afcbobk`f^i b fdr^i^jlp ilp `lbcf`fbkqbp ab mlqbk`f^p pbjbg^kqbp ab tl_qbkfbkal bi pfdrfbkqb pfpqbj^ ab b`r^`flkbp
'6-44(g
&g* h(@g*h < y?n@g\n m^o^ g < 0+1+----X8?
Dpq^pb`r^`flkbp mrbabk obplisbopb bk qloj^ pr`bpfs^ obpmb`ql ^ ilp sb`qlobp@0+@1+ŒŒŒŒ Rf i^ pbofb ab mlqbk`f^p ab W&t' nrb obpriq^ `lksbodb bk rk `fboqlfkqbos^il Hui; n1+ bkqlk`bp W&t' pboŠrk^ plir`fŽk abi mol_ibj^ ab s^ilo fkf`f^i'6-43( bk bi fkqbos^il th ; n+ pfbkal n < jfk wnh+n1x-
Olo bgbjmil+ pf ?&t' bp rk^ j^qofw `lkpq^kqb ?* bkqlk`bp ?k < ? X ?g < Nm^o^g:&990+^pŒnrb bi pfpqbj^ ab b`r^`flkbp '6-44( pb `lksfboqb bk
@0< ?@* &g * h(@g*h < ?@0n- m^o^ g y 0-
Qbplisfbkal bp^p b`r^`flkbp pr`bpfs^jbkqb bk`lkqo^jlp
m^o^ g y 0-
Olo q^kql bk bpqb`^pl i^ pbofbplir`fŽk qlj^ i^ cloj^
-2- Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
Dpql bpqŠ ab ^`rboal `lk bi obpriq^al l_qbkfal ^kqbp m^o^ ilp pfpqbj^p ifkb^ibpeljld‹kblp `lk `lbcf`fbkqbp `lkpq^kqbp-
/'*( 8SN[LRLRX\
0- Rb^k l rk^ crk`fŽk ab s^ilobp ob^ibp v P rk^ crk`fŽk j^qof`f^i jt 0+^j_^p `lkqfkr^pbk rk fkqbos^il .- Rb^ ? rk^ j^qofw `lkpq^kqb j Wj- Cbjlpqo^o nrb bi mol_ibj^ abs^ilo fkf`f^i
u&&t' < l&t'? W&t' * O&t'* W&]' < @*
qfbkb i^ plir`fŽk
bk H* alkab m&t' < Iz l&p' `p -1- Blkpfabo^o bi `^pl m^oqf`ri^o abi bgbo`f`fl 0 bk bi nrb ? pb^ kl pfkdri^o+ ];M* l&t';0t*
v O&t' < tA* pfbkal B rk sb`qlo `lkpq^kqb- Cbjlpqo^o nrb i^ plir`fŽk pb `lksfboqb bk
2- Rb^k ?&p' rk^ crk`fŽk j^qof`f^i j t j v C&p' < a!&%',Rb^k O&p'* W&p' v @ j^qof`bp`lirjk^ j W0- Rrmlkd^jlp nrb
C%&p'< ?%&p'C&p'
bk rk fkqbos^il ^_fboql H, Rf ] D H v pf ?& v P plk `lkqfkr^p bk H* abjlpqo^o nrb bimol_ibj^ ab s^ilo fkf`f^i
u&&p' < ?%'o( W&p'* O&p'* W&]' < @*
qfbkb i^ pfdrfbkqb plir`fŽk bk H8
W&t' < a?&!%'a+?&]'@ * a?&!*'H8a+?&p'O&p' p,
3- Rb^ C&p' < b!'H(- Dpqb bgbo`f`fl jrbpqo^ bgbjmilp ab crk`flkbp j^qof`f^ibp ?&p' m^o^ i^pnrb C%&p'< ?%&p'C&p',^( Prb pb^ ?&p' < p%?*alkab ? bp rk^ j^qofw `lkpq^kqb jtj v o rk bkqbol mlpfqfsl-Cbjlpqo^o nrb C%&p'< ?%&p'C&p'bk ', //+ * //( ’
_( Rb^ ?&p' rk mlifkljfl bk p `lk j^qof`bp `ljl `lbcf`fbkqbp
i?&p' < Hpn?nk
Y4=
Baikopn]_e‰j `ah paknai] `a ateopaj_e] -2.
pfbkal ilp `lbcf`fbkqbp mbojrq^_ibp ?*?* < ?*?* m^o^ qlalp ilp n v o- Cbjlpqo^o nrbC%&p'< ?%&p'C&p'bk ', //+ * //(-
b( Qbplisbo bi pfpqbj^ ifkb^i eljld‹kbl
u&&p'< '. * p?' W&p'* W&M' < @
bk bi fkqbos^il ', //+ //(+ alkab ? bp rk^ j^qofw `lkpq^kqb j Wj-4- Rrmlkd^jlp nrb i^ crk`fŽk j^qof`f^i+ jo_j* ?&t' ^ajfqb rk abp^ooliil bk pbofb ab ml,
qbk`f^p `lksbodbkqb m^o^ {ui ; n , Cbp^oolii^o rk mol`bafjfbkql m^o^ obplisbo+ jbaf^kqbabp^ooliil bk pbofb+bi pfdrfbkqb pfpqbj^ ifkb^i eljld‹kbl ab pbdrkal loabk9
W!&t' < ?&t'W&t'* `lk W&M' < @* W%&M'< B-
5- Blkpfabo^o bi pfpqbj^ ab pbdrkal loabk u!&t' * ?W&t' < N+`lk X'N( < @* W%&M'< balkab ? bp rk^ j^qofw `lkpq^kqb j Wj- Cbjlpqo^o nrb bi pfpqbj^ qfbkb i^ pbofb ab ml,qbk`f^p plir`fŽk
`lksbodbkqb m^o^ , // ; t ; * // ’
6-10 Cbjlpqo^`fŽk abi qblobj^ ab bufpqbk`f^mlo bi j‹qlal ab i^p ^molufj^`flkbppr`bpfs^p
Dk bpq^ pb``fŽk abjlpqo^jlp i^ bufpqbk`f^ v rkf`fa^a ab rk^ plir`fŽk m^o^`r^inrfbo pfpqbj^ ifkb^i eljld‹kbl
'6-45( W%&p'< ?&p'W&p'*
alkab ?&p' bp rk^ crk`fŽk j^qof`f^i j Wj+ `lkqfkr^ bk rk fkqbos^il ^_fboql b,Cbjlpqo^objlp nrb m^o^rk mrkql `r^inrfbo^ ] ab H v `r^inrfbo sb`qlo fkf`f^i @bufpqb bu^`q^jbkqb rk^ plir`fŽk u&p' bk H nrb p^qfpc^`b i^ `lkaf`fŽk fkf`f^iW&]' < @,
Tp^objlp bi i†pk`k `a ]lnktei]_ekjao oq_aoer]o+nrb bp rk j‹qlal fqbo^qfsl^mif`^_ib q^j_f‹k ^ lqolp jr`elp mol_ibj^p- Erb mr_if`^al mofjbol mlo Kflrsfiibbk 0727 bk `lkbufŽk `lk bi bpqrafl ab i^p b`r^`flkbp afcbobk`f^ibp ifkb^ibp ab pb,drkal loabk- LŠp q^oab crb buqbkafal mlo I- B^nr‹ bk 0753+ K- Er`ep bk 076/+v F- Ob^k^ bk 0777 ^i bpqrafl ab i^p b`r^`flkbp ifkb^ibp ab loabk j- Dk 078/†jfib Of`^oa '0745,0830( buqbkafŽ bi j‹qlal ^i ^_^o`^o q^j_f‹k i^p b`r^`flkbpafcbobk`f^ibp kl ifkb^ibp- Dk ob`lkl`fjfbkql ^ pr `lkqof_r`fŽk crka^jbkq^i+ ^i,drklp ^rqlobp il `fq^k `ljl bi i†pk`k `a Ne_]n`k Di fkqbo‹p abi j‹qlal kl bp
163 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
pŽil qbŽof`l pfkl nrb q^j_f‹k pb rp^ bk ^idrklp `^plp m^o^ l_qbkbo i^p ^molufj^,`flkbp krj‹of`^p ab i^p plir`flkbp-
Di j‹qlal bjmfbw^ qlj^kal rk^ prmrbpq^ plir`fŽk ab i^ b`r^`fŽk '6-45(-Slj^jlp `ljl q^i bi sb`qlo fkf`f^i a^al @*pf _fbk bpql kl bp bpbk`f^i- Rrpqfqrfjlpbkqlk`bp bpq^ prmrbpq^ plir`fŽk bk bi pbdrkal jfbj_ol ab i^ b`r^`fŽk v l_qbkb,jlp rk^ krbs^ b`r^`fŽk afcbobk`f^i
W&'p(< ?'p(@-
&Dk bpq^ b`r^`flk bi pbdrkal jfbj_ol v^ kl `lkqfbkb i^ crk`fŽk fk`Ždkfq^+ ^pŒnrb i^ b`r^`fŽk mrbab obplisbopb fkjbaf^q^jbkqb fkqbdo^kal ^j_lp jfbj_olp-bkqob ] v t+ pfbkal t rk mrkql ^o_fqo^ofl ab H, Dpq^ b`r^`fŽk qfbkb bu^`q^jbkqbrk^ plir`fŽk v+bk H nrb p^qfpc^`b i^ `lkaf`fŽk fkf`f^i W*&]' < @* l pb^
W0&t' < @ * x&!?'p(@ `p-
Qbbjmi^w^jlp ^elo^ W&p' mlo W*&p' bk bi pbdrkal jfbj_ol ab i^ b`r^`fŽkafcbobk`f^i lofdfk^i '6-45( l_qbkfbkal rk^ krbs^ b`r^`fŽk afcbobk`f^i
W-&p'< ?&p' W0&p',
Dpq^ b`r^`fŽk qfbkb rk^ pli^ plir`fŽk X1 bk H `lk i^ `lkaf`fŽk W1&]' < @*
'6-46(
Rrpqfqrfjlp bkqlk`bp X1 bk bi pbdrkal jfbj_ol ab '6-45( v obplisbjlp i^ b`r^`fŽkobpriq^kqb m^o^ abqbojfk^o X2 `lk W2&]' < @*X ^pŒpr`bpfs^jbkqb- Dpqb mol`bplbkdbkao^ rk^ pr`bpfŽk ab crk`flkbp Xl+ W! W1+ ŒŒŒ+ bk i^ nrb Xl < @ X alkabWg)* pb abqbojfk^ ^ m^oqfoab Wg jbaf^kqb i^ cŽojri^ ab ob`roobk`f^
'6-47( Wg)0'V( < @ * x&!?'p(Wep( `p m^o^ g < N+($)$ &&&&
Mrbpqol l_gbqfsl bp abjlpqo^o nrb i^ pr`bpfŽk ab crk`flkbp ^pŒabcfkfa^ `lk,sbodb e^`f^ rk^ crk`fŽk iŒjfqb X nrb bp rk^ plir`fŽk ab i^ b`r^`fŽk afcbobk`f^i'6-45( bk H v nrb q^j_f‹k p^qfpc^`b i^ `lkaf`fŽk fkf`f^i W&]' < @, K^p crk`flkbpXl+ W! Wa+ -ŒŒ pb ii^j^k ]lnktei]_ekjao oq_aoer]oab X- @kqbp ab bpqraf^o i^ `lk,sbodbk`f^ abi mol`bpl firpqo^jlp bi j‹qlal `lk rk bgbjmil-
DIDLOKN- Blkpfabobjlp bi mol_ibj^ ab s^ilo fkf`f^iX&'q(<@X'q(+ W&M';@*
Baikopn]_e‰j `ah paknai] `a ateopaj_e] 16-4
alkab ? bp rk^ j^qofw `lkpq^kqb j Wj- R^_bjlp nrb i^ plir`fŽk bpqŠa^a^ mlo i^cŽojri^ W&t' < at?@ m^o^ qlal t ob^i- Cbjlpqo^objlp `Žjl bpq^ plir`fŽk pbmrbab l_qbkbo mlo bi j‹qlal ab i^p ^molufj^`flkbp pr`bpfs^p-
K^ efmŽqbpfpfkf`f^i bp Wk&t' < @, K^ cŽojri^ ab ob`roobk`f^ '6-47( klp a^
W0'V(< @ * Il&! ?@ `p < @ * t?@+
W1't( < @ * Il&! ?W0'p( `p < @ * cl&! '?@ * p?1@( `p < @ * t?@ * pt1?1@-
Olo fkar``fŽk bk`lkqo^jlp
K^ prj^ abi pbdrkal jfbj_ol bp rk^ prj^ &m^o`f^iab i^ pbofbab at?Œ Olo `lkpf,
drfbkqb `r^kal g y // bk`lkqo^jlp
ifj Wg't( < a!&?@g!! //
m^o^ qlal t- @pŒmrbp+bk bpqbbgbjmil mlabjlp abjlpqo^o afob`q^jbkqb nrb i^p^molufj^`flkbp pr`bpfs^p `lksbodbk e^`f^ rk^ plir`fŽk abi mol_ibj^ ab s^ilo fkf,`f^i bk ', //+ * // (-
Baikopn]_e‰j `a h] _kjrancaj_e] `a h] oq_aoe‰ja h]o ]lnktei]_ekjao oq_a,oer]o-Ulis^jlp ^elo^ ^ i^ pr`bpfŽk dbkbo^i abcfkfa^ cilo i^ cŽojri^ ab ob`roobk,`f^ '6-47(- O^o^ abjlpqo^o nrb i^ pr`bpfŽk `lksbodb bp`of_fjlp `^a^ q‹ojfklWg&V' `Žjl rk^ prj^ qbibp`Žmf`^+
'6-48(R(S
Wet( < Wk't( * J wWi*0't( , Wi't(x-j<N
O^o^ abjlpqo^o nrb Wg&V' qfbkab e^`f^ rk iŒjfqb `r^kal g y // abjlpqo^objlpnrb i^ pbofb
'6-5/(//
J wWi*h't( , Wi't(xj<N
`lksbodb m^o^`^a^ t ab H, @ q^i cfk _^pq^ abjlpqo^o nrb i^ pbofb-'6-50(
//
J 00 Wi*0't( , Wi't(HH
j<N
165 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
`lksbodb- Dk bpq^pbofbrqfifw^jlp bi `lk`bmql ab kloj^ ab rk^ j^qofw fkqolar`falbk i^ pb``fŽk 6-2: i^ kloj^ ab rk^ j^qofw bp i^ prj^ ab ilp s^ilobp ^_plirqlp abqlalp prp q‹ojfklp-
Blkpfabobjlp rk pr_ fkqbos^il ^`lq^al v `boo^al .0 ab . nrb `lkqbkd^ ]-Cbjlpqo^objlp nrb m^o^ qlal t ab .0 i^ pbofb'6-50( bp j^vlo^a^ mlo rk^ pbofb`lksbodbkqb ab `lkpq^kqbp fkabmbkafbkqbpab t- Dpql fjmif`^ nrb i^ pbofb`lksbo,db qjebkniaiajpa bk I{-
O^o^ e^`bo rk^ bpqfj^`fŽk ab i^ j^dkfqra ab ilp q‹ojfklp ab '6-50( rqfifw^,jlp obmbqfa^jbkqb i^ cŽojri^ ab ob`roobk`f^- Hkf`f^ijbkqb+ qbkbjlp
Xi'u( , Wk&t' < x&!?&p'@ `p ,
O^o^ j^vlo pbk`fiibw+prmlkd^jlp nrb ] ; t- Dkqlk`bp mlabjlp bp`of_fo
'6-51( 00Xi'u( , Wk&t'HH< 00 x&! ?&p'@ `p 00 z oGG?&p'/GHHAHHp,
Orbpql nrb `^a^ bibjbkql ab ?&p' bp crk`fŽk `lkqfkr^ bk Z+`^a^ bibjbkqlbpqŠ ^`lq^al bk bi fkqbos^il `boo^al ^`lq^al Y|, Olo `lkpfdrfbkqb HH@'q(00z L+alkab L bp i^ prj^ ab i^p `lq^p ab qlalp ilp bibjbkqlp ab ?&p' bk bi fkqbos^ilh,9 'Di k•jbol L abmbkab ab .0&( Olo `lkpfdrfbkqb bi fkqbdo^kal ab '6-51( bpqŠ^`lq^al mlo HHAHHL+^pŒnrb qbkbjlp
00Wz&t' + Wk&t'HHz x&! HHAHHL `p < HHAHHK&t + ]'
m^o^ qlal t = ] bk .0-Tqfif`bjlp ^elo^ i^ cŽojri^ ab ob`roobk`f^ rk^ sbw jŠp m^o^ bumobp^oi^
afcbobk`f^ X1 , Xi bk crk`fŽk ab Xi , Xl+ v irbdl bjmib^jlp i^ bpqfj^`fŽk nrb^`^_^jlp ab l_qbkbo m^o^ Xi , Xl+ X pb abar`b
0HW0&t' + Wz&t'HH< ++x&!?&p'wWz&p'+ Wk&p'xp! y w%!GG?&p'//HHAHHK&p + ]' `p
z HHAHHL1 Gt &p\ ]' `p < HHAHHK1&t + ](1
] -
m^o^qlal t = ] bk 00& Olo fkar``fŽk bk`lkqo^jlp
Lj*i' 'i)z00Wi)z&t' + Wi&t'H0 z HHAHH t + ] m^o^ i < N+0+1+--- +
&i * 0(
v m^o^qlal t = ] ab .0- Rf t ; ] rk o^wlk^jfbkql m^ob`fal a^ i^ jfpj^ abpfdr^i,a^a `lk Gt + ]h bk ird^o ab &t + ]', Rf abpfdk^jlp `lk J i^ ilkdfqra abi fkqbos^il
Baikopn]_e‰j `ah paknai] `a ateopaj_e] -22
0! bkqlk`bp qbkbjlp Gt + ]h 889J m^o^ qlal t ab .0 ^pŒnrb l_qbkbjlp i^ ^`lq^`fŽk
Ki)/Ji)/0H Xj*0'u( , Wi't(00 9bp:9 ZA\,,,, YJ[J V 3 @$($)$ &&&$
&i * 0(0
m^o^ qlal t ab .0&Olo `lkpfdrfbkqb i^ pbofb ab '6-50( bp j^vlo^a^ mlo i^ pbofb`lksbodbkqb
y 'KJ(i*hHHAHHJy,, < HHAHH&a+&0J, 0(-
j<N &i * 0(0
Dpql abjrbpqo^ nrb i^ pbofb '6-50( `lksbodb rkfclojbjbkqb bk .0-Di o^wlk^jfbkql ^kqboflo abjrbpqo^ nrb i^ pr`bpfŽk ab ^molufj^`flkbp pr`b,
pfs^p pfbjmob `lksbodb v bk .0 i^ `lksbodbk`f^ bp rkfclojb- Rb^ W i^ crk`fŽkiŒjfqb- Dpql bp+abcfkfjlp W&t' m^o^ `^a^ t bk .0 mlo
W&t' < ifj Wg&t',g+) //
Cbjlpqo^objlp nrb W qfbkb i^p molmfba^abp pfdrfbkqbp9^( u bp `lkqfkr^ bk .++
_( W&t' < @ * Qy?&p' W&p'`p m^o^ qlal t ab .0&b( W&]' < @ b W%&t' < ?&t' W&t' m^o^ qlal t ab .0&
K^ m^oqb`( abjrbpqo^ nrb W bp rk^ plir`fŽk abi mol_ibj^ ab s^ilo fkf`f^i bk .0&
Baikopn]_e‰j `a ^(- B^a^ crk`fŽk Wg bp rk^ j^qofw `lirjk^ `rvlp bib,jbkqlp plk crk`flkbp bp`^i^obp+ `lkqfkr^p bk .0& B^a^ bibjbkql ab i^ crk`fŽkiŒjfqb W bp bi iŒjfqb ab rk^ pr`bpfŽk rkfclojbjbkqb `lksbodbkqb ab crk`flkbp`lkqfkr^p+ ^pŒnrb+ pbd•k bi qblobj^ 00-0 abi slirjbk 0+ `^a^ bibjbkql ab W bpq^j_f‹k `lkqfkr^ bk J+ Olo `lkpfdrfbkqb X bp `lkqfkr^ bk .0&
Baikopn]_e‰j `a _(+ K^ cŽojri^ ab ob`roobk`f^ '6-47( bpq^_ib`b nrb
Olo `lkpfdrfbkqbWg)/&V' < @ * q&?&p'Wep' `p,
W&t' < ifj Wg)z&t' < @ * ifj HV ?&p'Wg&p' p < @ * H&!?&p'hei Wg&p'ph,*ll h,*ll ] ] g+)_8k
; @ * HV ?&p'W&p' `p,]
Di fkqbo`^j_fl abi pŒj_lil ab iŒjfqb `lk bi pfdkl fkqbdo^i bp sŠifal mlo i^ `lk,sbodbk`f^ rkfclojb ab i^ pr`bpfŽk wWgx bk .0&
-23 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
Baikopn]_e‰j `a `(- K^ b`r^`fŽk W']( < @ obpriq^ ^i jljbkql ab _(- Cb,_fal ^i ^m^oq^al ^(+bi fkqbdo^kal ab _( bp `lkqfkrl bk h+pŒnrb+ bk sfoqra abimofjbo qblobj^ crka^jbkq^i abi `Ši`ril+ W&'t( bufpqbv bp fdr^i ^ ?'t( W't( bk .++
Di fkqbos^il h*p^_bjlp nrb bp rk pr_fkqbos^il `r^inrfbo^ ab Gboo^al v^`lq^al v nrb `lkqbkd^ ], Rf h*pb ^jmiŒ^+bi mol`bpl m^o^l_qbkbo W&t' kl s^oŒ^mlonrb pŽil fk`irvb i^ fkqbdo^`fŽkab ] ^ t- Orbpql nrb m^o^ qlal t ab . bufpqbrk pr_ fkqbos^il ab . `boo^al v ^`lq^al v nrb `lkqfbkb ] v t+ bufpqbrk^ plir`fŽkbk qlal bi fkqbos^il Z+
SDNQDL@ 6-06- SDNQDL@ CD TMHBHC@C O@Q@ RHRSDL@R KHMD@KDR GNLNF†-
MDNR- Qe ? &p' ao _kjpejq] aj qj ejpanr]hk ]^eanpk h+h] a_q]_e‰j `ebanaj_e]h
W&'p(< ?'p(W'p(
peaja ] hk i…o qj] okhq_e‰j aj H mqa o]peob]_a qj] _kj`e_e‰j eje_e]h `]`] W'](<@-
Baikopn]_e‰j- Rb^k Y b W alp plir`flkbp bk I- Rb^ H0 `r^inrfbo pr_fkqbo,s^il ab h ^`lq^al v `boo^al nrb `lkqbkd^ ]- Cbjlpqo^objlp nrb X't( < W't(m^o^qlal t bk H[, Dpql fjmif`^ nrb Y < u bk qlal bi fkqbos^il .-&
Orbpql nrb Y b W plk plir`flkbp qbkbjlp
X&'p( , W&'p(< ?'p(wX'p( , W'p(x-
Difg^jlp t bk .0 b fkqbdobjlp bpq^b`r^`fŽk bkqob] v t `lk il nrb l_qbkbjlp
X't( , W't( < q&?'p(wX'p( , W'p(x `e-
Dpq^fjmif`^ i^ abpfdr^ia^a
'6-52( GGX't(, W't( 00 z K Hq&GGX'p(, W'p(00 `p 0+
alkab K bp rk^ `lq^ prmboflo ab 00 ?&p' 00 bk .0&Rb^ K* rk^ `lq^ prmboflo m^o^i^ crk`fŽk `lkqfkr^ HHY'q(, X'q(00 bk .0&Dkqlk`bp i^ abpfdr^ia^a '6-52( klp a^
'6-53( GGX't(, W't(0Gy KK0ht , ]h-
@mif`^kal '6-53( bk bi pbdrkal jfbj_ol ab '6-52( l_qbkbjlp
?lhe_]_e‰j `ah i†pk`k `a ]lnktei]_ekjao oq_aoer]o 168
Olo fkar``fŽk obpriq^
'6-54( HHY'u(, W&t' 00z KiKz Hu, ]-i
i
Br^kal i y // bi pbdrkal jfbj_ol qfbkab ^ N+^pŒnrb X&t' < W&t', Dpql `lj,mibq^ i^ abjlpqo^`fŽk-
Klp obpriq^alp ab bpq^ pb``fŽk mrbabk obprjfopb bk bi pfdrfbkqb qblobj^ abbufpqbk`f^ v rkf`fa^a-
SDNQDL@ 6-07- Qa] ? qj] bqj_e‰j i]pne_e]h j t j _kjpejq] aj qj ejpanr]hk]^eanpkh, Rf ] D {X @ao qj ra_pkn j,`eiajoekj]h _q]hmqean]+ah oeopai] heja]hdk,ikc†jak
W%&p'< ?&p' W&p'* W&]' < @*
peaja qj] v o‰hkqj] okhq_e‰jmqa ao qj ra_pkn j,`eiajoekj]h aj {-
6-11 @mif`^`fŽkabi j‹qlal ab ^molufj^`flkbp pr`bpfs^p ^ ilp pfpqbj^p kl ifkb^,ibp ab mofjbo loabk-
Di j‹qlal ab ^molufj^`flkbp pr`bpfs^p q^j_f‹k mrbab ^mif`^opb ^ ^idrklppfpqbj^p kl ifkb^ibp- Blkpfabobjlp rk pfpqbj^ ab mofjbo loabk ab i^ cloj^
'6-55( W%< D&p*j+
alkab D bp rk^ crk`fŽk sb`qlof^i k,afjbkpflk^i a^a^+ b W bp rk^ crk`fŽk sb`ql,of^i k,afjbkpflk^i fk`Ždkfq^ nrb e^v nrb abqbojfk^o- Prbobjlp rk^ plir`fŽk Wnrb p^qfpc^d^ i^ b`r^`fŽk
W%&p'< DYp*W&p'H
m^o^ `^a^ p bk rk `fboql fkqbos^il {v nrb q^j_f‹k p^qfpc^d^ rk^ `lkaf`fŽk fkf`f^ia^a^+ mlo bgbjmil W&]' < @*alkab ] D {X @ bp rk sb`qlo k,afjbkpflk^i a^al-
@i fdr^i nrb bk bi `^pl ifkb^i+ `lkpqorfjlp rk^ pr`bpfŽk ab ^molufj^`flkbppr`bpfs^p Wk* u[* W1 ŒŒŒ+ qlj^kal Wk < @ X abcfkfbkal Wg)[ bk crk`fŽk ab Wgjbaf^kqb i^ cŽojri^ ab ob`roobk`f^
'6-56( Wg)z&t' < @ * q&DYp*Wg&p'[ p m^o^ g < N+0+1+ ----
Hjmlkfbkal `fboq^p `lkaf`flkbp ^ E+ bpq^ pr`bpfŽk `lksbodboŠ e^`f^ rk^ crk`fŽkiŒjfqb W nrb p^qfpc^oŠ i^ b`r^`fŽk afcbobk`f^i v i^ `lkaf`fŽk fkf`f^i a^a^p-
-3+ Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
@kqbp ab ^sbofdr^o i^ `lksbodbk`f^ abi mol`bpl s^jlp ^ afp`rqfo ^idrklpbgbjmilp rkfafjbkpflk^ibp bibdfalp m^o^ firpqo^o ^idrk^p ab i^p afcf`riq^abp nrbmrbabk mobpbkq^opbbk i^ moŠ`qf`^-
DIDLOKN 0- Blkpfabobjlp bi mol_ibj^ ab s^ilo fkf`f^i kl ifkb^i v&< V1 * v1`lk u < N `r^kal t < N- B^i`ri^objlp ^idrk^p ^molufj^`flkbp ab i^ plir`fŽk-Difg^jlp W**&t' < N X abqbojfk^objlp i^p qobp pfdrfbkqbp ^molufj^`flkbp `ljlpfdrb9
h%!V2W0&t' < p1 `p < , +
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@elo^ pb sb bi bklojb qo^_^gl nrb pboŠ kb`bp^ofl m^o^ `^i`ri^o jŠp ^molufj^`fl,kbp- Olo bgbjmil+ i^p alp ^molufj^`flkbp pfdrfbkqbp W3 b W4 pboŠk mlifkljflpab do^alp 20 v 52+ obpmb`qfs^jbkqb-
Di moŽufjl bgbjmil jrbpqo^ lqo^ afcf`riq^a nrb mrbab mobpbkq^opb bk bi`Ši`ril ab i^p ^molufj^`flkbp pr`bpfs^p-
DIDLOKN 1- Blkpfabobjlp bi mol_ibj^+ ab s^ilo fkf`f^i+ kl ifkb^i v&< 0t )) a!* `lk u < N `r^kal t < N- Bljbkw^jlp `lk i^ crk`fŽk fkf`f^i Wk&t' < NX bk`lkqo^jlp
b!+• b&! ŒWht(- < l '1p * bi *0( `p < t1 * l bi *0 `p -
@nrŒ+kl pb mrbab pbdrfo ^abi^kqb mlo bi eb`el ab nrb i^ •iqfj^ fkqbdo^i kl mrbab`^i`ri^opb `ljl bumobpfŽk ab crk`flkbp bibjbkq^ibp- Ml l_pq^kqb+ m^o^ rk^ t a^a^bp mlpf_ib `^i`ri^o rk^ ^molufj^`fŽk krj‹of`^ ab i^ fkqbdo^i v `lk biil pb l_qfbkbrk^ ^molufj^`fŽk ab W1&t',
@ `^rp^ ab i^p afcf`riq^abp nrb ebjlp sfpql bk ilp alp •iqfjlp bgbjmilp+ bij‹qlal ab ^molufj^`flkbp pr`bpfs^p bk i^ moŠ`qf`^ kl bp bi jŠp •qfi m^o^ i^ abqbo,jfk^`fŽk bumiŒ`fq^ab plir`flkbp- Di ^rq‹kqf`l s^ilo abi j‹qlal `lkpfpqb bk prbjmibl m^o^ bpq^_ib`bo qblobj^p ab bufpqbk`f^-
Baikopn]_e‰j `a qj paknai] `a ateopaj_e] v qje_e`]` 170
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Ulis^jlp ^elo^ ^i qblobj^ ab bufpqbk`f^v rkf`fa^a m^o^pfpqbj^p kl ifkb^ibpab mofjbo loabk- Hjmlkfbkal obpqof``flkbp ^ab`r^a^p ^ i^ crk`fŽk nrb ^m^ob`bbk bi pbdrkal jfbj_ol ab i^ b`r^`fŽk afcbobk`f^i
W&< D't+ u'*
mlabjlp buqbkabo bi j‹qlal ab abjlpqo^`fŽk rp^al bk bi `^pl ifkb^i ab i^ pb`,`fŽk 6-10-
Rb^ Gbi fkqbos^il ^_fboql bk bi nrb abpb^jlp rk^ plir`fŽk- Rrmlkd^jlp nrb] D Gv nrb @ bp rk sb`qlo k,afjbkpflk^i a^al- Cbpfdkbjlp `lk R rk `lkgrkqlbk bi bpm^`fl ab afjbkpfŽk &j * 0( a^al mlo
p< w&t*W' H Zu , ]h y d* HHW + AHHz gx*
alkab d = N v g = l- ZRfj < 0+bp rk ob`qŠkdril `lk `bkqol bk &]* @'* `lk _^pb0d v ^iqro^ 0g,[ Rrmlkd^jlp nrb bi aljfkfl ab E fk`irvb rk `lkgrkql R ab bpqbqfml v nrb E bp ^`lq^a^ bk R+pb^
'6-57( GGD&t*X(HHz K
m^o^qlal mrkql &t* X( ab R+pfbkal L rk^ `lkpq^kqb mlpfqfs^-Rbdrfa^jbkqb+ prmlkd^jlp nrb i^ crk`fŽk `ljmrbpq^ E&t' < D&t* W&t'' bp
`lkqfkr^ bk bi fkqbos^il &] + d* ] * d' m^o^ qla^ Zrk`fŽk W nrb pb^ `lkqf,kr^ bk &] + d* ] * d' v nrb qbkd^ i^ molmfba^a ab nrb &t* W&t'' D R m^o^qlal t bk &] + d* ] * d', Dpq^ efmŽqbpfp pbdro^ i^ bufpqbk`f^ ab i^p fkqbdo^ibpnrb pb mobpbkq^kbk bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p+ b fjmif`^ q^j_f‹ki^ `lkqfkrfa^a ab i^p crk`flkbp ^p( `lkpqorfa^p-
Efk^ijbkqb+ prmlkd^jlp nrb E p^qfpc^`brk^ `lkaf`fŽk ab i^ cloj^
GGD&t*W' + D&t* Y(HHz ? 0HW + YHH
m^o^ qlal m^o ab mrkqlp &t* W' v 'u+ Y( ab R+pfbkal ? rk^ `lkpq^kqb mlpfqfs^-bpq^ pb ii^j^ rk^ _kj`e_e‰j `a Jelo_depv bk elklo ab Qralime Kfmp`efqw+nrb crbbi mofjbol bk fkqolar`foi^ bk 0765- Tk^ q^i `lkaf`fŽk kl bp rk obpqof``fŽkjrvpbof^ m^o^ rk^ crk`fŽk v klp mbojfqb buqbkabo i^ abjlpqo^`fŽk ab i^ bufpqbk`f^v rkf`fa^a abi `^pl ifkb^i ^i kl ifkb^i-
SDNQDL@ 6-08- DWHRSDMBH@X TMHBHC@C CD K@R RNKTBHNMDR CD RHRSDL@R MN
KHMD@KDR CD OQHLDQ NQCDM- Qqlkjc]iko mqa E o]peob]_ah] ]_kp]_e‰j+h] _kj pe,
-3- Qeopai]o `a a_q]_ekjao `ebanaj_e]hao+
jqe`]` u h]o _kj`e_ekjao `a Jelo_depv ]jpao _ep]`]o aj qj _kjfqjpk Q- Qa] h ahejpanr]hk ]^eanpk '] , a+] * b(+ `kj`a a < jfk wd+g.Kx- Cteopa ajpkj_ao qj]u o‰hkqj] bqj_e‰j W `abeje`] aj J* oeaj`k W']( < @+p]h mqa 'u+ W't(( “ Q X
W&'t(< D't+ W't• l]n] _]`] t `a h-
Baikopn]_e‰j- Orbpql nrb i^ abjlpqo^`fŽk bp ^kŠild^ ^ i^ abi `^pl ifkb^ifkaf`^jlp pli^jbkqb ilp mofk`fm^ibp m^plp- Olkd^jlp WGG&t'< @ X abcfk^jlp i^pcrk`flkbp sb`qlof^ibp Wz+W1+ŒŒŒbk h jbaf^kqb i^ cŽojri^ ab ob`roobk`f^
'6-58( Wi)h&V' < @ * q&DYp* Wi&p'[ `p m^o^ i < N+0+1+ ----
O^k9 nrb i^ cŽojri^ ab ob`roobk`f^ qbkd^ pbkqfal kb`bpfq^jlp p^_bo pf &t* Wj 'u(D Q m^o^ `^a^ t ab h- Dpql pb abjrbpqo^ cŠ`fijbkqb mlo fkar``fŽk bk i- Br^kali < N qbkbjlp 't+ Wk't(( < 't+ @(+ nrb bpqŠ bk Q- Rrmlkd^jlp bkqlk`bp nrb&t* Wi&t€ D Q m^o^ rk i v `^a^ t ab h- Tqfifw^kal '6-58( v '6-57( l_qbkbjlp
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Orbpql nrb Zu , ]h 9' a m^o^ t bk h*bpql fjmif`^ nrb
Zl `r^i abjrbpqo^ nrb 'u+ Wi*h'V• D Q m^o^ `^a^ t bk h- Olo `lkpfdrfbkqb i^cŽojri^ ab ob`roobk`f^ qfbkb pbkqfal m^o^ qlal i y N X qla^ t ab h,
K^ `lksbodbk`f^ ab i^ pr`bpfŽk wWi'V(x pb bpq^_ib`b ^elo^ bu^`q^jbkqb `ljlbk i^ pb``fŽk 6-10- Dp`of_^jlp
h,i
Wet' < Wk&t' * wWi)h&t' + Wi&t'xj<N
v abjlpqobjlp nrb Wg&V' qfbkab e^`f^ rk iŒjfqb `r^kal g y // abjlpqo^kal nrbi^ pbofb
//
00 Wi)h&t' + Wi&t'/Gj<N
`lksbodb bk h-Dpql pb abar`b ab i^ abpfdr^ia^a
K?i Zu .j*i K?i j*i00 Wi)h&t' + %Wi&V'0H z , ] ;& b
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Cfan_e_eko -3.
nrb pb abjrbpqo^ mlo fkar``fŽk+ rp^kal i^ cŽojri^ ab ob`roobk`f^ v i^ `lkaf`fŽkab Kfmp`efqw-Cbcfkfjlp bkqlk`bp i^ crk`fŽk iŒjfqb X mlo
W&t' < ifj Wi&t'j,,=ll
m^o^`^a^ t ab / v `ljmol_^jlp nrb p^qfpc^`bi^ b`r^`fŽk fkqbdo^i
W&t' < @ * qDYp* W&p'[ `p*
bu^`q^jbkqb `ljl bk bi `^pl ifkb^i- Dpql abjrbpqo^ i^ bufpqbk`f^ab rk^ plir`fŽk-K^ rkf`fa^a mrbab bkqlk`bp abjlpqo^opb mlo bi jfpjl j‹qlal rqfifw^al m^o^ab,jlpqo^o bi qblobj^ 6-06-
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0- Blkpfabo^o bi mol_ibj^ ifkb^i ab s^ilo fkf`f^i
u&*u<1a!&+ `lk: u < 0 `r^kal t < N -
^( G^ii^o i^ plir`fŽk bu^`q^ W ab bpqb mol_ibj^-_( @mif`^o bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p+ m^oqfbkal ab i^ crk`fŽk fkf`f^iWk&t' < 0-Cbqbojfk^o Wj&t' bumiŒ`fq^jbkqb v abjlpqo^o nrb
ifj Wj&t' < W&t'
m^o^ qlal t ob^i-1- @mif`^o bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p ^i mol_ibj^ ab s^ilo fkf`f^i kl ifkb^i
u&<V*u1+ `lk u < N `r^kal t < N-
Slj^o Wk&t' < N `ljl crk`fŽk fkŒ`f^i v `^i`ri^o W*&t' ,2- @mif`^o bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p ^i mol_ibj^ ab s^ilo fkf`f^i kl ifkb^i
u&< 0 )tu1+ `lk u < N `r^kal t < N-
Slj^o Wk&t' < N `ljl crk`fŽk fkf`f^i v `^i`ri^o W*&t' ,3- @mif`^o bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p ^i mol_ibj^ ab s^ilo fkf`f^i kl ifkb^i
`lk u < N `r^kal t < N-
173 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
O^oqfo ab i^ ~j^i^ƒ crk`fŽk fkf`f^i Wk&t' < ($ `^i`ri^o& u*&t'* v `ljm^o^o `lk ilp obpri,q^alp abi bgbjmil 0 ab i^ pb``fŽk 6-11-
4- Blkpfabo^o bi mol_ibj^ ab s^ilo fkf`f^i kl ifkb^i
`lk u < i `r^kal t < N-
^( @mif`^o bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p+ m^oqfbkal ab i^ crk`fŽk fkf`f^iWk&t' < 0+ X `^i`ri^o W*&t',_( Rb^ P < Z,0+0\W Z,0+0\- G^ii^o bi jbklo L q^i nrb Gb&t*v(0 z L bk P- G^ii^ork fkqbos^il / < &+a*a' q^i nrb i^ doŠcf`^ ab qla^ crk`fŽk ^molufj^kqb X- bk ($ bpq‹bk P-b( RrmŽkd^pb nrb i^ plir`fŽk v < W&t' qfbkb rk abp^ooliil bk pbofb ab mlqbk`f^p bk rkbkqlokl abi lofdbk- Cbqbojfk^o ilp pbfp mofjbolp q‹ojfklp kl krilp ab bpb abp^ooliil v`ljm^o^o bi obpriq^al `lk bi abi ^m^oq^al ^(-
5- Blkpfabo^o bi mol_ibj^ ab s^ibo fkf`f^i
u&<G*u1+ `lk u < N `r^kal t < N-
^( @mif`^o bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p+ m^oqfbkal ab i^ crk`fŽk fkf`f^iWk&t' < N+X `^i`ri^o W,&t',
_( Cbjlpqo^o nrb qla^ crk`fŽk ^molufj^k qb X- bpqŠ abcfkfa^ bk qlal bi bgb ob^i-`( Tqfifw^o bi qblobj^ 6-08 m^o^ abjlpqo^o nrb bi mol_ibj^ ab s^ilo fkf`f^i qfbkb mloil jbklp rk^ plir`fŽk bk `r^inrfbo fkqbos^il ab i^ cloj^ &+d*d',a( Qbplisbo i^ b`r^`fŽk afcbobk`f^i mlo pbm^o^`fŽk ab s^of^_ibp v abjlpqo^o ^pŒnrbbufpqb rk^ pli^ plir`fŽk X abi mol_ibj^ ab s^ilo fkf`f^i bk bi fkqbos^il &+%Rn.1+ %Rn.1( Xkfkdrk^ bk rk fkqbos^il jŠp ^jmifl- Dk bpqb bgbjmil+ i^p ^molufj^`flkbp pr`bpfs^p bpqŠkabcfkfa^p bk qlal bi bgb ob^i+ mbol `lksbodbk e^`f^ rk^ crk`fŽk iŒjfqb •kf`^jbkqb bkbi fkqbos^il &+%Rn-0*%Rn-0',
6- Arpnrbjlp alp crk`flkbp v < W&t' v v < X&t' nrb p^qfpc^d^k pfjriqŠkb^jbkqb bi pfp,qbj^ ab b`r^`flkbp
u&<v+ v&< t2&u * v(
`lk i^p `lkaf`flkbp fkf`f^ibp v < 0 X v < 0.1 `r^kal t < N- Bljbkw^o `lk i^p crk,`flkbp fkf`f^ibp Wk&t' < 0+ Xk&t' < 0.1+ X bjmib^o bi j‹qlal ab ^molufj^`flkbp pr`bpŒ,s^p m^o^ l_qbkbo i^p crk`flkbp ^molufj^kqbp
V 2t4 t5 t8
W1&t' < i * , * , * , * ]1 3/ 5/ 081 &
7- Blkpfabo^o bi pfpqbj^ ab b`r^`flkbp
u&<1t*v+ v&< 2tu * t1v+
?lnktei]_ekjao oq_aoer]o v lqjpko befko `a klan]`knao 174
`lk s^ilobp fkf`f^ibp v < 1 X v < N `r^kal t < N- O^oqfo ab i^p crk`flkbp fkf`f^ibpWk&t' < 1+ Xk&t' < N+ X `lk bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p abqbojfk^o W*&t'v X*&t',
8- Blkpfabo^o bi mol_ibj^ ab s^ilo fkf`f^i
`lk u < 4 b u&< 0 `r^kal t < N-
B^j_f^o bpqb mol_ibj^ bk lqol bnrfs^ibkqb nrb fk`irv^ rk pfpqbj^ ab alp b`r^`flkbp`lk alp crk`flkbp fk`Ždkfq^p v < W&t' v v < X&t'* pfbkal v < u&-@mif`^o bkqlk`bp bij‹qlal ab ^molufj^`flkbp pr`bpfs^p+ m^oqfbkal ab i^p crk`flkbp fkf`f^ibp Wk&t' < 4 vXk&t' < 0+ v abqbojfk^o W*&t' v X*&t',
0/- Rb^ b rk^ crk`fŽk abcfkfa^ bk bi ob`qŠkdril P < Z,0+ 0I W Z,0+ 0I abi jlal pfdrfbkqb9
N pŒ t < N+
0u-t pf t9z…M b GuhR t1+
-&t*u' y w0t pf t9z…M b u < t1+
+0t pf t9z…M b u : +t1Œ
^( Cbjlpqo^o nrb Gb&t*v(0 z 1 m^o^ qlal &t* v( ab P-_( Cbjlpqo^o nrb b kl p^qfpc^`b rk^ `lkaf`fŽk ab Kfmp`efqwbk P-b( O^o^ `^a^ `lkpq^kqb B nrb `rjmib HBHz 0+ abjlpqo^o nrb v < At& bp rk^ plir`fŽkabi mol_ibj^ ab s^ilo fkf`f^i v&< b&t* u'* `lk v < N `r^kal t < N- Cbjlpqo^o nrb i^doŠcf`^ ab `^a^ rk^ ab bp^p plir`flkbp bk ',0+0( bpqŠ bk Q-a( @mif`^o bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p ^i mol_ibj^ ab s^ilo fkf`f^i+ m^o,qfbkal ab Wk&t' < N- Cbqbojfk^o W**&t' v abjlpqo^o nrb i^p ^molufj^`flkbp `lksbodbke^`f^ rk^ plir`fŽk abi mol_ibj^ bk bi fkqbos^il ',0+0(-b( Qbmbqfo i^ m^oqb a(+ m^oqfbkal ab Wk&t' < t, Cbqbojfk^o W,&t' v abjlpqo^o nrb i^pcrk`flkbp ^molufj^k qbp `lksbodbk e^`f^ rk^ plir`fŽk afcbobkqb ab `r^inrfbo^ ab i^pabi ^m^oq^al b(+c( Qbmbqfoi^ m^oqb a(+ m^oqfbkal ab Wk&t' < t%,d( Qbmbqfoi^ m^oqb a(+ m^oqfbkal ab Wk&t' < t%e%,
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K^ fab^ _Špf`^ abi j‹qlal ab ^molufj^`flkbp pr`bpfs^p mrbab rp^opb kl pŽilm^o^ bpq^_ib`bo qblobj^p ab bufpqbk`f^ m^o^ b`r^`flkbp afcbobk`f^ibp pfkl q^j_f‹km^o^ lqolp jr`elp mol_ibj^p abi ^kŠifpfp- Di obpql ab bpqb `^mŒqril obclojri^ bi`fq^al j‹qlal bk rk^ cloj^ nrb ^jmiŒ^ jr`el bi ^i`^k`b ab prp ^mif`^`flkbp-
Dk i^ abjlpqo^`fŽk abi qblobj^ 6-07 `lkpqorfjlp rk^ pr`bpfŽk ab crk`flkbpwW` ab ^`rboal `lk i^ cŽojri^ ab ob`roobk`f^
-31 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
Di pbdrkal jfbj_ol ab bpq^cŽojri^ mrbab `lkpfabo^opb `ljl rk lmbo^alo R nrb`lksfboqb `fboq^pcrk`flkbp X bk lqo^p krbs^p R&W' jbaf^kqb i^ b`r^`fŽk
R'W( < @ * q&?W'p( `p-
Dk i^ abjlpqo^`fŽk abi qblobj^ 6-07 bk`lkqo^jlp nrb i^ plir`fŽk X abi mol_ibj^ab s^ilo fkf`f^i W%&p'< ?W&p'* W&]' < P* p^qfpc^`bi^ b`r^`fŽk fkqbdo^i
u < @ * c^&!? W'p( `p -
Dumobp^kal ‹pq^ `lk bi lmbo^alo R obpriq^ X < R&W', Dp ab`fo+i^ plir`fŽk X mbolj^kb`b fk^iqbo^a^ mlo bi lmbo^alo R- Tk^ q^i crk`fŽk X pb ii^j^ rk lqjpk befkabi lmbo^alo R,
Mrjbolplp b fjmloq^kqbp mol_ibj^p abi ^kŠifpfpmrbabk clojri^opb ab jlalnrb pr plir`fŽk abmbka^ ab i^ bufpqbk`f^ ab rk mrkql cfgl m^o^ ^id•k lmbo^alo-Olo `lkpfdrfbkqb jbob`b i^ mbk^ fkqbkq^oabp`r_ofo molmfba^abpab lmbo^alobp nrbd^o^kqf`bk i^ bufpqbk`f^ ab rk mrkql cfgl- Ulis^jlp ^elo^ ^ rk qo^q^jfbkql pfpqbjŠqf`l ab bpqbmol_ibj^-
o /'*. 8\YJLRX\URWNJUN\WX[VJMX\
O^o^ clojri^o bi j‹qlal ab ^molufj^`flkbp pr`bpfs^p bk rk^ cloj^ jŠp db,kbo^i `lksfbkb qo^_^g^o lk bpm^`flp ifkb^ibp- Rb^ Q rk &bpm^`flifkb^i `r^inrfbo^-Br^kal e^_i^jlp ab ^molufj^o rk bibjbkql t ab R jbaf^kqb lqol bibjbkqlu ab Q+`lkpfabo^jlp i^ afcbobk`f^ t , u+ nrb ii^j^jlp bi annkn ab ^molufj^,`fŽk- O^o^ jbafo bi q^j^•l ab bpb boolo fkqolar`fjlp rk^ kloj^ bk bi bpm^`fl-
CDEHMHBHˆM CD MNQL@- Qa] Q qj aol]_ek heja]h _q]hmqean]- Sj] bqj_e‰jna]h L `abeje`] aj Q oa hh]i] jkni] oe peaja h]o lnklea`]`ao oecqeajpao9
^( L't(::> N l]n] _]`] t `a R-_( L'_t( < Zb\ L't( l]n] _]`] t `a R u _]`] ao_]h]n _-b( L't * u( 9p9:L't( * L'u( l]n] pk`k l]n t a u `a R-a( L't( < N eilhe_] t < l-
Tk bpm^`fl ifkb^i `lk rk^ kloj^ ^pfdk^a^ pb ii^j^ aol]_ek heja]h jkni]`k-
K^ kloj^ ab t ^ sb`bp pb fkaf`^ `lk zzth bk ird^o ab L't(- Blk bpq^klq^,`fŽk i^p molmfba^abpcrka^jbkq^ibp pb bumobp^k9
^( HGt H::> N m^o^`^a^ t ab R-_( Hi`uii < ibi HiuiHm^o^qlal t ab R v qlal bp`^i^o _-
l lan]`knao `a _kjpn]__e‰j -32
_' GV * vii z {iuii * H{viim^o^ qlal m^o t b u ab Q-a( Hiu&i< N fjmif`^ t < N-Rf t b u bpqŠk bk Q+i^ kloj^ f Gt , vi H pb ii^j^ `eop]j_e] ab t ^ u-Rf bi bpm^`fl Q bp br`iŒabl+ qfbkb pfbjmob rk^ kloj^ nrb bp `lkpb`rbk`f^ abi
molar`ql fkqboflo+ bp ab`fo+ iiui { < 'u+ t' T1- Rfk bj_^odl+ klplqolp klp fkqbobp^ob,jlp mlo rk^ kloj^ bpmb`f^i nrb kl obpriq^ ab rk molar`ql fkqboflo-
DIDLOKN- J] jkni] `ah i…teik l j^u jkni]- Rb^ A'H( bi bpm^`fl ifkb^iab i^p crk`flkbp ob^ibp `lkqfkr^p bk rk fkqbos^il `boo^al v ^`lq^al b, Rf bw C A&H'*
abcfkfjlp
00cx 00 < j^u Hbw &t'H+VCH
alkab bi pŒj_lil abi pbdrkal jfbj_ol pfdkfcf`^ bi j^ufjl s^ilo ^_plirql abbw bk b, Di ib`qlo mrbab `ljmol_^o nrb bpq^ kloj^ dlw^ ab i^p `r^qol molmfba^,abp crka^jbkq^ibp-
K^ kloj^ abi jŠufjl kl pb abar`b abi molar`ql fkqboflo- O^o^ abjlpqo^oil_^pq^ e^`bo sbo nrb i^ kloj^ abi jŠufjl abg^ ab `rjmifo ^idrk^ molmfba^a nrbmlpbbk qla^p i^p kloj^p abar`fa^p ab molar`qlp fkqboflobp- Olo bgbjmil+ pf rk^kloj^ pb abar`b ab rk molar`ql fkqboflo+ i^ ~ibv abi m^o^ibildo^jlƒ
HHu* vi01 * Zu, vi01 < 1 HHuii1* 1 iHvii1
bp sŠifa^ m^o^ qlal m^o t b u ab Q- 'Ubo bgbo`f`fl 05 ab i^ pb``fŽk 0-02(- K^ ibvabi m^o^ibildo^jl kl pfbjmob nrba^ p^qfpcb`e^ mlo i^ kloj^ abi jŠufjl- Olobgbjmil+ pb^k t b u crk`flkbp bk bi fkqbos^il Z/+0\a^a^p mlo
t'p( < p+ u'p( < 0 , p-
Dkqlk`bp qbkbjlp H uii< Hivii < Hiu* vii < Ght + viim^o^ibildo^jl kl pb `rjmib-
0+ `lk il nrb i^ ibv ab\
o /'*/ AYN[JMX[N\MNLXW][JLLRmW
Dk bpq^ pb``fŽk `lkpfabo^jlp bi bpm^`fl ifkb^i kloj^ al A&H' ab qla^p i^pcrk`flkbp ob^ibp `lkqfkr^p bk rk fkqbos^il `boo^al v ^`lq^al H bk bi nrb HHcx 00 bpi^ kloj^ abi j^ufjl- Blkpfabobjlp rk lmbo^alo
R8nI( ,,=, B'I(
`rvl aljfkfl bp A&H' v `rvl ob`loofal bp rk pr_`lkgrkql ab A&H', Dpql bp+pf bw bp`lkqfkr^ bk H* bkqlk`bp R&bw 'q^j_f‹k bp `lkqfkr^ bk b, K^p pfdrfbkqbp cŽojri^pa^k ^idrklp bgbjmilp pbk`fiilp ab q^ibp lmbo^alobp- Dk `^a^ `^pl HU bp rk^ crk`fŽk
-33 Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
^o_fqo^of^ bk A&H' v R&al'&t' pb abcfkb m^o^ `^a^ t ab + mlo i^ cŽojri^ nrb pbfkaf`^
R&_l'&t' < ?_l&V'* alkab @ bp rk k•jbol ob^i cfgl+
R&_l'&t' < q_l&p' `p* alkab a bp rk mrkql cfgl bk h
R&_l'&t' < ^ * qbYp* _l&p'[ `p*
pfbkal ^ rk^ `lkpq^kqb v i^ crk`fŽk `ljmrbpq^ bYp*_l&p'[ `lkqfkr^ bk h-Mlp fkqbobp^k ^elo^ ^nrbiilp lmbo^alobp R m^o^ ilp nrb i^ afpq^k`f^ GGR&_l'+
+ R&hb%',/bp jbklo nrb bi molar`ql ab GG_l,ic&HHmlo rk^ `lkpq^kqb ] ; 0- Dplp pbii^j^k klan]`knao `a _kjpn]__e‰j: pb abcfkbk abi jlal pfdrfbkqb-
CDEHMHBHˆM CD TM NODQ@CNQ CD BNMSQ@BBHˆM- Sj klan]`kn R9 A&H'yA&H'oa hh]i] `a _kjpn]__e‰j oe ateopa qj] _kjop]jpa ]+mqa oa] N z ] ; 0+ p]h mqa l]n]pk`k l]n `a bqj_ekjao al v -m `a A&H' pajaiko
'6-6/(
J] _kjop]jpa ] oa hh]i] _kjop]jpa `a _kjpn]__e‰j l]n] R-
Lkp]9 K^ abpfdr^ia^a '6-6/( bp sŠifa^ pf v pli^jbkqb pf
GR&nl'&t' + R&pzH'&t'/ y X-iiom , q{I00 m^o^ qlal t`aH,
DIDLOKN 0- Rb^ R bi lmbo^alo abcfkfal mlo R&al'&t' < 'nl&t'* alkab +[ bp
`lkpq^kqb- Orbpql nrb
HR&_l'&t' + R&hb%'&t' H< G?hh_l&t' + //%&V'H+
qbkbjlp HHSBbm(, S'-m(ii < 0+[0 H ;O, -mii-Olo `lkpfdrfbkqb bpqb lmbo^alo bp rk lmb,o^alo ab `lkqo^``fŽk pf v pŽil pf i+[ ; 0+bk `rvl `^pl +[imrbab rp^opb `ljl `lkp,q^kqb ab `lkqo^``fŽk-
DIDLOKN 1- Rb^ RAnz('t( < ^ * Qy bYp+nz'p([ `p+ alkab b p^qfpc^`b rk^`lkaf`fŽk ab Kfmp`eŒqwab i^ cloj^
G-&t*u' + b%p€*w(0 z I Hv, w\
m^o^ qlal t ab H, v `r^ibpnrfbo^ w b v ob^ibp: I bp rk^ `lkpq^kqb mlpfqfs^- Cbpfd,
Raknai] `ah lqjpk befk l]n] klan]`knao `a _kjpn]__eˆj 067
kbjlp `lk J&H' i^ ilkdfqra abi fkqbos^il b, Rf IJ&H' ; 0 mlabjlp sbo cŠ`fijbkqbnrb R bp rk lmbo^alo ab `lkqo^``fŽk `lk i^ `lkpq^kqb ab `lkqo^``fŽk IJ&H', Dkbcb`ql+m^o^qla^ t ab H qbkbjlp
fR'al('t( , R'pl('t(H < Hq&wGYp+ al'p([ , bYp+ pl'p([x `p HpJfq hal'p( , pl'p( Hp Hy I Hibm, qmiii qp Hz IJ'H( Hibm, qmii-
Rf IJ&H' ; 0+bkqlk`bp R bp rk lmbo^alo ab `lkqo^``fŽk `lk `lkpq^kqb ab -`lkl l +
qo^``fŽk ] < IJ&H',
! 6-17 Sblobj^ abi mrkql cfgl m^o^lmbo^alobp ab `lkqo^``fŽk
Di qblobj^ pfdrfbkqb abjrbpqo^ nrb qlal lmbo^alo ab `lkqo^``fŽk qfbkb rkmrkql cfgl •kf`l-
SDNQDL@ 6-1/- Qa] R8A&H' y A&H' qj klan]`kn `a _kjpn]__eˆj, Cteopa qj]bqj_eˆj v oˆhk qj] al aj A&H' p]h mqa
'6-60 ( R'al( < pl -
Baikopn]_eˆj, Rb^ >Il `r^inrfbo crk`fŽk ab A&H' v abcfk^jlp rk^ pr`bpfŽkab crk`flkbp waljx jbaf^kqb i^ cŽojri^ ab ob`roobk`f^
alj*h < R'alj( m^o^ j < /+0+1+ ----
N_p‹osbpb nrb alj* I DB'I( m^o^`^a^ j- Cbjlpqo^objlp nrb i^ pr`bpfŽk wmHjx `lk,sbodb e^`f^ rk^ crk`fŽk iŒjfqbal ab A&H', Di j‹qlal bp m^ob`fal ^i rqfifw^al bki^ abjlpqo^`fŽk abi qblobj^ 6-07- Dp`of_fjlp `^a^ alj `ljl prj^ qbibp`Žmf`^+
'6-61(k,i
alj't( < yk't( * walg*h'V( , alg'V(xSc=
v mol_^jlp i^ `lksbodbk`f^ ab waljx abjlpqo^kal nrb i^ pbofb
'6-62(Ab(
alk't( * 19walg*h'V( , alht(xS4=
`lksbodb rkfclojbjbkqb bk H, Krbdl abjlpqo^jlp nrb i^ prj^ ab bp^ pbofbbp bimrkql cfgl nrb pb `fq^-
-4+ Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
K^ `lksbodbk`f^ rkfclojb ab i^ pbofb pb bpq^_ib`boŠ`ljm^oŠkali^ `lk i^pbofbdblj‹qof`^ `lksbodbkqb
alkab K < 00 Olif * Hiooiii+v ] bp i^ `lkpq^kqb ab `lkqo^``fŽk m^o^ R, K^ `ljm^,o^`fŽk i^ molmlo`flk^ i^ abpfdr^ia^a
'6-63(
nrb bp sŠifa^ m^o^qla^ t ab H v qlal g y 0- O^o^ abjlpqo^o '6-63( klqbjlp nrb
Olo `lkpfdrfbkqb i^ abpfdr^ia^a '6-63( nrba^oŠ mol_^a^ pf abjlpqo^jlp nrb
'6-64(
m^o^qlal g y 0- Cbjlpqobjlp ^elo^ '6-64( mlo fkar``fŽk- O^o^ g < 0 qbkbjlp
nrb bp i^ jfpj^ nrb '6-64(- O^o^ abjlpqo^o nrb '6-64( bp sŠifa^ m^o^ g * 0 pfil bp m^o^g l_pbosbjlp nrb
Orbpql nrb ‹pq^ bp sŠifa^ m^o^`^a^ t ab H q^j_f‹k ab_b pbo
Dpql abjrbpqo^ '6-64( mlo fkar``fŽk- Olo `lkpfdrfbkqb i^ pbofb '6-62( `lksbodbrkfclojbjbkqb bk \- Rf abpfdk^jlp mlo nn&t' pr prj^ qbkbjlp
'6-65(//
oo'u( < ifj nnj't( < ool'u( * J xooh*i'W( , nng'V(x+W&XX ;,2
K^ crk`fŽk oobp `lkqfkr^ bk H mlonrb bp i^ prj^ ab rk^ pbofbrkfclojbjbkqb
?lhe_]_ekjao `ah paknai] `ah lqjpk befk 180
`lksbodbkqb ab crk`flkbp `lkqfkr^p- O^o^ abjlpqo^o nrb _l bp rk mrkql cfgl ab R`ljm^o^jlp R&_l' `lk _l%j)h < R&ANj'% Tqfifw^kal i^ molmfba^a ab `lkqo^``fŽk abR qbkbjlp
Obol ab '6-61( v '6-65( bk`lkqo^jlp
alkab ebjlp rqfifw^al '6-63( bk bi •iqfjl m^pl- Olo `lkpfdrfbkqb '6-66( fjmif`^
`l
GR&_l'&t' + ANj*h'V(H z KJGVg*0Œg<j
Br^kal jykk i^ pbofb abi pbdrkal jfbj_ol qfbkab ^ /+ ^pŒnrb _lj)h&t'yR&nlVt',
Obol v^ mqa:lj)h&t'y:N&t' `r^kal jykk+ bpql abjrbpqo^ mqa_l&t' < R&_lVt' m^o^`^a^ t ab H, Olo `lkpfdrfbkqb _l < R& :l'* ^pŒnrb _l bp rk mrkql cfgl-
Olo •iqfjl abjlpqo^jlp nrb bpqb mrkql cfgl _l bp •kf`l- Rb^ -{: lqo^ crk`fŽkab A&-' q^i nrb R&pfH( < -{:- Sbkbjlp bkqlk`bp
[0 _l + qm[i < 00 R& _l' + R&pl' 00 z HW00_l + qmii ’
Dpql klp a^ 'i , ]( 0H_l , -{:fHz N- Orbpql nrb ] ; 0 mlabjlp afsfafo mlo 0 , ]
l_qbkfbkal i^ abpfdr^ia^a Hz`m, fc ifz N- Obol `ljl q^j_f‹k qbkbjlp Hi`m, -{:Hfz Nbiil pfdkfcf`^ nrb Hf _l + fc 0< N+X mlo q^kql _l + -{: < N- K^ abjlpqo^`fŽk abi qbl,obj^ abi mrkql cfgl e^ nrba^al `lk`irfa^-
’ 6-18 @mif`^`flkbp abi qblobj^ abi mrkql cfgl
O^o^ e^`bo sbo bi ^jmifl ^i`^k`b ab i^p ^mif`^`flkbp abi qblobj^ abi mrkqlcfgl il s^jlp ^ rqfifw^o m^o^ abjlpqo^o alp qblobj^p fjmloq^kqbp- Di mofjbol a^rk^ `lkaf`fŽk prcf`fbkqb m^o^ nrb rk^ b`r^`fŽk ab i^ cloj^ b&t* v( < N abcfk^ v`ljl crk`fŽk ab t-
SDNQDL@ 6-10- TM SDNQDL@ CD DWHRSDMBH@ CD K@ ETMBHˆM HLOK‡BHS@-
Qa] b qj] bqj_e‰j `abeje`] aj qj] ^]j`] P `a h] bkni]
P < w&t*u' 0 ] y t y ^ +,// ; u ; *lly-
-4- Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
Qqlkjc]iko mqa ateopa h] `aner]`] l]n_e]h B1b&t* u':(' u mqa o]peob]_a qj] `ao+ecq]h`]` `a h] bkni]
'6-67( M:iyB`&t*u'yK
l]n] pk`k lqjpk &t* u' `a P* `kj`a i u L okj _kjop]jpao p]haomqa i y L- Qq+lkjc]iko p]i^e…j mqa l]n] _]`] bqj_eˆj %N_kjpejq] aj Y]* ^[ h] bqj_eˆj _ki+lqaop] c&t' < bYt* :l&t'[ ao _kjpejq] aj Y]* ^[, Cjpkj_ao ateopa qj] u oˆhk qj]bqj_eˆj u < W&t'* _kjpejq] aj Y]* ^[ p]h mqa
'6-68(
l]n] pk`k t aj Y]* ^[,
bYt* W&t€' < N
M^oanr]_e‰j9 Dumobp^jlp bpqb obpriq^al af`fbkal nrb i^ b`r^`fŽk b't+ v( < Npfosb m^o^ abcfkfo v fjmiŒ`fq^jbkqb `ljl crk`fŽk ab t bk Y]* ^[,
Baikopn]_eˆj, Cbpfdkbjlp `lk b bi bpm^`fl ifkb^i ab i^p crk`flkbp `lkqf,kr^p bk Y]* ^[* v abcfk^jlp rk lmbo^alo R8 b z b jbaf^kqb i^ b`r^`fŽk
0R&%N'&V'< %N&t'+ + bYt* %N&t€'
L
m^o^ `^a^ t ab Y]* ^[, K^ `lkpq^kqb mlpfqfs^ L bp i^ ab '6-67(- K^ crk`fŽkR&%N'D b pfbjmob nrb &O&DB- Cbjlpqo^objlp nrb R bp rk lmbo^alo ab `lkqo^``fŽk-Tk^ sbw p^_fal bpql pb abar`foŠ nrb R qfbkb rk mrkql cfgl •kf`l u bk B- O^o^bpq^crk`fŽk W qbkaobjlp X < R&x%'il `r^i pfdkfcf`^
0W&t' < W&t' + K bYt* W&t€'
m^o^`^a^ t ab Y]* ^[, Dpql klp a^oŠ '6-68(+ `ljl nrboŒ^jlp-O^o^ abjlpqo^o nrb R bp rk lmbo^alo ab `lkqo^``fŽk `lkpfabobjlp i^ afcb,
obk`f^
'6-7/( R&%N'&t'+ R&/l'&t' < %N&t'\ /l&t' \bYt* nl&t€' + bYt* /l&t€',L
Rbd•k bi qblobj^ abi s^ilo jbafl m^o^i^ abofs^`fŽk qbkbjlp
YYt* %N&t'[+ zYt* /l&t€' < B`Yt* v&t'[Y%N&t'+ /l&t€' *
')( B*b&t*v( bp i^ abofs^a^ ab b&t*v( obpmb`ql ^ v+ j^kqbkfbkal t cfgl-
?lhe_]_ekjao `ah paknai] `ah lqjpk befk -4.
alkab v&t' bpqŠ pfqr^a^ bkqob _l&t' v zbHwt', Olo `lkpfdrfbkqb '6-7/( klp a^
&5,6/' R&_l'&t' + R&hl'&t' < Y_l&t' \ hl&t'['0 ] B`Yy v'V([(-
K^ efmŽqbpfp'6-67( fjmif`^ nrb
/;0 ] B`Yt* v&t'[ ; 0 ] j-, L , L
Dk `lkpb`rbk`f^ '6-70( klp a^ i^ abpfdr^ia^a
&5,60' GR&_l'&t' + R&hl'&t'H R G_l&t' + hl&t' H'0 , :( R l` Hi`m, 00&0. +
alkab ] < 0 , ihK- Orbpql nrb N ; i A L+ qbkbjlp N999::] ; 0- K^ abpfdr^i,a^a '6-71( bp sŠifa^ m^o^ qlal t ab Y]* ^[, Krbdl R bp rk lmbo^alo ab `lkqo^`,
`fŽk- Dpql `ljmibq^ i^ abjlpqo^`fŽk-K^ lqo^ ^mif`^`fŽk abi qblobj^ abi mrkql cfgl bpq^_ib`b rk qblobj^ ab bufp,
qbk`f^ m^o^ i^ b`r^`fŽk fkqbdo^i
&5,61' _l&t' < hl&t' * ?,H8I&t* p'_l&p' `p,
@nrŒzbHbp rk^ crk`fŽk a^a^+ `lkqfkr^ bk Y]* ;9% @ bp rk^ `lkpq^kqb a^a^+ v I rk^crk`fŽk a^a^ abcfkfa^ v ^`lq^a^ bk bi `r^ao^al
p< w&t*u' H] R t R ^* ] R u R ^x,
K^ crk`fŽk I pb ii^j^ bi jŠ_hak ab i^ b`r^`fŽk fkqbdo^i- Rb^ B bi bpm^`fl ifkb^iab i^p crk`flkbp `lkqfkr^p bk Y]* ^[, Rrmlkd^jlp nrb bi k•`ibl I bp q^i nrb bilmbo^alo R a^al mlo
R&_l'&t' < hl&t' * ?,H8I&t* p'_l&p' `p
^mif`^ B bk B- Dp ab`fo+ prmlkd^jlp nrb R'nl(•A pfbjmob nrb AN•A- Tk^ plir`fŽk ab i^ b`r^`fŽk fkqbdo^i bp `r^inrfbo crk`fŽk bwHab B nrb p^qfpc^d^ '6-72(-
SDNQDL@ 6-11- SDNQDL@ CD DWHRSDMBH@O@Q@ DBT@BHNMDR HMSDFQ@KDR- Qe+aj h]o_kj`e_ekjao eilqaop]o+ pajaiko
'6-73( I&t*W'/ R K
l]n] pk`k lqjpk 't+ v( `a R+ oeaj`k L = N+ajpkj_ao l]n] _]`] @ p]hmqa
'6-74( HI-g; 0]K'^ , ]'
-4/ Qeopai]o `a a_q]_ekjao `ebanaj_e]hao
ateopa qj] u o‰hkqj] bqj_e‰j m:aj b mqa o]peob]_ah] a_q]_e‰j ejpacn]h '6-72(-
Baikopn]_e‰j- Cbjlpqo^objlp nrb R bp rk lmbo^alo ab `lkqo^``fŽk- Sljb,jlp bk b alp crk`flkbp `r^ibpnrfbo^ m:0 v m:1 X `lkpfabobjlp i^ afcbobk`f^
Tqfifw^kal i^ abpfdr^ia^a '6-37( mlabjlp bp`of_fo
pfbkal ] < 0-[0 K&^ + ]', Olo '6-74( qbkbjlp Nz ] ; 0+^pŒnrb R bp rk lmbo^,alo ab `lkqo^``fŽk `lk ] `ljl `lkpq^kqb ab `lkqo^``fŽk- Olo `lkpfdrfbkqb R qfbkbrk mrkql cfgl m: •kf`l bk B- Dpq^crk`fŽk m: p^qfpc^`b'6-72(-
O@QSD1
4WjUR\R\WXURWNJU
7
64=6E=@ 7;98B8?6;4= 8? 64>A@C
8C64=4B8C H F86D@B;4=8C
7-0 Erk`flkbp ab Q! bk Q!+B^jmlp bp`^i^obp v sb`qlof^ibp
K^ m^oqb0 ab bpqbslirjbk pb abaf`^ mofk`fm^ijbkqb ^ i^p qo^kpcloj^`flkbpifkb^ibp
R9T,U
ab rk bpm^`fl ifkb^i T bk lqol bpm^`fl ifkb^i U- Dk i^ m^oqb1 mobp`fkafjlp abnrb R pb^ ifkb^i mbol obpqofkdfjlp ilp bpm^`flp T v U ^ pboab afjbkpfŽk cfkfq^-Blk`obq^jbkqb+ `lkpfabo^jlp crk`flkbp `lk bi aljfkfl bk bi bpm^`fl k,afjbkpfl,k^i Q! v `lk bi ob`loofal bk bi bpm^`fl j,afjbkpflk^i Q&!+
Br^kal ilp alp k•jbolp i v j plk fdr^ibp ^i+ rk^ q^i crk`fŽk pb ii^j^crk`fŽk ob^i ab rk^ s^of^_ib ob^i- Br^kal j < 0 X i = 0 pb ii^j^ crk`fŽk sb`,qlof^i ab rk^ s^of^_ib ob^i- Dk bi Ulirjbk 0 pb bpqraf^olk ^jmif^jbkqb bgbjmilpab q^ibpcrk`flkbp-
Dk bpqb`^mŒqrilprmlkbjlp j = 0 v i y 0- Br^kal i < 0 i^ crk`fŽk pbii^j^ crk`fŽk ob^i ab rk^ s^of^_ib sb`qlof^i l+ jŠp _obsbjbkqb+ rk _]ilk ao_]h]n-Br^kal i = 0 pb ii^j^ crk`fŽk sb`qlof^i ab rk^ s^of^_ib sb`qlof^i+ l pfjmib,jbkqb _]ilk ra_pkne]h-
Dpqb `^mŒqril buqfbkab ilp `lk`bmqlp ab iŒjfqb+`lkqfkrfa^a v abofs^a^+ ^ilp `^jmlp bp`^i^obp v sb`qlof^ibp- Klp B^mŒqrilp0/ v 00 buqfbkabk bi `lk`bmqlab fkqbdo^i-
Lkp]_e‰j9 Klp bp`^i^obppb abpfdk^oŠk `lk qfml ab ibqo^`loofbkqb+v ilp sb`,qlobp `lk qfml ab &ibqo kbdofq^-Rf b bp rk `^jml bp`^i^o abcfkfal bk rk mrkqlt < &t! ,,, *tj( bk Q!+ i^ klq^`fŽk b&t' v hp•- --- +tj( pb rp^k fkafpqfkq^jbkqb
m^o^abpfdk^o bi s^ilo ab b bk rk `fboql mrkql- Rfbbp rk `^jml sb`qlof^i mlkb,jlp b't( l b't
!--- +V-j( m^o^bi s^ilo ab i^ crk`fŽk bk t- Tqfifw^objlp bi molar`ql
fkqboflo -
186
187 A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao u ra_pkne]hao
j
w9W < 1VgWgg<h
v i^ `loobpmlkafbkqb kloj^ Zu\ < &t , t'y * alkab t < 'V! --- +Vj( bu< 'Wh& -- +Wj(&Klp mrkqlp ab Q1 loafk^of^jbkqb pb fkaf`^k mlo 'u+ u' bk ird^o ab &t** t1(: X ilpab Q2 mlo 't+ u+w( bk ird^o ab 't++ t1+ t++(-
Klp `^jmlp bp`^i^obp v sb`qlof^ibp abcfkfalp bk pr_`lkgrkql ab Q1 v Q2 pbmobpbkq^klk cob`rbk`f^ bk i^p ^mif`^`flkbp ab i^ L^qbjŠqf`^ ^ i^p Bfbk`f^p k^qr,o^ibp v ^ i^ HkdbkfboŒ^-Olo bgbjmil+ pf ^ `^a^ mrkql t ab i^ ^qjŽpcbo^ ib ^pfdk^,jlp rk k•jbol ob^i b&t' nrb obmobpbkqbi^ qbjmbo^qro^ bk t* i^ crk`fŽk b ^pŒabcfkfa^ bp rk `^jml bp`^i^o- Rf ^pfdk^jlp rk sb`qlo nrb obmobpbkqbi^ sbil`fa^aabi sfbkql bk ^nrbi mrkql+ l_qbkbjlp rk bgbjmil ab `^jml sb`qlof^i-
Dk mol_ibj^p ab EŒpf` nrb qo^q^k `lk `^jmlp bp`^i^obp l sb`qlof^ibp bpfjmloq^kqb p^_bo `Žjl s^oŒ bi `^jml ^i m^p^oab rk mrkql ^ lqol- Dk bi `^plrkf,afjbkpflk^i i^ abofs^a^ bp bi fkpqorjbkql j^qbjŠqf`l rqfifw^al m^o^bpqraf^oq^ibp `^j_flp- K^ qbloŒ ab i^ abofs^a^ bk bi `^pl rkf,afjbkpflk^i j^kbg^ crk,`flkbp abcfkfa^p bk fkqbos^ilp ^_fboqlp-O^o^ buqbkaboi^ qbloŒ^ Q! `lkpfabo^jlpdbkbo^ifw^`flkbp ab fkqbos^ilp ^_fboqlp ii^j^alp _kjfqjpko ]^eanpko-
7-1 Ali^p ^_fboq^pv `lkgrkqlp ^_fboqlp
Rb^k ] rk mrkql a^al bk Q! v n rk k•jbol mlpfqfsl a^al- Di `lkgrkql abqlalp ilp mrkqlp t ab Q! q^ibpnrb
Hiu, ^ii ; n
pbii^j^ j,^kh] ]^eanp] ab o^afl o v `bkqol ]- Cbpfdk^jlp bpqb`lkgrkql `lk @']:n(-K^ _li^ @']:n( bpqŠ`-jpqfqrfa^ mlo ilp mrkqlp `rv^ afpq^k`f^ ^ ] bp jbklo
nrb n- Dk Q bp pfjmibjbkqb rk fkqbos^il ^_fboql `lk mrkql jbafl bk ]- Dk Q1bp rk afp`l `fo`ri^o+ v bk Q2 bp rk pŽifal bpc‹of`l `lk `bkqol bk ] v o^afl n-
CDEHMHBHˆM CD OTMSN HMSDQHNQ- Qa] R qj oq^_kjfqjpk `a Q!+ v oqlkjc],iko mqa ] D R- Qa `e_a mqa ] ao lqjpk ejpanekn `a R oe ateopa qj] j,^kh] ]^eanp]_kj _ajpnk aj ]+ _quko lqjpko lanpaja_aj pk`ko ] R-
Dp ab`fo+qlal mrkql ] fkqboflo ab R mrbab olab^opb mlo rk^ j,^kh] @']( q^inrb @'](QQ- Di `lkgrkql ab qlalp ilp mrkqlp fkqboflobpab R pb ii^j^k bi ejpaneknab R v pb abpfdk^ `lk fk R- Tk `lkgrkql ^_fboql nrb `lkqbkd^ rk mrkql ] pb ii^j^^ sb`bp ajpknjk ab ]-
CDEHMHBHˆM CD BNMITMSN @AHDQSN- Sj _kjfqjpk R `a Q&&oa hh]i] ]^eanpkoe pk`ko oqo lqjpko okj ejpaneknao- Co `a_en+ R ao ]^eanpk oe u o‰hkoe R < fkqR-
@kh]o]^eanp]o v _kjfqjpko ]^eanpko -44
DIDLOKPR- Dk Q bi qfml jŠp pbk`fiil ab `lkgrkql ^_fboql bp rk fkqbos^il^_fboql- K^ obrkfŽk ab alp l jŠp fkqbos^ilp ^_fboqlpbp q^j_f‹k ^_fboql- Tk fkqbo,s^il `boo^al Y]* ^[ kl bp rk `lkgrkql ^_fboql mlonrb kfkdrkl ab ilp buqobjlpabi fkqbos^il mrbab bk`boo^opbbk rk^ 0,_li^ pfqr^a^ bkqbo^jbkqb bk bi fkqbos^ila^al-
K^ 1,_li^ Q < A' N: 0( af_rg^a^ bk i^ cfdro^ 7-0 bp rk bgbjmil ab `lkgrkql^_fboql bk Q1- Slal mrkql ] ab Q bp bi `bkqol ab rk afp`l pfqr^al mlo bkqbolbk Q-O^o^ ^idrklp mrkqlp bi o^afl ab bpqbafp`l bp jrv mbnrb•l-
@idrklp `lkgrkqlp ^_fboqlp bk Q1 mrbabk `lkpqorfopb qlj^kal bi molar`ql`^oqbpf^kl ab `lkgrkqlp ^_fboqlp bk Q&-Rf+?* X ?1 plk pr_`lkgrkqlp ab Q&+prmolar`ql `^oqbpf^kl ?* W?1 bp&bi `lkgrkql abcfkfal bk Q1 mlo
Dk i^ cfdro^ 7-1 pb e^ af_rg^al rk bgbjmil- Klp `lkgrkqlp ?+ v ?1 plk fkqbos^,ilp+ v ?+ W ?1 bp rk ob`qŠkdril-
Rf ?+ X ?1 plk pr_`lkgrkqlp ^_fboqlp ab Q +bkqlk`bp ?+ W ?1 pboŠrk pr_,`lkgrkql ^_fboql ab Q1- O^o^mol_^obpql+bifg^jlp rk mrkql `r^inrfbo^ ] < &]! ]1(
o
afp`l `fo`ri^o ?* -o
EHFTQ@ 7-0 Ch `eo_k @'M:0( ao qj _kjfqj, EHFTQ@ 7-1 Ch lnk`q_pk _]npaoe]jk `a `kopk ]^eanpk aj Q1 ejpanr]hko]^eanpkoao qj na_p…jcqhk]^eanpk-
bk ?+ W ?1Œ Sbkbjlp nrb abjlpqo^o nrb ] bp rk mrkql fkqboflo ab ?+ W ?1Œ
Orbpql nrb ?+ v ?1 plk ^_fboqlp bk Qi bufpqbrk^ i,_li^ @']+:o+( bk ?+ v rk^0,_li^ @&]1: n1( bk ?1Œ Rb^ n < jfkxo{+ n1x- Olabjlp cŠ`fijbkqb abjlpqo^o nrbi^ 1,_li^ &@&]9n' R:: ?* W ?1Œ Dk bcb`ql+pf t < 'u! t1( bp rk mrkql `r^inrfbo^ab @&]9 n' bkqlk`bp Hiu, ^ii ; n* ^pŒnrb Hu+, ]+h ; o+X HW1, ]10 ; n|+ Krbdlu+ “ @&]*9 o+(X V1 “ @&]9n1(- Olo `lkpfdrfbkqb u+ D @+X V-1 D @1& pŒnrb 'u+ t1(
“ @+W ?91ŒDpql abjrbpqo^ nrb qlal mrkql ab @']: n( bpqŠbk ?+ W ?1Œ Olo ilq^kql qlal mrkql ab ?+ W ?1 bp rk mrkql fkqboflo+ pŒnrb ?+ W ?1 bp ^_fboql-
Di ib`qlo ab_boŒ^ljmol_^o nrb rk pr_`lkgrkql ^_fboql ab Qi v^ kl bp rk`lkgrkql ^_fboql `r^kal pb `lkpfabo^ `ljl pr_`lkgrkql ab Q1+ mlonrb rk pr_,`lkgrkql ab Qi kl mrbab `lkqbkbo rk^ 1,_li^-
2// A…h_qhk ebanaj_e]h aj _]ilko ao_]h]naov ra_pkne]hao
CDEHMHBHNMDRCD DWSDQHNQ X EQNMSDQ@- Sj lqjpk t oa hh]i] atpanekn ]h_kjfqjpk Q `a Q! oe ateopa qj] j,^kh] @'t( mqa jk _kjpeaja lqjpko `a R- Ch _kj,fqjpk `a pk`ko hko lqjpko `a Q j atpaneknao] R oa hh]i] ah atpanekn`a R v oa `a,oecj] _kj atp R- Sj lqjpk mqa jk ao ejpaneknje atpanekn] R oa hh]i] lqjpk bnkj,pan] `a R- Ch _kjfqjpk `a pk`ko hko lqjpko bnkjpan] `a R ao h] bnkjpan] `a R v oa`aoecj] _kj ]o,
Dpqlp `lk`bmqlp pb obmobpbkq^kbk i^ cfdro^ 7-0- Di buqboflo ab R bp bi `lk,grkql ab qlalp ilp t q^ibp nrb Zu\ = 0- K^ colkqbo^ ab R i^ `lkpqfqrvbk qlalpilp t `lk 00 t 00 < 0-
7-2 Dgbo`f`flp
0- Rb^k b rk `^jml bp`^i^o abcfkfal bk rk `lkgrkql R v a rk k•jbol ob^i a^al- Di `lk,grkql ab qlalp ilp mrkqlp t ab R q^ibp nrb Y't( < a pb ii^j^ _kjfqjpk `a jerah ab b,'Dk rk `^mŒqril mlpqboflo pb afp`rqfoŠk mol_ibj^p dblj‹qof`lp v cŒpf`lpbk ilp nrb pb mob,pbkq^k `lkgrkqlp ab kfsbi-( O^o^ `^a^ rkl ab ilp `^jmlp bp`^i^obp pfdrfbkqbp+ R bp qlalbi bpm^`fl Q!- G^`bo rk af_rgl m^o^ abp`of_fo ilp `lkgrkqlp ab kfsbi `loobpmlkafbkqbp ^ilp s^ilobp a^alp ab _-^( Y't+ u' < t1 * y:1+ A < /+0+3+8-^(Y't+u( <aVW+ _ <a,1+a,h+ h+a+a1+a2Œ
`( Y't+ u' < `lp 't * u'* a < ,0+ N+q+qI1+ i-`(-b't+u+v(<t*u*v+ _< +/*.*/,b( bp€*u+w( < t1 * 1u1 * 2v1+ a < N+5+01-
N b't+ u+ w( < pbk &t1 * u1 * X1(+ a < ,0+ ,q+/+ ’-.1+0-
1- Dk `^a^& rkl ab ilp `^plp pfdrfbkqbp+ pb^ R bi `lkgrkql ab qlalp ilp mrkqlp &t* v( abimi^kl nrb p^qfpc^`bk i^p abpfdr^ia^abp a^a^p- G^`bo rk doŠcf`l jlpqo^kal bi `lkgrkql Rv bumif`^o+ dblj‹qof`^jbkqb+ pf R bp l kl ^_fboql- Hkaf`^o i^ colkqbo^ ab R bk bi doŠcf`l-
^( t1 * u1 ; 0 - e( 0 z t y 1 X 2 ; u ; 3-_( 2t1 * 1v1 ; 5- f( 0 ; t ; 1 v W = N-b( Zu\ ; i v Guh; i - g( t y u,a( t y N v W = N - h( t = u-b( Zu\ z i v Hvi z i - 0( u = t1 v Hui ; 1-N t = N v W ; N- j( 't1 * u1 , 0('3 , t1 , u1(&= N-d( tu ; H- k( '1t , t1 , u1('V1 * u1 , t( = N-
2- Dk `^a^ rkl ab ilp pfdrfbkqbp `^plp+ pb^ R bi `lkgrkql ab qlalp ilp mrkqlp &t*v+v'* bkbi bpm^`fl qof,afjbkpflk^i+ nrb p^qfpc^`bk i^p abpfdr^ia^abp a^a^p v abqbojfk^o pf Rbp l kl ^_fboql-^( Y1 , t1 , u1 , i = N-
_( Hui; 0+ Hvi ; 0+ X Hwi; i-`( t * u * w ; i-a( Hui z 0+ Hvi ; 0+ X Z^\ ; i-b( t * u * w ; 0 v t = N+u= N+ w = N-N t1*3u1*3v1,1t*05u*3/v*002 ;M-
Cfan_e_eko 2/0
3- ^( Rf ? bp rk `lkgrkql ^_fboql bk rk bpm^`fl ab afjbkpfŽk j v pf th D ?* abjlpqo^onrb bi `lkgrkql ? + xuy+ l_qbkfal prmofjfbkal ab ? bi mrkql t +bp ^_fboql-_( Rf ? bp rk fkqbos^il ^_fboql bk i^ ob`q^ ob^i v @ rk pr_fkqbos^il ab ? `boo^al+ ab,jlpqo^o nrb ? + @ bp ^_fboql- ')(b( Rf ? X @ plk fkqbos^ilp ^_fboqlp bk i^ ob`q^ ob^i+abjlpqo^o nrb ? 'i @X? s @ plk^_fboqlp-a( Rf ? bp rk fkqbos^il `boo^al bk i^ ob`q^ ob^i+ abjlpqo^o nrb pr `ljmibjbkql 'obp,mb`ql ^ i^ ob`q^ ob^i `ljmibq^( bp ^_fboql-
4- Cbjlpqo^o i^p pfdrfbkqbp molmfba^abp ab ilp `lkgrkqlp ^_fboqlp bk Q!9^( Di `lkgrkql s^`Œl / bp ^_fboql-_( C4 bp ^_fboql-`( K^ obrkfŽk ab rk^ `lib``fŽk `r^inrfbo^ ab `lkgrkqlp ^_fboqlp bp rk `lkgrkql ^_fboql-a( K^ fkqbopb``fŽk ab rk^ `lib``fŽk cfkfq^ ab `lkgrkqlp ^_fboqlp bp rk `lkgrkql ^_fboql-b( C^o rk bgbjmil m^o^ abjlpqo^o nrb i^ fkqbopb``fŽk ab rk^ `lib``fŽk fkcfkfq^ ab `lk,grkqlp ^_fboqlp kl bp kb`bp^of^jbkqb ^_fboq^-
Akjfqjpko _ann]`ko- Tk `lkgrkql R bk C4 oa ii^j^ _ann]`k pf pr `ljmibjbkqlQ! , R bp ^_fboql- Klp qobp bgbo`f`flp pfdrfbkqbp pb obcfbobk ^ i^p molmfba^abp ab ilp`lkgrkqlp `boo^alp-
5- Dk `^a^ rkl ab ilp pfdrfbkqbp `^plp+ pb^ R bi `lkgrkql ab qlalp ilp mrkqlp &t*u' ab Q1
nrb p^qfpc^`bk i^p `lkaf`flkbp a^a^p- G^`bo rk doŠcf`l jlpqo^kal bi `lkgrkql R v a^ork^ o^wŽkdblj‹qof`^ m^o^ bumif`^o pf R bp ^_fboql+ `boo^al+ `boo^al v ^_fboql ^ i^ sbw+l kf `boo^al kf ^_fboql-^( t1 *u1 zN- d( o p € :4::1+2:4::u :4::3-_( t1 *u1 ;N- e( h:4::t :4::1+2:4::u ;3-b( t1 * u1 :4:: 0 ’ f( u < t1-a( 0 ; t1 * u1 ; 1- g( u y t1-b( 0 :4::t1 * u1 :4::1- h( W y t1 eHui ; 1-c( 0 ; t1 * u1 :4::1- 0( u y t>- v Hui:4::1-
6- ^( Rf ? bp rk `lkgrkql `boo^al bk bi bpm^`fl k,afjbkpflk^i v t bp rk mrkql kl mboqb,kb`fbkqb ^ ?* abjlpqo^o nrb ? s xuy bp q^j_f‹k `boo^al-_( Cbjlpqo^o nrb rk fkqbos^il `boo^al Y]* ^[ bk i^ ob`q^ ob^i bp rk `lkgrkql `boo^al-b( Rf ? X @plk fkqbos^ilp `boo^alp bk i^ ob`q^ ob^i+abjlpqo^o nrb ? 'i @X? s @plk`boo^alp-
7- Cbjlpqo^o i^p molmfba^abp pfdrfbkqbp ab ilp `lkgrkqlp `boo^alp ab Q@- Orbabk rqfifw^opbilp obpriq^alp abi bgbo`f`fl 4-^( Di `lkgrkql s^`Œl / bp `boo^al-_( Q! bp `boo^al-b( K^ fkqbopb``fŽk ab rk^ `lib``fŽk `r^inrfbo^ ab `lkgrkqlp `boo^alp bp `boo^a^-a( K^ obrkfŽk ab rk k•jbol cfkfql ab `lkgrkqlp `boo^alp bp `boo^a^-b( C^o rk bgbjmil m^o^ mol_^o nrb i^ obrkfŽk ab rk^ `lib``fŽk fkcfkfq^ ab `lkgrkqlp`boo^alp kl bp kb`bp^of^jbkqb `boo^a^-
8- Rb^ R rk pr_`lkgrkql ab Q@-^( Cbjlpqo^o nrb fkqR v buqR plk ^j_lp `lkgrkqlp ^_fboqlp-_( Cbjlpqo^o nrb C4 < 'fkq R( s 'buq R( s^p+ bp rk^ obrkfŽk ab `lkgrkqlp afpgrkqlp+v rqfifw^obpql m^o^ abar`fo nrb i^ colkqbo^ ^p pfbjmob bp rk `lkgrkql `boo^al-
')( Rf ? X @ plk alp `lkgrkqlp+ i^ afcbobk`f^ ? , @ 'ii^j^a^ _kilhaiajpk `a @ nao,la_pk `a ?( bp bi `lkgrkql ab qlalp ilp bibjbkqlp ab ? nrb kl mboqbkb`bk ^ @-
2/1 A…h_qhk ebanaj_e]h aj _]ilko ao_]h]naou ra_pkne]hao
0/- C^al rk `lkgrkql R ab Q@ v rk mrkql -o `lk i^ molmfba^a ab nrb qla^ _li^ @&t' `lk,qfbkb mrkqlp fkqboflobp v buqboflobp ^ R pfjriqŠkb^jbkqb- Cbjlpqo^o nrb t bp rk mrkqlcolkqbo^ ab R- „Dp `fboq^ i^ molmlpf`fŽk fksbop^> Dpql bp+„qlal mrkql colkqbo^ ab Rqfbkb kb`bp^of^jbkqb bpq^ molmfba^a>
00- Rb^ R rk pr_`lkgrkql ab Q@-Cbjlpqo^o nrb buqR < fkq 'Q, , Q',01- Cbjlpqo^o nrb rk `lkgrkql R ab Q, bp `boo^al pf v pŽil pf Q < 'fkq R( r kQ,
7-3 KŒjfqbpv `lkqfkrfa^a
Klp `lk`bmqlp ab iŒjfqb v `lkqfkrfa^a pb mrbabk buqbkabo `lk c^`fifa^a ^ilp `^jmlp bp`^i^obpv sb`qlof^ibp- Elojri^objlp i^p abcfkf`flkbp m^o^`^jmlp sb`,qlof^ibp: i^p jfpj^p pb buqfbkabk ^ ilp `^jmlp bp`^i^obp-
Blkpfabobjlp rk^ crk`fŽk b9 R ,* Q&!+alkab R bp rk pr_`lkgrkql ab Q!+ Rf] D Q! v ^ a Q&!bp`of_fjlp
'7-0( heib't( < ^9cB,,,*N
&k*b't( ,* ^ `r^kal t ,* ]'
m^o^pfdkfcf`^onrb
'7-1( ifj Ghb&t'+ ^eh < N-Hiu,^ii,N
Di pŒj_lil ab iŒjfqb ab i^ fdr^ia^a '7-1( bp bi iŒjfqb `loofbkqb abi BŠi`ril bib,jbkq^i- Dk bpq^abcfkf`fŽk kl pb bufdb nrb bbpq‹ abcfkfa^ bk bi jfpjl mrkql ]-
Rf bp`of_fjlp d < t , ] +i^ fdr^ia^a '7-1( pb `lksfboqb bk
ifj Ghb&]* d' + _ii < N-HHeii,N
O^o^ ilp mrkqlp ab Q1 bp`of_fjlp &t* u' m^o^t v &]* ^' m^o^ ] v bumobp^jlp i^obi^`fŽk ab iŒjfqb'7-0( `ljl pfdrb9
Hfj b't+ u' < ^,&t,u' ,,,‹&q,^'
O^o^ ilp mrkqlp ab Q2 mlkbjlp t < 't+ u+w( v ] < ']+ ^* a( v bp`of_fjlp
ifj b't+ u+w( < ^ -&V*hG*X',* &j*^*a'
Tk^ crk`fŽk bpb ii^j^ _kjpejq] bk ] pfbbpqŠ abcfkfa^ bk ] v pf
ifj b't( < b'](-_'I
Cb`fjlp nrb bbp _kjpejq] aj qj _kjfqjpk R pfbbp `lkqfkr^ bk `^a^ mrkql ab R-
J‡iepao v _kjpejqe`]` 2/2
Orbpql nrb bp^p abcfkf`flkbp plk buqbkpflkbp afob`q^p abi `^pl rkf,afjbkpfl,k^i+ kl ab_b plomobkabonrb jr`e^p ab i^p molmfba^abp ab ilp iŒjfqbpv ab i^`lkqfkrfa^a mrbabk q^j_f‹k buqbkabopb-Olo bgbjmil+ ilp qblobj^p obi^qfslp ^ilp iŒjfqbpv ^ i^ `lkqfkrfa^a ab prj^p+ molar`qlp v `l`fbkqbp plk q^j_f‹k `fbo,qlp m^o^ `^jmlp bp`^i^obp- O^o^ `^jmlp sb`qlof^ibp+ilp `l`fbkqbp kl bpqŠk abcf,kfalp mbol qbkbjlp bi qblobj^ pfdrfbkqb obi^qfsl ^ prj^p+ jriqfmif`^`fŽk mlo bp,`^i^obp+molar`qlp fkqboflobp v kloj^p-
SDNQDL@ 7-0- Qe ifj b't( < ^ X ifj c't( < ah+pajaiko p]i^e†j9s_a $_Q
^( ifj Yb't( * c't([ < ^ * a-++,]_( ifj ?b't( < ?^ l]n] pk`k ao_]h]n @-
!'Ib( ifj b't(& c't( < ^ 9a-++\]a( ifj 00b't( 00 < Hi_ii-++\\ ]
Baikopn]_e‰j- RŽil s^jlp ^ abjlpqo^o i^p m^oqbpb( v a(9 i^p abjlpqo^`fl,kbp ab ^( v _( pb abg^k `ljl bgbo`f`flp m^o^bi ib`qlo-
O^o^ abjlpqo^o b( bp`of_fjlp
b't(& c't( , ^ 9a < Yb't( , ;9 ' Yc't( , a[ * ^• Yc't( , a[ * a& Yb't( , ;9'
@mifnrbjlp ^elo^ i^ abpfdr^ia^a qof^kdri^o v i^ abpfdr^ia^a ab B^r`ev,R`et^owl_qbkfbkal
l z 00x'u(- chV( , ^ - bii z 00x'u(!, _ii Hid'u( , b\ * Hi_iiHid'u( , `ii * Hi`ii 00x'u(, _ii•
Orbpql nrb zGGw't(, _ii ,* N v GGc't( , b\ ,* N `r^kal t ,* ]+ bpql morb_^ nrbHHIqu(-c't( , ^ , b\ ,* N `r^kal t ,* ]+ il `r^i abjrbpqo^ `(-
Slj^kal b't( < c't( bk bi ^m^oq^al `( bk`lkqo^jlp
ifj GGb't(001< Hi_001+
!,]
ab i^ nrb l_qbkbjlp a(-
DIDLOKN 0- Akjpejqe`]` v _kilkjajpao `a qj _]ilk ra_pkne]h- Rf rk `^j,ml sb`qlof^i b qfbkbilp s^ilobp bk Q&!+^a^ rkl ab ilp s^ilobp b't( qfbkb i `ljlmlkbkqbpv mlabjlp bp`of_fo
b't( < 'bz't(+ --Œ +bi't•-
2/3 A…h_qhk ebanaj_e]h aj _]ilko ao_]h]naov ra_pkne]hao
Klp i `^jmlp bp`^i^obp e-+--- +bipb ii^j^k _kilkjajpao abi `^jml sb`qlof^i b,Cbjlpqo^objlp nrb bbp `lkqfkrl bk rk mrkql pf+v pŽil pf+ `^a^ `ljmlkbkqb -gbp `lkqfkrl bk af`el mrkql-
Cbpfdkbjlp `lk ag bi h,‹pfjl sb`qlo `lloabk^al rkfa^a 'qlalp ilp `ljml,kbkqbp ab ag plk N bu`bmql bi h,‹pfjl+ nrb bp fdr^i ^ 0(- Dkqlk`bp H:-'t( sfbkba^al mlo bi molar`ql fkqboflo
Olo `lkpfdrfbkqb+ bi ^m^oq^al b( abi qblobj^ 7-0 abjrbpqo^ nrb `^a^ mrkql ab`lkqfkrfa^a ab b il bp q^j_f‹k ab b^ @abjŠp+ mrbpql nrb qbkbjlp
i
b't( < bg't(ag+R8S
i^ ^mif`^`fŽk obfqbo^a^ ab ilp ^m^oq^alp ^( v _( abi qblobj^ 7-0 abjrbpqo^ nrbrk mrkql ab `lkqfkrfa^a ab qlalp ilp i `ljmlkbkqbp .0&--- +bi bp q^j_f‹k mrkqlab `lkqfkrfa^a ab b,
DIDLOKN 1- Akjpejqe`]` `a h] bqj_e‰j e`ajpe`]`- K^ crk`fŽk fabkqfa^a+b't( < t+ bp `lkqfkr^ bk qlal Q!+ Olo q^kql prp `ljmlkbkqbp q^j_f‹k plk `lk,qfkrlp bk qlal Qk- Dplp plk j `^jmlp bp`^i^obp a^alp mlo
DIDLOKN 2- Akjpejqe`]` `a h]o pn]jobkni]_ekjao heja]hao-Rb^ b: Qk ] Qj
rk^ qo^kpcloj^`fŽk ifkb^i- Cbjlpqo^objlp nrb bbp `lkqfkr^ bk `^a^ mrkql ] abQ!+ Dk sfoqra ab i^ ifkb^ifa^a qbkbjlp
b'] * d( < b']( * b'd(-
Olo `lkpfdrfbkqb+ _^pq^ abjlpqo^o nrb b'd( , N `r^kal d , N - Olkfbkal d bkcrk`fŽk ab prp `ljmlkbkqbp qbkbjlp d < e0bi * --- * djaj- Tp^kal i^ ifkb^,ifa^a+ qbkbjlp b'd( < dzb'a0( * --- * djb'aj(- Dpql abjrbpqo^ nrb b'd( , N`r^kal d, N-
DIDLOKN 3- Akjpejqe`]` `a hko lkhejkieko `a j r]ne]^hao- Tk `^jml bp,`^i^o N abcfkfal bk Q! mlo rk^ cŽojri^ ab i^ cloj^
!63 !6
N&t' < z --- z b Vg0 ŒŒŒtgj3! z ;<2( I;&(( =
;H,2 gj<M
pb ii^j^ mlifkljfl ab j s^of^_ibp Vh& ŒŒŒt-9 Tk mlifkljfl bp `lkqfkrl bk qlal
J‡iepao v _kjpejqe`]` 2/4
Q! ab_fal ^ nrb bp rk^ prj^ cfkfq^ ab molar`qlp ab `^jmlp bp`^i^obp `lkqfkrlpbk qlal Q!- Olo bgbjmil+ rk mlifkljfl ab alp s^of^_ibp t b v+ a^al mlo
l m
N&t* u( < J J AeeVeueQc=Q4=
bp `lkqfkrl bk qlal mrkql &t* v( bk Q1-
DIDLOKN 4- Akjpejqe`]` `a h]o bqj_ekjao n]_ekj]hao- Tk `^jml bp`^i^o ba^al mlo z't( < N't(.O't(+ alkab N v P plk mliŒkljflp bk ilp `ljmlkbkqbpab t+- pb ii^j^ crk`fŽk o^`flk^i- S^i crk`fŽk bp `lkqfkr^ bk `^a^ mrkql bk alkabO&t' y N-
Orbabk `lkpqorfopb lqolp bgbjmilp ab crk`flkbp `lkqfkr^p `lk i^ ^vra^ abipfdrfbkqb qblobj^+ nrb bpqŠ obi^`flk^al `lk i^ `lkqfkrfa^a ab i^p crk`flkbp `lj,mrbpq^p-
SDNQDL@ 7-1- Qa]j b v c `ko bqj_ekjao p]hao mqa h] bqj_e‰j _kilqaop]bl c aop…abeje`] aj ] H oeaj`k
'b l c('t( <b'c't([ -
Qec ao _kjpejq] aj ] u bao _kjpejq] aj c'](+ h] bqj_e‰j_kilqaop] bl c ao _kj,pejq] aj ]-
Baikopn]_e‰j- Rb^k u <b't( v ^ < c'](- Sbkbjlp
b'c't([ , b'c']([ <b'u( , b'd(-
Olo efmŽqbpfp+u ,, ^ `r^kal t ,, ]+ ^pŒnrb qbkbjlp
iŒj Ghb'c't([ , b'c']([HH < ifj Ghb'u( , b'd( 00 < N-00#,]hhyM iHv,_ii,N
Olo `lkpfdrfbkq‹ ifj bYc't([ < bYc']([ +^pŒnrb bl c bp `lkqfkr^ bk ]-#y]
DIDLOKN 5- Di qblobj^ ^kqboflo fjmif`^ i^ `lkqfkrfa^a ab ilp `^jmlp bp`^,i^obp d* `r^kal d&t* u' bpqŠ a^a^ mlo cŽojri^p q^ibp `ljl
ild &t0 * h(+t*u
ild '`lp &t1 * h'[ ,
.+1 A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao v ra_pkne]hao
Dk bpqlp bgbjmilp i^p crk`flkbp plk `lkqfkr^p bk qlalp ilp mrkqlp bk ilp nrb bpqŠkabcfkfa^p- K^ mofjbo^ il bp bk qlalp ilp mrkqlp abi mi^kl v i^ pbdrka^ bk qlalp ilpmrkqlp bu`bmql bk bi lofdbk- K^ qbo`bo^ bp `lkqfkr^ bk qlalp ilp mrkqlp &t* v( bkilp nrb t * v <cb N+X i^ `r^oq^ bk qlalp ilp mrkqlp bk ilp nrb t1 * ekl pb^ rkj•iqfmil fjm^o ab ol .1- ZDi `lkgrkql ab ilp mrkqlp 'u+ v( q^ibp nrb t1 * e;j6Rf1+ j < 0+2+4+ --- +bp rk^ c^jfif^ ab `fo`rkcbobk`f^p `lk `bkqol bk bi lofdbk-\Dpqlp bgbjmilp abjrbpqo^k nrb i^p afp`lkqfkrfa^abp ab rk^ crk`fŽk ab alp s^of^,_ibp mrbabk pbo mrkqlp ^fpi^alp+ `ros^p+ l c^jfif^p ab `ros^p-
DIDLOKN 6- Tk^ crk`fŽk ab alp s^of^_ibp mrbab pbo `lkqfkr^ obpmb`ql ^`^a^ s^of^_ib pbm^o^a^jbkqb v bk `^j_fl pbo afp`lkqfkr^ `ljl crk`fŽk ab alps^of^_ibp- Dpql il ^mob`f^jlp bk bi bgbjmil pfdrfbkqb9
b't+ u' < tut0 * u0
pf &t* u' 9{‹ 'N+ N(+ baM+ N( < l-
O^o^ ilp mrkqlp &t* v( abi bgb t qbkbjlp v < N X b&t* v( < b&t* N( < N+ ^pŒnrbi^ crk`fŽk qfbkb bi s^ilo `lkpq^kqb N bk qlal bi bgb t- Olo `lkpfdrfbkqb+ pf mlkb,jlp v < N X `lkpfabo^jlp b pŽil `ljl crk`fŽk ab t+ af`e^ b bp `lkqfkr^ bk t < N-@kŠild^jbkqb+ b qfbkb bi s^ilo `lkpq^kqb N bk qlalp ilp mrkqlp abi bgb v+ ^pŒnrbpf mlkbjlp t < N X `lkpfabo^jlp b `ljl crk`fŽk pŽil ab v+ b bp `lkqfkr^ bkv < N- Ml l_pq^kqb+ `ljl crk`fŽk ab i^p alp s^of^_ibp+ b kl bp `lkqfkr^ bk bi lof,dbk- Dk bcb`ql+ bk `^a^ mrkql ab i^ ob`q^ v < t 'bu`bmql bk bi lofdbk( i^ crk`fŽkqfbkb bi s^ilo `lkpq^kqb 001 v^ nrb b&t* u( < t1 f&0t1
( < 001: mrbpql nrb bufpqbkmrkqlp bk bp^ ob`q^ q^k moŽufjlp ^i lofdbk `ljl nrbo^jlp v v^ nrb baM+ N( <0<$+i^ crk`fŽk kl bp `lkqfkr^ bk 'N+ N(-
7-4 Dgbo`f`flp
Klp bgbo`f`flp ab bpq^ pb``fŽk pb obcfbobk^ iŒjfqbp v ^ i^ `lkqfkrfa^a ab `^jmlp bp`^i^obpabcfkfalp bk pr_`lkgrkqlp abi mi^kl-
0- Dk `^a^ rkl ab ilp pfdrfbkqbp bgbjmilp pb abcfkb rk `^jml bp`^i^o b jbaf^kqb i^ b`r^,`fŽk a^a^ m^o^ qlalp ilp mrkqlp &t* v( abi mi^kl abcfkfalp mlo i^ bumobpfŽk abi pbdrkaljfbj_ol- Cbqbojfk^o bk `^a^ bgbjmil bi `lkgrkql ab mrkqlp 'u+ v( bk ilp nrb b bp`lkqfkr^-
_( Ypt+u( < ild 't1 * u1(-
_1
a( b't+u( < qd ,-u
b( b't+u( < ^ob qdh-t
0`( Y't+ u' < , `lp t0‹
ut
c( Y't+u( <^o` pbk .,] ----zt1 * u1
Cfan_e_eko 2/6
t * ud( Y't+ u' < ^obq^k,
H,,-
,tuf( Y&t* u' < t&/-%' ,
te( Y't+ u' < .,,-
!t0 * u0g( Y&t* u' < ^ob blp ,Ht-u,
1- Rf ifj b&t*v( < J* X pf bufpqbkilp alp iŒjfqbprkf,afjbkpflk^ibp&!%,/-'+&]*^'
heiY&t*u'!&'I
v heiY&t*u'0.,^
abjlpqo^o nrb
ifj YheiY&t*u'[ < ifj YGeiY&t*u'[ < J,t,] W,,^ u,,^ t,,]
Klp alp iŒjfqbpab bpq^ fdr^ia^a pb ii^j^k iŒjfqbpepan]`ko: ilp bgbo`f`flp abjrbpqo^knrb i^ bufpqbk`f^abi iŒjfqb_fafjbkpflk^i v ab ilp alp iŒjfqbprkfafjbkpflk^ibp+ fjmif`^ki^ bufpqbk`f^ b fdr^ia^a ab ilp alp ifjfqbp fqbo^alp- 'Di ob`Œmol`lkl pfbjmob bp `fboql-Dk bi bgbo`f`fl 3 pb a^ rk `lkqo^bgbjmil-(
2- Rb^ b&t*v( < &t + u'-&t * v( pf t * v z N- Cbjlpqo^o nrb
ifj YGeiY&t*u'[ < 0 mbol nrb ifj YheiY&t*u'[ < ,i ---,l s,N 0.,/ !+,l
Tqfifw^obpb obpriq^al v bi abi bgbo`f`fl 1 m^o^abar`fo nrb b&t*v( kl qfbkab ^ rk iŒjfqb`r^kal &t*v( z 'N+N(-
3- Rb^
V1u1Y't u'+++++* + V0u0* &t \ u'0
Cbjlpqo^o nrb
pfbjmob nrb V0u0* &t + u'0 ,zh9 N-
ifj YheiY&t*u'[ < ifj YGeiY&t*u'[ < N!+,l 0.,/ 0.,/ --,/
mbol nrb b&t*v( kl qfbkab ^ rk iŒjfqb`r^kal &t*v( z 'N+N(- YGj`e_]_eˆj8 Du^jfk^o bpl_ob i^ ob`q^ v < t,[ Dpqbbgbjmil abjrbpqo^ nrb bi ob`Œmol`labi bgbo`f`fl 1 kl pfbj,mob bp `fboql-
4- Rb^
x
0upbk ,
Y't+u( < N Wpf u y N+
pf u < N-
Cbjlpqo^o nrb b&t*v( z N `r^kal 'u+v( z 'N+N( mbol nrb
ifj ZHfjbp9t*u'[ ,zh9 ifj ZHfjYp•+u'[,00,/ t,k t,,k 00,*/
2/7 A…h_qhk ebanaj_e]h aj _]ilko ao_]h]naou ra_pkne]hao
Dumif`^o mlo nr‹ bpql- kl `lkqo^af`b bi bgbo`f`fl 1-5- Rf &t* v( z 'N+N(+mlkd^jlp b&t*v( < &t%+ u%'-&t%* u%',G^ii^o bi iŒjfqb ab b&t*u' `r^k,
al 'u+ v( z 'N+N( ^ il i^odl ab i^ ob`q^ v < it- „Dp mlpf_ib abcfkfo b'M+ N( ab jlal nrb bpb^ `lkqfkr^ bk 'N+N(>
6- Rb^ b&t*v( < N pf v9# N l pf v z t% X pb^ b&t*v( < 0 pf N ; v ; t%, Cbjlpqo^o nrbb&t*v( z N `r^kal 'u+ v( z 'N+N( ^ il i^odl ab `r^inrfbo ob`q^ mlo bi lofdbk- G^ii^ork^ `ros^ nrb m^pb mlo bi lofdbk ^ il i^odl ab i^ `r^i 'p^isl bk bi lofdbk( b&t*v( qfbkbbi s^ilo `lkpq^kqb 0- „Dp b `lkqfkr^ bk bi lofdbk>
7- Rf b&t*v( < Zpbk &t%* u%'[-&t%* u%' `r^kal 'u+ v( z 'N+N( „`Žjl ab_b abcfkfopb b&M*M'm^o^ nrb pb^ b `lkqfkr^ bk bi lofdbk>
8- Rb^ b rk `^jml bp`^i^o `lkqfkrl bk rk mrkql ] fkqboflo ^ rk `lkgrkql R ab Q!- Rfb&]' y N+abjlpqo^o nrb bufpqb rk^ k,_li^ @&]' bk i^ nrb b qfbkb bi jfpjl pfdkl nrb b&]',
0'. >J MN[R_JMJMNEL LJVYXN\LJUJ[[N\YNL]XJ OL _NL]X[
Dpq^pb``fŽk fkqolar`b i^p abofs^a^p ab `^jmlp bp`^i^obp-Dk i^ pb``fŽk 7-07pb afp`rqbk i^p abofs^a^p ab `^jmlp sb`qlof^ibp-
Rb^ b rk `^jml bp`^i^o abcfkfal bk rk `lkgrkql R ab Q! +v pb^ ] rk mrkqlfkqboflo ^ R- Cbpb^jlp bpqraf^o i^ s^of^`fŽk abi `^jml `r^kal klp abpmi^w^jlpabpab ] ^ rk mrkql moŽufjl- Olo bgbjmil+ prmlkd^jlp nrb b&]' bp i^ qbjmbo^,qro^ bk rk mrkql ] bk rk^ e^_fq^`fŽk `lk `^ibc^``fŽk v `lk rk^ sbkq^k^ ^_fboq^-Rf klp jlsbjlp e^`f^ i^ sbkq^k^ i^ qbjmbo^qro^ ab`ob`boŠ+mbol pf klp ^`bo`^jlp^i o^af^alo ab i^ `^ibc^``fŽk ^rjbkq^oŠ- Dk dbkbo^i+i^ s^of^`fŽk abi `^jml ab,mbkaboŠab i^ afob``fŽk bk i^ nrb klp jls^jlp ^ m^oqfoab ]-
Rrmlkd^jlp nrb pb obmobpbkq bp^ afob``fŽk jbaf^kqb lqol sb`qlo u, Dpqlbp+prmlkd^jlp nrb klp jlsbjlp abpab ] e^`f^ lqol mrkql ] * u+ pfdrfbkal bipbdjbkql ab ob`q^ nrb rkb ] `lk ] * u, B^a^ mrkql ab bpqbpbdjbkql qfbkb i^cloj^ ] * du+alkab d bp rk k•jbol ob^i- Dk i^ cfdro^ 7-2 pb jrbpqo^ rk bgbj,mil- K^ afpq^k`f^ abpab ] e^pq^ ] * du bpHieX00< Hei Hivii -
EHFTQ@ 7-2 Ch lqjpk ]&* du aop… aj h]na_p] l]n]hah] ] ] mqa l]o] lkn u-
EHFTQ@ 7-3 Ch lqjpk ] * du aop… aj h]j,^kh] @']: n( oe GGduhh; n-
J] `aner]`] `a qj _]ilk ao_]h]n naola_pk ] qj ra_pkn 2/8
Orbpql nrb ] bp rk mrkql fkqboflo ab R+ bufpqb rk^ k,_li^ @&]9o( pfqr^a^ bk,qbo^jbkqb bk R- Rf d pb bifdb ab j^kbo^ nrb Hei HHXHH; n+ bi pbdjbkql abpab ]e^pq^ ] * du bpq^oŠ bk R- 'Ubo cfdro^ 7-3( L^kqbkd^jlp d " N mbol 0/ _^pq^kqbmbnrb•l m^o^ nrb ] * du D R X `lkpqorv^jlp bi `l`fbkqb ab afcbobk`f^p
'7-2( ba] * du( , ba](
d
Di krjbo^alo ab bpqb `l`fbkqb mlkb ab j^kfcfbpql bi `^j_fl ab i^ crk`fŽk `r^kalklp abpmi^w^jlp abpab ] ^ ] * du - Di `l`fbkqb pb abkljfk^ ^ pr sbw bi lnkia,`ek `a r]ne]_e‰jab b bk bi pbdjbkql ab ob`q^ nrb rkb ] `lk ] * du - Mlp fkqb,obp^ bi `ljmloq^jfbkql ab bpb `l`fbkqb `r^kal d zN- Dpql klp iibs^ ^ i^ pfdrfbkqbabcfkf`fŽk-
CDEHMHBfˆM CD K@ CDQHU@C@ CD TM B@LON DRB@K@Q QDRODBSN @ TM UDBSNQ-
B]`k qj _]ilk ao_]h]nb9 R ,* Q +`kj`a R R:: Q!- Qa]j ] qj lqjpk ejpanekn] Ra u qj lqjpk ]n^epn]nek`a Q!+ J] `aner]`] `a b aj ] _kj naola_pk ] u oa nalna,oajp] _kj ah o‡i^khk b&']: u' v pb abcfkb
'7-3( b&' ( if ba] * du( , ba](]9u < 0j
d,M d
_q]j`k p]hh‡iepaateopa-
DIDLOKN 0- Rf W < M+ bi `l`fbkqb ab afcbobk`f^p '7-2( bp N m^o^ qlal d " N-^pŒmqab&']: M' bufpqb pfbjmob v bp fdr^i ^ N-
DIDLOKN 1- Baner]`] `a qj] pn]jobkni]_e‰j heja]h-Rf b9 R ,* Q bp ifkb^i+bkqlk`bp ba] * du( < ba]( * db'u( v bi `l`fbkqb ab afcbobk`f^p '7-2( bp fdr^i ^b'u( m^o^ qlal d " N- Dk bpqb `^pl+ b&']: u( bufpqb pfbjmob v bpqŠ a^a^ mlo
b&']:u( <b'u(
m^o^ qlal ] ab R v qlal u ab Q! - Cf`el ab lqol jlal+ i^ abofs^a^ ab rk^ qo^kplcloj^`fŽk ifkb^i obpmb`ql ^ u bp fdr^i ^i s^ilo ab i^ crk`fŽk bk u-
O^o^ bpqraf^o bi `ljmloq^jfbkql ab b pl_ob i^ ob`q^ nrb m^p^ mlo ] v ] * um^o^ u 8zb; M fkqolar`fjlp i^ crk`fŽk
c&p' < ba] * pu(-
Di qblobj^ nrb pfdrb obi^`flk^ i^p abofs^a^p c%&p'v b&'] * pu:u(-
20/ A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao v ra_pkne]hao
SDNQDL@ 7-2- Qe c'p( <b']*pu( v oe qj] `a h]o `aner]`]o c'p( kb&']*pu:u(ateopa+ajpkj_ao p]i^e†j ateopa h] kpn] v _kej_e`aj+
'7-4( c&'p( <b&'] * pu:u(-
Cj l]npe_qh]n+ _q]j`k p < N pajaiko d&'N( < G&']:u(-
Baikopn]_e‰j- Eloj^kal bi `l`fbkqb ab afcbobk`f^p m^o^d+ qbkbjlp
c'p * d( , c'p( HA] * pu * du( , H'] * pu(<
d d
G^`fbkal nrb d y N l_qbkbjlp '7-4(-
DIDLOKN 2- B^i`ri^o G&']:u' pf z't( < HHui01m^o^qlal t bk Q!+
Qkhq_e‰j- Olkd^jlp c'p( < bA] * pu( < '] * pu( - '] * pu( < ]& ] * Xp] 9u* p0u -u- Olo `lkpfdrfbkqb c&'p(< 1]& u * 1pu -u+ ^pŒnrb d&'N(< G&:w &:u( <
1]&u-Tk `loli^ofl pbk`fiil abi Sblobj^ 7-2 bp bi qblobj^ abi s^ilo jbafl m^o^
`^jmlp bp`^i^obp-
SDNQDL@ 7-3- SDNQDL@ CDK U@KNQ LDCHN O@Q@ CDQHU@C@R CD B@LONR
DRB@K@QDR- Qqlkjc]iko mqa ateopa h] `aner]`] c'^ * pu: u( l]n] _]`] p aj ahejpanr]hk N z p y 0- Cjpkj_ao l]n] qj _eanpk jŠiank na]h Maj ah ejpanr]hk ]^eanpkN ; M; 0 pajaiko
bA] * u( , bA]( < b&'v: u(+ alkab v < ] * &'u,
Baikopn]_e‰j- Olkd^jlp c'p( < bA] * pu(- @mif`^kal bi qblobj^ abi s^ilojbafl rkf,afjbkpflk^i ^ d bk bi fkqbos^il ZN+0\ qbkbjlp
c'G( , c'M( < c.|'(+ alkab N ; '(; 0-
Orbpql nrb c'0( , d'N( < ba] * ux , ba]( v c&'M(< h%'] * beu:u(+ bpql `ljlmibq i^ abjlpqo^`fŽk-
7-6 7N[R_JMJ\MR[NLLRXWJUN\b MN[R_JMJ\YJ[LRJUN\
Dk bi `^pl m^oqf`ri^o bk bi -nrb u bp rk sb`qlo qjep]nek+ bpql bp+`r^kalHivii< 0+i^ afpq^k`f^ bkqob] v ] * du bp Hei-Dk q^i `^pl bi `l`fbkqb ab afcbobk,
Baner]`]o l]n_e]hao `a kn`aj oqlanekn 200
`f^p '7-2( obmobpbkqbi moljbafl ab s^of^`fŽk ab b mlo qje`]` `a `eop]j_e] ^ ili^odl abi pbdjbkql ab ob`q^ nrb rkb ] `lk ] * du : i^ abofs^a^ b%&]9u( pbabkl,jfk^ `aner]`] `ena__ekj]h-
CDEHMHBHˆM CD CDQHU@C@R CHQDBBHNM@K X O@QBH@K- Rf W ao qj ra_pkn qje,p]nek+h] `aner]`] b%&]9u' oa hh]i] h] `aner]`] `ena__ekj]h `a b aj ] aj h] `ena_,_e‰j`a u- Cj l]npe_qh]n+oe u < ag 'ah g,†oeik ra_pkn _kkn`aj]`k qjep]nek( h]`aner]`] `ena__ekj]h H%']: ag( oa `ajkiej] `aner]`] l]n_e]h naola_pk ] ag W oanalnaoajp] p]i^e†j ia`e]jpa ah o‡i^khk Bgb&]', ?o‡ lqao
K^p pfdrfbkqbpklq^`flkbp pb rp^k q^j_f‹k m^o^ i^ abofs^a^ m^o`f^i Bgb&]'8
v
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10- Tk `lkgrkql R ab Q! pb ii^j^ _kjratk pf m^o^ qlal m^o ab mrkqlp ] v ^ ab Rbi pbdjbkql ab ob`q^ nrb rkb ] `lk ^ mboqbkb`b q^j_f‹k ^ R: af`el ab lqol jlal+p] * 'i , p(d D R m^o^ `^a^ p abi fkqbos^il N 94 p 94 0-^( Cbjlpqo^o nrb qla^ k,_li^ bp `lksbu^-_( Rf b%&t9u(< N m^o^ qlal t bk rk `lkgrkql `lksbul ^_fboql R v qlal u ab Q!+ ab,jlpqo^o nrb Gbp `lkpq^kqb bk R-
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ba] * d( , ba]( < ba] * d( , b'](- d-d
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Rrmlkd^jlp nrb ^mif`^jlp bi jfpjl o^wlk^jfbkql ^- rk `^jml bp`^i^o db,kbo^i- Rrmlkd^jlp nrb bufpqbi^ abofs^a^ b%&]9u( m^o^ rk `fboql u- Dkqlk`bp pfd ;/; N mlabjlp bp`of_fo
ba] * du( , ba]( < ba] * du( ,ba](- d-d
203 A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao v ra_pkne]hao
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heib'] * du( <ba](Pc=
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b't( ,,* b'](_q]j`k t ,,* ] ^ il i^odl ab qla^ ob`q^ nrb m^pb mlo ]- Dpql m^ob`b pr,dbofo nrb b bp `lkqfkr^ bk ]- Rfk bj_^odl+ plomobkab nrb bpq^ `lk`irpfŽk kl bpkb`bp^of^jbkqb `fboq^- Di bgbjmil nrb pfdrb jrbpqo^ rk `^jml bp`^i^o nrb qfbkbabofs^a^ afob``flk^i bk M bk `r^inrfbo afob``fŽk mbol nrb kl bp `lkqfkrl bk M,
DIDLOKN- Rb^ b bi `^jml bp`^i^o abcfkfal bk Q1 abi jlal pfdrfbkqb9
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J] `ebanaj_e]h 204
S^vilo ab mofjbo do^al- Rf bufpqb G&'](abpfdkbjlp `lk C']+ d( i^ afcbobk`f^
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`fŽk ifkb^i prdfbob rk j‹qlal ab buqbkabo bi `lk`bmql ab afcbobk`f^_fifa^a ^i`^pl ab rk k•jbol `r^inrfbo^ ab afjbkpflkbp-
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rk mrkql fkqboflo ^ R v @&]9 n' rk^ k,_li^ `lkqbkfa^ bk R- Rb^ r rk sb`qlo q^i nrbGGrhh; n* ab jlal nrb ] * r D @']: n',
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M^oanr]_e‰j9 K^ afcbobk`f^i R- bp rk^ qo^kpcloj^`fŽk ifkb^i+ kl rk k•jbol-Di s^ilo R,&r' bp rk k•jbol ob^i: bpqŠabcfkfal m^o^qlal mrkql r ab Q!- K^ afcb,obk`f^i crb fkqolar`fa^ mlo V- G- Xlrkd bk 08/7 v mlo L- Eo‹`ebq bk 0800 bk cloj^jŠp dbkbo^i-
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Hisii,N-
205 A…h_qhkebanaj_e]h aj _]ilko ao_]h]naou ra_pkne]hao
Di qblobj^ nrb pfdrb abjrbpqo^ nrb pf i^ afcbobk`f^i bufpqb+bp •kf`^- @pŒ,jfpjl klp af`b `Žjl `^i`ri^o R]'u( m^o^ qlal u ab Q!+
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Orbpql nrb b bp afcbobk`f^_ib bk ] qbkbjlp rk^ cŽojri^ ab S^vilo+
'7-0/( H'] * r( <ba]( * R]'r( * 0H b\ C']+ r(
m^o^ HHsff ; n m^o^ ^id•k n= N+ v alkab C']+ r( y N `r^kal 0Hb\ z N- Dk bpq^cŽojri^ qljbjlp r < du + pfbkal e ;/; N X Hei GGWGG; n, Dkqlk`bp 00rGG ; n,Orbpql nrb R‚ bp ifkb^i bp R]'r( < R]'du( < dR]'u(- Olo 0/ q^kql '7-0/( klp a^
'7-00( ba] * du( , ba]( < R' ( * GdhhhuhhC' (d ] u d ]+r -
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O^o^ abar`fo '7-8( rqfifw^jlp i^ ifkb^ifa^a ab Ro- Rf u < 'u! --- +Wj( qbkb,jlp u <1z<0Wgag* irbdl
0')* :[JMRNW]NMN WLJVYXN\LJUJ[
K^ cŽojri^ abi qblobj^ 7-4+ nrb bumobp^ e&'|:u( `ljl rk^ `lj_fk^`fŽkifkb^i ab ilp `ljmlkbkqbp ab u+mrbab bp`of_fopb `ljl rk molar`ql bp`^i^o+
j
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En]`eajpa `a qj _]ilk ao_]h]n 206
alkab [0b&]' bp bi sb`qlo `rvlp `ljmlkbkqbp plk i^p abofs^a^p m^o`f^ibpab b bk 7&
Tb']( < 'BH'](+ --- +Bjb']•-
Dpqbbp bi ii^j^al cn]`eajpa ab b, Di do^afbkqb [0b bp rk `^jml sb`qlof^i abcfkfalbk `^a^ mrkql ] bk bi nrb bufpqbk i^p abofs^a^p m^o`f^ibp B/b&]'* ,,, *Bjb&]'*S^j_f‹k bjmib^jlp i^ klq^`fŽk do^a b bk ird^o ab [0b, Di pŒj_lil [0 pb ibb~k^_i^ƒ-
K^ cŽojri^ ab S^vilo ab mofjbo loabk '7-0/( mrbab ^elo^ bp`of_fopb bki^ cloj^
'7-01( b'] * r( < b']( * Tb']( - r * 00 b\ C']+ r(+
bk alkab C&]* r' y N `r^kal 00sHHz N- Dk bpq^cloj^ pb m^ob`b ^ i^ cŽojri^ abS^vilo rkfafjbkpflk^i abpbjmb•^kal bi sb`qlo do^afbkqb [0b&]' bi m^mbiab i^ ab,ofs^a^ b%&]',,
@ m^oqfoab i^ cŽojri^ ab S^vilo mlabjlp abar`fo cŠ`fijbkqb nrb i^ afcbobk,`f^_fifa^a fjmif`^ i^ `lkqfkrfa^a-
SDNQDL@ 7-5- Rfqj _]ilk ao_]h]nb ao `eeanaj_e]^haaj :%ajpkj_ao b ao _kj,pejq] aj ]-
Baikopn]_e‰j- Cb '7-01( obpriq^
Gb'] * r( , b'](0 < GTb']( - r * zreeC']+ r(h-
@mif`^kal i^ abpfdr^ia^a qof^kdri^o v i^ ab B^r`ev,R`et^ow bk`lkqo^jlp
k888899Gb'] * r( , b']( H9999::HHUc'^(iiiisii * GGrGGGC']+r(h-
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207 A…h_qhkebanaj_e]h aj _]ilko ao_]h]naov ra_pkne]hao
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`fii^ obi^`fŽk dblj‹qof`^ `lk bi sb`qlo do^afbkqb- Rrmlkd^jlp mqaTb']( 8zG; MX abpfdkbjlp `lk '( bi Škdril cloj^al mlo Tb']( b u- Sbkbjlp bkqlk`bp
G&']:u( < Tb'](& u < HHUc'^(.HHHX.i lp a < 00Tb']( 00 lp a-
Dpql klp af`b nrb i^ abofs^a^ afob``flk^i bp bi `ljmlkbkqb abi sb`qlo do^afbkqbbk i^ afob``fŽk abi u- K^ cfdro^ 7-4 jrbpqo^ ilp sb`qlobp Tb']( b u ^mif`^alp ^imrkql ]- K^ abofs^a^ ^i`^kw^ bi s^ilo jŠufjl `r^kal `lp &H < 0+bpql bp+`r^kalu qfbkbi^ jfpj^ afob``fŽk nrb Tb'](- @abjŠp+ bpqbjŠufjl bp fdr^i ^ i^ ilkdf,qra abi sb`qlo do^afbkqb-Br^kal Uba]( bp loqldlk^i ^ u+ i^ abofs^a^ afob``flk^ib&']:u(ao N- Dk bi bpm^`fl ab alp afjbkpflkbp pb bp`of_b `lk cob`rbk`f^
y%f& ' \ ]b't+ u( - * ]b't+ u( -s t+ u , ]t 0 ]u H,
Dk qobpafjbkpflkbp i^ cŽojri^ `loobpmlkafbkqb bp
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7-02 Blkaf`fŽk prcf`fbkqb ab afcbobk`f^_fifa^a
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nrb v^ pb afp`rqfŽ bk i^ pb``fŽk 7-0/- O^o^ bp^ crk`fŽk bufpqbki^p alp abofs^a^pm^o`f^ibpBH'M( v BH'M( mbol b kl bp `lkqfkr^ bk M+-v mlo q^kql kl mrbabpbo afcbobk`f^_ib bk N-
Di qblobj^ nrb pfdrb abjrbpqo^ nrb i^ bufpqbk`f^ ab abofs^a^p m^o`f^ibp_kjpejq]o bk rk mrkql fjmif`^ i^ afcbobk`f^_fifa^a bk af`el mrkql-
SDNQDL@ 7-6- BNMCHBHˆM RTEHBHDMSD CD CHEDQDMBH@AHKHC@C- Qe ateopajh]o `aner]`]o l]n_e]hao B+[* ,,, *Bjb aj qj] _eanp]j,^kh] @']( v okj _kjpejq]oaj ]+ ajpkj_ao b ao `eeanaj_e]^haaj HG,
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alkab C&]* r' y N `r^kal 0Hb\ z N- Dpql mol_^oŠ bi qblobj^-Olkd^jlp @ < Hisii- Dkqlk`bp r < ?S* alkab Hirii< 0- L^kqbkd^jlp +[0/
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6- Rb^k b v d alp `^jmlp bp`^i^obp afcbobk`f^_ibp bk rk `lkgrkql ^_fboql R- Cbar`fo i^ppfdrfbkqbp molmfba^abp abi do^afbkqb9 ,^( do^a b < N pf b bp `lkpq^kqb bk R-_( do^a 'b * d( < do^a b * do^a d-`( do^a &a-' < b do^a b pf b bp `lkpq^kqb-a( do^a &bc' < bdo^a d * d do^a b,
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Pach] `a h] _]`aj] l]n] `aner]`]o `a _]ilko ao_]h]nao 210
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211 A…h_qhk ebanaj_e]h aj _]ilko ao_]h]naov ra_pkne]hao
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c'p * d( , c'p( < Tb']( - n'p * d( , n'p( * Hio'q* d( , n'p(00C'] u',d d d&
Pach] `a h] _]`aj] l]n] `aner]`]o `a _]ilko ao_]h]nao 212
G^`fbkal nrb d y N l_qbkbjlp '7-04(-
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213 A…h_qhk ebanaj_e]h aj _]ilko ao_]h]naov ra_pkne]hao
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^( Di sb`qlo do^afbkqb [0b bp kloj^i ^ b-_( K^ abofs^a^ afob``flk^i ab b bp `bol ^ 0/ i^odl ab b-b( K^ abofs^a^ afob``flk^i ab b qfbkb pr s^ilo jŠufjl bk i^ afob``fŽk
kloj^i ^ b-Qkhq_e‰j- Rf R bp rk sb`qlo rkfq^ofl q^kdbkqb^ b+ i^ abofs^a^ afob``flk^i
ab b]hk i^odl ab b bp bi molar`ql bp`^i^o Tb&R- Dpqbmolar`ql bp `bol pfZ/b bp mbombkaf`ri^o^ R*v ^i`^kw^ pr jŠufjl s^ilo pf [0b bp m^o^ibi^ ^ R,Olo `lkpfdrfbkqb i^p alp molmlpf`flkbp _( v `( plk `lkpb`rbk`f^p ab ^(- O^o^abjlpqo^o ^(+ `lkpfabobjlp rk^ `ros^ mi^k^ `r^inrfbo^ o`lk rk^ b`r^`fŽk sb`,qlof^i ab i^ cloj^ n'p( < V'p(e * W'p(f b fkqolarw`^jlp i^ crk`fŽk c'p( <bYn'p([-Dk sfoqra ab i^ obdi^ ab i^ `^abk^ qbkbjlp c&'p( < TbYn'p([ - n&'p(-Br^kal H&< b+i^ crk`fŽk d qfbkb bi s^ilo `lkpq^kqb a ^pŒnrb c%&p'< N pf n'p( D b- Orbpql nrbd&< Tb&n&+obpriq^nrb [0b bp mbombkaf`ri^o^ n&bk b: irbdl [0b bp kloj^i ^ b-
7-05 @mif`^`flkbp dblj‹qof`^p- Blkgrkqlp ab kfsbi- Oi^klp q^kdbkqbp
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be_ea `a jerah b't+ u+w( < `-
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abi sb`qlo do^afbkqb- Rb^ b rk `^jml bp`^i^o abcfkfal bk rk `lkgrkql Q ab Q! v`lkpfabobjlp ^nrbiilp mrkqlp t ab Q m^o^ ilp nrb b&t' qfbkb rk s^ilo `lkpq^kqb+mlo bgbjmil b't( < _- Cbpfdkbjlp bpb `lkgrkql mlo J'_(+ ab jlal nrb
J'_( < wt Ht D R X b't( < ax-
Di `lkgrkql J'_( pb ii^j^ _kjfqjpk `a jerah ab b- Dk Qz+ J'_( pb ii^j^ _qnr] `ajerah: bk Q! oqlanbe_ea `a jerah-
Dk jr`e^p ^mif`^`flkbp cŒpf`^ppb mobpbkq^k c^jfif^p ab `ros^p ab kfsbi- Olobgbjmil+ pf b't+ v( obmobpbkq^ i^ qbjmbo^qro^ bk 't+ u'* i^p `ros^p ab kfsbi ab b'`ros^p ab qbjmbo^qro^ `lkpq^kqb( pb ii^j^k eokpani]o- Di cirgl ab `^ilo qfbkbird^o bk i^ afob``fŽk abi `^j_fl jŠp oŠmfal ab i^ qbjmbo^qro^- Krbdl+ bk rk^elg^ mi^k^ abid^a^ bi cirgl ab `^ilo qfbkb ird^o ^ il i^odl ab rk^ c^jfif^ ab `ros^ploqldlk^ibp ^ i^p fplqboj^p- Dp^p pb ii^j^k h‡ja]o `a bhqfk: plk i^p qo^vb`qlof^ploqldlk^ibp ab i^p fplqboj^p- U‹^pb i^ cfdro^ 7-5-
Blkpfabobjlp ^elo^ rk `^jml bp`^i^o b afcbobk`f^_ib bk rk `lkgrkql ^_fboqlQ ab Q&[ v bu^jfkbjlp rk^ ab prp prmbocf`fbp ab kfsbi+ J&_', Rb^ ] rk mrkqlbk bp^ prmbocf`fb+v `lkpfabobjlp rk^ `ros^ opfqr^a^ bk i^ prmbocf`fb v nrb m^pbmlo ]+`ljl bpqŠ fkaf`^al bk i^ cfdro^ 7-6- Cbjlpqo^objlp nrb bi sb`qlo do^afbkqb
Rrmbocf`fb ab kfsbi /,&&%'
EHFTQ@ 7-7 Ch ra_pkn cn]`eajpa %Zhb ao jkni]h ]h lh]jk p]jcajpa ] 0HHi;. oql_n‡e_e_ `a jerahb&t*v+w( < _,
215 A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao v ra_pkne]hao
s bA]( bp kloj^i ^ bp^ `ros^ bk ]- Dpql bp+abjlpqo^objlp nrb U ba]( bp mbombk,af`ri^o ^i sb`qlo q^kdbkqbab obk ]- @ q^i cfk prmlkd^jlp nrb H&bpqŠabcfkfa^ m^o^,j‹qof`^jbkqb mlo rk^ crk`fŽk sb`qlof^i abofs^_ib n abcfkfa^ bk rk `fboql fkqbo,s^il H ab Q0
’ Orbpql nrb obpqŠpfqr^a^ bk i^ prmbocf`fbab kfsbi J&_'* i^ crk`fŽk n
p^qfpc^`bi^ b`r^`fŽk
bYn'p([ < a m^o^ qlal p`a H,
Rf c'p( < bYn'p([ m^o^p bk H* i^ obdi^ ab i^ `^abk^ bpq^_ib`b nrb
d&'p( < TbYn'p([ - n&'o(-
Orbpql nrb d bp `lkpq^kqb bk H* qbkbjlp c%&p'< N bk b, Dk m^oqf`ri^o+bifdfbkal p*
ab jlal nrb d'qi( < ] bk`lkqo^jlp nrb
Tb']( - n&'pG( < l-
Dp ab`fo+bi do^afbkqbab b bk ] bp mbombkaf`ri^o^i sb`qlo q^kdbkqbo&'qi(ljl pb^cfojŽ-
Sljbjlp ^elo^ rk^ c^jfif^ ab `ros^p bk i^ prmbocf`fbab kfsbi J&_' nrb m^pbkmlo bi mrkql ]- Rbd•k il af`el bk i^ afp`rpfŽk ^kqboflo+ilp sb`qlobp q^kdbkqbp^qla^p bp^p`ros^p plk mbombkaf`ri^obp i sb`qlo do^afbkqbTb']( - Rf ‹pqbkl bp `bol+af`elp sb`qlobp q^kdbkqbpabqbojfk^k rk mi^kl+ v bi do^afbkqb Tb']( bp kloj^i ^bpqbmi^kl- 'U‹^pb cfdro^ 7-7-( S^i mi^kl pb ii^j^ lh]jk p]jcajpa ^ i^ prmbocf`fbJ&_' bk ],
Dk bi Ulirjbk 0 pb sfl nrb rk mi^kl nrb m^pbmlo ] `lk sb`qlo kloj^i LbpqŠ `lkpqfqrfal mlo qlalp ilp mrkqlp t ab Q2 nrb p^qfpc^`bk i^ b`r^`fŽkL• 't , ]( < N- Olo `lkpfdrfbkqb bi mi^kl q^kdbkqb^ i^ prmbocf`fbab kfsbi J&_'
bk ] bpq^oŠ lkpqfqrfal mlo qlalp ilp mrkqlp t ab Q2 nrb p^qfpc^d^k
Tb']( - 't , ]( < l-
O^o^ l_qbkbo rk^ b`r^`fŽk `^oqbpf^k^ ab bpb mi^kl bumobp^objlp t+ :% v Tb'](bk crk`fŽk ab prp `ljmlkbkqbp- Dp`of_fbkal t < &t* v+w(+] < 'Wi&uz, X*'* v
Tb']( < BG.'](: * B`'](f * B]b'](g+
l_qbkbjlp i^ b`r^`fŽk `^oqbpf^k^
Cfan_e_eko .-2
@ ilp `^jmlp bp`^i^obpabcfkfalp bk Q1 pb ^mif`^ rk^ afp`rpfŽk m^ob`fa^-Dk bibgbjmil 2 ab i^ pb``fŽk ^kqboflo ebjlp abjlpqo^al nrb bi sb`qlo do^afbkqb rb'](bk rk mrkql ] ab rk^ `ros^ ab kfsbi bp mbombkaf`ri^o ^i sb`qlo q^kdbkqb^ i^`ros^ bk ], Olo `lkpfdrfbkqb i^ ob`q^q^kdbkqb^ i^ `ros^ ab kfsbi J&_' bk rk mrkql] < 'Vh& v{( qfbkb i^ b`r^`fŽk `^oqbpf^k^
Bzb']('t , Vh( * B`']('u , WG'< N-
0')/ 8SN[LRLRX\
0- Dk bpqb bgbo`f`fl mlabjlp prmlkbo i^ bufpqbk`f^ v `lkqfkrfa^a ab qla^p i^p abofs^a^pnrb pb `lkpfabobk- K^p b`r^`flkbp q;-&t*u'* t;V&p'* u;W&p' abcfkbk q `ljl crk`fŽkab p* mlkd^jlp q;D&p',^( @mif`^o i^ obdi^ ab i^ `^abk^ m^o^ abjlpqo^o nrb
N&'p( < /0 V&'p( * /0 W&'p(W_ W` &
alkab ]h-]t v ]h-]u pb e^k `^i`ri^al bk YV&p'* W&p'[,_( Dk cloj^ m^ob`fa^+ bumobp^o i^ abofs^a^ pbdrka^ D!&p' bk crk`fŽk ab i^p abofs^a^pab 0+W b W-Qb`r‹oabpb nrb i^p abofs^a^p m^o`f^ibp ab i^ cŽojri^ abi ^m^oq^al ^i plkcrk`flkbp `ljmrbpq^p a^a^p mlo
/0kt < B`YV'p(+ W'p([ +
/0 -ku < B`YV'p(+ W'p([-
1- Sbkfbkal bk `rbkq^ bi bgbo`f`fl 0 `^i`ri^o D%&p'v D!&p' bk crk`fŽk ab p bk `^a^ rkl abilp pfdrfbkqbp `^plp m^oqf`ri^obp9
^( G&t*u' < t0 * u0* V'p( < p+ W'p( < p0,_( Yp•+u' < aVW `lp 'tu1(+ V'p( < `lp p+ W'p( < pbk p-
b( Yp•+u' < ild Z'0 * aV0(.'0 * au0'[* V'p( < a* W'pW < a+p,
2- B^i`ri^o bk `^a^ `^pl i^ abofs^a^ afob``flk^i ab Gbk ilp mrkqlp v afob``flkbp nrb pbfkaf`^k9^( b&t*v+w( ;1t + 4v * 1w bk '1+1+ 0( bk i^ afob``fŽk ab i^ kloj^i buqboflo ^ i^bpcbo^ t&* v1 * w&< 8-_( b&t*v+ w( < t%+ v1 bk rk mrkql `r^inrfbo^ ab i^ prmbocf`fb o* v&* w&< 3 bk i^afob``fŽk ab i^ kloj^i buqboflo bk af`el mrkql-b( G't+v+w( < t&* v&, w&bk '2+3+4( ^ 0/ i^odl ab i^ `ros^ ab fkqbopb``fŽk ab i^p alpprmbocf`fbp 1t& * 1v&, w&< 14 X t& * v&< v&-
3- ^( G^ii^o rk sb`qlo T&t* v+w( kloj^i ^ i^ prmbocf`fb
217 A…h_qhkefanaj_q‹ aj _]ilko ao_]h]naov ra_pkne]hao
bk rk mrkql `r^inrfbo^ &t* v+w( ab i^ prmbocf`fb &t* v+w( z 'N+ N+N(-_( G^ii^o bi `lpbkl abi Škdril &H cloj^al mlo bi sb`qlo T&t* v+w( v bi bgb w v abqbo,jfk^o bi iŒjfqb ab `lp &H `r^kal 'u+ v+w(z 'N+N+N(-
4- K^p alp b`r^`flkbp a! `lp r < t v a! pbk r < v abcfkbk q v r `ljl crk`flkbp ab t b v+pb^k ‹pq^p q < S&t* v( v r < T&t* u', G^ii^o cŽojri^p bumiŒ`fq^pm^o^ Set* v( v T&t* u'*sŠifa^p m^o^ t = /+ v abjlpqo^o nrb ilp sb`qlobp do^afbkqbp &f0Set* v( v &f0T&t* v( plkmbombkaf`ri^obp bk `^a^ mrkql &t*u',
5- Rb^ b't+ u' < -vSWvS-^( Bljmol_^o nrb ]h-]t v ]h-]u plk `bol ^j_^p bk bi lofdbk-_( „Sfbkb i^ prmbocf`fb w < b&t*v( mi^kl q^kdbkqb bk bi lofdbk> YGj`e_]_eˆj8 Blkpfa‹,obpb i^ pb``fŽk molar`fa^ bk i^ prmbocf`fb mlo bi mi^kl t ;u,[
6- Rf 'ul+ Xl+wl( bp rk mrkql ab i^ prmbocf`fb w< tu+ i^p alp ob`q^p w< WMV* v < Xl Xw < VkW* t < ul pb `loq^k bk &tk* Xl+wl( v bpqŠk pfqr^a^p bk i^ prmbocf`fb- Bljmol_^o nrbbi mi^kl q^kdbkqb ^ bpq^ prmbocf`fb bk bi mrkql 'ul+ Xl+wl( `lkqfbkb ^ bp^p alp ob`q^p-
7- G^ii^o i^ b`r^`fŽk `^oqbpf^k^ abi mi^kl q^kdbkqb ^ i^ prmbocf`fb tuv < ah bk rk mrkqldbk‹of`l 'wl- Xl+wk(- Cbjlpqo^o nrb bi slirjbk abi qbqo^baol ifjfq^al mlo bpb mi^kl vilp qobp mi^klp `lloabk^alp bp 8]&.1-
8- G^ii^o rk m^o ab b`r^`flkbp `^oqbpf^k^p m^o^ i^ ob`q^ nrb bp q^kdbkqb ^ i^p alp prmbo,cf`fbp t&* v&* 1v&< 3 X w < a!&,60 bk bi mrkql '0+0+0(-
0/- G^ii^o rk^ `lkpq^kqb a q^i nrb bk qlal mrkql ab i^ fkqbopb``fŽk ab i^p alp bpcbo^p
&t + A(1 * u1 * Y1 < 2 v t1 * 'v , 0(1 * X1 < 0
ilp mi^klp q^kdbkqbp `loobpmlkafbkqbp pb^k mbombkaf`ri^obp bi rkl ^i lqol-00- Rf o+v o+ plk i^p afpq^k`f^p abpab rk mrkql 'u+ v( ab rk^ bifmpb ^ prp cl`lp+ abjlpqo^o
nrb i^ b`r^`fŽk o+* o+< `lkpq^kqb 'nrb p^qfpc^`bk bp^p afpq^k`f^p( fjmif`^ i^ obi^`fŽk
pfbkal R bi sb`qlo rkfq^ofl q^kdbkqb ^ i^ `ros^- Hkqbomobq^odblj‹qof`^jbkqb bpb obpri,q^al+ v `lk biil abjlpqo^o nrb i^ q^kdbkqb cloj^ Škdrilp fdr^ibp `lk i^p ob`q^p nrbrkbk &t* v( ^ ilp cl`lp-
01- Rf &f0G't+v+w( bp pfbjmob m^o^ibi^ ^ te * ue * vg+abjlpqo^o nrb G ab_b qlj^o s^ilobpfdr^ibp bk ilp mrkqlp '/+/+ ]' v '/+/+ +]',
7-07 Cfcbobk`f^ibpab `^jmlp sb`qlof^ibp
K^ qbloŒab i^ afcbobk`f^`fŽk m^o `^jmlp sb`qlof^ibp bp rk^ buqbkpfŽkafob`q^ab i^ qbloŒ^ kŠild^ m^o^ `^jmlp bp`^i^obp- Rb^ b9 R z Q&!rk `^jml sb`qlof^iabcfkfal bk rk pr_`lkgrkql R ab Q!- Rf ] bp rk mrkql fkqbofloab R b u rk sb`qlo`r^inrfbo^ ab Q! abcfkfjlp i^ abofs^a^c&'^: u' jbaf^kqb i^ cŽojri^
b&']: u' < henjb'] * du' + b']( +R(? d
pfbjmob nrb q^i iŒjfqbbufpq^-K^ abofs^a^c&'^: u'ao rk sb`qlo ab Q!-
Bebanaj_e]hao `a _]ilko ra_pkne]hao 218
Cbpfdkbjlp `lk bg bi h,‹pfjl `ljmlkbkqb ab bN_pbosbjlp nrb i^ abofs^a^ba]: u( bufpqbpf v pŽil pfb‡+']: u( bufpqbm^o^ `^a^ g < 0+1+--- +i+ bk `rvl `^plqbkbjlp
j
b&']:u( < 'bw']:u(+ --- +b:!']:u• < 1Hy']:u(ag&ScT
alkab ag bp bi h,‹pfjl sb`qlo `lloabk^al rkfa^a-Cb`fjlp nrb b bp `ebanaj_e]^ha bk rk mrkql fkqboflo ] pf bufpqbrk^ qo^kpclo,
j^`fŽk ifkb^i
q^i nrb
'7-05( ba] * r( <b']( * R]'r( * Zr\ C']+ r(+
alkabD'^+ r' ,* N`r^kal r ,* M, K^ cŽojri^ ab S^vilo ab mofjbo loabk '7-05( bpsŠifa^ m^o^qlal r q^i nrb Zr\ ; n m^o^rk `fboql n = N- Di q‹ojfkl C&]* r' bp rksb`qlo ab Q&!-K^ qo^kpcloj^`fŽk ifkb^i R• pb ii^j^ `ebanaj_e]h pkp]h l pfjmib,jbkqb `ebanaj_e]h ab b bk ]-
O^o^ ilp `^jmlp bp`^i^obp pb abjlpqoŽ nrb R]'u( bp bi molar`ql bp`^i^o abisb`qlo do^afbkqb Tb']( mlo u- O^o^ ilp `^jmlp sb`qlof^ibp abjlpqo^objlp nrbR]'u( bp rk sb`qlo `rvl `ljmlkbkqb g,†oeik bp bi molar`ql bp`^i^o Tbg']( - u-
SDNQDL@ 7-8- Qqlkjc]iko mqa b ao `efanaj_e]^ha aj ] _kj `ebanaj_e]h R]-Cteopa ajpkj_ao h] `aner]`]b&']: u(l]n] pk`k ] `a Q!+ v pajaiko
'7-06(
?`ai…o+ oeb < '.0&--- +bi( v oe u < 'W0+Œ-Œ+W+j(+pajaiko
j
'7-07( R]'u( < J Tbg']( -u ag < 'Tbh']( -u+--- +Tbi']( -u(-ScT
Baikopn]_e‰j- Q^wlkbjlp `ljl bk bi `^pl bp`^i^o- Rf u < M+ bkqlk`bpG&&]9 u( < M X R]' M' < M, Olo `lkpfdrfbkqb mlabjlp prmlkbo nrb u <:5 M, Sl,j^kal r < du bk i^ cŽojri^ ab S^vilo '7-05( qbkbjlp
ba] * du( , ba]( < R]'du( * HieviiC']+ r( < dR]'u( * GdhiHviiC']+ r(-
Cfsfafbkal mlo d v e^`fbkal nrb d y N l_qbkbjlp '7-06(-O^o^ abjlpqo^o '7-07( _^pq^ l_pbos^o nrb
b&']: u( <Hby']: u( ag <HTbe]( -WagŒ
g<h g<h
22/ A…h_qhkebanaj_e]h aj _]ilko ao_]h]naov ra_pkne]hao
K^ b`r^`fŽk '7-07( mrbab q^j_f‹k bp`of_fopbbk cloj^ jŠp pbk`fii^ `ljl rkmolar`ql j^qof`f^i+
pfbkal Bb']( i^ j^qofw i t j `rv^ cfi^ g,†oei] bp Td'](+ b u rk^ j^qofw `lirjk^j W0- K^ j^qofw Bb']( pb ii^j^ i]pnev f]_k^e]j] ab&c bk ]- Rr bibjbkql gf bp i^abofs^a^ m^o`f^iBfd'](- @pŒmrbp+qbkbjlp
, B`h']( B`h']( Bjbh'](
B`1']( B`1']( Bjb1'](
Bb']( <
\B`i']( B`i']( --- Bjbi']J
K^ j^qofw g^`l_f^k^ Bb']( bpqŠabcfkfa^ bk `^a^ mrkql bk bi nrb bufpq^k i^p ijabofs^a^p m^o`f^ibpB:.g'](-
K^ afcbobk`f^i R‚ pb bumobp^q^j_f‹k mlkfbkal b&'](- K^ abofs^a^ b&']( bprk^ qo^kpcloj^`fŽk ifkb^i: i^ j^qofw g^`l_f^k^ Bb']( bp rk^ obmobpbkq^`fŽkj^,qof`f^iab bp^ qo^kpcloj^`fŽk-
K^ cŽojri^ ab S^vilo ab mofjbo loabk qlj^ i^ cloj^
'7-08( ba] * r( <b']( *b&']('r( * Hisii C']+ r(+
alkab C&]* r' ,* M `r^kal r ,* M, Rb m^ob`b^ i^ cŽojri^ ab S^vilo rkfafjbkpfl,k^i- O^o^`^i`ri^o ilp `ljmlkbkqbp abi sb`qlo b&']('r( mlabjlp rqfifw^obi molar`,ql j^qof`f^i Bb'](r l i^ cŽojri^ '7-07( abi qblobj^ 7-8-
0')1 >J MRON[NWLRJKRURMJMRVYURLJUJLXW]RW^RMJM
SDNQDL@ 7-0/- Qeqj _]ilk ra_pkne]h. ao `ebanaj_e]^haaj 7&ajpkj_ao bao_kjpejqk aj ]-
Baikopn]_e‰j- Bljl bk bi `^pl bp`^i^o+^mif`^jlp i^ cŽojri^ ab S^vilom^o^ abjlpqo^o bpqb qblobj^- Rf e^`bjlp nrb r ,* M bk '7-08( bi boolo
i&00 C']+ r( ,* M- K^ m^oqbifkb^i b&&]' &r( qfbkab q^j_f‹k ^ M ab_fal ^ nrb i^pqo^kpcloj^`flkbp ifkb^ibp plk `lkqfkr^p bk M, Dpql `ljmibq^ i^ abjlpqo^`fŽk-
@i iibd^o ^nrŒ`lksfbkb abar`fo rk^ abpfdr^ia^a nrb pb rqfifw^oŠbk i^ ab,
J] nach] `a h] _]`aj] l]n] `ebanaj_e]hao `a _]ilko ra_pkne]hao 220
jlpqo^`fŽk ab i^ obdi^ ab i^ `^abk^ bk i^ moŽufj^ pb``fŽk- K^ abpfdr^ia^a pb ob,cfbob^ rk `^jml sb`qlof^i b afcbobk`f^_ib bk ]9 bii^ bpq^_ib`b nrb
'7-1/( 0Gb&']('r(0Gy Ke]( Hisii+j
alkab K.]( < 0GT&bg'](0G-ScT
O^o^ abjlpqo^oi^ rqfifw^jlp i^ b`r^`fŽk '7-07( grkql ^i^ abpfdr^ia^a qof^kdri^oab B^r`ev,R`et^ow l_qbkfbkal
0'*( >J [NPUJMNUJLJMNWJYJ[J MRON[NWLRJUN\MNLJVYX\_NL]X[RJUN\
SDNQDL@ 7-00- QDFK@ CD K@ B@CDM@- Qa]j b u c `ko _]ilko ra_pkne]haop]haomqa h] bqj_e‰j _kilqaop] d < b l c aop† `abeje`] aj qj ajpknjk `ah lqjpk ]-Qqlkjc]iko mqa c oa] `ebanaj_e]^ha aj :%_kj `ebanaj_e]h c.A](- Nkjc]iko ^ < c'](u oqlkjc]iko mqa b ao `ebanaj_e]^ha aj ^+ _kj `ebanaj_e]h b&'d(- Cjpkj_ao d ao`ebanaj_e]^ha aj 7&u h] `ebanaj_e]h d&']( reaja `]`] lkn
d&']( <b&'d( kc&'](+
mqa ao h] _kilkoe_e‰j `a h]o pn]jobkni]_ekjao heja]haob&'d( u c&'](-
Baikopn]_e‰j- Blkpfabobjlp i^ afcbobk`f^d'] * u( , e'^(m^o^ s^ilobp mb,nrb•lp ab iHv 00+v abjlpqobjlp nrb pb l_qfbkb rk^ cŽojri^ ab S^vilo ab mofjboloabk- Cb i^ abcfkf`fŽk ab d obpriq^
&6,0/' d'] * u( , d']( <bYc'] * u([ , bYc']([ <b'd * r( , b'd(+
pfbkal r < c'] * u( , c'](- K^ cŽojri^ ab S^vilo ^mif`^a^ ^ c'] * u(
klp a^
&6,00' r < c&']('u( * Hiv 00Cc']+ u(+ alkab Cc']+ u( ,, M `r^kal u \\ M-
K^ cŽojri^ ab S^vilo obi^qfs^ ]b'd * r(jko a^
'7-12( b'd ,0, r( , b'd( <b&'d('r( * HisiiC.d+ r(+
221 A…h_qhkebanaj_e]h aj _]ilko ao_]h]naou ra_pkne]hao
alkab C.^+r( , N `r^kal r \ N- @mif`^kal '7-11( bk '7-12( l_qbkbjlp
'7-13( b'^ * r( , b'^( <b&'^(c&']('u( * c&'_('iivii C+']+u• * HHsiiC.^+ r(
<b&'^(c&']('u( * HiviiC']+ u(+
`kj`aC']+ N( < N X
C']+ u( <b&'^('Cc']+ u• * L Ce^+ r(Hivii
'7-14( pf W%;D+N-
O^o^ `ljmibq^o i^ abjlpqo^`fŽk kb`bpfq^jlp mol_^o nrbD'^+ u( , N `r^kal u , N-Di mofjbo q‹ojfkl abi pbdrkal jfbj_ol ab '7-14( qfbkab ^ N `r^kal u + N
mlonrbD+'^+ u' \ l`r^ka` u + N X i^p qo^kpcloj^`flkbp ifkb^ibp plk `lkqfkr^pbkN --
Dk bi pbdrkal q‹ojfkl abi pbdrkal jfbj_ol ab '7-14( bi c^`qlo C.^+ r( \ Nmlonrb r, N `r^kal u, N- Di `l`fbkqb Hisii.iiviimboj^kb`b ^`lq^al mlonrb+pbd•k '7-11( v '7-1/( qbkbjlp
Hisiiz K+']( iHvii* iHviiGGC+']+W(GG-
Olo `lkpfdrfbkqb ilp alp q‹ojfklp abi pbdrkal jfbj_ol ab '7-14( qfbkabk ^ N`r^kal u , N+ ^pŒnrb C&]*u( , N-
Cb bpqb jlal+ ab '7-13( v '7-10( l_qbkbjlp i^ cŽojri^ ab S^vilo
d'] * u( , d']( <b&'^(c&']('u( * HiviiC']+u(+
`kj`aC']+u(, N `r^kal u, N- Dpql abjrbpqo^ nrb d bp afcbobk`f^_ib bk ]v nrb i^ afcbobk`f^i ?! &]' bp fdr^i ^ i^ `ljmlpf`fŽk b&&^' l c&&]' ,
0'*) Eloj^ VJ][RLRJUMNUJ[NPUJMNUJLJMNWJ
Rb^ d < b l c+ alkab d bp afcbobk`Œ^_ib bk ] v b afcbobk`f^_ib bk ^ < c'](-K^ obdi^ ab i^ `^abk^ bpq^_ib`b nrb
d&']( <b&'^( kc&'](-
Olabjlp bumobp^o i^ obdi^ ab 0z `^abk^ bk crk`fŽk ab i^p j^qof`bp g^`l_f^k^pBd'](+ Bb'^(+ v Bc'](mqa obmobpbkq^k i^p qo^kpcloj^`flkbp ifkb^ibp d&'](+b&'^(+v c&'](+ obpmb`qfs^jbkqb- Orbpql nrb i^ `ljmlpf`fŽk ab qo^kpcloj^`flkbp ifkb^ibp`loobpmlkab ^ i^ jriqfmif`^`fŽk ab prp j^qof`bp+ l_qbkbjlp
'7-15( Bd']( < Bb'^( Bc'](+ alkab ^ < c'](-
Dkni] i]pne_e]h `a h] nach] `a h] _]`aj] 222
Dpq^bp i^ ii^j^a^ bkni] i]pne_e]h `a h] nach] `a h] _]`aj]- S^j_f‹k mrbab bp,`of_fopb `ljl rk `lkgrkql ab b`r^`flkbp bp`^i^obp bumobp^kal `^a^ j^qofw bkcrk`fŽk ab prp bibjbkqlp-
Rrmlkd^jlp nrb ] D QO+ ^ < c']( D Q! + v b'^( D Qj- Dkqlk`bp d']( D Qj vmlabjlp bp`of_fo
K^ j^qofw Bd']( bp iVl+ i^ j^qofw Bb'^( bp i•:j+ v Bc']( bp rk^ j^qofwj t l* v sfbkbk a^a^p mlo
K^ b`r^`fŽk j^qof`f^i '7-15( bp bnrfs^ibkqb ^ il b`r^`flkbp bp`^i^obp+
j
Bfd:']( < B`:'^(Bfcg'](+ m^o^ f< 0+1+--- +iR`S
v f;/*0* ,,, *l,
Dpq^pb`r^`flkbp bumobp^ki^p abofs^a^p m^o`f^ibp ab ilp `ljmlkbkqbp ab d bkcrk`fŽk ab i^p abofs^a^p m^o`f^ibpab ilp `ljmlkbkqbp ab bv c,
DIDLOKN 0- Ctpajoe‰j `a h] nach] `a h] _]`aj] l]n] _]ilko ao_]h]nao-Rrmlkd^jlp nrb b bp rk `^jml bp`^i^o &i < 0(- Dkqlk`bp d q^j_f‹k 0/ bp vbufpqbkl b`r^`flkbp bk i^ obdi^ ab i^ `^abk^+ rk^ m^o^`^a^ rk^ ab i^p abofs^a^pm^o`f^ibpab d9
j
B fd']( < Bgb'^(B fcg'](+ m^o^ f < 0+1+--- +l-h<i
Di `^pl m^oqf`ri^ol < 0 v^ pb `lkpfaboŽ bk i^ pb``fŽk 7-04- Dkqlk`bp pb qfbkbi^•kf`^ b`r^`fŽk+
j
d&']( < B`'^(cy'](-R`S
Blkpfabobjlp ^elo^ l < 1 X j < 1- Olkd^jlp ] < &o*p' v ^ < 'u+u', Klp`ljmlkbkqbp+ t b u bpqŠkifd^alp ^ p v p mlo i^p b`r^`flkbp
t < ch&Q*p(+
223 A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao v ra_pkne]hao
K^ obdi^ ab i^ `^abk^ klp a^ rk m^o ab b`r^`flkbp m^o^ i^p abofs^a^p m^o`f^ibpab d9
Bzd'o+ p( < BH't+ u' Bzcz'o+ p( * BH't+ u' Bzc1'Q+p(+
B1d'o+ p( < BH't+ u' Byz'o+ p( * BH't+ u' B1c1'Q+p(-
Djmib^kal bi pfdkl ]+ q^j_f‹k pb mlkb bpqbm^oab b`r^`flkbp bk i^ cloj^
'7-16(kd kb kt kb ]u,<,,*,,+ko MV ko ]uko
kd kb kt kb ]u,<,,*,,-kp MV kp ]u kp
DIDLOKN 1- Akkn`aj]`]o lkh]nao- K^ qbjmbo^qro^ ab rk^ mi^`^ abid^a^pb obmobpbkq mlo rk `^jml bp`^i^o b* pfbkal b't+ v( i^ qbjmbo^qro^ bk 't+ u',Hkqolar`fbkal i^p `lloabk^a^p mli^obpt < n `lp '(+v < n pbk '(+i^ qbjmbo^qro^ pb`lksfboqb bk rk^ crk`fŽk ab n v '( abqbojfk^a^ mlo jbafl ab i^ b`r^`fŽk
m:'n+'(( <b'n `lp '(+n pbk'(( -
Dumobp^oi^p abofs^a^p m^o`f^ibpkm:fkn v km:fk'( bk crk`fŽk ab i^p abofs^a^p m^o,`f^ibp ]b-]t v ]b-]u,
Qkhq_e‰j- Tqfif`bjlp i^ obdi^ ab i^ `^abk^ bk i^ cloj^ '7-16(+ mlkfbkal&n*np' bk ird^o ab &o*p'* v n: bk ird^o ab d, K^p b`r^`flkbp
t < n `lp '(+ u < n pbkcklp a^k
W_, < `lp '(kn &
]u, < pbk ckn &
W_, < +npbkck&' *
]u, < n `lp '(W#$ (
Rrpqfqrvbkal bp^p cŽojri^p bk '7-16( l_qbkbjlp
'7-17(km: kb kb, < , `lp '( * , pbof‹kn MV ]u%
km: kb kb, < , n + pbk'( * n + `lp '( -k&' kt ]u
Dpq^pplk i^p cŽojri^p mbafa^p `loobpmlkafbkqbp ^ km:fkn v knlfk'(-
DIDLOKN 2- Baner]`]o l]n_e]hao `a oacqj`k kn`aj- Blkqfkr^kal bi bgbj,mil 1+ bumobp^oi^ abofs^a^ m^o`f^i ab pbdrkal loabk /1m:fM'(1 bk crk`fŽk ab i^pabofs^a^p m^o`f^ibpab b,
Qkhq_e‰j- Bljbk`bjlp `lk i^ cŽojri^ nrb a^ km:fk'( bk '7-17( v abofsbjlp
Dkni] i]pne_e]h `a h] nach] `a h] _]`aj] 224
obpmb`ql^ M* `lkpfabo^kal n `ljl rk^ `lkpq^kqb- Dk bi pbdrkal jfbj_ol e^valp q‹ojfklp+ `^a^ rkl ab ilp `r^ibp ab_b abofs^opb `ljl molar`ql- N_qbkbjlp^pŒ
z[1nl< ,n /0 k'oajM( \ noajM y '/0( * n /0 l'`lp M(* n `lp My '/0(//1 kt // // kt ]u // // ]u
&6,07' /0 k 'Mb( /0 k '/0(; +n `lp /,, npbkN, , , o pbk‹ , * n`lp M, , -kt /7 MV ]u // ]u
O^o^ `^i`ri^o i^p abofs^a^p ab ]h.]t v ]b .]u obpmb`ql ^ 7 ab_b qbkbopb bk`rbkq^ nrb `ljl crk`flkbp ab n v M+]b.]t v ]b.]u plk bqj_ekjao _kilqaop]oa^a^p mlo
/0 < Bzb'n `lp M+n pbkŽ(=E
vWN, < B`'n `lp M+n oajM(-]u
Olo `lkpfdrfbkqb+ prp abofs^a^p obpmb`ql^ M qfbkbk nrb abqbojfk^opb `lk i^ obdi^ab i^ `^abk^- @mifnrbjlp lqo^ sbw '7-16(+ obbjmi^w^kal Gmlo BG * lk il nrbpb l_qfbkb
y'/0( < k'Bzb(kt * k'Bzb(]u < /1
0 ',noajM( * /&0 'n_koM(-// MV kt // ]u // kt1 ]u kt
Cbi jfpjl jlal+ ^mif`^kal '7-16( obbjmi^w^kal b mlo B`* bk`lkqo^jlp
k 'Mb( k'B`( kt k'B`( ]u /&0 /&0// ku < z // * ]u // < kt ]u ',noaj M(* ku1 'n `lp M(-
Br^kal bpq^pcŽojri^p pb ^mif`^k bk '7-18( l_qbkbjlp
/1_l kb 1 1 /&0 1 /1b,1 < , n `lp M, * n pbk M, , n pbka `lp k ,,ka kt kt1 ]u kt
a kb 1 /1b 1 1 /1b+ n pbk , , n pbk'( `lp '( ,, * oblp a , -
]u MV ]u ku0
Dpq^ bp i^ cŽojri^ nrb abpbŠ_^jlp m^o^ /1_l.M'x1- EŽojri^p ^kŠild^p m^o^ i^pabofs^a^p m^o`f^ibp pbdrka^p /1_l.kn1+ /1_l.'kn //(+ v /1_l.'// kn( pb molmlkbkbk bi bgbo`f`fl 4 ab i^ moŽufj^ pb``fŽk-
225 A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao u ra_pkne]hao
0'** 8SN[LRLRX\
Dk bpqlp bgbo`f`flp mrbab prmlkbopb i^ afcbobk`f^_fifa^a ab qla^p i^p crk`flkbp nrb pb`lkpfabo^k-
0- K^ prpqfqr`fŽk p < c&t*u' `lksfboqb D&p' bk G&t*u'* pfbkal G&t*u' < DYc&t*u'[,^( Cbjlpqo^o nrb
^{ ]c, < D&Yc't+u([,]t ]t
v]z+ ]c]u < D Yc't+ u([ ]u -
_( Blkpfa‹obpb bi `^pl m^oqf`ri^o D&p'< bpbk p+ c&t* v( < `lp 'u&,* u%', B^i`ri^o ]h-]tv ]h-]u rqfifw^kal i^p cŽojri^p abi ^m^oq^al ^(- Bljmol_^o bi obpriq^al+ abqbojfk^kalG&t*v( bumiŒ`fq^jbkqb bk crk`fŽk ab t b v+ v `^i`ri^kal afob`q^jbkqb ]h-]t v ]h-]u ^
m^oqfoab h,1- K^ prpqfqr`fŽk q < &t + u'-0* r < 'u * u'-0 `^j_f^ b&q*r' bk Ne•+u', @mif`^o bk cloj^
^ab`r^a^ i^ obdi^ ab i^ `^abk^ m^o^ bumobp^o i^p abofs^a^p m^o`f^ibp ]D b]t v^E.^v bk crk`fŽk ab i^p abofs^a^p m^o`f^ibp ]h-]q v ]h-]r,
2- K^p b`r^`flkbp q < G&t*u'* t < V&o* p'* v < W&o*p' abcfkbk q `ljl crk`fŽk ab p v p+q < D&o*p',^( @mif`^o rk^ cloj^ ^ab`r^a^ ab i^ obdi^ ab i^ `^abk^ m^o^ bumobp^oi^p abofs^a^p m^o,`f^ibp ]DG]o v ]D.]p bk crk`fŽk ab ]zh]t+ ]z.]u+ ]t.]o+ atz•+ ]u.]o+ ]u.]pk_( Rf /&0.' ]t ]u( < /&0.' ]u ]t(+ abjlpqo^o nrb
b( Dk`lkqo^o cŽojri^p m^ob`fa^p m^o^ i^p abofs^a^p m^o`f^ibp ]1D.'ko kp(WG/1D.]p1-3- Qbplisbo bi bgbo`f`fl 2 bk `^a^ rkl ab ilp pfdrfbkqbp `^plp m^oqf`ri^obp9
^( V'o+ o( < o * p+ W'o+p( < op-_( V'o+ p( < op+ W'o+o( < ohp-b( V'o+ p( < 'o , p(.1+ W'o+p( < 'o * p(.1-
4- K^ fkqolar``fŽk ab i^p `lloabk^a^p mli^obp `^j_f^ fp•+v( bk :l&n* --'* alkab t < n `lp ..b v < n pbk ..- Dumobp^o i^p abofs^a^p m^o`f^ibp ab pbdrkal loabk ]1‡l.]n1+ /1‡l.' kn '/( v]0‡l.' // kn' bk crk`fŽk ab i^p abofs^a^p m^o`f^ibp ab h,Orbabk rqfifw^opb i^p cŽojri^pabar`fa^p bk bi bgbjmil 1 ab i^ pb``fŽk 7-10-
5- K^p b`r^`flkbp q < fp•+v+w(+ t < Ven* p+p'* v < W&n*o* p' v Y < X&n*o* p'* abcfkbk q`ljl crk`fŽk ab n+p v p+pb^ ‹pq^ q < Npn+o+p', @mif`^o i^ cloj^ ^ab`r^a^ ab i^ obdi^ab i^ `^abk^ m^o^ bumobp^oi^p abofs^a^p m^o`f^ibp ]D. ]n+ kD. ]o+v kDzkpbk crk`fŽk ab i^pabofs^a^p m^o`f^ibp ab 0+W+ W X Y-
6- Qbplisbo bi bgbo`f`fl 5 bk `^a^ rkl ab ilp `^plp m^oqf`ri^obp pfdrfbkqbp9
^( V'n+ o+p( < n * o * p+ W'n+o+p( < n , 1o * 2p+ X'n+ o+p( < 1n * o , p-_( V'n+ o+p( < o1 * Q1* p1+ W'n+o+p( < n1 , Q1 , p1+ X'n+ o+p( < o1 ] Q1 * p1-
7- K^p b`r^`flkbp q < G&t*v+v'* t < V&o*l- v < W&o*p'* Y < X&o*p' abcfkb q `ljl crk`fŽkab p v p+pb^ ‹pq^ q < D&o*p', @mif`^kal rk^ cloj^ ^ab`r^a^ ab i^ obdi^ ab i^ `^abk^bumobp^o i^p abofs^a^p m^o`f^ibp kD. ]o v ]Dz ]p bk crk`fŽk ab i^p abofs^a^p m^o`f^ibp ab0+W+W X Y-
Akj`e_ekjao oqbe_eajpaol]n] h] ecq]h`]` `a h]o `aner]`]o l]n_e]hao ietp]o 226
8- Qbplisbo bi bgbo`f`fl 7 bk `^a^ rkl ab ilp `^plp m^oqf`ri^obp pfdrfbkqbp9
^( V'o+ o( < Q1 * p1+ W'o+q( < Q1 , p1+ X'o+ q( < 1op-
_( V'o+ q( < o * p+ W'o+p( < o , p+ X'o+ q( < op-0/- K^p b`r^`flkbp q < G't+u'* t < V&n*p+p'* u < W&n*p+p' abcfkbk q `ljl crk`fŽk ab n+p v
/* pb^ ‹pq^ q < D&n*p+q(- @mif`^o rk^ cloj^ ^ab`r^a^ ab i^ obdi^ ab i^ `^abk^ v bumob,p^o i^p abofs^a^p m^o`f^ibp kDb ˆn + kDb]o v kDbkp bk crk`fŽk ab i^p abofs^a^p m^o`f^ibp ab
! W b X-00- Qbplisbo bi bgbo`f`fl 0/ bk `^a^ rkl ab ilp `^plp m^oqf`ri^obp pfdrfbkqbp9
^( V'n+ o+q( < o * o+ W'n+o+q( < p-
_( V'n+ o+q( < o * o * p+ W'n+o+q( < o1 * Q1 * p1Œ
`( V'n+ o+p( < n o + W'n+o+q( < oYp-01- Rb^ d't( <bYc't([+ alkab c < &cz* ,‹, *c,' bp rk `^jml sb`qlof^i afcbobk`f^_ib bk ]+
v Grk `^jml bp`^i^o afcbobk`f^_ib bk ^ < c&]', Tqfifw^o i^ obdi^ ab i^ `^abk^ m^o^ ab,jlpqo^o nrb bi do^afbkqb ab d mrbab bumobp^opb`ljl `lj_fk^`fŽk ifkb^i ab ilp sb`qlobpdo^afbkqbp ab ilp `ljmlkbkqbp ab c* ^pŒ9
j
%†hd&]'< 1 B`&^'%†hcg&]',h<i
02- ^( Rf b't+u+ w( < te * uf * vg abjlpqo^o nrb i^ j^qofw g^`l_f^k^ Bb't+u+v( bp i^j^qofw fabkqfa^a ab loabk 2-_( G^ii^o qlalp ilp `^jmlp sb`qlof^ibp afcbobk`f^_ibp b9 Q2 ,,,*Q2 m^o^ ilp nrb i^ j^,qofwg^`l_f^k^ kp9•+v+w( bp i^ j^qofw fabkqfa^a ab loabk 2-`( G^ii^o qlalp ilp `^jmlp sb`qlof^ibp afcbobk`f^_ibp b9 Q2&,,,*&Q2m^o^ilp nrb i^ j^qofwg^`l_f^k^ bp rk^ j^qofw af^dlk^i ab i^ cloj^ af^d &l&t'* m&u', n&v€* bk i^ nrb l* m v nplk crk`flkbp `lkqfkr^p a^a^p-
03- Rb^k b9 Q1 ,,,*Q1 v c9 Q2 ,,,*Q1 alp `^jmlp sb`qlof^ibp abcfkfalp abi pfdrfbkqb jlal9
b't+ u( < at*1We * pbk &u * 1t(f+
c'q+ r+ s( < 'q * 1r1 * 2s2( e * '1r , q1
(x-
^( B^i`ri^o `^a^ rk^ ab i^p j^qof`bp g^`l_f^k^p Bb pt+u' v Bc'q+ r+s',_( B^i`ri^o i^ crk`fŽk `ljmrbpq^ {-'q+s+ t( <bYc'q+ r+s'[,b( B^i`ri^o i^ j^qofw g^`l_f^k^ Bd '0+,0+0(-
04- Rb^kc9 Q2 ,,,*Q1 v c9 Q2 ,,,*Q2alp `^jmlp sb`qlof^ibp abcfkfalp `ljl pfdrb9
b't+u+v( < 't1 * u *v(e * '1t * u *v1(f+
^( B^i`ri^o `^a^ rk^ ab i^p j^qof`bp g^`l_f^k^p B &t* v+w( v Bcpq*r* s',_( B^i`ri^o i^ crk`fŽk `ljmrbpq^ d 'q+r+t( < bYc'q+ r+s'[,`( B^i`ri^o i^ j^qofw g^`l_f^k^ Bdeq*N+s',
o 0'*+ 6XWMRLRXWN\\^ORLRNW]N\YJ[J UJRP^JUMJMMNUJ\MN[R_JMJ\YJ[LRJUN\VRa]J\
Rf b bp rk^ crk`fŽk ob^i ab alp s^of^_ibp+i^p alp abofs^a^p m^o`f^ibpjfuq^pB/` v B1+pb kl plk kb`bp^of^jbkqb fdr^ibp- Blk i^ klq^`fŽk C0+a nrbobjlp
227 A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao v ra_pkne]hao
pfdkfcf`^o B0'B`( < k1ff'kt ku( v `lk B1+hb pfdkfcf`^o B1'B0b( < k1f.'ku kt(-Olo bgbjmil+ pf b bpqŠ abcfkfa^ mlo i^p b`r^`flkbp
t1 \ u1b't+ u( < tu 1 1 m^o^ 'u+ u( y 'N+N(+
t * u
bp pbk`fiil abjlpqo^o nrb B1,`&.* N( < ,0 X C+-a'N+ N( < 0- Dpql mrbab sbopb^pŒ9
bak+ N( < N+
K^ abcfkf`fŽk ab B1!b&.* N( bpq^_ib`b nrb
'7-2/( B0+zb'/+ N( < ifj Bzb'M+ g( , Bzb'M+ N( -
hzN g
@elo^ _fbk
Bzb'M+ N( < ifj b'd+ N( , baM+N( < NezN d
v+ pf &t*u' ", 'N+N(+ bk`lkqo^jlp
B b' (\ u't3 * 2V1u1 , u3(
0 t+ W , ,,,,,,,&,,, -'t1 * u1(1
Olo `lkpfdrfbkqb+ pf g ", N qbkbjlp B*b&M*g' < , g3- g2 < , g X mlo q^kql
Bzb'M+ g( , Bzb'M+ M(g < ,0-
@mif`^kal bpqb obpriq^al bk '7-2/( bk`lkqo^jlp nrb B1+hb'M+ N( < ,0- Blk o^,wlk^jfbkql m^ob`fal abjlpqo^jlp nrb C0-a'/+/( < 0+ X mlo q^kql B1-`'/+ N( ",", Bh*0b&.*M',
Dk bi bgbjmil nrb ^`^_^jlp ab `lkpfabo^o i^p alp abofs^a^p m^o`f^ibp jfu,q^p C+@ v B1**b plk ^j_^p kl `lkqfkr^p bk bi lofdbk- Orbab abjlpqo^opb nrbi^p alp m^o`f^ibp jfuq^p okj fdr^ibp bk rk mrkql ']+ ^( pf mlo il jbklp rk^ abbii^p bp `lkqfkr^ bk bi mrkql- Cbjlpqo^objlp mofjbol nrb plk fdr^ibp pf ]i^]oplk `lkqfkr^p- Blk j^vlo mob`fpfŽk+ qbkbjlp bi qblobj^ pfdrfbkqb-
SDNQDL@ 7-01- BNMCHBHˆM RTEHBHDMSD O@Q@ K@ HFT@KC@C CD K@R CDQHU@,
C@R O@QBH@KDR LHWS@R- Rf b ao qj _]ilk ao_]h]n p]h mqa h]o `aner]`]o l]n_e]haoBe[* BvG+ B0+1b X B1-` ateopaj aj qj _kjfqjpk ]^eanpk Q- Rf ']+ ^( ao qjlqjpk `a Q+v aj p]h lqjpk B0-vb v B1-` okj _kjpejq]o+ ajpkj_ao pajaiko
&6,1/' B0+1b']+ ^' < B1-`']+ ^',
Baikopn]_e‰j- Difg^jlp d v g kl krilp q^ibp nrb bi ob`qŠkdril Ped+ g(
Akj`e_ekjao oqbe_eajpao l]n] h] ecq]h`]` `a h]o `aner]`]o l]n_e]hao ietp]o 228-
`lk s‹oqf`bp ']+ ^(+ '] * d+^(+ '] * d+ ^ * g( v ']+ ^ * g( bpq‹ pfqr^al bk R-'U‹^pb cfdro^ 7-8-(
&]* ^ * g' &] * d* ^ * g'N((((((((((H
*
*&]* ^' &] * d* ^'
EHFTQ@ 7-8 U 'd+g( ao qj] _ki^ej]_e‰j `a hkor]hknao`a b aj hko r†npe_ao-
Blkpfabobjlp i^ bumobpfŽk
H-'d+g( <b'] * d+^ * g( , b'] * d+^( , b']+ ^ * g( * b']+ ^(-
Dp ‹pq^ rk^ `lj_fk^`fŽk ab ilp s^ilobp ab . bk ilp s‹oqf`bp ab P&d*g'* qlj^alp`lk ilp pfdklp ^idb_o^f`lp fkaf`^alp bk i^ cfdro^ 7-8- Dumobp^objlp p--'d+g( bk&crk`fŽk ab B-1-` v q^j_f‹k ab Bh‹1.-
Blkpfabobjlp rk^ krbs^ crk`fŽk F ab rk^ s^of^_ib abcfkfa^ mlo i^ b`r^`fŽk
E't( <b't+ ^ * g( , b't+ ^(
m^o^ qlal t `ljmobkafal bkqob ] v ] * d, 'Fblj‹qof`^jbkqb+ `lkpfabo^jlp ilps^ilobp ab . bk ^nrbiilp mrkqlp bk ilp nrb rk^ ob`q^ sboqf`^i `loq^ ilp i^alp eloŒ,wlkq^ibp ab P&d*g,' Sbkbjlp bkqlk`bp
'7-21( H-'d+g( < E'] * d( , E'](-
@mif`^kal bi qblobj^ abi s^ilo jbafl rkf,afjbkpflk^i ^i pbdrkal jfbj_ol ab'7-2( l_qbkbjlp E'] * d( , E']( < dE&'th(+ pfbkal Wi rk mrkql pfqr^al bkqob] v ] * d- Orbpql nrb E&'t( < Bhb't+ ^ * g( , Bhb't+ ^(+ i^ b`r^`fŽk '7-21(
pb qo^kpcloj^ bk
'7-22( H-'d+g( < dYBzb't0+ ^ * g( , Bzb't0+ ^([-
@mif`^kal bi qblobj^ abi s^ilo jbafl ^i pbdrkal jfbj_ol ab '7-22( l_qbkbjlp
'7-23(
23/ A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao v ra_pkne]hao
pfbkal v0rk mrkql pfqr^al bkqob ^ v ^ * g- Di mrkql 'Vh= XH( mboqbkb`b ^i ob`,
qŠkdril P&d*g',@mif`^kal bi jfpjl mol`bafjfbkql ^ i^ crk`fŽk F'u( < b'] * d+v( , b']+v(
bk`lkqo^jlp rk^ pbdrka^ bumobpfŽk m^o^ Hh&d*g'* l pb^+
'7-24(
alkab &t1+ W1( mboqbkb`b q^j_f‹k ^ P&d*g', Hdr^i^kal i^p alp bumobpflkbp abHh&d*g' X prmofjfbkal dg l_qbkbjlp
G^d^jlp ^elo^ nrb &d*g' ++ 'N+N( X qbkfbkal bk `rbkq^ i^ `lkqfkrfa^a ab C0-av B1Œhb bk bi mrkql &]*^( l_qbkbjlp '7-20(-
Di o^wlk^jfbkql ^kqboflo mrbab jlafcf`^opb m^o^ abjlpqo^o rk^ sbopfŽk j†pcrboqb abi qblobj^ 7-01-
SDNQDL@ 7-02- Qe b ao qj _]ilk ao_]h]n l]n] ah _q]h ateopaj h]o `aner]`]ol]n_e]hao Be[* B` WB1-` aj qj _kjfqjpk ]^eanpk R mqa _kjpajc] ']+ ^(+ v oe ]`ai…oB1-` ao _kjpejq] aj R- ajpkj_ao ateopa h] `aner]`] B0+1b']-^( X pajaiko
B0+1b']+^' < B1+0b']+^',
Baikopn]_e‰j- Cbcfk^jlp Hh&d*g' `ljl bk i^ abjlpqo^`fŽk abi qblobj^7-01- K^ m^oqb ab i^ abjlpqo^`fŽk nrb iibs^ ^ i^ b`r^`fŽk '7-23( bp sŠifa^+ aŠk,alklp
'7-25(
m^o^ rk `fboql 'WH&XH( abi ob`qŠkdril Ped* g', Di obpql ab i^ abjlpqo^`fŽk kl bp^mif`^_ib v^ nrb mob`fp^ ab i^ bufpqbk`f^ ab i^ abofs^a^ B/*0b&]* ^(+ nrb bp grpq^,jbkqb il nrb abpb^jlp abjlpqo^o-
K^ abcfkf`fŽk ab B0Œ1b&]* ( bpq^_ib`b nrb
'7-26( eB0+1b']+ ^' < ifj B1b'] * d* ^' + B1b']+ ^' ,Pc= d
Akj`e_ekjao oqbe_eajpaol]n] h] ecq]h`]` `a h]o `aner]`]o l]n_e]hao ietp]o 12/
U^jlp ^ abjlpqo^o nrb bpqbiŒjfqb bufpqbv nrb qfbkb bi s^ilo B1-`']+ ^(- @ m^o,qfo ab i^ abcfkf`fŽk ab B1b qbkbjlp
B0b']+ ^( < heib']+ ^ * g( , ba]+ ^(
S (((d= Sv
Bvb'] * d+ ( < zzib'] * d+ * g( , ba] * d+ ( -g!! N g
Olo q^kql bi `l`fbkqb ab afcbobk`f^p '7-26( mrbab bp`of_fopbabi pfdrfbkqb jlal
Bvb'] * d+ ( , Bvb']+ ^( < ifj eh'd+g( -d S(((d= dg
Sbkfbkal bk `rbkq^ '7-25( mlabjlp mlkboil bk i^ cloj^
'7-27( Bvb'] * d+^( , B1b']+ ^( \ 0} B b' (, rk 1+0 Vh * We -
d g!! N
O^o^ `ljmibq^o i^ abjlpqo^`fŽk qbkbjlp nrb mol_^o nrb
'7-28( ifj Zifj B1*`&Vh%Xi(\ < B1,`&]* ^',60’--’/ g%! N
Br^kal g y N+bi mrkql X0 z ^* mbol bp abp`lkl`fal bi `ljmloq^jfbkql ab VG
`ljl crk`fŽk ab g, Rf prmlkbjlp nrb VG pb ^molufj^ ^ ^id•k iŒjfqb+pb^ t+`r^kal g y N+bkqlk`bp mlo i^ `lkqfkrfa^a ab B1-p. abar`fjlp nrb
Orbpql nrb bi iŒjfqbt bpq^oŒbk bi fkqbos^il ] 94t 94],o,d+ mlabjlp prmlkbo nrbd y N X abar`fo '7-28(- Ml l_pq^kqb+mlo bi eb`el ab nrb t abmbkab ab g ab clo,j^ abp`lkl`fa^+ pb e^`b kb`bp^ofl rk ^odrjbkql ^idl jŠp pŽifal-
Dk sfoqra ab i^ b`r^`fŽk '7-27( p^_bjlp nrb bufpqbbi pfdrfbkqb iŒjfqb9
231 A…h_qhk `ebanaj_e]h aj _]ilko ao_]h]nao v ra_pkne]hao
Cbpfdkbjlp bpqbiŒjfqb `lk D&d', O^o^ `ljmibq^o i^ abjlpqo^`fŽk e^v nrb mol,_^o nrb
ifj D&d' < B0+`']+ ^',P'=
@ q^i cfk ^mbi^jlp ^ i^ abcfkf`fŽk ab `lkqfkrfa^a ab B1+` bk &]* ^(-Rb^ D rk k•jbol mlpfqfsl a^al- K^ `lkqfkrfa^a ab B1-` bk &]* ^( pfdkfcf`^
nrb bufpqbrk afp`l ^_fboql L `lk `bkqol bk &]*^( v o^afl 7+ mlo bgbjmil+ q^inrb
'7-3/( GB1-`'t+ u' + B1-`']+ _(0 ; z pfbjmob nrb 't+u' D L,
Rf bibdfjlp d v g ab j^kbo^ nrb Hei; Ž.1 v Ggh; 7.1+ qlal bi ob`qŠkdrilaf_rg^al bk i^ cfdro^ 7-8 bpq^oŠ`lkqbkfal bk bi bkqlokl L v+ bk m^oqf`ri^o+bimrkql 'Vh& XH( bpq^oŠbk L, Olo `lkpfdrfbkqb '7-3/( bp sŠifa^ `r^kal &t* v( <; 'Vh= XH( X mlabjlp bp`of_fo
'7-30(
L^kqbkd^jlp ^elo^ cfgl d v e^d^jlp nrb g y N- Di q‹ojfkl B0,hb&th< Wh( qfbkab^ D'd( v ilp lqolp q‹ojfklp ab '7-30( plk fkabmbkafbkqbpab g- Sbkbjlp mlo q^kql
M8899%-D&d'+ B1-`']+ _(0 z z ; D+
`lk q^i nrb N ; Hei; 7.1- Obol ‹pqb bp mob`fp^jbkqb bi pfdkfcf`^al ab i^ mol,mlpf`fŽk
ifj D'd( < B1-`']+ ^(SI)))b?
v+ `ljl v^ afgfjlp+ bpql `ljmibq^ i^ abjlpqo^`fŽk-
Lkp]9 Cb_boŠ l_pbos^opb nrb bi qblobj^ bp q^j_f‹k sŠifal pf bk ‹i bkrk`f^al fkqbo`^j,_f^jlp Bh,0b v B0-&z-
0'*, 8SN[LRLRX\_J[RX\
0- G^ii^o rk `^jml bp`^i^o b nrb p^qfpc^d^i^p alp `lkaf`flkbp pfdrfbkqbp,
Cfan_e_eko r]neko 232
^( Dufpqbk v plk kri^p i^p abofs^a^p m^o`f^ibp C{c'N+ N( X B1b&.* M',_( Dufpqb i^ abofs^a^ afob``flk^i bk bi lofdbk bk i^ afob``fŽk abi sb`qlo e* f v qfbkbbi s^ilo 2- Dumif`^o mlo nr‹ q^i crk`fŽk b kl mrbab pbo afcbobk`f^_ib bk '/+/(-
1- Rb^ b rk^ crk`fŽk abcfkfa^ `ljl pfdrb9
V1\u1
Y't+u( < u,,z,,* 1t u
pf &t*u' %! 'N+ N(+ Z'N+ N( < N-
B^i`ri^o+ `r^kal bufpq^k+i^p abofs^a^p m^o`f^ibp pfdrfbkqbp9 C{c'N+ N(+B`&M* M'*C1-iZ'N+ N(+ C0+a'/+ N(-
2- Rb^ b&t*v( <]]ytu2 pf &t*v( z 'N+N(+X abcfk^jlp b&M*N( < N-y,*u5
^( Cbjlpqo^o nrb i^ abofs^a^ n&M9]' bufpqb m^o^ qlal sb`qlo ] v `^i`ri^o pr s^ilobk crk`fŽk ab ilp `ljmlkbkqbp ab ]-_( Cbqbojfk^o pf b bp l kl `lkqfkr^ bk bi lofdbk-
3- Cbcfk^jlp b&t*v( < b9&!&00a+p%p m^o^ t< /+ v= N- B^i`ri^o ]b-]t bk crk`fŽk ab t b v-
4- Rrmlkd^jlp nrb i^p b`r^`flkbp q < b&t*u'* t < V&p'* v < u&p' abcfkbk q `ljl crk`fŽkab p+q < D&p', B^i`ri^o i^ abofs^a^ qbo`bo^ D!%&p'bk crk`fŽk ab i^p abofs^a^p abb*V*aW,
5- Di `^j_fl ab s^of^_ibp t < q * r* v < qr1 qo^kpcloj^ b&t*v( bk c&q*r', B^i`ri^o bis^ilo ab /1c.' kr kq( bk bi mrkql bk bi nrb q < 0+ r < 0+ p^_fbkal nrb
kY /1Y /1Y /1Y /1Y,<,<,<,,<,,<0^v ]t1 ]u1 ^u ^v ^v kt
bk af`el mrkql-
6- Di `^j_fl ab s^of^_ibp t < qr* v < &q1, s&( qo^kpcloj^ b&t*v( bk c&q*r',
^( B^i`ri^o kc.kq+ ]c kr v /1c.' ^r kr(aj crk`fŽk ab i^p abofs^a^p m^o`f^ibp ab b, 'Orb,ab prmlkbopb i^ fdr^ia^a ab i^p m^o`f^ibp jfuq^p-(_( Rf HH%Tb&t*v(ii&< 1 m^o^ qlal t b v+ abqbojfk^o i^p `lkpq^kqbp ] v ^ q^ibp nrb
'kc(1 'kc(1
] kq , ^ MT < q1 * r1-
7- Clp crk`flkbp E v F ab rk^ s^of^_ib v rk^ crk`fŽk w ab alp s^of^_ibp bpqŠk ifd^a^pmlo i^ b`r^`fŽk
YD&t' * F'v(\1 a•'K( < 0D%&t'E%'v(
`lk q^i nrb D&t' * E&u' y N- Cbjlpqo^o nrb i^ abofs^a^ m^o`f^i jfuq^ B*,/X&V*v( krk`^bp `bol- 'Orbab prmlkbopb i^ bufpqbk`f^ v `lkqfkrfa^a ab qla^p i^p abofs^a^p nrb^m^obw`^k-(
8- Tk `^jml bp`^i^o b bp ^`lq^al v `lkqfkrl bk rk ob`qŠkdril P < Y]*^[ W Ya*[, Rb ab,cfkb bk P rk krbsl `^jml bp`^i^o d abi jlal pfdrfbkqb9
c'q+r( < pYH9b't+ u' `tH `u,
233 A…h_qhkebanaj_e]h aj _]ilko ao_]h]naov ra_pkne]hao
^( Orbab abjlpqo^opb nrb m^o^ `^a^ q cfg^ bk Y]* ^[ i^ crk`fŽk ? abcfkfa^ bk Ya* [jbaf^kqb i^ b`r^`fŽk ?&u' < cb&t* v( `t bp `lkqfkr^ bk Ya* [, Tqfifw^o bpqb obpriq^alm^o^ abjlpqo^o nrb ]c-]r bufpqb v bp `lkqfkr^ bk bi ob`qŠkdril ^_fboql R < &]*^' W&a* ''bi fkqboflo ab P',_( RrmŽkd^pb nrb
-n9Ypb't+u(`t[ `u < pYH9b't+u(`u[ `tm^o^ qlal &q*r' ab P- Cbjlpqo^o nrb d bp afcbobk`f^_ib bk R v nrb i^p abofs^a^p m^o`f^,ibp jfuq^p B/*0c&S* r' v B0*hc&q* r' bufpqbk v plk fdr^ibp ^ b&q* r' bk `^a^ mrkql ab R-
0/- Dk obi^`fŽk `lk bi bgbo`f`fl 8- RrmŽkd^pb nrb q v r pb bumobp^k m^o^j‹qof`^jbkqb abipfdrfbkqb jlal9 q < ?&p'* r < @&p'9 X pb^ :l&p' < cY?&p'* @&p'[,^( Cbqbojfk^o :l%&p' bk crk`fŽk ab b*?& X @&-_( B^i`ri^o :l%&p'bk crk`fŽk ab p `r^kal b&t*v( < aV*0. v ?&p' < @&p'< b, 'RrmŽkd^pbnrb P bpqŠ pfqr^al bk bi mofjbo `r^ao^kqb-(
00- Rf b&t*v+w( < 'n u ?( - 'n u @(+pfbkal n < te * ue * vg v ? X @ plk sb`qlobp `lkp,q^kqbp+abjlpqo^o nrb Tb't+ u* w( < @ u 'n u ?( * ? u 'n u @(-
01- Rb^o < te * ue * vg v mlkd^jlp n < Hioii-Rf ? v @ plk sb`qlobp `lkpq^kqbp+ abjlp,qo^o nrb9 H
^( ? - T'y( < ] ? -n -n n1
_( @&T'? - T'y(( < \2?\&n\@\&\n\\ ?\&\@n n4 n2
02- G^ii^o bi `lkgrkql ab qlalp ilp mrkqlp &]* ^* a'* bk bi bpm^`fl ab 2 afjbkpflkbp+ bk ilp`r^ibp i^p alp bpcbo^p &t + ]'0 * 'v , ^'0 * 'w , a'0 < 0 X t0 * ,{ * Y1 < 0 pb `loq^kloqldlk^ijbkqb- 'Rrp mi^klp q^kdbkqbp ab_boŠk pbo mbombkaf`ri^obp bk `^a^ mrkql abfkqbopb``fŽk-(
03- Tk `fifkaol `rv^ b`r^`fŽk bp v < b&t' bp q^kdbkqb ^ i^ prmbocf`fb Y1 * 0tv * v < N bkqlalp ilp mrkqlp `ljrkbp ^ i^p alp prmbocf`fbp- G^ii^o b&t',