_FEYORE\@M@ POLFGHÜCELM @O ^MFMAÍ LOFPRG ROCEGFMH @O M[_ORG IML_HPM@ @O EFCOFEORÁM OHÅLPREM HELOFLEMP_RM OF EFCOFEORÁM OHOLPRGAOLÍFELM HMBGRMPGREG @O IÁ\ELM 2 HMBGRMPGREG , ? ‘LMRCM U @O\LMRCM @O _F LM^MLEPGR‑
IMLEHEPM@GR; Kumf Rg`rácuo{ CR_^G; 3EO=22
EFPOCRMFPO\ @OHCM@G( J_ABORPG AMRPÁFO[( YELOFPO GR@ÜÝO[( UMJER YMRCM\( LMPMHEFG
Ofprocm`g oh == `o kufeg `o 2>=> 2>=> ^REAOR \OAO\PRO
EFPRG@_LLEÜF
Of oh |ecueofpo efigrao jmbhmroag| mlorlm `o hg }uo |gf hg| lerluepg| RL `oh peoa~g `o lmrcm `o|lmrcm }uo |uiro uf lm~mlepgr( lm~mlepgr( ~gr hm efle`oflem `o uf ~mríaoprg
lgfgle`g
lgag
lgf|pmfpo
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peoa~g&
\o lgf|e`orm uf lerluepg RL m pg`g m}uoh igram`g ~gr ro|e|poflem| lgf`of|m`gro| g lm~mlepgro|& O|po pe~g `o lerluepg eflhuo m}uohhg| }uo luofpmf lgf auljm| ro|e|poflem| lm~mlepgro| }uo ~uo`o |or ro`ule`g& Of o|pm ûhpeam oz~oreoflem |o gb|oryg m prmyå| `o `g| auhpáaoprg| lgfolpm`g| m hm ro|e|poflem mh lm~mlepgr( lgag |o `eg oh lga~grpmaeofpg `o lmrcm `o|lmrcm `o mabg| ohoaofpg|& ^mrm ufm aokgr gb|orymleüf `o o|po oiolpg fg| ~orlmpmag| }uo oh o h peoa~g `o lmrcm `o|lmrcm `o uf lm~mlepgr ym m `o~of`or `o hm amcfepu` `o hm lm~mlepmflem `oh ymhgr `o hm ro|e|poflem( m }uo aeofprm| aí| ~o}uoýg |om aí| rí~e`g |o `mríf hg| oyofpg|& _f lm~mlepgr ro}ueoro ufm leorpm lmfpe`m` `o peoa~g ~mrm lmrcmr|o mh ymhgr `oh yghpmko m~helm`g ~gr hm iuofpo& Oh peoa~g `o~of`o `o hm lm~mlepmflem `o hm ro|e|poflem pgpmh of oh lerluepg `o lmrcm&
AMRLG POÜRELG ^mrm }uo |om ~g|ebho `o ofpof`or oh |ecueofpo efigrao( lrooag| prm|lof`ofpmh jmlor ufm broyo oz~helmleüf `o hm pográm påraefg| bí|elg| roiorofpo| mh poam& Lgaof{mroag| ofpgflo| lgf ufm lgrpm oz~helmleüf `o hg }uo |gf lerluepg| RL&
Lerluepg| RL
\o lgf|e`orm uf lerluepg RL m pg`g m}uoh igram`g ~gr ro|e|poflem| lgf`of|m`gro| g lm~mlepgro| *|o eflhuof hg| lm|g| of }uo oh jm ymreg| lm~mlepgro| g ro|e|poflem| }uo |o ~uo`of ro`uler m ufg o}ueymhofpo%& Hm iecurm ehu|prm uf okoa~hg `o uf lerluepg RL& Of oh `ebukg uf efporru~pgr lga~hopm oh lerluepg( `o ag`g }uo hm bmporám ~uo`o lmrcmr hm| ~hmlm| `oh lm~mlepgr& Lumf`g oh efporru~pgr o|pí lorrm`g( oh lm~mlepgr fg |o lmrcm `o efao`empg& Of yo{ `o hg mfporegr( hm lmrcm hhocm crm`umhaofpo m |u ymhgr `o o}uehebreg `o ] ] 1 1 LYg( of `gf`o Yg o| hm pof|eüf `o hm bmporám&
Lmrcm @o|lmrcm `o uf Lm~mlepgr
^reaorg ymag| lgf hm lmrcm `oh lm~mlepgr& Lgf|e`åro|o oh lerluepg of |oreo `o hm iecurm& Efelemhaofpo oh lm~mlepgr o|pí `o|lmrcm`g& \e |o leorrm oh efporru~pgr( hm lmrcm oa~eo{m m ihuer ~rg`uleof`g lgrreofpo of oh lerluepg( oh lm~mlepgr |o oa~eo{m m lmrcmr& _fm yo{ }uo oh lm~mlepgr m`}ueoro hm lmrcm aízeam( hm lgrreofpo lo|m of oh lerluepg& Lgflhueag| }uo;
Oh ozproag m peofo uf ~gpoflemh amgr }uo oh ozproag b `o hm ro|e|poflem R m }uo hm lgrreofpo ihuo `o m m b& @o mluor`g m hm ho `o Gja Ymb 1 ER
Hm ~hmlm ~g|epeym `oh lgf`of|m`gr b peofo amgr ~gpoflemh }uo hm ~hmlm focmpeym l( `o ag`g }uo Ybl 1 }'L&
Oh poraefmh ~g|epeyg `o hm bmporám m peofo amgr ~gpoflemh }uo oh poraefmh focmpeyg l( `o ag`g }uo Ylm 1 !Y !Yo ( `gf`o Yo o| hm ioa `o hm bmporám&
Mjgrm ~rglo`oag| lgf hm `o|lmrcm `oh lm~mlepgr& Lgf|e`oroag| hm iecurm( oh lerluepg lgf|pm `o uf lgf`of|m`gr( efelemhaofpo lmrcm`g lgf lmrcm ] ( ufm ro|e|poflem R |o leorrm oh efporru~pgr& Lgflhueag| }uo;
Lgag hm lgrreofpo ym `o m jmlem b( oh ~gpoflemh `o m o| aí| mhpg }uo oh ~gpoflemh `o b& ^gr hm ho `o Gja Ymb 1 ER& ER&
Of oh lgf`of|m`gr hm ~hmlm ~g|epeym m peofo aí| ~gpoflemh }uo hm focmpeym b( `o ag`g }uo Ybm 1 !}'L&
Lurym| `o Lmrcm @o|lmrcm `o uf Lm~mlepgr Lm~m lepgr Lmrcm `o uf Lm~mlepgr Lm~mlepgr
@o|lmrcm `o uf Lm~mlepgr
Lgf|pmfpo `o Peoa~g
Oze|pof leorpg| ~mríaoprg| }uo fg| ~oraepof `oiefer oh peoa~g `o lmrcm g `o|lmrcm `o uf lm~mlepgr lgfolpm`g m ufm iuofpo lgfpefum ao`emfpo ufm ro|e|poflem& M o|po ~mríaoprg |o ho `ofgaefm lgf|pmfpo `o peoa~g& _f lm~mlepgr ro}ueoro ufm leorpm lmfpe`m` `o peoa~g ~mrm lmrcmr|o mh ymhgr `oh yghpmko m~helm`g *O%& Oh peoa~g `o~of`o `o hm lm~mlepmflem *L% `o hm ro|e|poflem pgpmh *R% of oh lerluepg `o lmrcm& Oh peoa~g folo|mreg ~mrm }uo hm lmrcm mhlmflo oh 9<(2 / `o |u ymhgr iefmh |o hhmam lgf|pmfpo `o peoa~g lm~mlepeym o|pí `m`m ~gr; *LP% 1 R L
@gf`o LP |o `m of |ocuf`g| |e hm ro|e|poflem *R% o| of gja| hm lm~mlepmflem *L% o| of imrm`eg|& Lgf|e`ormf`g lm~mlepgro| e`omho|( |o lgflhuo }uo lgf uf peoa~g π( uf lgf`of|m`gr |o lmrcm g `o|lmrcm uf ~grlofpmko `oh 9
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Hm lurym `o lmrcm `o|lmrcm `o hg| lgf`of|m`gro| o| `o pe~g oz~gfoflemh( ~rg`uleåf`g|o ufm lmrcm g `o|lmrcm rí~e`m mh ~refle~eg( ~mrm yghyor|o auljg aí| hofpm lgf oh ~m|g `oh peoa~g&
GBKOPEYG\
=&
O|pu`emr hm lgf|pmfpo `o peoa~g `o uf lerluepg RL&
2&
@oporaefmr oz~oreaofpmhaofpo oh peoa~g `o lmrcm `o|lmrcm `o uf lm~mlepgr&
<&
Mfmhe{mr oz~oreaofpmhaofpo oh lga~grpmaeofpg `o hm pof|eüf hm lgrreofpo of hm lmrcm `o|lmrcm `o uf lm~mlepgr&
AMPOREMHO\
Lm~mlepgr
Ro|e|pgr
Iuofpo `o yghpmko
@g| auhpáaoprg|
Lrgfüaoprg
Lmbho| `o lgfozeüf
Pmbhorg `o ~ruobm
^RGLO@EAEOFPG ^RGLO\G @O LMRCM =& Mrao oh |ecueofpo lerluepg& FG @MPM @L Y
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0& \uao críielmaofpo hm| `g| lurym|& ?& ·]uå lgflhu|egfo| gbpeofo `oh ~m|g mfporegr7 R; Mabm| críielm| peofof pof`oflem oz~gfoflemh( hm crmielm Y = y| p peofo ufm pof`oflem focmpeym( aeofprm| }uo hm crmielm Y2 y| p peofo ufm pof`oflem ~g|epeym& O|pm críielm pgam o|pm igram( m }uo aeofprm| oh lm~mlepgr |o lmrcmbm hm ro|e|poflem o|pmbm |uireof`g ufm `o|lmrcm `erolpm& @o o|po ag`g hg| ymhgro| ao`e`g| ro|uhpmrgf efyor|g|& 9& Ofluofpro hm rohmleüf ampoaípelm }uo rohmlegfm Y= lgf p !>&>
1 3&:9>o
3& Ofluofpro hm rohmleüf ampoaípelm }uo rohmlegfm Y2 lgf p !>&=>0p
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:& Crmie}uo of ~m~oh aeheaoprm`g Y = y| p4 Y2 y| p4 mabm| of hm ae|am jgkm&
^RGLO\G @O LMRCM =& Lmabeo hm ~ghmre`m` `o Y =& 2& Mbrer \2 lorrmr \=( mfgpmr of hm pmbhm 2 hg| ymhgro| `o Y = Y2 ~mrm hg| peoa~g| `m`g|& Pmbhm 2 p*|%
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<& \uao críielmaofpo hm| `g| lurym|& 0& ·]uå lgflhu|egfo| gbpeofo `oh ~m|g mfporegr7 R; @o mluor`g lgf hg| ro|uhpm`g| `o hm| críielm| hm pof`oflem iuo oz~gfoflemh focmpeym ~mrm mabm|& O|pg |o `obo m }uo mh romhe{mr oh ~rglo|g `o `o|lmrcm `oh lm~mlepgr |o efyerpeü hm ~ghmre`m` `oh auhpeaoprg of hm ro|e|poflem( `o o|pm igram hm críielm ro|uhpg lm|e |eaehmr& ?& Ofluofpro hm rohmleüf ampoaípelm }uo rohmlegfm Y= lgf p !>&>?p
1 5&09:o
9& Ofluofpro hm rohmleüf ampoaípelm }uo rohmlegfm Y2 lgf p !>&>?p
1 5&?5:o
3& ·]uå |ecfeielm oh påraefg lgf|pmfpo `o peoa~g ~mrm uf lerluepg7 R; O| oh peoa~g `o lmrcm g `o|lmrcm `o uf lgf`of|m`gr lgfolpm`g m ufm iuofpo lgfpefum ao`emfpo ufm ro|e|poflem& Pmabeåf |o `oiefo lgag ohh peoa~g folo|mreg
~mrm }uo hm lmrcm mhlmflo oh 9<(2 / `o |u ymhgr iefmh *LO% |o hhmam lgf|pmfpo `o peoa~g lm~mlepeym :& ·]uå imlpgro| heaepmf hm ozmlpepu` `o hm| ao`elegfo| of hm oz~oreoflem7 R; Hm ~role|eüf mh agaofpg `o pgamr hg| peoa~g|& 5& Crmie}uo of ~m~oh aeheaoprm`g Y = y| p4 Y2 y| p4 mabm| of hm ae|am jgkm&
ROLGAOF@MLEGFO\
\ocuer pg`m| hm| ef`elmlegfo| `m`m| ~gr hm| cuám| hm| |ucoroflem| `m`m| ~gr oh ~rgio|gr of oh agaofpg of }uo |o ym m romhe{mr hm oz~oreoflem&
_pehe{mr hg| ef|pruaofpg| m`olum`g| ~mrm hm oz~oreoflem&
Pofor auljg lue`m`g of oh agaofpg `o jmlor hm holpurm g ao`eleüf( ~mrm m|á oyepmr orrgro| of oh líhluhg&
Pofor m amfg efigramleüf mlorlm `oh poam ~mrm ~g`or o|lhmrolor hm| `u`m| }uo ~uo`mf `mr|o&
LGFLH_\EGFO\ Huocg `o hm romhe{mleüf `o o|po efigrao( hgcrmag| lua~her lgf hg| gbkopeyg| `o hm oz~oreoflem `o ag`g }uo ~g`oag| oz~gfor hm| |ecueofpo| lgflhu|egfo|;
Fg| jm }uo`m`g lhmrg }uo oh peoa~g `o lmrcm `o|lmrcm `o uf lm~mlepgr( o| oz~oreaofpmhaofpo lm|e ecumh hg lga~rgbmag| lgf oh lerluepg mram`g of oh hmbgrmpgreg&
Mh lgfolpmr oh lm~mlepgr m ufm iuofpo `o ~g`or( o|po lm~mlepgr |o lmrcm `o amform rí~e`m( m |u yo{ mh mbrer oh efporru~pgr }uo lgfolpm oh lerluepg m hm iuofpo lorrmr oh efporru~pgr }uo lgfolpm mh lm~mlepgr lgf hm ro|e|poflem( o|po |o `o|lmrcm&
Oh peoa~g `o lmrcm `o|lmrcm `o uf lm~mlepgr ym m `o~of`or `o hm amcfepu` `o hm lm~mlepmflem oh ymhgr `o hm ro|e|poflem }uo jm of pg`g oh lerluepg( |o |mbo }uo |e hm amcfepu` `o hm lm~mlepmflem oh `o hm ro|e|poflem |gf crmf`o|( hm rolmrcm `oh lm~mlepgr o| aí| crmf`o ~org o| aí| hofpm of lmrcmr|o( |e hm| amcfepu`o| `o hm lm~mlepmflem oh `o hm ro|e|poflem |gf aí| ~o}uoýg|( |ulo`o pg`g hg lgfprmreg&
^mrm luhaefmr o|~ormag| }uo o|po efigrao hgcro hhofmr |u| oz~olpmpeym oz~olpmpeym|& |&
BEBHEGCRMIÁM
jpp~;''sss&agfgcrmiem|&lga'prmbmkg|=2'lerlu'lerlu
jpp~;''sss&ufelrga&lga'PupWlerluepgRL
\orsm Rmagf` M& "Ie|elm Pgag EE" Porlorm o`eleüf of o|~mýgh( O`epgremh Al Crms Jehh& Aåzelg( =552
Jmhhe`m @mye` ' Ro|feld Rgborp ' Drmfo Doffopj \& "Ie|elm Ygh&2" Porlorm o`eleüf of o|~mýgh( O`epgremh Lgfpefofpmh& Aåzelg( =559
Lupfohh Kgjf @& ' Kgf|gf Doffopj S& "Ie|elm" ^reaorm o`eleüf( O`epgremh Heau|m& Aåzelg( =5:9
\omr| Irmfle| S& ' [oamf|d Amrd S& ' Ugufc Jucj @& ' Iroo`amf Rgcor M& ‘Ie|elm _feyor|epmrem Ygh&2 " fgyofm o`eleüf( O`epgremh M``e|gf So|ho& Aåzelg( =55:
