Segmentación de imágenes a través de lógica difusa - Academica-e

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E.T.S. de Ingeniería Industrial,
Informática y de Telecomunicación
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Segmentación de imágenes a
través de lógica difusa y funciones
REF, de Dombi y penalti
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Grado en Ingeniería Informática
Trabajo Fin de Grado
Iñigo Aguas Ardaiz
Humberto Bustince Sola
Fco. Javier Fernández Fernández
Pamplona, 25 de junio de 2015
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QFOBMUJ &YQFSJNFOUP TVTUJUVDJ³O EF MB GVODJ³O 3&' QPS MB GVODJ³O EF
%PNCJ FO FM BMHPSJUNP QBSB MB PCUFOJDJ³O EFM VNCSBM ³QUJNP 3FQFUJDJ³O EF MPT FYQFSJNFOUPT DPO MB DPSSFDDJ³O PQPSUVOB 4FHNFOUBDJ³O EF JN¡HFOFT DPO BHSFHBOEP DPO GVODJPOFT 08"
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08" FO MB DPOTUSVDDJ³O EF MPT DPOKVOUPT EJGVTPT &YQFSJNFOUP TVTUJUVDJ³O EF MB NFEJB BSJUN©UJDB QPS GVODJPOFT
08" FO MB DPOTUSVDDJ³O EF MPT DPOKVOUPT EJGVTPT QBSB FM
BMHPSJUNP DPO GVODJ³O QFOBMUJ &YQFSJNFOUP TVTUJUVDJ³O EF MB NFEJB BSJUN©UJDB QPS GVODJPOFT
08" FO MB DPOTUSVDDJ³O EF MPT DPOKVOUPT EJGVTPT QBSB FM
BMHPSJUNP DPO GVODJ³O QFOBMUJ &YQFSJNFOUP TVTUJUVDJ³O EF MB NFEJB BSJUN©UJDB QPS GVODJPOFT
08" FO MB DPOTUSVDDJ³O EF MPT DPOKVUPT EJGVTPT QBSB FM BMHPSJUNP
EFM VNCSBM ³QUJNP QPS TJNJMJUVE $PODMVTJPOFT Z M­OFBT EF GVUVSP
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N­OJNP DPO SFTQFDUP B MPT PUSPT OJWFMFT EF HSJT Z RVF QPS FTP TF FTDPHF
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3FQSFTFOUBDJ³O EF MB QFSUFOFODJB EF MPT FMFNFOUPT QBSB MB M³HJDB EJGVTB
*N¡HFOFT VUJMJ[BEBT FO FM FYQFSJNFOUP Z TJHVJFOUFT *N¡HFOFT DPO SVJEP VUJMJ[BEBT FO FM FYQFSJNFOUP Z TJHVJFOUFT 9*
OEJDF EF UBCMBT
6NCSBMFT QBSB DBEB JNBHFO DPO MB GVODJ³O EF %PNCJ Z EJGFSFOUFT ‫ ܣ‬
6NCSBMFT QBSB DBEB JNBHFO DPO PUSBT WFSTJPOFT EF BMHPSJUNPT 3FTVMUBEP EF MBT TFHNFOUBDJPOFT QBSB FM BMHPSJUNP DPO 3&' Z %PNCJ DPO
WBSJPT ‫ _ ] ܣ‬
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EJGFSFOUFT WBMPSFT EF ‫ ܣ‬
6NCSBMFT QBSB MBT JN¡HFOFT DPO SVJEP DPO PUSBT WFSTJPOFT EF BMHPSJUNPT
6NCSBMFT QBSB MBT JN¡HFOFT DPO SVJEP DPO PUSBT WFSTJPOFT EF BMHPSJUNPT
6NCSBMFT QBSB DBEB JNBHFO DPO FM BMHPSJUNP DBMDVMBOEP MB GVODJ³O EF
QFSUFOFODJB B USBW©T EF VOB GVODJ³O QFOBMUJ 3FTVMUBEP QBSB FM OVFWP BMHPSJUNP B USBW©T EF QFOBMUJ DPO UPEBT MBT
GVODJPOFT QSPQVFTUBT &SSPSFT FO DPNQBSBDJ³O DPO MBT JN¡HFOFT TFHNFOUBEBT QPS FM FYQFSUP 6NCSBMFT QBSB DBEB JNBHFO SVJEP B USBW©T EFM BMHPSJUNP DBMDVMBOEP MB
GVODJ³O EF QFSUFOFODJB B USBW©T EF VOB GVODJ³O QFOBMUJ 3FTVMUBEP QBSB FM OVFWP BMHPSJUNP B USBW©T EF QFOBMUJ DPO UPEBT MBT
GVODJPOFT QSPQVFTUBT QBSB JN¡HFOFT DPO SVJEP 6NCSBMFT QBSB DBEB JNBHFO DPO FM BMHPSJUNP FO UPEBT TVT OVFWBT
WFSTJPOFT 3FTVMUBEP HS¡੗DP DPO FM BMHPSJUNP DPO MBT OVFWBT QSPQVFTUBT &SPSSFT EF MBT JN¡HFOFT PCUFOJEBT DPO PUSPT BMHPSJUNPT QBSB DBEB JNBHFO
DPO FM BMHPSJUNP FO UPEBT TVT WFSTJPOFT 6NCSBMFT QBSB DBEB JNBHFO SVJEPTB DPO FM BMHPSJUNP FO UPEBT TVT
WFSTJPOFT 3FQSFTFOUBDJ³O HS¡੗DB EFM SFTVMUBEP &SSPSFT QBSB DBEB JNBHFO SVJEPTB DPO PUSPT BMHPSJUNPT UPNBOEP DPNP
SFGFSFODJB MB WFSTJ³O # 6NCSBMFT Z UJFNQP EF D³NQVUP QBSB DBEB JNBHFO DPO FM BMHPSJUNP SFFTDSJUP B USBW©T EF GVODJPOFT EF %PNCJ 6NCSBMFT QBSB WFSTJ³O EFM BMHPSJUNP SFFTDSJUP DPO JN¡HFOFT SVJEPTBT
6NCSBMFT QBSB UPEBT MBT WFSTJPOFT EFM BMHPSJUNP 08" 6NCSBMFT QBSB UPEBT MBT WFSTJPOFT EFM BMHPSJUNP 08" QBSB JN¡HFOFT DPO SVJEP DPO MB
DPO MB
BQMJDBDJ³O EF
BQMJDBDJ³O EF
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6NCSBMFT QBSB UPEBT MBT WFSTJPOFT EFM BMHPSJUNP DPO MB BQMJDBDJ³O EF
08" 6NCSBMFT QBSB UPEBT MBT WFSTJPOFT EFM BMHPSJUNP DPO MB BQMJDBDJ³O EF
08" QBSB JN¡HFOFT DPO SVJEP 6NCSBMFT QBSB MB WFSTJ³O BHSFHBEB EFM BMHPSJUNP DPO MB BQMJDBDJ³O EF
08" 3FTVMUBEPT HS¡੗DPT QBSB MB WFSTJ³O BHSFHBEB EFM BMHPSJUNP DPO MB
BQMJDBDJ³O EF 08" 3FTVMUBEPT HS¡੗DPT QBSB MB WFSTJ³O BHSFHBEB EFM BMHPSJUNP DPO MB
BQMJDBDJ³O EF 08" 3FTVMUBEPT HS¡੗DPT QBSB MB WFSTJ³O BHSFHBEB EFM BMHPSJUNP DPO MB
BQMJDBDJ³O EF 08" FO JN¡HFOFT DPO SVJEP 6NCSBMFT QBSB DBEB JNBHFO DPO FM BMHPSJUNP B USBW©T MB BQMJDBDJ³O EF
08" 3FTVMUBEPT HS¡੗DPT QBSB FM BMHPSJUNP DPO MB BQMJDBDJ³O EF 08" 6NCSBMFT QBSB DBEB JNBHFO DPO FM BMHPSJUNP B USBW©T MB BQMJDBDJ³O EF
08" FO JN¡HFOFT DPO SVJEP 3FTVMUBEPT HS¡੗DPT QBSB FM BMHPSJUNP DPO MB BQMJDBDJ³O EF 08" FO
JN¡HFOFT DPO SVJEP # 4FHNFOUBDJPOFT QBSB MBT JN¡HFOFT DPO SVJEP B USBW©T EF MPT BMHPSJUNPT
EF PUSPT BVUPSFT # 4FHNFOUBDJPOFT QBSB MBT JN¡HFOFT DPO MPT BMHPSJUNPT EF PUSPT BVUPSFT 9*7
OEJDF EF BMHPSJUNPT
.BYJNJ[BDJ³O EF MB TJNJMJUVE 6NCSBMJ[BDJ³O EFM ¡SFB 4FMFDDJ³O EFM VNCSBM ³QUJNP 6NCSBMJ[BDJ³O HMPCBM 4FMFDDJ³O EFM VNCSBM ³QUJNP TFHºO 0UTV 4FMFDDJ³O EFM VNCSBM ³QUJNP NBYJNJ[BOEP MB FOUSPQ­B EF 3FOZJ
4FHNFOUBDJ³O QPS NFEJP EF ‫ܗ‬NFBOT 97
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QFOBMUJ " 'VODJ³O BVYJMJBS QBSB VUJMJ[BS MB 3&' DPO MBT GVODJPOFT QFOBMUJ
JNQMFNFOUBEBT " 'VODJ³O BVYJMJBS QBSB QPEFS MMFWBS B DBCP UPEBT MBT BHSFHBDJPOFT RVF TF
OFDFTJUBO QBSB DBMDVMBS VOB GVODJPO QFOBMUJ " 'VODJ³O QSJODJQBM RVF JNQMFNFOUB FM BMHPSJUNP DSFBOEP MPT DPOKVOUPT
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QFOBMUJ Z DSFB MPT DPOKVOUPT EJGVTPT DPO GVODJPOFT 08" " 'VODJ³O BVYJMJBS QBSB PCUFOFS MB NFEJB V 08" EFM PCKFUP " "MHPSJUNP JNQMFNFOUBEP DPO MB GVODJ³O PSJHJOBM BMH Z RVF EJTQPOF
EF GVODJPOFT 08" " "MHPSJUNP JNQMFNFOUBEP DPO FM BMHPSJNP Z RVF EJTQPOF EF GVODJPOFT
08" " "MHPSJUNP JNQMFNFOUBEP DPO FM BMHPSJUNP RVF EJTQPOF EF MB PQDJ³O
QBSB QSPCBS DPO EJGFSFOUFT WBMPSFT ‫ ܣ‬QBSB MB GVODJ³O EF %PNCJ " $BNCJP RVF TF EFCF MMFWBS B DBCP QBSB JOUFOUBS TPMVDJPOBS FM QSPCMFNB
RVF QSFTFOUBO MBT GVODJPOFT EF %PNCJ " 'VODJ³O QSJODJQBM EFM BMHPSJUNP EF VNCSBMJ[BDJ³O HMPCBM " 'VODJ³O QSJODJQBM EFM BMHPSJUNP EF 0UTV " 'VODJ³O QSJODJQBM EFM BMHPSJUNP EF NBYJNJ[BDJ³O EF MB FOUSPQ­B EF 3FOZJ
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DPNQBSBDJ³O 97**
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NPUJWBDJ³O QBSB JOWFTUJHBS Z DPOUSJCVJS FO FTUF ¡SFB 4F FYQMJDB UBNCJ©O MB SFMFWBODJB
EFM QSPCMFNB FO FM NBSDP EFM QSPDFTBNJFOUP EF JNBHFO Z MB TFHNFOUBDJ³O 'JOBMNFOUF
TF FTQFDJ੗DBO FM QSPQ³TJUP Z MPT PCKFUJWPT RVF TF IBO HVJBEP FTUB JOWFTUJHBDJ³O
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RVF MFT DBQBDJUBO QBSB MB SFTPMVDJ³O BVUPN¡UJDB EF QSPCMFNBT FT VO DBNQP GVOEBNFOUBM
EFOUSP EFM ¡SFB EF MB $PNQVUBDJ³O Z MB *OUFMJHFODJB "SUJ੗DJBM &TUF UJQP EF QSPDFTPT TF
VUJMJ[BO FO MB WJEB EJBSJB EF NVDIPT TFSFT IVNBOPT Z SFTVMUBO JOOBUPT FO FMMPT FO DBNCJP
TV JNQMFNFOUBDJ³O QBSB RVF MBT N¡RVJOBT MPT MMFWFO B DBCP TF DPOWJFSUF FO UPEP VO SFUP
EFCJEP B MB EJ੗DVMUBE EF MB JNJUBDJ³O EF MPT QSPDFTPT DFSFCSBMFT EF MBT QFSTPOBT
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TF QVFEF TFS DBQB[ EF EFUFSNJOBS UPEPT TVT FMFNFOUPT Q­YFMFT
FT EFDJS FTUPT TPO EF
GPSNB ੗OJUB Z EJTDSFUB " QBSUJS EF FTUB JEFB TF EJTQPOF EF EPT GPSNBT EF SFQSFTFOUBDJ³O
QBSB MBT JN¡HFOFT FO OJWFMFT EF HSJT FO MPT SBOHPT = ? ˛ ȉ Z = ? ˛ ȁ &O FM
QSJNFS DBTP EJSFNPT RVF MB JNBHFO FTU¡ OPSNBMJ[BEB "EFN¡T MBT JN¡HFOFT EJHJUBMFT
TFS¡O SFQSFTFOUBEBT QPS VOB NBUSJ[ RVF DPOUFOES¡ DBEB VOP EF TVT Q­YFMFT EF NBOFSB
PSEFOBEB
B
/JWFMFT EF HSJT
C
/PSNBMJ[BEB
D
(S¡੗DB
'JHVSB *NBHFO EJHJUBM FO EJGFSFOUFT SFQSFTFOUBDJPOFT
$PNP TF QVFEF BQSFDJBS FO MB ੗HVSB DVBOUP N¡T DFSDBOP B TFB FM OºNFSP N¡T OFHSP
TFS¡ FM OJWFM EF HSJT Z DVBOUP N¡T DFSDBOP B ³ N¡T CMBODP &O FM DBTP EF JN¡HFOFT
FO DPMPS TF VUJMJ[B FM GPSNBUP 3(# 3FE (SFFO Z #MVF
EPOEF FYJTUF VOB NBUSJ[ DPNP MBT
BOUFSJPSFT QPS DBEB VOP EF MPT DPMPSFT Z BM TVQFSQPOFSMBT TF PCUJFOF MB JNBHFO RVF WFNPT
IBCJUVBMNFOUF
%FࣲOJDJ³O 4F EF੗OF FM IJTUPHSBNB EF VOB JNBHFO ‫ ܄‬DPO OJWFMFT EF HSJT FO FM
JOUFSWBMP < > DPNP MB GVODJ³O ǻ
‫ ܝܚ ܝ‬EPOEF ‫ ܝܚ‬FT FM OºNFSP EF Q­YFMFT FO MB
JNBHFO DPO MB JOUFOTJEBE ‫ܝ‬
1SPDFTBNJFOUP EJHJUBM EF JNBHFO
6O FKFNQMP HS¡੗DP EF MB GVODJ³O EF IJTUPHSBNB QBSB VOB JNBHFO QVFEF FODPOUSBSTF FO
MB ੗HVSB )FSSBNJFOUB QBSB FM QSPDFTBNJFOUP EJHJUBM .࣌ࣟ-࣌࣍
.१ॺ-१२ BCSFWJBUVSB EF .BUSJY -BCPSBUPSZ
FT VOB IFSSBNJFOUB EF TPॏXBSF NBUFN¡UJDP
RVF PGSFDF VO MFOHVBKF EF QSPHSBNBDJ³O MFOHVBKF .
Z VO FOUPSOP EF EFTBSSPMMP
JOUFHSBEP 'VF DSFBEP FO QPS FM JOGPSN¡UJDP Z NBUFN¡UJDP $MFWF .PMFS FM DVBM
CVTDBCB VOB GPSNB BMUFSOBUJWB EF FKFDVUBS QSPHSBNBT EF ¡MHFCSB FO 'PSUSBO
&OUSF TVT QSFTUBDJPOFT C¡TJDBT FTU¡O MB NBOJQVMBDJ³O EF NBUSJDFT MB SFQSFTFOUBDJ³O EF
EBUPT Z GVODJPOFT P MB JNQMFNFOUBDJ³O EF BMHPSJUNPT BT­ DPNP MB DSFBDJ³O EF JOUFSGBDFT EF
VTVBSJP (6*
"EFN¡T FM QBRVFUF C¡TJDP EF .१ॺ-१२ QVFEF TFS FYQBOEJEP QPS NFEJP EF
UPPMCPYFT DPNP FT FM DBTP EF FTUF USBCBKP EPOEF TF VUJMJ[BS¡ MB SFMBUJWB B QSPDFTBNJFOUP EF
JNBHFO 4F QVFEF EJTQPOFS UBNCJ©O EFM TPॏXBSF 4JNVMJOL QBSB USBCBKBS DPOKVOUBNFOUF
B .१ॺ-१२
$POUSBTUF
&M DPOUSBTUF FT BRVFM DPODFQUP RVF OBDF EF MB EJGFSFODJB EF MB JOUFOTJEBE N¡T BMUB Z N¡T
CBKB EF VOB JNBHFO &TUP TF QVFEF BQSFDJBS EF NBOFSB DMBSB FO FM IJTUPHSBNB "T­ DVBOEP
VOB JNBHFO EJTQPOF EF VO HSBO SBOHP EJO¡NJDP JOUFSWBMP QBSB FM DVBM FM IJTUPHSBNB FT
EJGFSFOUF B FOUPODFT UFOES¡ VO DPOUSBTUF BMUP Z WJDFWFSTB &O MB ੗HVSB TF QVFEF WFS
VO FKFNQMP
B
*NBHFO PSJHJOBM
C
*NBHFO DPO QPDP DPOUSBTUF
D
*NBHFO DPO NVZ QPDP
DPOUSBTUF
'JHVSB *NBHFO EFM GPU³HSBGP DPO EJGFSFOUFT DPOUSBTUFT
$BQ­UVMP $PODFQUPT C¡TJDPT
1BSB
MMFWBS
B
DBCP
FTUF
BKVTUF
FO
.१ॺ-१२
TF
VUJMJ[B
MB
GVODJ³O
EPOEF
NJOUJOMJOFNBUMBCJNH@WBS FT MB WBSJBCMF EPOEF FTU¡ BMNBDFOBEB MB JNBHFO FO UJQP
NJOUJOMJOFNBUMBCFYUSFNPT@FOUSBEB FT VO WFDUPS RVF JOEJDB FOUSF DVBMFT FTU¡O
MPT WBMPSFT RVF TF EFCFO NPEJ੗DBS FO OVFTUSP DBTP TFS¡ WBD­P QBSB RVF DPKB UPEP FM
IJTUPHSBNB
Z EF NBOFSB TJN©USJDB NJOUJOMJOFNBUMBCFYUSFNPT@TBMJEB FT FM SBOHP EPOEF
EFCF FODPOUSBSTF FM IJTUPHSBNB EF MB JNBHFO EF TBMJEB
3VJEP FO MBT JNBHFOFT
4F DPOEJEFSB RVF VOB JNBHFO FTU¡ EFHSBEBEB DVBOEP UJFOF SVJEP FTUP FT DVBOEP UJFOF
EFGFDUPT DPO SFTQFDUP B MB JNBHFO PSJHJOBM ੗H -B QSJODJQBM GVFOUF EF SVJEP FO
JNBHFT EJHJUBMFT TF EB FO MB BERVJTJDJ³O P USBOTNJTJ³O EF MBT JNBHFOFT &TUP TF QVFEF
EFCFS B MBT DPOEJDJPOFT BNCJFOUBMFT P B MB DBMJEBE EF MPT TFOTPSFT EVSBOUF MB UPNB
EF MB JNBHFO 1PS FKFNQMP MB MVNJOPTJEBE FM QPMWP FO FM BNCJFOUF FUD QVFEFO TFS
EFUFSNJOBOUFT 1PS PUSB QBSUF FO FM DBTP EF MB USBOTNJTJ³O MBT JN¡HFOFT QVFEFO TFS
DPSSPNQJEBT QPS JOUFSGFSFODJBT FO FM NFEJP EF USBOTNJTJ³O QSJODJQBMNFOUF &TUP FT DMBSP
DVBOEP TF USBOTNJUF VOB JNBHFO EF VO TBU©MJUF ZB RVF MB BUN³TGFSB QVFEF JOUFSGFSJS Z
QSPWPDBS RVF MB JNBHFO SFDJCJEB FO MB 5JFSSB OP TFB FYBDUBNFOUF JHVBM
B
*NBHFO PSJHJOBM
C
*NBHFO DPO SVJEP ۜTBM Z
QJNJFOUB‫۝‬
D
*NBHFO DPO SVJEP HBVTJBOP
'JHVSB *NBHFO EF -FOB DPO EJGFSFOUFT UJQP EF SVJEP
-BT JN¡HFOFT DPO SVJEP UBNCJ©O TF QVFEFO DSFBS BSUJ੗DJBMNFOUF 1BSB FMMP VUJMJ[BNPT
VOB DJFSUB GVODJ³O ‫ ۻ‬EF EFHSBEBDJ³O B MB RVF B±BEJNPT VO SVJEP BM RVF MMBNBSFNPT ন EF
GPSNB RVF PCUFOESFNPT VOB OVFWB JNBHFO ‫ ܥ ܤ
ܔ‬RVF UFOES¡ VOB TFSJF EF JNQFSGFDDJPOFT
5PEP FM SVJEP DSFBEP EF FTUB GPSNB TF BQMJDBS¡ EJSFDUBNFOUF TPCSF MPT Q­YFMFT EF MB JNBHFO
MP RVF QSPWPDBS¡ DBNCJPT FO TV IJTUPHSBNB FO VOB GPSNB V PUSB "VO BT­ EFCFNPT UFOFS
FO DVFOUB RVF OP IBZ SFMBDJ³O EJSFDUB FOUSF MB JOUFOTJEBE OVFWB RVF UJFOFO MPT Q­YFMFT Z
MB BOUFSJPS
-³HJDB EJGVTB
&YJTUFO NVDIPT UJQPT EF SVJEP DPNP FM FYQPOFODJBM FM HBNNB FM VOJGPSNF FUD QFSP FO
FTUB NFNPSJB TF IBO VUJMJ[BEP FM HBVTJBOP Z FM EF UJQP JNQVMTJWP P EF ۜTBM Z QJNJFOUB‫۝‬
3VJEP HBVTJBOP
&TUF QVFEF TFS VOP EF MPT NPEFMPT EF SVJEP N¡T VUJMJ[BEP FO MB QS¡DUJDB EFCJEP B RVF
UJFOF VOB HSBO NBMFBCJMJEBE NBUFN¡UJDB #BTB TV GPSNB EF BDUVBS TPCSF MB JNBHFO FO MB
GVODJ³O HBVTJBOB EF QSPCBCJMJEBE
‫ ܦ
ܜ‬
˭঱঴
‫ܒ‬
˥
‫˥ܦ‬ভଝ
ଝ঴ଝ
EPOEF ‫ ܦ‬SFQSFTFOUB MB JOUFOTJEBE ভ MB NFEJB EF ‫ ܦ‬Z ঴ MB EFTWJBDJ³O FTU¡OEBS &TUF UJQP EF
SVJEP QVFEF DSFBSTF FO .१ॺ-१२ B USBW©T EF MB GVODJ³O
TBCJFOEP RVF
FT MB WBSJBCMF EPOEF FTU¡ BMNBDFOBEB MB JNBHFO FO UJQP
3VJEP EF UJQP ‫ړ‬TBM Z QJNJFOUB‫ڔ‬
&TUF UJQP EF SVJEP GPSNBMNFOUF MMBNBEP JNQVMTJWP IBDF RVF TF DPOWJFSUBO Q­YFMFT EF
GPSNB BMFBUPSJB FO Q­YFMFT DPO JOUFOTJEBE Z &TUB FT MB SB[³O EF TV QBSUJDVMBS OPNCSF
%F OVFWP ੗K¡OEPOPT FO .१ॺ-१२ QPESFNPT DSFBS JN¡HFOFT DPO FTUF UJQP EF SVJEP QPS
NFEJP EFM DPNBOEP
EF OVFWP
FT MB WBSJBCMF EPOEF TF BMNBDFOB MB JNBHFO Z
FT VO WBMPS FOUSF Z RVF IBDF
MBT WFDFT EF QSPCBCJMJEBE EF MB BQBSJDJ³O EFM SVJEP
&O FTUF USBCBKP TF IBO VUJMJ[BEP JN¡HFOFT DPO SVJEP QBSB DPNQSPCBS MB BEFDVBDJ³O P OP
EF MPT BMHPSJUNPT EF TFHNFOUBDJ³O BM SVJEP &KFNQMPT EF BNCPT UJQPT EF SVJEP TF IBO
QSFTFOUBEP FO MB ੗HVSB -³HJDB EJGVTB
-B M³HJDB EJGVTB GVF JOUSPEVDJEB QPS FM NBUFN¡UJDP - " ;BEFI <> FO DPO MB
JOUFODJ³O EF QPEFS FYUFOEFS MB M³HJDB DM¡TJDB P DSJQT EF GPSNB RVF QFSNJUJFSB NBOFKBS Z
QSPDFTBS MB JOGPSNBDJ³O RVF TF DPNQPOF EF U©SNJOPT JOFYBDUPT JNQSFDJTPT P TVCKFUJWPT
&T BM ੗O Z BM DBCP VO JOUFOUP EF JNJUBS MB GPSNB EF EFEVDDJ³O EFM DFSFCSP IVNBOP
QBSB USBTMBEBSMP B MBT N¡RVJOBT 4F DPNFO[BS¡ SFDPSEBOEP MB M³HJDB DM¡TJDB QBSB EFTQV©T
FYUFOEFS MPT DPODFQUPT B MB EJGVTB
$BQ­UVMP $PODFQUPT C¡TJDPT
&O QSJNFS MVHBS EF੗OJSFNPT FM VOJWFSTP ੗OJUP ‫ ܈‬DPO FM RVF TF USBCBKBS¡ EF GPSNB
RVF DPOUFOHB UPEPT BRVFMMPT FMFNFOUPT DPO MPT RVF TF EFTFF USBCBKBS FTUP FT ‫ ܈‬
]‫ܡ‬଒ ‫ܡ‬ଓ Ɨ ‫& _ ܚܡ‬O MB M³HJDB DM¡TJDB TJNQMFNFOUF BTJHOBNPT WFSEBEFSP P GBMTP B DBEB VOP
EF MPT FMFNFOUPT EFM DPOKVOUP RVF TF FTUVEJB 1PS FTUB SB[³O BM EF੗OJS VO DPOKVOUP ۴
QPESFNPT EFDJS RVF FTUF DPOUJFOF P OP B MPT FMFNFOUPT EFM VOJWFSTP ‫ ܈‬DPO VOB DFSUF[B
BCTPMVUB %F FTUB NBOFSB EBSFNPT VO WBMPS EF DVBOEP ‫ ܕܡ‬FTU© JODMVJEP FO ۴ WFSEBEFSP
Z VO WBMPS EF DVBOEP OP MP FTU© GBMTP
&O FTUB ºMUJNB JEFB TF SF੘FKB QPS NFEJP EF MB
GVODJ³O EF QFSUFOFODJB BM DPOKVOUP ۴ ভ۴ FDVBDJ³O ۴ ]
‫ ܕܡ‬ভ۴ ‫_܈ ˛ ܕܡ^ ܕܡ‬
ভ۴ ̉ ‫ ܈‬ɥ ] _ UBM RVF
ϴ
Ϸ
ϵ TJ ‫ ˛ ܡ‬۴
ভ۴ ‫ ܡ‬Ϸ
϶ TJ ‫ ˜ ܡ‬۴
1PEFNPT DPOTJEFSBS FM QSPCMFNB EF EFUFSNJOBS TJ VOB QFSTPOB FT BMUB P OP 1BSB MB M³HJDB
DM¡TJDB FTUF SB[POBNJFOUP TF TJNQMJ੗DBS¡ FO CVTDBS VO WBMPS B QBSUJS EFM DVBM QPEBNPT
EF੗OJS RVF DJFSUB QFSTPOB FT BMUB 1BSB FM TJHVJFOUF FKFNQMP UPNBSFNPT NFUSPT DPNP
SFGFSFODJB EPOEF ۴ FT FM DPOKVOUP EF MBT QFSTPOBT BMUBT %F FTUF NPEP ভ۴ TJ`‫ ܡ‬
Z FO PUSP DBTP ভ۴ &O MB ੗HVSB TF QVFEF WFS MB SFQSFTFOUBDJ³O EFM DPODFQUP ۜBMUP‫۝‬
QBSB MBT QPTJCMFT BMUVSBT RVF TF QVFEFO QSFTFOUBS
1FSUFOFODJB
WFSEBEFSP
GBMTP
/P BMUP
"MUP
BMUVSB N
'JHVSB 3FQSFTFOUBDJ³O EF MB QFSUFOFODJB EF MPT FMFNFOUPT QBSB MB M³HJDB DM¡TJDB
1PS PUSB QBSUF MB M³HJDB EJGVTB EJTQPOF EF MB GVODJ³O EF QFSUFOFODJB N¡T DPNQMFKB MP RVF
OPT IBDF QPEFS EFDJS RVF BMHVJFO FT ۜQPDP BMUP‫ ۝‬P ۜCBTUBOUF BMUP‫ ۝‬ZB RVF OP EBSFNPT VO
QBS EF WBMPSFT ] _
TJOP DVBMRVJFSB EF MPT DPOUFOJEPT FO FM JOUFSWBMP RVF EF੗OFO "T­
ভ۴ TFS¡ VOB GVODJ³O RVF BTJHOB VO WBMPS FOUSF Z B DBEB FMFNFOUP EF ۴
۴ ]
‫ ܕܡ‬ভ۴ ‫_܈ ˛ ܕܡ^ ܕܡ‬
ভ۴ ̉ ‫ ܈‬ɥ = ?
4J DPOUJOVBNPT DPO FM FKFNQMP TF WFS¡ RVF FM DPOKVOUP BMUP ۴
FTUB WF[ TF EF੗OF DPNP
FYQMJDB MB FDVBDJ³O ϴ
Ϸ
Ϸ
Ϸ
ϵ
ভ۴ ‫ ܡ‬Ϸ
Ϸ ‫ ˥ ܡ‬
Ϸ
϶
TJ
TJ
TJ
‫̸ܡ‬
‫ܡ‬
‫ ̷ ܡ‬
'VODJPOFT EF FRVJWBMFODJB SFTUSJOHJEB 3&'
&TUB OVFWB GVODJ³O EF QFSUFOFODJB IBDF RVF QPEBNPT EJTUJOHVJS [POBT EFOUSP EF TV
SFQSFTFOUBDJ³O ੗HVSB 4F UFOES¡ EF OVFWP MB FUJRVFUB ۜBMUP‫ ۝‬Z ۜOP BMUP‫ ۝‬RVF IBDFO
RVF TV QFSUFOFODJB TFB DFSUFSB 4F EJTQPOES¡ UBNCJ©O VOB QBSUF EF MB QFSUFOFODJB B MB
RVF MMBNBSFNPT ۜEJGVTP‫ ۝‬EPOEF FM DPOKVOUP OP B੗SNB TFS OJ ۜBMUP‫ ۝‬OJ ۜOP BMUP‫ ۝‬TJOP RVF FTU¡
FO VOB TJUVBDJ³O JOUFSNFEJB &O FTUF DBTP TF IBCMB EF RVF FM FMFNFOUP ܎‫ ܕ‬RVF TF FODVFOUSB
BI­ QFSUFOFDF B ۴ DPO HSBEP ভ۴ ܎‫ ܕ‬
1FSUFOFODJB
/P BMUP
%JGVTP
"MUP
BMUVSB N
'JHVSB 3FQSFTFOUBDJ³O EF MB QFSUFOFODJB EF MPT FMFNFOUPT QBSB MB M³HJDB EJGVTB
.¡T GPSNBMNFOUF EFOPUBSFNPT BM DPOKVOUP RVF JODMVZF B UPEPT MPT DPOKVOUPT EJGVTPT
DPNP Ț ‫ ܡ‬B UPEPT BRVFMMPT RVF TF FODVFOUSBO EF੗OJEPT TPCSF VO SFGFSFODJBM ੗OJUP ^‫ ^܈‬
‫ ܚ‬QPS MP RVF ‫ ܈‬OP TFS¡ VO DPOKVOUP WBD­P
'VODJPOFT EF FRVJWBMFODJB SFTUSJOHJEB 3&'
&M DPODFQUP EF GVODJ³O EF FRVJWBMFODJB SFTUSJOHJEB 3&' QPS TVT TJHMBT FO JOHM©T
TVSHF
EFM DPODFQUP EF FRVJWBMFODJB Z FM EF TJNJMJUVE <> &TUF DPODFQUP FT NVZ VUJMJ[BEP QBSB
MB DPNQBSBDJ³O EF JN¡HFOFT Z TV JOUFODJ³O FT EBS VOB NFEJEB EF D³NP EF JHVBMFT P
TJNJMBSFT TPO EPT FMFNFOUPT ‫ ܤ‬F ‫ ܥ‬1BSB QPEFS EF੗OJS FM DPODFQUP EF 3&' OFDFTJUBNPT
WBSJPT QSFWJBNFOUF
%FࣲOJDJ³O 6OB OFHBDJ³O FTUSJDUB FT BRVFMMB GVODJ³O ‫ ? = ̉ ܐ‬ɥ = ? RVF DVNQMF
RVF ‫ ܐ‬Z ‫ ܐ‬Z FT FTUSJDUBNFOUF EFDSFDJFOUF Z DPOUJOVB "EFN¡T TJ ‫ ܐ‬FT
JOWPMVUJWB TF DPOTJEFSB RVF TF IBCMB EF VOB OFHBDJ³O GVFSUF
%FࣲOJDJ³O -MBNBSFNPT BVUPNPS੗TNP ষ
B UPEBT BRVFMMBT GVODJPOFT EFM JOUFSWBMP
VOJEBE UBM RVF ষ ̉ = ? ɥ = ? TFBO DPOUJOVBT Z FTUSJDUBNFOUF DSFDJFOUFT QSPQJDJBOEP
RVF ষ
Z ষ
&O & 5SJMMBT <> FOVODJ³ FM TJHVJFOUF UFPSFNB
5FPSFNB 5FPSFNB EF 5SJMMBT
6OB GVODJ³O ‫ ? = ̉ ܐ‬ɥ = ? FT VOB OFHBDJ³O GVFSUF
TJ Z T³MP TJ FYJTUF VO BVUPNPSटTNP EFM JOUFSWBMP VOJEBE UBM RVF ‫ ܤ
ܐ‬ষ˥଒ ˥ ষ
‫ܤ‬
%FࣲOJDJ³O 6OB GVODJ³O ‫܅‬۸۹ ̉ = ? ɥ = ? FT MMBNBEB EF FRVJWBMFODJB SFTUSJOHJEB
DVBOEP DVNQMF RVF
$BQ­UVMP $PODFQUPT C¡TJDPT
‫܅‬۸۹
‫܅ ܥ ܤ‬۸۹
‫? = ˛ ܥ ܤ˓ ܤ ܥ‬
‫܅‬۸۹
‫ ܥ ܤ‬TJ Z T³MP TJ ‫ܥ ܤ‬
‫܅‬۸۹
‫ ܥ ܤ‬TJ Z T³MP TJ ‫ ܤ‬F ‫ ܥ‬³ TJ ‫ ܤ‬F ‫ ܥ‬
‫܅‬۸۹
‫܅ ܥ ܤ‬۸۹
‫ ? = ˛ ܥ ܤ˓ ܥ
ܐ ܤ
ܐ‬TJFOEP ‫ ܐ‬VOB OFHBDJ³O GVFSUF
˓‫ ? = ˛ ܦ ܥ ܤ‬TJ ‫ ܦ ̷ ܥ ̷ ܤ‬FOUPODFT ‫܅‬۸۹
‫܅ ̸ ܥ ܤ‬۸۹
‫ ܦ ܤ‬Z ‫܅‬۸۹
‫܅ ̷ ܦ ܥ‬۸۹
‫ܦ ܤ‬
1SPQPTJDJ³O 4FBO EPT BVUPNPSटTNPT ষ଒ Z ষଓ TF MMBNBS¡ GVODJ³O ‫܅‬۸۹ B MB
DPOTUSVDDJ³O RVF DVNQMB RVF
‫܅‬۸۹
‫ ܥ ܤ‬ষ˥଒
଒ ˥ ^ষଓ ‫ ˥ ܤ‬ষଓ ‫^ܥ‬
DPO ‫ ܤ
ܐ‬ষ˥଒
ଓ ˥ ষଓ ‫ܤ‬
"EFN¡T TJ UFOFNPT VOB ‫܅‬۸۹ Z VO BVUPNPSटTNP FO = ? MB BQMJDBDJ³O EF FTUPT ۹ ষ˫‫܅‬۸۹ FT PUSB ‫܅‬۸۹ 5FPSFNB 6OB GVODJ³O DPOUJOVB ‫܅‬۸۹ ̉ = ?ଓ ɥ = ? RVF DVNQMB RVF ‫܅‬۸۹
‫ ܤ‬
‫ ? = ˛ ܤ˓ ܤ‬FT VOB GVODJ³O ‫܅‬۸۹ BTPDJBEB DPO MB GVODJ³O ‫? = ̉ ۼ‬ଓ ɥ = ? DPO ‫ ۼ‬DPOUJOVB
Z BTPDJBUJWB TJ Z T³MP TJ FYJTUF VO BVUPNPSटTNP ষ FO = ? UBM RVF
‫܅‬۸۹
‫ ܥ ܤ‬ষ˥଒ ˥ ഈ
ষ
‫ ˥ ܤ‬ষ
‫ܥ‬ഈ
Z
‫ ܤ
ܐ‬ষ˥଒ ˥ ষ
‫ܤ‬
'VODJPOFT EF BHSFHBDJ³O
-BT GVODJPOFT EF BHSFHBDJ³O UJFOFO DPNP QSPQ³TJUP SFEVDJS MBT EJNFOTJPOFT EF MB
JOGPSNBDJ³O B QBSUJS EF MB DPNCJOBDJ³O EF MPT EBUPT EF FOUSBEB PCUFOJFOEP VOB TBMJEB RVF
MPT SFQSFTFOUF < > 4V BQMJDBDJ³O TF FYUJFOEF FO NVDIPT DBTPT QS¡DUJDPT Z UF³SJDPT
DPNP MB M³HJDB NVMUJFWBMVBEB DPOUSPM EJGVTP MB UPNB EF EFDJTJ³O FUD <> 4F EF੗OJS¡
VOB GVODJ³O EF BHSFHBDJ³O DPNP TJHVF
%FࣲOJDJ³O 4F EJDF RVF ‫ ܚ? = ̉ ܀‬ɥ = ? FT VOB GVODJ³O EF BHSFHBDJ³O EF
EJNFOTJ³O ‫ ܚ‬TJFNQSF RVF TBUJTGBHB
‫ܤ
܀‬଒ Ɨ ‫ ܚܤ‬TJ Z T³MP TJ ‫ܤ‬଒ Ɨ ‫ ܚܤ‬
‫ܤ
܀‬଒ Ɨ ‫ ܚܤ‬TJ Z T³MP TJ ‫ܤ‬଒ Ɨ ‫ ܚܤ‬
‫ ܀‬FT VOB GVODJ³O FTUSJDUBNFOUF DSFDJFOUF
%FࣲOJDJ³O 6OB GVODJ³O EF BHSFHBDJ³O ‫ ܀‬TFS¡ MMBNBEB NFEJB TJ
‫ܤ
ܚܕܙ‬଒ Ɨ ‫ܤ
܀ ̷ ܚܤ‬଒ Ɨ ‫ܤ
ܤ܎ܙ ̷ ܚܤ‬଒ Ɨ ‫ ܚܤ‬
'VODJPOFT EF BHSFHBDJ³O
&O FTUF QSPZFDUP TF VUJMJ[BS¡O NBZPSJUBSJBNFOUF MBT GVODJPOFT EF BHSFHBDJ³O
JEFNQPUFOUFT FTUP FT RVF DVNQMFO RVF ‫ ܤ
܀‬Ɨ ‫& ܤ˓ ܤ ܤ‬O QBSUJDVMBS VOB GVODJ³O EF
BHSFHBDJ³O JEFNQPUFOUF FT VOB NFEJB &OUSF MBT GVODJPOFT RVF VUJMJ[BSFNPT FODPOUSBNPT
MB NFEJB BSJUN©UJDB FM N­OJNP FM N¡YJNP P MB NFEJB HFPN©USJDB "EFN¡T TF EF੗OFO B
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ܠ‬଒ ̷ ‫
ܠ ̷ ܐ˪ܠ‬ଔ
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ঢ = ?
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‫ ܇ۻ‬
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‫ܠ‬ƚ
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ܠ‬ଓ ˥ ‫
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ࣲO TJ
‫
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ܠ‬ଔ ദ ˥ ‫
ܠ
ܜ‬ଔ ଒କ ঺ণଔ ഩ
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‫܁‬Θ‫܀‬
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TFS¡ QVFTUB FO GVODJ³O EFM FSSPS ZB RVF DPNP TF IB NPTUSBEP FTUF JS¡ EJTNJOVZFOEP
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ZB RVF OP EF EJTQPOF EF VO VNCSBM ‫ ܠ‬RVF EJWJEB MB NJTNB
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‫ܗ‬ഈഈ ࣲO QBSB
ࣲO QBSB
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‫ ܖ‬
଒
^‫^ ܗܞܒܠܟܡܘܐ‬
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IBTUB RVF + ̳ +BOU
QBSB ‫ ̉ ܖ‬IBTUB ‫ ۾‬IBDFS
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‫ܕ‬
ࣲO QBSB
EFWPMWFS JNH4FHNFOUBEB
‫ܖ‬
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FRVJWBMFODJB EF %PNCJ
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EF %PNCJ FO FM BMHPSJUNP EF NBYJNJ[BDJ³O EF MB TJNJMJUVE
&YQMJDBDJ³O EFM FYQFSJNFOUP
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MB DSFBDJ³O EF MPT DPOKVOUPT EJGVTPT 4F IBO MMFWBEP B DBCP FYQFSJNFOUPT DPO DBTJ
JN¡HFOFT &OUSF UPEPT FTUPT FYQFSJNFOUPT B DPOUJOVBDJ³O TF QSFTFOUBO MPT N¡T
SFFMFWBOUFT 1BSB FMMP TF UPNBS¡O MBT JN¡HFOFT RVF TF NVFTUSBO FO MB ੗HVSB 4F
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EF VO FYQFSUP TJ FYJTUFO
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SFTVMUBEPT TPO DPNQBSBEPT DPOUSB FM BMHPSJUNP EF NBYJNJ[BDJ³O EF MB TJNJMJUVE PSJHJOBM
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1BSB QPEFS DPOPDFS EF GPSNB FNQ­SJDB MB EJGFSFODJB FOUSF EPT JNBHFOFT TFHNFOUBEBT TF
DBMDVMB QBSB UPEBT FMMBT FM FSSPS DVBES¡UJDP NFEJP 4F QVFEF FYQSFTBS FM FSSPS DPNP
۸۶‫܄ ܄
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‫ܤ‬଒
‫ܥ‬଒
‫ ܁‬Θ‫܀‬
ଓ
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۰
ੲ ੳ
ੲ ੷
ੲ ੹੷
ੳ
ੳ ੴ੷
ੳ ੷
ੴ
੷
4JMMB
#MPRVFT
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ੴ
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ੲ੷
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"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੲ੷
6 (MPCBM
6 EF 0UTV
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4JMMB
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4PNCSB
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1PS PUSB QBSUF DBCF EFTUBDBS RVF FTUF SFTVMUBEP TF IB PCUFOJEP FO VO UJFNQP EF
DPNQVUBDJ³O EF BMSFEFEPS EF TFHVOEPT UBOUP QBSB MB WFSTJ³O DPO GVODJ³O
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‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
۰ ੲ ੹੷
۰ੳ
۰ ੳ ੴ੷
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WBSJPT ‫_ ] ܣ‬
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FSSPS DVBES¡UJDP NFEJP QBSB MBT JN¡HFOFT &O DPODSFUP TF IBDF DPO UPEBT MBT WFSTJPOFT
PCUFOJEBT DPO PUSPT MPT BMHPSJUNPT QSFTFOUBEPT TJO PCUFOFS OJOHºO SFTVMUBEP SFFMFWBOUF
4F QSFTFOUBO FO MB UBCMB MB DPNQBSBDJ³O RVF TF IBDF FOUSF MBT TFHNFOUBDJPOFT RVF
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SFTVMUBEPT RVF TF IBDFO N¡T JOUFSFTBOUFT RVF MPT BOUFSJPSFT %F OVFWP EF FTUB UBCMB
TF EFTQSFOEF EF RVF FO GVODJ³O EF MB JNBHFO RVF TF UPNF FM QBS¡NFUSP ‫ ܣ‬QBSB PCUFOFS
VOB NFKPS VNCSBMJ[BDJ³O
۰
"MH DPO ੲ ੹੷
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"MH DPO ੳ ੴ੷
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&OHSBOBKF
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JN¡HFOFT &T DVSJPTP DPNQSPCBS FM IFDIP EF RVF DPO MB NJTNB ‫ ܣ‬TF PCUJFOFO SFTVMUBEPT
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WBMPSFT EF ‫ܣ‬
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ੴ
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DPNQVUBDJ³O DSFDFS¡ CBTUBOUF GSFOUF B MB WFSTJ³O PSJHJOBM
3FTVMUBEPT
&O MBT UBCMBT Z TF NVFTUSBO MPT SFTVMUBEPT PCUFOJEPT QBSB UPEBT MBT JN¡HFOFT RVF
TF UPNBO DPNP NVFTUSB 4F IB EF EFTUBDBS RVF FTUF FYQFSJNFOUP BM JHVBM RVF UPEPT TF
IB MMFWBEP B DBCP DPO VO DPOKVOUP EF DBTJ JN¡HFOFT EF MBT RVF TF QSFTFOUBO MBT N¡T
TJHOJ੗DBUJWBT
4F QVFEF PCTFSWBS RVF DMBSBNFOUF MPT SFTVMUBEPT PCUFOJEPT TPO FYUSFNBEBNFOUF BMFKBEPT
EF MB SFBMJEBE 4F DSFBO ºOJDBNFOUF VNCSBMFT RVF OP QFSNJUFO MMFWBS B DBCP OJOHVOB
TFHNFOUBDJ³O EF GPSNB BEFDVBEB QPS MP RVF TF PNJUF MB QSFTFOUBDJ³O EF MPT SFTVMUBEPT
HS¡੗DPT BT­ DPNP EF MPT FSSPSFT FO FTUF FYQFSJNFOUP
&YQFSJNFOUP TVTUJUVDJ³O EF MB NFEJB BSJUN©UJDB QPS
GVODJPOFT 08" FO MB DPOTUSVDDJ³O EF MPT DPOKVOUPT EJGVTPT
QBSB FM BMHPSJUNP DPO GVODJ³O QFOBMUJ
&YQMJDBDJ³O EFM FYQFSJNFOUP
1BSB FTUF FYQFSJNFOUP TF TVTUJUVJS¡ MB NFEJB BSJUN©UJDB FO MB DSFBDJ³O EFM OVNFSBEPS
OFDFTBSJP FO FM BMHPSJUNP %F OVFWP TF IBS¡ DPO MBT EPT PQDJPOFT EF 08" QSFTFOUBEBT
%F GPSNB SFDVSSFOUF UBNCJ©O TF UJFOF FO DVFOUB RVF FM UJFNQP EF D³NQVUP TVCJS¡ EF
GPSNB FYUSBPSEJOBSJB N¡T BVO TJ SFDPSEBNPT RVF FTUF BMHPSJUNP JOJDJBMNFOUF IBD­B QPDPT
D¡MDVMPT Z QPS UBOUP VUJMJ[B QPDP UJFNQP
3FTVMUBEPT
4J TF FTUVEJBO MBT UBCMBT Z TF FODPOUSBS¡O EF OVFWP VOPT SFTVMUBEPT EFDFQDJPOBOUFT
QBSB MB VNCSBMJ[BDJ³O MMFWBEB B DBCP &YDFQUP FO DBTPT DPODSFUPT UPEPT FMMPT
EFQFOEJFOUFT EF ষ଒ ‫ܤ‬଑ଖ Z ষଓ ‫
ܤ‬
&YQFSJNFOUPT Z SFTVMUBEPT DPO GVODJPOFT EF BHSFHBDJ³O 08"
4JMMB
.FEJB
08" 08" #MPRVFT
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੲ੷
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੲ੷
.FEJB
08" 08" .FEJB
08" 08" -FUSBT
.FEJB
08" 08" .FEJB
08" 08" "MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੲ੷
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੲ੷
&OHSBOBKF
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੲ੷
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੲ੷
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੲ੷
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੲ੷
4PNCSB
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੲ੷
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੲ੷
5BCMB 6NCSBMFT QBSB UPEBT MBT WFSTJPOFT EFM BMHPSJUNP DPO MB BQMJDBDJ³O EF 08"
$BQ­UVMP 4FHNFOUBDJ³O EF JN¡HFOFT DPO BHSFHBOEP DPO GVODJPOFT 08"
3 HBVTJBOP
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੲ੷
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੲ੷
.FEJB
08" 08" .FEJB
08" 08" 3 JNQVMTJWP "MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੲ੷
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੲ੷
.FEJB
08" 08" 3 JNQVMTJWP "MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
ੲ੷
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੴ
"MH DPO ‫ۅۄۑ‬ੳ ੳ ˥ ഈ۱ ˥ ۲ഈੲ੷
5BCMB 6NCSBMFT QBSB UPEBT MBT WFSTJPOFT EFM BMHPSJUNP DPO MB BQMJDBDJ³O EF 08"
QBSB JN¡HFOFT DPO SVJEP
&YQFSJNFOUPT Z SFTVMUBEPT DPO GVODJPOFT EF BHSFHBDJ³O 08"
4F QVFEF PCTFSWBS RVF DMBSBNFOUF MPT SFTVMUBEPT PCUFOJEPT TPO FYUSFNBEBNFOUF BMFKBEPT
EF MB SFBMJEBE 4F DSFBO ºOJDBNFOUF VNCSBMFT RVF OP QFSNJUFO MMFWBS B DBCP OJOHVOB
TFHNFOUBDJ³O EF GPSNB BEFDVBEB QPS MP RVF TF PNJUF MB QSFTFOUBDJ³O EF MPT SFTVMUBEPT
HS¡੗DPT BT­ DPNP EF MPT FSSPSFT FO FTUF FYQFSJNFOUP
4JMMB
"MH DPO ৱੳ ৱੴ ۱
"MH DPO ৱੳ ۱ੴ Z ৱੴ ۱
"MH DPO ৱੳ ۱ੲ੷ Z ৱੴ ۱
"MH DPO ৱੳ ੳ ˥ ˭ੳ ˥ ۱ Z ৱੴ ۱
.FEJB
08" 08" #MPRVFT
"MH DPO ৱੳ ৱੴ ۱
"MH DPO ৱੳ ۱ੴ Z ৱੴ ۱
"MH DPO ৱੳ ۱ੲ੷ Z ৱੴ ۱
"MH DPO ৱੳ ੳ ˥ ˭ੳ ˥ ۱ Z ৱੴ ۱
.FEJB
08" 08" &OHSBOBKF
"MH DPO ৱੳ ৱੴ ۱
"MH DPO ৱੳ ۱ੴ Z ৱੴ ۱
"MH DPO ৱੳ ۱ੲ੷ Z ৱੴ ۱
"MH DPO ৱੳ ੳ ˥ ˭ੳ ˥ ۱ Z ৱੴ ۱
.FEJB
08" 08" -FUSBT
"MH DPO ৱੳ ৱੴ ۱
"MH DPO ৱੳ ۱ੴ Z ৱੴ ۱
"MH DPO ৱੳ ۱ੲ੷ Z ৱੴ ۱
"MH DPO ৱੳ ੳ ˥ ˭ੳ ˥ ۱ Z ৱੴ ۱
.FEJB
08" 08" 4PNCSB
"MH DPO ৱੳ ৱੴ ۱
"MH DPO ৱੳ ۱ੴ Z ৱੴ ۱
"MH DPO ৱੳ ۱ੲ੷ Z ৱੴ ۱
"MH DPO ৱੳ ੳ ˥ ˭ੳ ˥ ۱ Z ৱੴ ۱
.FEJB
08" 08" 5BCMB 6NCSBMFT QBSB UPEBT MBT WFSTJPOFT EFM BMHPSJUNP DPO MB BQMJDBDJ³O EF 08"
$BQ­UVMP 4FHNFOUBDJ³O EF JN¡HFOFT DPO BHSFHBOEP DPO GVODJPOFT 08"
3 HBVTJBOP
"MH DPO ৱੳ ৱੴ ۱
"MH DPO ৱੳ ۱ੴ Z ৱੴ ۱
"MH DPO ৱੳ ۱ੲ੷ Z ৱੴ ۱
"MH DPO ৱੳ ੳ ˥ ˭ੳ ˥ ۱ Z ৱੴ ۱
.FEJB
08" 08" .FEJB
08" 08" 3 JNQVMTJWP "MH DPO ৱੳ ৱੴ ۱
"MH DPO ৱੳ ۱ੴ Z ৱੴ ۱
"MH DPO ৱੳ ۱ੲ੷ Z ৱੴ ۱
"MH DPO ৱੳ ੳ ˥ ˭ੳ ˥ ۱ Z ৱੴ ۱
.FEJB
08" 08" 3 JNQVMTJWP "MH DPO ৱੳ ৱੴ ۱
"MH DPO ৱੳ ۱ੴ Z ৱੴ ۱
"MH DPO ৱੳ ۱ੲ੷ Z ৱੴ ۱
"MH DPO ৱੳ ੳ ˥ ˭ੳ ˥ ۱ Z ৱੴ ۱
5BCMB 6NCSBMFT QBSB UPEBT MBT WFSTJPOFT EFM BMHPSJUNP DPO MB BQMJDBDJ³O EF 08"
QBSB JN¡HFOFT DPO SVJEP
&YQFSJNFOUP TVTUJUVDJ³O EF MB NFEJB BSJUN©UJDB QPS
GVODJPOFT 08" FO MB DPOTUSVDDJ³O EF MPT DPOKVOUPT EJGVTPT
QBSB FM BMHPSJUNP DPO GVODJ³O QFOBMUJ
&YQMJDBDJ³O EFM FYQFSJNFOUP
&O FTUF DBTP EFCJEP B RVF FTUF BMHPSJUNP FT VOB NPEJ੗DBDJ³O EFM QSJNFSP TF WPMWFS¡
B VTBS GVODJPOFT 08" QBSB MB DSFBDJ³O EF MPT DPOKVOUPT EJGVTPT RVF SFQSFTFOUFO MBT
JN¡HFOFT
3FTVMUBEPT
&T DVSJPTP PCTFSWBS DPNP FM SFTVMUBEP DBNCJB EF GPSNB SBEJDBM &O MB 5BCMB TF QVFEFO
PCTFSWBS MPT VNCSBMFT RVF TF FODVFOUSBO BQMJDBEPT FO MBT JN¡HFOFT FO MB TJHVJFOUF UBCMB
&O DVBMRVJFS DBTP FTUF SFTVMUBEP UJFOF BºO VO QSPCMFNB QVFT TF HBTUB NVDIP UJFNQP
EF DPNQVUBDJ³O QBSB DPNP NVDIP JHVBMBS FM SFTVMUBEP TJOP OP FNQFPSBSMP DPNP TVDFEF
DPO BMHºO FKFNQMP
&YQFSJNFOUPT Z SFTVMUBEPT DPO GVODJPOFT EF BHSFHBDJ³O 08"
4JMMB
#MPRVFT
&OHSBOBKF
-FUSBT
4PNCSB
.FEJB
08" 08" 5BCMB 6NCSBMFT QBSB MB WFSTJ³O BHSFHBEB EFM BMHPSJUNP DPO MB BQMJDBDJ³O EF 08"
.FEJB
08" 08" 5BCMB 3FTVMUBEPT HS¡੗DPT QBSB MB WFSTJ³O BHSFHBEB EFM BMHPSJUNP DPO MB BQMJDBDJ³O
EF 08"
$BQ­UVMP 4FHNFOUBDJ³O EF JN¡HFOFT DPO BHSFHBOEP DPO GVODJPOFT 08"
4F QSFTFOUBO UBNCJ©O MPT SFTVMUBEPT EF BQMJDBS TPCSF JN¡HFOFT DPO SVJEP 4F WF RVF
DMBSBNFOUF FYJTUF VOB UFOEFODJB EF RVF MB TFHVOEB GPSNB EF DSFBS FM 08" IBHB RVF FM
VNCSBM TF EJTQBSF IBDJB VO FYUSFNP "VO BT­ Z EF OVFWP TF QVFEF BQSFDJBS DMBSBNFOUF
DPO MB JNBHFO TFHNFOUBEB EF MB UBCMB RVF MB TFHNFOUBDJ³O FT CBTUBOUF QFPS TJO DPOUBS
FM UJFNQP EF DPNQVUBDJ³O FYUSB RVF FT OFDFTBSJP
3 HBVTJBOP
3 JNQVMTJWP 3 JNQVMTJWP .FEJB
08" 08" 5BCMB 3FTVMUBEPT HS¡੗DPT QBSB MB WFSTJ³O BHSFHBEB EFM BMHPSJUNP DPO MB BQMJDBDJ³O
EF 08"
.FEJB
08" 08" 5BCMB 3FTVMUBEPT HS¡੗DPT QBSB MB WFSTJ³O BHSFHBEB EFM BMHPSJUNP DPO MB BQMJDBDJ³O
EF 08" FO JN¡HFOFT DPO SVJEP
&YQFSJNFOUP TVTUJUVDJ³O EF MB NFEJB BSJUN©UJDB QPS
GVODJPOFT 08" FO MB DPOTUSVDDJ³O EF MPT DPOKVUPT EJGVTPT
QBSB FM BMHPSJUNP EFM VNCSBM ³QUJNP QPS TJNJMJUVE
&YQMJDBDJ³O EFM FYQFSJNFOUP
&O FTUF DBTP TF DBNCJBS¡ MB NFEJB BSJUN©UJDB RVF TF FODVFOUSB FO MB DSFBDJ³O EFM DPOKVOUP
‫ ۻ‬RVF TF VUJMJ[B QBSB DPOPDFS MB TJNJMJUVE EF MBT JN¡HFOFT 4F NBOUFOES¡ EF FTUB GPSNB
&YQFSJNFOUPT Z SFTVMUBEPT DPO GVODJPOFT EF BHSFHBDJ³O 08"
EVSBOUF UPEP FM FYQFSJNFOUP šOJDBNFOUF DBNCJBS¡ MB NFEJB RVF TF FODVFOUSB FO MB
DSFBDJ³O EF MPT DPOKVOUPT EJGVTPT RVF TF DPNQBSBO DPOUSB ‫ ۻ‬
4F EJTUJOHVJS¡O EPT DBTPT QPS NFEJP EF MBT EPT GVODJPOFT 08" RVF TF IBO FYQMJDBEP
"RVFM RVF BDPHF B MB 08" FT FM "MH B
Z FM RVF NVMUJQMJDB QPS FM IJTUPHSBNB TFS¡
FM "MH C
3FTVMUBEPT
%F OVFWP TF WVFMWF B PCTFSWBS RVF OP TF EBO CVFOPT SFTVMUBEPT QBSB BRVFMMBT PQDJPOFT
RVF TJHVFO RVF TJHVFO UFOJFOEP MB DPOTUSVDDJ³O EFM DPOKVOUP ‫ ܠ܄‬QPS NFEJP EF 08"
&O DBNCJP TF PCTFSWB VO DBNCJP NVZ JOUFSFTBOUF ZB RVF QBSFDF RVF MB WFSTJ³O RVF TF
VUJMJ[B DPO MB NFEJB BSJUN©UJDB QFSP DPO 08" QBSB DSFBS FM DPOKVOUP ) PCUJFOF HSBOEFT
SFTVMUBEPT QBSB FM DBTP FO FM DVBM OP TF NVMUJQMJDB QPS FM IJTUPHSBNB "MH B
5BNQPDP
TF EFTEJ±FO MPT SFTVMUBEPT PCUFOJEPT DPO F 08" MB WFSTJ³O C
BVORVF OP TPO UBO
CVFOPT
4JMMB
"MH B
"MH C
.FEJB
08" 08" #MPRVFT
"MH B
"MH C
.FEJB
08" 08" &OHSBOBKF
"MH B
"MH C
.FEJB
08" 08" -FUSBT
"MH B
"MH C
.FEJB
08" 08" 4PNCSB
"MH B
"MH C
.FEJB
08" 08" 5BCMB 6NCSBMFT QBSB DBEB JNBHFO DPO FM BMHPSJUNP B USBW©T MB BQMJDBDJ³O EF 08"
&O FM DBTP EF MBT JN¡HFOFT DPO SVJEP MB UFOEFODJB FT FYBDUBNFOUF MB NJTNB $PNP IB
PDVSSJEP FO UPEPT MPT FYQFSJNFOUPT OP TF EJMVZF FM SVJEP ZB RVF DPO VO VNCSBM FTUF OP
$BQ­UVMP 4FHNFOUBDJ³O EF JN¡HFOFT DPO BHSFHBOEP DPO GVODJPOFT 08"
4JMMB
.FEJB
08" 08" .FEJB
08" 08" .FEJB
08" 08" .FEJB
08" 08" .FEJB
08" 08" "MH B
"MH C
#MPRVFT
"MH B
"MH C
&OHSBOBKF
"MH B
"MH C
-FUSBT
"MH B
"MH C
4PNCSB
"MH B
"MH C
5BCMB 3FTVMUBEPT HS¡੗DPT QBSB FM BMHPSJUNP DPO MB BQMJDBDJ³O EF 08"
&YQFSJNFOUPT Z SFTVMUBEPT DPO GVODJPOFT EF BHSFHBDJ³O 08"
QVFEF EFTBQBSFDFS &TUP TF TF NVZ DMBSP FO FM SVJEP JNQVMTJWP 4F TPMVDJPOBS­B DPO VO
੗MUSP
3 HBVTJBOP
"MH B
"MH C
.FEJB
08" 08" 3 JNQVMTJWP "MH B
"MH C
.FEJB
08" 08" 3 JNQVMTJWP "MH B
"MH C
.FEJB
08" 08" 5BCMB 6NCSBMFT QBSB DBEB JNBHFO DPO FM BMHPSJUNP B USBW©T MB BQMJDBDJ³O EF 08"
FO JN¡HFOFT DPO SVJEP
$BQ­UVMP 4FHNFOUBDJ³O EF JN¡HFOFT DPO BHSFHBOEP DPO GVODJPOFT 08"
3 HBVTJBOP
.FEJB
08" 08" .FEJB
08" 08" .FEJB
08" 08" "MH B
"MH C
3 JNQVMTJWP "MH B
"MH C
3 JNQVMTJWP "MH B
"MH C
5BCMB 3FTVMUBEPT HS¡੗DPT QBSB FM BMHPSJUNP DPO MB BQMJDBDJ³O EF 08" FO
JN¡HFOFT DPO SVJEP
$BQ­UVMP $PODMVTJPOFT Z M­OFBT EF GVUVSP
&O QSJNFS MVHBS DPO SFTQFDUP B MBT GVODJPOFT EF %PNCJ QPEFNPT DPNFOUBS RVF FTUBT
QBSFD­BO GVODJPOBS CJFO DPO VOB JNBHFO Z RVF TFS­B EFUFSNJOBOUF FM QBS¡NFUSP ‫ ܣ‬TJFOEP
EJGFSFOUF QBSB DBEB JNBHFO &TUP QBSFD­B JOEJDBS RVF TFS­B OFDFTBSJP QPEFS FOUSFOBS
DPO VO DPOKVOUP EF JN¡HFOFT VO TJTUFNB FYQFSUP QBSB QPEFS PCUFOFS TJFNQSF MB NFKPS
VNCSBMJ[BDJ³O FO GVODJ³O EF VOPT QBS¡NFUSPT EBEPT
"M VUJMJ[BS MB GVODJ³O EF %PNCJ FO DPOKVOUP DPO PUSBT P DPO FMMB NJTNB FT DVBOEP TF
DPODMVZF RVF FTUB GVODJ³O OP FT BEFDVBEB QBSB QPEFS IBDFS TFHNFOUBDJ³O EF JNBHFO /P
BM NFOPT DPO MB DPOTUSVDDJ³O EF DPOKVOUPT EJGVTPT RVF TF IB QSFTFOUBEP FO FTUF FTUVEJP
&TUP TF EFCF B RVF MBT GVODJPOFT EF %PNCJ OP DVNQMFO EF GPSNB BCTPMVUB RVF QBSB MB
GVODJ³O EF FRVJWBMFODJB ‫& ܤ ܤ
ܒ ܒ‬OUSBO B TPMVDJPOBS MB QBSBEPKB RVF TF QSPEVDF
DPO MB QSPQJFEBE ‫ ܤ
ܐ ܤ
ܒ‬MP RVF IBDF RVF TF DPOWJFSUB FO JOVUJM QBSB UPEBT OVFTUSBT
DPODMVTJPOFT
$PO SFTQFDUP BM N©UPEP RVF TF IB QSFTFOUBEP RVF VUJMJ[B MBT GVODJPOFT QFOBMUJ TFDDJ³O
TF EFCF EFDJS RVF DPOTVNF NVDIP N¡T UJFNQP EF QSPDFTBNJFOUP "IPSB CJFO
DJFSUBNFOUF MPT FSSPSFT DPNQBSBEPT DPO MPT SFTVMUBEPT PCUFOJEPT QPS PUSPT N©UPEPT
IBDFO WFS FM N©UPEP TBUJTGBDF EF NBOFSB NVZ CVFOB MB TPMVDJ³O EFM QSPCMFNB 4F
UJFOF RVF UFOFS FO DVFOUB RVF FO MB WFSTJ³O RVF TF IB JNQMFNFOUBEP DPO GVODJPOFT EF
%PNCJ FTUBT FO WF[ EF FNQFPSBS FM SFTVMUBEP MF IBDFO BCBSDBS VOB NBZPS BNQMJUVE EF
QPTJCJMJEBEFT BMHP RVF IBDF NFKPSBS FTUF DPO SFTQFDUP BM BMHPSJUNP PSJHJOBM PVUMBZFST
4J CJFO FT DJFSUP RVF TF OPUB VOB DJFSUB NFKPS­B EF MB QSPQVFTUB DVBOEP FO FM IJTUPHSBNB
RVF EJTQPOF EF WBSJPT N­OJNPT TPO N¡T TJNJMBSFT FOUSF T­
1PS PUSB QBSUF DPO SFMBDJ³O B MBT GVODJPOFT 08" QBSB TVTUJUVJS B MB NFEJB BSJUN©UJDB
TF DPNQSVFCB FYQFSJNFOUBMNFOUF RVF OP FT VOB CVFOB JEFB QBSB PCUFOFS VOB CVFOB
TFHNFOUBDJ³O फ़J[¡ FTUP TF EFCB B RVF BM PSEFOBS FM 08" TJ IBZ EPT Q­YFMFT EJGFSFOUFT
DPO JHVBM GSFDVFODJB EF ǻ
‫ ܝ‬TF FMJHF FM EF UPOBMJEBE N¡T BMUB 1PS FTUB SB[³O TJ FM SBOHP
EJO¡NJDP EF MB JNBHFO FT NVZ QFRVF±P IBCS¡ VOB TFSJF EF Q­YFMFT DPO UPOPT DFSDBOPT
B RVF PCUFOHBO VO HSBO CFOF੗DJP EF FMMP
$BQ­UVMP $PODMVTJPOFT Z M­OFBT EF GVUVSP
&TUB TJUVBDJ³O DBNCJB DVBOEP TF VUJMJ[BO MBT GVODJPOFT QFOBMUJ QBSB PCUFOFS FM NFKPS
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