Gigkrhf mi jænjynk ' lkuhgijf
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSK JFGSKZZ
63
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ
GIGKRHF MI JÆNJYNK
KBRF<
Uhuhidmf (Jfzf `fbh}fjhúd
SRKSHI]FRHK< YBHJFJHÚD<
MIZJRHSJHÚD MI IZ]RYJ]YRF X JFNHMFM MI GF]IRHFNIZ< Dügirk mi dhuiniz<
2
]hsk mi imhehjhk<
B
Fn}yrf min imhehjhk (`
5$99 g
Mhgidzhúd gidkr id zy bfzi (m
8$23 g
Mhgidzhúd gfxkr id zy bfzi (M
6:$13 g
Rinfjhúd nfmk gfxkr+nfmk gidkr > 2
6$=8
Ekrgf aikgè}rhjf mi nf snfd}f<
Hrriaynfr
FARIAFMKZ Aryizk< In }fgfök gæphgk min fariafmk aryizk k arfuf ziræ f nf }irjirf sfr}i min sirfn}i mi ydf nkzf gfjh|f k min izsizkr mi nf jfsf mi jkgsrizhúd id ydf nkzf sriefbrhjfmf$ Ehdk< In fariafmk ehdk. mibiræ jygsnhr jkd nkz rivyhzh}kz mi dk iz}fr jkd}fghdfmk. }idir yd gúmynk mi ehdyrf mi fjyirmk f nk izsijhehjfmk$
lkuhgijfCagfhn$jkg
`}}s<++lkuhgijf$}rhskm$jkg Sæahdf 2
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ
FAYF< Zi mibiræ jyhmfr in jkd}idhmk jnkryrkz x zynef}kz id in fayf vyi zi y}hnhji sfrf nf efbrhjfjhúd mi gkr}irkz x jkdjri}kz. fmigæz mi iuh}fr in jkd}idhmk mi gf}irhf kraædhjf k fn}kz jkd}idhmkz mi zúnhmkz mhzyin}kz. xf vyi jkgydgid}i zi jnkrf in fayf min zhz}igf mi zyghdhz}rk$
FJIRK MI RIEYIR\K< In rieyir|k nkdah}ymhdfn k ufrhnnfz mibiræ mibiræ zir jkrryafmk ipjis}k ipjis}k sfrf iz}rhbkz. ziaüd in jfzk$ Nfz ufrhnnfz jkrryafmfz mi rieyir|k jkd rizhz}idjhf f nf enyidjhf izsijhehjfmf (ex vyi ipjimf nkz =233 oa+jg. syimid igsnifrzi zhigsri vyi (ex zif in izeyir|k jkrrizskdmhid}i f ydf miekrgfjhúd mi 3$:9 )$ Nf gfnnf inij}rkzknmfmf jkd rieyir|k nhzk k jkrryafmk jkd ydf rizhz}idjhf (ex gfxkr f 9333 oa+jg$
JKDJRI]KZ< Zi mibiræ afrfd}h|fr srhdjhsfngid}i vyi in jkdjri}k jygsnf jkd nf rizhz}idjhf izsijhehjfmf id in srkxij}k x skr jkdzijyidjhf jkdzijyidjhf zi fziayrfræ zy myrfbhnhmfm$ Skr nk }fd}k. nfz rizhz}idjhfz srkgimhkz min jkdjri}k jkdjri}k mibiræd ipjimir zhigsri in ufnkr izsijçehjfmk mi e‘j. sfrf nk jyfn zi mi}irghdfræ id }kmkz nkz jfzkz zy imfm mi sryibf$ IMFM MI SRYIBF< 1 mçfz. 6= mçfz. 20 mçfz$
GYRKZ<
Jkdehdfmkz jkd jfmidfz x jfz}hnnkz mi jkdjri}k frgfmk. `ij`kz jkd bnkjo mi bfrrk ip}ryhmk$
Lyd}fz mi gkr}irk<
jigid}k
]hsk mi gkr}irk<
]hsk H
JFZ]HNNKZ<
F`kafmkz id gyrkz. id fnaydkz jfzkz zi yzfræ frgip. uir snfdkz iz}ryj}yrfniz$
Fjirk mi rieyir|k id jfz}hnnkz< Ex 7 =233 oa+jg2 e‘j 7 693 oa+jg2
E‘j min jkdjri}k<
ZHZ]IGF MI NKZFZ< Sriefbrhjfmfz x gfjh|fz ]hsk mi fskxk<
Gyrkz mi jfraf x jfmidfz mi jkdjri}k frgfmk$
Sirfn}i }k}fn mi nf nkzf< Gfjh|f mi 63 jg$ Fjirk mi rieyir|k<
ex 7 =233 oa+jg2
Jkdjri}k<
e½j 7 233 oa+jg2
RIJYBRHGHID]K GÇDHGK MI JKDJRI]KZ Aidirfniz<
6$9 jg$
Mhz}fdjhf nhbri id}ri ufrhnnfz<
6 ufrhnnf. sirk dk > 2$9 jg ú 6$9 uijiz min fariafmk aryizk igsnifmk$
lkuhgijfCagfhn$jkg
`}}s<++lkuhgijf$}rhskm$jkg Sæahdf :
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ
JHGID]FJHÚD Iz}f zi mhziöú mi fjyirmk f nkz rizyn}fmkz srkskrjhkdfmkz skr in iz}ymhk mi gijædhjf mi zyinkz. fzç jkgk min fdænhzhz min srkxij}k x mi nf iz}ryj}yrf$ iz}ryj}yrf$ Skr nk }fd}k< ]hsk mi jhgid}fjhúd<
Gfgskz}irçf x |fsf}fz mi jkdjri}k frgfmk$
Srkeydmhmf mi mizsnfd}i<
Izsijhehjfmk id in snfdk mi jhgid}fjhúd$
Fjirk mi rieyir|k<
Ufrhnnfz ex 7 =233 oa+ jg2
]hsk mi zyink<
HH
Jfsfjhmfm mi jfraf fmghzhbni min }irridk<
63 }kd+g2
Rijybrhghid}k gçdhgk mi jkdjri}k ipsyiz}k fn zyink<
=$33 jg
MHZIÖK IZ]RYJ]YRFN Gè}kmk mi mhziök< skr rizhz}idjhf x eyir|fz arfuh}fjhkdfniz$ Rizhz}idjhf min mhziök< Zkd nfz rizhz}idjhfz dkghdfniz jfnjynfmfz gimhfd}i nf }ikrçf aidirfn mi nf rizhz}idjhf mi gf}irhfniz x mi mhziök snæz}hjk min jkdjri}k$ jkdjri}k$ Skr nk vyi nfz rizhz}idjhfz mi mhziök ziræd hayfniz k gfxkriz f nkz ieij}kz$
FDÆNHZHZ MI JFRAFZ< JFRAFZ MI ZIRUHJHK<
Jfrafz izsijçehjfmfz izsijçehjfmfz skr in rianfgid}k aidirfn mi mi jkdz}ryjjhkdiz jkdz}ryjjhkdiz zhd zir feij}fmf skr efj}kriz$ efj}kriz$ F}idmhidmk f nfz rijkgidmfjhkdiz izsijhehjfmfz skr in rianfgid}k sfrf nfz jkdz}ryjjhkdiz min M$M$E$ (233=. rianfgid}k mi jkdz}ryjjhkdiz jkdz}ryjjhkdiz F$J$H$ (2330$ Nfz jfrafz ziræd nfz zhayhid}iz< JFRAFZ GYIR]FZ< Zkd nfz jfrafz sirgfdid}iz mibhmk fn sizk srkshk mi nkz gf}irhfniz$ JFRAFZ UHUFZ< Zkd nfz jfrafz arfuh}fjhkdfniz arfuh }fjhkdfniz vyi kbrfd id ydf jkdz}ryjjhúd x vyi dk }hidid jfræj}ir sirgfdid}i$
lkuhgijfCagfhn$jkg
`}}s<++lkuhgijf$}rhskm$jkg Sæahdf =
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ JFRAFZ FJJHMID]FNIZ< K bhid jfraf uhuf hdz}fd}ædif. nf jyfn zi jkdzhmirfræ sfrf in mhziök zçzghjk mi nf iz}ryj}yrf
x ziræ gidkr vyi nf jfraf uhuf arfuh}fjhkdfn$
FDÆNHZHZ MI INIGID]KZ IZ]RYJ]YRFNIZ ]kmkz nkz inigid}kz iz}ryj}yrfniz zifd gyrkz. jknygdfz. }rfbiz. nkzfz x jhghid}kz mibiræd mhgidzhkdfrzi mi }fn ekrgf vyi jygsnfd jkd jkd nfz dijizhmfmiz min srkxij}k srkxij}k fsiafmfz fn jrh}irhk min mhziök. sirk srhdjhsfngid}i zkgi}hmkz zkgi}hmkz f nf jkgbhdfjhúd gæz jrç}hjf mi jfrafz x bflk }kmkz nkz iz}fmkz skzhbniz mi izeyir|kz ( eniphúd. jfraf fphfn$ jkr}fd}i. }krzhkdfd}i. i}j $ Skr nk jyfn. eyirkd fdfnh|fmkz mi fjyirmk f nf }ikrçf aidirfn fj}yfn mi nf rizhz}idjhf rizhz}idjhf mi gf}irhfniz. srkskrjhkdædmkdkz srkskrjhkdædmkdkz iz}i jrh}irhk yd gfraid mi ziayrhmfm id nf iz}ryj}yrf$ Xf vyi sfrf mi}irghdfr nf rizhz}idjhf rivyirhmf f eniphúd skr jfrafz gyir}fz x uhufz uh ufz zi sfr}hú mi< Gy 7 6$= Gm / 6$1 Gn
Mkdmi?
Gm 7 gkgid}k skr jfraf gyir}f g yir}f Gn 7 gkgid}k skr jfraf uhuf Ghid}rfz vyi nf rizhz}idjhf r izhz}idjhf mi mhziök zi mi}irghdú gyn}hsnhjfdmk gyn}hsnhjfdmk nf rizhz}idjhf dkghdfn dkghdfn skr in efj}kr jkrrizskdmhid}i jkrrizskdmhid}i mi rimyjjhúd mi rizhz}idjhf$ rizhz}idjhf$ Iz jkduidhid}i fjnfrfr fjnfrfr vyi zyinid kjyrrhr kjyrrhr zkbrijfrafz id nkz inigid}kz inigid}kz iz}ryj}yrfniz. iz}ryj}yrfniz. fzç jkgk ufrhfjhkdiz id nkz gf}irhfniz nk vyi risirjy}hræ id nf iz}ryj}yrf$ Nfz gfadh}ymiz mi nfz jfrafz syimid ufrhfr mi nfz xf zysyiz}fz jkgk jkdzijyidjhf min uknygid mi nkz inigid}kz srhdjhsfngid}i$ Nfz jfrafz uhufz ufrhfd jkdzhmirfbnigid}i jkdzhmirfbnigid}i jkd in }higsk x mi yd imhehjhk f k}rk. mi gfdirf vyi zi rijkghidmf yd jkd}rkn mi jfnhmfm fmijyfmk fmijyfmk f nkz gf}irhfniz vyi hd}iruhidid id nf iz}ryj}yrf sfrf vyi in mhziök mi nf ghzgf }rfbfli mi fjyirmk fn srkxij}k rifnh|fmk$
FDÆNHZHZ MI NF IZ]RYJ]YRF X MI MHZIÖK ZÇZGHJK$ Nkz inigid}kz rizhz}id}iz f jfrafz nf}irfniz ziræd gyrkz jkdehdfmkz. jknygdfz x jfz}hnnkz nhafmkz skr }rfbiz x jfmidfz$ FR]HJYNK :99$ INIJJHÚD MIN ]HSK MI FDFNHZHZ H$ Fdænhzhz iz}æ}hjk x mhdæghjk$ ]kmk iz}ryj}yrf skmræ fdfnh|frzi gimhfd}i yd gè}kmk mhdæghjk ziaüd zi iz}fbniji iz}fbniji id in rianfgid}k$ Nfz iz}ryj}yrfz vyi dk sfzid mi 53g mi fn}k skmræd fdfnh|frzi. jkgk fn}irdf}huf. gimhfd}i in gè}kmk iz}æ}hjk
JFRFJ]IRÇZ]HJFZ MI NKZ GF]IRHFNIZ X RIZYGID DYGÈRHJK$ In srizid}i rizygid fdfnç}hjk iz in srkjimhghid}k igsnifmk id nf zknyjhúd min srkxij}k iz}ryj}yrfn min srk}k}hsk id jyiz}húd eydmfgid}fmk id< IZSIJHEHJFJHKDIZ IZSIJHEHJFJHKDIZ D$]$J$ M$E$
(233=
lkuhgijfCagfhn$jkg
`}}s<++lkuhgijf$}rhskm$jkg Sæahdf 9
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ Fzç jkgk in jrh}irhk iz}ryj}yrfn vyi dkrgf in fdænhzhz mi nf iz}ryj}yrf$
GF]IRHFNIZ$ Zi jkdzhmirfd nfz zhayhid}iz ef}hafz id nkz gf}irhfniz }idhidmk id jyid}f nf eydjhúd frvyh}ij}údhjf id uhakr$
GFNNF FJIRK< Nçgh}i mi enyidjhf<
ex 7 9333$33 oa+ jg2$
Rizhz}idjhf f nf }idzhúd<
e} 7 9133$33 oa+ jg2$
Fnfrafghid}k f nf rys}yrf id 63 <
0)
Mkbnfmk f 603¼ zkbri in gfdmrhn<
Uir }fbnf id nkz snfdkz iz}ryj}yrfniz$
Fjirk iz}ryj}yrfn<
F$Z$]$G$ F ‚ =:2
Nçgh}i mi rys}yrf<
95:5 oa+ jg2$
Nçg}i iz}æ}hjk<
ex 7 =233 oa+ jg2$
Eæ}haf mi }rfbflk<
ez 7 2633 oa+ jg2$
Mkbnfmk Dk$ :¼ Dk$ 9 f 83 arfmkz<
zkbri gfdmrhn< 5 / 5 MB
Mkbnfmk Dk$ :¼ Dk$ 0 f 83 arfmkz<
zkbri gfdmrhn< 5 / 62 mb$
JKDJRI]K< Rizhz}idjhf f nf jkgsrizhúd min jkdjri}k<
e ½j 7 oa+ jg2$
]fgfök dkghdfn gæphgk min fariafmk<
68 gg
Rizhz}idjhf srkgimhk f nf jkgsrizhúd jkgsrizhúd rivyirhmf< Uir snfdkz iz}ryj}yrfniz$ iz}ryj}yrfniz$
GYRKZ Mi bnkjo mi bfrrk ip}ryhmk$ Mhgidzhkdiz<
62p23p:2$9 jgz$
Rizhz}idjhf f nf jkgsrizhúd<
83 oa+ jg2$
Sizk skr gi}rk jyfmrfmk<
80 oaz$
Fn}yrf<
ufrhfbni
u rizhz}idjhf dkghdfn<
:$9 oa+ jg2$
lkuhgijfCagfhn$jkg
`}}s<++lkuhgijf$}rhskm$jkg Sæahdf 5
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ e , g rizh}idjhf dkghdfn f jkgsrizhúd<
=3 oa+ jg2$
Id gúmynk mi infz}hjhmfm<
263 333 oa+ jg2$
GKR]IRKZ (sfrf fzid}fr }fbhvyi ]hsk<
H
Srkskrjhúd (jigid}k ' jfn. fridf
6<6 6+=<9
Jkdjri}k sfrf jfz}hnnkz<
e ‐j 7 693 oa+ jg2$
NKZFZ ]HSK<
Gfjh|f mi jkdjri}k frgfmk jkd izsizkr mi 63 jg. uir snfdkz$
Sirfn}i mi diruhk mi }igsirf}yrf<
63p23 jgz jkd 2 ufrhnnfz mi 6+2‗
Sirfn}i mi bkuimhnnf<
65 jg
Sirfn}i }k}fn mi nkzf<
23 jgz$
Fjirk mi rieyir|k id nkzf<
ex 7 =233 oa+ jg2$
Jkdjri}k<
e½j 7 233 Oa+jg2
JKDZ]FD]IZ SFRF IN MHZIÖK SKR RIZHZ] RIZHZ]IDJHF$ IDJHF$ e,j 7 3$03 e ½j 7 653$33 oa+ jg2$ e ½j 7 3$09 e,j 7 6:5$33 oa+ jg2$ Rieyir|k nkdah}ymhdf nkdah}ymhdfn< n<
Fz$ghd 7
( 3$1 e ½j+ex bm
Fz 7
sbm
s$ghd 7
6=+ex
s$gæp 7
3$19 sb
sb 7
3$09 B n ( e ½j+ex 5669 5669+5669 / ex ( skrjid}fli sfrf sfrf rieyir|k f nf }idzhúd
Fz 7
6= bm+ ex
lkuhgijfCagfhn$jkg
`}}s<++lkuhgijf$}rhskm$jkg Sæahdf 1
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ Fz 7
3$15 sbp ( bm
F½z 7
Fz ( id in jid}rk min jnfrk+=. jkd}hdyk
Id nkz ip}rigkz Gy ( / > 3$9 Gy ( ' Rieyir|k }rfdzuirzfn
Zisfrfjhúd mi nkz fdhnnkz<
Srhgir fdhnnk f 9 jgz? fn jid}rk 23 jg. in riz}k jkdekrgi fn jænjynk iz}ryj}yrfn$
Jkdekrgi f nfz D]J ME 233=$ Nkdah}ym mi mizfrrknnk
Uir snfdkz iz}ryj}yrfniz$
FDÆNHZHZ ZÇZGHJK Id nf jkdzhmirfjhúd vyi `fji nf jnfzhehjfjhúd in rianfgid}k mi jkdz}ryjjhkdiz sfrf nf Jhymfm mi Jyirdfufjf Gkrinkz. Gèphjk
39+63+2363 Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
Jim$ Srke$ 9=88925
M$R$K$
Srkshi}frhk
lkuhgijfCagfhn$jkg
`}}s<++lkuhgijf$}rhskm$jkg Sæahdf 0
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ
Snfdkz Iz}ryj}yrfjhúd srksyiz}f ]fbnfz mi sizkz mi gf}irhfniz x jfrafz NKZF MI UHAYI]F X BKUIMHNNF MI 23 JG F\K]IF SNFDF ]ILF JYFMRFMK ARFDH]K GKR]IRK HGSIRGIFBHNH\FD]I ID]KR]FMK RINNIDK NHAIRK NKZF XIZK RIANFGID]K
F\K]IF HDJNHDFMF HDJNHDFMF ID]RISHZK 99
:0
JFRAF GYIR]F ∖
EFJ]KR MI JFRAF JFRAF GYIR]F EFJ]KRH\FMF JFRAF ARFUH]FJHKDFN Qg
:2 63
5= :2
:2 63 =2 629 253 :3 =3 911 6$= 031$0 633
253 :3 =3 =21
253 :3 =3 =25
981$0 =3
985$= 613
6$1 613
50
208
811$0 OA+G2
559$0 OA+G2
009$= OA+G2
Qg SFRF UHUHIDMF ↖
EFJ]KR MI JFRAF JFRAF UHUF EFJ]KRH\FMF JFRAF SFRF MHZIÖK Q (JG, 6$= / (JU ,6$1
lkuhgijfCagfhn$jkg
`}}s<++lkuhgijf$}rhskm$jkg Sæahdf 8
GIGKRHF MI JÆNJYNK Jfzf @fbh}fjhúd FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ
GYRK ]HSK DKUFBNKJO 62 ARFDH]K RISINNFMK RISINNFMK GYRK DKUFBNKJO 62 JFRAF GYIR]F ∖
EFJ]KR MI JFRAF JFRAF GYIR]F EFJ]KRH\FMF JFRAF SFRF MHZIÖK Q
5= =2 =2 80 2=5 6$= :==$= :==$= OA+G2
GYRK MI GFGSKZ]IRHF SHIMRF BRF\F GKR]IRK 13) MI SHIMRF :3) MI GKR]IRK JFRAF GYIR]F ∖
EFJ]KR MI JFRAF JFRAF GYIR]F EFJ]KRH\FMF JFRAF SFRF MHZIÖK Q
lkuhgijfCagfhn$jkg
2033 2633 6853 5:3 2983 6$= :525 :525 OA+G:
`}}s<++lkuhgijf$}rhskm$jkg Sæahdf 63
JYFMRK MI BFLFMF MI JFRAFZ F UHAFZ ' Srkxij}k dfdjx
IL I
DHUIN
: F
F\K]IF F\K]IF
:$39 :$19
3$33 3$33
3$33 3$33
3$33 3$33
3$33 3$33
3$33 612$23
2302$16 50=$=5
3$33 3$33
3$33 3$33
630$33 682$33
2683$16 63=0$55
]'6 ]'2
6$23 =$59 3$=3
2$33 3$33 3$13
6$09 3$33 3$33
:$93 3$33 3$33
3$33 3$33 3$33
612$23 612$23
221:$:8 50=$=5
2390$95 568$10
828$00 828$00
682$33 2=3$33 SYD]YFN
9525$32 25=5$:2 2=252$60
]': ]'= ]'9
0 ID]RISHZK F! ID]RISHZK F! ID]RISHZK
JNFRK :
JNFRK 9
]RFBI ZYGF Q (OA+G DK GB GBRI id (OA+G SIZK IZ]HGFMK
JNFRK 6
JNFRK 2
JNFRK =
NKZF NKZF ID]RISHZK7ÆR SRI]HN7FN]YRF F\K]IF7ÆRIF GYRK S$F$ IF ]RHBY]FRHF pSIZK GYRK ]RHBY]FRHF SKR (OA+G SKR SIZK MI SIZK MI NKZF NKZF
JYFMRK MI JKNYGDFZ UHAF VYI Uy ú S ILI JFRAF F
]2.]9.]9
Uy ú S
:938 :938$2 $23 3 6:.5 6:.530 30$3 $31 1
Uy ú S
OHNKZ ]K]FN IZ(S
DKGBRI
6:.5 6:.530 30$3 $31 1
:3129
O6
KBZIRUFJHKDIZ UFNKR GFPH GK GK MI JFRAF Z
↖ UFNKRIZ SFRF JFNJYNFR NFZ \FSF]FZ FHZNFMFZ
JYFMRK MI BFLFMF MI JFRAFZ F JHGID]FJHÚD ' Srkxij}k dfdjx NKZF NKZF F\K]IF7 ID]RISHZK7 SRI]HN7FN] ÆRIF GYRK ÆRIF ILI YRFpSIZK ]RHBY]F GYRK S$F$ ]RHBY]FRHF S$B$ RHF SKR GYRK SKR SIZK MI SIZK MI NKZF NKZF
6 : 0
6:1$15 6:1$15 6:1$15
2302$16 =:53$88 2210$21
828$00 828$00 828$00
6009$83 :8=0$00 2352$80
806$9= 806$9= 806$9=
ZYGF Q id (OA+G
5361$03 63:98$39 5:83$==
DKGBRI
JHG'2 JHG'6
BZIRUFJHKDI Z
K BZ BZ IR IRUF JH JH KD KDI Z
@HSIRIZ]Æ]HJF GÈDZYNF
JYFMRK MI JKNYGDFZ UHAF VYI Uy ú S ILI JFRAF F
]2.]9.]9
Uy ú S
:938 :938$2 $23 3 6:.5 6:.530 30$3 $31 1
Uy ú S
OHNKZ ]K]FN IZ(S
DKGBRI
6:.5 6:.530 30$3 $31 1
:3129
O6
KBZIRUFJHKDIZ UFNKR GFPH GK GK MI JFRAF Z
↖ UFNKRIZ SFRF JFNJYNFR NFZ \FSF]FZ FHZNFMFZ
JYFMRK MI BFLFMF MI JFRAFZ F JHGID]FJHÚD ' Srkxij}k dfdjx NKZF NKZF F\K]IF7 ID]RISHZK7 SRI]HN7FN] ÆRIF GYRK ÆRIF ILI YRFpSIZK ]RHBY]F GYRK S$F$ ]RHBY]FRHF S$B$ RHF SKR GYRK SKR SIZK MI SIZK MI NKZF NKZF
6 : 0
6:1$15 6:1$15 6:1$15
2302$16 =:53$88 2210$21
828$00 828$00 828$00
6009$83 :8=0$00 2352$80
ZYGF Q id (OA+G
806$9= 806$9= 806$9=
DKGBRI
5361$03 63:98$39 5:83$==
BZIRUFJHKDI Z
JHG'2 JHG'6
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF UHAF ZHGSNIGID]I FSKXFMF UIRZHKD 6$63 60+63+2330 JKDEKRGI F NFZ D]J'ME. GÈPHJK FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ
JKD JFRAF YDHEKRGIGID]I RISFR]HMF
lkuhgijfC`k}gfhn$jkg
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ
MF]KZ
DKGBRI MI NF UHAF →
rijybrhghid}k → fn}yrf mi nf uhaf → fdj`k mi nf uhaf → Nfrak mi nf uhaf → jfraf ydhekrgi q → rizhz}idjhf min jkdjri}k →
]'6
↓ iz}i iz in dkgbri vyi nniuf id in snfdk
m
7
68
r sirfn}i "`" b
7 7 7
2 23 2:
Nkd a Q E!j
7 7 7
:$39 2.683$16 293$33
EX
7
=.233$33
7
3$33:
jyfd}hf skr }igsirf}yrf
EFJ]KR MI RIMYJJHKD F ENIPHKD Er E$ MI RIMYJJHKD F JKR]FD]I Er
233 293
jg ↓ iz in ufnkr mi ` ' r jg ↓ rijybrhghid}k min fjirk f }idzhkd jg ↓ zi rijkghidmf in 63) min nfrak mi nf uhaf N jg ↓ zi rijkghidmf nf gh}fm mi ` g oa$g oa+jg2 6 ↓ Izjkahz}i nf ksjhkd → oa+jg2
↓
rizhz}idjhf min fjirk
→
3$332 zh nf uhaf dk iz}f f nf hd}igsirhi
→
3$33: zh nf uhaf iz}f f nf hd}igsirhi
7 7
3$83 3$03
7 7
653$33 6:5$33
oa+jg2 oa+jg2
2: 3 3
g
jfnjynk mi jkdz}fd}iz e,j e"j
NF JFRAF GYIR]F HDJNYXI IN SIZK SRKSHK MI NF UHAF JFNJYNK MIN SIZK MI NF UHAF MI JKDJRI]K b
7
e,j73$03 E!j e"j73$09 e , j
233 oa+jg2
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF UHAF ZHGSNIGID]I FSKXFMF UIRZHKD 6$63 60+63+2330 JKDEKRGI F NFZ D]J'ME. GÈPHJK FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ
JKD JFRAF YDHEKRGIGID]I RISFR]HMF
lkuhgijfC`k}gfhn$jkg
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ
MF]KZ
DKGBRI MI NF UHAF →
rijybrhghid}k → fn}yrf mi nf uhaf → fdj`k mi nf uhaf → Nfrak mi nf uhaf → jfraf ydhekrgi q → rizhz}idjhf min jkdjri}k →
]'6
↓ iz}i iz in dkgbri vyi nniuf id in snfdk
m
7
68
r sirfn}i "`" b
7 7 7
2 23 2:
Nkd a Q E!j
7 7 7
:$39 2.683$16 293$33
EX
7
=.233$33
7
3$33:
jyfd}hf skr }igsirf}yrf
EFJ]KR MI RIMYJJHKD F ENIPHKD Er E$ MI RIMYJJHKD F JKR]FD]I Er
233 293
jg ↓ iz in ufnkr mi ` ' r jg ↓ rijybrhghid}k min fjirk f }idzhkd jg ↓ zi rijkghidmf in 63) min nfrak mi nf uhaf N jg ↓ zi rijkghidmf nf gh}fm mi ` g oa$g oa+jg2 6 ↓ Izjkahz}i nf ksjhkd → oa+jg2
↓
rizhz}idjhf min fjirk
→
3$332 zh nf uhaf dk iz}f f nf hd}igsirhi
→
3$33: zh nf uhaf iz}f f nf hd}igsirhi
7 7
3$83 3$03
7 7
653$33 6:5$33
oa+jg2 oa+jg2
233 oa+jg2
jfnjynk mi jkdz}fd}iz e,j e"j
e,j73$03 E!j e"j73$09 e , j
NF JFRAF GYIR]F HDJNYXI IN SIZK SRKSHK MI NF UHAF JFNJYNK MIN SIZK MI NF UHAF MI JKDJRI]K b ` b p ` p 2= 3 3
7 7 7
2:$33 23$33 663$=3
g g oa+g
→
Qy
7
2.:36$66
oa+g
→
7
2.519$15
oa'g
JFNJYNK MIN GKGID]K GFPHGK Ggfp
sizk srkshk mi nf uhaf jfraf Q / in sizk srkshk mi nf uhaf
Ggfp7(q p Nkda p Nkda + 0
JFNJYNK MIN SKRJID]FLI BFNFDJIFMK MI FJIRK sb
7
3$3692
sgfp
7
3 $3 6 6 = :
sgfp73$19psb
sghd
7
3 $3 3 2 5 =
sghd7(3$1 p rfh| e ! j + Ex
sb7(e"j + Ex p (=033 + (5333 / Ex ↓
19) min sb
6
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggf p
7
2.519$15 oa'g
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$33999=2=5 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
3$33999=2=5 p 633 → 633 iz skr N7633 jg
v ' 2v /
2f
f7 b7 j7
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
2.519$15 7 JIRK 85:.932$23 7 JIRK 3$33999=2=5
3$999=2=536
v6 7
6$55515
'b / ∜(b 2 '=fj
v2 7
3 $: : : 2 =
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36318 sfrf mhgidzhkdfr
7
3 $3 6 6 = :
Riuhzhúd mi S gfp x S ghd s gf p
s7v2 p (e"j + Ex
↓ zi fsnhjk iz}f ekrgynf
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggf p
7
2.519$15 oa'g
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$33999=2=5 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
v ' 2v /
2.519$15 7 JIRK 85:.932$23 7 JIRK 3$33999=2=5
2f
f7 b7 j7
3$33999=2=5 p 633 → 633 iz skr N7633 jg
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
3$999=2=536
v6 7
6$55515
'b / ∜(b 2 '=fj
v2 7
3 $: : : 2 =
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36318 sfrf mhgidzhkdfr
7 7
3 $3 6 6 = : 3 $3 3 2 5 =
↓ zi fsnhjk iz}f ekrgynf
s7v2 p (e"j + Ex
Riuhzhúd mi S gfp x S ghd s gf p s ghd
IZ JKRRIJ]K '4 IZ JKRRIJ]K '4
s s
≭ ≩
3$36318 3$36318
≭
s gfp s ghd 3$366=: → Zhigsri zi mibid uirhehjfr iz}fz mizhayfnmfmiz 3$3325=
≩
zh zi jygsnid izkz 2 sfrfgi}rkz. iz ydf uhaf jkd fjirk bfnfdjifmk fn 19)
2
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
=$98
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz 2 :
dygirk = 7 : 7 ∖7
jg2
Fz7spbpm
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
2$9: 2$6=
jg2 jg2
= 51
jg2
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
2 g j d i f i r F
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
=$98
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz 2 :
jg2
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
dygirk = 7 : 7 ∖7
2$9: 2$6=
jg2 jg2
=$51
jg2
=$51 ≀
=$98
zfjfmk mi nf }fbnf (s ehdfn →
Fz7spbpm
↓ in
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
2 g j d i f i r F
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
}ikrhjk dijizfrhk
↚
Iz}i ufnkr mibi zir zhigsri nhairfgid}i hdeirhkr k sfrijhmk
RIUHZFGKZ IN S EHDFN JKRRIJ]K 4
s ehdfn
7
3 $3 6 3 8 0
s ehdfn7Fz+(bpm JKRRIJ]K 4
:
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332
ufrhnnfz 2 ' '
jyfd}hf
7
3$33:
F!z
7
6$20
jg
dygirk : 7 7 ∖7
6$=: '
jg2 jg2
6$=:
jg2
6$=: ≀
6$20
Fz7bpmpjyfd}hf
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf
:.938$23
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
3$36380 3$36380
≭ ≩
3$366=: 3$3325=
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332 jyfd}hf
7
3$33:
F!z
7
6$20
jg
dygirk : 7 7 ∖7
6$=: '
jg2 jg2
6$=:
jg2
6$=: ≀
6$20
ufrhnnfz 2 ' '
Fz7bpmpjyfd}hf
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
:.938$23
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf Ujr
7
6.035$9=
oa
Fi Ex iz}rhbk
7 7
3$5: 2.:33$33
jg oa+jg
jænjynk mi nf zisfrfjhkd mi iz}rhbkz
Z6
7
62$55
jg
Z2 Z: Z=
7 7 7
=3$=5 ::$05 66$8:
jg jg jg
' '
↓ ↓
Frif mi nf ufrhnnf vyi yzfrigkz jkgk iz}rhbk p 2 rfgfz Rizhz}idjhf Rizhz}idjhf mi izf ufrhnnf$ Fnfgbr d72:33? ufrhnnf7=23 ufrhnnf7=233 3
Z7(ErpFipEipm+(Uy'Ujr
=
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
7
]' 6
sirfn}i ` bfzi b rijybrhghid}k r Nkdah}ym mi uhaf
7 7 7 7
Ufrhnnfz mi nij`k hdeirhkr
7
Ufrhnnf mi nij`k zysirhkr
7
23$33 2:$33 6$93 :$39
jg jg jg g
dygirk mi shi|fz
dygirk mi ufrhnnf
2 :
* *
= :
2 '
* *
: '
dygirk mi shi|fz
dygirk mi ufrhnnf
DK]F< In Uy zi jkduhir}i id in S. vyi iz nf jfraf jkd vyi zi jfnjynfd nfz jknygdfz
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
7
]' 6
sirfn}i ` bfzi b rijybrhghid}k r Nkdah}ym mi uhaf
7 7 7 7
Ufrhnnfz mi nij`k hdeirhkr
7
Ufrhnnf mi nij`k zysirhkr
Iz}rhbkz min dygirk Zisfrfjhúd mi iz}rhbkz
23$33 2:$33 6$93 :$39
jg jg jg g
dygirk mi shi|fz
dygirk mi ufrhnnf
2 :
* *
= :
7
2 '
* *
: '
7 7
fnfgbrkd 6:
jg
dygirk mi shi|fz
dygirk mi ufrhnnf
zisfrfjhúd id nkz ip}rigkz mi nf uhaf
9
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF UHAF ZHGSNIGID]I FSKXFMF UIRZHKD 6$63 60+63+2330 JKDEKRGI F NFZ D]J'ME. GÈPHJK FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ
JKD JFRAF YDHEKRGIGID]I RISFR]HMF
lkuhgijfC`k}gfhn$jkg
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ
MF]KZ
DKGBRI MI NF UHAF →
rijybrhghid}k → fn}yrf mi nf uhaf → fdj`k mi nf uhaf → Nfrak mi nf uhaf → jfraf ydhekrgi q → rizhz}idjhf min jkdjri}k →
]'2
↓ iz}i iz in dkgbri vyi nniuf id in snfdk
m
7
68
r sirfn}i "`" b
7 7 7
2 23 60
Nkd a Q E!j
7 7 7
:$19 6.3=0$55 293$33
EX
7
=.233$33
7
3$33:
jyfd}hf skr }igsirf}yrf
EFJ]KR MI RIMYJJHKD F ENIPHKD Er E$ MI RIMYJJHKD F JKR]FD]I Er
233 293
jg ↓ iz in ufnkr mi ` ' r jg ↓ rijybrhghid}k min fjirk f }idzhkd jg ↓ zi rijkghidmf in 63) min nfrak mi nf uhaf N jg ↓ zi rijkghidmf nf gh}fm mi ` g oa$g oa+jg2 6 ↓ Izjkahz}i nf ksjhkd → oa+jg2
↓
rizhz}idjhf min fjirk
→
3$332 zh nf uhaf dk iz}f f nf hd}igsirhi
→
3$33: zh nf uhaf iz}f f nf hd}igsirhi
7 7
3$83 3$03
7 7
653$33 6:5$33
oa+jg2 oa+jg2
60 3 3
g
jfnjynk mi jkdz}fd}iz e,j e"j
NF JFRAF GYIR]F HDJNYXI IN SIZK SRKSHK MI NF UHAF JFNJYNK MIN SIZK MI NF UHAF MI JKDJRI]K b
7
e,j73$03 E!j e"j73$09 e , j
233 oa+jg2
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF UHAF ZHGSNIGID]I FSKXFMF UIRZHKD 6$63 60+63+2330 JKDEKRGI F NFZ D]J'ME. GÈPHJK FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ
JKD JFRAF YDHEKRGIGID]I RISFR]HMF
lkuhgijfC`k}gfhn$jkg
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ
MF]KZ
DKGBRI MI NF UHAF →
rijybrhghid}k → fn}yrf mi nf uhaf → fdj`k mi nf uhaf → Nfrak mi nf uhaf → jfraf ydhekrgi q → rizhz}idjhf min jkdjri}k →
]'2
↓ iz}i iz in dkgbri vyi nniuf id in snfdk
m
7
68
r sirfn}i "`" b
7 7 7
2 23 60
Nkd a Q E!j
7 7 7
:$19 6.3=0$55 293$33
EX
7
=.233$33
7
3$33:
jyfd}hf skr }igsirf}yrf
EFJ]KR MI RIMYJJHKD F ENIPHKD Er E$ MI RIMYJJHKD F JKR]FD]I Er
233 293
jg ↓ iz in ufnkr mi ` ' r jg ↓ rijybrhghid}k min fjirk f }idzhkd jg ↓ zi rijkghidmf in 63) min nfrak mi nf uhaf N jg ↓ zi rijkghidmf nf gh}fm mi ` g oa$g oa+jg2 6 ↓ Izjkahz}i nf ksjhkd → oa+jg2
↓
rizhz}idjhf min fjirk
→
3$332 zh nf uhaf dk iz}f f nf hd}igsirhi
→
3$33: zh nf uhaf iz}f f nf hd}igsirhi
7 7
3$83 3$03
7 7
653$33 6:5$33
oa+jg2 oa+jg2
233 oa+jg2
jfnjynk mi jkdz}fd}iz e,j e"j
e,j73$03 E!j e"j73$09 e , j
NF JFRAF GYIR]F HDJNYXI IN SIZK SRKSHK MI NF UHAF JFNJYNK MIN SIZK MI NF UHAF MI JKDJRI]K b ` b p ` p 2= 3 3
7 7 7
60$33 23$33 05$=3
g g oa+g
→
Qy
7
6.6:9$35
oa+g
→
7
6.889$22
oa'g
JFNJYNK MIN GKGID]K GFPHGK Ggfp
sizk srkshk mi nf uhaf jfraf Q / in sizk srkshk mi nf uhaf
Ggfp7(q p Nkda p Nkda + 0
JFNJYNK MIN SKRJID]FLI BFNFDJIFMK MI FJIRK sb
7
3$3692
sgfp
7
3 $3 6 6 = :
sgfp73$19psb
sghd
7
3 $3 3 2 5 =
sghd7(3$1 p rfh| e ! j + Ex
sb7(e"j + Ex p (=033 + (5333 / Ex ↓
19) min sb
6
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggf p
7
6.889$22 oa'g
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$339282396 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
3$339282396 p 633 → 633 iz skr N7633 jg
v ' 2v /
2f
f7 b7 j7
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
6.889$22 7 JIRK 19=.3=9$23 7 JIRK 3$339282396
3$928239399
v6 7
6$5056=
'b / ∜(b 2 '=fj
v2 7
3 $: 6 : 0 5
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36365 sfrf mhgidzhkdfr
7
3 $3 6 6 = :
Riuhzhúd mi S gfp x S ghd s gf p
s7v2 p (e"j + Ex
↓ zi fsnhjk iz}f ekrgynf
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggf p
7
6.889$22 oa'g
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$339282396 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
v ' 2v /
6.889$22 7 JIRK 19=.3=9$23 7 JIRK 3$339282396
2f
f7 b7 j7
3$339282396 p 633 → 633 iz skr N7633 jg
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
3$928239399
v6 7
6$5056=
'b / ∜(b 2 '=fj
v2 7
3 $: 6 : 0 5
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36365 sfrf mhgidzhkdfr
7 7
3 $3 6 6 = : 3 $3 3 2 5 =
↓ zi fsnhjk iz}f ekrgynf
s7v2 p (e"j + Ex
Riuhzhúd mi S gfp x S ghd s gf p s ghd
IZ JKRRIJ]K '4 IZ JKRRIJ]K '4
s s
≭ ≩
3$36365 3$36365
≭
s gfp s ghd 3$366=: → Zhigsri zi mibid uirhehjfr iz}fz mizhayfnmfmiz 3$3325=
≩
zh zi jygsnid izkz 2 sfrfgi}rkz. iz ydf uhaf jkd fjirk bfnfdjifmk fn 19)
2
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
:$:0
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz 2 6
dygirk = 7 : 7 ∖7
jg2
Fz7spbpm
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
2$9: 3$16
jg2 jg2
: 29
jg2
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
2 g j d i f i r F
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
:$:0
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz 2 6
jg2
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
dygirk = 7 : 7 ∖7
2$9: 3$16
jg2 jg2
:$29
jg2
:$29 ≀
:$:0
zfjfmk mi nf }fbnf (s ehdfn →
Fz7spbpm
↓ in
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
2 g j d i f i r F
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
}ikrhjk dijizfrhk
↚
Iz}i ufnkr mibi zir zhigsri nhairfgid}i hdeirhkr k sfrijhmk
RIUHZFGKZ IN S EHDFN JKRRIJ]K 4
s ehdfn
7
3 $3 3 8 1 9
s ehdfn7Fz+(bpm JKRRIJ]K 4
:
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332
ufrhnnfz 2 ' '
jyfd}hf
7
3$33:
F!z
7
6$33
jg
dygirk : 7 7 ∖7
6$=: '
jg2 jg2
6$=:
jg2
6$=: ≀
6$33
Fz7bpmpjyfd}hf
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf
2.620$2=
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
3$33819 3$33819
≭ ≩
3$366=: 3$3325=
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332 jyfd}hf
7
3$33:
F!z
7
6$33
jg
dygirk : 7 7 ∖7
6$=: '
jg2 jg2
6$=:
jg2
6$=: ≀
6$33
ufrhnnfz 2 ' '
Fz7bpmpjyfd}hf
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
2.620$2=
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf Ujr
7
6.::3$86
oa
Fi Ex iz}rhbk
7 7
3$5: 2.:33$33
jg oa+jg
jænjynk mi nf zisfrfjhkd mi iz}rhbkz
Z6
7
21$3=
jg
Z2 Z: Z=
7 7 7
2=9$2= :=$58 65$23
jg jg jg
' '
↓ ↓
Frif mi nf ufrhnnf vyi yzfrigkz jkgk iz}rhbk p 2 rfgfz Rizhz}idjhf Rizhz}idjhf mi izf ufrhnnf$ Fnfgbr d72:33? ufrhnnf7=23 ufrhnnf7=233 3
Z7(ErpFipEipm+(Uy'Ujr
=
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
7
]' 2
sirfn}i ` bfzi b rijybrhghid}k r Nkdah}ym mi uhaf
7 7 7 7
Ufrhnnfz mi nij`k hdeirhkr
7
Ufrhnnf mi nij`k zysirhkr
7
23$33 60$33 6$93 :$19
jg jg jg g
dygirk mi shi|fz
dygirk mi ufrhnnf
2 6
* *
= :
2 '
* *
: '
dygirk mi shi|fz
dygirk mi ufrhnnf
DK]F< In Uy zi jkduhir}i id in S. vyi iz nf jfraf jkd vyi zi jfnjynfd nfz jknygdfz
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
7
]' 2
sirfn}i ` bfzi b rijybrhghid}k r Nkdah}ym mi uhaf
7 7 7 7
Ufrhnnfz mi nij`k hdeirhkr
7
Ufrhnnf mi nij`k zysirhkr
Iz}rhbkz min dygirk Zisfrfjhúd mi iz}rhbkz
23$33 60$33 6$93 :$19
jg jg jg g
dygirk mi shi|fz
dygirk mi ufrhnnf
2 6
* *
= :
7
2 '
* *
: '
7 7
fnfgbrkd 21
jg
dygirk mi shi|fz
dygirk mi ufrhnnf
zisfrfjhúd id nkz ip}rigkz mi nf uhaf
9
3=+63+2363
Uhaf (]': ' puhafz
Hdmhji< Uhaf ~ Jfrafz ~ Aræehjk mi jfrafz ~ Rifjjhkdiz ~ Ijyfjhkdiz aidirfniz ~ Jfgskz ~ Izjyfjhkdiz zhg zhgsnhe snhehfmfz hfmfz ~ Aræehjkz ~ Ufnkriz ~ Ufnkri fnkrizz gæp gæphg hgkz kz ~ Mi}fnn Mi}fnniz iz min jænjynk ~ Kb}idir ufnkriz sfrf jyfnvyhir jk}f ~ Ufnkriz id fnaydfz jk}fz
Mf}kz Uhaf Nkdah}ym< 0$993333 Uhaf jkd}çdyf zhd igsk}rfghid}kz$ @hsiriz}æ}hjf$ Fskxk Fskx k d¼ 3 jk}f< 3$333333 3$333 333 mizjidz mizjidzk< k< 3$333333 3$333 333 Fskxk Fskx k d¼ 6 jk}f< 6$233333 6$2333 33 mizjidz mizjidzk< k< 3$333333 3$33 3333 Fskxk Fskx k d¼ 2 jk}f< :$233333 :$233 333 mizjidz mizjidzk< k< 3$333333 3$333 333 Fskxk Fskx k d¼ : jk}f< 9$393333 9$393 333 mizjidz mizjidzk< k< 3$333333 3$333 333 Fskxk Fskx k d¼ = jk}f< 0$993333 0$993 333 mizjidz mizjidzk< k< 3$333333 3$333 333 Infz}hjhmfm< Infz}hjhmfm< 2633$333333 2633$3333 33 Hdirjhf< =3333$333333 Ydhmfmiz<
lkuhgijfC`k}gfhn$jkg
3=+63+2363
Uhaf (]': ' puhafz
Hdmhji< Uhaf ~ Jfrafz ~ Aræehjk mi jfrafz ~ Rifjjhkdiz ~ Ijyfjhkdiz aidirfniz ~ Jfgskz ~ Izjyfjhkdiz zhg zhgsnhe snhehfmfz hfmfz ~ Aræehjkz ~ Ufnkriz ~ Ufnkri fnkrizz gæp gæphg hgkz kz ~ Mi}fnn Mi}fnniz iz min jænjynk ~ Kb}idir ufnkriz sfrf jyfnvyhir jk}f ~ Ufnkriz id fnaydfz jk}fz
Mf}kz Uhaf Nkdah}ym< 0$993333 Uhaf jkd}çdyf zhd igsk}rfghid}kz$ @hsiriz}æ}hjf$ Fskxk Fskx k d¼ 3 jk}f< 3$333333 3$333 333 mizjidz mizjidzk< k< 3$333333 3$333 333 Fskxk Fskx k d¼ 6 jk}f< 6$233333 6$2333 33 mizjidz mizjidzk< k< 3$333333 3$33 3333 Fskxk Fskx k d¼ 2 jk}f< :$233333 :$233 333 mizjidz mizjidzk< k< 3$333333 3$333 333 Fskxk Fskx k d¼ : jk}f< 9$393333 9$393 333 mizjidz mizjidzk< k< 3$333333 3$333 333 Fskxk Fskx k d¼ = jk}f< 0$993333 0$993 333 mizjidz mizjidzk< k< 3$333333 3$333 333 Infz}hjhmfm< Infz}hjhmfm< 2633$333333 2633$3333 33 Hdirjhf< =3333$333333 Ydhmfmiz< Eyir|fz id oae Gkgid}kz id oae Ñ g Nkdah}ymiz id g Ahrkz id rfmhfdiz
Jrh}irhk Jrh }irhk mi zhadkz< zhadkz<
9
Jkr}fd}iz skzh}huk skzh}huk z
Enij}kriz skzh}huk skzh}huk z
Ahrkz skzh}h skzh}h ukz
Enij`fz skzh}hufz
:
=
5
Jfrafz Jfrafz jkd}çdyfz Skzhjhúd Hdhjhk
Ehd
Gfadh}ym
3$33333 3$333333 3 0$993333 0$993333 9525$32 9525$323323 3323
E<+2363+Mfuhm Ayfmfrrfgf+]':+]':$@]G
6+1
3=+63+2363
Uhaf (]': ' puhafz
Aræehjk mi nf uhaf 9
:
=
5
Rizyn}fmkz min jænjynk< Rifjjhúd id nkz fskxkz< Eyir|f< 2=252$618500 Gkgid}k< 6580:$929:86 Fskxk d¼ 3 (3$333333< 61==$800698 Fskxk d¼ 6 (6$233333< 66:23$038913 Fskxk d¼ 2 (:$233333< 1362$139955 Fskxk d¼ : (9$393333< 68881$099=58 Fskxk d¼ = (0$993333< 0325$66:206 Jfraf }k}fn< }k}fn< =0632$=12595
Ijyfjhkdiz aidirfniz mi jkr}fd}iz x enij}kriz< Id diark fskxk z x igsk}rfg igsk}rfghid}kz. hid}kz. id rklk. jfrafz jf rafz syd}yfniz. id gkrfmk. gkgid} gkgid}kz. kz. id dfrfdlf. df rfdlf. jfrafz j frafz jkd}çdyfz. x id f|yn. jfrafz ufrhfbniz$
]7 '61==$800698Ñ>\'3$3333334 3 '66:23$038913Ñ>\'6$2333334 3 '1362$139955Ñ>\' :$2333334 3 '68881$099=58Ñ>\'9$39333343 '0325$66:206Ñ>\'0$9933334 3 /9525$323323Ñ>\'3$3333334 6 '9525$323323Ñ>\'0$9933334 6 G7 /61==$800698Ñ>\'3$3333334 6 /66:23$038913Ñ>\'6$2333334 6 /1362$139955Ñ>\' :$2333334 6 /68881$099=58Ñ>\'9$3933334 6 /0325$66:206Ñ>\'0$9933334 6 '9525$323323Ñ>\'3$3333334 2+2 /9525$3233 /9525$323323Ñ>\'0$9933334 23Ñ>\'0$9933334 2+2
Jfgskz< E<+2363+Mfuhm Ayfmfrrfgf+]':+]':$@]G
2+1
3=+63+2363
Dügirk
3 6 2 :
Uhaf (]': ' puhafz
Mhz}fdjhf%Fdj`yrf Hdhjhk Ehd Fdj`k 3$333333 6$233333 6$233333 6$233333 :$233333 2$333333 :$233333 9$393333 6$093333 9$393333 0$993333 :$933333
Ijyfjhkdiz zhgsnhehjfmfz (eúrgynfz id eydjhúd mi p< Jfgsk
Jkr}fd}iz Hdhjhk Eúrgynf
3
3$333333
/3$333p 2 '9525$323p /61==$800
Jfgsk
Hdhjhk
Enij}kriz Eúrgynf /3$333p : /206:$363p2 ' 61==$800p /3$333
3
3$333333
6
/3$333p 2 '9525$323p 6$233333 /6:359$180
6
/3$333p : /206:$363p2 ' 6$233333 6:359$180p /6:90=$812
2
:$233333
/3$333p 2 '9525$323p /23310$93=
2
:$233333
/3$333p : /206:$363p2 ' 23310$93=p /:5329$528
:
9$393333
/3$333p 2 '9525$323p /=3315$:98
:
9$393333
/3$333p : /206:$363p2 ' =3315$:98p /6:136=$181 Enij`fz
Jfgsk
3
6
Hdhjhk
Eúrgynf
/3$333333i/333p = ' 8$:15133i/332p : 2 3$333333 /0$12=8=6i/332p /3$333333i/333p /3$333333i/333 '6$:12:12i/336 /3$333333i/333p = ' 8$:15133i/332p : 2 6$233333 /5$9:2088i/33:p ' 6$:90=81i/33=p /0$69380:i/33: '6$:12:12i/336 /3$333333i/333p = ' 8$:15133i/332p : /6$33:829i/33=p 2 '
E<+2363+Mfuhm Ayfmfrrfgf+]':+]':$@]G
Eúrgynf
3
/3$333333i/333p 9 ' 2$:==619i/332p = /2$830:6=i/332p : 2 3$333333 /3$333333i/333p /3$333333i/333p /3$333333i/333 '6$:12:12i/336p /3$333333i/333
6
/3$333333i/333p 9 ' 2$:==619i/332p = /2$6115::i/33:p : ' 2 6$233333 5$182=05i/33:p /0$69380:i/33:p ' :$253:8=i/33: '6$:12:12i/336p /3$333333i/333
Ahrkz Jfgsk
Hdhjhk
/3$333333i/333p 9 ' 2$:==619i/332p = /:$:=5=61i/33:p : ' :+1
3=+63+2363
:
$
Uhaf (]': ' puhafz
:$53295:i/33=p /=$=3953=i/33= '6$:12:12i/336
/3$333333i/333p = ' 8$:15133i/332p : 2 9$393333 /2$33:060i/33=p ' 6$:136=0i/339p /2$8839:1i/339 '6$:12:12i/336
2
:
2
:$233333 6$036206i/33=p /=$=3953=i/33=p ' =$699862i/33= '6$:12:12i/336p /3$333333i/333 /3$333333i/333p 9 ' 2$:==619i/332p = /5$518:8:i/33:p : ' 2 9$393333 5$0931=3i/33=p /2$8839:1i/339p ' =$130392i/339 '6$:12:12i/336p /3$333333i/333
Id yd jknkr gæz jnfrk fsfrijid nfz jkdz}fd}iz mi ahrkz x enij`fz< IHA 3 x IHX 3$
Aræehjkz mi izeyir|kz jk}fd}iz. enij}kriz. ahrkz x enij`fz
Aræehjk mi jkr}fd}iz<
9
Izjfnf< 6655=$891,H,I
:
=
5
Aræehjk Aræeh jk mi enij}kriz< enij}kriz<
E<+2363+Mfuhm Ayfmfrrfgf+]':+]':$@]G
=+1
3=+63+2363
Uhaf (]': ' puhafz
9
Izjfnf< 5:51$819,H,I
:
=
5
Aræehjk mi ahrkz<
9
Izjfnf< 5::5$38=,H,I
:
=
5
Aræehjk Aræeh jk mi enij` en ij`fz< fz<
9
Izjfnf< 568:$3:6,H,I
: E<+2363+Mfuhm Ayfmfrrfgf+]':+]':$@]G
=
5
9+1
3=+63+2363
Uhaf (]': ' puhafz
Jkr}fd}iz % Enij}kriz Enij }kriz (ufnkr fsrkphgfmk< fsrkphgfmk< Jfgsk
3 6 2 :
6 2 :
Ufnkr ehdfn
3$333333 61==$800698 '9335$2:90=3 6$233333 5:6=$91:1:3 '=8:1$=59023 :$233333 2319$2=32:= '0::2$080=:0 9$393333 6655=$8913:6 '0325$66:206
Jfgsk
3
Hdhjhk
Jkr}fd}iz Ufnkr hdhjhfn
Ahrkz (zhd mhuhmhr id}ri IH Hdhjhk Ufnkr hdhjhfn Ufnkr ehdfn ' ' 6$:12:12i/336 :$115253i/332 ' 6$233333 0$:55553i/332 :$115253i/332 ' :$233333 0$:55168i/332 2$526:16i/33: ' 9$393333 5$::538=i/33: 2$526:6:i/33: 3$333333
Jfgsk
3 6 2 :
Hdhjhk
Enij}kriz Ufnkr hd hdhjhfn
Ufnkr eh ehdfn
3$333333 3$333333 6895$1=0118 6$233333 6895$1=832: 918$5=3529 :$233333 918$5:5168 5:51$81=538 9$393333 5:51$850193 '3$369529
Enij`fz (zhd mhuhmhr id}ri IH Jfgsk Hdhjhk Ufnkr hdhjhfn Ufnkr ehdfn 3 6 2 :
6$6===38i' 339 0$3955=6i' 6$233333 1$:2=268i' 33= 33: :$969529i' :$233333 2$1:=:19i'332 332 2$062933i' 9$393333 6$952933i'336 336 3$333333 3$333333i/333
Ufnkriz gæphgkz< Gkgid}k gæphgk id nf zijjhúd Skzhjhúd< 9$393333 Gfadh}ym< 5:51$81=538 Gfxkr ufnkr min izeyir|k jkr}fd}i Skzhjhúd< 9$393333 Gfadh}ym< 6655=$8913:6 Gfxkr ufnkr min ahrk (zhd mhuhmhr id}ri id}ri I,H Skzhjhúd< 0$993333 Gfadh}ym< 5::5$38:193 Gfxkr ufnkr miekrgfjhúd (zhd mhuhmhr id}ri I,H Skzhjhúd< 5$8:0233 Gfadh}ym< 568:$3:6293
Mi}fnniz min jænjynk< Zi `fjid ufrhfz ijyfjhkdiz< Ydf mi eyir|fz uir}hjfniz (∖EU73 Ydf mi gkgid}kz id in ip}rigk h|vyhirmk (∖G 373 9 ijyfjhkdiz mi enij`fz zybz}h}yhmfz skr jfmf ydf mi nfz skzhjhkdiz mi nkz fskxkz (Enij`f (Enij`f (X (X mhz}$ fskxk7Mizjidzk id in fskxk , IH. jirk zh dk `fx mizjidzk E<+2363+Mfuhm Ayfmfrrfgf+]':+]':$@]G
5+1
3=+63+2363
Uhaf (]': ' puhafz
Zi rizyinuid zh}yfdmk nfz ijyfjhkdiz id ydf gf}rç| mi ijyfjhkdiz. id iz}i srkarfgf zi skdi fn srhdjhshk nf mi nfz enij`fz . nf sidün}hgf. nf mi nkz gkgid}kz x nf ün}hgf nf mi nfz eyir|fz uir}hjfniz$ Gf}rh| vyi zi kb}hidi fn `fjir in jænjynk< Jkdz}fd}iz mi ahrkz x enij`fz enij`fz
Ahrk hdhjhfn IHA3
Enij`f hdhjhfn IHX 3
Fskxkz
6
]èrghdkz hdmisidmhid}iz
2
:
=
9
5$333333 3$333333 3$333333
3$333333
3$333333
3$333333 3$3 33333 3$333333
5$333333 1$233333 6$120333
3$333333
3$333333
3$333333 3$3 33333 2865$92839:
5$333333 68$233336 :2$150332 0$333333
3$333333
3$333333 3$333333 6=1=02$159529
5$333 $3333 333 :3$: :3$:3 3333 3336 620$1 0$1015 015=: 91$ 91$3555:6 5:6
5$:: 5$::66525 525
3$333333 3333 3$33 3$333 3333 86=19 =198$:1 8$:19 9333 333
5$3333 5$333333 33 96$:3 96$:333 333: 3: 529$3 529$325= 25=20 20 :81$3 :81$359= 59=:3 :3 69:$ 69:$6: 6:3=3 3=32 2 =2$01 =2$01933 9333 3 3$333 3$333333 333 1965 1965:20 :20$9 $933 33333 333 3$333333 3$333333 3$333333
6$233333
:$233333
9$393333 0$9 93333 2395:0$310629
3$333333 3$333333 6$333333
6$333333
6$333333
6$333333
6$333333 =0632$=12595
Mfr ufnkriz Jk}f< mhz}fdjhf Jfnjynfr
j Byzjfr m i e a
ufnkriz skr nf mirij`f Infz}hjhmfm skr ufnkr zhgbúnhjk zhgbúnhjk j Infz}hjhmfm m i e a ufn kr zhgbúnh zhgbúnhjk jk j Hdirjhf skr ufnkr m i e a
Sfrf kb}idir nkz ufnkriz mi nfz eydjhkdiz id yd syd}k jyfnvyhirf `fx vyi hd}rkmyjhr nf jk}f min syd}k x synzfr jfnjynfr$ Sfrf byzjfr ufnkriz mi nf mirij`f. k yzfr nf hdirjhf k infz}hjhmfm mi ekrgf zhgbúnhjfz. `fx vyi zinijjhkdfr nfz gfrjfz mi uirhehjfjhúd jkrrizskdmhid}iz$
Ufnkriz id syd}kz jkdjri}kz Jk}f
Jfgsk
3$333333 3
Jkr}fd}i
6$1==800i/33:
Enij} kr
3$333333i/333
Ahrk
'6$5::115i' 335
E nij`f
3$333333i/333
Sfrf uir nkz aræehjkz iz dijizfrhk yd dfuiafmkr jkgsf}hbni jkd in ekrgf}k zua. jkgk Gk|hnnf Ehriekp. Ksirf. Gk|hnnf id uirzhúd jkd ZUA. Zif Gkdoix. k jkd fnaydf ip}idzhúd vyi nk sirgh}f uhzyfnh|fr. jkgk nf mi Fmkbi sfrf Hd}irdi} Ipsnkrir$ Hdekrgi jrifmk skr PUHAFZ u3$32e
E<+2363+Mfuhm Ayfmfrrfgf+]':+]':$@]G
1+1
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF UHAF JKDKJHMKZ U X G UIRZHKD 6$33 38+39+2363 JKDEKRGI F NFZ D]J'ME. GÈPHJK FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ
lkuhgijfCagfhn$jkg
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ
MF]KZ
DKGBRI MI NF UHAF →
rijybrhghid}k → fn}yrf mi nf uhaf → fdj`k mi nf uhaf → rizhz}idjhf min jkdjri}k →
]':
↓ iz}i iz in dkgbri vyi nniuf id in snfdk
m
7
:8
r sirfn}i "`" b
7 7 7
2 =3 62
E!j
7
EX
7
=.233$33
7
3$33:
jyfd} hf hf skr }i gs gsi rf rf }y }yrf
EFJ]KR MI RIMYJJHKD F ENIPHKD Er E$ MI RIMYJJHKD F JKR]FD]I Er
233 293
293$33
7 7
3$83 3$03
7 7
653$33 6:5$33
jg ↓ iz in ufnkr mi ` ' r jg ↓ rijybrhghid}k min fjirk f }idzhkd jg ↓ zi rijkghidmf in 63) min nfrak mi nf uhaf N jg ↓ zi rijkghidmf nf gh}fm mi ` 6 ↓ Izjkahz}i nf ksjhkd → oa+jg2 oa+jg2
↓
233 oa+jg2
rizhz}idjhf min fjirk
→
3$332 zh nf uhaf dk iz}f f nf hd}igsirhi
→
3$33: zh nf uhaf iz}f f nf hd}igsirhi
jfnjynk mi jkdz}fd}iz e,j e"j
oa+jg2 oa+jg2
e,j73$03 E!j e"j73$09 e , j
NF JFRAF GYIR]F HDJNYXI IN SIZK SRKSHK MI NF UHAF
JFNJYNK MIN SKRJID]FLI BFNFDJIFMK MI FJIRK sb
7
3$3692
sgfp
7
3 $3 6 6 = :
sgfp73$19psb
sghd
7
3 $3 3 2 5 =
sghd7(3$1 p rfh| e ! j + Ex
sb7(e"j + Ex p (=033 + (5333 / Ex ↓
19) min sb
6
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggfp
7
5.:51$81 oa'g
DIAF]HUK
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$3390=8018 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
3$3390=8018 p 633 →
v ' 2v /
2f
f7 b7 j7
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
5.:51$81 7 JIRK 2.611.620$03 3$3390=8018 7 JIRK
3$90=801080
633 iz skr N7633 jg v6 7
6$5==26
'b / ∜(b 2 '=fj
v2 7
3 $: 9 9 1 8
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36692 sfrf mhgidzhkdfr
7
3 $3 6 6 = :
Riuhzhúd mi S gfp x S ghd s gf p
s7v2 p (e"j + Ex
↓ zi fsnhjk iz}f ekrgynf
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggfp
7
5.:51$81 oa'g
DIAF]HUK
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$3390=8018 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
v ' 2v /
5.:51$81 7 JIRK 2.611.620$03 3$3390=8018 7 JIRK
2f
f7 b7 j7
3$3390=8018 p 633 →
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
3$90=801080
633 iz skr N7633 jg v6 7
6$5==26
'b / ∜(b 2 '=fj
v2 7
3 $: 9 9 1 8
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36692 sfrf mhgidzhkdfr
7 7
3 $3 6 6 = : 3 $3 3 2 5 =
↓ zi fsnhjk iz}f ekrgynf
s7v2 p (e"j + Ex
Riuhzhúd mi S gfp x S ghd s gf p s ghd s s
s gfp s ghd
≭ ≩ 3$36692 ≭ 3$36692 ≩
IZ HDJKRRIJ]K '4 IZ JKRRIJ]K '4
3$366=: → Zhigsri zi mibid uirhehjfr iz}fz mizhayfnmfmiz 3$3325=
zh zi jygsnid izkz 2 sfrfgi}rkz. iz ydf uhaf jkd fjirk bfnfdjifmk fn 19)
2
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
9$:2
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz = '
dygirk = 7 3 7 ∖7
jg2
Fz7spbpm
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
9$31 '
jg2 jg2
9 31
jg2
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
2 g j d i f i r F
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
9$:2
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz = '
jg2
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
dygirk = 7 3 7 ∖7
9$31 '
jg2 jg2
9$31
jg2
9$31 ≀
9$:2
zfjfmk mi nf }fbnf (s ehdfn →
Fz7spbpm
↓ in
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
2 g j d i f i r F
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
}ikrhjk dijizfrhk
↚
Iz}i ufnkr mibi zir zhigsri nhairfgid}i hdeirhkr k sfrijhmk
RIUHZFGKZ IN S EHDFN JKRRIJ]K 4
s ehdfn
7
3 $3 6 3 8 1
s ehdfn7Fz+(bpm JKRRIJ]K 4
:
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332
ufrhnnfz 2 ' '
jyfd}hf
7
3$33:
F!z
7
6$:8
jg
dygirk = 7 7 ∖7
2$9: ' 2$9:
jg2 jg2
2$9: ≀
6$:8
Fz7bpmpjyfd}hf
jg2
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf
66.55=$85
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
3$36381 ≭ 3$36381 ≩
3$366=: 3$3325=
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332
ufrhnnfz 2 ' '
jyfd}hf
7
3$33:
F!z
7
6$:8
jg
dygirk = 7 7 ∖7
2$9: ' 2$9:
jg2 jg2
2$9: ≀
6$:8
Fz7bpmpjyfd}hf
jg2
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
66.55=$85
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf Ujr
7
6.853$9:
oa
Fi Ex iz}rhbk
7 7
3$5: 2.:33$33
jg oa+jg
jænjynk mi nf zisfrfjhkd mi iz}rhbkz
Z6
7
Z2 Z: Z=
7 7 7
' ' '
=$52
jg
22$08 22$08 22$08
jg jg jg
↓ ↓
Frif mi nf ufrhnnf vyi yzfrigkz jkgk iz}rhbk p 2 rfgfz Rizhz}idjhf Rizhz}idjhf mi izf ufrhnnf$ Fnfgbr d72:33? ufrhnnf7=23 ufrhnnf7=233 3
Z7(ErpFipEipm+(Uy'Ujr
=
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
sirfn}i ` bfzi b rijybrhghid}k r
7
]' :
7 7 7
=3$33 62$33 6$93
jg jg jg
dygirk mi shi|fz
7
dygirk mi ufrhnnf
= '
* *
= 3
2 '
* *
= '
dygirk mi shi|fz
7
DK]F< In Uy zi jkduhir}i id in S. vyi iz nf jfraf jkd vyi zi jfnjynfd nfz jknygdfz
DIAF]HUK
dygirk mi ufrhnnf
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
7
sirfn}i ` bfzi b rijybrhghid}k r
]' :
7 7 7
=3$33 62$33 6$93
jg jg jg
dygirk mi shi|fz
7
dygirk mi ufrhnnf
= '
* *
= 3
7
2 '
* *
= '
7 7
fnfgbrkd 9
jg
dygirk mi shi|fz
Iz}rhbkz min dygirk Zisfrfjhúd mi iz}rhbkz
DIAF]HUK
dygirk mi ufrhnnf
zisfrfjhúd id nkz ip}rigkz mi nf uhaf
9
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF UHAF ZHGSNIGID]I FSKXFMF UIRZHKD 6$63 60+63+2330 JKDEKRGI F NFZ D]J'ME. GÈPHJK FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ
JKD JFRAF YDHEKRGIGID]I RISFR]HMF
lkuhgijfC`k}gfhn$jkg
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ
MF]KZ
DKGBRI MI NF UHAF →
rijybrhghid}k → fn}yrf mi nf uhaf → fdj`k mi nf uhaf → Nfrak mi nf uhaf → jfraf ydhekrgi q → rizhz}idjhf min jkdjri}k →
]'=
↓ iz}i iz in dkgbri vyi nniuf id in snfdk
m
7
:8
r sirfn}i "`" b
7 7 7
2 =3 62
Nkd a Q E!j
7 7 7
=$63 2.5=5$:2 293$33
EX
7
=.233$33
7
3$33:
jyfd}hf skr }igsirf}yrf
EFJ]KR MI RIMYJJHKD F ENIPHKD Er E$ MI RIMYJJHKD F JKR]FD]I Er
233 293
jg ↓ iz in ufnkr mi ` ' r jg ↓ rijybrhghid}k min fjirk f }idzhkd jg ↓ zi rijkghidmf in 63) min nfrak mi nf uhaf N jg ↓ zi rijkghidmf nf gh}fm mi ` g oa$g oa+jg2 6 ↓ Izjkahz}i nf ksjhkd → oa+jg2
↓
rizhz}idjhf min fjirk
→
3$332 zh nf uhaf dk iz}f f nf hd}igsirhi
→
3$33: zh nf uhaf iz}f f nf hd}igsirhi
7 7
3$83 3$03
7 7
653$33 6:5$33
oa+jg2 oa+jg2
62 3 3
g
jfnjynk mi jkdz}fd}iz e,j e"j
NF JFRAF GYIR]F HDJNYXI IN SIZK SRKSHK MI NF UHAF JFNJYNK MIN SIZK MI NF UHAF MI JKDJRI]K b
7
e,j73$03 E!j e"j73$09 e , j
233 oa+jg2
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF UHAF ZHGSNIGID]I FSKXFMF UIRZHKD 6$63 60+63+2330 JKDEKRGI F NFZ D]J'ME. GÈPHJK FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ
JKD JFRAF YDHEKRGIGID]I RISFR]HMF
lkuhgijfC`k}gfhn$jkg
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ
MF]KZ
DKGBRI MI NF UHAF →
rijybrhghid}k → fn}yrf mi nf uhaf → fdj`k mi nf uhaf → Nfrak mi nf uhaf → jfraf ydhekrgi q → rizhz}idjhf min jkdjri}k →
]'=
↓ iz}i iz in dkgbri vyi nniuf id in snfdk
m
7
:8
r sirfn}i "`" b
7 7 7
2 =3 62
Nkd a Q E!j
7 7 7
=$63 2.5=5$:2 293$33
EX
7
=.233$33
7
3$33:
jyfd}hf skr }igsirf}yrf
EFJ]KR MI RIMYJJHKD F ENIPHKD Er E$ MI RIMYJJHKD F JKR]FD]I Er
233 293
jg ↓ iz in ufnkr mi ` ' r jg ↓ rijybrhghid}k min fjirk f }idzhkd jg ↓ zi rijkghidmf in 63) min nfrak mi nf uhaf N jg ↓ zi rijkghidmf nf gh}fm mi ` g oa$g oa+jg2 6 ↓ Izjkahz}i nf ksjhkd → oa+jg2
↓
rizhz}idjhf min fjirk
→
3$332 zh nf uhaf dk iz}f f nf hd}igsirhi
→
3$33: zh nf uhaf iz}f f nf hd}igsirhi
7 7
3$83 3$03
7 7
653$33 6:5$33
oa+jg2 oa+jg2
233 oa+jg2
jfnjynk mi jkdz}fd}iz e,j e"j
e,j73$03 E!j e"j73$09 e , j
NF JFRAF GYIR]F HDJNYXI IN SIZK SRKSHK MI NF UHAF JFNJYNK MIN SIZK MI NF UHAF MI JKDJRI]K b ` b p ` p 2= 3 3
7 7 7
62$33 =3$33 669$23
g g oa+g
→
Qy
7
2.156$92
oa+g
→
7
9.032$5=
oa'g
JFNJYNK MIN GKGID]K GFPHGK Ggfp
sizk srkshk mi nf uhaf jfraf Q / in sizk srkshk mi nf uhaf
Ggfp7(q p Nkda p Nkda + 0
JFNJYNK MIN SKRJID]FLI BFNFDJIFMK MI FJIRK sb
7
3$3692
sgfp
7
3 $3 6 6 = :
sgfp73$19psb
sghd
7
3 $3 3 2 5 =
sghd7(3$1 p rfh| e ! j + Ex
sb7(e"j + Ex p (=033 + (5333 / Ex ↓
19) min sb
6
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggf p
7
9.032$5= oa'g
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$339::39=1 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
3$339::39=1 p 633 → 633 iz skr N7633 jg
v ' 2v /
2f
f7 b7 j7
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
9.032$5= 7 JIRK 2.611.620$03 7 JIRK 3$339::39=1
3$9::39=168
v6 7
6$50:::
'b / ∜(b 2 '=fj
v2 7
3 $: 6 5 5 1
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36329 sfrf mhgidzhkdfr
7
3 $3 6 6 = :
Riuhzhúd mi S gfp x S ghd s gf p
s7v2 p (e"j + Ex
↓ zi fsnhjk iz}f ekrgynf
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggf p
7
9.032$5= oa'g
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$339::39=1 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
v ' 2v /
9.032$5= 7 JIRK 2.611.620$03 7 JIRK 3$339::39=1
2f
f7 b7 j7
3$339::39=1 p 633 → 633 iz skr N7633 jg
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
3$9::39=168
v6 7
6$50:::
'b / ∜(b 2 '=fj
v2 7
3 $: 6 5 5 1
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36329 sfrf mhgidzhkdfr
7 7
3 $3 6 6 = : 3 $3 3 2 5 =
↓ zi fsnhjk iz}f ekrgynf
s7v2 p (e"j + Ex
Riuhzhúd mi S gfp x S ghd s gf p s ghd
IZ JKRRIJ]K '4 IZ JKRRIJ]K '4
s s
≭ ≩
3$36329 3$36329
≭
s gfp s ghd 3$366=: → Zhigsri zi mibid uirhehjfr iz}fz mizhayfnmfmiz 3$3325=
≩
zh zi jygsnid izkz 2 sfrfgi}rkz. iz ydf uhaf jkd fjirk bfnfdjifmk fn 19)
2
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
=$1=
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz 2 2
dygirk = 7 = 7 ∖7
jg2
Fz7spbpm
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
2$9: 2$9:
jg2 jg2
9 31
jg2
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
2 g j d i f i r F
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
=$1=
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz 2 2
jg2
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
dygirk = 7 = 7 ∖7
2$9: 2$9:
jg2 jg2
9$31
jg2
9$31 ≀
=$1=
zfjfmk mi nf }fbnf (s ehdfn →
Fz7spbpm
↓ in
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
2 g j d i f i r F
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
}ikrhjk dijizfrhk
↚
Iz}i ufnkr mibi zir zhigsri nhairfgid}i hdeirhkr k sfrijhmk
RIUHZFGKZ IN S EHDFN JKRRIJ]K 4
s ehdfn
7
3 $3 6 3 8 1
s ehdfn7Fz+(bpm JKRRIJ]K 4
:
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332
ufrhnnfz 2 ' '
jyfd}hf
7
3$33:
F!z
7
6$:8
jg
dygirk : 7 7 ∖7
6$=: '
jg2 jg2
6$=:
jg2
6$=: ≀
6$:8
Fz7bpmpjyfd}hf
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf
9.556$62
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
3$36381 3$36381
≭ ≩
3$366=: 3$3325=
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332 jyfd}hf
7
3$33:
F!z
7
6$:8
jg
dygirk : 7 7 ∖7
6$=: '
jg2 jg2
6$=:
jg2
6$=: ≀
6$:8
ufrhnnfz 2 ' '
Fz7bpmpjyfd}hf
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
9.556$62
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf Ujr
7
6.853$9:
oa
Fi Ex iz}rhbk
7 7
3$5: 2.:33$33
jg oa+jg
jænjynk mi nf zisfrfjhkd mi iz}rhbkz
Z6
7
62$62
jg
Z2 Z: Z=
7 7 7
2=$1= 563$91 22$08
jg jg jg
' '
↓ ↓
Frif mi nf ufrhnnf vyi yzfrigkz jkgk iz}rhbk p 2 rfgfz Rizhz}idjhf Rizhz}idjhf mi izf ufrhnnf$ Fnfgbr d72:33? ufrhnnf7=23 ufrhnnf7=233 3
Z7(ErpFipEipm+(Uy'Ujr
=
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
7
]' =
sirfn}i ` bfzi b rijybrhghid}k r Nkdah}ym mi uhaf
7 7 7 7
Ufrhnnfz mi nij`k hdeirhkr
7
Ufrhnnf mi nij`k zysirhkr
7
=3$33 62$33 6$93 =$63
jg jg jg g
dygirk mi shi|fz
dygirk mi ufrhnnf
2 2
* *
= =
2 '
* *
: '
dygirk mi shi|fz
dygirk mi ufrhnnf
DK]F< In Uy zi jkduhir}i id in S. vyi iz nf jfraf jkd vyi zi jfnjynfd nfz jknygdfz
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
7
]' =
sirfn}i ` bfzi b rijybrhghid}k r Nkdah}ym mi uhaf
7 7 7 7
Ufrhnnfz mi nij`k hdeirhkr
7
Ufrhnnf mi nij`k zysirhkr
Iz}rhbkz min dygirk Zisfrfjhúd mi iz}rhbkz
=3$33 62$33 6$93 =$63
jg jg jg g
dygirk mi shi|fz
dygirk mi ufrhnnf
2 2
* *
= =
7
2 '
* *
: '
7 7
fnfgbrkd 62
jg
dygirk mi shi|fz
dygirk mi ufrhnnf
zisfrfjhúd id nkz ip}rigkz mi nf uhaf
9
3=+63+2363
Uhaf (]'9 ' puhafz
Hdmhji< Uhaf ~ Jfrafz ~ Aræeh ræehjk jk mi jfrafz ~ Rifjjhkdiz ~ Ijyfjhkdiz aidirfniz ~ Jfgskz ~ Izjyfjhkdiz zhgsn zhgsnheh hehfmfz fmfz ~ Aræehjkz ~ Ufnkriz ~ Ufnkriz gæphgkz ~ Mi}fnniz min jænjynk ~ Kb}idir ufnkriz sfrf jyfnvyhir jk}f ~ Ufnkr fnkriz iz id fnaydfz jk}fz
Mf}kz Uhaf Nkdah}ym< Nkdah}ym< 6$:33333 6$:33 333 Fskxk 6 (gúuhn< 3$333333 Fskxk 2 (ehlk< 3$533333 Infz}hjhmfm< Infz}hjhmfm< 2633$333333 2633$33333 3 Hdirjhf< =3333$333333 Ydhmfmiz< Eyir|fz id oae Gkgid}kz id oae Ñ g Nkdah}ymiz id g Ahrkz id rfmhfdiz
lkuhgijfC`k}gfhn$jkg
3=+63+2363
Uhaf (]'9 ' puhafz
Hdmhji< Uhaf ~ Jfrafz ~ Aræeh ræehjk jk mi jfrafz ~ Rifjjhkdiz ~ Ijyfjhkdiz aidirfniz ~ Jfgskz ~ Izjyfjhkdiz zhgsn zhgsnheh hehfmfz fmfz ~ Aræehjkz ~ Ufnkriz ~ Ufnkriz gæphgkz ~ Mi}fnniz min jænjynk ~ Kb}idir ufnkriz sfrf jyfnvyhir jk}f ~ Ufnkr fnkriz iz id fnaydfz jk}fz
Mf}kz Uhaf Nkdah}ym< Nkdah}ym< 6$:33333 6$:33 333 Fskxk 6 (gúuhn< 3$333333 Fskxk 2 (ehlk< 3$533333 Infz}hjhmfm< Infz}hjhmfm< 2633$333333 2633$33333 3 Hdirjhf< =3333$333333 Ydhmfmiz< Eyir|fz id oae Gkgid}kz id oae Ñ g Nkdah}ymiz id g Ahrkz id rfmhfdiz Jrh}irhk Jr h}irhk mi zhadkz<
9
Jkr}fd}iz skzh}h skzh}h ukz
Enij}kriz skzh}hukz
Ahrkz skzh}hukz
Enij`fz skzh}hufz
Izvyigf<
:
=
5
Uknfmh|k< 3$333333 Fskxk gúuhn Ufdk< Ufdk< 3$533333 3$53 3333 Fskxk ehlk Uknfmh|k< 3$133333
Jfrafz Jfrafz syd}yfniz Skzhjhúd
6$:33333
E<+2363+Mfuhm Ayfmfrrfgf+]'9+]'9$@]G
Gfadh}ym
6655=$398913
6+5
3=+63+2363
Uhaf (]'9 ' puhafz
Aræehjk mi nf uhaf 9
:
=
5
Rizyn}fmkz min jænjynk< Rifjjhúd id fskxkz< Fskxk F< '6:530$351:0: Fskxk B< 29212$62589: Jfraf }k}fn< }k}fn< 6655=$398913 6655=$3989 13
Ijyfjhkdiz aidirfniz mi jkr}fd}iz x enij}kriz< Id diark fskxkz x igsk}rfghid}kz. id rklk. jfrafz syd}yfniz. id gkrfmk. gkgid}kz. id dfrfdlf. jfrafz jkd}çdyfz. jkd}çdyfz. x id f|yn. jfrafz ufrhfbniz$
]7 /6:530$351:0:Ñ>\'3$33333343 '29212$62589:Ñ>\'3$5333334 3 /6655=$398913Ñ>\'6$:3333343 G7 '6:530$351:0:Ñ>\'3$3333334 6 /29212$62589:Ñ>\'3$53333346 '6655=$398913Ñ>\'6$:3333346
Jfgskz< Dügirk
3
Mhz}fdjhf%Fdj`yrf Hdhjhk Ehd Fdj`k 3$333333 3$533333 3$533333
E<+2363+Mfuhm Ayfmfrrfgf+]'9+]'9$@]G
2+5
3=+63+2363
6
Uhaf (]'9 ' puhafz
3$533333 6$:33333 3$133333
Ijyfjhkdiz zhgsnhehjfmfz zhgsnhehjfmfz (eúrgynfz (e úrgynfz id eydjhúd mi p< Jfgsk
Jkr}fd}iz Hdhjhk Eúrgynf
Jfgsk
Hdhjhk
Enij}kriz Eúrgynf
3
3$333333
/3$333p2 /3$333p ' 6:530$351
3
3$333333
/3$333p: /3$333p2 /6:530$351p /3$333
6
3$533333
/3$333p2 /3$333p /6655=$353
6
3$533333
/3$333p: /3$333p2 ' 6655=$353p /6965:$215 Enij`fz
Jfgsk
Ahrkz Jfgsk
Hdhjhk
3
6
/3$333333i/333p = /3$333333i/333p : 2 3$533333 /9$0:23:3i/33:p ' 6$965:20i/33=p /=$9=080:i/33: /0$65=0=6i/332
Eúrgynf
3
/3$333333i/333p 9 /3$333333i/333p = ' 2$250366i/33:p: 2 3$333333 /3$333333i/333p /3$333333i/333p /3$333333i/333 /0$65=0=6i/332p /3$333333i/333
6
/3$333333i/333p 9 /3$333333i/333p = /6$8==363i/33:p: ' 2 3$533333 1$9065:0i/33:p /=$9=080:i/33:p ' 8$381855i/332 /0$65=0=6i/332p /3$333333i/333
Eúrgynf
/3$333333i/333p = /3$333333i/333p : ' 2 3$333333 5$03=3:=i/33:p /3$333333i/333p /3$333333i/333 /0$65=0=6i/332
Hdhjhk
Id yd jknkr gæz jnfrk fsfrijid nfz jkdz}fd}iz mi ahrkz x enij`fz< IHA 3 x IHX 3$
Aræehjkz mi izeyir|kz jk}fd}iz. enij}kriz. ahrkz x enij`fz
Aræehjk mi jkr}fd}iz<
E<+2363+Mfuhm Ayfmfrrfgf+]'9+]'9$@]G
:+5
3=+63+2363
Uhaf (]'9 ' puhafz
9
Izjfnf< 6:530$351,H 6:530$351,H,I ,I
:
=
5
Aræehjk mi enij}kriz<
9
Izjfnf< 065=$0=6,H 065=$0=6,H,I ,I
:
=
5
Aræehjk mi ahrkz<
9
Izjfnf< ==83$552,H ==83$552,H,I ,I
: E<+2363+Mfuhm Ayfmfrrfgf+]'9+]'9$@]G
=
5
=+5
3=+63+2363
Uhaf (]'9 ' puhafz
Aræehjk mi enij`fz<
9
Izjfnf< 2=15$558,H 2=15$558,H,I ,I
:
=
5
Jkr}fd}iz % Enij}kriz (ufnkr (uf nkr fsrkphgfmk< Jfgsk
Hdhjhk
Jkr}fd}iz Ufnkr hdhjhfn
Ufnkr ehdfn
Jfgs k
Hdhjhk
Enij}kriz Ufnkr hdhjhfn
Ufnkr ehdfn
3
3$333333 '6:530$351:0: '6:530$351:0: 3
3$333333 3$ 3 $333333
6
3$533333 6655=$398913 6655=$398913
3$533333 065=$0=3::2 '3$333811
Jfgsk
3 6
Ahrkz (zhd mhuhmhr id}ri IH Hdhjhk Ufnkr hdhjhfn Ufnkr ehdfn
6
Jfgs k
' 3 6$5:2850i/33: 6 ' ' 3$533333 6$5:2858i/33: =$=83552i/33:
3$333333 0$65=0=6i/332
065=$0=3023
Enij`fz (zhd mhuhmhr id}ri IH Hdhjhk Ufnkr hdhjhfn Ufnkr ehdfn 3$333333 3$333333i/333 3$333333i/333 3$533333
':$396190i' 33=
' 2$=15558i/33:
Ufnkriz gæphgkz< Gkgid}k gæphgk id nf zijjhúd Skzhjhúd< 3$533333 Gfadh}ym< 065=$0=3023 Gfxkr ufnkr min izeyir|k jkr}fd}i Skzhjhúd< 3$333333 Gfadh}ym< '6:530$351:0: Gfxkr ufnkr min ahrk (zhd mhuhmhr id}ri I,H Skzhjhúd< 6$:33333 Gfadh}ym< '==83$552638 Gfxkr ufnkr miekrgfjhúd (zhd mhuhmhr id}ri I,H Skzhjhúd< 6$:33333 Gfadh}ym< '2=15$558608 E<+2363+Mfuhm Ayfmfrrfgf+]'9+]'9$@]G
9+5
3=+63+2363
Uhaf (]'9 ' puhafz
Mi}fnniz min jænjynk< Zygf mi gkgid}kz id in fskxk F< ∖ G F 7 3 7 /065=$0=3023 /3$533333 Rb Zygf mi gkgid}kz id in fskxk B< ∖ G B 7 3 7 /6965:$211:== '3$533333 Rb
Mfr ufnkriz Jk}f< mhz}fdjhf Jfnjynfr
Byzjfr j Byzjfr m i e a
ufnkriz u fnkriz skr nf mirij` mirij`ff j Infz}hjhmfm skr ufnkr zhgbúnhjk m i e a Hdirjhf skr s kr ufnkr zhgbúnh zhgbúnhjk jk j Hdirjhf m i e a
Sfrf kb}idir nkz ufnkriz mi nfz eydjhkdiz id yd syd}k jyfnvyhirf `fx vyi hd}rkmyjhr nf jk}f min syd}k x synzfr jfnjynfr$ Sfrf byzjfr ufnkriz mi nf mirij`f. k yzfr nf hdirjhf k infz}hjhmfm mi ekrgf zhgbúnhjfz. `fx vyi zinijjhkdfr nfz gfrjfz mi uirhehjfjhúd jkrrizskdmhid}iz$
Ufnkriz id syd}kz jkdjri}kz Jk}f
Jfgs k
3$333333 3
Jkr}fd}i
Enij}kr
'6$:53031i/33= 3$333333i/333
Ahrk
Enij`f
8$1233=8i'339 3$333333i/333
Sfrf uir nkz aræehjkz iz dijizfrhk yd dfuiafmkr jkgsf}hbni jkd in ekrgf}k zua. jkgk Gk|hnnf Ehriekp. Ksirf. Gk|hnnf id uirzhúd jkd ZUA. Zif Gkdoix. k jkd fnaydf ip}idzhúd vyi nk sirgh}f uhzyfnh|fr. jkgk nf mi Fmkbi sfrf Hd}irdi} Ipsnkrir$ Hdekrgi jrifmk skr sk r PUHAFZ PUHAFZ u3$32e
E<+2363+Mfuhm Ayfmfrrfgf+]'9+]'9$@]G
5+5
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF UHAF JKDKJHMKZ U X G UIRZHKD 6$33 38+39+2363 JKDEKRGI F NFZ D]J'ME. GÈPHJK FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ
lkuhgijfCagfhn$jkg
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ
MF]KZ
DKGBRI MI NF UHAF →
rijybrhghid}k → fn}yrf mi nf uhaf → fdj`k mi nf uhaf → rizhz}idjhf min jkdjri}k →
]'9
↓ iz}i iz in dkgbri vyi nniuf id in snfdk
m
7
:8
r sirfn}i "`" b
7 7 7
2 =3 69
E!j
7
EX
7
=.233$33
7
3$33:
jyfd} hf hf skr }i gs gsi rf rf }y }yrf
EFJ]KR MI RIMYJJHKD F ENIPHKD Er E$ MI RIMYJJHKD F JKR]FD]I Er
233 293
293$33
7 7
3$83 3$03
7 7
653$33 6:5$33
jg ↓ iz in ufnkr mi ` ' r jg ↓ rijybrhghid}k min fjirk f }idzhkd jg ↓ zi rijkghidmf in 63) min nfrak mi nf uhaf N jg ↓ zi rijkghidmf nf gh}fm mi ` 6 ↓ Izjkahz}i nf ksjhkd → oa+jg2 oa+jg2
↓
233 oa+jg2
rizhz}idjhf min fjirk
→
3$332 zh nf uhaf dk iz}f f nf hd}igsirhi
→
3$33: zh nf uhaf iz}f f nf hd}igsirhi
jfnjynk mi jkdz}fd}iz e,j e"j
oa+jg2 oa+jg2
e,j73$03 E!j e"j73$09 e , j
NF JFRAF GYIR]F HDJNYXI IN SIZK SRKSHK MI NF UHAF
JFNJYNK MIN SKRJID]FLI BFNFDJIFMK MI FJIRK sb
7
3$3692
sgfp
7
3 $3 6 6 = :
sgfp73$19psb
sghd
7
3 $3 3 2 5 =
sghd7(3$1 p rfh| e ! j + Ex
sb7(e"j + Ex p (=033 + (5333 / Ex ↓
19) min sb
6
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggfp
7
0.65=$0= oa'g
DIAF]HUK
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$335333==5 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
3$335333==5 p 633 →
v ' 2v /
2f
f7 b7 j7
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
0.65=$0= 7 JIRK 2.126.=66$33 3$335333==5 7 JIRK
3$5333==538
633 iz skr N7633 jg v6 7
6$5:2=2
'b / ∜(b 2 '=fj
v2 7
3 $: 5 1 9 0
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36683 sfrf mhgidzhkdfr
7
3 $3 6 6 = :
Riuhzhúd mi S gfp x S ghd s gf p
s7v2 p (e"j + Ex
↓ zi fsnhjk iz}f ekrgynf
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK
Ggfp
7
0.65=$0= oa'g
DIAF]HUK
Gr7ErpBpmpmpe"jpvp(6'3$9pv 2
v ' 2v / vT2 ' 2 v /
3$335333==5 7
fpT2
j
/ bp /
7
ER,b,m ,E‗j 3 p 7 'b ¶ ∜(b '=fj
3
Rizknuhidmk nf ijyfjhkd jyfmrf}hjf aidirfn
v ' 2v /
0.65=$0= 7 JIRK 2.126.=66$33 3$335333==5 7 JIRK
2f
f7 b7 j7
3$335333==5 p 633 →
GR[[[[ 7 3 2
Mizsilfdmk v x zhayhidmk in srkjimhghid}k f nf mirij`f
2
6 $3 3 3 2 $3 3 3
'
'3$9 v / v '
3$5333==538
633 iz skr N7633 jg v6 7
6$5:2=2
'b / ∜(b 2 '=fj
v2 7
3 $: 5 1 9 0
'b ' ∜(b 2 '=fj
2f Zi yzf iz}i ufnkr →
s
7
2f 3$36683 sfrf mhgidzhkdfr
7 7
3 $3 6 6 = : 3 $3 3 2 5 =
↓ zi fsnhjk iz}f ekrgynf
s7v2 p (e"j + Ex
Riuhzhúd mi S gfp x S ghd s gf p s ghd s s
s gfp s ghd
≭ ≩ 3$36683 ≭ 3$36683 ≩
IZ HDJKRRIJ]K '4 IZ JKRRIJ]K '4
3$366=: → Zhigsri zi mibid uirhehjfr iz}fz mizhayfnmfmiz 3$3325=
zh zi jygsnid izkz 2 sfrfgi}rkz. iz ydf uhaf jkd fjirk bfnfdjifmk fn 19)
2
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
5$01
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz = 2
dygirk = 7 : 7 ∖7
jg2
Fz7spbpm
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
9$31 6$=:
jg2 jg2
5 =8
jg2
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
2 g j d i f i r F
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK ID ]IDZHKD
Iz}i fjirk fbzkrbirf nf eniphúd mi nf uhaf x zi idjyid}rf id in nij`k hdeirhkr
Fz fnfgbrúd → Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
7
5$01
3 $: 6 1
3$5::
3$893
6$251
6
2
:
=
3 $1 6 : 6 $2 5 1 6 $8 1 8 2 $0 9 3 : $0 1 8 9 $3 5 1 5 $= 6 : 1 $8 6 1 66$:=6
6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
2$093 9$351 1$861 66$=36 69$960 23$250 29$592 :6$558 =9$:5=
ufrhnnfz = 2
jg2
Dügirk mi ufrhnnfz 9 5
: $9 5 : 5 $: : = 8 $0 8 1 6=$296 68$:81 29$::9 :2$359 :8$901 95$139
dygirk = 7 : 7 ∖7
9$31 6$=:
jg2 jg2
5$=8
jg2
5$=8 ≀
5$01
zfjfmk mi nf }fbnf (s ehdfn →
Fz7spbpm
↓ in
= $2 1 9 1 $5 3 6 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5 ↓ fvyç ↓ fvyç
1
0
8
=$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
9$133 63$6:= 69$0:9 2 2 $0 3 2 : 6 $3 : 5 =3$9:1 96$:3= 5:$::0 8 3 $1 2 0
5$=6: 66$=36 61$06= 29$592 : = $8 6 9 =9$53= 91$161 16$295 6 3 2 $3 5 8
2 g j d i f i r F
izjklk nkz ufnkriz mi nf }fbnf mi frrhbf izjklk nkz ufnkriz mi nf }fbnf mi frrhbf
}ikrhjk dijizfrhk
↚
Iz}i ufnkr mibi zir zhigsri nhairfgid}i hdeirhkr k sfrijhmk
RIUHZFGKZ IN S EHDFN JKRRIJ]K 4
s ehdfn
7
3 $3 6 6 2 =
s ehdfn7Fz+(bpm JKRRIJ]K 4
:
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332
ufrhnnfz 2 ' '
jyfd}hf
7
3$33:
F!z
7
6$1:
jg
dygirk = 7 7 ∖7
2$9: ' 2$9:
jg2 jg2
2$9: ≀
6$1:
Fz7bpmpjyfd}hf
jg2
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf
6:.530$31
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
3$3662= ≭ 3$3662= ≩
3$366=: 3$3325=
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK SKR ]IGSIRF]YRF
Iz}i fjirk zi idjyid}rk id in nij`k zysirhkr Zh nf uhaf zi idjyid}rf ipsyiz}f f nf hd}idsirhi zi yzfrf 3$33: Zh nf uhaf zi idjyid}rf srk}iahmf mi nf hd}igsirhi zi yzfrf 3$332
ufrhnnfz 2 ' '
jyfd}hf
7
3$33:
F!z
7
6$1:
jg
dygirk = 7 7 ∖7
2$9: ' 2$9:
jg2 jg2
2$9: ≀
6$1:
Fz7bpmpjyfd}hf
jg2
Zh in sirfn}i ribfzf nkz 19 jg. zi jknkjfrf id gimhk mi iz}i. fjirk skr }igsirf}yrf sfrf iuh}fr farhi}fghid}k id nf uhaf JFNJYNK MI NKZ IZ]RHBKZ
Nkz iz}rhbkz fbzkrbid nfz eyir|fz jkr}fd}iz aidirfmfz fn hd}irhkr mi nf uhaf jfnjynk mi nf eyir|f jkr}fd}i mi nf uhaf zhgsnigid}i fskxfmf Uy
7
6:.530$31
oa
Eyir|f jkr}fd}i Uy7(QypNkda+2 zh s ≭ 3$369
jfnjynk mi nf eyir|f jkr}fd}i vyi }kgf in jkdjri}k id nf uhaf Ujr
7
2.=02$13
oa
Fi Ex iz}rhbk
7 7
3$5: 2.:33$33
jg oa+jg
jænjynk mi nf zisfrfjhkd mi iz}rhbkz
Z6
7
Z2 Z: Z=
7 7 7
' ' '
=$3:
jg
60$31 60$31 60$31
jg jg jg
↓ ↓
Frif mi nf ufrhnnf vyi yzfrigkz jkgk iz}rhbk p 2 rfgfz Rizhz}idjhf Rizhz}idjhf mi izf ufrhnnf$ Fnfgbr d72:33? ufrhnnf7=23 ufrhnnf7=233 3
Z7(ErpFipEipm+(Uy'Ujr
=
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
sirfn}i ` bfzi b rijybrhghid}k r
7
]' 9
7 7 7
=3$33 69$33 6$93
jg jg jg
dygirk mi shi|fz
7
dygirk mi ufrhnnf
= 2
* *
= :
2 '
* *
= '
dygirk mi shi|fz
7
DK]F< In Uy zi jkduhir}i id in S. vyi iz nf jfraf jkd vyi zi jfnjynfd nfz jknygdfz
DIAF]HUK
dygirk mi ufrhnnf
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ VYI ZI MHBYLFRFD ID IN SNFDK
DKGBRI MI NF UHAF
7
sirfn}i ` bfzi b rijybrhghid}k r
]' 9
7 7 7
=3$33 69$33 6$93
jg jg jg
dygirk mi shi|fz
7
dygirk mi ufrhnnf
= 2
* *
= :
7
2 '
* *
= '
7 7
fnfgbrkd =
jg
dygirk mi shi|fz
Iz}rhbkz min dygirk Zisfrfjhúd mi iz}rhbkz
DIAF]HUK
dygirk mi ufrhnnf
zisfrfjhúd id nkz ip}rigkz mi nf uhaf
9
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF JKNYGDF RIJ]FDAYNFR F JKGSRIZHÚD ZHGSNI UIRZHKD 6$6 63'Dku'30 JKDEKRGI F NFZ D]J'3=. GÈPHJK FY]KR< FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ MF]KZ Dkgbri mi nf jknygdf Nkdah}ym mi nf jknygdf N 7 Jfraf Sy 7 Rizhz}idjhf min jkdjri}k E!j 7
lkuhgijfC`k}gfhn$jkg
O'6 209 1.0:8
→ → →
→
Rizhz}idjhf min fjirk
→
Ex
7
b
7
`
7
Rijybrhghid}k r
7 7
m
693 233
izjkahk ksjhkd * 6
oa+jg2
izjkahk ksjhkd * 6
jg
izjkahk ksjhkd * 6
jg
izjkahk ksjhkd * :
693
=233 9333
=233
62 69
62
69 23
yz}im zinijjhkdk nf zhayhid}i zijjhúd<
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ jg oa oa+jg2
23 6$93 60$93
jg jg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YDF JKNYGDF RIJ]FDAYNFR F JKGSRIZHÚD ZHGSNI UIRZHKD 6$6 63'Dku'30 JKDEKRGI F NFZ D]J'3=. GÈPHJK FY]KR< FRV$ LKZÈ UHJ]KR GIDIZIZ JFGSKZ MF]KZ Dkgbri mi nf jknygdf Nkdah}ym mi nf jknygdf N 7 Jfraf Sy 7 Rizhz}idjhf min jkdjri}k E!j 7
lkuhgijfC`k}gfhn$jkg
O'6 209 1.0:8
→ → →
→
Rizhz}idjhf min fjirk
→
Ex
7
b
7
`
7
Rijybrhghid}k r
7 7
m
NFZ JINMFZ FGFRHNNFZ ZKD NFZ VYI ZI NNIDFD JKD MF]KZ
693 233
izjkahk ksjhkd * 6
oa+jg2
izjkahk ksjhkd * 6
jg
izjkahk ksjhkd * 6
jg
izjkahk ksjhkd * :
693
=233 9333
=233
62 69
62
69 23
yz}im zinijjhkdk nf zhayhid}i zijjhúd< 62 p Frif Frif Fj 7
jg oa oa+jg2
23 6$93 60$93
jg jg
23 2=3
jg2 A
EFJ]KR MI RIMYJJHKD F ENIPHKD Er E$ MI RIMYJJHKD F JKR]FD]I Er
7 7
3$83 3$03
7 7
623$33 632$33
jfnjynk mi jkdz}fd}iz e,j e"j
oa+jg2 oa+jg2
e,j73$03 E!j e"j73$09 e , j
6
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK Rieyir|k gçdhgk x gæphgk f eniphúd
jyfd}hf mi fjirk
→
gçdhgk gæphgk srkgimhk
7 7 7
3$3633 3$3=33 3$3293
::)
7
3$3619
55)
7
3$3:29
s
7
3$3:29
Fz
7
1$03
jg2
Fz7spbpm
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NF JYFD]HF MI FJIRK Rieyir|k gçdhgk x gæphgk f eniphúd
jyfd}hf mi fjirk
gçdhgk gæphgk srkgimhk
7 7 7
3$3633 3$3=33 3$3293
::)
7
3$3619
55)
7
3$3:29
s
7
3$3:29
Fz
7
1$03
→
jg2
Fz7spbpm
2
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK fnfgbrúd Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
→
3$:61
3$5::
3$893
6 3$16: 6$251 6$818 2$093 :$018 9$351 5$=6: 1$861 66$:=6
2 6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
: 2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
ufrhnnfz
ufrhnnf *
:
:
=
=
ufrhnnfz
6$251 Dügirk mi ufrhnnfz = 9 2$093 :$95: 9$351 5$::= 1$861 8$081 66$=36 6=$296 69$960 68$:81 23$250 29$::9 29$592 :2$359 :6$558 :8$901 =9$:5= 95$139
5 =$219 1$536 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5
JFD]$ UFRHNNFZ
* EHNF
UFRHNNF *
:
2
=
1 =$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01 FRIF MI UFRHNNF
:$033 ↖
ufrhnnf *
JFD]$ UFRHNNFZ
* EHNF
UFRHNNF *
0 9$133 63$6:= 69$0:9 22$032 :6$3:5 =3$9:1 96$:3= 5:$::0 83$120
JKSHFR UFNKR MI NF ]FBNF
FRIF MI UFRHNNF
8 5$=6: 66$=36 61$06= 29$592 :=$869 =9$53= 91$161 16$295 632$358
2 g j d i f i r F
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MIN FJIRK fnfgbrúd Dk$ Mi ufrhnnf ↚ : = 9 5 1 0 8 63 62
→
3$:61
3$5::
3$893
6 3$16: 6$251 6$818 2$093 :$018 9$351 5$=6: 1$861 66$:=6
2 6$=29 2$9:= :$898 9$133 1$198 63$6:= 62$025 69$0:9 22$502
: 2$6:0 :$033 9$8:0 0$996 66$5:0 69$236 68$2:8 2:$192 :=$32:
ufrhnnfz
ufrhnnf *
:
:
=
=
ufrhnnfz :
=
=
5 =$219 1$536 66$015 61$636 2:$211 :3$=32 :0$=10 =1$93= 50$3=5
JFD]$ UFRHNNFZ
* EHNF
UFRHNNF *
:
2
=
1 =$800 0$051 6:$099 68$892 21$695 :9$=13 ==$086 99$=26 18$:01
JFD]$ UFRHNNFZ
* EHNF
UFRHNNF *
:
2
=
2 g j d i f i r F
JKSHFR UFNKR MI NF ]FBNF
FRIF MI UFRHNNF
:$033 JKSHFR UFNKR MI NF ]FBNF
zygf mi ufrhnnfZ jfnjynfmf skr jyfd}çf
>
8 5$=6: 66$=36 61$06= 29$592 :=$869 =9$53= 91$161 16$295 632$358
:$033
↖
1$53
0 9$133 63$6:= 69$0:9 22$032 :6$3:5 =3$9:1 96$:3= 5:$::0 83$120
FRIF MI UFRHNNF ↖
ufrhnnf *
:
6$251 Dügirk mi ufrhnnfz = 9 2$093 :$95: 9$351 5$::= 1$861 8$081 66$=36 6=$296 69$960 68$:81 23$250 29$::9 29$592 :2$359 :6$558 :8$901 =9$:5= 95$139
1$03 SKR NK ]FD]K IZ<
:
Fz 7 Fz 7
1$53 1$03
HDJKRRIJ]K RIUHZFR JRH]IRHK
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NKZ IZ]RHBKZ rizhz}idjhf min fjirk
Mhægi}rk min iz}rhbk
→
EX
7
7
→
2:33
oa+jg2
=233
izjkahk ksjhkd * 6
2:33
2
* ufrhnnf
2$9
2
izjkahk ksjhkd * 6 Mhægi}rk id jg →
f( b( j( Zisfrfjhkd id}ri iz}rhbkz Zisfrfjhkd id}ri iz}rhbkz f( b( j(
→ →
Z Z Z
7 7 7
6:$62 :3$12 5$33
jg jg jg
Z Z
7 7
5$33 :$33
JG JG
Z id dymkz Z id dymkz Z id dymkz
7 7 7
23$33 =1$93 53$33
jg jg jg
FN JID]RK MI NF JKNYGDF ID NKZ DYMKZ
3$5=
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI NKZ IZ]RHBKZ rizhz}idjhf min fjirk
Mhægi}rk min iz}rhbk
→
EX
7
7
→
2:33
oa+jg2
=233
izjkahk ksjhkd * 6
2:33
2
* ufrhnnf
2$9
2
izjkahk ksjhkd * 6 Mhægi}rk id jg →
f( b( j( Zisfrfjhkd id}ri iz}rhbkz Zisfrfjhkd id}ri iz}rhbkz
7 7 7
6:$62 :3$12 5$33
jg jg jg
Z Z
7 7
5$33 :$33
JG JG
Z id dymkz Z id dymkz Z id dymkz
7 7 7
23$33 =1$93 53$33
jg jg jg
Mhz}fdjhf fn dymk 7
53$33
JG
→ →
f( b( j( Zisfrfjhkd id}ri iz}rhbkz
Z Z Z
→
FN JID]RK MI NF JKNYGDF ID NKZ DYMKZ
ID NKZ DYMKZ
=
lkuhgijfC`k}gfhn$jkg
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ SFRF MHBYLFR ID IN SNFDK
RIZYN]FMKZ FJKGKMK MI IZ]RHBKZ ID JKNYGDFZ
JKNYGDF GIMHMFZ
O '6
Nfmk b Nfmk ` rijybrhghid}k r Nkdah}ym mi nf jknygdf
7 7 7 7
Ufrhnnfz / Ufrhnnfz
7 7
: * = : * = 5 S\FZ MI UFRHNNF
Iz}rhbkz min dügirk Zisfrfjhúd mi iz}rhbkz fn jid}rk Zisfrfjhúd mi iz}rhbkz id dymkz
7 7 7
2 5 :
FRGFMK
IZ]RHBKZ
62 23 6$9 2$09
jg jg jg g
dygirk mi shi|fz
dygirk mi ufrhnnf
FNFGBRKD jg jg
3$5=
Frv$ Lkzè Uhj}kr Gidiziz Jfgskz
JKDJNYZHKDIZ SFRF MHBYLFR ID IN SNFDK
RIZYN]FMKZ FJKGKMK MI IZ]RHBKZ ID JKNYGDFZ
JKNYGDF GIMHMFZ
O '6
Nfmk b Nfmk ` rijybrhghid}k r Nkdah}ym mi nf jknygdf
7 7 7 7
Ufrhnnfz / Ufrhnnfz
7 7
Iz}rhbkz min dügirk Zisfrfjhúd mi iz}rhbkz fn jid}rk Zisfrfjhúd mi iz}rhbkz id dymkz Nkdah}ym mizsyiz mi nkz sfökz
7 7 7 7
FRGFMK
IZ]RHBKZ
62 23 6$9 2$09
jg jg jg g
dygirk mi shi|fz
dygirk mi ufrhnnf
: * = : * = 5 S\FZ MI UFRHNNF 2 5 : 53
FNFGBRKD jg jg jg mkdmi kdmi ufd ufd nkz iz} iz}rhrhbkz b kz jir jirrf rfmk mkzz
9
Frv. Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YD JHGHID]K MI SHIMRF uirzhkd 6$63
68 MI KJ]YBRI MI 2330
FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ JKDEKRGI F NFZ D]J'233=
lkuhgijfC`k}gfhn$jkg ID NKZ IZSFJHKZ FGFRHNNKZ ZI HD]RKMYJID NKZ MF]KZ
MF]KZ BFZHJKZ Jhghid}k S 7
JHG'6 5$:8 }kd+g
x gfgs 7
2.533$33 oa+g: oa+g:
7
Srizhkd mi mhziök vR 7 efj}kr mi jfraf (e$j$ 7 jkrkdf 7
→ →
dkgbri min jhghid}k jfraf vyi rijhbi in jhghid}k
Sizk Sizk mi nf nf shimr shimrff (jfzh (jfzh zhig zhigsr srii jkdz} jkdz}fd fd}i }i
Rizhz}idjhf min }irridk 63$33 }kd+g2 6$63 Uirhehjfr zy ufnkr jkrkdf min jhghid}k 3$:3 g →
→
MHZI MHZI K SKR JKGS JKGSRIZ RIZHKD HKD 7
3$13 g
Bfzi B 7
Frif
3$13 g
Frif 7 (e$j$ p S+vR
lkuhgijfC`k}gfhn$jkg
Frv. Lkzè Uhj}kr Gidiziz Jfgskz
JFNJYNK MI YD JHGHID]K MI SHIMRF uirzhkd 6$63
68 MI KJ]YBRI MI 2330
FY]KR< FRV$ LKZI UHJ]KR GIDIZIZ JFGSKZ JKDEKRGI F NFZ D]J'233=
lkuhgijfC`k}gfhn$jkg ID NKZ IZSFJHKZ FGFRHNNKZ ZI HD]RKMYJID NKZ MF]KZ
MF]KZ BFZHJKZ Jhghid}k S 7
JHG'6 5$:8 }kd+g
x gfgs 7
2.533$33 oa+g: oa+g:
7
Srizhkd mi mhziök vR 7 efj}kr mi jfraf (e$j$ 7 jkrkdf 7
→ →
dkgbri min jhghid}k jfraf vyi rijhbi in jhghid}k
Sizk Sizk mi nf nf shimr shimrff (jfzh (jfzh zhig zhigsr srii jkdz} jkdz}fd fd}i }i
Rizhz}idjhf min }irridk 63$33 }kd+g2 6$63 Uirhehjfr zy ufnkr jkrkdf min jhghid}k 3$:3 g →
→
MHZI MHZI K SKR JKGS JKGSRIZ RIZHKD HKD 7
3$13 g
Bfzi B 7
Frif
3$13 g
Frif 7 (e$j$ p S+vR
JFNJYNK MIN SIRFN]I Bfzi B 7
sirfn}i "`" 7
zi rijkghidmf 6$9 ↚ gçdhgk 6
3$13
3$13 g
sidmhid}i7
`7B,6$9
6
6
l kuhgijfC`k}gfhn$jkg
Frv. Lkzè Uhj}kr Gidiziz Jfgskz
RIUHZHKD SKR JKR]FD]I Jfnjynfdmk jkd gkr}irk > 93 oa+jg2. vyi iz in jfzk gfz mizefukrfbni? u73$= Jhghid}k hd}irgimhk k mi mkbni izjfrshk Ur 7 3$95 >
3$95 3$13
Ur72 p ` p N p u IZ JKRRIJ]K
Jhghid}k mi nhdmirk. jknhdmfd}i k mi yd zknk izjfrshk Ur 7 3$20 >
3$20 3$13
IZ JKRRIJ]K
JKDJNYZHKD VYI ZI MHBYLFRF ID IN SNFDK Dkgbri min jhghid}k 7 jkrkdf 7 bfzi B 7 n} `
JHG'6 3$:3 g 3$13 g 3 13
u73$= N76 zh zi jygsni nf mizhayfnmfm nf fn}yrf ` iz jkrrij}f
Ur7 ` p N p u zh zi jygsni nf mizhayfnmfm nf fn}yrf ` iz jkrrij}f
Frv. Lkzè Uhj}kr Gidiziz Jfgskz
RIUHZHKD SKR JKR]FD]I Jfnjynfdmk jkd gkr}irk > 93 oa+jg2. vyi iz in jfzk gfz mizefukrfbni? u73$= Jhghid}k hd}irgimhk k mi mkbni izjfrshk Ur 7 3$95 >
3$95 3$13
IZ JKRRIJ]K
Jhghid}k mi nhdmirk. jknhdmfd}i k mi yd zknk izjfrshk Ur 7 3$20 >
3$20 3$13
IZ JKRRIJ]K
JKDJNYZHKD VYI ZI MHBYLFRF ID IN SNFDK Dkgbri min jhghid}k 7 jkrkdf 7 bfzi B 7 fn}yrf ` 7
JHG'6 3$:3 g 3$13 g 3$13 g
u73$= N76
Ur72 p ` p N p u
zh zi jygsni nf mizhayfnmfm nf fn}yrf ` iz jkrrij}f
Ur7 ` p N p u zh zi jygsni nf mizhayfnmfm nf fn}yrf ` iz jkrrij}f
2
l kuhgijfC`k}gfhn$jkg
\fsf}f zyli}f f jfraf fphfn
@klf mi Jænjynk vyi zknyjhkdf \fsf}fz jkd jfraf fphfn Mf}kz mi Id}rfmf< S
e M
J2
6 J
Gfadh}ym mi nf jfraf S Arysk fn vyi sir}idiji nf iz}ryj}yrf< Nkdah}ym mi J6< Nkdah}ym mi J2< Srkeydmhmfm mi mizsnfd}i Me< Rizhz}idjhf Rizhz}idjhf min jkdjri}k e!j< Jnfzi min jkdjri}k< Rizhz}idjhf Rizhz}idjhf min fjirk ex< Rizhz}idjhf Rizhz}idjhf min }irridk e }y <
:3$129 b 23 62 6$2 233 2 =233 63
]kd jg jg g 2 Oa+jg 2
Oa+jg
2
]kd+g
6$' Mf}kz mi id}rfmf 2$' Jænjynk min Frif mi nf |fsf}f. Srizhkdiz mi jkd}fj}k x Sirfn}i srinhghdfr :$' Riuhzhúd min Sirfn}i =$' Mhziök skr eniphúd 9$' Rizygid mi nf \fsf}f jkd Jfraf Fphfn
\fsf}f zyli}f f jfraf fphfn
@klf mi Jænjynk vyi zknyjhkdf \fsf}fz jkd jfraf fphfn Mf}kz mi Id}rfmf< S
e M
J2
6 J
Gfadh}ym mi nf jfraf S Arysk fn vyi sir}idiji nf iz}ryj}yrf< Nkdah}ym mi J6< Nkdah}ym mi J2< Srkeydmhmfm mi mizsnfd}i Me< Rizhz}idjhf Rizhz}idjhf min jkdjri}k e!j< Jnfzi min jkdjri}k< Rizhz}idjhf Rizhz}idjhf min fjirk ex< Rizhz}idjhf Rizhz}idjhf min }irridk e }y <
:3$129 b 23 62 6$2 233 2 =233 63
]kd jg jg g 2 Oa+jg 2
Oa+jg
2
]kd+g
6$' Mf}kz mi id}rfmf 2$' Jænjynk min Frif mi nf |fsf}f. Srizhkdiz mi jkd}fj}k x Sirfn}i srinhghdfr :$' Riuhzhúd min Sirfn}i =$' Mhziök skr eniphúd 9$' Rizygid mi nf \fsf}f jkd Jfraf Fphfn Mhziök x infbkrfjhúd<
Akd|fnk Nyak Jry| (88:63319 Lkzè Rklfz Akd|æni| (88:6668=
akd|fnk[nyakC`k}gfhn$jkg akd|fnk[nyak C`k}gfhn$jkg j`isi[j`isi [C`k}gfhn$jkg
Arysk G836 `}}s<++arkysz$gzd$jkg+Iz}ryj}yrfzxjhgid}fjhkdizIZHF'836 `}}s<++arkysz$ gzd$jkg+Iz}ryj}yrfzxjhgid}fjhkdizIZHF'836
@klf srkskrjhkdfmf f<
Akd|fnk Nyak Jry| 88:63319 (akd|fnk[nyakC`k}gfhn$jkg. (akd|fnk[nyakC`k}gfhn$jkg. akd|fnk[nyakC}kmh}k$jkg. Lkzè Rklfz Akd|æni| 88:6668= (j`isi[j`isi[C`k}gf (j`isi[j`isi[C`k}gfhn$jkg hn$jkg
\fsf}f zyli}f f jfraf fphfn
\fsf}f zyli}f f jfraf fphfn
Akd|fnk Nyak Jry| 88:63319 (akd|fnk[nyakC`k}gfhn$jkg. (akd|fnk[nyakC`k}gfhn$jkg. akd|fnk[nyakC}kmh}k$jkg. Lkzè Rklfz Akd|æni| 88:6668= (j`isi[j`isi[C`k}gf (j`isi[j`isi[C`k}gfhn$jkg hn$jkg
6$' Kb}idjhúd min ærif mi nf |fsf}f S y 7 S,EJ 7 S ] 7 S/Q jhgid}fjhúd 7 S ]y 7 S],EJ 7
F | n6
S]
y
7
7
e }y n
2
7
7
2n 2
7
N 7 J 6 / 2n 6
7
B 7 J 2
/
=:$32 :8$8= 99$82
]kd
9$98
g
666
jg
2$:= 2$=2
g g
Hd}rkmy|jf nkz ufnkriz B x N rimkdmifmkz< B7 6$: 6$: N7
]kd ]kd 2
g g
B
N
6$' Kb}idjhúd min ærif mi nf |fsf}f S y 7 S,EJ 7 S ] 7 S/Q jhgid}fjhúd 7 S ]y 7 S],EJ 7
S]
F |
y
7
n6
7
7
e }y n
2
7
2n 2
7
N 7 J 6 / 2n 6
7
B 7 J 2
/
=:$32 :8$8= 99$82
]kd
9$98
g
666
jg
2$:= 2$=2
g g
Hd}rkmy|jf nkz ufnkriz B x N rimkdmifmkz< B7 6$: 6$: N7 n
6$66
7
]kd ]kd 2
B
g g
N
g
2$' Srizhkdiz mi jkd}fj}k
v}y
7
vdy
7
S}y F |
Sy F |
2
7
::$38
]kd+g
7
29$=5
]kd+g
2
:$' Sirfn}i srinhghdfr
G y
m 7
7
v dy n
2
2
G y 6=$0 e ! j
7
/
5jg
7
6950=5:$:
Oa'jg
28$32
jg
Hd}rkmy|jf in ufnkr mi "m" rimkdmifmk m7 :9 =3 `7
jg jg
4
e }y
=$' Riuhzhúd min sirfn}i
99 =1
J 6 / m 7 J 2 / m 7 b3 7 2(J 6 / m / 2(J 2 U y 7 Sy 7 uy 7
U y
/
5$3:
Oa+jg
2
63$62
Oa+jg
2
m 7
23=
7
b3 m
=:$32
jg jg jg ]kd
U JR JR 7 ER e , j
u 4 Srkjimigkz f nf zhayhid}i riuhzhúd$$$
U JR
B
y
º =m
6=3
=m 7
6:3
>
jg jg
6=3
dk zi jygsni. kjysfrigkz nf ijyfjhúd 2$68 ú 2$23 mi nfz D]J'Jkdjri}k
` ª 53jg
=3
`7
=3
>
53
jg jg
zi jygsni nf jkdmhjhúd. iufnyfrigkz nf zhayhid}i$$$ G U d m
ª 2
vdy (n ' m
2
G 7
2
7
U d 7 v dy å à á n ' m õ ðñ 7
1$:9
]kd'g
68$:9
]kd
G
6$38
7
U d m
6$38
>
2
zi jygsni nf jkdmhjhúd$$$
»Zi jygsnid nfz }riz jkdmhjhkdiz; (z + d
z
$
$ 9$9: 9$35
$ u y 7U d +(b m7 UJR 7 ER,3$9,(e,j6+2 UY
4
2
Oa+jg Oa+jg2 UJR
riarizi fn syd}k : x zybf in sirfn}i$$$
9$' Mhziök skr eniphúd
G y 7
6950=5:$:
Oa'jg
6:$89
jg2
0$29
jg2
60$99
jg2
è G
ø ü7 ï ER ex | ÿ
Fz 7 ì
y
è 3$1 e ½j ø ü bm 7 ex ìï üÿ
Fz ghd 7 ì
6$:: Fz 7
Hd}rkmy|jf Hd}rkmy| jf in ærif mi fjirk f y}hnh|fr< Fz k Fz gçd ú 6$::Fz< 6:$05
jg2
Hd}rkmy|jf Hd}rkmy| jf in dügirk mi ufrhnnf f y}hnh|fr< 9 *
Ærif mi nf ufrhnnf<
jg2
6$81
Frgfmk< *
9
C
6=
jg
Rizygid mi nf \fsf}f jkd jfraf fphfn Rinnidk arfdynfr fn 89) SZ
e M
Jkdjri}k e!j7 233 Oa+jg2 Jnfzi 2 fariafmk gæphgk :+=". riuidhghid}k 63 jg (gæz gidkz 2$9 jg * 9
`
Snfd}hnnf mi jkdjri}k e!j7 633 Oa+jg. i7 9 jg
Me ` `gçd J6 J2 N B
d ç g `
J2 6 J
7 7 7 7 7 7 7
6$2 =3
29 23 62 6$: 6$:
g jg jg jg jg g g
N
* 9
B
C 6= jg jg
F}ræz$$$
C 6= jg id nij`k bflk Jfnjynfr k}rf |fsf}f$$$
\fsf}f zyli}f f jfraf fphfn
@klf mi Jænjynk vyi zknyjhkdf \fsf}fz jkd jfraf fphfn Mf}kz mi Id}rfmf< S
Gfadh}ym mi nf jfraf S Arysk fn vyi sir}idiji nf iz}ryj}yrf< Nkdah}ym mi J6< Nkdah}ym mi J2< Srkeydmhmfm mi mizsnfd}i Me< Rizhz}idjhf min jkdjri}k e!j< Jnfzi min jkdjri}k< Rizhz}idjhf min fjirk ex<
e M
J2
6 J
Rizhz}idjhf min }irridk e }y <
63$:5 b 633 62 6 233 2 =233 63
]kd jg jg g Oa+jg
2
Oa+jg
2
]kd+g
2
6$' Mf}kz mi id}rfmf 2$' Jænjynk min Frif mi nf |fsf}f. Srizhkdiz mi jkd}fj}k x Sirfn}i srinhghdfr :$' Riuhzhúd min Sirfn}i =$' Mhziök skr eniphúd 9$' Rizygid mi nf \fsf}f jkd Jfraf Fphfn Mhziök x infbkrfjhúd<
Akd|fnk Nyak Jry| (88:63319 Lkzè Rklfz Akd|æni| (88:6668=
akd|fnk[nyakC`k}gfhn$jkg akd|fnk[nyakC`k}gfhn$jkg j`isi[j`isi [C`k}gfhn$jkg
Arysk G836 `}}s<++arkysz$ gzd$jkg+Iz}ryj}yrfzxjhgid}fjhkdizIZHF'836
@klf srkskrjhkdfmf f<
Akd|fnk Nyak Jry| 88:63319 (akd|fnk[nyakC`k}gfhn$jkg. akd|fnk[nyakC}kmh}k$jkg. Lkzè Rklfz Akd|æni| 88:6668= (j`isi[j`isi[C`k}gfhn$jkg
6$' Kb}idjhúd min ærif mi nf |fsf}f S y 7 S,EJ 7
6=$93
S ] 7 S/Q jhgid}fjhúd 7
6:$=1 60$05
]kd ]kd ]kd
6$08
g
=9
jg
6$32 6$8
g g
S ]y 7 S],EJ 7
S]
F |
y
7
n6
7
7
e }y n
2
7
2n 2
7
N 7 J 6 / 2n 6
7
B 7 J 2
/
Hd}rkmy|jf nkz ufnkriz B x N rimkdmifmkz< 6 B7 6 N7 n
3$=9
7
2
B
g g
N
g
2$' Srizhkdiz mi jkd}fj}k
v}y
7
v dy
7
S}y F |
Sy F |
2
7
60$05
]kd+g
7
6=$9
]kd+g
2
:$' Sirfn}i srinhghdfr
G y
m 7
7
v dy n
2
2
G y 6=$0 e ! j
7
/
5jg
7
6=5062$9
Oa'jg
6:$3=
jg
Hd}rkmy|jf in ufnkr mi "m" rimkdmifmk 69 m7 23 `7 F}ræz$$$
jg jg Jkd}hdyfr$$$
4
e }y
=$' Riuhzhúd min sirfn}i
669 21
J 6 / m 7 J 2 / m 7 b3 7 2(J 6 / m / 2(J 2 U y 7 Sy 7 uy 7
U y
/
:$=
Oa+jg2
63$62
Oa+jg
m 7
20=
7
b3 m
6=$93
jg jg jg ]kd
JR 7 ER e , j U JR
2
u 4 Srkjimigkz f nf zhayhid}i riuhzhúd$$$
U JR
B
y
º = m
53
=m 7
633
4
53
jg jg
zi jygsni nf jkdmhjhúd. iufnyfrigkz nf zhayhid}i$$$
` ª 53jg
23
`7
23
>
53
jg jg
zi jygsni nf jkdmhjhúd. iufnyfrigkz nf zhayhid}i$$$ G U d m
ª 2
vdy (n ' m
2
7
3$59
]kd'g
U d 7 v dy å à á n ' m õ ðñ 7
=$:9
]kd
G 7
2
G
6
7
U d m
6
>
2
zi jygsni nf jkdmhjhúd$$$
»Zi jygsnid nfz }riz jkdmhjhkdiz; (z + d
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