A Zrngfmt Tfpnrt Nb
]keuiatfh Abbfaikbl cnr SI]K Mfii Ziamfefbt Vbhfr lukhabmf nc
Hr. E ] Doat Dy
Aaenho @ (16SI:1C) Argub ] @uear (16SI:8C) (E.Xfmo SI]K Hfsklb) ]udekttfh tn
Hr. Tf`oa ] Doat As a part nc SI?;<7 Ekbnr Zrngfmt
Hfpartefbt nc Fifmtrnbkms abh Mneeubkmatknb, Batknbai Kbstktutf nc Xfmobninly @arbata`a ]urato`ai st
1 Aprki 4:13
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
AD]XTAMX ]keuiatfh abbfaikbl ks a lfbfrai ahaptkvf ofurkstkm abh dfinbls tn tof miass nc bnb-hftfrekbkstkm ailnrktoes. Kt oas dffb appikfh tn sfvfrai mnedkbatnrkai prndifes crne varknus ckfihs nc smkfbmf abh fblkbffrkbl. Xoks rfpnrt hksmussfs onw skeuiatfh abbfaikbl mab df appikfh tn vfry iarlfsmaif kbtflratknb (SI]K) mfii piamfefbt prndife kb nrhfr tn ekbkekzf wkrfifblto abh mokp arfa. Xof ailnrktoe ks appikfh tn cuii mustne iaynut hfsklb. Zfri abh Zytonb mnhkbl iablualfs oavf dffb usfh tn kepifefbt tof ailnrktoe.
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf 1
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
MNBXFBX] AD]XTAMX
1
MNBXFBX]
4
IK]X NC CKLVTF]
=
1. Zrndife ]tatfefbt
8
1.1 Bffh cnr ofurkstkm ailnrktoe
8
1.4 Ndgfmtkvf cubmtknb
8
4. ]keuiatfh Abbfaikbl 4.1 Kbtrnhumtknb
6
4.4 Drkfc hfsmrkptknb
6
4.= Zsfuhn mnhf
3
=. ]keuiatfh Abbfaikbl cnr Ziamfefbt =.1 Lnvfrbkbl cubmtknbs
8.
6
< <
=.1.1 Kbktkai mnbckluratknb lfbfratknb
<
=.1.4 Envf lfbfratknb cubmtknb
<
=.1.= Mnst cubmtknb
?
=.1.8 Abbfaikbl smofhuif cubmtknb
1:
]keuiatknb Tfsuits
TFCFTFBMF]
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
11 1=
Zalf 4
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
IK]X NC CKLVTF] Cklurf 17 Xypkmai lrapo nc mnst vs Bn. nc mnbckluratknbs fxaekbfh
;
Cklurf 47 Zint nc tntai mnst vs Bn. nc mnbckluratknbs fxaekbfh
11
Cklurf =7 Tabhne kbktkai piamfefbt nc mfiis
11
Cklurf 87 Kbtfrefhkatf bnb nptkeai piamfefbt
14
Cklurf 67 Ckbai nptkeai piamfefbt
14
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf =
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
1. Zrndife ]tatfefbt 1.1 Bffh cnr ofurkstkm ailnrktoe SI]K mfii piamfefbt prndifes arf `bnwb tn df BZ mnepiftf. Xrykbl tn lft ab fxamt sniutknb dy fvaiuatkbl fvfry pnsskdif piamfefbt tn hftfrekbf tof dfst nbf wnuih ta`f tkef prnpnrtknbai tn tof camtnrkai nc tof buedfr nc enhuifs. Xoks eftonh ks, tofrfcnrf, kepnsskdif tn usf cnr mkrmukts wkto aby rfasnbadif buedfr nc enhuifs. A wkhf rablf nc ofurkstkm ailnrktoes fxkst kb tof iktfraturf cnr fcckmkfbtiy arrablkbl tof inlkm mfiis nb SI]K mokp. ]keuiatfh abbfaikbl ks nbmf sumo eftonh. A strnbl cfaturf nc skeuiatfh abbfaikbl eftonh ks toat kt ks dnto fccfmtkvf abh rndust.
1.4 Ndgfmtkvf cubmtknb
Xof eakb ndgfmtkvf nc skeuiatfh abbfaikbl piamfefbt ailnrktoe ks tn ekbkekzf tof tntai mokp arfa abh tof tntai fstkeatfh wkrf ifblto cnr aii tof mfiis.
Mokp arfa usalf bffhs tn df nptkekzfh kb nrhfr tn ckt enrf cubmtknbaikty kbtn a lkvfb mokp arfa.
\krf ifblto bffhs tn df nptkekzfh kb nrhfr tn rfhumf tof mapamktkvf hfiays assnmkatfh wkto inblfr mfiis abh spffh up nc tof npfratknb nc tof mokp. Xof
lnais
arf
minsfiy
rfiatfh
skbmf
ekbkekzkbl
tof
mokp
arfa
wkii
autneatkmaiiy rfhumf tof tntai wkrfifblto. wk rfifblto.
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf 8
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
4. ]keuiatfh Abbfaikbl 4.1 Kbtrnhumtknb
]keuiatfh abbfaikbl ks a lfbfrai ofurkstkm abh dfinbls tn tof miass nc bnb hftfrekbkbstkm ailnrktoes. Kt oas dffb appikfh tn sfvfrai mnedkbatnrkai prndifes crne varknus ckfihs nc smkfbmf abh fblkbffrkbl. Xofsf prndifes kbmiuhf
travfiikbl
saifseab
prndife,
lrapo
partktknbkbl,
quahratkm
assklbefbt, eatmokbl, ikbfar arrablfefbt, abh smofhuikbl. Kb tof arfa nc SI]K Hfsklb, skeuiatfh abbfaikbl oas dffb appikfh tn varknus poyskmai hfsklb stfps ik`f partktknbkbl, cinnrpiabbkbl abh mfii piamfefbt P1U.
4.4 Drkfc hfsmrkptknb
Xof lnai nc skeuiatfh abbfaikbl piamfefbt ailnrktoe P4U ks tn hftfrekbf a piamfefbt wkto ekbkeue pnsskdif mnst. A mnst cubmtknb ks hfckbfh sumo toat kt mnbsksts nc wkrf ifblto abh varknus pfbaitkfs cnr enhuif nvfriap, tntai mokp arfa, abh sn nb. Xof daskm prnmfhurf kb skeuiatfh abbfaikbl ks tn ammfpt aii envfs toat rfsuit kb a rfhumtknb kb mnst. Envfs toat rfsuit kb a mnst kbmrfasf arf ammfptfh wkto a prndadkikty toat hfmrfasfs wkto kbmrfasf kb mnst. A paraeftfr maiifh X, maiifh tof tfepfraturf, ks usfh tn mnbtrni tof ammfptabmf prndadkikty nc tof mnst kbmrfaskbl envfs. Oklofr vaiufs nc X mausf enrf sumo envfs tn df ammfptfh. Ammfptabmf prndadkikty ks lkvfb dy fxp(ΘM/X), wofrf ΘM ks tof mnst kbmrfasf. Kb tof dflkbbkbl, tof tfepfraturf ks sft tn a vfry oklo vaiuf sn enst nc tof envfs arf ammfptfh. Xofb tof tfepfraturf ks lrahuaiiy hfmrfasfh sn tof mnst kbmrfaskbl envfs oavf ifss moabmf nc dfkbl ammfptfh. Vitkeatfiy, tof tfepfraturf ks rfhumfh tn a vfry inw vaiuf sn toat nbiy envfs mauskbl a
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf 6
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
mnst rfhumtknb arf ammfptfh, abh tof ailnrktoe mnbvfrlfs tn a inw mnst mnbckluratknb.
4.= Zsfuhn mnhf
dflkb X 5 kbktkai^tfepfraturf0 Z 5 kbktkai^piamfefbt0 wokif (X 2 ckbai^tfepfraturf) hn wokif (buedfr^nc^trkais 9 trkai^ikekt) hn bfw^Z 5 ZFTXVTD(Z)0 ∃M 5 MN]X(bfw^Z) ” MN]X(Z)0 kc (∃M (∃M 9 :) tofb Z 5 bfw^Z0 fiskc (rabhne(:,1) 2 fxp(∃M fxp(∃M /X)) tofb Z 5 bfw^Z0 X 5 ]MOFHVIF(X)0 fbh
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf 3
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
=. ]keuiatfh Abbfaikbl cnr Ziamfefbt =.1 Lnvfrbkbl cubmtknbs
Xof purpnsf nc tof ailnrktoe ks tn ckbh a piamfefbt nc tof stabharh mfiis sumo toat tof tntai fstkeatfh kbtfrmnbbfmtknb abh nvfriap mnsts arf ekbkekzfh. \f hkvkhf nur ailnrktoe kbtn 8 prkbmkpai mnepnbfbts
Kbktkai mnbckluratknb lfbfratknb
Envf Lfbfratknb cubmtknb (ZFTXVTD)
Mnst Cubmtknb (MN]X)
Abbfaikbl ]mofhuif (]MOFHVIF)
=.1.1 Kbktkai mnbckluratknb lfbfratknb
\f start nur abbfaikbl prnmfhurf dy piamkbl tof mfiis nb tof mokp rabhneiy. \f piamf tof mfiis rabhneiy sn toat tof piamfefbt ks bnt nptkeai. Xof kbktkai arfa nmmupkfh dy tof mokp ks maimuiatfh. ]kbmf tof mfiis arf piamfh rabhneiy tous, tof hkstabmfs dftwffb tofe abh tof ifblto nc tofkr kbtfrmnbbfmtknb wkii df oulf. Bfxt wf wkii usf tof = hkccfrfbt cubmtknbs tn lft tof nptkeai piamfefbt cnr tof mokp.
=.1.4 Envf Lfbfratknb cubmtknb
Xoks ks tof ZFTXVTD cubmtknb kb psfuhn mnhf. Xn lfbfratf a bfw pnsskdif mfii piamfefbt, wf usf twn stratflkfs st ratflkfs a. Envf skblif mfii rabhneiy tn a bfw inmatknb nb tof mokp. d. ]wap tof pnsktknb nc twn mfiis m. Tntatf skblif mfii dy ;: :
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf <
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
Kb nur ailnrktoe wf usf aii torff stratflkfs rabhneiy dut wkto ckxfh prndadkikty.
3:% nc tof envf e nvf lfbfratknb ks hnbf tornulo rabhne envf (a)
4:% nc tof envf lfbfratknb ks hnbf tornulo rabhne envf (d)
4:% nc tof envf lfbfratknb ks hnbf tornulo rabhne envf (m)
=.1.= Mnst cubmtknb
Xoks ks tof MN]X cubmtknb kb psfuhn mnhf. Xof mnst cubmtknb kb nur ailnrktoe ks mneprksfh nc twn mnepnbfbts
5 1 + 4 m1 ks a efasurf nc tof tntai fstkeatfh wkrf-ifblto. Cnr aby mfii, wf ckbh nut tof wkrf-ifblto dy maimuiatkbl tof onrkznbtai abh tof vfrtkmai hkstabmf dftwffb kt abh kts nut mfii. Ift Ho(k,g) df tof onrkznbtai hkstabmf dftwffb mfii k abh kts gto nut mfii abh Hv(k,g) df tof vfrtkmai hkstabmf dftwffb mfii k abh kts gto nut mfii, tofrfcnrf tof tntai wkrf ifblto cnr tof mokp mab df hfrkvfh dy tof cniinwkbl eatofeatkmai fxprfssknb
1 5 (ℂ( , ) + ( ,))
wofrf tof sueeatknb ks ta`fb nvfr aii tof b mfiis kb a mkrmukt.
\ofb a mfii ks swappfh nr rntatfh kt eay sn oappfb toat twn mfiis nvfriap wkto famo ntofr. Ift N(K,g) kbhkmatf tof nvfriap dftwffb twn mfiis. Mifariy toks nvfriap ks ubhfskradif abh sonuih df ekbkekzfh. Kb nrhfr tn pfbaikzf tof nvfriap sfvfrfiy wf squarf tof nvfriap sn toat wf lft iarlfr pfbaitkfs cnr nvfriaps. Xof nvfriap pfbaity m4 ks lkvfb dy
(( ,))
!
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf ?
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
Xous wofb wf lfbfratf a bfw envf wf maimuiatf tof mnst cubmtknb cnr tof bfwiy lfbfratfh envf. Kc wf ckbh toat tof bfw envf oas a mnst ifssfr toab tof prfvknus dfst envf, wf ammfpt kt as tof dfst envf. Dut kc wf ckbh a sniutknb toat ks bnt mnst nptkeai, wf hn bnt rfgfmt kt mnepiftfiy. \f hfckbf ab Ammfpt cubmtknb wokmo ks tof prndadkikstkm ammfptabmf cubmtknb Kt hftfrekbfs woftofr tn ammfpt a envf nr bnt. \f oavf kepifefbtfh ab fxpnbfbtkai cubmtknb cnr tof ammfpt eftonh. \f arf ammfptkbl a bnb mnst nptkeai sniutknb dfmausf wf arf lkvkbl tof abbfaikbl smofhuif a moabmf tn envf nut nc a inmai ekbkeue wokmo kt eay oavf okt.
Cklurf 17 Xypkmai lrapo nc mnst vs Bn. nc mnbckluratknbs fxaekbfh P=U
Cnr fxaepif, kc a mfrtakb abbfaikbl smofhuif okts pnkbt D (inmai ekbkea) abh kc wf hn bnt ammfpt a bnb mnst nptkeai sniutknb, tofb tof abbfaikbl mabbnt rfamo tof lindai ekbkea. Dy uskbl tof ammfpt cubmtknb wf arf lkvkbl tof abbfaikbl smofhuif a moabmf tn lft nut nc tof inmai ekbkea. As a baturf nc tof ammfpt cubmtknb usfh dy us, tof prndadkikty nc ammfptkbl bnb mnst nptkeai
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf ;
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
sniutknb ks oklofr at tof dflkbbkbl nc tof abbfaikbl smofhuif. As tfepfraturf hfmrfasfs, sn hnfs tof prndadkikty nc ammfptkbl bnb-mnst nptkeai sniutknbs, skbmf tof pfrturdatknbs nc a mkrmukt ks oklofr at oklofr tfepfraturfs toab inwfr tfepfraturfs.
=.1.8 Abbfaikbl smofhuif cubmtknb
Xoks ks tof smofhuif cubmtknb kb psfuhn mnhf. At ckrst wf start tof abbfaikbl prnmfhurf crne a vfry oklo tfepfraturf 4:,:::@. \f rfhumfh nur tfepfraturf uskbl Xbfw 5 δX * X δX, tof mnnikbl ratf ks ckxfh dy us. Kbktkaiiy wf rapkhiy hfmrfasfh tof tfepfraturf (δ ( δX ≏ :.?). Kb tof ekhhif pnrtknb nc tof a bbfaikbl smofhuif wf rfhumfh tof tfepfraturf sinwiy ( δX ≏ :.;6), skbmf toks poasf ta`fs up tof eaxkeue (≏ (≏ <6%) nc tof abbfaikbl smofhuif. Kb tof inw tfepfraturf, tof tfepfraturf ks hfmrfasfh rapkhiy alakb(δ alakb( δX ≏ :.?). Xof stnppkbl mnbhktknb ks wofb tof tfepfraturf caiis dfinw 1::@. \ktokb famo tfepfraturf rablf wf fxpfrkefbtaiiy sft tof buedfr nc envfs. Nbmf tof buedfr nc envfs ks sft, wf ckx kt cnr tof rfeakbhfr nc tof smofhuikbl. Cnr fxaepif kb nur mnhf wf oavf sft tof buedfr nc ktfratknbs cnr tof ailnrktoe at 6*Buedfr^nc^Mfiis.
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf 1:
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
8. ]keuiatknb rfsuits
Cklurf 47 Zint nc tntai mnst vs Bn. nc mnbckluratknbs fxaekbfh.
Cklurf =7 Tabhne kbktkai piamfefbt nc mfiis
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf 11
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
Cklurf 87 Kbtfrefhkatf bnb nptkeai piamfefbt
Cklurf 67 Ckbai nptkeai piamfefbt
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf 14
SI?;<7 Ekbnr Zrngfmt Zrngfmt
4:13
TFCFTFBMF] P1U M.]fmofb abh A.]ablknvabbk-Skbmfbtfiik, ’Xof Xkedfr\nic Ziamfefbt abh Tnutkbl Zam`alf―, KFFF Gnurbai nc ]nikh ]tatf Mkrmukts, Mkrmukts , Sni. ]M-4:, Bn. 4, Aprki 1;?6.
P4U ]. @kr`patrkm`, M. Lfiatt abh E. Sfmmok, ’Nptkekzatknb dy skeuiatfh abbfaikbl― KDE Mneputfr ]mkfbmf/Fblkbffrkbl Xfmobninly \atsnb Tfs. Mfbtfr , [nc`tnwb Ofklots, B[, Xfmo. Tfp, 1;?4.
P=U @. ]oaonn`ar abh Z. Eazuehfr, SI]K Mfii Ziamfefbt Xfmobkqufs, Xfmobkqufs , Hfpartefbt nc Fifmtrkmai Fblkbffrkbl abh Mneputfr ]mkfbmf, Vbkvfrskty nc Ekmoklab.
Hfpt. nc F&M, BKX@ ]urato`ai ]urato`ai
Zalf 1=
