Seti: Another Signal In Sagittarius
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Transcript of Seti: Another Signal In Sagittarius
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8/13/2019 Seti: Another Signal In Sagittarius
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TKWH3 BF@WMKU THLFBI HF TBLHWWBUH[T
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HBF EKBUGTIKX
D@QXUHLMW 5124 EX HBF EKBUGTIKX
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Nhiks [ Bfg K
Ey Hbf Ekbrgsiky
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Wmk [ Nhiks 12
Ey
Hbf Ekbrgsiky
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Wmk [ Nhiks 12
Ey Hbf Ekbrgsiky
D`pyrhlmt 5125-5124 ey Hbf Ekbrgsiky
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Wbeik @n D`ftkfts
Hftr`gudth`fQrknbdkKphi`luk
Tyf`pshsDmbptkr 2Dmbptkr 5Dmbptkr 4Dmbptkr 7Dmbptkr ;Dmbptkr >Dmbptkr Dmbptkr 2
Ht hs dbiikg Wmk [rbfus Kfhlob ekdbusk wmktmkr `r f`t kxtrbtkrrkstrhbisiknt tmkhr tmuoeprhft hf `ur pmyshds bs wkii bs b okssblk tmbt skkos t`d`ok nr`o tmk sbok rklh`f `n spbdk bs TKWHs \`w shlfbi, `r rbfg`oiy
kv`ivhfl systkos bfg Fbturk d`fvkrlk `f `fk fuoekr (fhfk-nhntms), tmk[rbfus hftklrbi hs `fk d`opbdt stbtkokft tmbt koe`ghks kvkrytmhfl. Ht hsoy ekihkn, hn y`u rkbg tmhs st`ry, y`u ohlmt blrkk ht hs wmbt mbppkfs hnLypshks g` pmyshds.
Hbf EkbrgsikyCuiy 22, 5124
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, 711tm`n bf Kbrtm gby, bfg b lrbo t` ek tmk wkhlmt `n b duehd dkfthoktkr`n wbtkr bt stbfgbrg tkopkrbturk bfg prkssurk, wmhdm hs zkr` gklrkksdkfthlrbgk bfg tmk prkssurk bt skb ikvki. \k gknhfk `fk gklrkk dkfthlrbgkey sbyhfl zkr` gklrkks hs tmk tkopkrbturk bt wmhdm wbtkr nrkkzks, bfg 211gklrkks dkfthlrbgk hs tmk tkopkrbturk bt wmhdm wbtkr e`his. Wmhs hs tmkoktrhd systko, bfg wk drkbtkg ht hf tkros `n tmk w`rig wk jf`w. Bfg wkdrkbtkg ht s` tmbt ey bsshlfhfl b Lrkkj prknhx, ihjk Jhi` (okbfhfl tm`usbfg)wmkf bttbdmkg t` oktkr, okbfs b tm`usbfg oktkrs, `r ey bsshlfhfl tmkLrkkj prknhx dkfth (okbfhfl mufgrkgtm) hs `fk mufgrkgtm `n b oktkr. Wmbt
hs b oktkr hs b mufgrkg dkfthoktkrs, bfg b jhi`oktkr hs 2111 tm`usbfgoktkrs. Wmk systko hs usknui ekdbusk f`t `fiy mbvk wk gkrhvkg tmk ufhtsnr`o pmyshdbi pr`pkrthks, tmk ghnnkrkft ufhts hf tmk systko lr`w bsouithpiks `n tkf. T`, hn wk wbft t` w`rj whtm okbsurhfl s`oktmhfl sobii,ihjk bf bd`rf, wk gksdrhek ht whtm dkfthoktkrs, bfg hn wk w`rj whtms`oktmhfl ibrlk, ihjk tmk ghboktkr `n tmk kbrtm wk usk jhi`oktkrs.
Ekn`rk tmk oktrhd systko, wk okbsurkg qubfththks hf tkros `n nkkt bfgp`ufgs, wmhik skd`fgs mbvk biwbys ekkf d`fstbft t` e`tm tmk n``t-p`ufgsystko bfg tmk oktrhd systko. Qr`ebeiy ekdbusk skd`fgs brk gkrhvkg nr`otmk 4>; gby, twkivk o`ftm, ykbr bfg tmk 57 m`ur gby, wmhdm mhst`rhdbiiy
gkvki`pkg nr`o whsk dbikfgbr objkrs `vkr tm`usbfgs n ykbrs. Eut tmkn``t objks ihttik skfsk, `fiy d`ohfl pkrmbps nr`o tmk mkbrsby sm`k shzk `nb jhfl, bfg tmk p`ufg nr`o L`g jf`ws wmkrk. Tthii nurtmkr, tmhs systkow`uig skko f`t t` ek tmbt prblobthd hf tmbt tmkrk brk twkivk hfdmks hf bfgn``t bfg tmrkk nkkt hf b ybrg, b nbr dry nr`o tmk skfshehihty `n tmk oktrhdsystko wmkrk bii shzks `r bo`ufts brk b ouithpik `n tkf `n bf`tmkr.
Kur`pk usks tmk oktrhd systko, ihjk r`bg shlfs brk hf jhi`oktkrs, bfg sm`kshzks hf dkfthoktkrs. \k usk ohiks n`r `ur r`bg shlfs bfg hfdmks n`r sm`kshzks. M`wkvkr, ekdbusk `n tmk prblobthd fbturk `n tmk oktrhd systko,Bokrhdbf bfg Kur`pkbf sdhkfthsts usk tmk oktrhd systko bihjk. @ntkf,
m`wkvkr, ekdbusk tmk n``t-p`ufg systko hs sthii hf usk hf Wmk [fhtkg Ttbtks,sdhkfthst s`okthoks nhfg tmkoskivks mbvhfl t` l` t` tmk knn`rt `n d`fvkrthflgbtb tmky fkkg nr`o nkkt bfg p`ufgs t` oktkrs bfg jhi`lrbos.
Eut wmbt hn H sbhg f`t `fiy brk e`tm tmk oktrhd systko bfg tmk n``t-p`ufgsystko d`ffkdtkg t` tmk [fhvkrsk eut t` `fk bf`tmkr hf b wby tmbt w`uigsullkst tmk kv`iuth`f `n tmkhr gkvki`pokfts hs ghnnkrkft tmbf tmk mhst`ry wkjf`w0 Wmbt hs wmbt H skko t` ek nhfghfl.
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Ht hs bf kxtrb`rghfbry tmhfl, tmk gbfdk `n tmk dkiksthbi e`ghks hf tmkmkbvkfs tmbt mbs ekkf `eskrvkg shfdk bfdhkft thoks, bfg n`ufg t` ekgksdrhebeik hf tkros `n tmk o`st w`fgr`us bspkdts `n e`tm fuoekr bfg
lk`oktry.
Ekdbusk `n tmk o`th`f `n tmk kbrtm br`ufg tmk suf, tmk stbrs whii bppkbr hftmk sbok p`shth`f hf tmk sjy n`ur ohfutks kbrihkr kbdm fhlmt, bs tmk kbrtmr`tbtks, objhfl tmko rhsk bfg skt, s` tmbt hf tmk d`ursk `n tmk 4>; gby ykbrtmky whii mbvk obgk b d`opiktk c`urfky br`ufg tmk sjy. Wmk Kbrtm l`ksbr`ufg tmk Tuf `fdk hf tmhs 4>; gby ykbr, bfg 4>; hs di`sk t` 4>1, wmhdmbrk tmk fuoekr `n gklrkks hf b dhrdik. \k mbvk ghvhgkg up tmk dhrdik ihjktmhs, ekdbusk 4>1 hs ghvhsheik kvkfiy ey tmk gklrkks hf spkdhbi trhbfliks3 Wmkkquhibtkrbi trhbflik (>1->1->1), tmk 7;-7;-81, bfg tmk 41->1-81, obgk eygrbwhfl hf tmk bithtugk `n tmk >1->1->1 trhbflik.
Hf turf, tmk O``f l`ks br`ufg tmk Kbrtm b ihttik o`rk tmbf twkivk thoks hfb ykbr. Wwkivk hs tmk sobiikst beufgbft fuoekr. Ht hs kvkfiy ghvhsheik ey 2,5, 4, 7, >, bfg 25. Ht fhdkiy `rehts tmk Kbrtm hf be`ut 41 gbys, bfg wkbirkbgy okfth`fkg 41 ghvhgks fhdkiy hft` 4>1. T`, wk mbvk tmk twkivko`ftm ykbr bfg tmk 41 gby o`ftm. \k g`ueik `ur sobiikst beufgbftfuoekr, 25 t` lkt 57, bfg wk ghvhgk `ur gby hft` 57 m`urs, tmk gby ekhfltmk thok ht tbjks tmk kbrtm t` rkv`ivk `f hts bxhs.
\k tmkf ghvhgk kbdm m`ur hft` >1 ohfutks, bfg kbdm ohfutk hft` >1skd`fgs. \k birkbgy okfth`fkg >1 ghvhgks fhdkiy hft` 4>1 gklrkks. \k
ghvhgk kbdm qubrtkr `n tmk o``f hft` < gbys, s` tmbt bntkr b o`ftm wk mbvkdi`sk t` hts bppr`xhobtk `rehtbi pkrh`g `n 41 gbys.
\k mbvk g`fk b l``g c`e tmbt eklbf whtm tmk bfdhkfts, `n objhfl tmko`th`fs `n tmk dkiksthbi e`ghks, wmhdm brk ihjk b fbturbi di`dj, t` nht tmkowhtm tmk jky fuoekrs, bfg lk`oktrhks. Ht w`uig skko tmhs hs wmbt wk mbvkg`fk. Ht hs bobzhfl t` ok tmbt tmk kbrtm bfg o``f dbok be`ut hf b wbytmbt tmky o`vk s` di`skiy t` sudm b sdmkok.
F`w H nhfg tmbt tmkrk hs b yhf bfg ybfl hf tmk [fhvkrsk `n 8/; bfg ;/4,rkspkdthvkiy nr`o wmhdm dbf ek gkrhvkg wmbt H dbii tmk [rbfus kqubth`f,
bfg, ht skkos t` rkd`fdhik tmk oktrhd systko whtm tmk n``t p`ufg systko,bfg nurtmkr, tm`ulm muobf hfvkfth`fs, sm`w tmko d`ffkdtkg f`t cust t``fk bf`tmkr, eut t` tmk D`so`s.
G` bii stbr systkos hf tmk [fhvkrsk, kspkdhbiiy tm`sk tmbt m`st hftkiihlkftihnk, mbvk sudm bf kxtrb`rghfbry strudturk bs `urs, pkrmbps hfghdbthfl tmkybrk hf tmk [fhvkrsk n`r b rkbs`f, bs urs sbys be`ut us0 Obfuki dibhokg mkmbg ekkf bii bdr`ss tmk Lbibxy, bfg tmbt tm`ulm ghnnkrkft, tmky ghg.
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Oy D`sohd Brdmbk`i`ly hs ebskg `f tmk hgkb tmbt 8/; hs tmk Xhf `n tmk[fhvkrsk, ;/4 hs tmk Xbfl `n tmk [fhvkrsk, bfg 2; (Obfukis fuoekr, O) hstmk oblhd fuoekr. \htm tmksk tmrkk fuoekrs wk d`fstrudt b [fhvkrsk tmbt
skkos strhjhfliy o`rk tmbf d`hfdhgkftbi. Wmk Bppkfghx bt tmk kfg `n tmke``j mbs gbtb uskg bfg dbiduibth`fs f`t g`fk.
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BK-4;
H wr`tk b sm`rt st`ry ibst fhlmt, dbiikg Lypsy Tmbobfhso bfg tmk [fhvkrsk
be`ut tmk BK-4; ufht, wmhdm hs tmk ufht hf tmk o`vhk bfg e``j 51123 BTpbdk @gyssky tmbt MBI rkp`rts whii nbhi bfg ghsd`fthfuk d`ooufhdbth`ft` Kbrtm. H gkdhgkg t` rkbg tmk pbssblk gkbihfl whtm tmk kvkft hf 5112 bfgMBI, tmk smhp d`oputkr, rkp`rts ht whii nbhi hf whtmhf
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Ht wbsft b nbr wbij bt bii, tmk kquhvbikft `n b nkw dhty ei`djs nr`o tmkdbvks. \k lkt t` tmk st`rk, wmhdm wbs b d`uftkr nbdhfl tmk strkkt, f`t fktmbt y`u d`uig kftkr. Mk sbys t` tmk obf ekmhfg tmk d`uftkr, lhvk ok ;oktkrs `n m`sk. Wmk obf ekmhfg tmk d`uftkr puiikg `nn nhvk oktkrs n m`sk
nr`o tmk sphfgik, bfg dut tmk m`sk t` tmbt ikfltm. Mk stbtkg b vbiuk hfpksktbs, obyek =11, `r s`, (be`ut khlmt g`iibrs bt tmk thok) bfg tmkTmbobf t`ig ok t` lhvk tmbt bo`uft t` tmk obf ekmhfg tmk d`uftkr, wm`wbs Tpbfhsm. H pbhg tmk obf, bfg wk iknt.
H dbrrhkg tmk m`sk, bfg tmk Tmbobf wbijkg bi`fl shgk ok ufthi wk brrhvkgbt mhs dbvk wmkrk H wbs stbyhfl. \k kftkrkg tmk dbvk st`ppkg bt tmk wbijwby ektwkkf ihvhfl r``o bfg jhtdmkf, bfg mk sbhg3 n`ii`w ok. \k wkfttmr`ulm b tuffki tmbt mbg be`ut tmrkk dmboekrs hf tmk dbvk, bfg kftkrkg`fk `f `ur rhlmt bs wk wkrk mkbghfl hf, bfg wk st`ppkg bfg ekn`rk ok wbsb d`iikdth`f `n wmbt H ksthobtkg t` ek nhntkkf rueekr m`sks shtthfl `f lr`ufg.
Wmk Tmbobf t`ig ok t` skt tmk `fk H mbg cust e`ulmt mho `f tmk ni``r whtmtmk `tmkrs. H ghg, bfg wk iknt tmk dmboekr, bfg mk iknt tmk dbvk, bfg Hrktrkbtkg t` b d`udm hf tmk dbvk ihvhfl r``o.
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Lypshks mbvk b wby `n jf`whfl tmhfls be`ut b pkrs`f, wmktmkr `r f`t `fkghsdi`sks ht t` tmko hf w`rgs, bfg Wmk Tmbobf wbs bwbrk tmbt H f`t `fiyw`rjkg hf Bstr`f`oy, eut tmbt oy w`rj hf bstr`f`oy hfv`ivkg jf`whfl
bfg g`hfl kikdtr`fhds.
T`, obyek b wkkj `r tw` bntkr H mbg e`ulmt mho b m`sk, mk dbok t` mhs dbvkwmkrk H wbs stbyhfl, bfg bsjkg ok hn H w`uig ek beik t` hfstbii bf bftkffbn`r tkikvhsh`f bt bf bpbrtokft wmkrk mhs fkpmkw ihvkg.
T` tmhs thok H wbs f`t dbrryhfl b m`sk tmr`ulm Wmk Tbdr`o`ftk, eut bfbftkffb.
Wmkrk wkrk skvkrbi `n us `f tmk pbth`, `f b mhii bgcbdkft t` tmk bpbrtokft `nWmk Tmbobfs Fkpmkw, hfstbiihfl bf bftkffb n`r tkikvhsh`f rkdkpth`f.
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H bo f`w hf T`utmkrf Dbihn`rfhb, bt tmk m`usk `n oy o`tmkr, ht hs ibtk btfhlmt, smk hs b bsikkp, bfg H bo be`ut 57 ykbrs `ig bfg H gkdhgk t` i``j `uttmk whfg`w, kbst, bdr`ss Wmk Btibfthd, t` Tpbhf. Hookghbtkiy H skk tmk
Tmbobf, hf mhs ihvhfl r``o, wmkrk H mbg kbtkf b e`wi `n tmk Lypsy s`updbiikg Qudmkr`, bfg H mkbr tmk w`rg Bftkffb. H f`w rkbihzk wmkf Hhfstbiikg tmk bftkffb, H mbg ekd`ok `fk, bfg wbs rkdkhvhfl okssblks nr`otmk Tmbobf.
Wmk Tmbobfs Dmhigrkf wkrk nibokfd` luhtbrhsts, bfg H ikbrfkg nr`o tmko,t` piby tmk luhtbr. H bo f`w pibyhfl nibokfd`, whtm hfstrudth`fs nr`o tmksmbobf t` put tmk lypsy spbdk pr`lrbo hft` oy oushd. H rkbihzk H bo f`tcust bfy bftkffb, eut tmk BK4; tmbt obinufdth`fkg be`brg Wmk Ghsd`vkrycust ekn`rk ht brrhvkg bt tmk pibfkt Cuphtkr hf Brtmur D. Dibrjks bfgTtbfiky Juerhdjs 51123 B Tpbdk @gyssky. Wmk Tmbobf tkiis ok,
tkikpbtmhdbiiy, tmbt tmhs thok tmk ohssh`f w`ft nbhi.
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H bo wbtdmhfl Ttbr \brs bfg skk b spbdksmhp, wmhdm hs tw` `ei`fl dbpsuiksniyhfl d`ffkdtkg hf tbfgko. Wmk Lypsy Tmbobf sbys t` ok tkikpbtmhdbiiy3Gh`s ks ufb hgkb3 s`f g`s. H ufgkrstbfg tmbt t` okbf L`g hs bf hgkb3
tmkrk brk tw` kikokfts. T` H l` tmr`ulm ihnk ebshfl oy ihnk `f tmk fuoekrtw`.
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@fdk `fk mbs tbstkg Tpbhf, tmbt pkrs`f i`fls t` rkturf. H ibfg hf Obgrhg,F`rtmkrf Tpbhf, Wmk Dbpht`i. Wmk Tpbfhbrgs jf`w oy gksthfbth`f hsLrbfbgb, T`utmkrf Tpbhf, Wmk Lypsy Fkhlme`rm``g dbiikg Wmk
Tbdr`o`ftk, tmk dbvks, bfg hookghbtkiy rkd`lfhzk H bo ufgkr tmk spkii `nb Lypsy Tmbobf, bfg wmbt hs o`rk tmbt H bo Wmk BK4; Bftkffb n`r WmkLypsy Tpbdk Qr`lrbo. Nibokfd` ekhfl nibokfd`, tmk Tpbfhbrgs g` f`tufg` tmk spkii, eut rkpr`lrbo tmk hfstrudth`fs n`r ok, tmk BK4; Bftkffb,s` tmbt wmkf H brrhvk ebdj hf tmk [fhtkg Ttbtks, oy nibokfd` whii f`w stbtktmkhr hgkb `n b spbdk pr`lrbo. Ht wbs `n d`ursk, nibokfd` ekhfl nibokfd`,bf bttkopt t` `ut-g` tmk Lypsy spbdk pr`lrbo.
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H bo ebdj hf tmk [fhtkg Ttbtks bfg H bo bt tmk m`usk `n oy o`tmkr, ht hsfhlmt thok blbhf, smk hs bsikkp, bfg H i``j `ut tmk whfg`w kbst, bdr`ss tmkBtibfthd, t` Tpbhf, bfg tmhs thok H g` f`t skk tmk ihvhfl r``o `n tmk lypsy
smbobf, eut tmk strkkts `n Obgrhg bt fhlmt, bfg bii tmk pk`pik, bfg tmk w`rgCuphtkr d`oks t` ohfg bfg H bo be`ut t` sby `n d`ursk, Cuphtkr, bfg WmkTpbfhsm hftkrrupt bfg sby Xks, y`u brk rhlmt ht hs tmk ibrlkst pibfkt hf tmks`ibr systko, y`u brk rhlmt t` d`fshgkr ht, bii kisk whii ni`w nr`o ht.
H jf`w rbth`s, hf obtmkobthds brk tmk o`st hftkrksthfl sueckdt, ihjk ph, tmkrbth` `n tmk dhrduonkrkfdk `n b dhrdik t` hts ghboktkr, bfg tmk l`igkf rbth`,s` H d`fshgkr tmk rbth` `n tmk `reht `n Tbturf (tmk skd`fg ibrlkst pibfkt hftmk s`ibr systko) t` tmk `reht `n Cuphtkr bt tmkhr di`skst bppr`bdmks t` WmkTuf, bfg nhfg ht hs fhfk-nhntms (fhfk d`opbrkg t` nhvk) wmhdm ghvhgkg `ut hs`fk p`hft khlmt (2.=).
H tmkf pr`dkkg t` tmk fkxt i`lhdbi stkp3 f`t rbth`s, eut pr`p`rth`fs. B rbth`hs tmhs d`opbrkg t` tmbt, eut b pr`p`rth`f hs tmhs hs t` tmbt bs tmhs hs t` tmbt.T` tmk quksth`f hs3 Tbturf hs t` Cuphtkr bs wmbt hs t` wmbt0 @n d`ursk tmkbfswkr hs bs L`ig hs t` Thivkr. L`ig hs ghvhfk: shivkr hs fkxt g`wf `f tmk ihst.@n d`ursk `fk g`ks f`t d`opbrk b g`zkf `rbflks t` b mbin g`zkf bppiks, eutb g`zkf `n `fk t` b g`zkf `n tmk `tmkr, hn `fk wbfts t` kxtrbdt bfy jhfg `nokbfhfl. Eut bt`os `n l`ig bfg shivkr brk f`t okbsurkg hf g`zkfs, eut hfo`iks. T` H d`opbrkg b o`ik `n l`ig t` b o`ik `n shivkr, bfg H sbhg f` wby, hths fhfk-nhntms, bfg Tbturf hs hfgkkg t` Cuphtkr bs L`ig hs t` Thivkr.
H sbhg t` oyskin3 M`w nbr g`ks tmhs l`0 Wmk Tmbobfs s`f `fdk t`ig ok mkwbs hf i`vk whtm tmk o``f. T` H d`opbrkg tmk rbghus `n tmk suf, tmkghstbfdk nr`o hts dkftkr t` hts surnbdk t` tmk iufbr `rehtbi rbghus, tmkghstbfdk nr`o tmk dkftkr `n tmk kbrtm t` tmk dkftkr `n tmk o``f. Ht wbs Fhfkd`opbrkg t` Nhvk blbhf!
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2, ;.7,
(21)Okrdury Ubghus/Kbrtm Ubghus(21)Okrdury @reht/Kbrtm @reht
(kbrtm rbghus)/(o``f rbghus)?7(gklrkks hf b dhrdik)(o``f ghstbfdk)/(suf ghstbfdk)? 4.< ~ 4.>
Wmkrk brk be`ut bs obfy gbys hf b ykbr bs gklrkks hf b dhrdik.
(^`iuok `n Tbturf/^`iuok @n Cuphtkr)(^`iuok @n Obrs) ? 1.4< duehd kbrtmrbghh~ 4.>
Wmk ibttkr dbf ek d`fvkrtkg t` 4.> ey ouithpiyhfl ht ey (Kbrtm Obss/ObrsObss) ekdbusk Kbrtm hs be`ut tkf thoks bs obsshvk bs Obrs.
;.7
Cuphtkr @reht/Kbrtm @rehtTbturf Obss/Fkptufk Obss
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Hn wk d`fshgkr bs wkii tmk skqukfdk wmkrk wk eklhf whtm nhvk bfg bgg fhfkt` kbdm suddksshvk tkro3 ;, 27, 54, 45Wmkf, tmk strudturk `n tmk s`ibrsystko bfg gyfbohd kikokfts `n tmk [fhvkrsk bfg Fbturk hf lkfkrbi brk
thkg up hf tmk tw` skqukfdks3
;, 27, 54, 45,
bfg
2.=, 4.>, ;.7,
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kbrtm. Wm`ulm ht hs oudm o`rk obsshvk tmbf kbrtm, ht hs oudm ibrlkr bfgtmkrkn`rk ikss gkfsk. Wmbt wbs wmy ht d`oks `ut t` mbvk tmk sbok surnbdklrbvhty.
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H bsjkg wmbt fkkgs t` ek g`fk t` s`ivk Oy Fkptufk Kqubth`f, ey l`hfl gkkpwhtm tmk luhtbr hf T`ikb Q`r Euikrbs. H n`ufg tmk bfswkr wbs tmbt H ghgftmbvk kf`ulm hfn`robth`f t` s`ivk ht.
Wmkf H rkbihzkg H d`uig drkbtk tmk d`opikokft `n tmk Fkptufk kqubth`f eyi``jhfl bt tmk Xbfl `n ;/4, shfdk tmk Fkptufk kqubth`f dbok nr`o tmk Xhf`n 8/;.
\k usk tmk sbok oktm`g bs n`r tmk Fkptufk kqubth`f3
Ttbrt whtm = bfg bgg ; t` kbdm bgghth`fbi tkro (wk tmr`w b twhst ey f`tstbrthfl whtm ;)
;/4 ?6 =, 24, 2=, 54,
Ihst tmk fuoekrs tmbt brk wm`ik fuoekr ouithpiks `n ;/43
;/4f ? 2...4, 8..4,
Wmhs hs bf brhtmokthd skqukfdk whtm d`oo`f ghnnkrkfdk 4.4. Ht dbf ekwrhttkf3
(bPf) ? 4 + 4.4f
Wmhs dbf ek wrtttkf3
Kbrtm @rehtbi # + (Cuphtkr Obss/Tbturf Obss)f ? bPf
Iktthfl f ? 4 wk nhfg bPf ? 24
Wmk di`skst t` tmhs hs tmk obss n [rbfus, wmhdm hs 27.;7 kbrtm obssks. HnFkptufk hs tmk Xhf pibfkt, tmkf [rbfus hs tmk Xbfl pibfkt. Wmhs hs
hftkrksthfl ekdbusk H mbg n`ufg tmbt [rbfus bfg Fkptufk wkrk ghnnkrkftobfhnkstbth`fs `n tmk sbok tmhfl. H mbg wrhttkf3
H dbiduibtk tmbt tm`ulm Fkptufk hs o`rk obsshvk tmbf [rbfus, hts v`iuok hsikss sudm tmbt tmkhr pr`gudts brk di`sk t` kquhvbikft. Hf obtm3
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55
FPv ? v`iuok `n FkptufkFPo ? obss `n Fkptufk[Pv ? v`iuok `n [rbfus[Po ? obss `n [rbfus
(FPv)(FPo) ? ([Pv)([Po)
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54
Bii tmbt hs iknt t` g` hs t` d`fshgkr ph, tmk dhrduonkrkfdk `n b dhrdik t` htsghboktkr, bfg pmh, tmk l`igkf rbth`, shfdk tmky brk tw` o`st hop`rtbft, hnf`t o`st ekbuthnui rbth`s hf obtmkobthds.
H mbvk n`ufg fhfk-nhntms `ddurs tmr`ulm`ut fbturk hf tmk r`tbth`f `n pktbis
br`ufg b b ni`wkr n`r b o`st p`puibr brrbflkokft, hf tmk `rehts `n cuphtkr
t` sbturf hf tmkhr di`skst bppr`bdmks t` tmk suf, hf tmk rbth` `n tmk o`ibr
obssks `n l`ig t` shivkr, bfg hf tmk rbth` `n tmk s`ibr rbghus t` tmk iufbr
`reht. H f`w nurtmkr l` `f t` sby tmbt tmhs fhfk-nhntms ufhnhks tmk tw` o`st
hop`rtbft rbth`s hf obtmkobthds ph bfg tmk l`igkf rbth` (pmh), hf tmbt
ph + pmh ? 4.272 + 2.>2= ? 7.
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57
Hf Tuoobry, tmhs o`st ekbuthnui d`fstbft hf Fbturk, `n fhfk-nhntms, wmhdmufhnhks ph bfg tmk l`igkf rbth`, tmk tw` o`st ekbuthnui rbth`s hfobtmkobthds, hs tmk o`st p`puibr brrbflkokft `n pktbis br`ufg b ni`wkr,
bfg hs hf tmk rbth` `n tmk o`ibr obssks `n l`ig t` shivkr, tmk o`st prkdh`us `ntmk oktbis. @fk d`uig `fiy lukss tmbt sudm w`uig ek f`thdkbeik tmr`ulm`uttmk ufhvkrsk bfg w`uig ek f`thdkg ey `tmkr hftkiihlkft ihnk hf tmk ufhvkrsk,bfg, bs sudm tmk rkibth`fsmhp w`uig ek hgkbi n`r trbfsohssh`f `n b okssblkey `tmkr hftkiihlkft ihnk n`ros hf tmk ufhvkrsk t` sby t` tmk rkdkhvkr3 H bomkrk bfg mbvk f`thdkg ht. Wmk durh`us tmhfl hs tmbt ht kxhsts hf `ur s`ibrsystko hf tmk rbth` `n tmk `reht `n Tbturf bt hts di`skst bppr`bdm t` tmk sufd`opbrkg t` tmk `reht `n Cuphtkr bt hts di`skst bppr`bdm t` tmk suf,oysthdbiiy putthfl tmk Kbrtm bt `fk ufht nr`o tmk Tuf (Cuphtkr bfg Tbturfekhfl tmk ibrlkst bfg o`st obsshvk hf tmk s`ibr systko, tmk Kbrtm tmbtpibfkt wmhdm mbre`rs hftkiihlkft ihnk hf tmk T`ibr Tystko), bfg hf tmk rbth`
`n tmk Tufs rbghus t` tmk `rehtbi rbghus `n tmk o``f (o``f-kbrtmskpbrbth`f). Wmk quksth`f hs wmy g`ks tmhs rkibth`fsmhp n`r ph bfg tmkl`igkf rbth` `n fhfk-nhntms f`t cust kxhst tmr`ulm`ut tmk [fhvkrsk hf l`ig,shivkr, bfg pkrmbps ni`wkr pktbi brrbflkokfts, eut o`rk i`dbiiy hf `urs`ibr systko0 G`ks ht okbf muobfs mbvk s`ok jhfg `n ghvhfk spkdhbifksshf tmk d`so`s0 \mhik wk dbf jf`w tmbt tmk fhfk-nhntms pmkf`okf`f w`uigek rkprkskftkg ey l`ig bfg shivkr tmr`ulm`ut tmk ufhvkrsk, wk durrkftiydbff`t jf`w wmktmkr tmk hfmbehtbfts `n `tmkr stbr systkos mbvk ht hf tmkhrsuf (stbr) tmky `reht bfg b o``f tmbt ohlmt `reht tmkhr pibfkt `r hf tmkrbth` `n tmk `rehts `n tmk ibrlkst pibfkts hf tmkhr stbr systko putthfl tmkhrpibfkt bt `fk ufht nr`o tmkhr stbr. Wmk bfswkr t` tmhs kfhlob, H tmhfj, oust
ek `n kxtrb`rghfbry pr`nufghty.
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H mbvk tbijkg be`ut m`w 8/;, wmhdm H mbvk n`ufg kxhsts hf Fbturk bfg tmk[fhvkrsk, ufhnhks ph bfg tmk l`igkf rbth` (pmh)3
(ph) + (pmh) ? 4.272 + 2.>2= ? 7.
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5>
H mbvk f`w ghsd`vkrkg tmbt Obfuki wbs hf Kflibfg n`r o`rk tmbf `fkrkbs`f. Mk wbs t` okkt whtm b Nrkfdmobf wm` wbs b rkprkskftbthvk n`rtmk Eurkbu @n \khlmts Bfg Okbsurks `f b ohssh`f t` dmbflk tmk oktm`g `n
gknhfhfl tmbt ghstbfdk dbiikg tmk jhi`oktkr.
Bppbrkftiy ht mbg s`oktmhfl t` g` whtm mhs m`sk d`iikdth`f fuoekrhflnhntkkf m`sks bfg mhs nkkihfl tmbt L`g wbs bf hgkb `n wmhdm tmkrk brk tw`kikokfts. Ht w`uig skko mk dbrrhkg b lrkbt skdrkt tmbt wbs mbfgkg g`wf t`mho nr`o mhs bfdkst`rs bs tmky pbsskg tmr`ulm tmk w`rig ey n``t bt thoks,dboki bt `tmkr thoks, bfg dbrbvbf bt `tmkr thoks d`opiktkiy ufjf`wf,stbrthfl hf Hfghb bfg kfghfl hf Tpbhf.
Wmk Ghnnkrkfthbi Kqubth`f
H tm`ulmt ht wbs rkbiiy thok H s`ivk b ghnnkrkfthbi kqubth`f. H dm`sk Wmk[rbfus Kqubth`f.\k f`w gktkrohfk lhvkf tmk bddkikrbth`f hf tmk [rbfus kqubth`f hs 4.4kbrtm lrbvhthks, tmkf wmbt hs tmk hfhthbi vki`dhty hf tmk kqubth`f, wmhdm hstmk fuoekr 40
(v) ? 4 + 4.4t (Wmk [rbfus Kqubth`f)
(v)?bt?(44/21)t wmkrk ^ hs vki`dhty, b hs bddkikrbth`f, bfg t hs thok.
4?(44/21)t
(t) ? 41/44
8=1 do/s/s ? l ? tmk surnbdk lrbvhty `n tmk kbrtm
(8=1 do/s/s)(4.4)?4,547 do/s/s
(4,547 do/s/s)(41/44 s) ? 5,871 do/s ? vP1 vP1 hs tmk hfhthbi vki`dhty
Wmus wk dbf wrhtk tmk [rbfus kqubth`f bs3
(v) ? 5,871 do/s + (4,547 do/s/s)t
Wmhs hs tmk ghnnkrkfthbi kqubth`f3
(gx) ? (5,871 do/s)gt + (4,547 do/s/s)t gt
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54,=5; ?71
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5=
stbrtkg t` trbdk bfg okbsurk tmk nhrst `rehts br`ufg tmk li`ek0 \k tmkf`etbhfkg tmk kxbdt okbsurkokfts ey `eskrvhfl tmk hrrkluibrhthks hf tmk`rehts `n tmk nhrst brthnhdhbi sbtkiihtks hf `rgkr t` dbiduibtk tmk truk smbpkbfg ghokfsh`fs `r `ur li`ek.
Dmbtkibhf sullksts kxtrbtkrrkstrhbis, okbsurkg tmk kbrtm ey `rehthfl ht hftmk sbok wby bfg lbvk `ur ufhts `n okbsurkokft t` `ur pbst, ghstbftbfdkst`rs, >;,111 ykbrs bl`. Wmk bfdkst`rs `n Obfuki, jfkw tmhs bt ikbst btm`usbfg ykbrs bl`, bfg d`ffkdtkg ht, nurtmkr, t` Wmk D`so`s. Wmk whfgei`ws hf bf kfgikss skb `n sbfg. Uhghfl `f ht hs b v`hdk erkbjhfl up bfgghsbppkbrhfl hft` tmk bhr3 Ib thib, Lubgbdbih.
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B Tkd`fg I``j Bt Wmk [rbfus Hftklrbi
[rbfus Hftklrbi Nr`o 1 W` 2; Tkd`fgs
(5,871do /s)gt+ (4,547do /s /s)1
2;
" tgt1
2;
" ?7.1
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hf tmbt tmky brk d`ffkdtkg t` `fk bf`tmkr tmr`ulm tmk [fhvkrsk bfgFbturk0
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Wmk T`urdk @n @fk N`urtm Hf Wmk [rbfus Hftklrbi
2 jo ? 2/(21,111)(2/7)D wmkrk D ? 5(ph)UPk
D hs tmk dhrduonkrkfdk `n tmk Kbrtm bfg UPk hs tmk rbghus `n tmk Kbrtm.
UPk ?>,4
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45
Blbhf, wk n`ufg 8/; rkdurrkft hf tmk [fhvkrsk bfg Fbturk. Wmk LypsyTmbobf mbs hfghdbtkg tmbt 2; hs bt tmk mkbrt `n obttkrs. \k uskg 8,;, bfg2; t` d`fstrudt tmk n`ii`whfl qubgrbthd3
Wmk brkb `n b rkdtbflik hs 2;. Wmk ikfltm, i, hs 8 o`rk tmbf tmk whgtm
ouithpihkg ey ;3
w5+8w " 4 ? 1
w ? 1.45
\k tmkf obgk b qubgrbthd hf thok3
2; ?2
5lt
5
t5?
41
l
Ekdbusk `n tmk rksuit n`r w, wk dm`sk l ? 45 nkkt/skd/skd bs `pp`skg t` tmkvbiuk hf oktkrs l ? 8.= oktkrs/skd/skd
t5 ?41nt
45nt/skd/skd
t?1.8>=skd
\k f`tk tmbt 2-1.8>= ?1.145
H nhfg tmbt hftkrksthfl. Wmk Tmbobfs 2; skd`fgs gksdrhekg oktkrs hf tmk
[rbfus Hftklrbi bfg tmk fuoekrs hf fhfk-nhntms bfg tmkhr bvkrblk, f`t t`okfth`f tmkrk wbs tmk tw` uskg t` bvkrblk fhfk bfg nhvk, f`w ht hspr`n`ufgiy d`ffkdtkg t` tmk 45 `n kbrtm surnbdk lrbvhty hf nkkt.
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44
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47
Q`ufgs Bfg Jhi`lrbos
Kbriy `f hf oy w`rj, wmkf H nhrst f`thdkg fhfk-nhntms hf tmk s`ibr systkobfg fbturk, H wbs hftrhlukg ey tmk nbdt tmbt tmkrk hs fhfk-nhntms `n b gklrkkdkfthlrbgk pkr kvkry gklrkk n Nbmrkfmkht. H mbg trhkg t` nhfg tmk pmyshdbi
d`ffkdth`f d`fdkrfhfl tmhs, bfg ikbrfkg Nbmrkfmkht wbs d`fstrudtkg s`tmbt nrkkzhfl tkopkrbturk, `r fkbr tmkrk, ihtkrbiiy tmk tkopkrbturkokbsurkg ey b tmkro`oktkr hf b ohxturk `n sbit bfg hdk, pkrmbps s`okwbtkr, wbs t` ek tbjkf bs 45 gklrkks bfg tmk uppkr ihoht wbs gktkrohfkgey tmk muobf e`gy tkopkrbturk bs okbsurkg ey b tmkro`oktkr hf bfbropht t` ek b vbiuk br`ufg 8< `r 8=. \my tmksk vbiuks wkrk dm`skf Hd`uig f`t nhfg bfy rkbs`f n`r tmbt wbs g`duokftkg. H ghg p`st tmhs st`ry t`s`ok jhfg `n b ghsdussh`f lr`up. Ibtkr H mbg p`stkg oy ghsd`vkry `n fhfk-nhntms t` tmk C`skpm Dbopekii ghsdussh`f n`ruo bfg s`ok`fk tmkrk sbhgfhfk-nhntms wbs hf tmk kqubth`f tmbt d`fvkrts dkfthlrbgk t` Nbmrkfmkht. Hfkvkr tbijkg be`ut oy kbrihkr w`rj hf tmbt brkb, cust sbhg, yks tmkrk hs
fhfk-nhntms gklrkk dkfthlrbgk pkr kvkry gklrkk `n Nbmrkfmkht. Mk jkptsbyhfl y`u mbvk t` bgg tmhrty-tw`. H d`uig f`t d`fvhfdk mho wmbt H wbssbyhfl wbs truk. Bgghfl tmk tmhrty-tw` hs t` zkr` tmk rkibth`fsmhp s` `fkdbf d`fvkrt dkfthlrbgk t` Nbmrkfmkht. Wmbt hs tmkhr sdbiks brk ghnnkrkft3Dkishus eklhfs bt 1 gklrkks hs nrkkzhfl bfg Nbmrkfmkht eklhfs bt 45 hsnrkkzhfl tkopkrbturk. Wmbt g`ks f`t dmbflk tmk nbdt tmbt tmkrk hs fhfk-nhntms gklrkk dkfthlrbgk pkr kvkry gklrkk `n Nbmrkfmkht. Mk wbsprkskfthfl tmk n`rouib tmbt d`fvkrts `fk tkopkrbturk t` tmk `tmkr.
W` tmk obttkr bt mbfg3 Wmk Lypsy Tmbobfs 2; skkos t` rkd`fdhik oktrhdghstbfdks whtm nkkt, e`tm systkos usk tmk skd`fg t` okbsurk thok. Wmk
[rbfus hftklrbi hs gkrhvkg nr`o fhfk-nhntms, wmhdm wk skk ufhnhks tmk oktrhdokbsurkokft `n tkopkrbturk whtm tmbt `n tmk n``t-p`ufgs Nbmrkfmkht.Wmbt `fiy ikbvks us fkkghfl t` nhfg tmk d`ffkdth`f ektwkkf tmk oktrhdsystkos lrbos bfg jhi`lrbos whtm tmk p`ufg, s` wk mbvk gkbit whtm tmkobttkr wmkrk obss bfg wkhlmt brk d`fdkrfkg. B lrbo hs fhdkiy gknhfkg bstmk bo`uft `n wbtkr hf b duehd dkfthoktkr. Bii H dbf sby, bt tmhs p`hft, hstmbt `fk p`ufg hs 7;4.;8 lrbos, bfg tmbt objks ht kxbdtiy 1.;8 lrbosnr`o b wm`ik fuoekr. Ht mbs s`oktmhfl t` g` whtm fhfk-nhntms0
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4;
Lktthfl B Tkfsk @n Wmk [rbfus Kqubth`f
Wmus wk dbf wrhtk tmk [rbfus kqubth`f bs3
(v) ? 5,871 do/s + (4,547 do/s/s)t
Wmhs hs tmk ghnnkrkfthbi kqubth`f3
(gx) ? (5,871 do/s)gt + (4,547 do/s/s)t gt
[rbfus Hftklrbi Nr`o 1 W` 2; Tkd`fgs
(5,871do /s)gt+ (4,547do /s /s)1
2;
" tgt1
2;
" ?7.1= gklrkks N) bt skb ikvki.
Hn wk wrhtk, wmkrk 2,54; jo/mr (obdm 2) ? 1.474 jo/s, tmkf3
47,411 do/s ?5,871 do/s + (4547 do/s/s)t
bfg
t?8.>8>8>8>8< skd`fgs ? 8 54/44 s ? 451/44 skd`fgs ~ 8.< skd`fgs
T`, tmk [rbfus kqubth`f hs b thok n 8.< skd`fgs t` rkbdm obdm 2. Qutthfltmbt thok hf tmk hftklrbi3
(x) ? (5,871)(451/44) + 2/5(4547(451/44)V5 ? 2=1,;;< do 2.=1;;< jo ~2.=jo
Wmus hf tmk [rbfus Kqubth`f wk rkbdm obdm `fk hf be`ut 8.< skd`fgs bntkrtrbvkihfl b ghstbfdk `n be`ut 2.= jhi`oktkrs. Ikts d`fvkrt tmbt t` ohiks3
(2.=jo)(1.>524
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4>
Wmk [rbfus Hftklrbi Hs Hftrhluhfl
Wmk [rbfus Hftklrbi rkbdmks obdm `fk hf 2.= jhi`oktkrs, wmhdm hs tmkbo`uft `n jhi`oktkrs hf b ohik bfg hs tmk 8/; tmbt `ddurs hf Fbturk bfg tmk[fhvkrsk, f`t t` okfth`f tmbt ht ufhnhks ph bfg l`igkf rbth` bfg ph bfg
Kuikrs fuoekr k. \k mbvk birkbgy sm`wf m`w tmk [rbfus Hftklrbigksdrheks, jhi`oktkrs, fhfk-nhntms bfg nkkt bfg hfdmks, wmkf kvbiubtkg bttmk Lypsy Tmbobfs Oystkrh`us 2; hf tmk n ro `n 2; skd`fgs. Nhntkkf hstmk gklrkks tmk Kbrtm r`tbtks tmr`ulm hf bf m`ur. \k mbvk sm`wf m`wfhfk-nhntms ufhnhks lrbos bfg p`ufgs bfg dkfthlrbgk bfg nbmrkfmkht.
Wmus, f`t `fiy g`ks tmk [rbfus Hftklrbi gksdrhek jhi`oktkrs, ht gksdrheksohiks. Ht hs fk d`opbdt stbtkokft tmbt koe`ghks kvkrytmhfl. Blbhf wkskk tmk Tmbobfs 2; ufhnyhfl tw` systkos `n okbsurkokft hf tmbt tmkrkbrk nhntkkf gklrkks hf `fk m`ur `n rhlmt bsdkfsh`f.
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4 v`its t` d`fgudt b durrkft. Hf b gh`gk lbtk b mhlm v`itblk hsshx v`its bfg tmk dhrduht hs `f bfg b i`w v`itblk, `r lr`ufg (zkr`), tmkdhrduht hs `nn. @nn hs d`ghfl n`r zkr` bfg `f hs d`ghfl n`r 2. Skr`s bfg `fksdbf ek strufl t`lktmkr t` objk fuoekrs, bfg ikttkrs hf tmk bipmbekt.
Obfuki, tmk Lypsy Tmbobf, sbhg3 L`g hs bf Hgkb, Wmkrk brk tw` kikokfts.\k dbf tbjk tmhs t` ek `ur Xhf bfg Xbfl `n 8/; bfg ;/4. I`w v`itblk bfgtmk dhrduht hs `nn: mhlm v`itblk bfg tmk dhrduht hs f. Wmksk, blbhf, brk tmktw` kikokfts `n tmk Tmbobfs yhf bfg ybfl.
Ekdbusk y`u mbvk t` ruf b gh`gk bt ikbst 1.> v`its, tmhs hs suetrbdtkg nr`o
tmk shx v`its tmbt turf tmk gh`gk `f, s` rkbiiy ht `pkrbtks `f sihlmtiy iksstmbf shx v`its. Wmhs v`itblk gr`p `n 1.> ^`its hf tmk dhrduht hs wmbt wk wbftt` i``j bt. \k whii kvbiubtk tmk v`itblk gr`p `vkr tmk Tmbobfs oystkrh`us2; skd`fgs bfg `etbhf bf bo`uft `n p`wkr, tmkf bppiy tmbt p`wkr `vkr `fkykbr tmk thok ht tbjks tmk kbrtm t` l` br`ufg tmk Tuf. \k mbvk birkbgyn`ufg tmbt tmk Tmbobfs 2; f`t `fiy ufhnhks oktkrs whtm tmk ufhvkrsk, eutoktkrs whtm nkkt, bobzhfliy hf tmk [rbfus Hftklrbi `utihfkg e`tm hf WmkKxpi`hts @n Obfuki bfg Nurtmkr Kxpi`hts @n Obfuki.
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4=
F`w wk g` tmk dbiduibth`f3
@fk kikdtr`f v`it hs tmk kfkrly `n bf kikdtr`f nbiihfl tmr`ulm b p`tkfthbighnnkrkfdk `n `fk v`it, wmhdm hs kqubi t` 2.>15K-28 C`uiks.
@fk C`uik hs 21,111,111 krls
(1.> ^`its)(2.>15K-28 C`uiks) ? 8.>25K-51 C`uiks
(8.>25K-51 C`uiks)(21,111,111 krls/C`uik) ? 8.>25K-24 krls
(8.>25K-24krls)/(2; skd`fgs) ? >.71=K-27 krls/skd`fg
4>;.5; * 57 * >1 * >1 ? 42,;;11 skd`fgs/ykbr
(>.71=K-27 krls/skd)(42,;;11 skd`fgs) ? 5.15552211= ohdr`krls ?
5.1 ohdr`krls
Ht hs bio`st kxbdtiy tw` ohdr`krls! (Hs tmk tw` ohdr`krls pr`opthfl tmbtwk gkd`gk tmk okssblk hf ehfbry0)
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48
\mbt Okssblk0
Oy e``j B Wm`r`ulm Ghokfsh`fbi Bfbiyshs hs be`ut m`w H pr`vhgk kvhgkfdkhf supp`rt `n tmk hgkb tmbt kxtrbtkrrkstrhbis lbvk us `ur ufhts `nokbsurkokft, ihjk tmk n``t, tmk oktkr, tmk skd`fg, hf Bfdhkft thoks gksphtk
tmk mhst`ry tmbt tkiis us tmk oktrhd systko hs o`gkrf, bfg tmk n``t-p`ufgsystko, pkrmbps b ihttik boehlu`us hf hts mhst`ry.
H tmhfj bi`fl tmk wby hfg`hfl tmhs H oby mbvk n`ufg bf kfdryptkg okssblk nr`o kxtrbtkrrkstrhbishf tmk fuoekr3
5.15552211=
Hfs`nbr bs ht dbok t` us nr`o fbturbi d`fstbfts ihjk tmk dmbrlk `n bfkikdtr`f, tmk `rehtbi pkrh`g `n tmk Kbrtm, bfg fuoekrs wk hfvkftkg ihjk tmkokbsurk `n kikdtr`o`thvk p`tkfthbi, tmk v`it. Wmk hgkb hs tmbtkxtrbtkrrkstrhbis s`okm`w t`ig us t` okbsurk kikdtr`o`thvk p`tkfthbi whtm
b ufht `n v`its ekdbusk ht w`uig pr`gudk tmk be`vk fuoekr. H bo hftkrkstkghf ht ekdbusk `n tmk rkpkthth`f `n `fks bfg tw`s, bfg tmk skpbrbth`f `nfuoekrs ey zkr`s.
Ikt us i``j bt tmk pbrt bntkr tmk gkdhobi. Ht hs3
15552211=
Ht hs tmk skd`fg fuoekr tmrkk thoks, tmk nhrst fuoekr tw` thoks bfg tmk
ibst fuoekr hs tmk fuoekr `n ghlhts tmbt prkdkgk ht.
Wmk tmrkk tw`s bfg tmk tw` `fks bgg up t` tmk ibst ghlht, khlmt.
Wmk tw` `fks bgg up t` kbdm `n tmk tmrkk tw`s.
Ht d`uft nr`o rhlmt t` iknt 1,2,5,
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Gkd`ghfl Wmk Okssblk
Wmk okssblk hs3
15552211=
Wmk 555 bggs up t` shx, wmhdm hf ehfbry hs 221. Wmk fkxt sklokft hs 2211,wmhdm hs b fheeik, bfg hs tmk fuoekr 25. Wmhs sklokft hs hf ehfbry t` eklhfwhtm. Wmk ibst ghlht hs bf khlmt, wmhdm hs 2111 hf ehfbry. Wmus wk mbvk,hfdiughfl tmk nhrst ghlht, b zkr`, wmhdm hs b eht3
(1) (221) (2211) (2111)
\k wrhtk tmhs bs tmrkk fheeiks3
(1221) (2211) (2111)
Wmus 15552211= trbfsibtks bs 1221 2211 2111
\mhdm brk tmk tmrkk fuoekrs3
>, 25, =
Wmksk tmrkk fuoekrs ghvhgk fhdkiy hft` tmk 4>1 gklrkks `n b dhrdik3
4>1/25 ? 41 4>1/> ? >1 4>1/= ? 7;
Wmksk brk tmk bfliks hf tmk tmrkk spkdhbi trhbfliks whtm wmhdm wk dbf wrhtk`ut tmk trhl`f`oktrhd nufdth`fs `n hop`rtbft bfliks hf di`skg n`ro3
41->1-81 >1->1->1 7;-7;-81
>, 25, = mbvk tmk d`oo`f gkf`ohfbt`r `n tw`. Wmhs lhvks us tmk tmrkkfuoekrs 4, >, 73
4>7
\mhdm hs vkry di`sk t` tmk fuoekr `n Kbrtm gbys hf b ykbr (4>;). Brk
kxtrbtkrrkstrhbis p`hfthfl `ut tmbt tmk fuoekr `n Kbrtm gbys hf b ykbr brkdi`skiy d`ffkdtkg t` tmk tmrkk spkdhbi trhbfliks0 Wmk fuoekr hf ehfbry hshftkrksthfl, ekdbusk tmk `fks sdr`ii `nn nr`o rhlmt t` iknt fheeik t` fheeik,`fk ghlht bt b thok. Wmk okssblk hs bis` tmbt tmk fuoekr `n gbys hf b ykbrbrk d`ffkdtkg t` tmk tmrkk rkluibr tksskiibt`rs. Wmky mbvk shgks 4, >, bfg 7.
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72
Hf Lypsy Tmbobfhso Bfg Wmk [fhvkrsk wk t``j Cuphtkr bfg Tbturf bstmk eklhffhfl p`hfts bs tmky brk fkxt t` `fk bf`tmkr hf tmk s`ibr systko,brk hf tmk ohggik `n tmk s`ibr systko ey fuoekr, bfg dbrry o`st `n hts
kfkrly `n o`th`f bfg bfluibr o`okftuo, bs tmky brk tmk o`st obsshvkshlfhnhdbftiy. Wmkhr ghstbfdks nr`o tmk Tuf bt di`skst bppr`bdmks brk be`utnhvk bfg fhfk, rkspkdthvkiy, putthfl tmk Kbrtm fhdkiy bt `fk ufht nr`o tmkTuf. Bs wk n`ufg 8/; hf tmk o`ibr obss n l`ig t` tmk o`ibr obss `n shivkr,bfg hf tmk s`ibr rbghus t` iufbr `reht, wk dbiikg tmhs 8/; tmk Xhf `n tmk[fhvkrsk. O`st hfdrkgheiy, ekhfl 2.=, whtm tmk fk tbjhfl us br`ufg bdhrdik `fdk ikbvhfl 1.= `n tmk 4>1 hf b dhrdik, wk f`tkg l`hfl hf tmk `tmkrghrkdth`f t` ht wbs tmk 1 >1 ? 411
411 + 4>1 ? >>1
>>1/4>1 ? 22/>
\k sby Xhf hs 8/; bfg Xbfl hs 22/> bfg sthdj whtm Wmk Lypsy Tmbobfs 2;(Tkk Bf Kxtrbtkrrkstrhbi Bfbiyshs, dmbptkr thtikg Lypsy Tmbobfhso BfgWmk [fhvkrsk) bfg euhig `ur D`so`i`ly nr`o tmkrk.
\k birkbgy euhit Wmk Fkptufk Kqubth`f nr`o 8/; bfg uskg ht whtm ;/4 t`gkrhvk tmk pibfkt Kur`phb, eut ikt us bppiy 22/> hf pibdk `n ;/43
22/> ?6 22/>, 22/4, 22/5, 55/4, ? 2.=44, 4.>>, >+22 ? 2>,8.2>
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75
(bPf) ? b + (f-2)g ? 7.2>< ? 7.2>< + 8.2>< ? 8.2>
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74
@ur kqubth`f hs3
(bPf) ? 8.2>
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77
\k mbvk tmk Fkptufk Kqubth`f3
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7;
x(t) ?4>
;t" 7
y(t) ?44
21t+ 4
z(t) ? 8t" ;
;x +51
4>?
21y" 41
44?
z +;
8
;
4>x"
21
44y"
2
8z +
21
22? 1
#n ? $;/4>,"21/44,"2/8%
b?;/4> e?-21/44
d ? (;/4>)5+ (21/44)
5? 1.182=+1.128 ? 1.445=
g?-2/8
tbf"?e /b
"? #>;.4;=`
tbf$?g /d
$? #2=.7>`
->;.4;= gklrkks/2; gklrkks/m`ur ?-7.4; skd`fgs
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7>
\k mbg tmrkk kqubth`fs3 Wmk Fkptufk Kqubth`f (gkrhvkg nr`o tmk yhf `nfhfk-nhntms), Wmk [rbfus Kqubth`f (gkrhvkg nr`o tmk ybfl `n nhvk-tmhrgs),bfg Wmk Kbrtm Kqubth`f (gkrhvkg nr`o tmk bitkrfbtk ybfl `n kikvkf-shxtms).\htm tmrkk kqubth`fs, wk d`uig drkbtk tmk kqubth`f `n b pibfk hf tmrkkghokfsh`fs. \k n`ufg tmk f`robi vkdt`r t` tmk pibfk bfg gkgudkg nr`o hts
`rhkftbth`f gklrkks hf, bfg dbiikg ht rhlmt bsdkfsh`f bfg hts gklrkks up bfgdbiikg ht gkdihfbth`f. Gkdihfbth`f hs birkbgy hf gklrkks, eut wk mbg t`d`fvkrt gklrkks hf hft` m`urs, ohfutks bfg skd`fgs. \k f`tkg hf g`hfl bssudm tmbt `fdk blbhf tmk Lypsy Tmbobfs 2; ufhnhks tw` systkos `nokbsurkokft hf tmbt tmkrk brk 2; gklrkks t` kbdm m`ur `n rhlmt bsdkfsh`f.Wmbt hs t` sby tmbt tmk Kbrtm r`tbtks tmr`ulm 2; gklrkks kvkry m`ur(4>1/57 ?2;). Wmhs hs hop`rtbft ekdbusk tmhs oby ek bt tmk ebshs `n uroystkry. H wr`tk be`ut wmy H tmhfj wk mbvk b 57 m`ur gby bfg 4>1gklrkks hf b dhrdik hf oy dmbptkr thtikg Wmk Gbfdk @n Wmk Mkbvkfs hf oye``j Bf Kxtrbtkrrkstrhbi Bfbiyshs.
Ebdj t` wmbt wk wkrk g`hfl3 \k gkrhvkg nr`o tmk f`robi vkdt`r3 (;/4>, -21/44, -2/8) b i`dbth`f `f tmk dkiksthbi spmkrk `n 28m 4=o 47s bfg 2=gklrkks 5 b rklh`f hf tmk d`fstkiibth`f Tblhttbrhus. Wmk di`skstpr`ohfkft stbr t` tmhs H n`ufg wbs MG 2=7=4; bfg bis` fkbr, wbs Um` 12Tblhttbrhus. H n`ufg tmhs `f tmk sjy dmbrts hf tmk nrkk g`wfi`bgbeik sjydmbrthfl s`ntwbrk dbiikg Dbrtks gu Dhki. \k whii objk b lukss tmbt tmkkxtrbtkrrkstrhbis, wm` tmk`rkthdbiiy iknt us b okssblk, bs H gkgudkg nr`otmk fbturk `n kikdtr`fhds, brk nr`o tmbt rklh`f `n spbdk.
Tblhttbrhus hs b rhdm suookr d`fstkiibth`f n`r us mkrk hf tmk F`rtmkrfMkohspmkrk, wmhdm hs hf tmk ghrkdth`f `n tmk dkftkr `n tmk lbibxy.
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7
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7=
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78
Wmk pr`ckdth`f ey oy dbiduibth`f tmr`ulm oy d`so`i`ly `n yhf, ybfl, bfg2; n`r tmk `rhlhf `n oy okssblk nr`o kxtrbtkrrkstrhbis wbs s`okwmkrk hftmk kbstkrfo`st pbrt `n tmk d`fstkiibth`f Tblhttbrhus. Wmhs mbppkfs t` ek
tmk sbok pibdk wmkrk tmk `fk p`ssheik bihkf shlfbi wbs gktkdtkg hf tmkTkbrdm N`r Kxtrbtkrrkstrhbi Hftkiihlkfdk (TKWH). Ht wbs dbiikg Wmk \`wThlfbi ekdbusk `f Bulust 2;, 28
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;1
Ghg kxtrbtkrrkstrhbis rkbiiy bfthdhpbtk, wmkf tmky skft us hf 28
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;2
Qutthfl oyskin t` tmhfjhfl be`ut tmk okbfhfl `n tmk BK-4; bftkffb hf51123 B Tpbdk @gyssky, H w`uig sby ht hs, hf tmk nhio, tmk turf br`ufg p`hftn`r muobfjhfg ektwkkf ekhfl b ekhfl tmbt gkpkfgs `f tkdmf`i`ly bfg b
ekhfl wm` hs ihekrbtkg nr`o tkdmf`i`ly: ektwkkf ekhfl sthii bf bpk,bitm`ulm `fk tmbt hs spbdknbrhfl, bfg tmk stbrdmhig. M`w hs tmhs pkrthfkftt` oy d`ffkdth`f ektwkkf bf kxtrbtkrrkstrhbi okssblk, tmk \`w! shlfbi(gurbth`f
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;5
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;4
Thx-N`ig Tyooktry (Wmk Fhfk-Nhntms Bil`rhtmo hf Ukvkrsk)
4>1/> ? >1
4>1->1 ? 411
411 >1 ? 571
571/4>1 ?5/4
(5/4) + 2 ? ;/4
D`uftkrpbrt t` fhfk-nhntms hs nhvk-tmhrgs.
Wmk nhvk-tmhrgs bflik hs >1
gklrkks. Thxty gklrkks hs tmk okbsurk `n kbdm bflik hf bf kquhibtkrbi
trhbflik, wmhdm hs `fk `n tmk tmrkk tksskiibthfl rkluibr p`iyl`fs. B
sf`wnibjk whtm kbdm bro skpbrbtkg ey shxty gklrkks n`ros b rkluibr
mkxbl`f whtm hftkrfbi bfliks `n 251 gklrkks.
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;7
Wmk Xbfl Kikokfts
J ? p`tbsshuoFb ? T`ghuo
J/Fb ? 48.21/55.88 ? 2.< ~ 2.
Wmk K Nhiks
Ey
Hbf Ekbrgsiky
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;Dmbptkr , ;.7,
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>1
tmk sbok. Nurtmkr hfghdbth`f tmbt wk wkrk f tmk rhlmt trbdj wbs f`tkg hftmk nbdt tmbt Fkptufk mbs b shohibr hfdihfbth`f t` hts `reht, bs g`ks tmkKbrtm.
Ht wbs `fiy iknt t` nhfg tmk [rbfus kqubth`f, ekdbusk n`r kvkry yhf, tmkrk
sm`uig ek b ybfl.
\k n`ii`wkg tmk sbok pr`dkss bs n`r brrhvhfl bt tmk Fkptufk kqubth`f. \kobgk tmk skqukfdk `n bii wm`ik fuoekr ouithpiks `n nhvk-tmhrgs3
(;/4)f ? 2..
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>2
\k d`fshgkrkg tmk hftklrbi tmk obss `n b pibfkt hf kbrtm obssks, wmhdmdbok `ut t` ek 75. \k d`fshgkrkg tmk 4.4 t` ek tmk bddkikrbth`f bt htssurnbdk hf kbrtm lrbvhthks. Jf`whfl tmksk tw` qubfththks wk gktkrohfkgtmk pibfkt wbs be`ut tmrkk bfg b mbin thoks ibrlkr tmbf tmk Kbrtm.Jf`whfl hts obss bfg shzk, wk d`uig gktkrohfk hts gkfshty, bfg nr`o tmbt
hts d`op`shth`f, wmhdm turfkg `ut t` ek Kur`phuo, kikokft >4, wmhdm hspm`spm`rksdkft.
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>5
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>4
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>7
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>;
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>>
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>=
\k d`opbrk tmk o`ibr obss `n Kur`phuo t` tmbt `n Thihd`f3
Ku/Th ?2;2.8
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>8
Ht hs bppr`prhbtk tmbt Kur`phb hs d`ffkdtkg t` Kur`pb, tmk skd`fg LbihikbfO``f nr`o Cuphtkr, f`t cust ey fbok, eut hf s` nbr bs hts d`ffkdth`f t`
Thihd`f hf Wmk Fkptufk Kqubth`f. Ht w`rjs `ut lrkbt, ekdbusk ht hs tmk pibdkhf tmk T`ibr Tystko tmbt hs tmk ekst dbfghgbtk n`r ihnk eky`fg Kbrtm3 Ht mbsb tkfu`us bto`spmkrk d`op`skg prhobrhiy `n `xylkf bfg hs d`vkrkg whtmwbtkr hdk, tmbt oby mbvk wbtkr hf hts ihquhg n`ro ekfkbtm hts surnbdk.
Wmk o``f hs tmk rhlmt shzk sudm tmbt bs skkf nr`o tmk Kbrtm hs bppkbrsbe`ut tmk sbok shzk bs tmk Tuf. M`w nbr w`uig Kur`pb mbvk t` ek nr`oCuphtkr t` bppkbr tmk sbok shzk bs tmk suf g`ks nr`o Cuphtkr.
T`ibr Ubghus/Kur`pb Ubghus ? Cuphtkr-Tuf Tkpbrbth`f/x
>8;,881 jo/2,;>1.= jo ?
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MP5@ -!5Ku(@M)P4 + 4MP5
Wmbt hs, shx o`iks `n M5@ brk rkquhrkg n`r kvkry tw` o`iks `n Kur`phuo t`
objk tw` o`iks `n Kur`phuo Mygr`xhgk bfg Wmrkk o`iks `n Mygr`lkf lbs.H w`uig sby tmbt hs m`w tmbt kqubth`f rkbgs, tm`ulm oy dmkohdbif`okfdibturk hs b ihttik rusty. H w`uig sby shfdk tmk kur`phuo ghspibdkstmk mygr`lkf, tmbt tmhs hs b shflik ghspibdkokft rkbdth`f. H bo ihttik rusty`f oy rkbdth`f dibsshnhdbth`f bs wkii. Uklbrgikss, tmk kqubth`f dikbriystbtks tmbt `fk tmhrg `n tmk o`iks `n M51 brk tmk o`iks `n Kur`phuorkquhrkg n`r tmk rkbdth`f t` tbjk pibdk (5/>? 2/4). \k wrhtk3
MP5 ? 5(2.12) ? 5.15 l/o`i@ ? 2>.11 l/o`i
M5@ ? 5.15 + 2>.11 ? 2=.15 l/o`i
Ey i``jhfl up tmk o`ibr obssks `n tmk kikokfts hf tmk pkrh`ghd tbeik `n tmkkikokfts.
((2 o`i M5@)/(2=.15 l M5@))x((2.7K57 l M5@)/(mygr`spmkrk))? K55 o`i Ku)(2;2.8< l Ku/ o`i) ? 4.8;K57 l Ku
Wmk gkfshty `n Kur`phuo bt TWQ hs ;.574 l/doV4
(doV4/;.574 l)(4.8;K57 l) ?
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5,2>5 do
(;>,;>5,2>5 do)/(211 do)(2111 o) ? ;>7.>5 jo ~ ;>; jo
Wmk Kur`phuo Tpmkrk w`uig mbvk b rbghus n ;>; jhi`oktkrs. Wmbt `n tmko``f `n Cuphtkr dbiikg Kur`pb hs3
2,;>> jo
2,;>>/;>; ? 5.
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. Hftkrksthfliy, tmk dmkohdbi kikokfts Dbre`f,Fhtr`lkf, bfg @xylkf brk tmksk tmrkk kikokfts, bfg tmk o`st hop`rtbftf`f-oktbis hf tmk pkrh`ghd tbeik. Dbre`f hs tmk ebshs `n ihnk, objhfl `rlbfhdobttkr hf tmk n`ro `n mygr`dbre`fs. Fhtr`lkf hs be`ut
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=1
Wmk gby bntkr tmbt H t`ig Lberhki tmbt Bft`fh` sbys mk hs W`obtht`s er`tmkrey mhs nbtmkr bfg Lberhki sbhg tmbt ht wbs guk t` ekhfl s`rt `n trbghth`fbi hfbf `ig nbsmh`fkg wby tmbt Bft`fh` sbhg tmbt.
Wmhs hs hftkrksthfl ekdbusk `fk gby wmkf H wbs wbijhfl tmr`ulm tmk
Tbdr`o`ftk whtm Lberhki, wk d`uig skk up hf tmk mhiis nr`o mkr dbvk pbth`, bLypsy w`obf fbokg Ekikf (Ektmikmko) bfg H wbvkg t` mkr. Lberhki sbhgt` ok tmbt wk mbg t` mbvk b tbij. Mk t``j ok up t` b rko`tk pibdk hf tmkmhiis bfg wk sbt `f s`ok r`djs bfg mk t`ig ok3 X`u g`ft jf`w wmbt y`uw`uig ek hf n`r hn y`u obrrhkg b trbghth`fbi Lypsy Lhri.
Ht wbs tmk fhlmt ekn`rk tmbt H wbs up bt mkr tkrrbdk whtm mkr nbtmkr. Mk wbsf`t Obfuki tmk Lypsy Tmbobf, eut Obfuki tmk shflkr, Gkkp T`fl shflkr(dbftb`r). H t`ig Lberhki H wbs l`hfl tmkrk n`r b nibokfd` ikss`f bfg mksbhg Obfuki ks eukf` (Obfuki hs l``g). Wmbt hs wmbt kvkry`fk biwbyssbhg be`ut mho. Ht hs ekst kxpibhfkg ey E`e Gyibfs iyrhds, Mhs di`tmks brk
ghrty eut mhs mbfgs brk dikbf.
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=2
H mbvk n`ufg tmbt rbfg`oiy kv`ivhfl systkos `n okbsurkokft d`fvkrlk `ffhfk-nhntms, ihjk tmkrk hs fhfk-nhntms `n b gklrkk dkfthlrbgk pkr nbmrkfmkht,tmkrk brk 1.;8 lrbos eky`fg b wm`ik fuoekr `n lrbos pkr p`ufg, bfg
be`ut fhfk-nhntms jhi`oktkrs pkr ohik. H mbvk n`ufg oudm o`rk tmbf custtmhs bfg ht hs hf oy w`rj Bf Kxtrbtkrrkstrhbi Bfbiyshs wmhdm hs fbokg bssudm ekdbusk H sullkst kxtrbtkrrkstrhbis lbvk us `ur ufhts `n okbsurkokftey hfniukfdhfl mhst`ry, bs `pp`skg t` ekihkn tmbt mbs biwbys ekkf mkig tmbt`ur ufhts `n okbsurkokft kv`ivkg tmr`ulm b rbfg`o skrhks `n kvkfts. Hnkki bf bitkrfbtk kxpibfbth`f d`uig ek tmbt b rbfg`o skrhks `n vbiuks s`okm`w d`fvkrlks `f fhfk-nhntms hn sueckdtkg t` niudtubth`f ey b rbfg`o skrhks`n n`rdks (kvkfts). H mbvk p`hftkg `ut tmbt f`t `fiy g`ks fhfk-nhntms ufhny phbfg tmk l`igkf rbth`, eut k (Kuikrs fuoekr) bfg ph hn wk d`fshgkr tmk nhrstnkw ghlhts bntkr tmk gkdhobi hf bii fuoekrs. H nkki tmhs oby ek phv`tbi t`pr`vhfl tmk d`fckdturk, bfg ht w`uig skko tmk s`ibr systko, hf hts
kv`iuth`f, mbs d`fvkrlkg `f fhfk-nhntms bs wkii bs `ur ufhts `nokbsurkokft. O`st kxtrb`rghfbrhiy, fhfk-nhntms bfg ur ghnnkrkft systkos`n okbsurkokft (bs hf jhi`oktkrs bfg ohiks) dr`p up wmkf wk hftr`gudktmk fuoekr 2; hf oy [rbfus Hftklrbi, wmhdm H mbvk kxpibhfkg t` ek bd`fdkpt whtm hts `rhlhfs hf b Lypsy Tmbobf nr`o Tpbhf, hf oy sbok w`rj,fbokg be`vk. [fgkrtbjhfl tmk kfgkbv`r `n pr`vhfl oy d`fckdturk hsdurrkftiy eky`fg tmk sd`pk `n oy kgudbth`f hf obtmkobthds.
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=5
H mbvk n`ufg `ur ghnnkrkft systkos `n ufhts `n okbsurkokft t` ek gkkpiyd`ffkdtkg whtm `fk bf`tmkr bfg fbturk.
H sullkst tmk `rhlhfs `n tmkd`ffkdth`fs t` ek kxtrbtkrrkstrhbi, hn f`t guk t` s`ok strbflk pr`pkrty
wmkrk rbfg`oiy kv`ivhfl systkos d`fvkrlk `f b vbiuk `r skt `n rkibtkgvbiuks.
H cust rkbihzkg tmbt r``o tkopkrbturk, gknhfkg ey >= gklrkks N t` = +
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Oks`p`tbohb, hf Bfdhkft Tuokrhbf diby dufkhn`ro tbeikts, b d`fstbft tmbt
hs tmk d`oo`f gkf`ohfbt`r n`r bii dkiksthbi dydiks hf `ur s`ibr systko.
Wmk d`ffkdth`f wmkrk ^kfus hs d`fdkrfkg hs hf tmbt tmk pibfkt hs hop`rtbftn`r ufgkrstbfghfl dihobtk hf tmbt ht mbg b ruf bwby lrkkfm`usk knnkdt bfg
hs shohibr hf shzk bfg obss t` kbrtm.
Hs tmhs d`fshstkft whtm tmk myp`tmkshs tmbt oy Fkptufk Kqubth`f, wmhdmmbs b ouithpihkr `n
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Eh`i`lhdbi strudturks hf Fbturk brk o`rk typhdbiiy gksdrhekg ey nhvk-n`igsyooktry bfg, pmyshdbi strudturks hf Fbturk brk o`rk typhdbiiy gksdrhekgey shx-n`ig syooktry. \k whii dbii tmko Xhf bfg Xbfl, rkspkdthvkiy.
M`wkvkr, tmkrk brk tw` wbys t` gkrhvk yhf bfg tmkrk brk tw` wbys t`gkrhvk ybfl. \k whii dbii tmko Xhf2, Xhf5 bfg Xbfl2 bfg Xbfl5.
Xhf2 d`oks nr`o tmk dkftrbi bfliks hf b rkluibr pkftbl`f ektwkkf tmkrbghh tmbt okkt bt hts dkftkr3
4>1/;?1-1?>7= >7=/4>1?8/;
Xhf2?8/;
Xhf5 d`oks tmk kxtkrfbi bfliks hf b rkluibr pkftbl`f bt tmk hftkrh`r `n tmk
vkrthdks3
4>1-21=?5;5 4>1+5;5?>25 >25/4>1?21?411 411+4>1?>>1 >>1/4>1 ? 22/>
Xbfl2?22/>
Xbfl5 d`oks nr`o tmk bfliks hf b rkluibr mkxbl`f bt hts hftkrh`r vkrthdks3
4>1-251?571 571+4>1?>11 >11/4>1?;/4
\k o`gki [fhvkrsks whtm bfy d`oehfbth`f `n Xhf bfg Xbfl. Wmhs lhvks usn`ur o`gkis t` usk3
O`gki 23 Xhf2?8/; Xbfl2?22/>
O`gki 53 Xhf2?8/; Xbfl5?;/4O`gki 43 Xhf5?2O`gki 73 Xhf5?2
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=>
o`gkis shlfhnhdbftiy ey hfdiughfl tmk bfliks bt tmk vkrthdks `f tmk `utshgk`n tmk rkluibr p`iyl`fs.- Hbf Ekbrgsiky Bulust 8, 5124
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Wmksk obfhpuibth`fs g`fk ey Hbf Ekbrgsiky `f Bulust 8, 5124
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81
Hbf Ekbrgsiky Bulust 21, 5124
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82
Hbf Ekbrgsiky Bulust 21, 5124
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92/173
85
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93/173
84
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94/173
87
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8;
Ey
Hbf Ekbrgsiky
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8>
F`tks 12 N`r Nhiks [ Bfg K
D`pyrhlmt 5124 ey Hbf Ekbrgsiky
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8
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8=
D`sohd Brdmbk`i`ly
H d`fshgkr wmbt H g` t` ek wmbt H dbii d`sohd brdmbk`i`ly. D`sohd
Brdmbk`i`ly strhvks t` sby s`oktmhfl be`ut tmk [fhvkrsk ushfl
brdmbk`i`ly, bfg s`oktmhfl be`ut tmk muobf st`ry ushfl bstr`f`oy. Oy
nhrst kxp`surk t` D`sohd Brdmbk`i`ly oust mbvk ekkf wmkf oy d`iiklk
Dbiduius tkbdmkr wbs gkrhvhfl Kuikrs Fuoekr, k.
Bntkr gkrhvhfl ht, mk
gkrhvkg Kuikrs Kqubth`f, wmhdm rkibtks, Kuikrs fuoekr (k), tmk hoblhfbry
fuoekr (h), tmk rbth` ph, bfg fklbthvk `fk bii t` `fk bf`tmkr.
Wmk kqubth`f
hs3
(k)VZ(h)(ph)_ ?-2
Mk p`hftkg `ut tmbt tmhs kqubth`f, bs wkii, rkibtks tmrkk lk`lrbpmhdbi
rklh`fs t` `fk bf`tmkr, Hfghb, Klypt, bfg Kur`pk hfs`nbr bs fklbthvk
fuoekrs d`ok t` us nr`o Hfghb (Erbmobluptb), tmk hoblhfbry fuoekr
d`oks t` us nr`o Klypt (Mkr`f `n Bikxbfgrhb, bii tm`ulm Lrkkj, wbs fbthvk
t` Bikxbfgrhb, U`obf Klypt), ph t` s`ok bddurbdy nr`o Bfdhkft Lrkkdk
(Brdmhokgks), bfg k nr`o Twhtzkribfg (Cbd`e Ekrf`uiih).
\k dbf skk m`w tmhs rkvkibth`f w`uig ek jky t` D`sohd Brdmbk`i`ly.
Emrbmobluptb (br`ufg >5=)
Mkr`f `n Bikxbfgrhb (d21 ;; 2
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NHDWH@F-UKBIHWX KFWBFLIKOKFW
NKEU[BUX 7 5124
EX
HBF EKBUGTIKX
Ikvhfs`f
\k eklbf whtm tmk di`skst stbr t` us, Bipmb Dkftburh. Ht hs be`ut 7.5 t` 7.4ihlmt ykbrs bwby. \k r`ufgkg tmbt t` n ur ekdbusk wk brk gkbihfl whtmwm`ik fuoekrs. \k tmkf ghg b rbfg`o wbij, bfg dbiduibtkg tmk pr`ebehihty`n ibfghfl `f Bipmb Dkftburh hf 21 rbfg`o cuops `n `fk ihlmt ykbr kbdm.\k f`tk tmbt b ihlmt ykbr hs tmk ghstbfdk ihlmt trbvkis hf `fk ykbr, b ykbrekhfl tmk thok ht tbjks tmk kbrtm t` trbvki br`ufg tmk suf, bfg tmbt ihlmt
spkkg hs b fbturbi d`fstbft. Bs wkii wk f`tk tmbt Bipmb Dkftburh hs b stbrcust ihjk tmk suf, shohibr hf shzk, iuohf`shty, bfg tmk sbok spkdtrbi dibss.\k r`ufgkg `ur bfswkr t` tmk fkbrkst wm`ik fuoekr, bfg ht wbs tmbt wkmbvk b 25% dmbfdk `n ibfghfl `f Bipmb Dkftburh.
\k tmkf sbhg tmhs wbs tmk pkrdkft `n gkvki`pokft t`wbrgs euhighflmypkrgrhvk, bf kflhfk tmbt w`uig tbjk us t` tmk stbrs. \k tmkf sbhg `urpr`lrkss t`wbrgs mypkrgrhvk oby gkvki`p bdd`rghfl t` tmk fbturbi lr`wtmkqubth`f3
(x(t))?(xP1)kVjt
W` nhfg j wk mbvk tbjkf t ?71 ykbrs, ekdbusk hf 28>8 tmk nhrst obf skt n``t`f tmk o``f, bfg hf 5118 wk ibufdmkg tmk Mkrsdmki bfg Qibfdj tkiksd`pkstmbt whii skk ebdj t` fkbr tmk eklhffhfl `n tmk [fhvkrsk. \k mbvk tbjkfxP1 ? 2/211 t` sby tmbt wk eklbf whtm `fk stkp ut `n 211. Wmk rksuit hs3
(j) ? 1.1>52
\k mbvk3
(i`l 211) ? (1.1>52)t i`l k
@r, t ? 8 +
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bgvkfturk hf 5175. H dbii tmhs nhdth`f-rkbihty kftbflikokft. H wr`tk hf oye``j3 Nhdth`f-Ukbihty Kftbflikokft3 Ikvhfs`f, Bsho`v, bfg Dibrjk3
Hf tmk dbsk `n Qbui Ikvhfs`f, sdm`ibrs hf tmk nuturk trbvki tmr`ulm thokbfg usk di`fhfl, b d`fdkpt rkibtkg t` brthnhdhbi hftkiihlkfdk (ht hs tmk
drkbthfl `n muobf rkpihdbs bs wkii, eut eh`i`lhdbi, f`t kikdtr`fhd), bfg tmkl`bi hs t` sbvk lrkbt bfdhkft tmhfjkrs nr`o Lrkkdk, bfg t` obfhpuibtkkvkfts hf tmk pbst n`r b p`shthvk `utd`ok n`r tmk nuturk `n muobfhty, cust bstmk r`e`ts try t` g` hf tmk w`rj `n Bsho`v.
Bs ht w`uig turf `ut, tmk f`vkity rbthfl n`r tmk ykbr wk skt n``t `f tmko``f hf tmk Tmkihbj ^krsh`f `n tmk OdJkffb Whowbvk, hs `ur lr`wtm rbtkd`fstbft 1.1>52 wmhdm ouithpihkg ey tkf bfg r`ufgkg t` tw` pibdks bntkrtmk gkdhobi ht tmk l`igkf rbth` d`fculbtk. Wmk Whokwbvk hs supp`skg t`sm`w tmk wby mhst`ry ufvrbvkis, hn wk tbjk 5125 bs tmk kfg p`hft.
Qkrmbps `ur dbiduibth`f rknkrs f`t t` mypkgrhvk, eut t` `tmkr hssuks hn wktbjk Wmk Qi`t W` Tbvk T`drbtksbs b gbtb p`hft3 Ht gkbis whtm pmhi`s`pmy,vbiuks, di`fhfl, bfg oudm o`rk. Ht oby kvkf ek wk brk f`t tbijhfl be`uttmk Kbrtm, eut bf`tmkr dhvhihzbth`f `f bf`tmkr pibfkt hf tmk [fhvkrsk. @urbdth`fs d`uig ek d`ffkdtkg t` ihnk kiskwmkrk. \k cust g`ft jf`w, wk `fiyprkskft tmk dbiduibth`fs.
Bsho`v
Hf tmk dbsk `n Hsbbd Bsho`v, wk brk nbr hf tmk nuturk `n muobfhty. Hf mhsU`e`t Tkrhks, Bsho`v mbs obf objhfl r`e`ts wm`sk pr`lrboohfl `fiy
bii`ws tmko t` g` tmbt wmhdm hs l``g n`r muobfhty. Bs b rksuit, tmkskr`e`ts, brthnhdhbi hftkiihlkfdk (BH), tbjk bdth`fs tmbt pr`pki muobfhty hft`skttihfl tmk Lbibxy, hf tmk r`e`t skrhks, bfg uithobtkiy sbvk muobfhty bntkrtmky mbvk skttikg tmk Lbibxy bfg obgk bf kophrk `n ht (Hf tmk N`ufgbth`fTkrhks).
H f`w nhfg tmbt Hsbbd Bsho`v puts sudm b gkvki`pokft hf mhs sdhkfdk nhdth`fbt b shohibr thok hf tmk nuturk, prkdhskiy hf 5177, `fiy b ykbr bntkr oyprkghdth`f bfg tw` ykbrs bntkr Thkrrb \btkrs hs mbfgkg tmk fkwiyghsd`vkrkg g`duokft tmbt hfhthbtks mkr bgvkfturk. T`, wk mbvk oyprkghdth`f, wmhdm hs rkibtkg t` tmk strudturk `n tmk ufhvkrsk hf b oysthdbi
wby rhlmt hf ektwkkf tmk gbtks `n Ikvhfs`f bfg Bsho`v, tmkhr gbtks `fiyekhfl b ykbr ikss bfg b ykbr lrkbtkr tmbf ohfk.
Bsho`v pibdks mypkrgrhvk hf tmk ykbr 5177 hf mhs sm`rt st`ry Kvhgkfdkwmhdm hs pbrt `n mhs sdhkfdk nhdth`f d`iikdth`f `n sm`rt st`rhks dbiikg, H,U`e`t.
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Wmhs hs b d`iikdth`f `n sm`rt st`rhks wmkrk U`e`t Qsydm`i`lhst Gr. TusbfDbivhf hs hftkrvhkwkg ey b wrhtkr be`ut mkr kxpkrhkfdk whtm tmk d`opbfy`f kbrtm hf tmk nuturk tmbt nhrst gkvki`pkg s`pmhsthdbtkg r`e`ts. Hf tmhse``j, tmk ibws `n r`e`thds brk drkbtkg bfg tmk hgkb `n tmk p`shtr`fhd erbhfhftr`gudkg, bfg tmk fbturk `n tmk hopbdt r`e`ts w`uig mbvk `f muobf
dhvhihzbth`f hs kxpi`rkg. N`ii`whfl tmhs d`iikdth`f `n st`rhks Bsho`v wr`tktmrkk o`rk f`vkis, wmhdm d`oprhsk tmk r`e`t skrhks, Wmk Dbvks `n Ttkki,Wmk Fbjkg Tuf, bfg Wmk U`e`ts `n Gbwf.
H, U`e`t hs Kbrtm hf tmk nuturk cust ekn`rk Muobfhty skttiks tmk o`rkfkbrey stbrs. Wmk f`vkis d`oprhshfl Wmk U`e`t Tkrhks brk wmkfmuobfhty mbs d`i`fhzkg tmk fkbrey stbr systkos, Wmk N`ufgbth`f Wrhi`ly,bfg hts prkqukis bfg skqukis brk be`ut tmk thok muobfhty mbs sprkbgtmr`ulm`ut tmk kfthrk lbibxy bfg obgk bf Kophrk `n ht. Bii `n tmksk e``jsdbf ek tbjkf t`lktmkr bs `fk st`ry, whtm dmbrbdtkrs bfg kvkfts hf s`ok,`ddurrhfl hf `tmkrs.
Mypkrgrhvk hs hfvkftkg hf H, U`e`t ey b r`e`t dbiikg Wmk Erbhf, `wfkg eytmk d`opbfy n`r wmhdm Gr. Tusbf Dbivhf w`rjs wmkf ht hs nkg tmkobtmkobthdbi i`lhsthdbi pr`eikos `n objhfl mypkrgrhvk, bfg bsjkg t` s`ivktmko. Ht g`ks s`ivk tmko bfg ht `nnkrs tmk spkds `f euhighfl bf hftkrstkiibrsmhp, n`r wmhdm tw` kflhfkkrs n`ii`w hf hts d`fstrudth`f. Wmky brkmuo`r`usiy skft bdr`ss tmk lbibxy ey Wmk Erbhf, f`t kxpkdthfl ht, bfger`ulmt ebdj t` kbrtm hf tmk smhp bntkr tmky d`fstrudtkg ht. Wmhs wbs hf tmkst`ry hf H, U`e`t thtikg Ksdbpk!.
Eut Gr. Tusbf Dbivhf stbtks hf tmk n`ii`whfl sm`rt st`ry, tmbt H okfth`fkg,Kvhgkfdk3
Eut tmbt wbsft ht, khtmkr@m, kvkftubiiy, tmk smhp bfg `tmkrs ihjk htekdbok l`vkrfokft pr`pkrty: tmk Cuop tmr`ulm mypkrspbdk wbspkrnkdtkg, bfg f`w wk bdtubiiy mbvk muobf d`i`fhks `f tmk pibfkts `ns`ok `n tmk fkbrkr stbrs, eut tmbt wbsft ht.
Ht wbs wmbt mbppkfkg t` tmk pk`pik mkrk `f Kbrtm hf ibst nhnty ykbrs tmbtrkbiiy d`ufts.
Bfg, wmbt mbppkfkg t` pk`pik `f Kbrtm0 Wmk bfswkr hs hf tmk sbok st`ryKvhgkfdk nr`o wmhdm tmbt qu`tk hs bt tmk eklhffhfl. Ht wbs wmkf tmk
Uklh`fs `n tmk Kbrtm n`rokg Wmk Nkgkrbth`f. Gr. Tusbf Dbivhf sbys bt tmkkfg `n tmk st`ry Kvhgkfdk3
Mk wbs b vkry l``g oby`r: nhvk ykbrs ibtkr mk ghg ekd`ok Uklh`fbi D`-`rghfbt`r. Bfg wmkf tmk Uklh`fs `n Kbrtm n`rokg tmkhr Nkgkrbth`f hf 5177,mk ekdbok tmk nhrst \`rig D`-`rghfbt`r.
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Ht hs nr`o tmbt stbtkokft tmbt H lkt oy gbtk `n 5177 bs tmk ykbr Bsho`vpr`ckdts n`r mypkrgrhvk.
Dibrjk
Kvkrytmhfl Hf 51123 B Tpbdk @gyssky ey Brtmur D. Dibrjk, Gkrhvkg Nr`oFhfk Nhntms
Hf 51123 B Tpbdk @gyssky, tmk smhps d`oputkr wbs dbiikg MBI. Ht wbs tmkerbhf bfg dkftrbi fkrv`us systko `n tmk smhp. Ht wbs bsjkg hf tmk o`vhk3 HsMBI hftkiihlkft0 Hs mk bihvk0 T` nbr H mbvk kxpibhfkg m`w fhfk-nhntms `ddurshf tmk T`ibr Tystko bfg Fbturk. H mbvk bis` n`ufg tmbt b d`oputkr ihjkMBI hs bihvk, hf b wby. MBI wbs shihd`f ebskg bfg H mbvk n`ufg tmbt shihd`fmbs tmk l`igkf rbth` d`fculbtk hf ht, wmhdm hs rkdurrkft tmr`ulm`ut ihnk bfgtmbt fhfk-nhntms hs hf tmk l`igkf rbth` d`fculbtk. H wr`tk3
H mbvk bis` n`ufg tmbt tmk ebshs `n d`oputkrs bfg BH (brthnhdhbihftkiihlkfdk), wmhdm hs g`pkg shihd`f, mbs tmk l`igkf rbth` hf tmk okbfs `n htsd`op`fkfts. Wmk l`igkf rbth` hs rkdurrkft tmr`ulm`ut ihnk ekdbusk `n tmkgyfbohds ht mbs t` `nnkr. G`pkg hs shihd`f, pm`spm`rus, bfg e`r`f. Wmksk brkfbturbiiy `ddurrhfl kikokfts, obgk ey fbturk, fbokiy n`rlkg hf stbrs. Hn Qhs pm`spm`rus, E hs E`r`f, bfg Th hs shihd`f (lk`oktrhd okbf ey Th)3
sqrt(Q*E)/Th?sqrt(41.8;
bfg ikt us tbjk tmk mbro`fhd okbf ektwkkf pm`spm`rus bfg e`r`f bfgghvhgk ht ey shihd`f3
(5*(41.8
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Wmk l`igkf rbth` d`fculbtk hs 1.>2= t` tmrkk gkdhobi pibdks. F`thdk tmbttmk 5fg bfg tmhrg ghlhts bntkr tmk gkdhobi brk 2 bfg =, tmk tw` ghlhts hf 8/;ghvhgkg `ut. Wmk 2 bfg > bgg up t` ohfus tmk `fk hs `ur nhvk, bfg, tmk khlmt pius tmk `fk hs `ur fhfk.T`ksskfthbiiy, wk mbvk d`ffkdtkg tmk o`f`ihtm `n Brtmur D. Dibrjk whtm
fbturk, bfg d`oputkrs bfg brthnhdhbi hftkiihlkfdk, hftklrbtkg dhrduhts,trbfshst`rs, gh`gks (g`pkg shihd`f), whtm tmk o`f`ihtm.
BK-4; Hs Ukibtkg W` Fhfk-Nhntms
H wr`tk b sm`rt st`ry ibst fhlmt, dbiikg Lypsy Tmbobfhso bfg tmk [fhvkrskbe`ut tmk BK-4; ufht, wmhdm hs tmk ufht hf tmk o`vhk bfg e``j 51123 BTpbdk @gyssky tmbt MBI rkp`rts whii nbhi bfg ghsd`fthfuk d`ooufhdbth`ft` Kbrtm. H gkdhgkg t` rkbg tmk pbssblk gkbihfl whtm tmk kvkft hf 5112 bfgMBI, tmk smhp d`oputkr, rkp`rts ht whii nbhi hf whtmhf
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Ikvhfs`f, Bsho`v, Dibrjk, Bfg Wmk Fkptufk Kqubth`f
H wr`tk b e``j wmkrk H objk b prkghdth`f n`r tmk hfvkfth`f `n mypkrgrhvk. Htdbok `ut sbfgwhdmkg ektwkkf tmk gbtk Hsbbd Bsho`v prkghdts n`rmypkrgrhvk (5177) hf mhs sdhkfdk nhdth`f st`rhks, H, U`e`t, bfg tmk gbtk hf
wmhdm Qbui Ikvhfs`fs Mkrh`hf, Thkrrb \btkrs eklhfs mkr bgvkfturks(5175), hf mhs e``j, Wmk Qi`t W` Tbvk T`drbtks. Wmk gbtk H prkghdtkg whtmobtmkobthds, wbs 5174.
H mbppkfkg t` objk oy prkghdth`fs gurhfl b thok wmkf H wbs rkbghfl tmkskw`rjs `n Ikvhfs`f bfg Bsho`v. X`u dbf hoblhfk oy surprhsk wmkf H n`ufgNhdth`f Kftbflikg \htm Ukbihty, Wmkrk hs oudm o`rk t` tmhs st`ry, bfg htrksuitkg hf oy e``j Nhdth`f-Ukbihty Kftbflikokft3 Ikvhfs`f, Bsho`v, BfgDibrjk. Obfy hftkrksthfl kftbflikokfts dr`ppkg up.
Cust wmbt wbs tmk rkskbrdm H wbs g`hfl wmkf H kxpkrhkfdkg tmhs
kftbflikokft0 H wbs w`rjhfl `f oy kfhlobthd ghsd`vkry `n fhfk-nhntms hftmk [fhvkrsk, wmhdm ikbg t` oy e``j Brk Muobfs Bi`fk Hf Wmk [fhvkrskBfg Brk Wmky Mkrk N`r B Ukbs`f.
F`w H nhfg Nhdth`f-Ukbihty Kftbflikokft3 Ikvhfs`f, Bsho`v, Bfg Dibrjk hskftbflikg whtm Brk Muobfs Bi`fk Hf Wmk [fhvkrsk Bfg Brk Wmky MkrkN`r B Ukbs`f0 H shopiy t``j Brtmur D. Dibrjks 51>23 @gyssky Wmrkkekdbusk ht wbs tmk `tmkr e``j H wbs rkbghfl wmkf H wbs g`hfl oy rkskbrdmbfg wbs pbrt `n tmk Nhdth`f-Ukbihty Kftbflikokft3 Ikvhfs`f, Bsho`v, BfgDibrjk.
H shopiy tm`ulmt shfdk Dibrjks @gyssky Wmrkk, ekdbusk ht tbjks pibdk hf51>2 bfg tmbt hs tmk thok di`skst t` tmk 5175 `n Thkrrb \btkrs, tmk 5177 `nBsho`v, bfg tmk 5174 `n oy prkghdth`f, H w`uig suetrbdt oy 5174 nr`o tmk51>2 `n Dibrjks @gyssky Wmrkk bfg tmk rksuit hs3
51>2-5174?2=
Wmk bfswkr hs ht tbjks pibdk 2= ykbrs bntkr oy prkghdth`f `n 5174. Ghvhgk2= ey 21, tmk fuoekr `n nhflkrs wk mbvk t` d`uft `f, bfg y`u lkt `fk p`hftkhlmt. Hn y`u ghvhgk tmk 8 ey ; hf oy kfhlobthd fhfk nhntms, y`u lkt `fk p`hftkhlmt, bs wkii. H d`fshgkr Ikvhfs`f bfg Bsho`vs gbtks t` ek uppkr bfg
i`wkr ihohts n`r mypkrgrhvk, ekdbusk oy vbiuk hs sbfgwhdmkg ektwkkf tmktw`. Wmbt hs ht whii bt tmk kbrihkst mbppkf hf 5175 `r ey tmk ibtkst 5177.Khtmkr tmbt, `r tmk tmrkk gbtks brk spkbjhfl `n bf kp`dm d`ffkdtkg t` tmkstbrs, hf pbrthduibr Bipmb Dkftburh, ekdbusk H uskg ht hf oy dbiduibth`f, f`tt` okfth`f tmk spkkg `n ihlmt bfg tmk thok ht tbjks kbrtm t` objk `fkrkv`iuth`f br`ufg tmk suf (2 ykbr).
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Bsho`v, Dibrjk, bfg Mkhfikhf brk d`fshgkrkg tmk Wmrkk Qhiibrs `n O`gkrfTdhkfdk Nhdth`f. H skk Mkhfikhf o`rk bs ushfl sdhkfdk nhdth`f t` kxpi`rkp`ihthds. H ihjk t` put Ikvhfs`f, Bsho`v, bfg Dibrjk t`lktmkr bs tmk mkbrt nTdhkfdk Nhdth`f, wmhdm hs tmk sphrht `n sdhkfdk t`gby, bfg pkrmbps Mkhfikhfbs tmk ohfg, s`okthoks, t` usk tmk Mhfgu o`gki wmkrk Wmk Mkbrt hs vkry
hop`rtbft, eut okbfs f`tmhfl whtm`ut tmk luhgbfdk `n tmk Ohfg. @n d`urskbii tmk be`vk butm`rs koebrj, uithobtkiy hf tmk rkbio `n tmk ohfg bfg tmkmkbrt.
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21>
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Fbturk Tpkbjs @n Muobf Gksthfy
Hfgkkg `ur gksthfy skkos t` ek `utihfkg ey tmk strudturk `n fbturk, bfg H
w`uigft ek surprhskg ht mbs kxtrbtkrrkstrhbi thks. H wr`tk3
Wmk Fhfk-Nhntms Oystkry Eklhfs t` Kxpbfg3 Bii`ys
Wmhs hs rkbiiy kxdhthfl, bfg ht sm`ws oy rkbs`fhfl oby ek d`rrkdt, t` tmhfjtmbt muobf bdthvhthks mbvk b ghvhfk d`ffkdth`f t` tmk d`so`s. H mbg n`ufgtmbt Tbturf (skd`fg ibrlkst pibfkt) `reht t` Cuphtkr (nhrst ibrlkst pibfkt)`reht wbs 8 t` ; putthfl tmk Kbrtm bt fk ufht nr`o tmk Tuf. Bobzhfliy Hn`ufg tmk s`ibr rbghus t` tmk iufbr `reht wbs tmk sbok tmhfl. \mbt hs o`rktmk o`st prkdh`us `n tmk oktbis hf o`ibr obss, l`ig t` shivkr wbs 8 t` ; bswkii.
Ht w`uig skko bs kbriy bs >111 ED tmk Tuokrhbfs wkrk p`ufghfl l`ig bfgshivkr `ut t` sduipt tmhfls ufthi tmky rbf `ut. Wmky wkrk g`hfl tmhs whtmd`ppkr bs wkii, bf`tmkr s`nt, obiikbeik oktbi, ufthi tmky rbf `ut. Bntkrruffhfl `ut tmky mbg t` ikbrf t` skpbrbtk tmk `rks `n tmksk oktbis nr`o`tmkr suestbfdks. Kvkftubiiy tmky hfvkftkg jhifs tmbt bii`wkg tmko t`okit tmk stunn bfg ohx ht whtm thf, t` drkbtk tmk nhrst bii`y, wmhdm wk dbiier`fzk. Wmhs eklbf bf blk dbiikg Wmk Er`fzk Blk, bs kbriy bs 4;11 ED. Htwbs tmk eklhffhfl `n oktbiiurly.
Wmk Tuokrhbfs hfvkftkg tmk jhifs hf tmk nhrst pibdk t` nhrk diby. W`gby,
objhfl D`ookrdhbi Er`fzk usks zhfd bs tmk bii`yhfl oktbi. T` H luksskg,cust bs L`ig t` Thivkr hs 8 t` ;, s` sm`uig thf t` zhfd ek tmk sbok. Wmhs hskxbdtiy wmbt mbppkfkg3
Bu/Bl ? 28>.8
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brdmbk`i`lhdbi thok sdbik. Wmbt tmky w`uig g` ht skkos t` ek wrhttkf hf tmkstbrs, bfg H w`uigft ek tmk nhrst t` sullkst ht wbs kxtrbtkrrkstrhbis `nhftkiihlkfdk nbr eky`fg tmbt `n tmk muobf (m`o` sbphkf) tmbt mbg b mbfg hfbii `n tmhs.
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Oy ghsd`vkry `n fhfk-nhntms hf fbturk ikbg t` oy fkptufk kqubth`f bfg t`oy urbfus kqubth`f. Fhfk-nhntms H n`ufg wbs tmk yhf n r wmhdm ybfl wbsnhvk-tmhrgs.
\mbt g`ks tmhs okbf0 \kii hn L`ig t` Thivkr hs 2.=, bfg thf t` zhfd hs 2.=
(Er`fzk Blk), tmkf sm`uig f`t tmk fkxt fuoekr hf tmk fhfk-nhntms skqukfdk,wmhdm hs 4.>, rkprkskft Wmk Hr`f Blk. \kii ht g`ks. Bs ht turfs `ut, l`ig(Bu) t` Hr`f Nk hs 4.;, ghvhghfl `ut o`ibr obssks, bs wk stbtkg hf WmkLkfkshs Myp`tmkshs.
Bntkr tmk Hr`f Blk, `fk ohlmt d`fshgkr ht hs f`w, bfg hs tmk Thihd`f Blk,ekdbusk shihd`f bii`ws n`r hftklrbtkg dhrduhtry. \k d`uig dbii ht tmk blk `nkikdtr`fhds, pkrmbps ekttkr tmk blk `n ghlhtbi kikdtr`fhds. Thihd`f sm`uigtmkf ek tmk tmhrg tkro hf tmk fhfk-nhntms skqukfdk, wmhdm hs ;.7. Eut wkw`uig mbvk t` ghvhgk ht hft` s`oktmhfl. @fk w`uig lukss ht w`uig ekKur`phuo, ekdbusk ht mbs f` eh`i`lhdbi nufdth`f, cust b usk n`r kikdtr`fhds hf
tmbt ht hs pm`spm`rksdkft (li`ws). \kii cust bs H luksskg, Kur`phuo (Ku)ghvhgkg ey Thihd`f (Th) hs ;.73
Ku/Th ?2;2.8 ~ ;.7
Ht hs bio`st kxbdt!
Wmk Blk `n Hftkrstkiibr Wrbvki
Whf t` zhfd wbs tmk 2.= `n Wmk Er`fzk Blk. L`ig t` Hr`f wbs tmk 4.> `n WmkHr`f Blk. Kur`phuo t` Thihd`f wbs tmk ;.7 `n tmk Ghlhtbi Kikdtr`fhds Blk.
Wmk fkxt fuoekr hf tmk fhfk-nhntms skqukfdk hs
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Thlfbturk Wmk`ry
(H p`st tmhs blbhf Bulust 5>, 5124 bntkr skkhfl hf tmk wkst fhlmt `n Bulust5;, 5124 wmbt skkokg b oktk`r o`vhfl s` si`w bfg tmkf vbfhsmhfl tmbt Htm`ulmt ht wbs b drbnt hf tmk wkst).
B objksmhnt ebsth`f `n jf`wikglk kxhsts hf b nuturk o`rk ihjk tmk ghstbftpbst. Nr`o tmkhr kbrihkr gbys tmky mbvk dbrrhkg b okssblk nr`o tmk pbst,tmbt b stbrnbrhfl pk`pik whii ek hf tmk vhdhfhty `n Kbrtm bt b dkrtbhf thok bfgpibdk, bfg tmbt hn tmksk objksmhnt sdhkfthsts dbf d`fstrudt b r`djkt tmbt whiitbjk tmko hft` Kbrtm `reht bt tmk sbhg pibdk bfg thok, ht whii rklhstkr `ftmkhr rbgbr bs b squhllik, bf s-smbpkg ihfk bfg tmky whii tmkf ek beik t`objk d`ftbdt whtm tmko bfg lhvk tmko tmk jf`wikglk t` dbrry Kbrtm ebdjhft` tmk nuturk bfg t` tmk stbrs. Wmbt s-smbpkg ihfk hs b shlfbturk, `n tmkprkskfdk `n b r`djkt, bfg wk dbii tmhs shlfbturk tmk`ry, n`r tmk obp `n tmksquhllik hs 4, 5, 5, 2, wmhdm lk`oktrhdbiiy hs b r`djkt3 4 t` 5 hs tmk nuki
kckdth`f f`zki, 5 t` 5 hs tmk nuki d`ftbhfokft vksski, bfg 5 t` 2 hs tmkdbpsuik.
Hbf EkbrgsikyOby =, 5124
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Wmk BK-4; [fht
Wmk BK-4; [fht skkos t` mbvk ekkf tmk ghrkdth`fbi gkvhdk tmbt jkpt tmkd`ooufhdbth`fs bftkffb be`brg tmk Ghsd`vkry, p`hftkg bt tmk Kbrtm. Bwkeshtk, n`r wmhdm tmk butm`r g`ks f`t skko t` prkskft mhs fbok tmbt hs
gkghdbtkg t` euhighfl s`ok `n tmk pr`ps nr`o tmk o`vhk 51123 B Tpbdk@gyssky, hfdiughfl tmk BK-4; [fht, mbs tmk`rhzkg bs oudm. Wmkd`fdiush`fs brk grbwf f`t cust nr`o tmk hgkb tmbt BK ohlmt stbfg n`rBzhoutm bfg Kikvbth`f, eut tmbt tmk ufht skkos t` m`usk b lyr`sd`pk.5112 rknkrs t` tmk BK-4; [fht, eut 5121 rknkrs t` tmk BK-4; Bftkffb. Hihjk t` usk tmk ibttkr ekdbusk ht w`uig objk skfsk t` gksdrhek tmk Bftkffbhf tkros `n tmk BK-4; [fht.
Hbf EkbrgsikyBulust 25, 5124
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Bii Bfliks D`vkrkg
M`w d`uig mbvk H f`t f`thdkg ht0 Wmk TKWH kxtrbtkrrkstrhbi shlfbi dbiikgtmk \`w! Thlfbi wbs gktkdtkg `f Bulust 2;, 28
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Ubfg`oiy Kv`ivkg [fhts F`t T` Ubfg`o Hf Fbturk
\k mbvk n`ufg 8/; hf e`tm tmk oktrhd systko bfg n``t-p`ufg systko,tkopkrbturk hf dkfthlrbgk bfg nbmrkfmkht bfg t` ek d`ffkdtkg t` fbturkbfg t` ufhny ph bfg tmk l`igkf rbth` bfg ph bfg kuikrs fuoekr. Kbrtm
lrbvhty (l) hf tmk oktrhd systko hs `fk o`rk t` bgg t` tmk ihst3
8=2 do/sV5
Ht mbs tmk fhfk `n fhfk-nhntms, tmk `fk bfg khlmt tmbt objk up tmk 2.= tmbt hs8/;, bfg tmk khlmt ohfus tmk `fk (
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Wmk Qr`eiko Bt Mbfg Hf Oy Kxtrbtkrrkstrhbi Bfbiyshs 12
Hf oy w`rj,B Wm`r`ulm Ghokfsh`fbi Bfbiyshs (Kxtrbtkrrkstrhbi Bfbiyshs12), H sullkst tmbt tmk skvkftm bfg khlmtm pibfkts, [rbfus bfg Fkptufk,tmk ibst tw` pibfkts `ut nr`o tmk suf, mbvk s`oktmhfl t` g` whtm tw`
pr`lrbos muobfs brk koebrjhfl `f3 mypkrspbdhbi trbvki wmkrk Fkptufk hsd`fdkrfkg, bfg b pr`ckdt lkfkshs wmkrk [rbfus hs d`fdkrfkg, pr`ckdtlkfkshs ekhfl ihjk objhfl kbrtm hft` bf Bsho`vhbf Lbhb. Wmk dm`hdkektwkkf tw` sudm pr`lrbos hs put ekn`rk L`ibf Wrkvhzk ey tmk r`e`tGbfkki @ihvbw, hf N`ufgbth`f bfg Kbrtm,ey Hsbbd Bsho`v. M`wkvkr, hn wkd`fshgkr tmbt kxtrbtkrrkstrhbis lbvk us `ur oytm`i`ly, e`tm tmk 25 skbtpbftmk`f `n Bfdhkft Lrkkdk tmbt sbt up`f @iyopus, bfg tmk 25 skbtpbftmk`f `n tmk ^kgbs hf Hfghb, nr`o tmk s`urdk hf Bfdhkft Tuokr wmkrkdhvhihzbth`f eklbf, tmkf hfgkkg wk skk tmk shlf hfs`nbr bs tmk Lrkkj L`g,Fkptufk, hs tmk skb l`g, bfg b mypkrspbdhbi spbdk pr`lrbo hs sktthfl sbhiup`f tmk d`sohd `dkbf t` usk tmk oktbpm`r `n Dbri Tblbf, bfg [rbfus wbs
tmk s`f bfg musebfg n`r Lbhb, tmk drkbt`r `n Kbrtm, n`r wm`o wk lukss tmkBsho`vhbf Lbhb wbs fbokg, f`t t` okfth`f Lbhb Wmk`ry `n CboksI`vki`dj, wm` tmk`rhzkg tmbt Kbrtm hs ihjk b mulk supkr`rlbfhzo, b shohibrd`fdkpt t` tmk Bsho`vhbf Lbhb bfg t` b pr`ckdt lkfkshs, wm`sk fbohfld`oks nr`o b Ttbr Wrkj o`vhk, bfg hs shohibr hf hgkb t` tmk I`vki`djhbf bfgBsho`vhbf Lbhb.
Tudm tmhfls ekhfl hf `ur oytm`i`ly, bfg sdhkfdk nhdth`f, sudm bs Ttbr Wrkj,bfg N`ufgbth`f bfg Kbrtm, oby ek s`oktmhfl t` tbjk o`rk skrh`usiy bsrkbi, hn `fk rkbgs oy w`rj Nhdth`f-Ukbihty Kftbflikokft. Hfgkkg, ht w`uigskko hf tmbt, Qbui Ikvhfs`f, Hsbbd Bsho`v, bfg Brtmur D. Dibrjk brk
kftbflikg whtm muobf gksthfy, hfs`nbr bs tmkhr nhdth`f hs bdtubiiy kvhgkfdkhf supp`rt `n tmk trbckdt`ry t`wbrgs mypkgrhvk, wmhdm hs nurtmkr supp`rtkgey tmk Tmkihbj ^krsh`f `n Wmk OdJkffb Whokwbvk, bfg tmk l`igkf rbth`d`fculbtk hn y`u rkbg tmk Dmbptkr thtikg Nhdth`f-Ukbihty Kftbflikokft hfoy w`rj B Wm`r`ulm Ghokfsh`fbi Bfbiyshs. Hf tmk sbok w`rj ht hs dikbrtmbt H wbs skt `f oy d`ursk `n ghsd`vkry ey Lypshks, kvkf bs nbr bs H mbvkd`ok t` ekihkvk tmky brk w`rjhfl `f b pr`ckdt lkfkshs bfg tmbt tmky brk tmkrkbs`f H mbvk ekkf g`hfl tmk vkry sbok. \`uig ht ek t`` e`ig t` sullkst,nr`o kvkrytmhfl tmbt mbs ekkf sbhg mkrk, tmbt Bihkfs skft Lrkkdk hf tmkghrkdth`f `n mypkrspbdhbi trbvki, bfg tmbt tmky skft Hfghb `f b d`ursk n`rLbhb, `r b pr`ckdt lkfkshs, hf tmbt Lypshks brk nr`o Hfghb0 H sby tmhs hf
d`ffkdth`f whtm tmk hgkb tmbt e`tm Bfdhkft Lrkkdk, bfg tmk ^kgbs `n Hfghbmbvk twkivk skbt pbftmk`fs `n Tuokrhbf `rhlhf. Ikt us tbjk b i``j bt tmbtmhst`ry bfg wmbt ht skkos t` hopiy, erhkniy.
Hbf Ekbrgsiky Obrdm 42, 5124
\k Brk Hf B Wmhrg Wrbfshth`f
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\k ghl up tmk Bssyrhbf ruhfs hf Oks`p`tbohb, bfg nhfg tmksk pk`pik mbg bfufgkriyhfl ibflublk ekfkbtm tmkhr `wf. T` wk ghl gkkpkr bfg nhfg WmkTuokrhbfs, wm`sk `rhlhfs brk ufjf`wf, eut tmbt hfvkftkg dhvhihzbth`f3tkxthiks, p`ttkry, blrhduiturk, wrhttkf ibflublk, o`fky, obtmkobthds,l`vkrfokft bfg hfsthtuth`fbihzkg rkihlh`f be`ut 25,111 ykbrs bl`.
Wmk okdmbfhso `n tmk sprkbg `n tmkhr duiturk tmr`ulm tmk w`rig hs3 WmkMhtthtks `n tmk wkstkrf thp `n Bshb sprkbg tmk pbftmk`f `n twkivk skbts n`rtmk L`gs kbst t` Hfghb (Wmk ^kgbs) bfg wkst t` Lrkkdk (@iyopus). Wmky g`tmhs vhb tmk M`rhtks, `r Murrhbfs, wm` wkrk `n Tuokrhbf duiturk bs tmkymbg b Jhflg`o tmbt sprkbg nr`o tmk wkstkrf e`rgkr `n Oks`p`tbohb t`Bfbt`ihb, tmk Kbstkrf e`rgkr `n Wurjky.
Wmk w`rsmhp `n tmk nhrst L`g nr`o wmhdm bii `tmkrs hf tmk w`rig wkrko`gkikg wbs fbokg Bf, `r Bfu. Mk bfg mhs whnk, Bftu, sbt up`f tmktmr`fks hf tmk mkbvkfs bfg wkrk Jhfl bfg Rukkf `n tmk L`gs. Hf wrhthfl
tmk ghvhfk fboks, tmk Tuokrhbfs put b stbr ekn`rk tmk ikttkrs spkiihfltmko.
Bfu bfg Bftu, bdd`rghfl t` bfdhkft Tuokrhbf Dufkhn`ro vhshtkg kbrtm bttmk tkopik hf [ruj. Wmky ghg f`t stby. Mk wm` stbykg wbs tmkhr s`f Kihi.Mk wbs d`fshgkrkg i`rg `n tmk ibfg, bfg lbvk tmk Tuokrhbfs tkdmf`i`ly.Ibtkr, tmk Mkerkw L`g, Ki`mho, hs sbhg t` mbvk b whnk bs wkii. Mkr fbok hsBsmkrb. Wmky brk pbrbiikis t` Bfu bfg Bftu.
\k brk hftkrkstkg hf tmrkk trbfshth`fs. 511,111 ykbrs bl`, bfbt`ohdbiiyo`gkrf muobfs, o`rk tmbf ihjkiy gksdkfgkg nr`o M`o` Krkdtus, brk
dmhpphfl st`fks, bfg mufthfl. Bii `n tmk suggkf, 211,111 ykbrs bl` tmkybrk dmhpphfl st`fks hft` bitbrs bfg hfvkftkg smbobfhso. Wmk dbvkpbhfthfls hf Nrbfdk bfg Tpbhf sm`w m`w tmky mbvk f`w hfvkftkgTmbobfhso, tmk dbvk pbhfthfl gkphdthfl tmkhr c`urfky t` tmk sphrht w`rigtmr`ulm tmkhr Tmbobf, wm` pkrmbps obgk tmk c`urfky whtm fbturbimbiiudhf`lkfhd. Wmksk mbiiudhf`lkfhd ohlmt mbvk ekkf tmk dbusk `n tmhstrbfshth`f t` pr`t`d`fsdh`usfkss.
Wmk fkxt trbfshth`f wk brk hftkrkstkg hf hs Tmbobfhsthd dmbflk`vkr nr`ow`rsmhphfl sphrhts t` skttihfl g`wf, g`hfl blrhduiturk bfg w`rsmhpphfl tmkL`gs hf tmk sjy, Bfu, bfg Bftu. Blbhf, be`ut 25,111 ykbrs bl`.
\k oby ek kftkrhfl b trbfshth`f f`w, nr`o w`rsmhpphfl l`gs hf tmk sjy, t`bebfg`fhfl L`g bfg ekd`ohfl tmk stbrdmhig, b pk`pik bgbptkg t` ihvhfl hfspbdk, eky`fg Kbrtm. Wmhs skkos t` ek tmk okssblk `n Brtmur D. Dibrjk hfmhs Tpbdk @gyssky F`vkis. Wmhs d`uig ek b sphrhtubi C`urfky bs wkii. \kg`ft jf`w wmbt wk whii nhfg bo`fl tmk stbrs. Wmkrk oby ek b stkiibrs`dhkty birkbgy `ut tmkrk whtm wmhdm wk mbvk t` hftklrbtk.
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Hbf EkbrgsikyObrdm 22, 5124
Wmbt \mhdm H Mbg Kbrihkr \rhttkf
Dmbptkr 2
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Ht wbs bii vkry d`fnushfl bfg mk mbg cust stbrtkg rkbghfl Wmk Hihbg bfg nkitmk oby dmbflk mhs ohfg bntkr mk rkbg Wmk @gyssky. Wmbt wmhdm mk nkitrkbiiy fkkgkg t` ek g`fk wbs t` mbvk b sdm`ibr hf Lrkkj bfg U`obf mhst`rykvbiubtk tmk wm`ik tmhfl. Mk mbg ykt t` ikbrf bfytmhfl be`ut F`rskOytm`i`ly t` bgg t` mhs pr`eiko.
Hbf EkbrgsikyT`okthok Hf 5125
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Tkt Wmk`ry 12
B skt hs b d`iikdth`f `n vbiuks lr`upkg bdd`rghfl t` `fk hgkb. Wmbt hs tmkybii eki`fl t` tmk skt hn tmky mbvk s`oktmhfl hf d`oo`f. Ht hs oy m`pk tmbttmhs fkw skt whii rksuit hf
Wmk fkw skt hs, b pibfkt eki`fls t` tmk skt hn ht mbs tw` vbiuks tmk sbok hftkros `n `ur m`ok pibfkt, Kbrtm. Mkrk hs wmbt H mbvk n`ufg bi`fl tm`skihfks3
Cuphtkr3 Hts `rehtbi pkrh`g, `r ykbr, okbsurkg hf Kbrtm ykbrs, hs be`ut tmksbok bs hts rbghus (ghstbfdk nr`o hts dkftkr t` hts surnbdk) hn ht hs okbsurkghf kbrtm rbghh.
Okrdury3 Hts ghstbfdk nr`o tmk suf (`rehtbi rbghus) hn okbsurkg hf tkros ntmk `rehtbi rbghus `n kbrtm, hs tmk sbok bs hts rbghus hn okbsurkg hf kbrtm
rbghh.
Obrs3 Wm`ulm ht hs sobiikr tmbf tmk kbrtm ht sphfs si`wkr s` tmbt hts gby hstmk sbok gurbth`f bs tmbt `n tmk kbrtm. Ht mbs bf hfdihfbth`f t` hts reht tmksbok bs tmk kbrtm.
Fkptufk3 Wm`ulm ht hs o`rk obsshvk tmbf tmk kbrtm, ht mbs tmk sboksurnbdk lrbvhty bs tmk kbrtm ekdbusk ht hs oudm ibrlkr. Ht mbs bf hfdihfbth`ft` hts `reht tmbt hs tmk sbok bs tmk kbrtm.
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Tkt Wmk`ry 15
Hf oy pbpkr Tkt Wmk`ry 12 H lr`up n`ur pibfkts hft` `fk skt, Okrdury,Obrs, Fkptufk, bfg Cuphtkr gknhfhfl tmk skt bs b pibfkt eki`fls t` ht hn htmbs tw` dmbrbdtkrhsthds tmk sbok hf tkros `n ur m`ok pibfkt Kbrtm. Wmbt
ikbvks tmrkk pibfkts utshgk `n tmk skt, ^kfus, Tbturf, bfg [rbfus. H nhfgtmky d`oprhsk b skt bs wkii. Ht hs gknhfkg b pibfkt eki`fls t` tmk skt hn ht mbstmrkk dmbrbdtkrhsthds tmk sbok bs Kbrtm, `r bt ikbst `fk tmbt d`oks hfskd`fg pibdk t` tm`sk hf Tkt 12 `r thks whtm `fk hf Tkt 12.
\mkf H sby dmbrbdtkrhsthd, H okbf pmyshdbi dmbrbdtkrhsthd bs tmky kxhst hftmk nhkig `n pmyshds, ihjk obss, shzk, `rehtbi pkrh`g, r`tbth`fbi vki`dhty, bfgs` n`rtm. F`t dmbrbdtkrhsthds sudm bs shohibr d`op`fkfts t` tmk dmkohdbid`op`shth`f `n tmkhr bto`spmkrks3 tmbt w`uig ek tmk rkbio `n dmkohstry.
Wmk Dmbrbdtkrhsthds n`r tmhs Tkt 15 brk3
^kfus3 Ht mbs b shzk di`sk t` tmbt `n tmk Kbrtm. Hts rbghus hs 1.878 Kbrtmrbghh. Ht mbs b obss di`sk t` tmbt `n tmk Kbrtm (1.=2;1 tmbt `n tmk Kbrtm).Bfg, b surnbdk lrbvhty di`sk t` tmbt `n tmk Kbrtm (1.=
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Ukskbrdm @n Hsmtbr Mbs Ekst Q`ssheik Uksuit
\k mbvk dkftkrkg `f Hsmtbr ekdbusk smk wbs tmk diuk wk wkrk ikbg t`pursuhfl. Tmk hs rkprkskftkg ey tmk pibfkt ^kfus (hop`rtbft) bfg wbsjf`wf bs ^kfus t` tmk U`obfs, bs Bpmr`ghtk t` tmk Bfdhkft Lrkkjs, bfg
Bstbrtk t` tmk Mkerkws. Wmk Tuokrhbfs mbg fuoekrs t` rbfj tmk L`gs bfg;1 wbs tmk mhlmkst. Fbturbiiy tmbt wbs bsshlfkg t` Bfu. Hftkrksthfliy,Hsmtbr wbs lhvkf tmk fuoekr 2; ey tmk Tuokrhbfs. Wmhs hs l``g ekdbusk 2;hs `fk `n tmk tmrkk fuoekrs hf oy D`so`i`ly tmbt wbs lhvkf t` us ey tmkLypsy Tmbobf Obfuki. H mbg wrhttkf3
Wmk Hop`rtbfdk @n
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Wmk Okbfhfl @n Wmk Qibfkts
\k mbvk obgk tw` skts `ut `n tmk pibfkts ebskg `f tmkhr pmyshdbidmbrbdtkrhsthds. Wmky brk3
Tkt 12 ? (Okrdury, Obrs, Cuphtkr, Fkptufk)Tkt 15 ? (^kfus, Tbturf, [rbfus)
M`w wk brrhvkg bt tmko brk hf tmk dmbptkrs Tkt Wmk`ry 12 bfg Tkt Wmk`ry15. Wmhs hs kvhgkfdk hf supp`rt `n tmk hgkb tmbt Fkptufk rkprkskftsmypkrspbthbi trbvki (Fkptufk hs Tkb L`g bfg mypkrspbdhbi trbvki hs sktthflsbhi up`f tmk d`sohd `dkbf), tmbt ht p`hfts t` Cuphtkr (Cuphtkrs hs tmknbtmkr `n Bp`ii` bfg Wmk Bp`ii` Ohssh`fs wkrk tmk nhrst ohssh`fs t` WmkO``f), bfg hf tmbt Obrs pr`ohsks t` ek Fkw Kbrtm.
Nurtmkr, ht hs kvhgkfdk hf supp`rt `n tmk hgkb tmbt [rbfus rkprkskfts
objhfl tmk Kbrtm hft` bf Bsho`vhbf `r I`vki`djhbf Lbhb, tmbt hs b Qr`ckdtLkfkshs ekdbusk ht hs Lk`kflhfkkrhfl bfg [rbfus wbs tmk s`f bfg musebfg`n Lbhb, tmk drkbt`r `n Kbrtm. Bfg, nurtmkr hf tmbt ^kfus hs b nbhikg Kbrtm,bfg mbs ekkf `n lrkbt hftkrkst t` l`vkrfokfts t` stugy m`w pibfkts dbf ekobgk t` suddkkg bs nbr bs ekhfl mbehtbeik. \k w`uig sby hfs`nbr bsFktpufk p`hfts t` Cuphtkr, tmbt [rbfus p`hfts t` Tbturf.
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25>
Ukskbrdm @n Hsmtbr Mbs Ekst Q`ssheik Uksuit
\k mbvk dkftkrkg `f Hsmtbr ekdbusk smk wbs tmk diuk wk wkrk ikbg t`pursuhfl. Tmk hs rkprkskftkg ey tmk pibfkt ^kfus (hop`rtbft) bfg wbsjf`wf bs ^kfus t` tmk U`obfs, bs Bpmr`ghtk t` tmk Bfdhkft Lrkkjs, bfg
Bstbrtk t` tmk Mkerkws. Wmk Tuokrhbfs mbg fuoekrs t` rbfj tmk L`gs bfg;1 wbs tmk mhlmkst. Fbturbiiy tmbt wbs bsshlfkg t` Bfu. Hftkrksthfliy,Hsmtbr wbs lhvkf tmk fuoekr 2; ey tmk Tuokrhbfs. Wmhs hs l``g ekdbusk 2;hs `fk `n tmk tmrkk fuoekrs hf oy D`so`i`ly tmbt wbs lhvkf t` us ey tmkLypsy Tmbobf Obfuki.
Hsmtbr Bfg Mkr Ubfjhfl
Ht hs bppr`prhbtk tmbt Hsmtbr (^kfus) wbs rbfjkg 2; ey tmk Tuokrhbfshfs`nbr bs smk wbs tmk pbtr`fkss `n Fhfkvkm, bfg tmk Fhfkvkm D`fstbft wbsn`ufg hf Fhfkvkm ekdbusk 2; hs ihjk b Fhfkvkm D`fstbft n`r ghokfsh`fbi
bfbiyshs. Wmk Fhfkvkm D`fstbft hs ihjk b d`oo`f gkf`ohfbt`r n`r pkrh`gsbfg dydiks hf tmk s`ibr systko.
Hbf EkbrgsikyBprhi 5, 5124
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25 b wm`ik fuoekr `n thoks. Wmksuo `n tmksk fuoekrs hs 2>, wmhdm hs lrkbtkr tmbf 25. Obrs hs tmk n`urtmpibfkt `ut nr`o tmk suf. Wwkivk ghvhgkg ey n`ur hs tmrkk, bfg tmk kbrtm hstmk tmhrg pibfkt `ut nr`o tmk suf. Wmus `fdk blbhf tmk kbrtm bfg Obrs brkd`upikg.
H dbf d`upik tmko blbhf. Kikokfts brk bt`os, bfg tmk fuoekrs `n
pbrthdiks tmbt d`fsthtutk tmko gktkrohfk tmk kikokft, bfg hts rkibthvkobss, `r o`ibr obss bs ht hs dbiikg. Wmk bto`spmkrk `n Obrs hs o`stiyD@5, be`ut 8; pkrdkft. Wmk kbrtm bto`spmkrk hs o`rk tmbf 81 pkrdkft`xylkf bfg fhtr`lkf. H dbiduibtk D@5 t` mbvk b o`ibr obss `n 77.12 bfgkbrtm bhr t` mbvk b o`ibr obss `n 5=.;. Wmk Obrs `rehtbi ghstbfdkd`opbrkg t` tmk kbrtm `rehtbi ghstbfdk hs be`ut 2.;. Wmk o`ibr obss `n D@5d`opbrkg t` tmk o`ibr obss `n bhr hs be`ut 2.;. Wmbt hs tmk obrs-sufghstbfdk hs t` tmk kbrtm-suf ghstbfdk bs Obrthbf bhr hs t` kbrtm bhr.
Ht l`ks nurtmkr tmbf tmbt. Hn tmk kbrtm surnbdk lrbvhty hs 2, tmbt `n Obrs hs1.4=1. Wmbt hs b rbth` `n 5.>4. Wmk o`ibr obss `n `xylkf lbs (@5) wmbt wk
erkbtm, hs 45.11. Wmk o`ibr obss `n dbre`f, tmk ebshs `n ihnk bs wk jf`w ht,hs 25.12. Wmbt hs b rbth` `n 5.>>. Wmbt sbys ht tbjks be`ut tmk sbok kfkrly t`ihnt b o`ik `n dbre`f `f kbrtm, bs ht g`ks t` ihnt b o`ik `n `xylkf (@5) `fobrs tmk sbok ghstbfdk.Kbrtm bfg Obrs brk ykt nurtmkr d`upikg3
Wmk kbrtm bto`spmkrk wbs `fdk o`stiy dbre`f gh`xhgk (D@5) ihjk tmkobrs bto`spmkrk hs t`gby, ufthi pibft ihnk dbok bi`fl bfg stbrtkg
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25=
d`fvkrthfl tmk dbre`f gh`xhgk hft` `xylkf, ushfl ihlmt nr`o tmk suf bfg hftmk pr`dkss objhfl tmk o`st nufgbokftbi sulbr, liud`sk (wmhdm hs bt tmke`tt`o `n tmk n``g dmbhf). B pr`dkss dbiikg pm`t`syftmkshs.Liud`sk hs D>M25@>. H dbiduibtk liud`sk mbs b o`ibr obss `n 2=1.2> bfgwbtkr, wmhdm d`vkrs o`st `n tmk surnbdk `n tmk kbrtm, dmkohdbi n`rouib
M5@, H dbiduibtk mbs b o`ibr obss `n 2=.12>.
2=1.2> ghvhgkg ey 2=.12> hs be`ut 21 bfg tmk kbrtm hs be`ut 21 thoks bsobsshvk bs obrs. Wmbt hs, liud`sk hs t` wbtkr bs tmk kbrtm obss hs t` tmkobss `n obrs.
X`u brk pr`ebeiy w`fgkrhfl wmy H bo s` bobzkg tmbt Obrs bfg kbrtm brks` d`upikg kophrhdbiiy. \kii tmk pibfkt Okrdury hs t`` m`t t` supp`rtmuobf ihnk ekdbusk ht hs s` di`sk t` tmk suf, ^kfus mbs tmk sbok pr`eiko.Eut tmk kbrtm hs tmk fkxt pibfkt `ut bfg tmk rhlmt ghstbfdk nr`o tmk suf t`ek f`t t`` wbro t` supp`rt ihnk.PWmk fkxt pibfkt bntkr tmk kbrtm hs Obrs,
bfg ht oby ek d`ig, eut f`t t`` d`ig t` d`i`fhzk, `r kvkf `fk gby tkrrbn`ro(objk mbehtbeik n`r muobfs). Wmk fkxt pibfkt bntkr Obrs hs Cuphtkr, f`tcust t`` d`ig, eut o`stiy lbs, s` tmkrk hs f`tmhfl s`ihg t` stbfg `f. Wmk fkxtpibfkt, Tbturf, kvkf d`igkr bfg o`stiy lbsk`us bs wkii. Wmk trkfgd`fthfuks `f t` Fkptufk bfg [rbfus. Qiut` hs cust tmhs d`ig ihttik gwbrnpibfkt, wm`sk tmhf bto`spmkrk d`iibpsks wmkf ht hs nurtmkr nr`o tmk suf.X`u skk tmkf wmy H bo s` bobzkg Obrs bfg kbrtm brk d`upikg ey tmkskfuoekrs, tmky bdtubiiy mbvk `fk tmhfl hf d`oo`f, s`ihg pibfkts, f`tdihobthdbiiy t`` m`t n`r muobfs, `r t`` d`ig.
Wmksk fuoekrs tmbt d`upik Obrs whtm kbrtm, skko t` sby tmk pibfkt hs
tmkrk bs b stkpphfl st`fk t` tmk stbrs, tmbt ht hs thok t` wbgk `ut hft` tmkd`sohd `dkbf, t` usk tmk oktbpm`r `n Dbri Tblbf, `r shfj. Wmbt hs, n`r s`okrkbs`f wk mbvk wmbt wk fkkg, eut b dmbiikflk mbs ekkf put t` us. \k mbvkt` `vkrd`ok `ur pr`eikos, ihjk spkfghfl o`fky bfg rks`urdks `f wbrhfstkbg `n spbdk kxpi`rbth`f. Tpbdk kxpi`rbth`f dbf s`ivk tmk kd`f`ohddrhshs. D`i`fhzhfl Obrs w`uig lkfkrbtk b obsshvk hfgustry tmbt w`uigdrkbtk w`rj mkrk `f kbrtm hf kvkry skdt`r, n`r kvkry`fk, bfg, ht w`uig bii ekpbhg n`r ey tmk rks`urdks tmbt brk `ut tmkrk hf tmk s`ibr systko. Bs Dbebisbys t` Qbssw`rtmy hf Wmhfls t` d`ok ey M.L. \kiis3
Bfg hn wkrk f` o`rk tmbf bfhobis, wk oust sfbtdm kbdm ihttik sdrbp `n
mbpphfkss, bfg ihvk, bfg sunnkr, bfg pbss, obttkrhfl f` o`rk tmbf bii tmk`tmkr bfhobis g` `r mbvk g`fk. Ht hs tmhs, `r tmbt. Bii tmk ufhvkrsk `rf`tmhfl. \mhdm smbii ht ek Qbssw`rtmy0 \mhdm smbii ht ek0
H ekihkvk wk brk bt tmbt thok hf mhst`ry, bfg tmk Fbf`NKW obrjs ht. ErhbfLhidmrhst hs w`rjhfl `f tmk Fbf`NKW hgkb. Nhkig Knnkdt Wrbfshst`rs brk uskgt` dmbrlk ihlmt fbf`pbrthdiks, s` tmky dbf ek kckdtkg `ut tmk ebdj kfg `n bsmhp whtm b skrhks `n oblfkthd nhkigs obgk ey stbdjs `n ohdr`dmhp
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d`op`fkfts, oudm tmk sbok wby dmbrlkg pbrthdiks brk bddkikrbtkg eykikdtr`oblfkts hf b pbrthdik bddkikrbt`r. Wmk fbf`NKW smhp dbf rkbdm 81%tmk spkkg `n ihlmt, tmk`rkthdbiiy, hn euhit ihlmt bfg `utshgk tmk kbrtmslrbvhty. @n d`ursk tmk smhp hs b stbrsmhp tmbt w`uig tbjk o`rk tmbf n`urykbrs t` rkbdm tmk fkbrkst stbr, eut uskg t` l` t` obrs ohlmt `fiy tbjk b
d`upik m`urs `r s`.
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Lkftikokf, nurtmkr, Obrs hs Fkw Kbrtm. H mbvk g`fk tmhs3
\k jf`w tmbt 8/; `ddurs hf obfy oystkrh`us wbys hf fbturk, hfdiughflTbturfs ghstbfdk nr`o tmk suf `n 8 (di`skst bppr`bdm) putthfl Cuphtkrs btnhvk (di`skst bppr`bdm), bfg tmk kbrtm bt `fk. Ikt us d`fshgkr b ebibfdk. Hn
tw` wkhlmts `n kqubi obss brk pibdkg `f `pp`shtk kfgs `n b ebibfdk, tmkf t`ek ebibfdkg tmk nuidruo oust ek pibdkg bt tmk dkftkr. Eut hn `fk obss hshfdrkbskg, tmkf tmk nuidruo whii mbvk t` ek o`vkg di`skr t` tmk mkbvhkr kfghn tmk ebibfdk hs f`t t` thp. Wmhs hs tmk Ibw `n Ikvkrs. Ht stbtks tmbt tmkobssks brk hfvkrskiy pr`p`rth`f t` tmkhr ghstbfdks nr`o tmk nuidruo. W`wrhtk ht obtmkobthdbiiy,
O2/O5?I5/I2
@r, kquhvbikftiy
(O2)(I2)?(O5)(I5)
Hn wk d`fshgkr tmk thok wmkf Tbturf bfg Cuphtkr, tmk tw` o`st obsshvke`ghks hf tmk s`ibr systko brk hf `pp`shth`f, tmbt hs wmkf tmky brk `f`pp`shtk shgks `n tmk suf bfg nbdhfl `fk bf`tmkr, tmkf ey tmk be`vkhfn`robth`f tmky brk skpbrbtkg ey 27 ufhts. Cuphtkr hs 4.47 thoks bsobsshvk bs Tbturf. Ey `ur ibw `n ikvkrs be`vk, tmbt okbfs
I2/I5?4.47
I2+I5?27
Wmus
7.47I5?27 bfg
I5?4.55;=
27-4.55?21.
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Wmk Lkfkshs Myp`tmkshs
Ht hs oy lukss tmbt Wmk Lkfkshs Qr`ckdt objhfl b ihnk sustbhfhfl pibfkt w`uig ek bttbhfbeik ey ushfl b pibfkt hf `reht br`ufg b stbr `n b iuohf`shtytmbt hs bes`iutk oblfhtugk zkr` bt b ghstbfdk nr`o ht tmbt hs tmk sbok bs tmk
ghstbfdk ektwkkf tmk pibfkt Tbturf bfg tmk Tuf. H dbii tmhs Wmk LkfkshsMyp`tmkshs.
Wmk mhfts mhggkf hf Fbturk tmbt ikbgs ok t` tmhs lukss brk3
2.
Wmk kfkrly rkquhrkg t` o`vk tmk kbrtm nr`o tmk suf t` hts `reht `n`fk bstr`f`ohdbi ufht hs be`ut 87.5 s`ibr iuohf`shthks rbghbtkg `vkrb ykbr, b fuoekr di`sk t` tmk fuoekr `n fbturbiiy `ddurrhflkikokfts, wmhdm brk 85. 85 s`ibr iuohf`shthks brk di`sk t` tmkiuohf`shty `n bf bes`iutk oblfhtugk zkr` stbr. Wmkrk brk prkdhskiy=;.;5;. Hn wk bvkrblk tmhs whtm 211 s`ibr iuohf`shthks wk mbvk
85.5; s`ibr iuohf`shthks, vkry di`sk t` tmk fuoekr `n fbturbiiy`ddurrhfl kikokfts.5.
Tbturf mbs tmk o`st pr`ohfkft rhfl systko hf tmk s`ibr systko. Ht hsbe`ut 21 thoks nurtmkr nr`o tmk suf tmbf tmk Kbrtm hs nr`o tmk suf,bfg hn bf bes`iutk oblfhtugk zkr` stbr hs be`ut 211 s`ibriuohf`shthks, ey tmk hfvkrsk squbrk ibw tmk mbehtbeik z`fk `n bfbes`iutk oblfhtugk zkr` stbr hs tmk sbok ghstbfdk nr`o tmbt stbr bsTbturf hs nr`o tmk Tuf.
4.
H n`ufg bes`iutk oblfhtugk zkr` stbrs mbvk b d`ffkdth`f whtm bfkfhlobthd `ddurrkfdk `n 4.< hf tmk [fhvkrsk.
D`fdkrthfl fuoekr 4, tmk ibttkr p`hft, H mbg wrhttkf be`ut tmr`ulm oydmbrbdtkr Ik`fbrg hf Wmk Tkdrkt @n Fkptufk3
Ik`fbrg rknkrrkg t` mhs pkrh`ghd tbeik `n tmk kikokft