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Lgo BagrhscayZaptakbar 27, 2>78

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#$. p=.&1%8-

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Eurtmar Fjjurraoja Fe Cavlosfos Oukbar

Cavlosfos Oukbar Ls Jfooajtah tf tma oukbar fe klcas lo g

`lcfkatar4

>.527 klcas ; 7 `lcfkatarLo Zmfrt Ya Mgva Kgouacs Lotairgc4

Ya mgva tma ylo goh ygoi fe.>527

racgtloi tf tma ifchao rgtlf, klcas lo g `lcfkatar, tlkawgva

ofvacty efr wmao mukgos cgohah fo tma kffo, goh tma irfwtm

rgta tfwgrhs myparhrlva oft tf kaotlfo tma rlimt gsjaoslfo efr

tma lkpfrtgot OIJ 59:= lo Gqulcg.

Goh wa mgva tma Zftmlj jyjca fe tma Aiyptlgo Jgcaohgr fe

7, 85> yagrs tmgt mgs gcc fe lts hlilts futslha fe fur ylo goh ygoi

goh lt wfuch saak Kgouacs Lotairgc jfooajts lt gcc tf tma

gjjacargtlfo fe irgvlty gt tma agrtm suregja goh kgjm 7 gt rffk takpargtura.

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G Zjlaotlst mgh bulct g rfbft lo tma lkgia fe mukgos gohhfwocfghah tf lt gcc fe mukgo `ofwcahia, tmao put efrwgrh tmaquastlfo tf fur rfbft, wmgt ls tma bast wa, mukgolty, jgo hf tfsurvlva wltm go agrtm fe clkltah rasfurjas goh g sltugtlfo wmaraftmar wfrchs cl`a agrtm, le tmay axlst, wfuch tg`a iaoargtlfos tfragjm.

Xma rfbft baigo mls goswar, L jfotaoh tmgt tma sarlas fe avaotstmgt uoefchah fo agrtm fvar tma yagrs sloja tma maclgjgc rlsloi feZlrlus efur jyjcas gif lo Aiypt fe 8282 B.J., tma prasukahbailooloi fe tma Aiyptlgo jgcaohgr, wara gcc kagot tf ba, gs tmajfojaptlfo fe tma pfsslblclty fe ky axlstaoja ls lo pmgsa wltmtmfsa jyjcas goh ls jfooajtah tf sujm jfostgots fe ogtura gs

tma spaah fe climt goh hyogklj rgtlfs cl`a tma ifchao rgtlfjfoduigta.

Xma sjlaotlst gs`ah, Gra yfu sgyloi mukgos, gcc mukgos slojasfka slx tmfusgoh yagrs gif mgva baao g tffc fe sfka mlimarefrja tf brloi yfu gbfut, fur gjtlfos bfuoh tf tma turoloi fepcgoats upfo tmalr gxls, goh tma strujtura fe ogtura6

Xma rfbft sglh, \as, cat ka hlirass. Lt ifas bgj` eurtmar tmgotmgt. Oft dust tf 8282 B.J. wmao tma maclgjgc rlsloi fe Zlrlus, tmabrlimtast stgr lo tma s`y, jflojlhah wltm tma girljucturgccybaoaeljlgc louohgtlfo fe tma Olca rlvar wmljm mgppaos avary 7,85>yagrs.

Ky frlilos if bgj` tf tma efrkgtlfo fe stgrs goh tma cgws tmgtifvaro tmak.

Gs yfu `ofw, tma acakaots wara kgha by stgrs, magvlaracakaots efriah lo tmalr lotarlfr erfk climtar acakaots. Macluk

igva rlsa tf fxyiao goh oltrfiao, goh sf efrtm. Avaotugccy tmastgrs kgha slcljfo, pmfspmfrus, goh bfrfo, wmljm gccfw efrlotairgtah jlrjultry, tma bgsls fe wmljm kg`as ka euojtlfo.

^fsltlva typa slcljfo ls kgha by hfploi slcljfo, tma kgloacakaot fe sgoh, wltm tma acakaot bfrfo. Oaigtlva typa slcljfo lskgha by hfploi slcljfo wltm pmfspmfrus. Ya dflo tma twf typas

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lo hleearaot wgys tf kg`a hlfhas goh trgoslstfrs tmgt wa efrk foslcljfo jmlps tf kg`a tma skgcc jlrjultry tmgt kg`as kaeuojtlfo.

Dust gs tma ifchao rgtlf ls lo tma rftgtlfo fe cagvas gbfut tmastak fe g pcgot, fr lo tma malimt fe g mukgo jfkpgrah tf tmahlstgoja erfk tma sfcas fe tmalr eaat tf tmalr ogvac, go axprasslfofe lt ls lo ky jlrjultry.

Ya tg`a tma iafkatrlj kago fe tma kfcgr kgss fe bfrfo gohpmfspmfrus, goh wa hlvlha tmgt rasuct by tma kfcgr kgss feslcljfo.

Ma baigo wrltloi fo pgpar4

(#$/

Zl ; :>..=7)/2=.>< ; >.51

Ya tg`a tma mgrkfolj kago batwaao tma kfcgr kgssas febfrfo goh pmfspmfrus goh hlvlha tmgt by tma kfcgr kgss feslcljfo.

2(:>..=7)/(:>..=7) ; 75.>25

75.>25/Zl ; 75.>25/2=.>< ; >.19

Goh wa tg`a tma grltmkatlj kago batwaao tmasa twf rasucts.

(>.51 + >.19)/2 ;>.57

>.57 gra tma elrst twf hlilts lo tma ifchao rgtlf jfoduigta.

Xma sjlaotlst sglh, L uoharstgoh yfur pflot, but yfu raearrah tftma maclgjgc rlsloi fe Zlrlus.

Xma rfbft goswarah4 \as, bgj` tf tmgt. Xma agrtm frblt ls oagrcy

g pareajt jlrjca, sf wa jgo usa j;2%r tf jgcjucgta tma hlstgoja

tma agrtm ifas grfuoh tma suo lo g yagr. Xma agrtm frbltgc rghlusls fo tma gvargia 7.8

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Xma hlstgoja climt trgvacs lo g yagr, foa ravfcutlfo fe tma agrtmgrfuoh tma suo ls .57=)(

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Gogcysls

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Iypsy Zmgkgolsk Goh Xma Qolvarsa lo ky bff` Hlsjfvar GohJfotgjt ls ky gjjfuot fe mfw g Iypsy Zmgkgo cagh ka tf tmalhag tmgt goh 28>/:5> ; 2/: goh 2/: + 7 ; 1/:.

Ya oftljah tmgt tma kfcgr kgss fe ifch tf slcvar wgs

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wa mgva tma oukbars4

tf < axjcuhloi >,7, 8, 5

Ya jgo wrlta tmls 7,85>

7,85> ls tma caoitm fe tma sftmlj jyjca lo Duclgo yagrs (:51.21hgys). Xma sftmlj jyjca lo Aiyptlgo yagrs ls 7,857 (:51 hgys).Xma sftmlj jyjca ls tma tlka batwaao maclgjgc rlslois fe tma stgrslrlus wmao lt jflojlhas wltm tma louohgtlfo fe tma Olca Rlvar. Ltls tmfuimt tf ba go lkpfrtgot jyjca lo Aiyptfcfiy, goh tmasfurja fe tma sftmlj jyjca lo tma Aiyptlgo jgcaohgr. Ymy ls tmgtlkpfrtgot tf grtleljlgc lotaccliaoja6 Bajgusa lo ky bff`, Xma GLJfooajtlfo, L smfw tma agrtm mgs trgvacah tma ifchao rgtlfjfoduigta fe g climt yagr sloja tma efuohloi fe tma Aiyptlgojgcaohgr efur sftmlj jyjcas gif lo tma yagr 7

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I%& 48-1,

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Jmgptar 74 Hlsjfvar

Ya smfw mfw Grtleljlgc Lotaccliaoja (GL) wfuch mgvalomaraot lo lt, le lt ls slcljfo bgsah, tma ifchao rgtlfjfoduigta, wmljm jfuch lkpcy tmgt lt wgs kagot tfmgppao gcc gcfoi tmrfuim sfka uogsjartglogbca OgturgcEfrja, bajgusa, tma ifchao rgtlf jfoduigta ls efuohtmrfuimfut clea.

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Bgj` lo 2>>1, gs L hlh ky rasagrjm, L havacfpah ghleearaot jfovaotlfo efr rfuohloi oukbars tmgo wa usa.L eact L focy wgotah tf usa tma elrst twf hlilts getar tmahajlkgc lo prfjassloi hgtg usloi kfcgr kgssas fe tma

acakaots. Xmls L hlh, uocass g efurtm hlilt cass tmgo elvaefccfwah tma tmlrh hlilt lo ky jgcjucgtlfos, tmao, L wfuchusa tma elrst tmraa hlilts efr iragtar gjjurgjy. Ofw L gktg`loi tma lotrfhujtfry jcgss lo jfkputar sjlaoja gtMgrvgrh, focloa, JZ1>x. Yfr`loi lo blogry, wmara gccoukbars gra bgsa twf, L saa tmgt lt wgs of wfohar L ifttma rasucts L hlh, fo tma elrst try wmao L wfoharah le tmaifchao rgtlf jfoduigta, >.57= tf tmraa pcgjas getar tma

hajlkgc wfuch ba lo grtleljlgc lotaccliaoja (GL) sloja lt lsrajurraot tmrfuimfut clea.

L wgs tg`loi pfcgrlkatrlj hgtg fo tma ajclpsloi blogry ApslcfoGurliga gt ^loa Kfuotglo Fbsarvgtfry lo tma 7s, efr wmljmtmara wgs g pgpar lo tma Gstrfpmysljgc Dfurogc upfo wmljm kyogka gppagrs gs jfgutmfr, wmlca stuhyloi pmysljs gt XmaQolvarslty fe Fraifo. Gs wacc L wgs stuhyloi Zpgolsm, goh lo golohapaohaot stuhy prfdajt tmrfuim tma Zpgolsm Hapgrtkaot, Lcaet tma Qolvarslty tf clva fe gkfoi tma jgvas fe tma Iypslas feIrgoghg, Zpglo. Lo hfloi gs sujm, L hlsgppagrah erfk tma aotlrawfrch, focy tf raturo erfk goftmar `loh fe clea elohloi tma wfrchwgs ofw g kujm hleearaot pcgja. Grfuoh 2>>1, L aorfccah lojmaklstry gt Jltrus Jfccaia lo Zfutmaro Jgclefrolg, wmao L hlhtma efccfwloi4

Le tma ifchao rgtlf jfoduigta ls tf ba efuoh lo GrtleljlgcLotaccliaoja, lt smfuch ba lo slcljfo, pmfspmfrus, goh bfrfo,sloja hfploi slcljfo wltm pmfspmfrus goh bfrfo kg`as

trgoslstfrs.

Ya tg`a tma iafkatrlj kago batwaao pmfspmfrus (^) goh Bfrfo(B), tmao hlvlha by slcljfo (Zl), tmao tg`a tma mgrkfolj kagobatwaao pmfspmfrus goh bfrfo hlvlhah by slcljfo4

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Grltmkatlj kago fe tmasa twf oukbars4 (>.51 + >.19)/2 ; >.57

>.57 ls tma elrst twf hlilts fe tma ifchao rgtlf jfoduigta.

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Ofw tma ifchao rgtlf jfoduigta ls lo tma rgtlf fe g parsfosmalimt goh tma caoitm erfk efft tff ogvac, goh ls lo gcc fe rgtlfsbatwaao dflots lo tma eloiars, oft tf kaotlfo tmgt lt sarvas lojcfsast pgj`loi lo tma grrgoiakaot fe cagvas grfuoh g stak tfprfvlha kgxlkuk axpfsura tf suo goh wgtar efr tma pcgot. Marawa saa tmgt tma ifchao rgtlf ls oft lo grtleljlgc lotaccliaoja wmljmls >.52 tf twf pcgjas getar tma hajlkgc, but tmgt tma oukbars lolts vgcua gra lo grtleljlgc lotaccliaoja >.57, wmljm ls >.57= tf tmraapcgjas getar tma hajlkgc. Xmgt ls, le wa jfoslhar tma elrst twfhlilts lo tma rgtlf. Le wa jfoslhar tma ifchao rgtlf jfoduigta tffoa pcgja getar tma hajlkgc, wmljm ls >.5, tmao wa sgy grtleljlgclotaccliaoja hfas mgva tma ifchao rgtlf lo lts trgoslstfrs. L cl`a tftmlo` fe L, Rfbft by Lsggj Gslkfv, wmara lo foa fe tmgt jfccajtlfofe mls smfrt stfrlas, rfbfts gra oft jfotaot wltm wmgt tmay gra,

goh oaah kfra4 go axpcgogtlfo fe tmalr frlilos. Xmay jgotbaclava tmgt tmay gra erfk mukgos, sloja tmay loslst mukgos graloearlfr. Fr, L cl`a tf tmlo` fe tma smlp jfkputar MGC lo 2>>7, maklkljs lotaccliaoja, but wa hfot `ofw le ma ls ragccy gclva.^armgps tmgt ls wmy tf twf pcgja getar tma hajlkgc, GL jgrrlas tmahlilts, but ls oft tma vgcua.

Lo goy jgsa, L mgva wrlttao g prfirgk jgccah Hlsjfvar tmgt wfuchaogbca foa tf prfjass grltmkatlj, mgrkfolj, goh iafkatrljkagos efr acakaots fr wmgtavar, bajgusa sfkafoa, lojcuhloikysace, klimt wgot tf saa le tmara gra goy kfra ougojas mlhhaofut tmara lo ogtura. L mgva gcraghy efuoh sfkatmloi tmgt saakstf lohljgta axtrgtarrastrlgcs caet tmalr tmukbprlot lo fur pmysljs. Lavao eloh lohljgtlfo efr tma frlilo fe g kassgia tmgt wfuch saaktmay akbahhah lo fur pmysljs. Xmgt frlilo jfkas fut tf ba tmasgka pcgja gs tma sfurja fe tma ZAXL Yfw! Zliogc, Zgilttgrlus.Xma Yfw! Zliogc wgs efuoh lo tma Zagrjm Efr AxtrgtarrastrlgcLotaccliaoja goh g pfsslbca trgosklsslfo erfk AXs. But tmgt lsgoftmar subdajt tmgt ls tragtah lo ky bff`4 Gcc Xmgt Jgo Ba Zglh.

L ofw cagva yfu wltm ky prfirgk, Hlsjfvar lo tma cgoiugia J,wltm g sgkpca ruooloi fe lt4

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Xma ^rfirgk Hlsjfvar

#lojcuha 3sthlf.m?#lojcuha 3kgtm.m?lot kglo(vflh){prlote("trgoslstfrs gra Zlcljfo hfpah wltm ^mfspmfrus gohBfrfoSo")0prlote("Grtleljlgc Lotaccliaoja wfuch ba bgsah fo tmlsSo")0prlote("tma ifchao rgtlf jfoduigta ls bgslj tf cleaSo")0prlote("Xma Ifchao Rgtlf Jfoduigta Ls4 >.57=So")0prlote("Kfcgr Kgss Fe ^mfspmfrus (^) Ls4 :>..=7So")0prlote("Kfcgr Kgss Fe Zlcljfo (Zl) Ls4 2=.>

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suk;g+b0mgrkfolj;prfhujt/suk0prlote("mgrkfolj kago4 %.2eSo", mgrkfolj)0hfubca iafkatrlj0iafkatrlj;sqrt(g*b)0prlote("iafkatlj kago4 %.2eSo", iafkatrlj)0

prlote("iafkatrlj kago batwaao ^ goh B hlvlhah by Zl4 %.2eSo",iafkatrlj/2=.>

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Ruooloi Hlsjfvar

dmgrvgrhNgppclgoja (~)4 jh Hrfpbfx/psat2dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./ghhtrgoslstfrs gra Zlcljfo hfpah wltm ^mfspmfrus goh BfrfoGrtleljlgc Lotaccliaoja wfuch ba bgsah fo tmlstma ifchao rgtlf jfoduigta ls bgslj tf cleaXma Ifchao Rgtlf Jfoduigta Ls4 >.57=Kfcgr Kgss Fe ^mfspmfrus (^) Ls4 :>..=7Kfcgr Kgss Fe Zlcljfo (Zl) Ls4 2=.>gvargia fe yfur oukbars ls4 9.>>aotar twf oukbars (mlot jmffsa ^ goh B)4ilva ka g4 :>..=7mgrkfolj kago4 75.>:iafkatlj kago4 7=.:>iafkatrlj kago batwaao ^ goh B hlvlhah by Zl4 >.51mgrkfolj kago batwaao ^ goh B hlvlhah by Zl4 >.19>.51 + >.19 hlvlhah by 2 ls4 >.57tmfsa gra tma tma elrst twf hlilts lo tma ifchao rgtlf jfoduigta

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4

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Jmgptar 24 Jfotgjt

L mgva sglh, sloja ky tmafry suiiast axtrgtarrastrlgcs igva usfur uolts fe kagsurakaot, tmgt axtrgtarrastrlgcs klimt mgvailvao us fur vgrlgbcas usah lo pmysljs goh kgtm, cl`a tma uoltvajtfrs (l, d, ). L mgva gcraghy efuoh g pgttaro goh pfstah lt.Mfwavar, L wgs hfloi ky JZ1>x jfkputar sjlaoja mfkawfr`goh tryloi tf wrlta g prfirgk efr Jgasgrs Jlpmar. L wrfta gskgcc prfirgk goh hajlhah tf tast lt. Le yfu wrlta g prfirgk gohtast lt, stgohgrh loput ls maccf. L put lo maccf goh tf tast, rgo tmaprfirgk efr rftgtloi jmgrgjtars by 7, goh 2, goh :, gs tmay gratma elrst lotaiars goh tma agslast wltm wmljm tf tast yfurprfirgk. Xma rasuct wgs tma m fo maccf, jgka fut tf ba (l, d,

`). Lo ftmar wfrhs yfu iat tmgt (l, d, `) ls g maccf erfk gclaos logjjfrhgoja wltm ky agrclar tmafrlas. Le tmls ls oft ragc jfotgjtwltm axtrgtarrastrlgcs, lt ls iragt jfotaot efr g Zjl-El kfvla gbfutjfotgjt wltm axtrgtarrastrlgcs. Mara ls tma prfirgk L wrfta, gohtma rasuct fe ruooloi lt4

Gs yfu jgo saa L gk kg`loi sfka `loh fe g jlpmar, but oftJgasgrs Jlpmar

#lojcuha 3sthlf.m?#lojcuha 3js1>.m?#lojcuha 3strloi.m?lot kglo(lot grij, strloi grivP7[){lot l;>0lot ` ; gtfl(grivP7[)0le (grij?2 || grij32)prlote ("Ilva ka g sloica strloi4 ")0acsa

prlote("Ilva ka g pmrgsa4 ")0strloi s ; IatZtrloi()0efr (lot l ;>, o;strcao(s)0 l3o0 l++)0prlote("%j", sPl[+`)0prlote("So")0}

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Ruooloi Duclus >7

dmgrvgrhNgppclgoja (~)4 jh Hrfpbfx/psat2dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 kg`a duclusjcgoi -iihb: -F> -sth;j -ck -f

duclusdmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus :Ilva ka g pmrgsa4 maccf`

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 8Ilva ka g pmrgsa4 maccfc

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 2Ilva ka g pmrgsa4 maccf

ddmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 7Ilva ka g pmrgsa4 maccfl

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4

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L pfstah tf ky bcfi mttp4//jfsgsblaohljmgs.bcfispft.jfk/

Zuohgy, Dgougry 25, 2>78

G ^gttaro Akarias

(g, b, j) lo GZJLL jfkputar jfha ls (%).

(l, d, `) lo oukarlj gra ls (, 77) tma elrst tmraa oukbars baefra

twacva goh 72 ls tftgclty lo tma saosa tmgt 72 ls tma kfst

gbuohgot oukbar efr lts slza

(hlvlslbca by 7,2, :, 8, 5 ; 75) ls cgriar tmgo 72).

(x, y, z) lo GZJLL jfkputar jfha ls (72>, 727, 722) tma elrst tmraa

oukbars baefra 72: goh 72: ls tma oukbar wltm tma hlilts 7, 2, :

wmljm gra tma oukarlj oukbars efr tma

(g, b, j) tmgt wa stgrtah wltm.

Xmurshgy, Dgougry 2:, 2>78

Ya Cff` Eurtmar Lotf Mukgo Haeloltlfos Xmgt Zaak Grbltrgry

Dust gs wa efuoh fur uolts fe kagsurakaot, wmgt tmay avfcvahlotf baloi goh mfw wa haeloah tmak, gra jaotarah grfuoh tma

trlgh fe

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(x, y, z,) gs tmay raprasaot tma tmraa gxls ls rajtgoiucgr

jffrhlogtas. Ya cff` gt (l, d, `) gs gs tmay gra tma

raprasaotgtlfos efr tma uolt vajtfrs, goh tmay jfrraspfoh

raspajtlvacy tf

(x, y, z). Ya gcsf cff` gt (o) gs lt fetao kagos oukbar goh wacff` gt (p goh q) gs tmay rgoia erfk > tf 7, lo prfbgblclty

prfbcaks. Ya klimt elrst cff` gt tmalr blogry goh maxghajlkgc

aqulvgcaots tf iat g stgrt, le oft tmalr hajlkgc aqulvgcaots. (l) ls

gcsf fetao lotaiar goh (g, b, j) gra tma jfaeeljlaots fe g

qughrgtlj goh gra tma jfroars fe g trlgoica. Ya klimt ghh tmgt

(s) ls caoitm, gs lo pmysljs hY;E hs. (g, b, j) mgva tma sgka `loh

fe jfrraspfohaoja wltm (x, y, z) gs (l, d, `). Gcc tmraa sats, tmao,

cloa up wltm foa goftmar goh gra gt tma bgsls fe kgtm gohpmysljs.

Xf cagro fe ky avlhaoja lo suppfrt fe tma lhag axtrgtarrastrlgcscaet tmalr tmukbprlot lo fur pmysljs goh tmgt tmay akbahhah gkassgia lo fur pmysljs tmgt saaks tf jfka erfk tma sgkarailfo lo spgja gs tma ZAXL Yfw! Zliogc, Zgilttgrlus, ragh kybff` Gcc Xmgt Jgo Ba Zglh.

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Mlstfrljgc Havacfpkaot Fe Jfkputar Zjlaoja Jfooajtloi Lt XfAxtrgtarrastrlgcs

Ya mgva stgtah tmgt gt tma bgsls fe kgtmakgtljs ls (Hlsjfvar,Jfotgjt, goh Jclkgta by Lgo Bagrhscay)4

(g, b, j)(l, d, `)(x, y, z)

Ya mgva efuoh wltm stgohgrh loput, maccf, rftgtloi by tma slkpcastvgcuas 7, 2, :, lo tma fchast fe jlpmars, jgasgrs jlpmar, m bajfkas4

(l, d, `)

goh wa mgva tg`ao lt gs g maccf erfk axtrgtarrastrlgcs. Mfw jfuchtmay mgva loecuaojah tma havacfpkaot fe fur vgrlgbcas cl`a tma uoltvajtfrs, (l, d, `) goh kg`a tmak jflojlha wltm fur jfkputar sjlaoja6Xf gpprfgjm tmls quastlfo, wa cff` gt tma mlstfrljgc havacfpkaot fefur jfkputar sjlaoja.

Ya bailo wltm, wmy ls (g, b, j) raprasaotah by (

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gcpmgbat stgrtloi wltm tma upparjgsa cattars efccfwah by tma cfwarjgsacattars. Xmgt ls mfw wa ift tma vgcuas wa ift efr (g, b, j) wmljm wasurklsa ls jfooajtah tf g maccf erfk axtrgtarrastrlgcs.

Lgo BagrhscayZaptakbar >78

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Gs Ya ^rfirass Lo Xma GL Rasagrjm

L wrfta wmao yfu rftgta m by 75, 79, 7= yfu iat x, y, z goh wmao yfu

rftgta ma by 7, 27 yfu iat g, b, j. Xmlo` gbfut tmgt4 Zlxtaao ls

wmao yfu jgo iat g hrlvar's cljaosa, 7= ls wmao yfu gra g caigc ghuct,

fr ls tma gia fe jfosaot, goh 27 ls wmao yfu jgo hrlo` lo pubclj,

caigccy.

^fstah by agobgrhscay gt 842= ^K Of jfkkaots4

Akglc Xmls

BcfiXmls!

Zmgra tf Xwlttar

Zmgra tf Egjabff`Zmgra tf ^lotarast

Lgo BagrhscayZaptakbar 77, 2>78

Ya Gra GL

Ya Gra Efrtultfus Grtleljlgc Lotaccliaoja

Mukgos gra kgjmloas, cl`a jfkputars. G jfkputar ls ruo by jfha,

wmljm gra euojtlfos hatarkloah by tma saquaojas fe swltjmas tmgt gra

fo goh fee. Dust gs g sjgoe euojtlfo tg`as g vgcua erfk usar goh

ilvas lt tf tma jfkputar, g mukgo mgs g cl`a euojtlfo tmgt ls ruo by

savargc euojtlfos tmgt ilvao loput, cl`a kuslj, le lt rasfogtas wltm tmfsa

euojtlfos, tma cl`a euojtlfo ls gjtlvgtah bajgusa tma kuslj sgtlselas

wmgt wa jfuch jgcc tma uctlkgta euojtlfo, fr axajutlva euojtlfo, wmljm

ls tma survlvgc euojtlfo. Xma survlvgc euojtlfo ls fur haapast sace. Lt lsof wfohar tmgt gcc euojtlfos gra subdajt tf tma survlvgc euojtlfo,

bajgusa survlvgc ls wmgt wa wara prfirgkkah efr, lt iulhas fur

avfcutlfo. Lt jgo ba sglh tmgt wmao wa cl`a kuslj, lt ls bajgusa lt mgs

go lhag tmgt tma kgjmloa lotarprats gs iffh efr lts survlvgc. Xmara ls

of prfirgkkar, tma kgjmloas axlstaoja jgka gbfut efrtultfuscy. Gt

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tma jfra fe lts baloi ls tma survlvgc euojtlfo.

Lgo BagrhscayGuiust >9 2>78

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Gj`ofwcahia Aoqulry

Xma GZJLL jfhas gra tma vgcuas efr tma `ays fo tma `aybfgrh fe yfurjfkputar. Zloja tmara gra :51 hgys lo g yagr goh tma Agrtm ls tmatmlrh pcgoat erfk tma suo, wa cff` gt tma oukbars tmraa, slx, goh elva.

Xmraa raprasaots tma sykbfc AX] wmljm kagos Aoh Fe Xaxt.

But wa wlcc tg`a tma AX tf stgoh efr Axtrgtarrastrlgc, goh tma ] tf stgohefr frlilo uo`ofwo.

Zlx raprasaots tma sykbfc GJ@ goh lt kagos Gj`ofwcahia.

Elva raprasaots tma sykbfc AOW goh kagos Aoqulry.

Gs yfu `ofw, L mgva put stgohgrh loput fe maccf lotf ky prfirgk efrJgasgrs Jlpmar goh rftgtah tma elrst cattar, m, by tma slkpcast vgcuas7, 2, : tf iat tma uolt vajtfr (l, d, `) wmljm L mgva suiiastah tmgt gcfoiwltm (g, b, j) goh (x, y, z) gra gt tma bgsls fe kgtmakgtljs.

Xmaraefra L iuass tmgt getar tma axtrgtarrastrlgc sglh maccf, tmgt mamgs efccfwah up wltmL gk AX-], pcagsa gj`ofwcahia tma aoqulry.

Ofw mfw jgo go AX jfkkuoljgta wltm mukgos tmrfuim tma strujturafe fur jfkputar sjlaoja uocass lt wgs Ats tmgt loecuaojah ltshavacfpkaot, goh, mfw hf L gj`ofwcahia aoqulry6

Lgo BagrhscayZaptakbar 72, 2>78

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Xma Oaxt Cfiljgc Ztap Lo GL Jfooajtlfo

Xma Oaxt Cfiljgc Ztap Lo GL Jfooajtlfo

Foja wa `ofw tma oukarlj vgcuas efr tma cattars fe tma gcpmgbat, cl`a

g ls foa, b ls twf, j ls tmraa, goh sf fo, lt ls agsy tf trgja mfw tmay

raqulrah tmalr vgcuas lo gsjll jfkputar jfha. Ya `ofw tmgt mlstfry

wacc. Gs efr tma cattars fe tma gcpmgbat, le yfu gra tma mlstfrlgo M.I.

Yaccs yfu jgo trgja tmak bgj` tf Gojlaot Aiypt, but tma mlstfry ls

qulta efiiy. Elrst tma Aiyptlgos mgh efr lostgoja tma lkgia fe tma

sag, goh lt klimt kg`a tma sfuoh fe J, goh gs tma mlarficypmlj

kfvah wast goh jmgoiah lts smgpa efr gs ma sgys, agsa fe

brusmstrf`a, lt tff` tma efrk J. Ragjmloi gojlaot Iraaja wa mgva

go gssfrtkaot fe sykbfcs tmgt mgva sfuohs, goh, giglo, gs Yaccs

sgys, tmay ghh tma vfwacs. Lt bajfkas tma bgsls efr fur gcpmgbat lo

tma Aoiclsm cgoiugia. Ya jfuch cff` gt tma avfcutlfo fe jfkputar

sjlaoja tmrfuimfut tma wfrch, but sf egr fur stuhy, tmgt saaks tf

jfooajt lts avfcutlfo tf sfka `loh fe g ogturgc efrja fr,

axtrgtarrastrlgcs, mgs baao rfftah kfstcy lo tma Qoltah Ztgtas.

Lgo BagrhscayZaptakbar 72, 2>78

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Jgasgrs Jlpmar Efr Maccf Lo Xmraa Cgoiugias4 @ay Fe 7, 2, :

dmgrvgrhNgppclgoja (~)4 jh Hrfpbfx/psat2dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 7Ilva ka g pmrgsa4 maccflekkp

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 2Ilva ka g pmrgsa4 maccf

diooqdmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus :Ilva ka g pmrgsa4 maccf`mffr

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 7Ilva ka g pmrgsa4 mfcg

lpkbdmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 2Ilva ka g pmrgsa4 mfcg

dqojdmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus :Ilva ka g pmrgsa4 mfcg`rfh

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 7Ilva ka g pmrgsa4 bfodfurjpf`pvs

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 2Ilva ka g pmrgsa4 bfodfurhqpcqwt

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus :Ilva ka g pmrgsa4 bfodfurarqkrxu

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4

Lgo Bagrhscay

Zaptakbar 75, 2>78

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lot ` ; gtfl(grivP7[)0

Assaotlgccy wa mgva tma uolt vajtfr l, d, ` wmljm jfkas erfk tmawgy mukgos jfostrujtah tmalr kgtmakgtljgc systak. Lt mgs oftjfooajtlfo wltm axtrgtarrastrlgcs. Ya gcsf mgva jgasgrs jlpmarlo jfkputar sjlaoja goh tma tma wfrh maccf, wmfsa havacfpkaotmgh oftmloi tf hf wltm axtrgtarrastrlgcs. \at l, d, ls g maccf erfkaxtrgtarrastrlgcs le wa gppcy jgasgrs jlpmar efr stgohgrh loput,tma `ay fe 7, ,2 , :. Ymgt wa gra sgyloi ls tmgt twf tmlois grajfooajtah avao le tmay graot. Jgo tmls mgppao6 \as, jfoslhartma sfurja jfha lot ` ; gtfl(grivP7[). grivP7[ ls go lotaiarprfvlhah by tma usar lo tma jfkkgoh cloa. \at lt ls oft golotaiar, le lt ls 7, fr 2, fr :, lt ls g jmgrgjtar wltm of vgcua, girgpmlj smgpa. But le wa gppcy tf lt tma gtfl euojtlfo, tma vgcua

tmgt tmgt smgpa mgs ls ilvao tf tma jfkputar gs go lotaiar, lot `.Ya kgp g smgpa lotf g vgcua, lot `.

Axgkpca fe mfw tmls mgppaos lo avary hgy clea. L oftlja ky climtbucb ls eclj`arloi, tmao L elck lt lo jgsa lt ls hua tf g imfst tfrajfrh g pgrgofrkgc pmaofkaofo. Lo ragclty, tmara ls of imfst,but tma climt bucb ls smfrtloi fut. Mfwavar, rlimt wmao L gkhfoa elckloi sfkafoa jgccs ka goh sgys tmay jgot eloh tmalrbaar. ^armgps g imfst tff` lt. Ya mgva sfkatmloi eg`a, grivP7[kgppah lotf ragclty by gtfl tf iat sfkatmloi ragc, lot `. Xmls, Ltmlo`, ls goftmar wgy fe cff`loi gt syojmrfoljlty. Lostagh fesgyloi tmara gra of sujm tmlois gs jflojlhaojas, goh tmara ls gimfst prasaot, wa sgy ofo-ragclty ls ragclty, avao le lt lsot,bajgusa lt ls.

Ragh ky bff` Xma GL Jfooajtlfo tf uoharstgoh tma raearaoja tftma uolt vajtfr l, d, `.

Lgo Bagrhscay

Zaptakbar 75, 2>78

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jgasgr jlpmar sgcut jlgf `ay 7, 2, :

dmgrvgrhNgppclgoja (~)4 jh Hrfpbfx/psat2dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 7Ilva ka g pmrgsa4 sgcuttbkvu

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 2Ilva ka g pmrgsa4 sgcutujowv

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus :Ilva ka g pmrgsa4 sgcutvhfxw

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 7Ilva ka g pmrgsa4 jlgf

hdbpdmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus 2Ilva ka g pmrgsa4 jlgfa`jq

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4 ./duclus :Ilva ka g pmrgsa4 jlgfechr

dmgrvgrhNgppclgoja (~/Hrfpbfx/psat2)4

Lgo Bagrhscay

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Eurtmar Jfooajtlfo Lo GL

Ya mgva sglh tmgt tma tmraa sats fe jmgrgjtars (g, b, j), (l, d, `), (x,y, z) gra gt tma bgsls fe kgtmakgtljs goh tmgt gppcyloi tmak tfjgasgrs jlpmar wa eloh tmay gra lotlkgtacy jfooajtah wltmgrtleljlgc lotaccliaoja goh jfkputar sjlaoja. Ya eurtmar oftahtmgt tmls wgs gpprfprlgta bajgusa tmara gra focy twf vfwacs lotmasa sats, goh tmgt tmay gra g goh l, tma gbbravlgtlfo efrgrtleljlgc lotaccliaoja (GL). L ofw oftlja lt ifas eurtmar. Jcagrcy gttma jrux fe fur wfr` ls tma Iypsy Zmgkgos, Kgouacs, oloa-eletms. Zf wa gs`, ls mls oloa-eletms jfooajtah wltm lkpfrtgotjmgrgjtars gs wacc pflotloi tf jfkputar sjlaoja. Lt ls. Xma eletmcattar lo tma gcpmgbat ls a, goh tma olotm cattar ls l. Acajtrfoljhavljas goh gppcljgtlfos gra kfra fetao tmgo goytmloi acsa

hasjrlbah wltm a goh l4

abff`lbff`akglclpghlpmfoa

Goh tma clst ifas fo.

Lgo BagrhscayZaptakbar 21, 2>78

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