Diseño Planta de Tratamiento de Aguas Residuales de Valdivia
September 18, 2022 | Author: Anonymous | Category: N/A
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Zlkvjrskmbm mj Pbltkbec mj @dkaj Ib`uatbm mj Klejlkjrïb Mjpbrtbojltc mj Klejlkjrïb Ruïok`b
MKPJÒC MJ ZLB XABL]B MJ ]^B]BOKJL]C ] ^B]BOKJL]C MJ BEZBP ^JPKMZBAJP MCOK@KAKB^KBP Znk`bmb jl Ybamkvkb, ^jekðl mj Acs ^ïcs, @dkaj.
Kltjerbltjs7
Gubl Iacrjs @ësbr L÷òjz Blmrës Ybrebs
@ursc7
Iulmbojltcs mj Klejlkjrïb bonkjltba
Xrcijscr7
Kelb`kc Pjp÷avjmb
Byumbltjs7 Byumbltj s7
Gjlkijr @rksðstcoc @rksðstcoc Jokakc Zaacb
Ij`db mj jltrjeb7
>= mj becstc mj >8>2
^jsuojl Jl ja prjsjltj klicroj sj mjsbrrcaab ja mksjòc mj ulb pabltb mj trbtbokjltc mj beubs rjskmubajs pbrb ab `coulb mj vbamkvkb, unk`bmb jl ab ^jekðl mj Acs ^ïcs, `bpbz mj bnbstj`jr ba :8% mj ab pcnab`kðl urnblb, `clskmjrblmc acs prc`jscs mj prjtrbtbokjltc, trbtbokjltc prkobrkc y trbtbokjltc sj`ulmbrkc. Ab pabltb mjtjroklbmb `ujltb `cl acs prc`jscs mj ikatrb`kðl y mjsbrjlbmcr, `coc prjtrbtbokjltc, j`ubakzbmcr y sjmkojltbmcr prkobrkc, `coc trbtbokjltc prkobrkc y bkrjb`kðl y sjmkojltb`kðl `coc pbrtj mja trbtbokjltc sj`ulmbrkc, mjnkmc b abs `brb`tjrïstk`bs mja beub b ab sbakmb mja trbtbokjltc, sj `clskmjrb quj lc js lj`jsbrkc ab prjsjl`kb mj ul trbtbokjltc tjr`kbrkc. B ac abrec mj acs ÷atkocs bòcs sj db vkstc ul `abrc buojltc buojltc jl abs l lcrobtkvbs crobtkvbs rjijrkmbs rjijrkmbs b ab `bakmbm `bakmbm mja beub mj ab pcnab`kðl, jstc pcr su `abrb rjab`kðl `cl ab `bakmbm mj vkmb mj abs pjrsclbs, pjrc ul ib`tcr kopcrtbltj pbrb ab `bakmbm mj vkmb mj abs pjrsclbs js ja `ðoc sj trbtbl acs mjsj`dcs prcmu`kmbs pcr jstbs, jl jstj `bsc jl pbrtk`uabr, lcs `jltrbrjocs jl ja trbtbokjltc mj abs beubs rjskmubajs mcok`kakbrkbs, jstc mjnkmc b quj pcr abs lcrobs quj sj utkakzbl ja mïb mj dcy, lc pjroktjl quj abs beubs rjskmubajs mcok`kakbrkbs, aajeujl b acs `ujrpcs mj beubs `cl jajvbmbs `cl`jltrb`kcljs mj baeulcs `cltboklbltjs quj scl lc`kvcs pbrb ab sbaum p÷nak`b y ja ojmkc bonkjltj. Js kopcrtbltj rj`ba`br rj`ba` br quj ulb pabltb mj trbtbokjltc lc js ouy mkstkltb b ulb klmustrkb, tbonkël tkjlj su `cstc klvcau`rbmc y bulquj lc lcs `jltrbrjocs jl ja tjob ocljtbrkc klvcau`rbmc, js rjajvbltj `jr`kcrbrsj mj quj ab pabltb sjb ac oâs jik`kjltj pcsknaj y jstë `uopakjlmc abs mkijrjltjs lcrobs quj sj aj mjnjl bpak`br.
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@cltjlkmc ^jsuojl .................................................................................................................................. >
Ïlmk`j ........................................................................................................................................ = ]bnabs ................................................................................................................................... = Kaustrb`kcljs .......................................................................................................................... = 2. Cngjtkvcs ............................................................................................................................... : Cngjtkvcs ejljrbajs ejljrbajs77 ................................................... .......................... ................................................... .................................................... ................................. ....... : Cngjtkvcs jspj`ïik`cs7 jspj`ïik`cs7 ................................................. ........................ ................................................... .................................................... ................................. ....... : >. Kltrcmu``kðl........................................................................................................................... 9 0. Obr`c ]jðrk`c ....................................................................................................................... 5 0.2 Beubs rjskmubajs ............................................................................................................. 5 0.> Beubs rjskmubajs rjskmubajs mcok`kakbrkbs mcok`kakbrkbs ............................................... ......................................................................... .......................................... ................ 5 0.0 ]rbtbokjltc mj beubs rjskmubajs rjskmubajs mcok`kakbrkbs ................................................................. ............................................. .................... 4 Xrjtrbtbokjltc.................................................................................................................... 4 ]rbtbokjltc ]rbtbokjl tc Xrkobrkc.................................................... .......................... .................................................... ................................................... ............................ ... 4 ]rbtbokjltc ]rbtbokjl tc sj`ulmbrkc.................................................... .......................... ................................................... .................................................. ......................... 4 ]rbtbokjltc tjr`kbrkc .......................................................................................................... ; =. Mjsbrrcaac pabltb mj trbtbokjltc trbtbokjltc .................................................. ......................... ................................................... ........................................ .............. 28 =.2 Mj`rjtcs ........................................................................................................................ 28 =.> Jqukpcs ......................................................................................................................... 28 =.>.2 Xrjtrbtbokjltc7 Xrjtrbtbokjltc7 .................................................... .......................... .................................................... ................................................... ........................... 28 =.>.> ]rbtbokjltc prkobrkc7 prkobrkc7.................................................... ......................... .................................................... ........................................... .................. 28 =.>.0 ]rbtbokjltc ]rbtbokjltc sj`ulmbrkc sj`ulmbrkc ............................................... ......................................................................... ............................................ .................. 22 :. Mbtcs .................................................................................................................................. 2> 9. ^jsuatbmcs y mks`uskcljs .................................................................................................... 2= 9.2 @bumba ........................................................................................................................... 2= 9.> @brb`tjrkzb`kðl mja mja jiaujltj jiaujltj ................................................... .......................... ................................................... ........................................ .............. 2: 9.0 Mkojlskcljs Mkojlskcljs mj acs jqukpcs jqukpcs ....................................................... ............................. .................................................... ................................... ......... 2: 9.= Jstblquj mj bkrjb`kðl ................................................................................................... 29 9.: Mkberbob mj iaugc y Abycut..................................................... ........................... ................................................... ........................................ .............. 25 @cl`auskcljs .......................................................................................................................... 2; ^jijrjl`kbs ............................................................................................................................. >8 Lcojl`abturb Lcojl`ab turb.................................................... ........................... ................................................... .................................................... ............................................ .................. >2 Bpëlmk`js Bpëlm k`js ..................................................... ........................... .................................................... ................................................... ................................................ ....................... >> Bpëlmk`j Bpëlm k`j B7 Ybacrjs Ybacrjs mj rjijrjl`kbs .................................................. ........................ .................................................... ................................... ......... >> Bpëlmk`j Bpëlm k`j N7 @âa`uacs @âa`uacs.................................................. ......................... ................................................... .................................................... ............................... ..... >= 0
Ïlmk`j ]bnabs ]bnab 2> Jvcau`kðl @brb`tjrkzb`kðl @brb`tjrkzb`kðl mj beubs rjskmubajs rjskmub ajsmja mcok`kakbrkbs .......................... ............. 2> ]bnab mj acsprcojmkc `cltboklbltjs jl abs jtbpbs trbtbokjltc....................................... mj beubs rjskmubajs .... 2> ]bnab 0 Jik`kjl`kb y `brb`tjrkzb`kðl iksk`cquïok`b iksk`cquïok`b.................................................. ......................... ........................................... .................. 20 ]bnab = Ybacrjs mj acs `bumbajs mj jltrbmb b ab pabltb mj trbtbokjltc. trbtbokjltc. ................................... 2= ]bnab : Jik`kjl`kb y `brb`tjrkzb`kðl `brb`tjrkzb`kðl `clskmjrbmb `clskmjrbmb pbrb trbtbokjltc. trbtbokjltc. .......................................... ......................... ................. 2: ]bnab 9 Jvcau`kðl mj acs `cltboklbltjs mj b`ujrmc `cl ja lkvja mj jik`kjl`kb `clskmjrbmc pbrb abs jtbpbs jtbpbs mja trbtbokjltc trbtbokjltc .................................................................... .......................................... ..................................................... ................................... ........ 2: ]bnab 5 Mksjòc tblquj mjsbrjlbmcr mjsbrjlbmcr ................................................ ....................... ................................................... ........................................ .............. 2: ]bnab 4 Mksjòc sjmkojltbmcr sjmkojltbmcr prkobrkc prkobrkc ...................................................................... ............................................. ....................................... .............. 29 ]bnab ; @crrkjltjs mja trbtbokjltc................................................... .......................... ................................................... ........................................ .............. 25 ]bnab 28 Lcojl`abturb Lcojl`abturb .................................................. ......................... ................................................... .................................................... ............................... ..... >2 ]bnab 22 sunïlmk`js sunïlmk`js y vbrkbltjs vbrkbltjs ................................. ............................................................ .................................................... .................................. ......... >2 ]bnab 2> Xbrâojtrcs mj mksjòc pbrb tblqujs mjsbrjlbmcrjs mj prjtrbtbokjltc ..................... >> ]bnab 20 @cl`jltrb`kclj @cl`jltrb`kcljss oâxkobs o âxkobs pjroktkmbs pjroktkmbs ................................................. ....................... ................................................ ...................... >> ]bnab 2= Ybacrjs jstâlmbr utkakzbmcs pbrb mjtjroklbr ja vcauojl mja jstblquj mj bkrjb`kðl ... >0
Kaustrb`kcljs Kaustrb`kðl 2 Znk`b`kðl mj ^ïc Ybamkvkb y mjsjoncquë mjsjoncquë ba C`ëblc Xb`ïik`c ................................ 9 Kaustrb`kðl > @clsuoc mj beub pctbnaj pcr dbnktbltjs, jl Ybamkvkb, pcr Beubs Më`kob P.B. ... 2= Kaustrb`kðl 0 Mkberbob Mkberbob mj iaugc mj ab pabltb mj trbtbokjltc. trbtbokjltc. ..................................................... ............................................ ......... 25 Kaustrb`kðl = Abycut mj ab pabltb mksjòbmb mksjòbmb .......................................................................... ................................................ ............................... ..... 24
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2. Cngjtkvcs Cngjtkvcs ejljrbajs7 Mksjòbr ulb pabltb mj trbtbokjltc mj beubs rjskmubajs mcok`kakbrkbs pbrb ab `coulb mj Ybamkvkb, rjekðl mj Acs ^ïcs, @dkaj. Ruj acerj bnbstj`jr ba :8% mj ab pcnab`kðl urnblb.
Cngjtkvcs jspj`ïik`cs7
@ba`uabr `bumba y `brb`tjrkzb`kðl `brb`tjrkzb`k ðl mj `bmb trbtbokjltc mj ab pabltb mj trbtbokjltc mj beubs rjskmubajs.
Cntjljr ab `brb`tjrkzb`kðl `brb`tjrkzb`k ðl iksk`cquïok`b mj ul ^KA.
Mksjòbr ab pabltb pabltb mj trbtbokjltc mj beubs rjskmubajs.
@ba`uabr abs mkojlskcljs mj acs jqukpcs prcpujstcs.
@clstru``kðl mj ul mkberbob Abycut.
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>. Kltrcmu``kðl Js mj `clc`kokjltc ejljrba quj ja beub rjprjsjltb `jr`b mja 58% mj ab supjrik`kj mja pabljtb, lc cnstbltj, scac ja >,:% mj jstb js bptb pbrb ja `clsuoc duoblc y sk `clskmjrbocs, ac bij`tbmc quj sj db vkstc jstj rj`ursc pcr sktub`kcljs `coc `bajltbokjltc eacnba prcmu`kmc pcr ja batc erbmc mj `cltboklb`kðl pcr mjs`breb mj beubs rjskmubajs c jiaujltjs, bulquj, sjbl rjeuabmcs, ab mkijrjl`kb mj abs rjeuab`kcljs jltrj acs pbïsjs mjsbrrcaabmcs mjsbrr caabmcs y sunmjsbrrcaabmcs y acs a cs quj jstâl jl vïb mj mjsbrrcaac scl tbl erblmjs y pc`c jstrk`tbs quj vjocs `coc mj b pc`c jstj rj`ursc dïmrk`c sj db vkstc mkjzobmc y pjrgumk`bmc. Pk `clskmjrbocs ab ac`bakmbm Ybamkvkb, jl ab `uba vkvjl barjmjmcr mj 255.888 dbnktbltjs (@jlsc, >8>8) rcmjbmcs mj ârjbs vjrmjs, vkmb skavjstrj, js mj`kr, `brb`tjrïstk`cs mja sur mj @dkaj, `clmk`kcljs b`jptbnajs mj lkvjajs ojmkc bonkjltbajs js mj vktba kopcrtbl`kb pbrb ab pcnab`kðl y sus creblksocs dbnktbltjs sjeukr obltjlkjlmc jstb sktub`kðl mj nkjljstbr, bsï, nrklmblmc ulb pabltb mj trbtbokjltc `bpbz mj `uopakr `cl abs rjeuabrkzb`kcljs mbmbs pcr ajy `dkajlb mja :8% mj ab pcnab`kðl ab ac`bakmbm. Mj b`ujrmc `cl ac bltjrkcr, sj jspj`kik`bl 0 mj`rjtcs pbrb ja `uopakokjltc mja trbtbokjltc mja beub jl @dkaj. Ybamkvkb, skjlmc pbrtj mj ab rjekðl mj Acs ^ïcs, sj jl`ujltrb bnrbzbmb pcr ulb sjrkj mj rïcs, trjs jspj`ïik`bojltj, mj acs `ubajs, scac ulc mj jaacs mjsjonc`b jl ja c`ëblc pb`kik`c, ^ïc Ybamkvkb, pcr ac tbltc, pbrb ab cntjl`kðl mj ul jiaujltj trbtbmc quj `uopab `cl ja mj`rjtc rjeuabtcrkc vkejltj pbrb ja mjsjoncquj mjsjoncquj jl rïcs j jss ja M.P L¸ ;8/>882 (N@L, >882).
Kaustrb`kðl 2 Znk`b`kðl mj ^ïc Ybamkvkb y mjsjoncquë ba C`ëblc Xb`ïik`c
9
0. Obr`c ]jðrk`c 0.2 Beubs rjskmubajs Abs beubs rjskmubajs c sjrvkmbs scl bqujaabs beubs quj dbl skmc usbmbs y mjsj`dbmbs pcr b`tkvkmbmjs mcoëstk`bs, klmustrkbajs, berï`cabs c eblbmjrbs quj tkjljl ul oksoc ikl mj b`ujrmc `cl ja skstjob mj `blbakzb`kðl, mclmj sjrâl trbtbmbs `cl ja ikl mj rjmu`kr ab `cl`jltrb`kðl mja `cltboklbltj quj bij`tj acs pbrâojtrcs mj `bakmbm mja jiaujltj. (Crcz`c, >88:) Jstbs beubs rjskmubajs scl `abskik`bmbs `cl trjs tðpk`cs tbajs `coc abs `brb`tjrïstk`bs, iïsk`bs, quïok`bs y/c nkcaðek`bs.
@brb`tjrïstk`bs iïsk`bs7 prjsjl`kb iïsk`bs7 prjsjl`kb mj scakmcs vksknajs c mj obycr tbobòc, tjopjrbturb, cacr, `cacr
@brb`tjrïstk`bs quïok`bs7 prjsjl`kb quïok`bs7 prjsjl`kb tbltc mj `copcljltjs creâlk`cs `coc `co c klcreâlk`cs y tbonkël mj crkejl ebsjcsc.
nkcaðek`bs7 jl jaabs sj jl`ujltrbl ok`rccreblksocs `coc baebs, @brb`tjrïstk`bs nkcaðek`bs7
nb`tjrkbs jltrj ctrbs. @cltklublmc, ctrc tkpc mj `abskik`b`kðl quj rj`knjl abs beubs rjskmubajs js rjspj`tc b su `copcsk`kðl, js mj`kr, bqujaacs pbrâojtrcs quj pjroktjl kmjltkik`br ja tkpc mj `cltboklbltj jl ja jiaujltj.
Pcakmcs jl suspjlskðl (PP)7 Xbrtï`uabs sðakmbs quj pjroblj`jl jl suspjlskðl jl beub `coc ul `cackmj.
Mjoblmb quïok`b mj cxïejlc (MRC)7 @bltkmbm mj cxïejlc lj`jsbrkc pbrb cxkmbr tcmb
ab obtjrkb creâlk`b y cxkmbnaj prjsjltj jl beub rjskmuba. Mjoblmb nkcquïok`b mj cxïejlc (MNC)7 (MNC)7 @bltkmbm mj cxïejlc quj `clsuojl acs ok`rccreblksocs ba prcakijrbr jl beub rjskmuba.
0.> Beubs rjskmubajs mcok`kakbrkbs Js bqujaab beub quj prcvkjlj mja bnbstj`kokjltc mj ulb pcnab`kðl, mjnkmc b su usc, dbl ocmkik`bmc abs prcpkjmbmjs iksk`cquïok`bs y nkcaðek`bs. Xcr ac tbltc, abs beubs rjskmubajs `cltkjljl tbltb obtjrkb creâlk`b `coc klcreâlk`b prcakijrblmc `kjltcs mj ok`rccreblksocs (Xk`bmc, >829). Jstbs scl rj`caj`tbmbs pcr ja skstjob mj ba`bltbrkaabmc mj ab ac`bakmbm kl`auyjlmc tbonkël ctrbs ârjbs, `coc abs klmustrkbajs c berbrkbs. Jstbs beubs scl trbtbs y vjrtkmbs ulb vjz iklbakzbmc ja trbtbokjltc b ul `ujrpc mj beub. 5
0.0 ]rbtbokjltc mj beubs rjskmubajs mcok`kakbrkbs Ja trbtbokjltc js ja `clgultc mj jtbpbs mj mkvjrsbs cpjrb`kcljs ulktbrkbs. Jstbs jtbpbs jstâl mkvkmkmbs jl prjtrbtbokjltc, trbtbokjltc prkobrkc, trbtbokjltc sj`ulmbrkc y trbtbokjltc tjr`kbrkc. Xrjtrbtbokjltc Pj jl`ujltrb jl ab `bnj`jrb mj klstbab`kðl, js ul skstjob mj sjpbrb`kðl mj erblmjs scakmcs c mj erbl mj `bltkmbm mj brjlbs `cl ja ikl mj prctjejr y jvktbr ja mjsebstj prcerjskvc prcerjskv c mj acs jqukpcs jl abs jtbpbs pcstjrkcrjs, bmjoâs, prcvjj ab cnstru``kðl mj abs mkstkltbs ulkmbmjs mj ab klstbab`kðl (Cscrkc, >820). Jxkstjl vbrkcs tkpcs mj jqukpcs pbrb jstj sj`tcr mja trbtbokjltc, lc cnstbltj, pbrb mksjòc mja prjsjltj scac sj `clskmjrbrâ ab cp`kðl mj ikatrcs mj rjgbs y/c mjsbrjlbmcr, mjtbaabmcs jl ja bpbrtbmc mj jqukpcs y b``jscrkcs. ]rbtbokjltc Xrkobrkc Jl`brebmc mj icrob prkl`kpba jl ab sjpbrb`kðl iïsk`b mj acs `copcljltjs mja beub rjskmuba, pcr ac tbltc, sj jl`breb mj ab rjoc`kðl mj bqujaacs `cltboklbltjs `bpb`js mj sjmkojltbr, bmjoâs mj b`jktjs y erbsbs y mj scakmcs mj ojlcr tbobòc quj lc iujrcl bpbrtbmcs pcr ab jtbpb bltjrkcr. Mj icrob ejljrba, abs cpjrb`kcljs jl`brebmbs mja prc`jsc scl ab sjmkojltb`kðl, iactb`kðliac`uab`kðl, jakoklblmc barjmjmcr mja 98% ba 58% mj acs sðakmcs suspjlmkmcs tctbajs (Cscrkc, >820). Mjnkmc quj, acs sðakmcs suspjlmkmcs tctbajs pcsjjl `kjrtb vjac`kmbm mj mj`bltb`kðl, sj `clskmjrbl trjs vbrkbnajs kopcrtbltjs.
^jlmkokjltc mj sjmkojltb`kðl7 Xcr`jltbgj sjmkojltb`kðl7 Xcr`jltbgj mj pbrtï`uabs jakoklbmbs jl ja prc`jsc mj
sjmkojltb`kðl ulb vjz iklbakzbmc jstj. Yjac`kmbm mj bsjltbokjltc mj ab pbrtï`uab7 pbrtï`uab7 ^jab`kclbmb ab luojrc mj ^jylcams, `ublmc jstj js obycr c ojlcr b ab ulkmbm, sj `ba`uab pcr ojmkc mj abs ajyjs mj Ljwtcl c Ptcfj rjspj`tkvbojltj. Bpëlmk`j …
^blec mj mjsncrmbokjltc7 Pktub`kðl mjsncrmbokjltc7 Pktub`kðl jl ab `uba ulb pbrtï`uab sjmkojltb bltjs mj sbakr mj ab `ujl`b, jstâ rjab`kclbmb `cl ab a b vjac`kmbm `rïtk`b y mkvk mkvkmj mj ab prciulmkmbm mj ab `ujl`b mj sjmkojltb`kðl pcr ja tkjopc mj mjtjl`kðl dkmrâuak`b.
]rbtbokjltc sj`ulmbrkc Jl`brebmb jx`auskvbojltj jx`auskvbo jltj pcr prc`jscs nkcaðek`cs pbrb ab rjmu``kðl mj `copcljltjs creâlk`cs. Jstj prc`jsc `clvkjrtj ab obtjrkb creâlk`b mksujatb jl ja beub rjskmuba jl scakmcs sjmkojltbnajs iac`uajltcs (^cgbs, >88>) pcr ja ibvcrj`kokjltc mj mjsbrrcaac mj acs ok`rccreblksocs ojmkbltj ul buojltc mj ab mcsks mj bkrj quj klojmkbtbojltj mjspuës scl sjpbrbmcs pcr sjmkojltb`kðl 4
jl ja jstblquj mj sjmkojltb`kðl. Acs prc`jscs nkcaðek`cs oâs utkakzbmcs scl acs acmcs b`tkvbmcs y acs ikatrcs pjr`cabmcrjs. Jstb jtbpb js mj erbl kopcrtbl`kb mjnkmc ba blâaksks mj acs pbrâojtrcs mj `abskik`b`kðl mj MNC, quj pujmjl aajebr b rjocvjr jl ul 4:% b ;:% jstj pbrâojtrc ulb vjz iklbakzbmc (^cgbs, >88>). ]rbtbokjltc tjr`kbrkc Cngjtkvc prkl`kpba js `copajojltbr acs prc`jscs bltjrkcrjs mjs`rktcs pbrb acerbr jiaujltjs oâs purcs, `cl ojlcr `breb mj `cltboklbltj (^cgbs, >88>). Pj acerb pcr ojmkc mj trbtbokjltcs iksk`cquïok`cs quj kl`auyjl prj`kpktb`kcljs, ikatrb`kcljs, `acrb`kcljs pbrb ulb kltjlsb rjmu``kðl mj acs lkvjajs mj lutrkjltjs klcreâlk`cs (Cscrkc, >820). @bnj rj`ba`br quj, sje÷l blâaksks mj abs beubs rjskmubajs pbrb ja sj`tcr sur mja pbïs, lc sj mjtj`tbl vbacrjs klbmj`ubmcs, sbavc pcr ab prjsjl`kb mj pjqujòbs `cl`jltrb`kcljs ikjrrc y oblebljsc jl baeulcs sj`tcrjs mj jstb zclb (Ijrlblmjz, >82:), pcr ac tbltc, mj b`ujrmc b acs jstumkcs rjbakzbmcs pcr ja Klstktutc mj ^j`urscs mj Beub mj ]jxbs y mja Pkstjob Zlkvjrsktbrkc ]jxbs B&O, klmk`bl quj ba sjr `copcljltjs tïpk`cs mj ab tkjrrb, ba `cltb`tc `cl ja beub pujmjl mkscavjrsj, b`brrjâlmcacs db`kb abs beubs suntjrrâljbs, c nkjl pcr acs b`ujmu`tcs mj ab zclb, bmjoâs, rjikjrjl quj jl nbgbs `cl`jltrb`kcljs lc `busbl prcnajobs pbrb ab sbaum (O`Ibrablm & Oclty, >882). @clskmjrblmc ja blâaksks bltjrkcr, pbrb ja prjsjltj prcyj`tc lc sj rjbakzbrâ ulb jtbpb mj trbtbokjltc tjr`kbrkb. Xcr ctrc abmc, abs beubs rjskmubajs, mjspuës mj jxpjrkojltbr acs oëtcmcs mja trbtbokjltc sj`ulmbrkcs scl bptbs pbrb su aknjrb`kðl b rïcs. Lc cnstbltj, lc js bptb pbrb ja `clsuoc duoblc. Ab prcmu``kðl mja beub pctbnaj rjqukjrj pcstjrkcrjs trbtbokjltcs pbrb jakoklbr ok`rccreblksocs pctjl`kbaojltj pbtðejlcs, rjmu`kr ab turnkmjz (ojmkmb mj abs pbrtï`uabs mksujatbs), jakoklbr ja sbncr y ja cacr, y rjmu`kr ab `bltkmbm mj sustbl`kbs quïok`bs pjsbmbs tbajs `coc dkjrrc y oblebljsc (Cscrkc, >820).
;
=. Mjsbrrcaac pabltb mj trbtbokjltc =.2 Mj`rjtcs Mj b`ujrmc `cl ab lcrobtkvb `dkajlb, quj rkej `cl `kjrtcs pbrâojtrcs b `uopakr, mjtbaabmcs jl ja bpëlmk`j B pbrb ab jokskðl mj `cltboklbltjs db`kb `ujrpcs mj beub.
Mj`rjtc 98;7 Xbrb 98;7 Xbrb mjs`breb mj rjskmucs aïqukmcs b skstjobs mj ba`bltbrkaabmc.
Mj`rjtc ;87 Mjs`brb ;87 Mjs`brb mj rjskmucs aïqukmcs b beubs obrklbs y `cltkljltbajs supjrik`kbajs. Mj`rjtc =97 =97 ^jeuab ^jeuab mjs`breb mj rjskmucs aïqukmcs b beubs suntjrrâljbs
Xbrb ja prjsjltj, y mjnkmc b ab `jr`blïb `cl ja ^ïc quj mjsjonc`b mkrj`tbojltj ba `ujrpc mj beub c`jâlk`c, sj `clskmjrbrb pbrb ja `uopakokjltc mj acs pbrâojtrcs ja mj`rjtc ;8 mja bòc >888. =.> Jqukpcs Pj mjtbaabl acs jqukpcs quj sjrâl `clskmjrbmcs pbrb ja mksjòc y mj ab pabltb mj trbtbokjltc mj beubs rjskmubajs. =.>.2 Xrjtrbtbokjltc7
Mjsnbstj mj scakmcs7 ^jtkjlj ab obycr `bltkmbm pcsknaj mj sðakmcs erujscs y nbsurbs, prc`jsc quj sj rjbakzb b trbvës mj mcs `blbajs mj 8,58 o mj bl`dc, oâs ulc mj jojrejl`kb jl mjrkvb`kðl. Jstcs `blbajs prjsjltbl jl su kltjrkcr ul `clgultc mj rjgbs butcoâtk`bs. Jstbs rjgbs jstâl `clstktukmbs pcr ulbs nbrrbs jl pcsk`kðl vjrtk`ba c kl`aklbmbs, y sjpbrbmbs b kltjrvbacs keubajs (BeubsMj`kob, >8>8).
Mjsbrjlbmcr7 Mjsbrjlbmcr7 Jxtrbj Jxtrbj mj abs beubs ab obycr `bltkmbm mj pbrtï`uabs mj batb vjac`kmbm mj sjmkojltb`kðl, tbajs `coc brjlb, erbvb y ctrbs obtjrkbs okljrbajs, y, pcr ctrc, jakoklbr abs erbsbs, jspuobs y mjoâs obtjrkbajs iactbltjs oâs akejrbs quj ja beub (BeubsMj`kob, >8>8).
=.>.> ]rbtbokjltc prkobrkc7 ]blquj mj j`ubakzb`kðl7 @cltrcab ja klerjsc mja `bumba b ab jtbpb pbrb quj abs jtbpbs pcstjrkcrjs obltjlebl ul `bumba `clstbltj y jqukaknrbmc. jqukaknrbmc.
Pjmkojltbmcr prkobrkc7 Jl`brebmc mj ab sjpbrb`kðl mj acs sðakmcs suspjlmkmcs mja beub, pcr jij`tc mj ab erbvjmbm mclmj abs beubs klerjsbl jl ja `jltrc mja jstblquj y iauyjl jl icrob rbmkba db`kb su pbrjm pjrkojtrba. Acs sðakmcs mjpcsktbmcs jl ja iclmc sj `clmu`jl db`kb ab pbrtj `jltrba mja skstjob ojmkbltj ul skstjob mj rbsqujtbs mj iclmc quj `clmu`jl acs sðakmcs dbstb ja pultc mj sbakmb (BeubsMj`kob, >8>8). >8>8).
28
=.>.0 ]rbtbokjltc sj`ulmbrkc
Jstblquj mj bkrjb`kðl7 ^jb`tcr blbjrðnk`c, quj prcpcr`kclb cxïejlc y obltkjljl acs creblksocs bjrðnk`cs suspjlmkmcs y ojz`abmcs `cl ja beub pbrb ba`blzbr ulb batb tbsb mj mjerbmb`kðl creâlk`b y mj jakoklb`kðl mj lutrkjltjs (Crcz`c, >88:). >88:).
Pjmkojltbmcr sj`ulmbrkc7 @uopaj `cl `brb`tjrïstk`bs skokabrjs ba sjmkojltbmcr prkobrkc, lc cnstbltj, lc pcsjjl ja `clgultc mj nbrrjmcrjs mj acmc, quj sj jl`brebl mj quktbr ab jspuob y ab lbtb. Bmjoâs, sj rjtcrlb ul >:% ba skstjob `coc rj`kr`uab`kðl, y ja rjstc vb b su mkspcsk`kðl iklba (Crcz`c, >88:). >88:).
22
:. Mbtcs @clskmjrblmc quj ja :8% mj ab pcnab`kðl mj Ybamkvkb js mj 44.:88 dbnktbltjs quj ejljrbl ul `bumba prcojmkc mkbrkc mj ;89>.= Vo 0/mïb_. Pj mjiklj ab `brb`tjrkzb`kðl mj beubs rjskmubajs prcojmkc mj b`ujrmc `cl klicroj prjsjltbmc pcr ab Mkvkskðl mj ^j`urscs Dïmrk`cs y Ojmkc Bonkjltj mja mja Mjpbrtbojltc Mjpbrtbojltc mj Klejlkjrïb Klejlkjrïb @kvka @kvka mj ab Zlkvjrskmbm Zlkvjrskmbm mj @dkaj jl nbsj ba aknrc Klejlkjrïb mj Beubs ^jskmubajs7 ]rbtbokjltc, vjrtkmc y rjutkakzb`kðl (Ojt`bai, Jmmy, & ]`dcnblceacus, 2;;8). Pj mjseacsbl acs prkl`kpbajs pbrâojtrcs b trbtbr.
]bnab 2 @brb`tjrkzb`kðl prcojmkc mj beubs rjskmubajs mcok`kakbrkbs
Xbrâojtrc
Zlkmbm
Mënka
Ojmkb
Iujrtj
Pðakmcs tctbajs
oe/a
0 0:8 :8
5>8 5>8
2>88
Pðakmcs mksujatcs
oe/a
>:8
:88 :88
4:8
Ikgcs
oe/a
2=:
088
:>:
Ycaâtkajs
oe/a
28:
>88
0>:
Pðakmcs suspjlmkmcs Ikgcs
oe/a oe/a
288 >8
>>8 ::
0:8 5:
Ycaâtkajs
oe/a
48
29:
>5:
Pðakmcs sjmkojltbnajs
oe/a
:
28
>8
MNC:
oe/a
228
>>8
=88
Lktrðejlc tctba
oe/a
>8
=8
4:
Iðsicrc tctba
oe/a
=
4
2:
Mja oksoc sj cntkjljl ab jvcau`kðl mj acs `cltboklbltjs mj b`ujrmc `cl `bmb ulb mj abs jtbpbs mja trbtbokjltc.
]bnab > Jvcau`kðl mj acs `cltboklbltjs jl abs jtbpbs mja trbtbokjltc mj beubs rjskmubajs
Jtbpbs Beubs sjrvkmbs `rumbs Jiaujltj trbtbokjltc prkobrkc Jiaujltj trbtbokjltc sj`ulmbrkc ^joc`kðl mj lutrkjltjs Jiaujltj trbtbokjltc tjr`kbrkc
MNC oe/a
PP] oe/a
L oe/a
X oe/a
>:8 248 08 >8 98
>>8 288 08 >8 48
:8 =: =8 28 =:
28 ; ; 2 ;
2>
@cltklublmc, sj `clskmjrb ulb jik`kjl`kb jik`kjl`k b tjðrk`b jl pcr`jltbgj mj abs jtbpbs mj ab pabltb jl nbsj b acs mbtcs brrcgbmcs pcr ja @jltrc Xblbojrk`blc mj Klejlkjrïb Pblktbrkb y @kjl`kbs @kjl`k bs mja Bonkjltj (^cgbs, >88>). ]bnab 0 Jik`kjl`kb y `brb`tjrkzb`kðl iksk`cquïok`b
Jtbpb
MNC
PP]
L
X
Xrjtrbtbokjltc Xrkobrkc Pj`ulmbrkc ]jr`kbrkc
8-28 >:-=: 58-;: ;>-;4
8-28 =8-58 5:-;: ;0-;4
8-28 28->8 28->8 >8-=8
8-28 28->8 28->8 >8-=8
20
9. ^jsuatbmcs y mks`uskcljs 9.2 @bumba Mj b`ujrmc `cl acs mbtcs mj ab Pupjrkltjlmjl`kb mj Pjrvk`kcs Pblktbrkcs quj mb b `clc`jr ja lkvja mj `clsuoc mj beub pctbnaj mja pbïs, jl ja `uba, tbnuabmcs pcr rjekðl. Pj tcob `coc rjijrjl`kb acs mbtcs cntjlkmcs pcr pbrtj mj Beubs Më`kob P.B, `copbòïb jl`breb mja trbtbokjltc mj beubs rjskmubajs mj ul batc pcr`jltbgj mj ab `coulb mj Ybamkvkb. Pj jspj`kik`b quj, ja ebstc mkbrkc prcojmkc mj `bmb dbnktbltj aajeb b 2>4 aktrcs y jl pjrkcmc jstkvba ba`blzb 2:5 A (PPKP, >884).
Kaustrb`kðl > @clsuoc mj beub pctbnaj pcr dbnktbltjs, jl Ybamkvkb, pcr Beubs Më`kob P.B.
Pj cntkjljl, pcr ac tbltc, acs `bumbajs mj beubs rjskmubajs quj klerjsbl b ab pabltb, mj b`ujrmc `cl ab pcnab`kðl b bnbstj`jr, js mj`kr, ja :8% mj acs dbnktbltjs mj Ybamkvkb, 44.:88 pjrsclb.
]bnab = Ybacrjs mj acs `bumbajs mj jltrbmb b ab pabltb mj trbtbokjltc.
@bumba Xrcojmkc Oâxkoc
Ybacr Vo0 /mïb_ ;89>.= 2222:.9
2=
9.> @brb`tjrkzb`kðl mja jiaujltj @clicroj b acs mbtcs cntjlkmcs mj ab tbnab :.0, sj `clskmjrbl abs skeukjltjs jik`kjl`kbs mj rjoc`kðl mj `cltboklbltjs jl pcr`jltbgj.
]bnab : Jik`kjl`kb y `brb`tjrkzb`kðl `clskmjrbmb pbrb trbtbokjltc.
Jtbpb Xrjtrbtbokjltc Xrkobrkc Pj`ulmbrkc ]jr`kbrkc
MNC : >: 44 ;:
PP]T 28 :: 4: ;:
L : 28 >8 =8
X : 28 28 =8
Bdcrb, sj sj cntkjljl cntkjljl abs `cl`jltrb` `cl`jltrb`kcljs kcljs mj mj acs `cltboklbltjs `cltboklbltjs mj b`ujrmc b`ujrmc `cl ab tbnab :.>. :.>.
]bnab 9 Jvcau`kðl mj acs `cltboklbltjs mj b`ujrmc `cl ja lkvja mj jik`kjl`kb `clskmjrbmc pbrb abs jtbpbs mja trbtbokjltc
Jtbpbs
MNC oe/a
PP] oe/a
L oe/a
X oe/a
>:8 248 08 20
>>8 288 08 22
:8 =: =8 08
28 ; ; 9
Beubs sjrvkmbs `rumbs Jiaujltj trbtbokjltc prkobrkc Jiaujltj trbtbokjltc sj`ulmbrkc Jiaujltj trbtbokjltc tjr`kbrkc 9.0 Mkojlskcljs mj acs jqukpcs @âa`uacs y `clskmjrb`kcljs jl bpëlmk`j N.
]bnab 5 Mksjòc tblquj mjsbrjlbmcr
Xbrâojtrc Iaugc oâsk`c ]kjopc mjtjl`kðl iaugc Ycauojl Bl`dc Xrciulmkmbm Aclektum ]kjopc rjtjl`kðl dkmrâuak`c Bkrj rjqujrkmc rjqujrkmc Brjlkaab rjtkrbmb
Ybacr ;89>.= 0.: >5.8> 2.: 2.: 2> =.0 =.> 2.95
Zlkmbm o0/mïb okl o0 o o o okl o0/okl o0/mïb
2:
]bnab 4 Mksjòc sjmkojltbmcr prkobrkc
Xbrâojtrc Mkâojtrc Xrciulmkmbm ]kjopc rjtjl`kðl scakmcs Ârjb Ycauojl
Ybacr 2> : 0.00 220 :9:
Zlkmbm o o o/d o> o0
]kjopc rjtjl`kðl dkmrâuak`c
2.=;
d
9.= Jstblquj mj bkrjb`kðl Ja jstblquj mj bkrjb`kðl utkakzbmc jl jstb pabtb sj mjtjroklð sje÷l ab j`ub`kðl 2= mja bpëlmk`j, , ja `uba `cl ab `uba sj pumc mjtjroklbr quj ja vcauojl lj`jsbrkc pbrb jstj jqukpc js mj mjnjrâ sjr c`upbmc pcr ul scac jstbquj mj icrob rj`tbleuabr. Abs mkojlskcljs mja jqukpc lc pujmjl sjr mjtjroklbmbs, mjnkmc b quj lc sj mkspclj mj ulb rjeab ikbnaj pbrb mjtjroklbr mk`dcs vbacrjs.
5>,=
29
9.: Mkberbob mj iaugc y Abycut.
Kaustrb`kðl 0 Mkberbob mj iaugc mj ab pabltb mj trbtbokjltc.
]bnab ; @crrkjltjs mja trbtbokjltc
Luojrb`kðl 2 > 0 = : 9 5 4 ; 28 22
@crrkjltj Biaujltj mj beubs rjskmubajs mcok`kakbrkbs mcok`kak brkbs Beubs rjskmubajs ikatrbmb Pcakmcs mj erbl tbobòc Beub rjskmuba mjsbrjlbmb Brjlbs y erbsbs @bumba j`ubakzbmc mj beubs rjskmubajs Pcakmcs mj`bltbmcs Beub sjmkojltbmb Beub rjskmuba `cl ok`rccreblksocs suspjlmkmcs Mjerbmb`kðl mj obtjrkb creâlk`b Jiaujltj trbtbmc
25
Kaustrb`kðl = Abycut mj ab pabltb mksjòbmb
24
@cl`auskcljs Mj b`ujrmc `cl acs cngjtkvcs pabltjbmcs, sj `cl`auyj 2. Pj acerð `ba`uabr `ba`uabr ab `brb`tjrkzb`kðl iksk`cquïok`b iksk`cquïok` b mja ^KA jstumkbmc. >. Pj mksjòb ulb pabltb mj trbtbokjltc trbtbokjlt c mj beubs rjskmubajs mj b`ujrmc `cl acs pbrâojtrcs cntjlkmcs `cl ja ikl mj bnbstj`jr ba :8% mj acs dbnktbltjs mj Ybamkvkb. 0. Ab pabltb `uopaj `cl ajy `dkajlb, jstblmc jl jl acs pbrâojtrcs `crrj`tcs mbmcs pcr ja ja mj`rjtc ;8/>882 mj acs mkstkltcs `cltboklbltjs. =. Pj mksjòb ul Abycut mj b`ujrmc `cl acs jqukpcs prcpujstcs pbrb mkstrknukracs mkstrknukr acs jl ja tjrrjlc mj ab pabltb mksjòbmb.
2;
^jijrjl`kbs BeubsMj`kob. Beubs Mj`kob. (>8>8). (>8>8). Cptkokzb`kðl jstb`kðl mjpurbmcrb mj beubs sjrvkmbs mj ab `kumbm mj Ybamkvkb. Ybamkvkb. Cntjlkmc mj dttps7//sjkb.sjb.ecn.`a/br`dkvcs/>8>8/89/24/BljxcS0Ybamkvkb. 2SXBPS22:S^jvS8.pmi Bonkjltj, M. m. (>88:). @rktjrkcs mj `bakmbm mj beubs c jiaujltjs trbtbmcs pbrb usc jl rkjec. rkjec. Zlkvjrskmbm mj @dkaj, Mjpbrtbojltc mj Klejlkjrïb @kvka. Pbltkbec mj @dkaj7 Mkvkskðl mj ^j`urscs Dïmrk`cs y Ojmkc Bonkjltj. Cntjlkmc mj dttp7//nknakctj`bmkektba.sbe.ecn.`a/mc`uojltcs/ojmkcSbonkjltj/`rktjrkcsS`bakmbmSsujacsSbeubsSberk`cab s/pmiSbeubs/rjsuojlSjgj`utkvc.pmi N@L. (>882). Mj`rjtc ;8. ;8. @dkaj7 Nknakctj`b mja @clerjsc Lb`kclba mj @dkaj. Cntjlkmc mj dttps7//www.n`l.`a/ajy`dkaj/lbvjebr3kmLcrob?24>905 @jlsc, @. L. (>8>8). Nknakctj`b mj @clerjsc Lb`kclba mj @dkaj. @dkaj. Cntjlkmc mj dttps7//www.n`l.`a/skkt/rjpcrtjs`coulbajs/`coulbsSv.dtoa3bllc?>8>8&km`co?2=282 Ijrlblmjz, P. (>82:). ]rbtbokjltc y mkspcsk`kðl mj beubs rjskmubajs mj pabltbs mj trbtbokjltc mj beub pctbnaj jl @dkaj. Pbltkbec @dkaj. mj @dkaj. Cntjlkmc mj dttp7//rjpcsktcrkc.u`dkaj.`a/nktstrjbo/dblmaj/>>:8/20002;/]rbtbokjltc-mj-mkspcsk`kcl-mjbeubs-rjskmubajs-jl-pabltbs-mj.pmi6sjqujl`j?2 O`Ibrablm, O., & Oclty, M. (>882). Xrcnajobs mja beub pctbnaj. pctbnaj. Pkstjob Zlkvjrsktbrkc ]jxbs B&O. ]jxbs7 Klstktutc mj ^j`urscs ^j`urscs mj Beub mj ]jxbs. Cntjlkmc Cntjlkmc mj dttps7//tjxbswbtjr.tbou.jmu/rjscur`js/ib`tsdjjts/a:=:2skrclblmobl.pmi Ojt`bai, Jmmy, & ]`dcnblceacus, E. (2;;8). Klejlkjrïb mj beubs rjskmubajs7 trbtbokjltc, vjrtkmc y rjutkakzb`kðl. rjutkakzb`kðl. O`Erbw-Dkaa. Crcz`c, B. (>88:). Nkcklekjljrïb mj beubs rjskmubajs. rjskmubajs. Ncectâ7 Bsc`kb`kcl @caconkblb mj Klejlkjrïb sblktbrkb y bonkjltba. Cntjlkmc mj dttps7//nccfs.ecceaj.`a/nccfs3da?js&ar?&km?t:w:JWi2YdO@&ck?ilm&pe?XX25&mq?beu bs+rjskmubajs+&cts?OyY`aINxPb&ske?KF8PmP5MzyZ]0GMfJqji`9aAMy8&rjmkrSjs`?y# v?cljpbej&q?beubs%>8rjskmubajs&i?ibasj Cscrkc, O. (>820). Jstumkc y blâasks tj`lk`c-j`clðok`c mj pabltb mj trbtbokjltcs mj beubs rjskmubajs. Zlkvjrskmbm rjskmubajs. Zlkvjrskmbm mja Nïc-Nïc, Mjpbrtbojltc Mjpbrtbojlt c mj Klejlïjrkb Oë`blk`b , @cl`jp`kðl. Cntjlkmc mj dttp7//rjpcnkn.unkcnkc.`a/gspuk/nktstrjbo/2>0=:954;/2=5/0/Cscrkc%>8Xjtjrsjl%>@%>8 Obr`cs.pmi Xk`bmc, P. (>829). Jvbaub`kðl iïsk`c-quïok`b, nkcaðek`b j dkmrcmklâok`b mja iul`kclbokjltc mj skstjobs mj trbtbokjltc prjibnrk`bmcs pbrb ja trbtbokjltc mj beubs rjskmubajs mcok`kakbrkbs. ]j`lcaðek`c mcok`kakbrkbs. ]j`lcaðek`c mj @cstb ^k`b, Klejlkjrïb bonkjltba. @brtbec7 ]J@. Cntjlkmc mj dttps7//dma.dblmaj.ljt/>>04/;>>9 ^cgbs, ^. (>88>). Pkstjobs mj ]rbtbokjltc mj Beubs ^jskmubajs. EJP]KÐL KL]JE^BA MJ ]^B]BOKJL]C MJ BEZBP ^JPKMZBAJP. ^JPKMZBAJP. Cntjlkmc mj dttps7//m2wqtxts2xzaj5.`acumirclt.ljt/:52>050=/EJP]KCLSKL]JE^BASMJAS]^B]BOK JL]CSB^-wktd-`cvjr-pbej-v>.pmi3Jxpkrjs?29>5=:02==&Pkelbturj?mtjueUi22bakJsUY:LegyTdsd`OfnruNTJs0`ng2NR:APG]0:I0YwNe:Bkc^4yLPXG0`~is 02`UJwo`:0EbCOeUPtX2i4b22XRcwRF9w-8R2p~=24o`l0L2 PPKP, E.Ecnkjrlc m. (>884). b `clc`jr lkvja mj `clsuoc mj beub pctbnaj jl ja pbïs. pbïs. @dkaj7 mj PKPP @dkaj.mb Cntjlkmc mj dttps7//www.skss.ecn.`a/:49/brtk`ajs-5990Srj`urscS:.pmi >8
Lcojl`abturb
]bnab 28 Lcojl`abturb
Ybrkbnaj
Pkoncaceïb
@bumba ]kjopc Ycauojl Xcnab`kðl rjb ]bsb mj prcmu``kðl mj acmcs @cjik`kjltj mj rjtcrlc @cl`jltrb`kðl mj nkcobsb ^blec mj mjsncrmbokjltc ]kjopc mj rjtjl`kðl dkmrâuak`b @cl`jltrb`kðl mj sustrbtc
Mkojlskcljs
Zlkmbmjs
- -: : tkjopc ∕
]bnab 22 sunïlmk`js y vbrkbltjs
Ybrkbnaj @cl`jltrb`kðl mj sustrbtc klk`kba Iaugc prcojmkc mj beub rjskmuba mcok`kakbrkb @clsuoc mj beub pjr `âpktb Yjac`kmbm mj bsjltbokjltc `rktk`b mj ab pbrtï`uab Xrciulmkmbm
Pkoncaceïb
ℌ
Mkojlskcljs
ℌ
Zlkmbm
ℌ ℌ
>2
Bpëlmk`js Bpëlmk`j B7 Ybacrjs mj rjijrjl`kbs ]bnab 2> Xbrâojtrcs mj mksjòc pbrb tblqujs mjsbrjlbmcrjs mj prjtrbtbokjltc
]bnab 20 @cl`jltrb`kcljs oâxkobs pjroktkmbs
@cltboklbltj Brsëlk`c B`jktj y erbsbs Bauoklkc Ncrc MNC: pD Pcakmcs suspjlmkmcs tctbajs Icsicrc Dkjrrc Lktrðejlc Lïquja Oblebljsc
Zlkmbm Pkoncaceïb M.P L¸ ;8/>882
> : ℌ
>8 >8
8,:5: 0: 9,8∞4,: 48 28 : :8 8,> 8,0
>>
]bnab 2= Ybacrjs jstâlmbr utkakzbmcs pbrb mjtjroklbr ja vcauojl mja jstblquj mj bkrjb`kðl
Xbrâojtrc
vbacr
8,8: 2 =088 ==8
>0
Bpëlmk`j N7 @âa`uacs N.2 @âa`uac mja `bumba beub pctbnaj y beub rjskmuba Mj b`ujrmc `cl acs mbtcs jstbnaj`kmcs, Ybamkvkb pcsjj ulb pcnab`kðl mj 255.888 dbnktbltjs, mjnkmc quj ab pabltb mksjòbmb scac bnbstj`jrâ ba :8% mj ab pcnab`kðl, js mj`kr, 44.:88 dbnktbltjs. @clskmjrblmc quj ja `clsuoc ojlsuba mj beub pctbnaj prcojmkc js mj 995.888 o 0, barjmjmcr mj 2>4 A/mïb y jl ëpc`b jstkvba js mj 2:5 A/mïb, sj cntkjlj quj.
? ð ð ∕ ∕ .2 ï 2888 ? 44.:88 ∕ 2>4 ∕ 8.4 ï 2888 ?;89>.= ï â ï ? ð ∕ 2888 â ∕ .> ? 44.:88 ∕ 2:5 ∕ 8.4 â ï 2888 â ï ?2222:.9
N.> @âa`uac mj acs jqukpcs N.>.2 Xrjtrbtbokjltc
Mksjòc mja tblquj mjsbrjlbmcr7
Mj b`ujrmc `cl acs vbacrjs rjijrjl`kbajs mj ab tbnab … , sj mksjòb ja jstblquj mjsbrjlbmcr `cl acs skeukjltjs `âa`uacs. ]kjopc mj rjtjl`kðl mj iaugc bsuokmc pbrb `ba`uabr ja vcauojl tctba, `clskmjrblmc ul `bumba oâxkoc mj cpjrb`kðl7 0.: oklutcs.
? ∕ â .0
>=
2222:. 2:.9 / ? 0.: ∕ 2==82 ï ∕ 222 ? >5.8.8>> @clskmjrblmc ul bl`dc mj 2,: o y ulb prciulmkmbm mj 2,: o, sj bsuoj ulb prcpcr`kðl Bl`dc7Batc Bl`dc7Ba tc mj 272, 272, pcr ac tbltc, sj acerb `ba`uabr `ba`uabr ab aclektum mja tblquj. tblquj.
? ℌ ∕ .= >5. 8 > ? 2.: ∕ 2.: ? 2> Pkeukjlmc, sj `ba`uabl acs pbrâojtrcs mj rjtjl`kðl dkmrâuak`b, ja `clsuoc mj bkrj y `bltkmbm mjsbrjlbmb. ]kjopc mj rjtjl`kðl dkmrâuak`b7
? .: ? 8.>5.28:8>/ ? >:>:5,5,0 ? =.0 ^jqujrkokjltc mj bkrj, sj bsuoj 8,0: o 0/o*okl.
? ? ∕ ∕ .9 ? ? 2> ∕ 8.0∕: ? =.> Ab `bltkmbm mj brjlkaab rjtkrbmb pcr ab cpjrb`kðl ulktbrkb, `clskmjrblmc abs supcsk`kcljs ojl`kclbmbs, y tbonkël ab mj 8.2: o0/280o08, bmjoâs, `clskmjrb ja `bumba jl ocmc mj prjvjl`kðl.
/28 ∕ â 8. 2 : ? .5 28
?8. ? 8.2: /2828∕ 2222:. 2222:.9 /ï
>:
? 2.95 ï N.>.> ]rbtbokjltc prkobrkc
Mksjòc mj sjmkojltbmcr prkobrkc prkobrkc
Mj b`ujrmc `cl acs mbtcs mj `bumba oâxkoc y prcojmkc, bmjoâs mj, ab `bltkmbm mj brjlkaab rjtkrbmb pcr ab jtbpb mj prjtrbtbokjltc, sj `ba`uabl acs `bumbajs b trbnbgbr jl jstb jtbpb mja trbtbokjltc.
½ ? ∞ .4 . 4 ½ ?;89>.= ï ∞ 2.95 ï ½ ?;898.50 ï ½â ? â ∞ .; . ; ∞ 2.9955 ï ½â ?2222:.9 ï ½â ?22220.;0 ï @cltklublmc, sj bsuojl abs ojmkmbs mja jstblquj, `clskmjrblmc 2> o mj mkâojtrc y ulb prciulmkmbm mj : o, sj acerb `ba`uabr ab tbsb mj mjsncrmbokjltc.
? ℌ ? ℌ ? ? .28 ? ;898.9 5∕0ï .00 ℌ ?48.2: ï ? 0.00 Pj `clskmjrb, pcr ac tbltc, ârjb mj acs jstblqujs mj 220 o> y ul vcauojl mj :9: o 0, bdcrb sj `ba`uab ja tkjopc mj rjtjl`kðl dkmrâuak`b.
.22 ? ½ ℌ ? :9: o0 ? 8.889> ï ? 2.=; ℌ ;898.50 ï
>9
N.>.0 ]rbtbokjltc sj`ulmbrkc Xbrb ja `âa`uac mja vcauojl mja bkrjbmcr sj usbrâ ab skeukjltj j`ub`kðl7
2 ? ∕∕( ∞ ) .2> ∕ Pj tcobrâl abs skeukjltjs `clskmjrb`kcljs7 Pj bsuokrâ bsuokrâ ul T, `cl`jltrb`kðl mj PP jspjrbmcs jl ja ja rjb`tcr, jstâlmbr mj vbacr
=088
Pj bsuoj ul [ jstâlmbr mj vbacr
bkrjbmcr Pj bsuoj ul
8,8:, quj `crrjspclmj ba rjlmkokjltc pcr mïb mja
?= , vbacr jstâlmbr pbrb acs bkrjbmcrjs mj rjskmucs mcok`kakbrkcs.
`crrjspclmj ba vbacr akoktj mj ab MNC: mjtjroklbmc pcr ja mj`rjtc suprjoc ;8 `crrjspclmj ba vbacr mj MNC: prjsjltj jl ab `crrkjltj mj jltrbmb mja bkrjbmcr.
Ja vbacr mja vcauojl mja jstblquj mja bkrjbmcr qujmb mjtjroklbmc pcr ab skeukjltj j`ub`kðl7
? ∕∕( ∞ ) .20 2 ∕ (248 ∞ =8) ∕ = ï _ ∕8,8: V ∕8,8: 22220. ; 0 0V ? =088 ?5>,=
>5
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