Libro Concentracion Minerales 1 - 22

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

AJYFT IB DNFTB IB NF FTK@AFYRUF?

DJADBAYUFDKJA IB MKABUFNBT M. Jswfnij Eustfmfatb Uÿf Faf Dbdknkf @fvkrkf Dfrtf`baf Jsdfr Ofkmb Ubstrbpj Efbaf

K.M.M., MTd, WcI K.V., MTd K.M.M. MTd., WcI

KATYKYRYJ IB MKABUFNBT DKMBS HFDRNYFI IB MKAFT BTDRBNF IB MFYBUKFNBT WUJ@UFMF DRUUKDRNFU KA@BAKBUÍF IB MKAFT [ MBYFNRU@KF

6

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

WUBTBAYFDKJA

Bn `rupj ib prjhbsjrbs ibn ærbf djajdkmkbatj batkbab Mbtfnur`kf ibn Wrj`rfmf Durrkdunfr Ka`bakbríf ibibn Mkafs y Mbtfnur`kf, bn `ustjBxtrfdtkvf ib prbsbatfr f ustbibs ua pbquböj tbxtj qub bs bn rbsuntfij ib nf fdumunfdkôa ib ajtfs ib dnfsb f trfvës ib njs föjs, ba njs qub cfa pfsfij dkbatjs ib aubstrjs qubrkijs fnumajs y njs dufnbs cfa tbakij nf pfdkbadkf ib sbr aubstrj iksdípunjs y qub ajs cfa ifij nf fnb`ríf ib vbrnjs `rfiufijs djmj prjhbskjafnbs ib nf mkabríf qub f su vbz cfa djatrkeukij fn ibsfrrjnnj ib Djnjmekf. Nfs ajtfs ib dnfsb aj sbræa aubvfs pfrf aubstrjs bxfnumajs, tfn vbz nbyëaijnfs rbdjrifræa mjmbatjs ikhídknbs ib su dfrrbrf uakvbrsktfrkf, kastfatbs nnbajs ib bspbrfazf ib fnb`ríf y ib ua sbatkmkbatj ib hjrmfdkôa ba ka`bakbríf qub ba su mjmbatj hub ua dfmkaj ijnjrjsj y ikhídkn, pbrj qub cf sbrvkij ib efsb pfrf qub „Yrfefoj y Ubdtktui” njs fdjmpföb iurfatb nf vkif qub sb kakdkj ba nf dnfustrjs ib nf Hfduntfi ib Mkafs. Bstb tbxtj aj bstæ fdfefij, dfif vbz fpfrbdba aubvfs tbdajnj`ífs, aubvfs katbrprbtfdkjabs, pbrj njs huaifmbatjs ib nf sbpfrfdkôa sônkij-sônkij sk`uba vk`batbs, pubs nfs nbybs ib nf mbdæakdf y nf tbrmjikaæmkdf qub sjstkbaba djmj `rfaibs pknfrbs nf djadbatrfdkôa ib mkabrfnbs pbrmfabdba djmj vfnkjsfs ojyfs ibn djajdkmkbatj cumfaj y sustbatfa nfs prkadkpfnbs ckpôtbsks y tbjrífs ib njs hbaômbajs ib sbpfrfdkôa qub sk`ub vk`batbs ba nf fdtufnkifi Bstb tbxtj iksbrtfræ sjerb bstjs huaifmbatjs y aj prbtbaib kr mæs fnnæ, dja nf bspbrfazf ib qub aubstrjs bxfnumajs qub duntkvba ba bstf níabf ib trfefoj sk`fa ibsfrrjnnfaij y barkqubdkbaij bn djajdkmkbatj ibn ærbf.

Bn qubfsbtrfvës prbsbatfrf fquí tkbab rfídbs baBxtrfdtkvf njs prjhbsjrbs cfa skij njstrfefoj pkjabrjs ibn tkbmpj ib nfsus Mbtfnur`kf ba nfqub Hfduntfi ib Mkafs, sja bnnjs njs ka`bakbrjs ib Mkafs y Mbtfnur`kf Nuks Fnebrtj Mbzf Tfudbij, Nuks Bmknkj Tæadcbz _fpftf, Ojsë Xkdbatb Ukadôa Wkaj y Ofkrj @ômbz (q.b.p.i.), njs dufnbs hubrja njs hjrofijrbs ibn KM DKMBS y duyj nb`fij rbdkekmjs y cumknibmbatb fimkakstrfmjs y nf pjabmjs fn sbrvkdkj ib nf mkabríf ba bn pfís.

M. J. Eustfmfatb, Eustfmfatb, F. D. @ @fvkrkf, fvkrkf, J. O. Ubstrbpj, Mbibnnía, Hberbrj ib 5770

5

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

KAIKDB Wæ`kaf

6 6.6. 6.5. 6.4.

@BABUFNKIFIBT IB NF DJADBAYUFDKÔA IB MKABUFNBT Ibhkakdkôa ib tbajr Jeobtkvj huifmbatfn ib nf djadbatrfdkôa Kmpjrtfadkf y uekdfdkôa ib nf djadbatrfdkôa ib mkabrfnbs ba bn djatbxtj mkabrj — mbtfnÿr`kdj

5. 5.6. 5.5 5.4 5.9. 5.2.

KAIKDBT MBYFNRU@KDJT 0 Efnfadbs ib mfsf ba ua djadbatrfijr ba bstfij bstfdkjafrkj 0 Dnfskhkdfdkôa ib njs Íaikdbs Mbtfnÿr`kdjs 3 Ubnfdkja batrb batrb nf Ubdupbrfdkôa ( U  U) y nf Ufzôa ib Barkqubdkmkbatj ( U.B   66 Kaikdbs mbtfnur`kdjs y trfzijs ib pnfatfs 65 Jtrfs bxprbskjabs ib njs íaikdbs mbtfnÿr`kdjs usfijs ba jpbrfdkôa ib 64 pnfatfs djadbatrfijrfs

4

NFT WFUYKDRNFT MKSYFT [ NF DJADBAYUFDKJA IB MKABUFNBT

9. 9.6. 9.5.

KAYUJIRDDKÔA FN IKTBÖJ [ YUF_FIJ DJADBAYUFDKÔA IB MKABUFNBT Jeobtkvj ib dfif btfpf ib djadbatrfdkôa Nf rbdkrdunfdkôa ib djrrkbatbs

2. 2.6.

DJADBAYUFDWJA @UFXKYFDKJAFN

2.5.

IB

WNFAYFT

6 4 9 2

62 IB

rbqubrkmkbatjs pfrf uaf bhkdkbatb djadbatrfdkôa `rfvktfdkjafn   Ykpjs huaifmbatfnbs ib djadbatrfdkôa `rfvktfdkjafn

60 60 60 54 54 52

2.4 2.9 2.2

Tbpfrfdkôa ba mbikjs ibasjs Tbpfrfdkôa ba nbdcjs bstrftkhkdfijs-Ok`s Tpfrfdkôa ba pbnídunfs (hknms)

58 46 95

8.

HNJYFDKÔA BTWRMFAYB

93

8.6 8.5. 8.4

Ybrmjikaæmk Ybrmjikaæmkdf df ib nf hnjtfdkôa y ficbskôa pfrtídunf eureuof Ubfdtkvjs ib hnjtfdkôa Fn`uajs bobmpnjs ib nf tbdajnj`íf ib nf hnjtfdkôa h njtfdkôa bspumfatb

27 22 80

0.

EKENKJ@UFHKF

06

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

6.

@BABUFNKIFIBT IB NF DJADBAYUFDKÔA IB MKABUFNBT

Nf djadbatrfdkôa mkabrfnbsibbsuaf nf jpbrfdkôa ba nf ibtbrmkafij, dufn sb bnbvfmbikfatb b bnn tbajr bnj djadbatrfdkôa (ba ib pjrdbatfob) mbaf j mkabrfn usj ib bqukpjs ib sbpfrfdkôa sônkij-sônkij prjiudkëaijsb fsk nf sb`rb`fdkôa ib ijs j mæs bspbdkbs mkabrfnô`kdfs y `babrfr uaf djrrkbatb barkqubdkif ba ua mkabrfn ib katbrës. Wfrf bnnj, sb pubiba kmpnbmbatfr ijs mëtjijs ib sbpfrfdkôa, fsí?

f.

Mëtjijs qub bmpnbfa ikhbrbatbs prjpkbifibs hískdfs j vjnumëtrkdfs ib nfs suestfadkfs mkabrfnbs.

Bn `rupj ib tbdajnj`ífs qub fsjdkf f bstjs mëtjijs sb dfrfdtbrkzfa pjr sbr hubrtbmbatb ibpbaikbatbs ibn tfmföj ib pfrtídunf y nfs prjpkbifibs ikhbrbadkfnbs qub `babrfa nf sbpfrfdkôa pubiba sbr? Ikhbrbadkf ib vbnjdkifi ib sbikmbatfdkôa, f trfvës ib nf ikhbrbadkf ib •  ibaskifi ib njs sônkijs (Djadbatrfdkôa @rfvkmëtrkdf) Ikhbrbadkfs ib mjvkmkbatj ba ua dfmpj mf`aëtkdj ib katbaskifi vfrkfenb, •  f trfvës ib nf ikhbrbadkf ib nf susdbptkeknkifi mf`aëtkdf ib njs mkabrfnbs (Djadbatrfdkôa Mf`aëtkdf) Vubifrsb ficbrkij j sfntfr ib uaf pnfdf mbtænkdf, pjr ikhbrbadkfs ba nf •  djaiudtkvkifi bnëdtrkdf dufaij nfs pfrtídunfs bstæa ibatrj ib ua dfmpj bnëdtrkdj (Djadbatrfdkôa Bnëdtrkdf).

e.

Mëtjijs qub usfa prjpkbifibs hískdj-químkdfs ib supbrhkdkb, tfnbs djmj?

  Nf fisjrdkôa j aj ib f`uf ba nf supbrhkdkb ibn sônkij, pjr nj tfatj njs qub •fisjrefa f`uf sb cumbdtfræa (ckirjhínkdjs) y jtrjs qub aj sb cumbdtfa (ckirjhôekdjs). Njs qub aj fisjreba f`uf (pjr bobmpnj fzuhrb, tfndj, `rfhktj y mjnkeibaktf), sbræa rbdcfzfijs pjr bn mbikj fdujsj y sk sb nbs djnjdf dbrdf ib uaf eureuof ib fkrb sfnirífa bmebekijs ba ëstf y hnjtfrífa. Nj fatbrkjr kmpnkdf fn`uafs jtrfs djaikdkjabs qub sb ibtfnnfrfa mæs fibnfatb. Fisjrdkôa sbnbdtkvf ib ua tbasjfdtkvj ib tfn mfabrf qub sb prjiuzdf uaf •  f`njmbrfdkôa sbnbdtkvf ua mkabrfn j vfrkjs mkabrfnbs y mfatbabr ikspbrsjs f njs njs ibmæs mkabrfnbs fdjmpföfatbs, nj dufn bs muy ÿtkn dufaij sb prjdbsfa mkabrfnbs ib tfmföjs ib `rfaj untrfhkajs (batrb 67.7 y 6.7 ²m) y djnjkifnbs (> 6.7 ²m). Ba dfif uaj ib njs dfsjs, sk bn tbasjfdtkvj tbasjfdtkvj bs ua pjnímbrj sb djajdb bn

6

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

prjdbsj djmj hnjdunfdkôa sbnbdtkvf y sk bs ua kôa hjrmfaij ua djmpnboj kajr`æakdj sb djajdb djmj djf`unfdkôa sbnbdtkvf. Nf Yfenf 6 mubstrf njs ikhbrbatbs mëtjijs ib djadbatrfdkôa qub subnba utknkzfrsb kaiustrkfnmbatb y nfs prjpkbifibs ikhbrbadkfn qub utknkzf dfif uaj ib bnnjs< nj mksmj qub njs ajmerbs ib njs fpfrftjs mæs bmpnbfijs. Wfrf qub sb prjiuzdf uaf fibdufif sbpfrfdkôa, ibeb bxkstkr batrb njs mkabrfnbs f sbpfrfr fn mbajs ua prjpkbifi qub tba`f vfnjrbs rbnftkvfmbatb ikhbrbatbs, tfnbs djmj `rfvbifi bspbdíhkdf, susdbptkeknkifi mf`aëtkdf, djaiudtkvkifi bnëdtrkdf j uaf rbpubstf hkskdjquímkdf supbrhkdkfn ekba ikhbrbatb. Bstf prjpkbifi sb ibajmkafræ WUJWKBIFI IKHBUBADKFN. Bn jeobtkvj `babrfn sbræ batjadbs< barkqubdbr bn mkabrfn bnkmkafaij `fa`f y mkakmkzfaij nfs përikifs ib mkabrfn ÿtkn ba dufatj sbf pjskenb.

Yfenf 6. 

Ikhbrbatbs Mëtjijs ib Djadbatrfdkôa ib Mkabrfnbs y Fn`uajs Bqukpjs Bmpnbfijs

Ajmerb ibn Mëtjij Djadbatrfdkôa @rfvktfdkjafn Djadbatrfdkôa Mf`aëtkdf Djadbatrfdkôa bnëdtrkdf

Wrjpkbifibs qub bmpnbf pfrf sbpfrfr

Tbikmbatfijr, Ckirjdkdnôa, Ok`, Ikhbrbadkf ib vbnjdkifi ib Dfafnôa Dfafnbtfs, Mbsf Xkerftjrkf, sbikmbatfdkôa ib njs mkabrfnbs Bspkrfn, Djajs ib Tbpfrfdkôa Dbatríhu`fs, batrb jtrjs Tusdbptkeknkifi mf`aëtkdf Tbpfrfijr mf`aëtkdj ib tfmejr, (ftrfddkôa j aj hrbatb f uaf rjiknnjs mf`aëtkdjs, sbpfrfijr Mf`abtj u kmæa) mf`aëtkdj tkpj „dfrrusbn”, btd. Tbpfrfijr bnëdtrkdj ib fntf katbaskifi Djaiudtkvkifi bnëdtrkdf

Ckirjhjekdkifi y/j ckirjhknkifi ibn mkabrfn (mjofmkbatj j aj) aj) Fisjrdkôa bspbdíhkdf ib ua Hnjdunfdkôa sbnbdtkvf pjnímbrj y hjrmfdkôa ib hnôdunj Fisjrdkôa bspbdíhkdf ib kjabs Djf`unfdkôa kajr`æakdjs y hjrmfdkôa ib uaf sbnbdtkvf djæ`unj

Hnjtfdkôa bspumfatb

Wrkadkpfnbs fpfrftjs

Dbnifs ib hnjtfdkôa y djnumafs ib hnjtfdkôa Tbikmbatfijr Tbikmbatfijr

Nf Hk`urf 6 mubstrf ijs prjdbsjs ib djadbatrfdkôa ba mfqukafs djmuabs dja njs ikhbrbatbs prjiudtjs qub sb jetkbaba< djadbatrfijs, mbikjs y djnfs. Fn`uafs mæqukafs djmj nf mbsf vkerftjrkf y nf bspkrfn `babrfa trbs prjiudtjs< ska bmefr`j, bstf aj bs uaf sktufdkôa sktufdkôa típkdf, njs dufnbs sbrífa sbrífa djadbatrfijs, mbikjs y djnfs. Mæs fibnfatb ibtfnnfrbmjs bstb fspbdtj, ib efstfatb kmpjrtfadkf ba nf jpbrfdkôa uaktfrkf ib djadbatrfdkôa.

5

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

6.6.

IBHKAKDKÔA IBN YBAJU

Bn djadbptj ib tbajr sb usf prkadkpfnmbatb ba nf mkabríf mbtænkdf, pbrj sb pubib cfdbr uaf bxtrfpjnfdkôa pfrf su usj ba mkabríf ib mkabrfnbs kaiustrkfnbs, nj dufn sb fsjdkf fn pjrdbatfob (ba ka`nës  ib mkabrfn rbspbdtjqub fnfsb tjif f mfsf mkabrfn bxtrfíif bs kmpjrtfatb ba„`rfib”) bn ibsfrrjnnj ib njsÿtkn jeobtkvjs prbtbaiba fndfazfr ba nf djadbatrfdkôa ib mkabrfnbs. Wjibmjs ibhkakr bn tbajr ib ua mkabrfn djmj nf rbnfdkôa qub bxkstb batrb nf dfatkifi mæskdf ib mkabrfn ib katbrës j ÿtkn rbspbdtj f nf dfatkifi mæskdf j vjnumëtrkdf ba nf mbaf. Wjr nj tfatj, bn tbajr sb pubib bxprbsfr ba `rfmjs ib mkabrfn ÿtkn pjr tjabnfif ib mftbrkfn tjtfn, ba pjrdbatfob, ba mknk`rfmjs (m`) pjr mbtrj dÿekdj ib mftbrkfn tjtfn, btd.

Hk`urf 6.  Btfpfs ib Djadbatrfdkôa dja sus Ikhbrbatbs Wrjiudtjs. f) Mbsf Xkerftjrkf. e) Ok`. Ijaib F, D, M, Y? sja njs Hnuoj Mæskdjs (ba tja/cr, l`/sb` , btd) ib nfs djrrkbatbs ib fnkmbatfdkôa, djadbatrfijs, mbikjs y djnfs rbspbdtkvfmbatb, t f , t d , t m , t t ? sja njs tbajrbs ba nfs djrrkbatbs ib fnkmbatfdkôa, mkbatrfs qub mbikjs djadbatrfijs, y djnfs rbspbdtkvfmbatb

Tb ibeb tbabr ba dubatf qub ψ f , ψ D  D   ψ t  t  sja nfs hrfddkjabs ba pbsj ib sônkijs ba nfs punpfs ib fnkmbatfdkôa, djadbatrfijs, mbikjs y djnfs rbspbdtkvfmbatb, nj dufn bs muy kmpjrtfatb dufaij sb bstfenbdba njs efnfadbs ib f`ufs y mkabrfn. Djmj bobmpnj, ba mkabríf ib bxpnjtfdkôa ib vbtfs ib jrj njs tbajrbs ib bxpnjtfdkôa pubiba sbr 65 ` ib jrj pjr tjabnfif ib mkabrfn tjtfn bxtrfíij (65 `pt), mkbatrfs ba nf mkabríf ib fnuvkôa pubiba sbr ib 627 m` ib jrj pjr m4 ib mkabrfn bxtrfíij. Wfrf nf mkabríf ibn djerb njs tbajrbs ibebr sbr mfyjrbs fn 6.2% pfrf ibpôsktjs mfskvjs< bstj qukbrb ibdkr, qub cfy 6.2 L` ib Du ba dfif 677 L` ib mkabrfn bxtrfíij ib nf mkaf, ba jtrjs. jtr js.

4

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

Ib fdubrij f nf ibhkakdkôa fatbrkjr, mftbmætkdfmbatb tbabmjs qub? Ybajr t  =

6.5.

Dfatkifi ib mkabrfn

ÿtkn

Dfatkifi tjtfn ib mkabrfnbs bxtrfíijs

 

(6)

JEOBYKXJ HRAIFMBAYFN IB NF DJADBAYUFDKÔA.

Fcjrf sb pjiræ batbaibr bn jeobtkvj huaifmbatfn ib nf djadbatrfdkôa, bn dufn bs bnbvfr bn tbajr ib uaf bspbdkb mkabrfnô`kdf ba uaf djrrkbatb qub sb ibajmkaf DJADBAYUFIJ D . Bstb tbajr sb ibajtfræ djmj t d. (vbr hk`urf 5) Ib fdubrij f nj fatbrkjr, ba nf djrrkbatb ibajmkafif DJNFT sb ikmkaukræ suestfadkfnmbatb bn tbajr ib nf bspbdkb mkabrfn ib katbrës ( t t t ), j nj qub bs bvkibatb, sb bnbvfræ bn tbajr ib nfs bspbdkbs mkabrfnbs qub fdjmpföfa bn mkabrfn ib katbrës.

Fnkmbatj (F)< tbajr t f

WUJDBTJ IB DJADBAYUFDKÔA

Djnfs (Y)< tbajr t t 

Djadbatrfij (D) tbajr t d Hk`urf 5. Bsqubmf `babrfn ib sbpfrfdkôa ba ua djadbatrfijr ibtfnnfaij bn nf djrrkbatb ib batrfif (Fnkmbatj), y nfs djrrkbatbs ib sfnkifs (Djadbatrfij y Djnfs) Ba bn dfsj kibfn, bn tbajr ib nf bspbdkb mkabrfn ib katbrës ba nfs djnfs (t t t)  ibebræ sbr aunj j dbrdfaj f dbrj ( t t t ↕ 7 ). Fcjrf ekba, djmj bs muy ikhídkn fndfazfr ba njs prjdbsjs sktufdkjabs kibfnbs, sb pjsbb uaf mbtf ba nfs pnfatfs ib djadbatrfdkôa, nf dufn bs fndfazfr ua vfnjr ib t t t   suhkdkbatbmbatb míakmj, ib fdubrij f nfs nkmktfdkjabs tbdajnô`kdfs y hískdfs ib nf sbpfrfdkôa. Ib fdubrij f nj fatbrkjr t D  1 t f

1 t t 

 

 

dja

t t  ↕ 7  

(5)

9

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

Ibeb ajtfrsb qub nf ibsk`ufnifi ba nf bdufdkôa 5, bs bstrkdtf y aj pbrmktb nf k`ufnifi, pubs ba bn bn dfsj ib qub fn`uaf ib nfs ibs ibsk`ufnifibs k`ufnifibs sb trfashjrmb ba uaf k`ufnifi, bn sbpfrfijr sb bstæ djmpjrtfaij mbtfnÿr`kdfmbatb djmj ua pfrtkijr ib mubstrf skmpnbmbatb.

6.4.

KMWJUYFADKF [ REKDFDKÔA IB NF DJADBAYUFDKÔA MKABUFNBT BA BN DJAYBSYJ MKABUJ — MBYFNßU@KDJ

IB

Nf djadbatrfdkôa ib mkabrfnbs bs uaf btfpf katbrmbikf ba bn djatbxtj ib nf mbtfnur`kf bxtrfdtkvf y fn`uafs vbdbs btfpf hkafn ib fn`uafs pnfatfs, prkadkpfnmbatb ba bn dfsj ib ib mkabrfnbs kaiustrkfnbs. Tb pubib vbr ba nf Hk`urf 4, qub nf btfpf ib djadbatrfdkôa rbdkeb ua mftbrkfn qub cfyf fndfazfij ua euba `rfij ib nkebrfdkôa, bnbvf su tbajr y nj pfsfrf f btfpfs sk`ukbatbs ekba sbf, ib prjdbsjs pkrjmbtfnÿr`kdjs j ckirjmbtfnÿr`kdjs, djmj bs bn dfsj ibn enfaqubj mbikfatb bn usj ib sjnudkjabs fdujsfs ib fn`uajs mkabrfnbs kaiustrkfnbs. Tb pubib pnfatbfr qub f kmpjrtfadkf ib nf djadbatrfdkôa ib njs mkabrfnbs rfikdf ba vfrkjs fspbdtjs, f sfebr?   Bnkmkaf ibn dkrduktj ib pnfatf, mkabrfnbs qub aj pjsbba rkqubzf fn`uaf y qub `babrfa djstjs ib mfaboj y trftfmkbatj, djmj nfs `fa`fs j mkabrfnbs fdjmpföfatbs ib rbdcfzj. 

  Bnkmkaf ibn dkrduktj ib pnfatf, mkabrfnbs duyf prbsbadkf pubib prbsbatfr djasbdubadkfs ab`ftkvfs ba bn prjdbsj ib bxtrfddkôa mbtfnÿr`kdf sk`ukbatb djmj pkrktfs, frbafs ib dufrzj ba fn`uajs dfsjs y mftbrkf jr`æakdf, btd.



  Ba fn`uafs jdfskjabs bn prjiudtj jetbakij ib nf djadbatrfdkôa yf bs ua mftbrkfn dja vfnjr kaiustrkfn y djmbrdkfn, djmj bs bn dfsj ibn nfvfij ib dfrejabs, duyj djadbatrfij bs prjiudtj hkafn ib nf pnfatf, dfreôa ska bstërkn j frbafs sknídbfs pfrf huaikdkôa, djadbatrfijs ib jrj btd.

Ibeba rbnfdkjafrsb bstjs fspbdtjs fn jeobtkvj huaifmbatfn ib nf djadbatrfdkôa (vbr bdufdkôa 5,) y f njs tbajrbs ib mkabrfnbs bxtrfíijs ib nfs mkafs, nfs dufnbs `babrfnmbatb sja muy efojs j ska vfnjr djmbrdkfn. Djmj sb pubib ibiudkr< nf djadbatrfdkôa ib mkabrfnbs ba fn`uafs jdfskjabs pubib nnb`fr f sbr btfpf hkafn pjr bobmpnj ba nf prbpfrfdkôa y nfvfij ib dfrejabs, ba bn prjdbsfmkbatj ib mkabrfnbs kaiustrkfnbs djmj tfndj, hnujrktf, rjdf hjshôrkdf, frbaf sknídbf pfrf huaikdkôa, batrb jtrjs. Wjr jtrj nfij, nf btfpf ib djadbatrfdkôa sbríf, ba fn`uafs jdfskjabs, nf prkmbrf btfpf ibatrj ibn djatbxtj mkabrj-mbtfnÿr`kdj, qub ifríf vfnjr f`rb`fij f njs mkabrfnbs bxtrfíijs.

2

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

Nf dfpfdkifi ib djadbatrfdkôa y pjr baib ib bnkmkafr djnfs muy pjerbs ba njs prjdbsjs ib djadbatrfdkôa, sb bvfnÿf utknkzfaij ikhbrbatbs íaikdbs qub ifa kibf ib nf bhkdfdkf ib nf sbpfrfdkôa y ib nf dfnkifi ib njs prjiudtjs jetbakijs.

CJMJ@BAK_FDKÔA MKAF

HUF@MBAYFDKÔA Yrkturfdkôa & mjnkbaif DNFTKHKDFDKÔA

DJADBAYUFDKÔA Enfaqubj

Hk`urf 4. 

 D       k r            D        d      u      f     r      fn              `     a      f      b t          

Djnfs f ikspjskdkôa hkafn

Yrftfmkbatjs tërmkdjs

Bsqubmf @njefn ib uaf Wnfatf Djadbatrfijrf ib Mkabrfnbs

8

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

5.

KAIKDBT MBYFNßU@KDJT

Njs íaikdbs mbtfnÿr`kdjs sja aÿmbrjs fikmbaskjafnbs qub prbdksfa nf dfnkifi ib nf sbpfrfdkôa bhbdtufif ba uaf j vfrkfs btfpfs ib djadbatrfdkôa, y fibmæs prjpjrdkjafa pfrf bn bsdfnfmkbatj ba bn ikmbaskjafmkbatj ib bqukpjs y/j pnfatfs ibkahjrmfdkôa djadbatrfdkôa. Bs abdbsfrkj qub nf ibtbrmkafdkôa ib njs íaikdbs bstb fpjyfif pjr ua efnfadb ib mfsf ba bn prjdbsj ib sbpfrfdkôa, ibekij f qub sk bnnj aj sb rbfnkzf prbvkfmbatb, bn dændunj ib njs íaikdbs pubib `babrfr aÿmbrjs fesurijs j kadjcbrbatbs y qub ibsjrkbatba nfs ibdkskjabs y bn faænksks ib njs dkrduktjs ib djadbatrfdkôa. Tb fsumb ba tjijs njs dfsjs qub nf sbpfrfdkôa y njs mubstrbjs sb rbfnkzfa ba bstfij bstfdkjafrkj, bstj bs dufaij nf vfrkfdkôa ib nfs prjpkbifibs ibn skstbmf sja kavfrkfatbs dja bn tkbmpj. Aôtbsb qub sk aj sb badubatrf bn skstbmf ba bstfij bstfdkjafrkj, skaj ba bstfij trfasdkbaib, nj qub ka`rbsf fn bqukpj y/j prjdbsj aj bs k`ufn bxfdtfmbatb f nj qub sfnb, ibekij ib f uaf fdumunfdkôa ib mfsfqub ibatrj ib njs bqukpjs nj kavfrkfatbs tfatj nfs djaikdkjabs jpbrfdkôa aj `frfatkzfa ua mubstrbj `babrby pjr iftjs ba bn tkbmpj.

5.6.

Efnfadbs ib mfsf ba ua djadbatrfijr ba bstfij bstfdkjafrkj

Nf Hk`urf 9, mubstrf ua djadbatrfijr dja ijs prjiudtjs, djadbatrfijs y djnfs. Njs hnuojs mæskdjs, sjerb uaf efsb sbdf ib dfif uaf ib nfs djrrkbatbs sb rbprbsbatfa dja nbtrfs mfyÿsdunfs, mkbatrfs njs tbajrbs dja nfs nbtrfs mkaÿsdunfs. Tk sb rbfnkzf ua efnfadb mfdrjsdôpkdj ib mfsf sb pubib tbabr qub?

 Hnuoj   mæskdj   ib   Hnuoj   mæskdj   ib   mkabrfn   qub   batrf  =  mkabrfn   qub   sfnb   

(4f)

 F =  D + Y  

(4e)

Wjr nj tfatj? Cfdkbaij ua efnfadb mkdrjsdôpkdj, sb tkbab qub?

Mkabrfn ib katbrës Mkabrfn  ib  katbrës     =  qub batrf qub   sfnb     Ubsdrkekbaij ba tërmkajs ib nfs vfrkfenbs usfifs sb tkbab qub?

0

(9f)

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

 F ⋂ t f

= D  ⋂ t  D  + Y ⋂ t t   

(9e)

Ibeb ajtfrsb qub bn efnfadb mkdrjsdôpkdj ib nf bdufdkôa 9e bstæ rbhbrkij ba tërmkajs ibn mkabrfn ib katbrës y pjr nj tfatj, bn sb`uaij tërmkaj ib nf ibrbdcf ib bstf bdufdkôa sb fsjdkf fjnfnfs përikifs baib bn djadbatrfdkôa prjdbsj, bstj pjr bs, nfs fn mkabrfn qub fefaijaf bn prjdbsj mæqukaf djnfs. ib katbrës

Fnkmbatj , F tbajr t f

DJADBAYUFIJU

DJADBAYUFIJ , D  tbajr t D 

 , Y  DJNFT tbajr t t 

Hk`urf 9.

5.5.

Bsqubmf ib ua Djadbatrfijr dja Ijs Wrjiudtjs.

Dnfskhkdfdkôa ib njs Íaikdbs Mbtfnÿr`kdjs

Njs íaikdbs mbtfnÿr`kdjs njs pjibmjs ikvkikr ba ijs tkpjs< Íaikdbs qub rbnfdkjafa dfnkifi ib nf djadbatrfdkôa b íaikdbs qub rbnfdkjafa dfpfdkifi ibn dkrduktj ib djadbatrfdkôa, prkadkpfnmbatb pfrf usjs ib bsdfnfmkbatj.

5.5.6. Íaikdbs qub Ubnfdkjafa Dfnkifi.  Bstjs sja njs qub prjpjrdkjafa kahjrmfdkôa fdbrdf ib nf dfnkifi ib njs prjiudtjs jetbakijs, ekba sbf ba nf btfpf ib djadbatrfdkôa j `njefnmbatb ba nf pnfatf.

Ubdupbrfdkôa. (U). Tb ibhkab nf rbdupbrfdkôa djmj nf rbnfdkôa qub bxkstb •  ba uaf jpbrfdkôa ib djadbatrfdkôa batrb bn pbsj ibn mftbrkfn ÿtkn j ib katbrës qub cfy ba bn djadbatrfij dja rbspbdtj f nf dfatkifi ib bsb mksmj mkabrfn qub cfy ba nf fnkmbatfdkôa, j qub ka`rbsô f nf jpbrfdkôa.  U =

Wbsj ib mkabrfn ib katbrës ba djadbatrfi j   Wbsj ib mkabrfn ib katbrës ba fnkmbatj

(2)

3

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

Ib fdubrij fn efnfadb mkdrjsdôpkdj ib nf bdufdkôa 9, sb pubib jetbabr qub?

Wbsj ib mkabrfn Ybajr  ib     ib katbrës  ba  =    Wbsj ib   ∐    (8)   Djadbatrfi j  Djadbatrfi j   = D  ⋂ ⋂ t D      Djadbatrfi j    Ib nf mksmf mfabrf sb pubib dfndunfr bn pbsj ib mkabrfn ÿtkn ba nf djrrkbatb ib fnkmbatj, jetbakëaijsb qub? Wbsj ib mkabrfn    ib katbrës ba  =  F ⋂ t    f      Fnkmb atj 

(0)

Ubbmpnfzfaij nfs bdufdkjabs 8 y 0 ba 2, sb jetkbab qub?  U =

D ⋂ t D   F ⋂ t f

 

(3)

Nj fatbrkjr kaikdf qub uaf rbdupbrfdkôa, pjr bobmpnj, ib 7.37 pfrf ua prjdbsj ibtbrmkafij, su`kbrb qub bn 37% ibn mkabrfn ib katbrës sb rbdupbrf ba nf djrrkbatb ib djadbatrfij y bn rbstfatb 57% sfnb ibn bqukpj j dkrduktj pjr nf djrrkbatb ib djnfs.

•  Ufzôa ib barkqubdkmkbatj (U B). Tb ibhkab bstb íaikdb djmj nf rbnfdkôa qub bxkstb batrb bn tbajr (j pjrdbatfob) ib mkabrfn ÿtkn ba bn djadbatrfij rbspbdtj fn tbajr (j pjrdbatfob) ibn mksmj mkabrfn ba nf fnkmbatfdkôa, batjadbs?  U B  

=

t D  t f

 

(;)

Tk sb djaskibrf nf ibsk`ufnifi pnfatbfif ba nf bdufdkôa 5, bn vfnjr ib nf rfzôa ib djadbatrfdkôa  U B   ba uaf uaf jpbrfdkôa ib djadbatrfdk djadbatrfdkôa, ôa, i ibebr bebr sbr skbmprb mfyjr qub nf uakifi. Ba bn dfsj ib qub  U B   sb k`ufnb f nf uakifi, aj sb prjiudb djadbatrfdkôa ifij qub bn t d sbríf k`ufn fn t f b kríf djatrf bn jeobtkvj ib bstf jpbrfdkôa uaktfrkf. Wjr jtrj nfij, mkbatrfs mæs nbofaj bstë ib nf uakifi (y qub sbf mfyjr qub bnnf) mbojr sbræ nf djadbatrfdkôa< nj qub qukbrb ibdkr qub sb bstæ barkqubdkbaij fÿa mæs bn djadbatrfij rbspbdtj fn tbajr ib fnkmbatj.  fnkmbatj. 

;

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

Íaikdb ib Tbnbdtkvkifi K.T.  Bstb íaikdb mbtfnÿr`kdj djmpfrf nf dfnkifi ib •  sbpfrfdkôa batrb ijs bspbdkbs (F) y (E) qub sb ibsbfa sbpfrfr ba bn prjdbsj ib djadbatrfdkôa. Tb ibhkab mftbmætkdfmbatb djmj nf sk`ukbatb rbnfdkôa.  K .T . =

t f ( F) * t t  ( E )

 

(67)

t f ( E ) *t t  ( F)

Ijaib? t f(F)  y t f(E)  sja njs tbajrbs ib njs djmpjabatbs (F) y (E) ba nf fnkmbatfdkôa ib nf jpbrfdkôa. Njs tbajrbs t t t  (F) y t t t  (E) sja ib njs djmpjabatbs (F) y (E) ba nfs djnfs rbspbdtkvfmbatb. 5.5.5.

Íaikdbs qub Ubnfdkjafa Dfpfdkifi.

Bstjs íaikdbs dja nf kahjrmfdkôa abdbsfrkf pfrf bsdfnfmkbatj, ikmbaskjafmkbatj y sbnbddkôa ib bqukpjs ib djadbatrfdkôa.

•  Ufzôa ib djadbatrfdkôa (UD). Tb ibhkab djmj nf rfzôa batrb bn hnuoj mæskdj ib sônkijs ba nf fnkmbatfdkôa  F  dja rbspbdtj fn hnuoj ib sônkijs ba bn djadbatrfij D   (vbr hk`urf 9).  UD   = =

 F D 

 

(66)

Aôtbsb qub bstb íaikdb aj if kahjrmfdkôa ib dfnkifi, skaj ib dfpfdkifi, bstj bs, ib njs hnuojs qub batrfrja y sfnkbrja ibn sbpfrfijr y pbrmktb dfndunfr pjr bobmpnj duæatfs tjabnfifs sb ibeba fnkmbatfr pfrf prjiudkr uaf tjabnfif ib djadbatrfij.

•  Ubaikmkbatj ib Djadbatrfdkôa (X ). Tb ibhkab djmj nf rbnfdkôa batrb hnuoj mæskdj ba bn djadbatrfij rbspbdtj fn hnuoj mæskdj ib sônkijs ba nf fnkmbatfdkôa (vbr hk`urf 9), j sbf qub? • 

X  =

D   F

=

6  UD 

 

(65)

Aôtbsb qub bs bn kavbrsj ib nf rfzôa ib djadbatrfdkôa y prjpjrdkjaf k`ufn kahjrmfdkôa.

•  Bhkdkbadkf ib nf Tbpfrfdkôa (B). (B). Bs ua íaikdb qub djmekaf nf kahjrmfdk kahjrmfdkôa ôa jetbakif ba njs fatbrkjrbs aumbrfnbs, bn dufn sb ibhkab djmj?  B  =

 U

∕ X 

6 ∕ X  KIBFN

 

(64)

67

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

Ijaib X  KIBFN bs bn rbaikmkbatj kibfn, bn dufn sb ibtfnnfræ f djatkaufdkôa.

5.4.

Ubnfdkja batrb nf Ubdupbrfdkôa

( U  U) y nf Ufzôa ib

Barkqubdkmkbatj ( U.B.)  Ajrmfnmbatb ba uaf jpbrfdkôa ib djadbatrfdkôa njs íaikdbs ib Ubdupbrfdkôa  U y Ufzôa ib barkqubdkmkbatj  U.B . sja djmpnbtfmbatb fatf`ôakdjs. Ba nf hk`urf 2 6.7

7.3    )    %    (    U7.8   a    ô    k   d   f   r   b 7.9   p   u   d    U   b

7.5

7.7 7.3

6.7

6.5

6.9

6.8

6.3

5.7

5.5

5.9

Ufzôa ib Barkqubdkmkbatj U.B. (6/6)

5.8

 

Hk`urf 2. Ubnfdkôa 2. Ubnfdkôa batrb nf Ubdupbrfdkôa y nf Ufzôa ib Barkqubdkmkbatj ba uaf jpbrfdkôa ib djadbatrfdkôa ba uaf sjnf btfpf Tb`ÿa nf hk`urf 2, sb pubib vbr qub sk nf jpbrfdkôa ib djadbatrfdkôa jdurrb ba uaf ÿakdf btfpf, aj bs rbdjmbaifenb qub sb bxkof vfnjrbs fntjs ib fmejs íaikdbs mbtfnÿr`kdjs. Nj fatbrkjr kmpnkdf qub sônj bs pjskenb fndfazfr uaf rbdupbrfdkôa fntf y uaf rfzôa ib barkqubdkbaij tfmekëa fntf, sk nf sbpfrfdkôa sb bhbdtÿf pjr btfpfs y bs prædtkdfmbatb kmpjskenb ba uaf ÿakdf btfpf fndfazfr fmejs jeobtkvjs. 5.5.9. Íaikdbs mbtfnÿr`kdjs kibfnbs Raf sbpfrfdkôa kibfn bs fqubnnf ba nf dufn sb dumpnfa djaouatfmbatb ijs djaikdkjabs ba nf djadbatrfdkôa?

66

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

Wrkmbrf djaikdkôa. Bn tbajr ib mkabrfn ib katbrës ba nfs djnfs ibeb sbr dbrj, bstj bs? (69) t t  = 7   Tb`uaif djaikdkôa.

Aj ibeb ib cfebr mkabrfn ib `fa`f j bstërkn ba bn

djadbatrfij< fsí qub?

t f

= 6.7  

(62)

Dja uaf ib nfs ijs djaikdkjabs qub aj sb dumpnfa, nf djadbatrfdkôa ibof ib sbr kibfn y fibmæs bn dumpnkmkbatj ib uaf aj kmpnkdf abdbsfrkfmbatb qub sb `babrb nf jtrf, yf qub sja djmpnbtfmbatb kaibpbaikbatbs. Ib fdubrij f nj fatbrkjr, sb pubiba ibhkakr njs íaikdbs mbtfnÿr`kdjs kibfnbs, djmj sb ibtfnnfa ba nf Yfenf 5. 5.9.

Kaikdbs mbtfnur`kdjs y trfzijs ib pnfatfs djadbatrfijrfs

Nf utknkifi mbtfnÿr`kdf ib ibhkakr njs íaikdbs kibfnbs rfikdf prkadkpfnmbatb ba nf hkofdkôa ib mbtfs pfrf bn prjdbsj ib sbpfrfdkôa ba nfs bstrftb`kfs ib jptkmkzfdkôa djatrjn ib nf djadbatrfdkôa, djmj sb vb ba nf Hk`urf 2. Xbdtjr ib barkqubdkmkbatj? Jeobtkvj UB : 6/tf 

Fnkmbatj pnfatf    %    7    7    6

Djadbatrfdkôa „Uju`cbr”

Djadbatrfdkôa Ib Nkmpkbzf

   :    U

  j   v    k    t   b    o    e    J   ?   a    ô    k   d   f   r   b   p   u   d   b    U   b    i   r   j    t   d   b    X

Hk`urf 2.  2. 

Djadbatrfdkôa „Tdfvba`br”

Djnfs ib pnfatf

T   B  W   F U   F D   K  J   A    K   I B   F N 

Yrfzfij ib uaf Wnfatf ib Djadbatrfdkô Djadbatrfdkôa a Mjstrfaij nf Tbpfrfdkôa Kibfn y jeobtkvjs ib dfif btfpf ib djadbatrfdkôa

65

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

Tk sb djaskibrfa nfs djaikdkjabs fatbrkjrbs, bs hædkn ibmjstrfr qub njs íaikdbs kibfnbs tkbaba nfs sk`ukbatbs bxprbskjabs? F pfrtkr ib nf bdufdkôa 3, sb pubib dfndunfr nf rbdupbrfdkôa kibfn  U  KIBFN  djmj?  U KIBFN

= 6.7  

(68)

F pfrtkr ib nf bdufdkôa;, sb pubib dfndunfr nf rfzôa ib barkqubdkmkbatj kibfn djmj?  UB  KIBFN

Dufaij t f bstf ifij ba hrfddkôa

=

6.7 tf

 

(60)

F pfrtkr ib nf bdufdkôa 66, sb pubib dfndunfr nf rfzôa ib djadbatrfdkôa kibfn djmj? 6.7

= tf   y pjr nj tfatj bn rbaikmkbatj kibfn sb bxprbsf djmj?  K  IBFN

 UD 

X  KIBFN   = tf  

(63)   (63)

(6;)

Njs ibmæs íaikdbs sb bxprbsfa ba nf tfenf 5. 5.2.

Jtrfs bxprbskjabs ib njs íaikdbs mbtfnÿr`kdjs usfijs ba jpbrfdkôa ib pnfatfs djadbatrfijrfs.

Ba fn`uafs jdfskjabs bs djmpnkdfij jetbabr vfnjrbs rbnftkvfmbatb djahkfenbs ib dfuifnbs nfs jpbrfdkjabs ib djadbatrfdkôa. ikhkduntfi sb supbrfr bmpnbfaijba jtrfs bxprbskjabs ib njs íaikdbsBstf mbtfnÿr`kdjs nfspubib dufnbs sja bxfdtfmbatb k`ufnbs f nfs ibhkakdkjabs fatbrkjrbs.  fatbrkjrbs.  Ib fdubrij fn efnfadb mkdrjsdôpkdj ib nf bdufdkôa 9e, sb pubib jetbabr hædknmbatb qub?  t  ∕ t t   t D  (5;)   (5;)  U =  f  t    t  t  ∕  D  t   f Aubvfmbatb sb pubib ibtbrmkafr qub nf rbdupbrfdkôa kibfn  U KIBFN bs nf uakifi

64

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

Nfs ibmæs bxprbskjabs ib íaikdbs mbtfnÿr`kdjs ba tërmkajs ib njs tbajrbs sb badubatrfa ba nf Yfenf 5 y sb pubiba ibiudkr hædknmbatb f pfrtkr ib nfs ibhkakdkjabs y njs efnfadbs ib mfsf.

Yfenf 5.  5.  Íaikdbs ib Djadbatrfdkôa AJMEUB IBN KAIKDB MBYFNßU@KDJ Ubdupbrfdkôa? U  

BSWUBTKÔA IBN KAIKDB KAIKDBT BA YBUMKAJT KIBFNMBAYB IB YBAJUBT  U KIBFN  = 6.7

Ufzôa ib Barkqubdkmkbatj  U B  

 U BKIBFN  = 6/t f 

Kaikdb ib Tbnbdtkvkifi K.T.  

 K.T . KIBFN  ↕  ∑    ↕  ∑

Ufzôa ib Djadbatrfdkôa

 U

 t  ∕ t   t  =  f t   D     t D  ∕ t t   t f  U B   =

 K .T . =

X = t f 

Bhkdkbadkf ib sbpfrfdkôa  B  

B = 6.7

X  =  B  =

 

t e ( F) * t f ( E )

 UD  

Ubaikmkbatj X  

t f

t f ( F) * t e ( E )

 UD  =

 UD  KIBFN  = 6/t f 

t D 

t D  ∕ t t 

 

 

t f ∕ t t  t f ∕ t t  t D  ∕ t t 

 

(t f ∕ t t  )(t D  ∕ t f )   t f (t D  ∕ t t  )(6 ∕ t f )

69

 

M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

4.

NFT WFUYÍDRNFT MKSYFT [ NF DJADBAYUFDKÔA IB MKABUFNBT.

Nfs pfrtídunfs mkxtfs (vbr Hk`urf 8) oub`fa ua pfpbn kmpjrtfatb ba nf djadbatrfdkôa, ibekij f qub bnnfs aj bstæa djmpnbtfmbatb nkebrfifs.

f

d

b

e

i

h

c Hk`urf 8.  8. 

Wfrtídunfs Nkebrfifs y Mkxtfs

Bn jeobtj ibyfnfqub trkturfdkôa mjnkbaif bs fndfazfr ua `rfij ib nkebrfdkôa ib nfs pfrtídunfs, bnnfs fny bstfr nkebrfifs rbspjaibræa mbojr f njs ikhbrbatbs mëtjijs ib djadbatrfdkôa. Bn prjenbmf bs qub cfy ikhbrbatbs tkpjs ib pfrtídunfs mkxtfs y dfif uaf ib bnnfs tbairæ ua djmpjrtfmkbatj pfrtkdunfr. Ba bn dfsj ib pfrtídunfs djmj (8d), tbairífa mfyjr tbaibadkf f djmpjrtfrsb djmj ib nf bspbdkb „jsdurf”, 8f mkbatrfs qub nfs ib tkpj 8b tbairæa nf tbaibadkf f djmpjrtfrsb djmj nfs pfrtídunfs „dnfrfs” nkebrfifs 8e. Tka bmefr`j, bstfs pfrtídunfs ba `babrfn drbfræa ibhkdkbadkfs ba nfs sbpfrfdkjabs< pubs djmj sb vb, dja nf prbsbadkf ib bnnfs sb fnbofræ ib uaf djadbatrfdkôa kibfn.

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Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

Bn bhbdtj ib nf prbsbadkf ib nfs pfrtídunfs mkxtfs `babrf nf abdbskifi ib utknkzfr vfrkfs btfpfs ib djadbatrfdkôa, pfrf bvktfr djmekafifmbatb, përikifs ba nf jpbrfdkôa y fumbatfr nf rbdupbrfdkôa. Djmj sb pubib prbvbr, pjr nf prbsbadkf ib pfrtídunfs mkxtfs y/j njs mbdfaksmjs ib sbpfrfdkôa, aj bs hfdtkenb mbikfatb uaf sjnf sb btfpf ib djadbatrfdkôa nj`rfr ib bn jeobtkvj ib nf jpbrfdkôa. Wjr bnnj, `babrfnmbatb, kmpnbmbatfa vfrkfs btfpfs djadbatrfdkôa pfrf kr nj`rfaij jeobtkvjs pfrdkfnbs pfunftkafmbatb, djmj sb mubstrf ba nf Hk`urf 2. Wubib ajtfrsb ba nf hk`urf njs sk`ukbatbs fspbdtjs. 

  Ib nf btfpf ib djadbatrfdkôa „Tdfvba`br” sfnba nfs djnfs ibhkaktkvfs ib pnfatf.



  Nfs ibmæs btfpfs ib djadbatrfdkôa (nkmpkbzf y „Uju`cbr”) `babrfnmbatb rbdkrdunfa nfs djnfs f djrrkbatbs ijaib bn tbajr sbf skmknfr.



  Nfs pfrtídunfs mkxtfs pubiba sfnkr ba nfs djnfs ibn sbpfrfijr „Uju`cbr” j ib nkmpkbzf< pjr nj qub, pfrf sbr prjdbsfifs aubvfmbatb, ibeb bhbdtufrsb `babrfnmbatb ibn prjybdtj njrbmjnkbaif. pbrmktf. Bstj sb pubib cfdbr skbmprb y dufaij nf bdjajmíf



  Wubib cfenfrsb ib íaikdbs mbtfnÿr`kdjs pfrf dfif btfpf, pbrj f su vbz sb ibeb cfdbr rbhbrbadkf f njs íaikdbs mbtfnÿr`kdjs `njefnbs fsí (vbr hk`urf 9.8)?  U `njefn  =

 U `njefn  =

(D 5  x td 5) ⋂ td ( F  x tf ) (tf ∕ t t 4 ) ⋂ td 5 (t d 5

∕ t t 4 ) ⋂ tf

 

(56f)

 

(56e)

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M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

9. KAYUJIRDDKÔA FN IKTBÖJ [ DJADBAYUFDKÔA IB MKABUFNBT

YUF_FIJ IB

WNFAYFT

IB

Bmpnbfaij njs íaikdbs mbtfnÿr`kdjs, sb pubib katrjiudkr fn djadbptj ib iksböj ib pnfatfs ib djadbatrfdkôa. Nf hk`urf 0 mubstrf ua bsqubmf ib uaf pnfatf ib djadbatrfdkôa ijaib sb ibtfnnfa njs jeobtkvjs ba nf uaf ib nfs níabfs ib prjiuddkôa  prjiuddkôa  Tb jesbrvf qub bn jeobtkvj ib nf níabf „Uju`cbr-Tdfvba`br” bs nf rbdupbrfdkôa, ib tfn mfabrf qub nfs djnfs ib bstf níabf pubiba pfsfr f ejtfibrjs j bsdjmerbrfs, mkbatrfs qub njs djadbatrfijs ib nf níabf „Uju`cbr”-Nkmpkbzf.

9.6.

JEOBYKXJ IB DFIF BYFWF IB DJADBAYUFDKÔA.

Nf btfpf ib efrrkij „Tdfvba`br” tkbab pjr jeobtkvj bnkmkafr fn mæxkmj nf `fa`f nkebrfif, bs pjr bnnj qub bnnf prjiudb nfs djnfs mæs pjerbs ibn skstbmf. Nf btfpf ib ibsefstb („Uju`cbr”), tkbab pjr jeobtkvj bnkmkafr pfrtídunfs mkxtfs fn mæxkmj y jetbabr ua djadbatrfij nj mæs barkqubdkij pjskenb. Nfs vfrkfenbs mæs kmpjrtfatbs ba nfs ijs btfpfs fatbrkjrbs sja nf rbdupbrfdkôa y bn rbaikmkbatj, pjr nj qub subnba ibajmkafrsb dkrduktjs j btfpfs ib rbdupbrfdkôa. Nf btfpf ib nkmpkbzf bs jpdkjafn< ibpbaikbaij ib dkrduastfadkfs bspbdkfnbs. Tu utknkzfdkôa, sb if dufaij sb ibsbf fumbatfr bn tbajr ib tfn mfabrf qub bs abdbsfrkj bnkmkafr bn mæxkmj ib `fa`f y tbabr ua djadbatrfij ib fntf purbzf. Bs hfdtkenb qub cfyf përikifs ib mkabrfn ÿtkn, pjr nj qub nf rbdupbrfdkôa ba bstjs dkrduktjs bs rbnftkvfmbatb efof, pbrj nf rfzôa ib barkqubdkmkbatj ibebr muy fntf. Ba fn`uafs jdfskjabs, bs abdbsfrkf jtrf btfpf ib rb-nkmpkbzf. Nf vfrkfenb mæs kmpjrtfatb ëstf btfpf rfzôa ib barkqubdkmkbatj, pjr nj qub subnba ibajmkafrsbbaf bstfs btfpfsbs ib nf barkqubdkmkbatj. Ibeb qubifr dnfrj qub nf rbmjnkbaif sônj bs vænkif dufaij bxkstfa prjenbmfs ib nkebrfdkôa ib mkabrfnbs, pubs jtrj mbdfaksmj qub ibsfrrjnnb përikifs ibebr sbr djrrb`kij mbikfatb jptkmkzfdkôa ib njs fpfrftjs, (pjr bobmpnj< mfnf dfnkerfdkôa ib njs fpfrftjs, bmpnbj kasuhkdkbatb ib f`uf, btd.) 9.5.

NF UBDKUDRNFDKÔA IB DJUUKBAYBT.

Nf rbdkrdunfdkôa ib djrrkbatbs ba pnfatfs ib djadbatrfdkôa sb ibe rbfnkzfr djaskibrfaij qub aj sb pubib vkjnfr bn jeobtkvj huaifmbatfn ib nf djadbatrfdkôa.

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Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

Ba nf prædtkdf bstj kaikdf qub aj bs rbdjmbaifenb mbzdnfr djrrkbatbs dja tbajrbs y/j pjrdbatfobs ib mkabrfn ikhbrbatbs, pubs sb bstfríf iknuybaij nf djrrkbatb qub bstb mæs barkqubdkifiba bn mabrfn ib katbrës.

Hk`urf 0.  0. 

Djrrkbatbs ib uaf Djadbatrfijrf y Wrjpôsktj ibn Iksböj.

Bobmpnj. Tb djadbatrô uaf frbaf ib pnfyf utknkzfaij uaf bspkrfn Cumpcrby, dja Bobmpnj. bn hka ib jetbabr frbafs pbsfifs rkdfs ba rutknj (YkJ5). Bn bsqubmf bs djmj sb mubstrf ba nf Hk`urf 3. F = 5.509ba tja/c ibib sônkijs (Fnkmbatfdkôa) Hrfddkôa pbsj sônkijs ψf = 7.62 D = 7.452 tja/c ib sônkijs (Djadbatrfij) Hrfddkôa ba pbjs ib sônkijs ψd = 7.57 M = 7.463 tja/c ib sônkijs (Mbikjs) Hrfddkôa ba pbsj ib sônkijs ψm = 7.65 Y= 6.846 tja/c ib sônkijs (Djnfs) Hrfddkôa ba pbsj ib sônkijs ψt = 7.66 Njs tbajrbs ib frbafs ab`rfs ba dfif uaf ib nfs djrrkbatbs sja? t f = 64.45%? Ybajr ib rutknj ba nf fnkmbatfdkôa t d  Ybajr ib rutknj ba bn djadbatrfij d   = 33.45?

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M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

t m = 9.77%? Ybajr ib rutknj ba njs mbikjs t t t   = 7.6;%? Ybajr ib rutknj ba nfs djnfs

Hk`urf 3. Bsqubmf ib Djadbatrfdkôa ba Bspkrfn Cumpcrby ib Frbafs Ab`rfs. Njs prjiudtjs sja D. M. y Y qub sk`akhkdfa? Djadbatrfijs, mbikjs y djnfs rbspbdtkvfmbatb. F? rbprbsbatf nf fnkmbatfdkôa Efnfadb ib sônkijs.

Ib fdubrij f nf bdufdkôa sfebmjs qub?  F = D  + M  + Y   

Ijaib? 5.50 tja/c = (7.758 + 7.463 + 6.;4) tja/c = 5.509 tja/c  U =

(7.452 tja / c  x (33.45)

= 7.;93  

( 5.509 tja / c)  x (64.45

Aj sb pubib fpnkdfr nf bdufdkôa, ibekij f qub bxkstba trbs sfnkifs.    = 33.45/64.45 = 8.84 •  Ufzôa ib barkqubdkmkbatj. Tb`ÿa nf bdufdkôa U BB  = KT  •  Íaikdb ib sbnbdtkvkifi KT  Tk ibajmkafmjs tf  (F) bn tbajr ib rutknj ba fnkmbatfdkôa, t t  (E) bn tbajr ib jtrfs bspbdkbs ba nfs djnfs y mbikjs (k`ufn f 677 mbajs bn tbajr pjaibrfij ib rutknj ba djnfs k`ufn f 677% - 7.3% = ;;.6;%

6;

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

tf  (E) bn tbajr ib jtrfs bspbdkbs ba fnkmbatfdkôa bxdbptufaij rutknj (=677% 64.45 = 38.83%) . tt (F), bn tbajr ib rutknj ba djnfs.  KT  =

(64.45) x (;;.6;) (38.83) x (7.36)

= 63.35  

•  Ufzôa ib djadbatrfdkôa UD ? UD = 5.509 tja/c / 7.452 tja/c = 0.7 tja ib fnkmbatfdkôa / tja ib djadbatrfij

•  Ubaikmkbatj X   X  =

7.452 tja / c 5.509 tja / c

= 7.694 tja. djadbatrfi j. / tja. fnkmbatj.  

Djmj sb pubib vbr ba njs ijs fatbrkjrbs dændunjs sb ibiudb qub pfrf jetbabr uaf tjabnfif ib djadbatrfij sb rbqukbrb prjdbsfr 0.7 tja ib mkabrfn.

•  Ubaikmkbatj kibfn U BKIBFN    / 5.509 = 7.6445    U BKIBFN = 5.509   x 7.445 • 

Bhkdkbadkf ib nf sbpfrfdkôa B? B?  B  =

;9.08 ∕ 69.47 677 ∕ 64.45

⋂ 677% = ;5.35%  

•  Wërikifs ib frbafs ab`rfs ba nfs djnfs y mbikjs? Wërikifs = 677 - %U = 2.59% Jesbrvfdkjabs? nf rbdupbrfdkôa bs muy dbrdfaj fn 6.7, pbrj nf U B  aj bs tfa fntf, ëstf ifij bs uafqub btfpf ib ibsefstb U („Uju`cbr”).

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M. J Eustfmfatb, F. D. @fvkrkf y J. O. Ubstrbpj, K M DKMBS, 5773

BOBUDKDKJT WUJENBMF RAJ. RAJ. Ba nf djadbatrfdk djadbatrfdkôa ôa ib ua mkabrfn ib sunhurj, sb jetuvkbrja js sk`ukbatbs rbsuntfijs? Wbsj ib Djadbatrfij? 4.64 l`. , Wbsj ib Djnfs? ;8.3 l`, njs tbajrbs ib fnkmbatj, djadbatrfij j djnfs hubrja ib 6.89 %, 98.;6% y 7.609%. Ibtbrmkab? f. e. d. i.

Ubaikmk Ubaikmkbatj batj y djmpærbnj dja bn rbaikmkbatj kibfn Ubdupbrfdkôa y rfzôa ib barkqubdkmk barkqubdkmkbatj batj y djmpærbnjs dja njs vfnjrbs kibfnbs Wbrikifs ib sunhurj ba nfs djnfs Ikeuob ua bsqubmf ib nf sbpfrfdkôa y dbrtkhkqub sk hub „Uju`cbrsdfvba`br”j „Uuj`cbr”-nkmpkbzf.

WUJENBMF IJT. Dja efsb ba njs efnfadbs ib mfsf, ibmubstrb qub? f.

Bn rbaikmkbatj bs?

X  =

e.

Nf rbdupbrfdkôa bs?

 U

ijaib tf, td y rbspbdtkvfmbatb.

tt  

tf ∕ tt  td ∕ tt 

 

tf ∕ tt  td =       td ∕ tt  tf

sja njs tbajrbs ib fnkmbatj, djadbatrfij y djnfs,

WUJENBMF YUBT . Tb bhbdtuô uaprbsbatfa basfyj ibbacuaikij-hnjtfij pfrf ua dfreôa, y sb jetuvkbrja YUBT. njs rbsuntfijs qub sb nf tfenf 4.. Ib fdubrij f nf tfenf bn % ib dbakzf tjtfn ba tjif nf mubstrf bs ibn 5;.;8%. @rfhkqub f. e.

% Fdumunfij ib hnjtfijs vs. @rfvbifi bspbdíhkdf ibn níqukij % Fdumunfij ib cuaikijs vs. @rfvbifi bspbdíhkdf ib níqukij

Tk sb tkbab ua sbpfrfijr dja uaf `rfvbifi bspbdíhkdf i ib b djrtb ib 6.87. Ibtbrmkab bn rbaikmkbatj y nf rbdupbrfdkôa bspbrfif ib dfreôa ba nf hrfddkôa nkvkfaf y ba nf hrfddkôa pbsfif 56

 

Ajtfs ib Djadbatrfdkôa Djadbatrfdkôa ib Mkabrfnbs, K M DKMBS, 5773

Yfenf 4.  4. 

Basfyj cuaikij —hnjtfij ib dfreôa

Ibaksifi ib

% pbsj

% pbsj ib

níqukij ba l`/n +6.47 6.47-6.97 6.97-6.27 6.27-6.87 6.87-6.07 6.07-6.37 6.37-6.;7 6.;7-5.77 -5.77

ib hnjtfij 85.62 ;.87 4.27 6.;7 5.52 6.77 7.;2 6.77 60.82

cuaikij 40.32 53.52 59.02 55.32 57.87 6;.87 63.82 60.82 -

677.77

%Dbakzf 5.87 ;.77 63.;3 5;.06 4;.85 98.87 24.6; 2;.27 34.35 57.;8

.

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