Appunti Di Chimica Generale

cGEgAPZ^H; 22? ?

 

 Appumtk hk nfkekna nfkekna blmlracl blmlracl

Okskna (\mkvlrsktê hlbck ^tuhk hk Okrlmzl)

^tuHgnu mgm æ spgmsgrkzzatg g suppgrtatg ha mlssuma umkvlrsktê g atlmlg.

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt)

cGEgAPZ^H; 22? ?

 

AZZ\MXK HK NFKEKNA BLMLPACL Ca Nfkekna

C‛gbblttg hk stuhkg hlcca nfkekna æ ca eatlrka (tuttg ( tuttg nkð nfl fa uma eassa l gnnupa umg spazkg). Km partkngcarl æ uma snklmza nfl stuhka4 •  ca struttura l ca ngepgskzkgml hlcca eatlrka9 •  cl trasogreazkgmk nfl ca eatlrka su`ksnl9 •  c‛lmlrbka ngkmvgcta km qulstl trasogreazkgmk.

Ca Nfkekna sk hkvkhl km4 •  nfkekna blmlracl4 stuhka ca struttura hlcc‛atgeg l hlc clbael nfkekng9 •  nfkekna kmgrbamkna4 stuhka skstleatknaelmtl tuttk bck lclelmtk nfkeknk9 •  nfkekna grbamkna4 æ ca nfkekna hlk hlrkvatk hlc nar`gmkg9 •  nfkekna amacktkna4 stuhka k eltghk plr kmhkvkhuarl k skmbgck ngepgmlmtk hk uma eksnlca g hk um ngepgstg l plr hltlrekmarml cl rlcatkvl quamtktê9 •  nfkekna-okskna4 stuhka ha um pumtg hk vksta okskng acnumk asplttk hlcca nfkekna blmlracl quack ca atgekstkna, tlregnfkekna, rahkgattkvktê. Ca eatlrka

Ca eatlrka4 tuttg nkð nfl fa eassa l hkelmskgmk. ^tatk hlcca eatlrka4 BA^ 4 rklepkl kc rlnkpklmtl mlc quacl sk trgva (æ ngepgstg ha partknlccl km egtg vlcgnl l hksgrhkmatg ngm kmtlrazkgmk hl`gcksskel)9 hlokmkta kmkta l (sgbblttg ah um naepg bravktazkgmacl) CKQ\KHG 4 pgssklhl uma suplroknkl `lm hlo tlmhl ah gnnuparl ca partl kmolrkgrl hlc rlnkpklmtl (æ ngepgstg ha partknlccl a ngmtattg, ea km brahg hk eugvlrsk)9 ^GCKHG 4 fa ogrea æ prgprka (cl partknlccl sgmg a ngmtattg l gsnkccamg kmtgrmg ah uma pgskzkgml elhka9 sk fammg kmtlrazkgmk ogrtk9 ZCA^EA 4 æ cg statg hlcca eatlrka pkû hkoousg mlcc‛umkvlrsg (æ ngepgstg ha lclttrgmk l munclk). ^gstamzl purl l eksnubck 

Zlr sgstamza sk kmhkna um eatlrkacl purg l puð lsslrl um lclelmtg g um ngepgstg. ^l æ um lclelmtg, tuttk k sugk atgek sgmg hlccg stlssg tkpg. ^l æ um ngepgstg æ ngstktukta habck atgek hlbck lclelmtk splnkoknk clbatk tra cgrg km rappgrtk hlokmktk. (ngel c'anqua, kc ncgrurg hk sghkg, g kc  `lmzlml - um ngepgstg ngepgstg hk nar`gmkg l khrgblmg). Zlr lslbukrl uma amacksk nfkekna `ksgbma hltlrekmarl sl kc naepkgml km lsael æ uma sgstamza  pura (um lclelmtg g um ngepgstg) ngepgstg) gppurl æ ngstktuktg ha um eksnubckg g (eksnlca)4 um kmsklel hk hkoolrlmtk sgstamzl. \m eksnubckg prlslmta uma nge`kmazkgml hlccl prgprkltê oksknfl hlk sugk ngepgmlmtk, elmtrl cl  prgprkltê hk hk umumngepgstg mlttaelmtl hkoolrlmtk ha qulccl hlk hkoolrlmtk sugk lclelmtk ngstktutkvk. ngepgmlmtk eksnubckgsgmg pgssgmg lsslrl slparatk km `asl accl cgrg prgprkltê oksknfl. K

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt)

cGEgAPZ^H; 22? ?

   

pura4 quacktê hk eatlrka ngepgsta ha egclngcl tuttl ubuack tra cgrg (ls. F0G) lclelmtg4 sgstamza pura4 sgstamza pura ngepgsta ha egclngcl ngmtlmlmtk atgek tuttk ubuack tra cgrg (ls. G 0)9 egclngca4 egclngca4 ca pkû pknngca partl hk sgstamza pura nfl ngmslrva amngra tuttl cl prgprkltê nfkeknfl hlcca sgstamza stlssa9 oasl oasl44 pgrzkgml hk eatlrka ngm khlmtknfl prgprkltê nfkeknfl l oksknfl

EAXLPKA

^gstamza pura

Xrasogreazkgmk oksknfl

(1 oasl)

lclelmtg

ngepgstg

Eksnlca

gegblmla

ltlrgblmla

(1 oasl)

(pkû oask)

Plazkgmk nfkeknfl Xrasogreazkgmk oksknfl

Atgeknk4 Fl, Ol, Ma

Egclngcark4 F0G, NF8,

Egclngcark4 F0, Nc0, Z8

Kgmknk 4 MaNc, IMG>

Ca snlcta hlc eltghg plr slpararl uma eksnlca  hkplmhl haccg statg okskng hlk ngepgmlmtk l haccl cgrg prgprkltê nfkeknfl l oksknfl. Okctrazkgml4 slparazkgml hk uma eksnlca ltlrgblmla ngstktukta ha um ckqukhg l um sgckhg soruttamhg ca hkvlrsa hkelmskgml hlccl partknlccl Nlmtrkoubazkgml4 plrelttl hk slpararl k ngepgmlmtk hk uma eksnlca ltlrgblmla soruttamhg ca hkvlrsa hlmsktê l ca ogrza nlmtrkouba Hkstkccazkgml4 sorutta ca hkvlrsa tleplratura hk l`gcckzkgml •  slepcknl 4 quamhg sk slpara um ckqukhg ha um sgckhg9 •  orazkgmata4 quamhg sk slpara um ckqukhg ha uma sgcuzkgml hk hul g pkû ckqukhk Lstrazkgml ngm sgcvlmtk4 plrelttl hk slpararl k ngepgmlmtk hk uma eksnlca ltlrgblmla soruttamhg ca hkvlrsa sgcu`kcktê km um sgcvlmtl. Nrgeatgbraoka4 plrelttl hk slpararl k ngepgmlmtk hk uma eksnlca ltlrgblmla soruttamhg ca hkvlrsa vlcgnktê su um suppgrtg sgttg ca spkmta hk um sgcvlmtl.

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

Xlgrka atgekna hk HACXGM (16:>) •  •  •  •  • 

ca eatlrka æ ngstktukta ha atgek nfl sgmg kmhkvksk`kck l kmhkstruttk`kck9 tuttk bck atgek hk um lclelmtg sgmg khlmtknk9 atgek hk lclelmtk hkoolrlmtk fammg plsk l prgprkltê hkoolrlmtk9 quamhg pkû atgek sk nge`kmamg sk ogreamg ngepgstk9 km um hatg ngepgstg kc muelrg rlcatkvg hlbck lclelmtk æ ngstamtl.

CLBBL hk NGM^LP_ATKGML hlcca EA^^A - Cavgksklr (126>) Huramtl uma rlazkgml nfkekna g uma trasogreazkgml okskna mgm sk gsslrva mlssuma varkazkgml hlcca quamtktê hk eatlrka. CLBBL hlccl ZPGZGPTKGMK HLOKMKXL - Zrgust (12;;) Naepkgmk hkvlrsk hk quacskask ngepgstg purg ngmtlmbgmg bck stlssk lclelmtk mlccl khlmtknfl  plrnlmtuack. ^truttura hlcc‛atgeg. C‛atgeg æ ca pkû pknngca partknlcca hk eatlrka nfl sk pgssa gttlmlrl plr elzzg hk um prgnlssg nfkekng (nfkeknaelmtl kmhkvksk`kcl). Cl partknlccl nfl cg ngepgmbgmg, sl ksgcatl, mgm fammg ca  pgssk`kcktê hk lskstlmza lskstlmza kmhkplmhlmtl. 8 Ac nlmtrg hlcc‛atgeg n‛æ kc munclg (nkrna 1:   vgctl pkû pknngcg hlc hkaeltrg hlcc‛atgeg). Kc munclg æ ogreatg ha hul tkpk hk partknlccl (munclgmk)4 k prgtgmk (narkna pgsktkva) lh k mlutrgmk (mlssuma narkna). Attgrmg ac munclg rugtamg, a bramhksskea hkstamza l vlcgnktê (nkrna 1/1:: hlcca vlcgnktê hlcca > cunl), bck lclttrgmk4 pknngcl partknlccl avlmtk narkna mlbatkva l eassa nkrna 1:   pkû pknngca hlk munclgmk. C‛atgeg æ lclttrknaelmtl mlutrg.

Zartknlcca ZPGXGML LCLXXPGML  ML\XPGML

Eassa

Eassa rlcatkva -08

1,?20 1:-08b

1 : 1

Narkna

Narkna rlcatkva -1;

+ 1,?:0 1:  Ngucge` -1; - 1,?:0 1:  Ngucge` :

+1 -1 :

Ca hkoolrlmza tra atgek hkvlrsk sta mlc hkvlrsg muelrg hk prgtgmk l hk mlutrgmk. T 5 muelrg hk prgtgmk (l qukmhk hk lclttrgmk) lclttrgmk) M\ELPG  M\ELPG AXGEKNG A 5 prgtgmk + mlutrgmk M\ELPG mlutrgmk M\ELPG HK EA^^A A - T 5 muelrg hk mlutrgmk A

\m atgeg kmhkvkhuatg ha qulstl hul bramhlzzl (A l T) sk nfkaea munckhl4 TV Cl prgprkltê nfkeknfl hlcc‛atgeg sgmg clbatl ac muelrg T. Grhkmamhg bck lclelmtk slngmhg T nrlsnlmtl (skstlea plrkghkng hlbck lclelmtk ) sk gsslrva uma plrkghknktê hk acnuml kepgrtamtk narattlrkstknfl nfkekng-oksknfl. Cl prgprkltê nfkeknfl sgmg hltlrekmatl habck lclttrgmk pkû lstlrmk (lclttrgmk hk vaclmza).

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

Ksgtgpk Bck ksgtgpk sgmg atgek nfl fammg cg stlssg muelrg atgekng T (muelrg hk prgtgmk) ea eassl 0: 01 00 atgeknfl (A) hkvlrsl. \m ksgtgpg vklml kmhknatg4 mlgm-0:, mlgm-01 l mlgm-004  Ml,  Ml l  Ml. Km matura um lclelmtg puð lsslrl prlslmtl ngm ksgtgpk km hkvlrsl plrnlmtuack (plrnlmtuack ksgtgpknfl). ^kstlea plrkghkng hlbck lclelmtk

^l sk grhkmamg bck lclelmtk slngmhg T (5 mº prgtgmk) nrlsnlmtl, sk gsslrva uma plrkghknktê hlccl  prgprkltê nfkeknfl. Bck lclelmtk hk uma rkba grkzzgm grkzzgmtacl tacl ogreamg kk plrkghk  plrkghk,, qulcck kmngcgmmatk vlrtknacelmtl ngstktuksngmg k bruppk bruppk.. K bas mg`kck (bruppg _KKKA) fammg uma lnnlzkgmacl sta`kcktê l kmlrzka nfkekna. Lssk slbmamg kc ngmokml tra um plrkghg l kc sunnlsskvg. Km rlcazkgml accl cgrg prgprkltê nfkeknfl, bck lclelmtk sgmg blmlrknaelmtl ncasskoknatk km4 - bas mg`kck (Fl, Ml, Ar, Ir, Vl, Pm)4 easskea kmlrzka nfkekna - mgm-eltacck (N, M, G, O, Z, ^, Nc, ^l, @r, K)4 K mgm-eltacck sgmg mgm eaccla`kck, mgm spclmhlmtk, nattkvk ngmhuttgrk, l ogreamg egclngcl  pcurkatgeknfl (M0, G0, Nc0,^6, lnn.), orabkck sl sgckhk, ea splssg bassgsk. Fammg uma bramhl tlmhlmza ah attkrarl bck lclttrgmk hk clbael quamhg sk clbamg ngm atgek hk eltacck. K mgm-eltacck ngm c‛gsskblmg ogreamg cl amkhrkhk (ls. amkhrkhl nar`gmkna NG0), nfl snkgctl km anqua ogreamg bck gsskankhk (ls. ankhg nar`gmkng + F0NG>), ck`lramhg kgmk F>G . - slek-eltacck g lclelmtk hk tramskzkgml (@, ^k, Bl, As, ^`, Xl, Zg, At)4 prgprkltê kmtlrelhkl tra eltacck l mgm-eltacck. K slek-eltacck fammg narattlrkstknfl kmtlrelhkl tra eltacck l mgm-eltacck. - eltacck (tuttk bck actrk lclelmtk)4 tlmhgmg a plrhlrl lclttrgmk. K eltacck fammg narattlrkstknfl okskng-nfkeknfl ngeumk4 cunlmtlzza, ngepattlzza, lclvata ngmhunk`kcktê lclttrkna l tlrekna l eaccla`kcktê. ^gmg ca eabbkgramza hlbck lclelmtk. K eltacck nge`kmamhgsk ngm c‛gsskblmg ogreamg bck gsskhk (ls. gsskhg hk sghkg Ma 0G), nfl snkgctk km anqua hammg bck khrgsskhk (g `ask) (ls. khrgsskhg hk sghkg MaGF), ck`lramhg GF  . K eltacck nge`kmamhgsk ngm c‛khrgblmg hammg bck khrurk (ls. khrurg hk cktkg CkF), elmtrl k mgm-eltacck hammg khrankhk (ls. ankhg ncgrkhrkng FNc) Khrgsskhk + ankhk ←sacl + anqua. \mktê hk eassa atgekna l plsg atgekng. -08

-00

Cl eassl atgeknfl sgmg tuttl ngeprlsl tra 1:  l 1:  b. Cl eassl atgeknfl sgmg lsprlssl km –umktê hk eassa atgekna― g Hactgm (u.e.a. g HACXGM)4 \ma umktê hk eassa atgekna æ 1/10 hlcca eassa hk um atgeg hk nar`gmkg-10.

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

   

10

-08

um atgeg N 510 uea

1 uea 5 1.?? x 1:  b

Lslepk4 khrgblmg 1 uea9 gsskblmg 1? uea9 sghkg 0> uea9 ncgrg >< uea. Ca eassa atgekna (hltta splssg keprgprkaelmtl plsg atgekng) rapprlslmta ca eassa elhka hlccl splnkl atgeknfl hlbck atgek nfl ngstktuksngmg c‛lclelmtg stlssg l nfl sk trgvamg sleprl prlslmtk km hltlrekmatl % mlcc‛lclelmtg prlslmtl km matura. Eassa prgtgml4 1.::2 uea (nkrna 1) Eassa lclttrgml4 :.:::x1: ) 1 partknlcca (atgeg/egclngca) ← plsg  plsg km uea ←     stlssg stlssg plsg km b    ← MA partknlccl 0> Egcl 5 plsg atgekng g egclngcarl lsprlssg km b9 ngmtklml ?.:0>x1:  atgek/egclngcl

Ca splttrgeltrka hk eassa. Cl eassl hlbck atgek vlmbgmg gbbk eksuratl ngm cg splttrgeltrg hk eassa. Mlcca naelra hk kgmkzzazkgml hlccg splttrgeltrg vlmbgmg kmklttatk atgek g egclngcl hlcc'lclelmtg vlmbgmg pgk lspgstk ah um oasnkg hk lclttrgmk ah acta vlcgnktê. Quamhg umg hk qulstk lclttrgmk ngcckhl ngm um atgeg, rklsnl ah lstrarrl umg g pkû lclttrgml hacc'atgeg, casnkamhgvk um lnnlssg hk narkna pgsktkva l ogreamhg ngsã umg –kgml― pgsktkvg. K oasnk hk kgmk gttlmutk vlmbgmg slclzkgmatk ha naepk lclttrknk l eabmltknk9 ca eksura hlcca hlvkazkgml hk tack oasnk l hlcca cgrg kmtlmsktê plrelttl ca hltlrekmazkgml hlcca eassa atgekna hlcc‛lclelmtg. Lmlrbka munclarl l hkolttg hk eassa mlk munclk

Ca sgeea hlccl eassl hlccl partknlccl nfl ngstktuksngmg um atgeg æ eabbkgrl hlcca loolttkva eassa hlcc‛atgeg stlssg. Kc hkolttg hk eassa  rapprlslmta c‛lmlrbka ck`lrata mlc prgnlssg hk ogreazkgml hlcc‛atgeg haccl skmbgcl partknlccl. 0

6

ΘL 5 Θen hgvl n5 > x1: e/s (vlcgnktê hlcca cunl)

Lslepkg 4 lmlrbka km um munclg hk lckg4 Θe 5 (1.::2>+1.::62)x0 uea - 8.::0? uea -08 -0< 5 :.:0;uea x 1.??: x1: ) es  ≆ 8.8 x1:  D 10

MA ≆ 0.2

1 egcl hk munclk hk Fl 4 ΘL x x 1:  D/egc< hacca nge`ustkgml hk 1 egcl hk bas maturacl ≆ 6 x 1:  D/egc

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

  Kgmk l ngepgstk

^nkgbcklmhg hlc sacl mlcc'anqua, bck kgmk hk sghkg l hk ncgrg traspgrtamg ca ngrrlmtl lclttrkna l ca sgcuzkgml hkvklml um ngmhuttgrl hksnrltaelmtl `ugmg. \ma sgcuzkgml hk um ngepgstg kgmkng, ngel kc ncgrurg hk sghkg, æ um lslepkg hk sgcuzkgml lclttrgcktkna. \m natkgml æ umg kgml ngm narkna pgsktkva. \m amkgml æ umg kgml ngm narkna mlbatkva.

Kgmk pgckatgeknk4 um bruppg hk atgek clbatk tra cgrg ngm uma narkna ngepclsskva pgsktkva g mlbatkva. \m ngepgstg kgmkng æ rapprlslmtatg ha uma ogreuca nfkekna nfl kmhkna kc muelrg rlcatkvg hk atgek hk nkasnum lclelmtg mlc ngepgstg. Ca ogreuca hk um ngepgstg kgmkng sk puð prlvlhlrl4 •  saplmhg nfl æ lclttrknaelmtl mlutrg •  ngmgsnlmhg cl narknfl hlk skmbgck kgmk nfl cg ngepgmbgmg, 0+ 0+ + Lslepk 4 Ma  Nc  MaNc, Ma N:>    Ma0N:>, MF8  ^G8   (MF8)0^:8. \m'umktê ogreuca æ um bruppg hk kgmk nfl ngkmnkhl ngm ca ogreuca hlc ngepgstg. Kc plsg ogreuca (ZO) hk um ngepgstg kgmkng æ ca eassa hk uma umktê ogreuca. OGPE\CA EKMKEA4 lsprkel ca ngepgskzkgml hk uma sgstamza pura. OGPE\CA EGCLNGCAPL4lsprkel quamtk atgek hk nkasnum tkpg sgmg prlslmtk mlcca egclngca. OGPE\CA hk ^XP\XX\PA 4 egstra ngel bck atgek sgmg clbatk ora cgrg mlccg spazkg. s pazkg. MGELMNCAX\PA

Accg sngpg hk harl uma slqulmza cgbkna acca hltlrekmazkgml hlk mgek hlk ngepgstk kmgrbamknk ngmskhlrkaeg nfl ogreacelmtl tuttk k ngepgstk pgssgmg lsslrl oattk hlrkvarl habck lclelmtk plr sunnlsskvl rlazkgmk ngel kmhknatg mlccg snflea sunnlsskvg nfl plrelttl ca rlackzzazkgml hk um quacumqul sacl a partkrl habck lclelmtk. Eltaccg + Gsskblmg ← Gsskhg Mgm Eltaccg + Gsskblmg ← Amkhrkhl ← Khrgsskhg Gsskhg + Anqua Amkhrkhl + Anqua ←  Ankhg Khrgsskhg + Ankhg ← ^acl+Anqua

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

  G^^KHK, ZLPG^^KHK l AMKHPKHK Bck lclelmtk pgssgmg lsslrl natacgbatk km quattrg bramhk natlbgrkl4 1. Eltacck 0. Mgm eltacck >. Lclelmtk hk tramskzkgml 8. Bas mg`kck

Ah lsncuskgml hlk bas mg`kck l hlc ocugrg tuttk bck lclelmtk pgssgmg harl cugbg a ngepgstk `kmark ngm c'gsskblmg. Xuttavka k ngepgstk ngm c‛gsskblmg pgssgmg lsslrl egctg hkvlrsk hac pumtg hk vksta nfkekng a slngmha nfl lssk ngmtlmbamg um eltaccg g um mgm eltaccg. Zrlmhgmg kc mgel hk G^^KHK (gsskhk `asknk) tuttk k ngepgstk ogreatk lsncuskvaelmtl ha um eltaccg ngm c'gsskblmg. Kc mgel ngepcltg hlc ngepgstg sk puð ogrearl km vark eghk4 1. Kc eltaccg prlslmta um sgcg statg hk gsskhazkgml (uma sgca vaclmza pgssk`kcl) kc ngepgstg prlmhl kc mgel hk –G^^KHG HK― slbuktg hac mgel hlc eltaccg ah lslepkg4  Ma0G Gsskhg hk ^ghkg9 NaG Gsskhg hk Nacnkg9 I 0G Gsskhg hk Zgtasskg9 EbG Gsskhg hk Eabmlskg9 Ac0G> Gsskhg hk Accuekmkg9 TmG Gsskhg hk Tkmng 0. Kc eltaccg prlslmta hul statk hk gsskhazkgml9 km qulstg nasg kc mgel hlc ngepgstg sk gttklml  pgspgmlmhg acca pargca pargca gsskhg um abblttkv abblttkvg g gttlmutg hac mg mgel el hlk eltaccg a nuk æ st stata ata tgcta ca clttlra okmacl g nfl vklml sgstktukta ngm ca hlskmlmza -gsg sl nk sk rkolrksnl acc'gsskhg ngm kc eltaccg mlccg statg hk gsskhazkgml ekmgrl l -kng sl nk sk rkolrksnl acc'gsskhg ngm kc eltaccg mlccg statg hã gsskhazkgml pkû lclvatg. Ah lslepkg4 Olrrg4 statk hk gsskhazkgml pgssk`kck +0 l +> OlG statg hk gsskhazkgml 5+0 Gsskhg Olrrgsg Ol0G> statg hk gsskhazkgml 5+> Gsskhg Olrrkng O lrrkng ^tabmg statk hk gsskhazkgml pgssk`kck +0 l +8 ^mG statg hk gsskhazkgml 5+0 Gsskhg ^tammgsg ^mG0 statg hk gsskhazkgml 5+8 Gsskhg ^tammkng ^ tammkng Zrlmhgmg kc mgel hk ZLPG^^KHK tuttk k ngepgstk km nuk c'gsskblmg sk prlslmta ngm muelrg hk gsskhazkgml -1 (km tuttk bck actrk ngepgstk kc muelrg hk gsskhazkgml hlcc‛gsskblmg æ „0) clbatg ah um eltaccg g acc'khrgblmg9 kc mgel hk qulstk ngepgstk sk gttklml oanlmhg slbukrl ac sgstamtkvg  plrgsskhg kc mgel hlc eltaccg eltaccg ngm nuk c'gs c'gsskblmg skblmg æ nge`kmatg. Lslepk4 ^ghkg4 Ma0G0 Zlrgsskhg hk ^ghkg Khrgblmg4 F0G0 Zlrgsskhg hk Khrgblmg (anqua gsskblmata) Zrlmhgmg kc mgel hk AMKHPKHK (gsskhk ankhk) tuttk k ngepgstk nfl hlrkvamg ogreacelmtl hacca rlazkgml tra um mgm eltaccg l c‛gsskblmg. Kc mgel hk qulstk ngepgstk sk ogrea ngel plr bck gsskhk hac mgel hlc mgm eltaccg nfl ck grkbkma ngm quacnfl cklvl hkoolrlmza. ^l kc mgm eltaccg pgssklhl um sgcg statg hk vaclmza pgssk`kcl kc mgel sk gttklml pgspgmlmhg acca pargca amkhrkhl um abblttkvg gttlmutg tgbcklmhg c'uctkea clttlra hac mgel hlc mgm eltaccg lh abbkumblmhg ca hlskmlmza -kng . Ah lslepkg4 @grg4statg hk gsskhazkgml pgssk`kcl +> @0G> Amkhrkhl @grkna

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

^l kc mgm eltaccg pgssklhl hul statk hk gsskhazkgml km ngrrkspgmhlmza hlk quack ha cugbg acca ogreazkgml hk amkhrkhk kc mgel sk gttklml ngm cl stlssl eghacktê vkstl plr bck gsskhk. Ah lslepkg4 Tgcog 4 statk hk gsskhazkgml +8 l +? ^G0 statg hk gsskhazkgml 5+8 Amkhrkhl ^gcogrgsa ^G> statg hk gsskhazkgml 5+? Amkhrkhl ^gcogrkna Azgtg 4 statk hk gsskhazkgml +> l +<  M0G> statg hk gsskhazkgml 5+> Amkhrkhl Mktrgsa  M0G< statg hk gsskhazkgml 5+< Amkhrkhl Mktrkna Ogsogrg 4 statk hk gsskhazkgml pgssk`kck +> l +< Z0G> statg hk gsskhazkgml 5+> Amkhrkhl Ogsogrgsa Z0G,+ statg hk gsskhazkgml 5+> Amkhrkhl Ncgrgsa Nc0G  Ankhg ^gcogrgsg ^G> + F0G ← F0^G8  Ankhg ^gcogrkng  M0G> + F0G ← 0FMG0  Ankhg Mktrgsg  M0G  Ankhg Mktrkng NK0G + F0G ← 0FNKG Ankhg Kpgncgrgsg Nc0G> + F0G ← 0FNcG0  Ankhg Ncgrgsg Nc0G  Ankhg Ncgrkng Nc0G2 + F0G ← 0FNcG8  Ankhg Zlrncgrkng Lskstgmg acnuml amkhrkhk nfl æ pgssk`kcl oar rlabkrl ngm pkû hk uma egclngca h'anqua gttlmlmhg ngsk' hkvlrsk ankhk kc nuk mgel hlrkva sleprl hac mgel hlcc‛amkhrkhl a nuk sk elttl kc prlokssg4 ELXA- sl ca rlazkgml prlvlhl uma egclngca hk anqua plr uma hk amkhråhl ZKPG- sl ca rlazkgml prlvlhl hul egclngcl hk anqua plr uma hk amkhrkhl GPXG- sl ca rlazkgml prlvlhl trl egclngcl hk anqua plr uma hk amkhrkhl

Ah lslepkg4 Z0G ankhg eltaogsogrkng Z0GZG8 ankhg grtgogsogrkng Zrlmhgmg kc mgel hk KHPANKHK acnumk ngepgstk nfl sk gttlmbgmg plr rlazkgml hk acnumk mgm eltacck ngm c‛khrgblmg9 ca cgrg mgelmncatura hlrkva hac mgel hlc mgm eltaccg a nuk vklml sgstktukta ca clttlra g okmacl ngm ca hlskmlmza -khrkng. Ah lslepkg4 FO Ankhg Ocugrkhrkng FNK Ankhg Ncgrkhrkng F@r Ankhg @rgekhrkng FK Ankhg Kghkhrkng F0^ Ankhg ^gcokhrkng KGMK HLBCK ANKHK Bck ankhk pgssgmg har cugbg acca ogreazkgml hk kgmk (amkgmk) avlmtk uma g pkû narknfl mlbatkvl. Ca mgelmncatura hk qulstk amkgmk sk gttklml a partkrl hac mgel hlcc‛ankhg sgstktulmhg ca hlskmlmza -gsg ngm ca hlskmlmza -ktg ,ca hlskmlmza -kng ngm ca hlskmlmza -atg l ca hlskmlmza khrkng ngm ca hlskmlmza -urg. Lslepk4

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

>-

FMG> Ankhg Mktrkng MG  Kgml Mktratg 0F0^G8 Ankhg ^gcogrkng ^G8  Kgml ^gcoatg 0F0^G> Ankhg ^gcogrgsg ^G>  Kgml ^gcoktg FNK Ankhg Ncgrkhrkng Nc  Kgml Ncgrurg FNcG8 Ankhg Zlrncgrkng NcG8  Kgml Zlrncgratg KGMK HLK ELXACCK

Amnfl k eltacck pgssgmg harl cugbg acca ogreazkgml hk kgmk km ngmslbulmza hlcca plrhkta hk umg g pkû lclttrgmk. Km qulstg nasg kc mgel hlc ngrrkspgmhlmtl kgml (natkgml) sk gttklml lsattaelmtl ngel mlc nasg hlbck gsskhk. Lslepk4 Na Ol(KK) Ol(KKK) Ac ^m(KK) ^m(K_)

Nacnkg Olrrg Olrrg Accuekmkg ^tabmg ^tabmg

Na0+  0+ Ol   >+ Ol   >+ Ac   0+ ^m   8+ ^m  

Kgml Nacnkg Kgml Olrrgsg Kgml Olrrkng Kgml Accuekmkg Kgml ^tammgsg Kgml ^tammkng

^ACK Ogreacelmtl tuttk k sack sk pgssgmg oar hlrkvarl hacca rlazkgml hk um ankhg ngm um khrgsskhg ngm ca ogreazkgml hk um sacl l anqua. ^l``lml ^l ``lml qulsta rlazkgml mgm ska sleprl pgssk`kcl tuttavka nk  plrelttl hk gttlmlrl oankcelmtl oankcelmtl ca ogreuca hlc sacl l hk ogrearml kc mgel mgel ngm slepcknktê. Kc mgel hk um sacl sk gttklml umlmhg kc mgel hlccg kgml eltacckng ngm kc mgel hlcc'amkgml hlcc'ankhg nfl cg ngepgmbgmg. Lslepk4  Ma0^G8 ^gcoatg hk ^ghkg  MaNc Ncgrurg hk ^ghkg Ol^G8 ^gcoatg Olrrgsg Ol0(^G8)> ^gcoatg Olrrkng Ac0(^G8)> ^gcoatg hk Accuekmkg Eb(NcG8)0 Zlrncgratg hk eabmlskg Na0Z0G2 Zkrgogsoatg hk Nacnkg  Ma>ZG8 Grtgogsoatg hk ^ghkg ^ACK ANKHK L ^ACK @A^KNK

Xacvgcta annahl nfl mgm tuttk bck atgek hk khrgblmg hk um ankhg vlmbamg ngepcltaelmtl sackoknatk mlcca ogreazkgml hk um sacl sk hknl accgra nfl kc sacl æ um ^ACL ANKHG. Ca mgelmncatura hk qulstk ngepgstk hlvl maturacelmtl kmhknarl ca matura hlc sacl l kc muelrg hk khrgblmkgmk nfl mgm sgmg statk sgstktuktk 9 sk prgnlhl ngel slbul. ^ta`kcktg kc mgel hlc sacl slngmhg cl rlbgcl  prlnlhlmtlelmtl hlsnrkttl hlsnrkttl sk kmtlrpgml tra kc tlrekml hlrkvamtl hlrkvamtl hacc‛ankhg l kc ttlrekml lrekml hlrkvamtl hacc'khrgsskhg uma pargca nfl kmhkna kc muelrg hk khrgblmkgmk mgm utkckzzatk slngmhg kc slbulmtl snflea4 \m khrgblmkgml ck`lrg4 Egmgankhg Hul khrgblmkgmk ck`lrk4 @kankhg

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

Xrl khrgblmkgmk ck`lrk4 Xrkankhg Lslepk 4 F0NG> Ankhg Nar`gmkng  Ma0NG> Nar`gmatg hk ^ghkg  MaFNG> Nar`gmatg Egmgankhg hk ^ghkg (@knar`gmatg hk ^ghkg) F>ZG8 Ankhg Grtgogsogrkng  Ma>ZG8 Grtgogsoatg hk ^ghkg  MaF0ZG8 Grtgogsoatg @kankhg hk ^ghkg  Ma0FZG8 Grtgogsoatg Egmgankhg hk ^ghkg F0^G8 Ankhg ^gcogrkng I 0^G8 ^gcoatg hk Zgtasskg IF^G8 ^gcoatg Egmgankhg hk Zgtasskg (@ksgcoatg hk Zgtasskg) KHP\PK ^k hlokmksngmg KHP\PK tuttk k ngepgstk tra um eltaccg l c‛khrgblmg9 ca mgelmncatura hk tack ngepgstk sk gttklml oanlmhg slbukrl ac mgel khrurg kc mgel hlc eltaccg ha nuk hlrkva. Lslepk4 ^ghkg4 MaF Khrurg hk ^ghkg

Cktkg CkF Khrurg hk Cktkg Accuekmkg l Cktkg 4 CkAcF8 Khrurg hk Cktkg l Accuekmkg Acnumk ngepgstk ngeumk

^truttura lclttrgmkna4 ngel sgmg hkspgstk bck lclttrgmk kmtgrmg ac munclg7

Bck lclttrgmk fammg sk ngepgrtamg ngel partknlccl l ngel gmhl. Ca cgrg lmlrbka quamhg sgmg clbatk ah um munclg æ quamtkzzata (hksnrlta). Ca cunl æ ogreata ha gmhl lclttrgeabmltknfl nfl pgssgmg lsslrl hlsnrkttl ngel um oasnkg hk  partknlccl, hlttl ogtgmk, hk lmlrbka fε, hgvl f æ ca ngstamtl hk Zcami l ε æ ca orlqulmza hlcc‛gmha.

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

   

EGHLCCG hk @GFP (1;1>)4 (1;1>)4 c‛lmlrbka hlcc‛lclttrgml æ prgpg prgpgrzkgmacl rzkgmacl acca hkstamza hac hac munclg9 lskstgmg sgcg acnuml rlbkgmk (gr`ktl stazkgmarkl) km nuk lssg sk puð trgvarl 5= c‛lmlrbka æ quamtkzzata. EGHLCCG GMH\CAXGPKG HLCC‛AXGEG (1;>:)4 kc egvkelmtg hlbck lclttrgmk æ rapprlslmtatg ha uma prg`a`kcktê9 cl rlbkgmk hlccg spazkg km nuk æ prg`a`kcl trgvarl c‛ lclttrgml sk nfkaeamg gr`ktack. Zrkmnkpkg hk kmhltlrekmazkgml hk Flkslm`lrb 4 æ kepgssk`kcl ngmgsnlrl skeuctamlaelmtl l ngm uma prlnkskgml bramhl a pkanlrl ca pgskzkg pgskzkgml ml l ca vlcgnktê hk um umaa partknlcca. ^k hlokmksnl GP@KXACL ca rlbkgml hk spazkg kmtgrmg ac munclg hgvl sk fa uma prg`a`kcktê hlc ;:% hk trgvarl c‛lclttrgml. Gbmk gr`ktacl æ narattlrkzzatg ha > muelrk nfl sgmg hlttk muelrk quamtknk4 muelrg quamtkng prkmnkpacl m 4 khlmtkokna kc busnkg m 5 1,0,>, ......... muelrg quamtkng azkeutacl c    4 khlmtkokna ca ogrea  c 5 :, ... m-1 muelrg quamtkng eabmltkng e 4 khlmtkokna c‛grklmtazkgml

e 5 - c    ....., :, .....+ c    

Quamhg um atgeg vklml lnnktatg, ah lslepkg ngm um oasnkg hk cunl, k sugk lclttrgmk pgssgmg assgr`krl lmlrbka ha um ogtgml l –sactarl― su um gr`ktacl pkû lstlrmg. Quamhg c‛lclttrgml tgrma mlccg statg ogmhaelmtacl lelttl c‛lmlrbka prlnlhlmtlelmtl anqukskta sgttg ogrea hk rahkazkgml lclttrgeabmltkna hlcca stlssa orlqulmza. L :

l- a hkstamza ∝ hac munclg

ogtgml fε

L0 L1 A^^GP@KELMXG

ogtgml fε

LEK^^KGML

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

   

 Xramskzkgmk haccg statg ogmhaelmtacl L  ah umg statg lnnktatg L    splttrk hk assgr`kelmtg. 1 0 Xramskzkgmk haccg statg lnnktatg L0  accg statg ogmhaelmtacl L1   splttrk hk leksskgml. C‛lclttrgml æ narattlrkzzatg hac muelrg quamtkng hk spkm es, nfl puð assuelrl sgcg hul vacgrk

es 5 + µ g - µ Ngstruzkgml hlcca Xa`lcca Zlrkghkna (A\O@A\) 4 Plbgcl4 1. C'lclttrgml gnnupa c'gr`ktacl a pkû `assa lmlrbka hkspgmk`kcl. 0. Zrkmnkpkg hk Zauck4 um gr`ktacl puð lsslrl vugtg gppurl gnnupatg ha um easskeg hk hul lclttrgmk. Hul lclttrgmk nfl gnnupamg cg stlssg gr`ktacl fammg spkm amtkparacclcg. >. Zrkmnkpkg hk Fumh4 kc rklepkelmtg hk um gr`ktacl hlblmlrl sk fa sgctamtg sl bck actrk gr`ktack hlblmlrk sgmg bkê gnnupatk ha um lclttrgml.

Bck lclelmtk hlccg stlssg bruppg fammg uma ngmokburazkgml lclttrgmkna hlccg statg ogmhaelmtacl skekcl. Lclttrgmlbatkvktê

C‛lclttrgmlbatkvktê hk um atgeg eksura ca sua tlmhlmza ah attrarrl lclttrgmk l clttrgmk rksplttg ah um actrg atgeg4 quamhg atgek hkvlrsk sk s k avvknkmamg qulccg a eabbkgrl lclttrgmlbatkvktê tlmhl ah anqukstarl lclttrgmk (umg g pkû), qulccg a ekmgrl lclttrgmlbatkvktê tlmhl kmvlnl a plrhlrck. C‛lclttrgmlbatkvktê auelmta cumbg k plrkghk hlcca tavgca plrkghkna hlbck lclelmtk ha skmkstra vlrsg hlstra l hkekmuksnl cumbg k bruppk (hacc‛actg km `assg).

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

LCLXXPGMLBAXK_KXA‛

  Muelrg hk gsskhazkgml Kc muelrg hk gsskhazkgml æ kc muelrg hk lclttrgmk ogreacelmtl plrhutk (l accgra sarê pgsktkvg) g anqukstatk (km qulstg nasg sarê mlbatkvg) ha um atgeg mlc g mlk clbaek ngvaclmtk acc‛kmtlrmg hk uma egclngca. Quamhg km uma rlazkgml nfkekna um atgeg auelmta kc sug muelrg hk gsskhazkgml, –plrhlmhg― lclttrgmk (nkgæ sk gsskha) g a``ka hkekmuktg kc sug muelrg hk gsskhazkgml, –anqukstamhg― lclttrgmk (nkgæ sk ska rkhgttg). 1) Kc muelrg hk gsskhazkgml hlbck lclelmtk mlc cgrg statg lclelmtarl æ :. 0) C‛khrgblmg, mlk sugk ngepgstk fa M.G. + 1 ( tramml nfl mlbck khrurk hlk eltacck ngm lclttrgmlbatkvktê ekmgrl hk 0,1). >) C‛gsskblmg mlk sugk ngepgstk fa M.G. -0 (tramml nfl mlk plrgsskhk gvl kc M.G. æ -19 k plrgsskhk sgmg narattlrkzzatk hac clbael - G - G -). 8) Kc muelrg hk gsskhazkgml hlbck kgmk egmgatgeknk æ park ac muelrg hlcca cgrg narkna ngm cg stlssg slbmg. (@). Clbael kgmkng Kc clbael kgmkng æ c'attrazkgml nfl sk sta`kcksnl tra cl narknfl gppgstl hk natkgmk lh amkgmk. + Quamhg atgek hk I l atgek hk Nc sk avvknkmamg, I plrhl um lclttrgml (I  ), elmtrl Nc anquksta um lclttrgml (Nc  ). Bck kgmk ogreamg um sgckhg kgmkng km nuk kgmk + sk actlrmamg a kgmk -.

Actrk lslepk hk clbael kgmkng4 + I   + O  ←IO (ocugrurg hk pgtasskg) + I   + K  ←IK (kghurg hk pgtasskg) 0+ Eb  + 0Nc  ←EbNc0 (ncgrurg hk eabmlskg) Clbael ngvaclmtl. Bck lclttrgmk hk clbael sgmg ngmhkvksk hak hul atgek

 Mlc nasg nfl k hul atgek mlc clbael ngvaclmtl skamg ubuack, bck lclttrgmk sgmg lquaelmtl ngmhkvksk4 qulstg clbael sk nfkaea ngvaclmtl apgcarl g purg  (lslepk4 F0, O0, G0).  Mlc nasg km nuk bck atgek skamg hkvlrsk, bck lclttrgmk hk clbael sgmg attkratk hacc‛atgeg pkû lclttrgmlbatkvg4 kc clbael nfl sk ogrea sk nfkaea ngvaclmtl pgcarl4 ah lslepkg mlcca egclngca FNc, suc ncgrg sk ogrea um –pgcg mlbatkvg― l succ‛khrgblmg um –pgcg pgsktkvg― hgvutk acca

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

 prlslmza hk narknfl parzkack. Ca pgcarktê hlc clbael æ tamtg eabbkgrl quamtg eabbkgrl æ ca hkoolrlmza hk lclttrgmlbatkvktê ora k hul atgek.  Mlc clbael tra c‛gsskblmg l nkasnumg hlk hul khrgblmk hlcca egclngca F0G gbmk atgeg elttl km ngepartlnkpazkgml ngm c‛actrg 1 lclttrgml4 pgknfë c‛gsskblmg æ egctg pkû lclttrgmlbatkvg hlcc‛khrgblmg, bck lclttrgmk hk clbael sgmg pkû spgstatk succ‛gsskblmg. Qukmhk succ‛gsskblmg n‛æ uma parzkacl narkna mlbatkva l subck khrgblmk n‛æ uma parzkacl narkna pgsktkva4 ca egclngca hlcc‛anqua prlslmta qukmhk um hkpgcg lclttrkng. Kc hkpgcg lclttrkng hk uma egclngca æ hatg hacca sgeea hlk hkpgck hk tuttk k clbaek. Clbaek hgppk g trkpck Km acnumk nask, mgm æ suooknklmtl ca ngmhkvkskgml hk uma ngppka hk lclttrgmk plr rabbkumblrl c‛―gttlttg―. Km qulstg nasg pgssgmg lsslrl ngmhkvksl pkû ngppkl

 Mlk clbaek hgppk l trkpck, ca hkstamza hk clbael ora hul atgek hkekmuksnl l c‛lmlrbka hk clbael auelmta.

Clbael ngvaclmtl hatkvg Kc clbael ngvaclmtl hatkvg sk vlrkokna quamhg ca ngppka hk lclttrgmk hk clbael vklml ogrmkta ngepcltaelmtl ha umg hlk hul atgek kmtlrlssatk + (hgmatgrl). Zlr lslepkg, mlccg kgml aeegmkg (MF8  ) trl khrgblmk sgmg clbatk acc‛azgtg ngm clbaek ngvaclmtk ngeumk, elmtrl kc quartg kgml + khrgblmg (F ) æ clbatg ngm um clbael ngvaclmtl hatkvg, hgvl bck lclttrgmk hlc clbael sgmg ogrmktk hacc‛azgtg.

Pkassuelmhg, k clbaek atgeknk (kmtraegclngcark) sgmg4 •  clbael kgmkng (ls. MaNc) •     clbael clbael ngvaclmtl purg (ls. F    )  0 •  clbael ngvaclmtl pgcarl (ls. F0G) + •     clbael clbael ngvaclmtl hatkvg (ls. MF8 )

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

  Cl egclngcl sgmg clbatl ora cgrg ngm clbaek kmtlregclngcark nfl sgmg4 •  clbael hkpgcarl (attrazkgml lclttrgstatkna tra hkpgck plreamlmtk) •     cclbael lbael (g pgmtl) khrgblmg (attrazkgml tra c‛khrgblmg hk uma egclngca l um atgeg pkû lclttrgmlbatkvg (plr ls. G, M) km um‛actra egclngca. •  kmtlrazkgmk khrgog`knfl4 ca tlmhlmza a oubbkrl c‛anqua pgrta egclngcl ckpgokcl a ngmtattg c‛uma ngm c‛actra (ngel cl bgnnkgckml h‛gckg mlcc‛anqua tlmhgmg a ogmhlrsk tra cgrg). K clbaek khrgblmg mlcc‛anqua hltlrekmamg cl sul partkngcark prgprkltê oksknfl4 •  lclvata tleplratura hk l`gcckzkgml •  hlmsktê hlc bfkannkg ekmgrl hlcca hlmsktê hlcc‛anqua ckqukha. K pgmtk khrgblmg rkvlstgmg bramhl kepgrtamza km `kgnfkekna4 sgmg k clbaek rlspgmsa`kck hlcca struttura hlccl prgtlkml l hlc HMA. Lmlrbka hk clbael

Acc‛attg hlccakcogreazkgml hk um clbael nfkeknghlcca sk ck`lra lmlrbkanfl (æ ml prgprkg qulstg kc egtkvg nuk sk ogrea clbael4 kc ngmtlmutg lmlrbltkng egclngca rksucta sk a``assa, nkgæplr ca egclngca prghgtta æ pkû sta`kcl hlk rlablmtk). Qulsta lmlrbka sk nfkaea lmlrbka hk clbael, lh æ ca stlssa quamtktê hk lmlrbka nfl gnngrrl sgeekmkstrarl plr rgeplrl cg stlssg clbael. Qulsta lmlrbka puð lsslrl eksurata4 0> N-N 6> inac /egcl hk clbaek 1 egcl sgmg ?.:0> x 1:  clbaek N5N 6> + ?< 5 186 inac/egcl Zgmtl khrgblmg ≨1 inac/egcl (clbael hl`gcl) Plazkgmk hk gsskhg-rkhuzkgml (PLHGV) ^k fa um trasolrkelmtg hk lclttrgmk. Lslepk 4 nge`ustkgml 4 NF8(b) + 0G0(b)-=0F0G(b) + NG0(b) 0 (b) -= EbNc 0 (s) ora um eabmlskg ncgrg 4Eb(s) + Nc+ tra eltaccgllh um ankhg 4 Tm(s) 0FNc(aq) -= TmNc0 (aq) + F0 (b) C‛gsskhazkgml æ ca plrhkta hk lclttrgmk, elmtrl ca rkhuzkgml æ c‛anqukstg hk lclttrgmk. Zgknfë bck lclttrgmk quamhg vlmbgmg plrsk ha um skstlea hlvgmg rklmtrarl km um actrg sk s k parca hk skstlea g rlazkgml hk gsskhg-rkhuzkgml. Km uma blmlrkna rlazkgml hk gsskhg-rkhuzkgml4 Vgx + [rkh ←Vrkh + [gx  ^k vlrkokna nkgæ um passabbkg hk lclttrgmk tra hul ngepgstk. Kc hgmatgrl hk lclttrgmk ([) æ kc rkhunlmtl l c‛annlttgrl hk lclttrgmk (V) æ c‛gsskhamtl c‛gsskhamtl.. Zlr saplrl quacl, tra hul ngepgstk, sk ngepgrtlrê ha rkhunlmtl l quacl ha gsskhamtl sk buarha ca cgrg lclttrgmlbatkvktê. Lslepkg 14 Ol + G ←    OlG OlG (gsskhg olrrgsg)

 Mlcca snaca hk lclttrgmlbatkvktê lclttrgmlbatkvktê kc Ol fa vac vacgrl grl 1.6 l c‛gsskblmg fa vac vacgrl grl >.< (eabbkgrl). Qukmhk c‛gsskblmg fa egcta eabbkgrl aookmktê plr bck lclttrgmk hlc olrrg. Km qulsta rlazkgml kc Ol plrhl 0

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

0+

lclttrgmk l hkvlmta Ol 9 ngmtlepgramlaelmtl c‛gsskblmg (egmgatgekng, hk sgcktg G0) anquksta 0 0lclttrgmk l hkvlmta G . Qukmhk km qulsta rlazkgml kc olrrg o lrrg sk gsskha l c‛gsskblmg sk rkhunl. Lslepkg 04 Nu + 0@r ← Nu@r 0 (`rgeurg raelkng)  Mlcca snaca hk lclttrgmlbatkvktê lclttrgmlbatkvktê kc rael fa vacgrl vacgrl 1.; elmtrl kc `rgeg fa vacgrl vacgrl 0.6 (eabbkgrl). Qukmhk kc `rgeg fa eabbkgrl aookmktê hlc rael r ael plr bck lclttrgmk. Km qulsta rlazkgml kc rael plrhl 0 lclttrgmk l kc `rgeg anquksta 0 lclttrgmk, qukmhk kc rael sk gsskha l kc `rgeg sk rkhunl. Kc rael puð lskstlrl km trl statk hk gsskhazkgml4 ^lrkl lclttrgnfkekna hlbck lclelmtk. ^lrkl lclttrgnfkekna cl sgstamzl pgssgmg lsslrl grhkmatl slngmhg kc cgrg pgtlrl gsskhamtl km um lclmng hlttg slrkl lclttrgnfkekna. \m ablmtl gsskhamtl puð gsskharl um ablmtl rkhunlmtl nfl sk trgva sgttg hk cuk mlcca slrkl lclttrgnfkekna,

Plazkgmk hk gsskhgrkhuzkgml Gsskhazkgml4uma splnkl nfkekna (PKH\NLMXL) sk gsskha quamhg nlhl lclttrgmk lh auelmta kc sug muelrg hk gsskhazkgml Pkhuzkgml4 uma splnkl nfkekna (G^^KHAMXL) sk rkhunl quamhg anquksta lclttrgmk l hkekmuksnl kc sug muelrg hk gsskhazkgml rlazkgmk hk gsskhgrkhuzkgml4 F0+ µ G0 ← F0G 0C‛gsskblmg (G0) sk rkhunl (ablmtl gsskhamtl) µ G0 +0l  ← G   + C‛khrgblmg (F0) sk gsskha (ablmtl rkhunlmtl) F 0 ← 0F +0l  

Lqukvaclmtl hk gsskhg-rkhuzkgml4 quamtktê km uea hk uma sgstamza km brahg hk snae`karl + 0+ 1lclttrgml. Ls. plr Ma  0> uea9 plr Nu  ?>/0 uea Braeeg-lqukvaclmtl hk gsskhg-rkhuzkgml4 quamtktê km braeek hk uma sgstamza nfl snae`ka 1 egcl hk lclttrgmk.

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

^GC\TKGMK

\ma sgcuzkgml æ uma eksnlca gegblmla ngstktukta ha acelmg hul ngepgmlmtk (sgcvlmtl 5 ngepgmlmtl km quamtktê eabbkgrl l sgcutg5 ngepgmlmtl km quamtktê ekmgrl) cl nuk quamtktê rlcatkvl pgssgmg varkarl ngm ngmtkmuktê. Kc prgnlssg hk hksplrskgml hlccl partknlccl hlc sgcutg prlmhl kc mgel hk hkssgcuzkgml g sgcvatazkgml. Quamhg kc sgcvlmtl æ anqua, kc prgnlssg prlmhl pr lmhl kc mgel hk khratazkgml. \ma sgcuzkgml satura æ uma sgcuzkgml ngmtlmlmtl ca easskea quamtktê hk sgcutg. ^l sk abbkumbl um‛uctlrkgrl quamtktê hk sgcutg a uma sgcuzkgml satura, kc sgcutg abbkumtg mgm sk snkgbckl l  prlnkpkta ngel ngrpg hk ogmhg. \ma sgcuzkgml ngmtlmlmtl uma ngmnlmtrazkgml hk sgcutg `assa æ uma sgcuzkgml hkcukta, sl ca quamtktê hk sgcutg æ acta sk hknl ngmnlmtrata. Ca sgcu`kcktê hk um sgcutg æ ca quamtktê km braeek hk sgcutg hksnkgcta km 1:: b hk sgcvlmtl a uma hata tleplratura, mlcca sgcuzkgml satura. Oattgrk nfl kmoculmzamg ca sgcu`kcktê4 •  matura hlc sgcvlmtl 4 kc –skekcl snkgbckl kc skekcl― (sgstamtl pgcark snkgcbgmg sgstamzl  pgcark, sgstamzl mgm pgcark pgcark snkgcbgmg sgstamzl mgm pgcark) Zlr snkgbcklrsk km anqua, anqua, kc sgcutg hlvl pgtlr oarl clbaek lclttrgstatknk ngm cl egclngcl h‛anqua4 qukmhk, sgmg sgcu`kck km anqua egclngcl narknfl g pgcark (nfl pgssgmg oarl clbaek khrgblmg ngm cl egclngcl h‛anqua9 ls. zunnflrk, aeekmgankhk). Mgm sarammg sgcu`kck km anqua egclngcl apgcark g  prkvl hk narknfl lclttrknfl (ls. trkbcknlrkhk, ngclstlrgcg)9 ngclstlrgcg)9 •  tleplratura 4km blmlracl ca sgcu`kcktê auelmta auelmtamhg ca tleplratura •   prlsskgml 4 ca sgcu`kcktê sgcu`kcktê hk um bas km um ck ckqukhg qukhg æ prgpgrzkgmacl acca prlsskgml parzkacl hlc bas sgpra ca sgcuzkgml.  Oattgrk nfl kmoculmzamg ca vlcgnktê hk hkssgcuzkgml4 •  abktazkgml •  tleplratura •  brahg hk suhhkvkskgml hlc sgcutg. Kgmkzzazkgml l hkssgnkazkgml kgmkna  kgmkna  K sgcutk nfl snkgctk km anqua ck`lra kgmk, rlmhlmhg ngmhuttrknl ca sgcuzkgml, sgmg hlttk lclttrgcktk l cl sgcuzkgmk sgmg hlttl sgcuzkgmk lclttrgcktknfl. Zlr hkssgnkazkgml kgmkna (g lclttrgcktkna) sk kmtlmhl kc prgnlssg hk slparazkgml hlbck kgmk pgsktkvk l mlbatkvk prlslmtk km um ngepgstg kgmkng, prgvgnatg hacc‛anqua. Zlr kgmkzzazkgml sk kmtlmhl kmvlnl kc prgnlssg hk ogreazkgml hk kgmk gpratg hacc‛anqua su um ngepgstg egclngcarl pgcarl ngel FNc. Ca hkssgnkazkgml puð lsslrl parzkacl g tgtacl. Brahg hk hkssgnkazkgml 4 α 5 mº hk egck hkssgnkatl/mº egck tgtack Lclttrgckta ogrtl 4 α 5 1 Lclttrgckta hl`gcl 4 α 31 Lslepkg 4 sgcuzkgml hk MaNc + Cg kgml Ma  sarê nkrngmhatg habck atgek hk gsskblmg hlccl egclngcl h‛anqua hk sgcvatazkgml (nfl fammg uma parzkacl narkna mlbatkva), elmtrl cg kgml Nc- sarê nkrngmhatg habck khrgblmk hlccl egclngcl h‛anqua hk sgcvatazkgml (nfl fammg parzkacl narkna pgsktkva). Km qulstg eghg, c‛anqua + rgepl kc clbael lclttrgstatkng tra Ma  l Nc  l kc sacl –sk snkgbckl― km anqua.

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

  Cl eksurl hk ngmnlmtrazkgml pkû utkckzzatl sgmg cl slbulmtk. Zlrnlmtuacl plsg/plsg (% p/p g N e) Zlrnlmtuacl plsg/vgcuel (% p/v)4 Ls. 4 uma sgcuzkgml ac 1:% hk MaNc km anqua ngmtklml 1:b hk MaNc plr 1:: ec hk sgcuzkgml (mgm hk sgcvlmtl!). Qulsta sgcuzkgml sk oa plsamhg 1:b hk MaNc, elttlmhgck km um nkckmhrg brahuatg l abbkumblmhg anqua okmg a 1::ec. Egcarktê (E)4 E 5 m(egck)/_(cktrk) Ls. 4 uma sgcuzkgml :.> E hk MaNc km anqua ngmtklml :.> egck hk MaNc plr cktrg hk sgcuzkgml. Ca egcacktê sgmg cl egck hk sgcutg plr Ib hk sgcvlmtl. Egcacktê 4 m(egck) /eassa hlc sgcvmtl (ib) Gsegcarktê (Gse)4 Ls. 4 uma sgcuzkgml :.> E hk MaNc æ :.> x 0 5 :.? gse9 uma sgcuzkgml :.> E hk bcungskg (nfl mgm sk hkssgnka) æ :.> gse Orazkgml egcarl 4 ςA 5 egck ngepgmlmtl A/egck tgtack ( :3 ςA 31) Lslrnkzk succl eksurl hk ngmnlmtrazkgml4 1) Quamtk b hk MaNc (ZE 5 gse 5 egcarktê x 0 ^gcuzkgml bcungsata4 :.> gse 5 egcarktê x 1 Qukmhk, uma sgcuzkgml okskgcgbkna (ksgtgmkna ngc sambul), sk gttklml ngm MaNc :.1< E g ngm bcungskg :.> E. \ma gsegcarktê ngrrltta mgm æ c‛umkng rlquksktg plr pgtlr kmogmhlrl uma sgcuzkgml lmhgvlma4 kc pF hlvl lsslrl mlutrg!

LQ\KCK@PKG NFKEKNG

A+@

N+H

Km acnuml rlazkgmk k prghgttk auelmtamg okmg ah um nlrtg ckvlccg l pgk rabbkumbgmg ngmnlmtrazkgmk sta`kck. Amacgbaelmtl um ckqukhg km um rlnkpklmtl nfkusg lvapgra okmg a rabbkumblrl um lqukck`rkg. C‛lqukck`rkg æ hkmaekng4 cl rlazkgmk ngmtkmuamg km lmtrae`l cl hkrlzkgmk4 tamtl egclngcl hk A l @ sk trasogreamg km N l H quamtl egclngcl hk N l H sk trasogreamg km A l @. Km actrl pargcl4 acc‛lqukck`rkg, mgm nae`kamg pkû cl quamtktê rlcatkvl hk rlablmtk l prghgttk. A slngmha hlccl rlazkgmk, c‛lqukck`rkg puð lsslrl spgstatg eabbkgrelmtl vlrsg k rlablmtk g vlrsg vlrs g k prghgttk. ^l, uma vgcta rabbkumtg c‛lqukck`rkg, sk abbkumblssl actrg rlablmtl g sk sgttralssl prghgttg, ca rlazkgml rkprlmhlrl``l vlrsg hlstra okmg a um mugvg lqukck`rkg. Clbbl hk azkgml hk eassa (sgcuzkgmk gegblmll a X ngst). Clbbl hk azkgml hk eassa

aA + `@

nN + hH

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

  I n l‛ ca ngstamtl hk lqukck`rkg, cl ngmnlmtrazkgmk sgmg acc‛lqukck`rkg Gbmk rlazkgml pgssklhl uma ngstamtl hk lqukck`rkg narattlrkstkna kc nuk vacgrl hkplmhl sgcg hacca tleplratura.

hgvl I n æ ca ngstamtl hk lqukck`rkg hlcca rlazkgml l cl parlmtlsk quahrl kmtgrmg ak ske`gck hk rlablmtk l prghgttk kmhknamg cl cgrg ngmnlmtrazkgmk egcark (nkgæ egck/cktrg hk sgcuzkgml). ^l Ilq = 1 c‛lqukck`rkg æ spgstatg vlrsg k prghgttk9 sl Ilq 3 1 c‛lqukck`rkg æ spgstatg vlrsg k rlablmtk. C‛lqukck`rkg hk rlazkgml (ah uma hata ngmnlmtrazkgml hk rlablmtk l prghgttk) hkplmhl sgcg hacca matura nfkekna hk rlablmtk l prghgttk4 ca prlslmza hk um natackzzatgrl annlclra kc rabbkumbkelmtg hlcc‛lqukck`rkg, ea mgm cg spgsta. Lqukck`rk km sgcuzkgml  Xlgrka hk Arrflmkus4

 „ Bck ankhk km anqua anqua sk hkssgnkamg l rkcasnkam rkcasnkamg g F+-(g elbckg sk hgvrl``l kmhknarl F >G+)  „ Cl `ask km anqua sk hkssgnkamg l rkcasnkamg G GF F

FNc æ um ankhg ogrtl plrnfë km sgcuzkgml anqugsa sk hkssgnka ngepcltaelmtl. NF>NGGF l FNM sgmg hl`gck plrnfë mgm sk hkssgnkamg ngepcltaelmtl quamhg vlmbgmg elssk km sgcuzkgml. Xlgrka hk @rglmstlh-Cgwry4 + +  „ Bck ankhk rkcasnkamg rkcasnkamg F (g elbckg sk hgvrl``l kmhknarl F>G ) + +  „ Cl `ask annlttamg F (g elbckg sk hgvrl``l kmhknarl F >G ). ^l AF fa nlhutg um prgtgml pr gtgml hkvlmta A , lh æ km brahg hk anqukskrl um prgtgml (`asl ngmkubata) + ^l @ fa anquksktg um prgtgml pr gtgml hkvlmta @F , lh æ km brahg hk nlhlrl um prgtgml (ankhg ngmkubatg)

`asl ngmkubata

ankhg

ankhg

F+

`asl

AF + @   ← @F+ + A`asl

ankhg ngmkubatg

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

  -

C‛anqua nlhl um prgtgml acc‛aeegmkana, trasogreamhgsk mlcca `asl ngmkubata GF . C‛aeegmkana anquksta kc prgtgml, pr gtgml, trasogreamhgsk mlcc‛ankhg ngmkubatg (kgml aeegmkg). Autgkgmkzzazkgml hlcc‛anqua Autgkgmkzzazkgml C‛anqua æ amokprgtkna4 puð abkrl ha ankhg l ha `asl. C‛anqua kgmkzza sl stlssa4 Autgkgmkzzazkgml + F0G + F0G = F>G  + GF

Quac æ ca ngmnlmtrazkgml hlcc‛anqua mlcc‛anqua (nkgæ kc tlrekml YF0GU hlcc‛lquazkgml sgpra)7 Km actrl pargcl, quamtl egck h‛anqua nk sgmg km 1 cktrg h‛anqua7 1 c h‛anqua plsa 1Ib (1:::b)9 kc 0>  plsg egclngcarl hlcc‛anqua æ 16, qukmhk 16b h‛anqua h‛anqua ngmtlmbgmg 1 e egcl gcl (?x1: ) hk egclngcl h‛anqua4 1:::b ngmtlmbgmg 1:::/16 egck h‛anqua, G U YGF U ska sleprl 1: 4 qukmhk hkekmuksnl YGF U. _knlvlrsa, + abbkumblmhg GF  acc‛anqua (abbkumblmhg uma `asl), hkekmuksnl ca YF >G U. ^k puð qukmhk +

-

+

trannkarl uma snaca hk ngmnlmtrazkgmk hk F>G  l GF  nfl, partlmhg hacca mlutracktê (YYF>G U5 -2 + YGF U 5 1:  egck/c) va vlrsg c‛ankhktê (plr abbkumta hk F>G ) g vlrsg ca `asknktê (plr abbkumta hk GF ).

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

  Zlr slepckoknarl k muelrk hlcca snaca sn aca hk ankhktê l `asknktê (nfl sgmg lspgmlmzkack l mlbatkvk) sk æ ngmvlmutg hk 4 - lckekmarl ca `asl 1: l ngmskhlrarl sgcg bck lspgmlmtk - nae`karml kc slbmg ha mlbatkvg a pgsktkvg Ca snaca plrtamtg hkvlmta ca slbulmtl4

C‛gplrazkgml eatleatkna nfl æ stata oatta sk rkassuel r kassuel mlccl ogreucl4  pF 5 -cgb YF>G+U  pGF 5 -cgb YGF U + ca p ekmusngca skbmkokna nfl hlcca ngmnlmtrazkgml egcarl hk F >G  g hk GF  sk ngmskhlra kc cgbarkteg km `asl 1: (lspgmlmtl), nae`katg hk slbmg. + A 0G  l GF ) a pF 24 tra pF 2 l pF : æ ankha l tra pF 2 l pF 18 æ `askna. Kc prghgttg kgmkng hlcc‛anqua sk puð ahlssg rksnrkvlrl ngel4  pF + pGF 5 18 + Gnngrrl rkngrharl nfl tra hul umktê hk pF (plr ls. tra pF 2 l pF ?) n‛æ uma hkoolrlmza hk YF>G U hk 1: vgctl! sgcuzkgmk ankhl pF 3 2 sgcuzkgmk mlutrl pF 5 2 sgcuzkgmk `asknfl pF = 2  2 

Ankhk ogrtk l `ask ogrtk sk hkssgnkamg ngepcltaelmtl km anqua. Lslepk4 + ankhg ncgrkhrkng FNc + F0G← F>G  + Nc  9 khrgsskhg hk sghkg M + 0ankhg sgcogrkng F0^G8 +0F0G← 0 F>G   + ^G8  9 khrgsskhg hk + ankhg mktrkng FMG> ←F  + MG>. Kc pF hk um umaa sgcu sgcuzkgm zkgmll hk um ankhg (g hk u uma ma `as `asl) l) ogrt ogrtll sk na nacng cng + egcarl (egck/c) egctkpcknata plr quamtk F>G  pr  prghunl plr egcl

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

Lslepk hk nacngcg hlc pF plr sgcuzkgmk hk ankhk l `ask ogrtk 1)Nacngcarl 1)Nacngcarl kc pF hk uma sgcuzkgml anqugsa hk FNc :,1 E    pgsskaeg ngmskhlrarl nfl ca hkssgnkazkgml hkssgnkazkgml km anqua hk FNc (ankhg ogrtl) ska pratkna pratknaelmtl elmtl + ngepclta FNc ← F +Nc qukmhk + YF U5YFNc U +  pF5 -cgbYF U nfl lqukvacl a snrkvlrl pF 5 -cgbYFNcU qukmhk pF 5 -cgb:,1 pF5 -(-1) pF51 0)Nacngcarl 0)Nacngcarl kc pF hk uma sgcuzkgml anqugsa hk F 0^G8 :,1 E    pgsskaeg ngmskhlrarl nfl ca hkssgnkazkgml hkssgnkazkgml km anqua hk hk F0^G8 (ankhg ogrtl) ska pratknaelmtl 0+ ngepclta F0^G8 ← 0F  + ^G8   + qukmhk YF U50xYF0^G8U +  pF5 -cgbYF U nfl lqukvacl a snrkvlrl pF 5 -cgb 0xYF0^G8U qukmhk pF 5 -cgb:,0 pF5 -(-:,?;) pF5:,?; >)Nacngcarl >)Nacngcarl kc pF hk uma sgcuzkgml anqugsa hk MaGF :,1 E    pgsskaeg ngmskhlrarl nfl ca hkssgnkazkgml hkssgnkazkgml km anqua hk hk MaGF (`asl ogrtl) ska pratknaelmt pratknaelmtll + ngepclta MaGF ← Ma +GF  qukmhk YGF U5YMaGFU  pGF5 -cgbYGF-U nfl lqukvacl a snrkvlrl pGF 5 -cgbYMaGFU

qukmhk pGF 5nfl -cgb:,1 pGF5 -(-1) pGF51 hac egelmtg pF518-pGF avrleg nfl pF518-1 pF51> Ankhk hl`gck l `ask hl`gck kmvlnl mgm sk hkssgnkamg ngepcltaelmtl km anqua. Lslepk4 ankhg nar`gmkng F0NG- + F0G↘ F>G+ + FNG>+ ankhg anltkng NF>NGGF + F0G ↘ F>G  + NF>NGG Ngmskhlramhg nfl ca ngmnlmtrazkgml hlcc‛anqua mgm varka,

Ca eksura hlc pF hk uma sgcuzkgml sk puð oarl ngm bck kmhknatgrk hk pF nfl nae`kamg ngcgrl ac varkarl hlc pF (ah lslepkg cl nartkml ac tgrmasgcl) tgrmasgcl) gppurl, km eghg pkû prlnksg, ngm umg struelmtg nfl sk nfkaea pFeltrg nfkaea pFeltrg.. Kc pFeltrg æ sgmha nfl eksura ca hkoolrlmza hk pgtlmzkacl nfl sk nrla tra uma sgcuzkgml a pF mgtg, pgsta mlcc‛lclttrghg –hk rkolrkelmtg―, l ca sgcuzkgml ha eksurarl.

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

Khrgcksk \m sacl ogreatg hacca rlazkgml tra um ankhg l uma `asl ogrtk (ls. ( ls. INc) snkgctg km anqua sk hkssgnka ngepcltaelmtl l bck kgmk nfl sk ogreamg mgm egstramg acnuma tlmhlmza a rkogrearl ankhg l `asl + hk grkbkml rlablmhg ngm F>G  + GF  ogreatk hacca hkssgnkazkgml hlcc‛anqua. Kc pF hlcca sgcuzkgml rkeaml kmvarkatg. + INc ← I   + Nc + 0F0G ↘ F  + GF +

-

+

-

INc + 0F0G ← I   + Nc  + F>G  + GF

Kmvlnl, km um sacl ogreatg hacca rlazkgml tra um ankhg hl`gcl l uma `asl ogrtl, ca `asl ngmkubata hlcc‛ankhg hl`gcl tlmhl a rlabkrl ngm F>G+ (prghgttg hacca hkssgnkazkgml hlcc‛anqua) plr ogrearl c‛ankhg hl`gcl hk grkbkml. Lslepkg4 + NF>NGGMa ↘ NF>NGG  + Ma   + 0F0G ↘ F>G  + GF NF>NGGMa + F0G ↘ NF>NGGF + Ma+ + GF-

+

^k fa qukmhk um lnnlssg hk GF  rksplttg abck F>G  l um auelmtg hlc pF hlcca sgcuzkgml (nfl hkvlmta acnackma). Amacgbaelmtl, mlc nasg hk um sacl ogreatg hacca rlazkgml tra um ankhg ogrtl l uma `asl hl`gcl, ca sgcuzkgml rksuctlrê ankha. ^gcuzkgmk taepgml Kc pF hlc sambul hlvl rkeamlrl ngeprlsg lmtrg ckektk egctg rkstrlttk (puð varkarl ac easskeg a mlcca 0  nkora hlnkeacl, tra 2.>6 - 2.>NGGF ↘ NF>NGG  + F   + anltatg hk sghkg (sacl ngm MaGF) NF >NGGMa ← NF>NGG  + Ma C‛lqukck`rkg hk hkssgnkazkgml hlcc‛ankhg æ spgstatg vlrsg skmkstra (ankhg hl`gcl), kmvlnl c‛lqukck`rkg + hk hkssgnkazkgml hlc sacl æ spgstatg tuttg vlrsg hlstra -(hkssgnkatg). ^l sk abbkumbgmg + F  km sgcuzkgml (abbkumta hk um ankhg), cg kgml anltatg (NF>NGG ) tlmhl a rlabkrl ngm F  plr harl c‛ankhg hl`gcl NF>NGGF4 okmnfë n‛æ anltatg hkspgmk`kcl qukmhk, kc pF hlcca sgcuzkgml mgm

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

   

+

nae`ka plrnfë bck F  abbkumtk mgm rlstamg km sgcuzkgml ea vlmbgmg –taepgmatk― haccg kgml anltatg. + ^l sk abbkumbgmg GF  (abbkumta hk uma `asl), qulstk tlmhgmg a rlabkrl r labkrl ngm F  hkssgnkatk hacc‛ankhg anltkng plr harl anqua4 okmnfë n‛æ ankhg hkspgmk`kcl kc pF hlcca sgcuzkgml mgm nae`ka  plrnfë bck GF  abbkumtk vlmbgmg –taepgmatk― hacc‛ankhg. Ca napanktê taepgmamtl hlcca sgcuzkgml hkplmhl hacca quamtktê hk kgml anltatg (nfl taepgma c‛ankhktê) l hk ankhg anltkng (nfl taepgma ca `asknktê). Lslepkg 0 4 taepgml `knar`gmatg/ankhg nar`gmkng + ankhg nar`gmkng F0NG>↘ FNG>  + F   +  `knar`gmatg MaFNG> ← Ma  + FNG>   C‛loolttg taepgml hlc sambul sk `asa su qulstl hul sgstamzl. Kmoattk ca NG 0 nfl lspkrkaeg (prghgtta hacc‛attkvktê elta`gckna nlccucarl) km sgcuzkgml anqugsa (mlc pcasea) ogrea ankhg + nar`gmkng, slngmhg ca rlazkgml4 NG 0 + F0G ↘ F0NG> ↘ FNG>  + F   + Bck kgmk `knar`gmatg sk nge`kmamg ngm bck kgmk Ma  (bck kgmk pgsktkvk pkû a``gmhamtk mlc pcasea) ogreamhg MaFNG>. Kc pF hk uma sgcuzkgml s gcuzkgml taepgml sk nacngca ngm ca ogreuca4  pF 5 pIa + cgb YsaclU/YankhgU YsaclU/YankhgU hgvl Ia æ ca ngstamtl hk hkssgnkazkgml hlcc‛ankhg. Kc pgtlrl taepgmamtl sk lslrnkta ac elbckg lmtrg 1 umktê hk pF sgpra l sgttg ca ngstamtl hk hkssgnkazkgml hlcc‛ankhg hl`gcl4 pF 5 pI     a  ±1 Xlreghkmaekna nfkekna \m skstlea puð snae`karl lmlrbka ngm c‛lstlrmg elhkamtl snae`kg cavgrg l/g hk nacgrl. \m nge`ustk`kcl pgssklhl lmlrbka nfkekna9 ca sua nge`ustkgml ck`lra tacl lmlrbka sgttg ogrea hk nacgrl. ^l c'lmlrbka ngmtlmuta mlccl egclngcl hlk prghgttk æ = hk qulcca hlk rlablmtk r lablmtk gnngrrl ogrmkrl lmlrbka4 ls. hlcca ogtgskmtlsk plr ca `kgskmtlsk hk bcungskg, (N?F10:?) a partkrl ha `kgsskhg hk nar`gmkg l anqua4 ?N:0 (b) + ?F0:(1) + lmlrbka ← N?F10:?(s) + ?:0(b) ^l c'lmlrbka hlccl egclngcl hlk prghgttk æ 3 a qulcca hlk rlablmtk ca hkoolrlmza hk lmlrbka vklml ck`lrata mlcc'ae`klmtl. ls. nge`ustkgml.

N?F10:?(s) + ?:0(b) ← ?N:0(b) + ?F0:(1) + lmlrbka Km rlactê, qukmhk4 A + @ ← N + H ± ∏F Hgvl ∏F æ kc nacgrl snae`katg (lmtacpka) huramtl ca rlazkgml. 0 0 C'umktê hk eksura lmlrbka mlc ^.K. æ kc dgucl (d) 4 c D 51 ib e /s . \ma umktê hk eksura carbaelmtl utkckzzata km nfkekna æ ca nacgrka (nac)4 quamtktê hk lmlrbka mlnlssarka plr auelmtarl hk cºN ca tleplratura hk 1 b hk anqua.4 1 nac 5 8.168 d Lslepkg 14 N + G0 ← NG0 + ;8 inac 10b + >0b← 88b + ;8 inac qulsta rlazkgml æ lsgtlrekna (svkcuppa nacgrl). Lslepkg 04 8> inac + F0 + Nc0 ← 0FNc 8> inac + 0b + 21b ← 2>b qulsta rlazkgml æ lmhgtlrekna (rknfklhl nacgrl).

∏F 5 -;8 inac/egcl

∏F 5 8> inac/egcl

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

Cl rlazkgmk lsgtlreknfl km blmlrl sgmg spgmtamll l cl rlazkgmk lmhgtlreknfl km blmlrl mgm sgmg spgmtamll4 ea ca spgmtamlktê hlcca rlazkgml mgm hkplmhl sgcg hac nacgrl snae`katg (∏F). Gnngrrl ngmskhlrarl amnfl ca varkazkgml hlc hksgrhkml egclngcarl (lmtrgpka (lmtrgpka)) hlc skstlea huramtl ca trasogreazkgml. \m auelmtg hlc hksgrhkml egclngcarl hlc skstlea huramtl ca trasogreazkgml ca oavgrksnl. Ca varkazkgml hk lmtrgpka æ hlokmkta hac tlrekml X∏^. Qukmhk, ca spgmtamlktê hk rlazkgml hkplmhl ska hac nacgrl snae`katg (∏F), nfl hacca varkazkgml hlc hksgrhkml egclngcarl (X∏^). Hlokmkaeg uma bramhlzza nfl clbfk qulstl hul oumzkgmk hk statg, c‛lmlrbka c‛lmlrbka ck`lra (B)4 ∏B 5 ∏F - X∏^ Qulsta lquazkgml skbmkokna4 ca varkazkgml hk lmlrbka ck`lra hk um skstlea huramtl uma trasogreazkgml nfkekna (lmlrbka okmacl „ lmlrbka kmkzkacl) hkplmhl hacca varkazkgml hk lmtacpka l hacca varkazkgml hk lmtrgpka. \ma rlazkgml lmhgtlrekna (∏F = :) puð lsslrl spgmtamla, sl ca varkazkgml hk lmtrgpka æ pgsktkva (auelmta kc hksgrhkml egclngcarl huramtl ca trasogreazkgml) l eabbkgrl hlc ngmsueg hk nacgrl. \ma rlazkgml æ spgmtamla sl ∏B 3 : (rlazkgml lsglrbgmkna). ^l ∏B = :, ca rlazkgml mgm avvklml mlcca hkrlzkgml km nuk æ snrktta (lmhglrbgmkna), elmtrl æ spgmtamla mlcca hkrlzkgml gppgsta. Quamhg ∏B 5 : ca rlazkgml æ acc‛lqukck`rkg. Qukmhk, ca varkazkgml hk lmlrbka ck`lra huramtl uma trasogreazkgml æ uma eksura hlcca tlmhlmza hlc skstlea a trasogrearsk. Kc `kcamnkg lmlrbltkng hlcca rlazkgml (nkgæ kc ∏B) hkplmhl sgcg haccg statg kmkzkacl l haccg statg okmacl, quacumqul ska stata ca –straha― nfkekna slbukta hac skstlea plr trasogrearsk. Nfl rlcazkgml n‛æ tra ∏B l ngstamtl hk lqukck`rkg hlcca rlazkgml7 Km sgstamza, nk hammg lmtrae`l uma eksura hlcca tlmhlmza hlcca rlazkgml ah avvlmkrl mlc slmsg kmhknatg hacca orlnnka. A``kaeg hlttg sgpra nfl quamhg Ilq = 1 c‛lqukck`rkg hk rlazkgml æ spgstatg vlrsg k prghgttk, qukmhk ∏B sarê mlbatkvg. _knlvlrsa, quamhg Ilq 3 1, c‛lqukck`rkg æ spgstatg vlrsg k rlablmtk l ∏B sarê  pgsktkvg. _lhkaeg gra pkû mlc hlttabckg ngel varka kc ngmtlmutg hk lmlrbka ck`lra hlc skstlea ∏B 3 : (rlazkgml spgmtamla) huramtl uma rlazkgml tkpg4 A + @ ← N + H

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

Ca varkazkgml hk lmlrbka ck`lra (∏B) æ mlbatkva (ngmtlmutg lmlrbltkng hlk prghgttk ekmgrl hlk rlablmtk), qukmhk ca rlazkgml prgnlhl spgmtamlaelmtl vlrsg k prghgttk. Zlrð lmlrbltknaelmtl, ca –straha― vlrsg k prghgttk mgm æ tutta km hksnlsa4 k rlablmtk hlvgmg passarl attravlrsg umg statg a tramskzkgml)) prkea hk pgtlrsk trasogrearl mlk prghgttk. eabbkgrl ngmtlmutg lmlrbltkng (statg (statg hk tramskzkgml C‛lmlrbka C‛lmlrbka hk attkvazkgml æ qulcca quamtktê hk lmlrbka mlnlssarka plr pgrtarl tuttl cl egclngcl hlk rlablmtk accg statg hk tramskzkgml. Zlr oarl um parabgml, keeabkmkaeg hk rgeplrl a eltê um plzzg hk clbmg4 hg``kaeg prkea  pklbarcg. Mlc egelmtg km nuk æ pklbatg (ea mg mgm m amngra splzzatg) fa um ngm ngmtlmutg tlmutg lmlrbltkng eabbkgrl hlc plzzg hk clbmg a rkpgsg (plr lslepkg puð soubbkrek hk eamg l rgeplrek um hlmtl). Qulstg statg ngrrkspgmhl accg statg hk tramskzkgml. A qulstg pumtg, kc pkû æ oattg l ca –rlazkgml―  prgnlhl ngm ca rgttura ngepclta ngepclta hlc plzzg hk cclbmg lbmg km hul oraeelmtk (k prghgttk hlcca hlcca rlazkgml). Cg statg hk tramskzkgml vklml rabbkumtg statkstknaelmtl ha um nlrtg muelrg hk egclngcl mlcc‛umktê hk tlepg, nfl sk vlmbgmg a trgvarl egelmtamlaelmtl km umg statg hk eabbkgrl ngmtlmutg lmlrbltkng. Zkû acta æ ca –ngcckmltta― ha suplrarl, plrð, l ekmgrl sarê kc muelrg hk egclngcl nfl rkusnkrammg a suplrarca, mlcc‛umktê hk tlepg. \m natackzzatgrl (plr lslepkg, bck lmzkek) a``assa c‛lmlrbka hk attkvazkgml hlcca rlazkgml, ogreamhg um ngepclssg ngm k rlablmtk, akutamhgck ah assuelrl cg statg hk tramskzkgml. Qukmhk, mlcc‛umktê hk tlepg, pkû egclngcl rkusnkrammg a suplrarl ca `arrklra hk attkvazkgml4 ca rlazkgml sarê annlclrata, ea kc lΘB hlcca nae`ka plrnfë hkplmhl sgcgZlr hacca matura nfkekna hk rlablmtk l prghgttk mgm hac rlazkgml plrngrsg MGM lmlrbltkng hlcca trasogreazkgml. tgrmarl acc‛lslepkg hlc plzzg hk clbmg, kc natackzzatgrl km qulstg nasg pgtrl``l lsslrl uma egrsa nfl tklml kc plzzg hk clbmg um pg‛ pklbatg l ek oankckta kc ngepktg hk rgeplrcg. Mlc nasg hlbck lmzkek, qulstk clbamg kc su`stratg hkstgrnlmhgml um pg‛ ca egclngca, km eghg nfl mlc ngepclssg lmzkea-su`stratg kc su`stratg assgekbcka pkû ac sug statg hk tramskzkgml nfl ac su`stratg matkvg. Km hlokmktkva, kc natackzzatgrl a``assa c‛lmlrbka hk  hk attkvazkgml, ea mgm spgsta c‛lqukck`rkg hk rlazkgml (mgm eghkokna ΘB më I lq lq). sl ∏B 3: rlazkgml spgmtamla (lsglrbgmkna) sl ∏B =: rlazkgml mgm spgmtamla (lmhglrbgmkna) sl ∏B 5: rlazkgml acc‛lqukck`rkg

A^ZLXXG XLPEGHKMAEKNG Ca tlreghkmaekna nk hknl sl uma rlazkgml r lazkgml æ lsglrbgmkna g lmhglrbgmkna, gvvlrg ngel æ spgstatg c'lqukck`rkg. A 35= @ ^l BAº l B@º sgmg cl lmlrbkl ck`lrl stamharh hk A l @, ∏Bº hlcca rlazkgml 5 B@º „ BAº

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?

 

  Km nfkekna grbamkna egctg splssg cl rlazkgmk r lazkgmk lsglrbgmknfl sgmg amnfl lsgtlreknfl. \ma rlazkgml æ lsgtlrekna quamhg ∏Fº æ mlbatkvg. ^l uma rlazkgml æ lmhglrbgmkna g pgng lsglrbgmkna, ca rlazkgml mgm amhrê a ngepcltlzza, a elmg hk usarl usar l um loolttg hk eassa (carbg lnnlssg hk A g rkegzkgml hk @) ∏Bº 5 ∏Fº „ X∏^ B l F tlmhgmg a hkekmukrl, ^ ah auelmtarl Ea uma rlazkgml puð amnfl lsslrl lsglrbgmkna lh lmhgtlrekna, quamhg æ oavgrkta lmtrgpknaelmtl, ea soavgrkta lmtacpknaelmtl sl ∏Fº = : l ∏^º = : lsslmhg ∏Bº 5 ∏Fº „ X∏^ nk sarê uma tleplratura ac hk sgpra hlcca quacl ∏Bº hkvlmtlrê mlbatkva. A^ZLXXG NKMLXKNG Kc ∏Bºhê kmogreazkgmk succ'lqukck`rkg hk uma rlazkgml, ea mgm ca vlcgnktê ca rlazkgml avvklml. Acnuml rlazkgmk sgmg egctg vlcgnk (ah lslepkg cl rlazkgmk ankhg-`asl), ea actrl sgmg egctg clmtl, tamtg ha mgm avvlmkrl plr mucca. _k sgmg splnkl nfkeknfl nfl, pur pgtlmhg harl uma rlazkgml lsglrbgmkna, sgpravvkvgmg a cumbg. Lssl sgmg hlttl eltasta`kck. Ah lslepkg, sl elsngckaeg um acnamg ngel c'lsamg l c'gsskblmg, mgm sunnlhl mucca plr um tlepg pratknaelmtl kmokmktg. Ca eksnlca lsamg/gsskblmg æ eltasta`kcl. Amnfl umrlazkgmk plzzg hkhkclbmg g mgk stlssk skaeg eltasta`kck km prlslmza hk G0! Kmoattk cl nge`ustkgml sgmg rlazkgmk egctg clmtl. Ha ngsa hkplmhl ca vlcgnktê hk uma rlazkgml7 Gbmk rlazkgml prlvlhl uma `arrklra lmlrbltkna ha suplrarl

Ca vlcgnktê hk uma rlazkgml hkplmhl hac ∏Batt. Zkû æ actg pkû ca rlazkgml sarê clmta. A tleplratura ae`klmtl acnuml rlazkgmk sgmg egctg vlcgnk lh avvlmbgmg spgmtamlaelmtl mgm applma sk elsngcamg k rlattkvk. Actrl rknfklhgmg ekmutk, grl g bkgrmk. Actrl kmokml sgmg tamtg clmtl ha mgm avvlmkrl km pratkna eak. Nk sgmg lsslmzkacelmtl hul eghk plr annlclrarl uma rlazkgml clmta 1) Ogrmkrl lmlrbka km eghg nfl kc skstlea rklsna a suplrarl ca `arrklra lmlrbltkna 0) A``assarl ca `arrklra lmlrbltkna ngm um natackzzatgrl. Km matura lskstgmg natackzzatgrk (lmzkek) nfl ngmslmtgmg um'gsskhazkgml ngmtrgccata hlbck acnamk.

^narknatg ha HAPCA K^A@LC PGELPG F\ANAN (harca.rgelrgJstuh.umkok.kt) cGEgAPZ^H; 22? ?