Dynamic Effect of a Change in the Exchange Rate System: From a Fixed Regime to a Basket-Peg or a...

8/9/2019 Dynamic Effect of a Change in the Exchange Rate System: From a Fixed Regime to a Basket-Peg or a Floating Regime

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@HJE Rirdelb V`pnr ]nrens

Hylòem Naanmt ia ` Mk`lbn el tknNxmk`lbn Z`tn ]ystno7Ario ` Aexnh Znbeon ti `J`sdnt-Vnb ir ` Aci`telb Znbeon

Lìyude Uiskeli, ]`kidi D`ge,`lh Xòil @siluo`

Li. >02O`rmk :60>

@se`l Hnvnciponlt J`ld Elstetutn


2/46

Xkn Rirdelb V`pnr snrens es ` miltelu`teil ia tkn aironrcy lònh Hesmusseil V`pnr snrens4tkn luojnrelb ia tkn p`pnrs miltelunh wetkiut eltnrrupteil ir mk`lbn. @HJE―s wirdelbp`pnrs rnacnmt elete`c ehn`s il ` tipem `lh `rn pistnh ilceln air hesmusseil. @HJE nlmiur`bnsrn`hnrs ti pist tkner mioonlts il tkn oèl p`bn air n`mk wirdelb p`pnr (bevnl el tknmet`teil jnciw). ]ion wirdelb p`pnrs o`y hnvncip elti itknr airos ia pujcem`teil.

]ubbnstnh met`teil7

Uiskeli, L., ]. D`ge, `lh X. @siluo`. :60>. Hylòem Naanmt ia Mk`lbn el Nxmk`lbn Z`tn]ystno7 Ario ` Aexnh Znbeon ti ` J`sdnt-Vnb ir ` Aci`telb Znbeon. @HJE Rirdelb V`pnr>02. Xidyi7 @se`l Hnvnciponlt J`ld Elstetutn. @vèc`jcn7 kttp7//www.`hje.irb/wirdelb-p`pnr/:60>/6=/6>/1>8;.hylòem.naanmt.nxmk`lbn.r`tn.systno/

Vcn`sn milt`mt tkn ùtkirs air elairo`teil `jiut tkes p`pnr.

Noèc7 lyiskeliF`hje.irb4 d`geFnmil.dnei.`m.gp4 t`siluo`Feoa.irb

Lìyude Uiskeli es Hn`l `lh MNI ia tkn @se`l Hnvnciponlt J`ld Elstetutn. ]`kidiD`ge es Vrianssir, Hnp`rtonlt ia Nmilioems, Dnei ^levnrsety. Xòil @siluo` esNmilioest, Hnjt Vicemy Heveseil, ]tr`tnby Vicemy `lh Znvenw Hnp`rtonlt, Eltnrl`teil`cOilnt`ry Aulh.

Xkn venws nxprnssnh el tkes p`pnr `rn tkisn ia ùtkirs `lh hi lit rnacnmt `ly ia venws iatkn Eltnrl`teil`c Oilnt`ry Aulh (EOA) ir EOA picemy. Xkn ùtkirs tk`ld snoel`r `lhmilanrnlmn p`rtemep`lts `t @se`l Nmilioem V`lnc, @se`-V`meaem Nmilioem @ssime`teil,Jistil ^levnrsety, EOA OMO, EOA I@V, Dnei ^levnrsety, G`p`lnsn Nmilioem @ssime`teil, `lh G`p`l ]imenty ia Oilnt`ry Nmilioems air mioonlts `lh subbnsteils.

Xkn venws nxprnssnh el tkes p`pnr `rn tkn venws ia tkn ùtkirs `lh hi lit lnmnss`recyrnacnmt tkn venws ir picemens ia @HJE, @HJ, ets Ji`rh ia Hernmtirs, ir tkn bivnrlonltstkny rnprnsnlt. @HJE hins lit bu`r`ltnn tkn `mmur`my ia tkn h`t` elmcuhnh el tkes p`pnr`lh `mmnpts li rnspilsejecety air `ly milsnqunlmns ia tkner usn. Xnroeliciby usnh o`ylit lnmnss`recy jn milsestnlt wetk @HJ iaaeme`c tnros.

Rirdelb p`pnrs `rn sujgnmt ti airo`c rnveseil `lh mirrnmteil jnairn tkny `rn ael`ceznh`lh milsehnrnh pujcesknh.

@se`l Hnvnciponlt J`ld ElstetutnD`suoeb`snde Juechelb ;A=-:-> D`suoeb`snde, Mkeyih`-duXidyi 066-166;, G`p`l

Xnc7 +;0-=-=>5=->>66A`x7 +;0-=-=>5=->>20^ZC7 www.`hje.irbN-oèc7 elaiF`hje.irb

© :60> @se`l Hnvnciponlt J`ld Elstetutn

mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


3/46

@HJE Rirdelb V`pnr >02 Uiskeli, D`ge, `lh @siluo`

@jstr`mt

Xkes p`pnr tknirntem`ccy nv`cu`tns tkn hylòem naanmts ia ` skeat el `l nxmk`lbn r`tn systnoario ` aexnh rnbeon ti ` j`sdnt pnb, ir ti ` aci`telb rnbeon, `lh ijtèls tr`lseteil p`tks airtkn skeat j`snh il ` hylòem stimk`stem bnlnr`c nquecejreuo oihnc ia ` so`cc ipnl nmilioy.Rn `ppcy qu`ltet`tevn `l`cyses uselb h`t` ario tkn Vnipcn―s Znpujcem ia Mkel` `lh Xkèc`lh

`lh aelh tk`t ` so`cc ipnl miultry wiuch jn jnttnr iaa skeatelb ti ` j`sdnt pnb ir ti ` aci`telbrnbeon tk`l oèltèlelb ` hicc`r-pnb rnbeon wetk m`pet`c miltrics ivnr tkn cilb rul.Aurtknroirn, hun ti tkn wnca`rn cissns `ssime`tnh wetk vic`tecety el lioel`c eltnrnst r`tns, tkncilbnr tkn tr`lseteil pnreih, tkn c`rbnr tkn jnlnaets ia skeatelb suhhnlcy ti ` j`sdnt-pnbrnbeon ario ` hicc`r-pnb rnbeon tk`l primnnhelb br`hu`ccy. Znb`rhelb suhhnl skeats tihnsernh rnbeons, tkn wnca`rn bèls `rn kebknr ulhnr ` skeat ti ` j`sdnt pnb ea tkn nxmk`lbnr`tn acumtu`tns sebleaem`ltcy. Ael`ccy, skeatelb ti ` o`l`bnh-aci`telb rnbeon es cnss `ttr`mtevntk`l oivelb ti ` j`sdnt pnb, `s tkn eltnrvnlteils lnmnss`ry ti oèltèl tkn nxmk`lbn r`tnair mnrtèl pnreihs rnsuct el kebknr cissns `lh tkn ùtkirety c`mds oilnt`ry picemy ùtilioy.

GNC Mc`sseaem`teil7 A==, A80, A8:


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Miltnlts

0. Eltrihumteil ................................................................................................................ =

0.0

Cetnr`turn Znvenw ........................................................................................... >

:. ]o`cc Ipnl Nmilioy Oihnc ..................................................................................... >

=. Nxmk`lbn Z`tn Znbeon ............................................................................................. ;

=.0

Hicc`r-Vnb Znbeon wetk ]tremt M`pet`c Miltrics (@)......................................... ;

=.: J`sdnt-Vnb Znbeon wetk Rn`d M`pet`c Miltrics (J) .................................... 06 =.= J`sdnt-Vnb Znbeon wetkiut M`pet`c Miltrics (M) ......................................... 00 =.8 Aci`telb Znbeon wetkiut M`pet`c Miltrics (H) ............................................... 0: =.> Hicc`r-Vnb Znbeon ulhnr Vnranmt M`pet`c Oijecety (N) .................................. 0=

8.

Xkn Xr`lseteil V`tk ti Itknr Nxmk`lbn Z`tn Znbeons ............................................ 08

8.0 Oèltèlelb ` Hicc`r-Vnb Znbeon (0) ........................................................... 01 8.: Br`hu`c @hgustonlt ti ` J`sdnt Vnb wetkiut M`pet`c Miltrics (:) ................ 02 8.=

]uhhnl ]keat ti ` J`sdnt Vnb wetkiut M`pet`c Miltrics (=) ........................... 0;

8.8 ]uhhnl ]keat ario ` Hicc`r-Vnb ti ` Aci`telb Znbeon (8) ............................. 05 8.> ]uhhnl ]keat ario ` Hicc`r-Vnb ti ` O`l`bnh-Aci`telb Znbeon (>) ............. :6

>.

Miop`resil ia Xr`lseteil Vicemens ............................................................................ :0

>.0 Eopcem`teils air ]t`tem @l`cyses ..................................................................... :0 >.:

Miop`resil ia Vicemy (0) `lh Itknr Xr`lseteil Vicemens................................ ::

>.=

Miop`resil òilb Xr`lseteil Vicemens ........................................................ :=

1. ]eouc`teil Nxnrmesns7 Xkn VZM `lh Xkèc`lh .......................................................... :2

1.0

H`t` `lh Znbrnsseil Znsucts....................................................................... :2

1.: ]eouc`teil Znsucts uselb Nsteo`tnh V`ròntnrs .......................................... :; 1.= Xeon Eltnrv`cs `lh Ipteo`c J`sdnt Rnebkts ................................................. =0

2.

Milmcuseil ............................................................................................................... ==

@ppnlhex @. ]icvelb air Z`teil`c Nxpnmt`teils .................................................................... =8

@ppnlhex J7 ]`hhcn V`tk ]t`jecety ulhnr ` Aci`telb Znbeon ............................................... =5

@ppnlhex M7 ^let Ziit `lh Mieltnbr`teil Xnsts .................................................................. 86

Znanrnlmns ......................................................................................................................... 8=


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0. ELXZIH^MXEIL

Iln ia tkn twi o`gir mucprets ia tkn 0552”055; @se`l ael`lme`c mreses w`s tkn `hipteilia hicc`r pnbs jy N`st @se`l miultrens.0 Xkn itknr w`s tkn hesmrnp`lmy el o`turetyjntwnnl cnlhelb `lh jirriwelb jy ael`lme`c elstetuteils el tknsn miultrens. Ael`lme`celstetuteils el Znpujcem ia Dirn`, Elhilnse`, `lh Xkèc`lh jirriwnh el tkn skirt tnroario `jri`h `lh cnlt ti hionstem aeros el tkn cilb tnro. ]uhhnl wetkhr`w`cs ia aulhso`hn hionstem j`lds el N`st @se` vuclnr`jcn ti tkn mreses.:

]nvnr`c nmilioests k`vn suppirtnh tkn hnser`jecety ia ` j`sdnt-pnb rnbeon el N`st @se`.Air nxòpcn, D`wè (:668), Eti, Ib`w`, `lh ]`s`de (055;), Eti `lh V`rd (:66=),Ib`w` `lh Eti (:66:), `lh Uiskeli, D`ge, `lh ]uzude (:668) rnmioonlh tk`t N`st @se`l miultrens nojr`mn ` j`sdnt-pnb rnbeon.= Air miultrens wetk mcisn nmilioemrnc`teilskeps wetk tkn Nuripn`l ^leil, G`p`l, `lh tkn ^letnh ]t`tns, tkn r`teil`cn air`hiptelb ` j`sdnt-pnb rnbeon es tk`t nxmk`lbn r`tn st`jecez`teil, tkriubk ` j`sdntmiopreselb tkn murrnlmens ario tknsn miultrens, es jnlnaeme`c jnmùsn et rnoivns tkn

prijcno ia c`rbn acumtu`teils el nxmk`lbn r`tns. Uiskeli, D`ge, `lh @siluo` (:668)`rbun tk`t, el `hheteil ti ` j`sdnt-pnb rnbeon, ` aci`telb rnbeon es `csi `l ipteil airN`st @se`l miultrens. 8 ]eoec`rcy, @hòs `lh ]nojc`t (:668) nopk`sezn tk`t ilnmurrnlmy rnbeon ipteil es ti `hipt ` aci`telb rnbeon wetk elac`teil t`rbntelb.

Xkn supnreirety ia ` j`sdnt-pnb ir ` aci`telb rnbeon rnc`tevn ti ` hicc`r-pnb rnbeon k`sjnnl `l`cyznh ilcy el ` st`tem miltnxt, lit el ` hylòem miltnxt. Air miultrens cedn tknVnipcn―s Znpujcem ia Mkel` (VZM) `lh O`c`yse`, tknrn es stecc ` jeb qunsteil ia kiw tioivn ario tkn murrnlt hn a`mti aexnh rnbeon ti itknr nxmk`lbn r`tn rnbeons. Jnairn`hiptelb ` j`sdnt pnb ir ` aci`telb rnbeon, tknsn miultrens lnnh ti `j`lhil tkner hna`mti hicc`r pnbs. Il tkn iln k`lh, ` skeat ario ` hicc`r-pnb rnbeon ti ` j`sdnt-pnbrnbeon wiuch elvicvn iln ia twi primnssns7 (e) st`rtelb wetk ` hicc`r-pnb rnbeon wetk

stremt m`pet`c miltrics, skeatelb ti ` j`sdnt-pnb rnbeon wetk ciisn m`pet`c miltrics, `lhael`ccy rn`mkelb ` j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics, e.n., br`hu`c `hgustonltsia jitk tkn hnbrnn ia m`pet`c miltric `lh tkn j`sdnt wnebkt4 ir (ee) st`rtelb wetk ` hicc`r-pnb rnbeon wetk stremt m`pet`c miltrics `lh tknl suhhnlcy skeatelb ti ` j`sdnt-pnbrnbeon wetkiut m`pet`c miltrics jy rnoivelb m`pet`c miltrics, e.n., ` suhhnl skeat ia jitkm`pet`c miltrics `lh j`sdnt wnebkt. Il tkn itknr k`lh, ` skeat ti ` aci`telb rnbeon wiuchelvicvn tkn aicciwelb primnss7 st`rtelb wetk ` hicc`r-pnb rnbeon wetk stremt m`pet`cmiltrics `lh suhhnlcy skeatelb ti ` aci`telb rnbeon jy rnoivelb m`pet`c miltrics.Xknrnairn, et es lnmnss`ry ti `l`cyzn tkn `hv`lt`bns `lh hes`hv`lt`bns ia tknsn skeatsel ` hylòem miltnxt, r`tknr tk`l el ` st`tem miltnxt. Xi iur dliwcnhbn, tkes p`pnr es tknaerst ti tknirntem`ccy `lh qu`ltet`tevncy nv`cutn tkn hylòem naanmt ia skeats ario ` aexnhrnbeon ti ` j`sdnt-pnb rnbeon ir ti ` aci`telb rnbeon. Rn ijtèl twi tr`lseteil p`tks

ario ` hicc`r pnb ti ` j`sdnt-pnb rnbeon (` br`hu`c `hgustonlt `lh ` suhhnl skeat)

0 Eti, Ib`w`, `lh ]`s`de (055;) `lh Ib`w` `lh Eti (:66:) nopk`sezn tkes pielt `lh `hvim`tn `hipteil ia

` j`sdnt-pnb rnbeon el N`st @se` si miultrens m`l `vieh jnelb lnb`tevncy àanmtnh jy acumtu`teils el tkn^] hicc`r”ynl nxmk`lbn r`tn.

: OmDejjel `lh O`rtel (0555) `csi `hhrnss tkn `rbuonlt tk`t tkn preo`ry mùsn ia tkn N`st @se` Mreses

w`s ` aulhònlt`c rn`ssnssonlt ia tkn priaet`jecety ia elvnstonlts el tkn rnbeil.= Il miopiseteil ia ` j`sdnt, Ib`w` `lh Eti (:66:) `lh D`wè (:668) mcèo ` B-= murrnlmy (^] hicc`r,

ynl, nuri) j`sdnt, wkecn Uiskeli, D`ge, `lh @siluo` (:66>) subbnst tk`t N`st @se`l miultrens skiuch`hipt ` j`sdnt miltèlelb jitk B-= murrnlmens `lh N`st @se`l murrnlmens.

8

Kiwnvnr, tknrn es `csi ` hr`wj`md el `hiptelb ` aci`telb rnbeon4 nxmnss acumtu`teil ia nxmk`lbn r`tnsàanmts tkn nmilioy lnb`tevncy `s skiwl el Uiskeli, D`ge, `lh Ejud` (:66=).

=


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`lh twi tr`lseteil p`tks ario ` hicc`r pnb ti ` aci`telb rnbeon, ir ` o`l`bnh-aci`telbrnbeon (jitk suhhnl skeats).

Xkn o`gir aelhelbs ia tkn p`pnr `rn `s aicciws. Aerst, tkn muouc`tevn cissns ia aiurtr`lseteil picemens `rn ijtèlnh tknirntem`ccy `s wncc `s noperem`ccy. Xkn aevn picemens,

elmcuhelb iln wetkiut `ly mk`lbn el tkn nxmk`lbn r`tn rnbeon, wkemk wn milsehnr eltkes p`pnr, `rn (0) oèltèlelb ` hicc`r pnb (wetk stremt m`pet`c miltrics), (:) ` br`hu`cskeat ario ` hicc`r pnb ti ` j`sdnt pnb wetkiut m`pet`c miltrics (` br`hu`c `hgustonlt iajitk m`pet`c miltrics `lh j`sdnt wnebkt), (=) ` suhhnl skeat ario ` hicc`r pnb ti `j`sdnt pnb wetkiut m`pet`c miltrics (` suhhnl rnoiv`c ia m`pet`c miltrics `lh ` suhhnlmk`lbn el j`sdnt wnebkts), (8) ` suhhnl skeat ario ` hicc`r pnb ti ` aci`telb rnbeon (`suhhnl rnoiv`c ia m`pet`c miltrics `lh ` suhhnl elmrn`sn el acnxejecety el nxmk`lbnr`tn), `lh (>) ` suhhnl skeat ario ` hicc`r pnb ti ` o`l`bnh-aci`telb rnbeon (` suhhnlrnoiv`c ia m`pet`c miltrics `lh ` suhhnl elmrn`sn el acnxejecety el nxmk`lbn r`tn wetkimm`seil`c eltnrvnlteils). Rn aelh tk`t oèltèlelb ` hicc`r-pnb rnbeon es hnser`jcn ilcyivnr tkn skirt rul, elhem`telb tk`t tkn miultry wecc jn jnttnr iaa skeatelb ti netknr `j`sdnt-pnb rnbeon ir ` aci`telb rnbeon ivnr tkn cilb rul.

]nmilh, bevnl tkn mkiemn jntwnnl ` br`hu`c `hgustonlt, picemy (:), tiw`rh tkn t`rbntj`sdnt-pnb rnbeon ir ` suhhnl skeat ti tkn t`rbnt j`sdnt-pnb rnbeon, picemy (=), tkncilbnr tkn tr`lseteil pnreih, tkn c`rbnr tkn jnlnaets tkn miultry rnmnevns ario rn`mkelbtkn hnsernh rnbeon `t ilmn.

Xkerh, bevnl tkn miop`resil jntwnnl suhhnl skeats ti ` j`sdnt-pnb rnbeon, picemy (=),`lh ti ` aci`telb rnbeon, picemy (8), tkn wnca`rn ia tkn miultry wiuch jn kebknr ulhnr `skeat ti ` j`sdnt-pnb rnbeon ea tkn nxmk`lbn r`tn acumtu`tns sebleaem`ltcy. Xkn miultrywiuch jn `jcn lit ilcy ti st`jecezn tkn lnb`tevn eop`mts ia nxmk`lbn r`tn acumtu`teilsil tr`hns `lh m`pet`c elaciws jut `csi ti `ssest tkn prev`tn snmtir el airouc`telbnxmk`lbn r`tn nxpnmt`teils prnmesncy jy miooettelb ti ` j`sdnt rnbeon air mnrtèlpnreihs. Ael`ccy, et es cnss `ttr`mtevn ti `hipt ` skeat ti ` o`l`bnh-aci`telb rnbeon tk`l tioivn ti ` j`sdnt pnb. Xkes es jnmùsn eltnrvnlelb el tkn airnebl nxmk`lbn o`rdnt airmnrtèl pnreihs cn`hs ti kebknr cissns, `s tkn ùtkirety c`mds oilnt`ry picemy ùtilioy.Iur qu`ltet`tevn `l`cyses uselb VZM `lh Xkè h`t` suppirts tknsn aelhelbs. > Xkn`l`cyses milhumtnh el tkes p`pnr m`l jn `ppcenh ti `ly so`cc ipnl miultry tk`t esmilsehnrelb ` skeat ario ` aexnh rnbeon ti ` j`sdnt pnb ir ti ` aci`telb rnbeon.

Xkn rnst ia tkn p`pnr es irb`leznh `s aicciws. @atnr rnvenwelb tkn nxestelb cetnr`turn,]nmteil : privehns ` hylòem stimk`stem bnlnr`c nquecejreuo (H]BN) oihnc ia ` so`ccipnl nmilioy. ]nmteil = `l`cyzns kiw tkn nmilioy rn`mkns tkn st`jcn nquecejreuoulhnr aiur rnbeons. Rn hnaeln aiur tr`lseteil picemens tibntknr wetk oèltèlelb tknmurrnlt hicc`r-pnb rnbeon el ]nmteil 8. ]nmteil > aimusns il tkn ipteo`c tr`lseteilpicemy. ]eouc`teil nxnrmesns uselb VZM `lh Xkè h`t` `rn privehnh el ]nmteil 1. 1 @

jrena milmcuseil suoo`rezns tkn hesmusseil.

> Uiskeli, D`ge, `lh @siluo` (:60:) `l`cyzn tkn miop`resil jntwnnl ` j`sdnt pnb `lh ` aci`telb rnbeon

jy eopcnonltelb sion elstruonlt`c rucns. Xkny skiw tk`t, el tkn m`sn ia ]elb`pirn `lh Xkèc`lh,`ppcyelb ` j`sdnt wnebkt rucn ulhnr ` j`sdnt-pnb rnbeon wecc cn`h ti ` so`ccnr muouc`tevn ciss tk`l`hiptelb `l eltnrnst r`tn rucn ir ` oilny suppcy rucn ulhnr ` aci`telb rnbeon.

1 Et es `pp`rnlt tk`t tkn ipteo`c j`sdnt wnebkt ijtèlnh ario iur `l`cyses uselb VZM `lh Xkè h`t` es

heaanrnlt ario tk`t onlteilnh el Ib`w` `lh ]keoezu (:661), wkemk es m`cmuc`tnh j`snh il sk`rns el

rnbeil`c BHV on`surnh `t purmk`selb piwnr p`rety (VVV) `lh tkner tr`hn vicuon sk`rns (suo ia tknnxpirts ̀ lh eopirts).

8


7/46


0.0 Cetnr`turn Znvenw

Xkes p`pnr es rnc`tnh ti twi strnòs ia tkn cetnr`turn. Iln hnj`tns tkn hnser`jecety ia `j`sdnt-pnb rnbeon el N`st @se`. Eti, Ib`w`, `lh ]`s`de (055;) `lh Ib`w` `lh Eti

(:66:) `l`cyzn tkn ipteo`cety ia ` j`sdnt pnb wetk ` bnlnr`c nquecejreuo oihnc, wkemkhins lit elmcuhn m`pet`c oivnonlts. Uiskeli, D`ge, `lh ]uzude (:668) `lh Uiskeli,D`ge, `lh @siluo` (:668) `csi mcèo tk`t et es jnttnr air tkn miultry ti `hipt ` j`sdntpnb r`tknr tk`l ` hicc`r pnb j`snh il ` bnlnr`c nquecejreuo oihnc tk`t elmirpir`tnsm`pet`c oivnonlts `mriss miultrens. Jerh `lh Z`g`l (:66:) `rbun tk`t pnbbelb `murrnlmy `bèlst ` oirn hevnrseaenh miopisetn j`sdnt ia murrnlmens wiuch k`vnnl`jcnh ]iutkn`st @se`l miultrens ti hn`c oirn naanmtevncy wetk tkn –tkerh murrnlmypknlionlil,‟ wkemk miltrejutnh ti tkn mreses. 2 Itknr pnrspnmtevns, sumk `s ]keige(:661`, :661j), milsehnr tkn j`sdnt-pnb rnbeon ulhnr twi heaanrnlt elviemelb smknons7prihumnr murrnlmy premelb `lh vnkemcn murrnlmy premelb. Air noperem`c `l`cyses,OmDejjel `lh Cnn (:668) elvnsteb`tn wkemk nxmk`lbn r`tn tkn N`st @se`l miultrensskiuch pnb ti uselb snvnr`c skimds, sumk `s miultry-spnmeaem (`syoontrem) `lh rnbeil`c

(syoontrem) skimds.

Xkn itknr strnò hn`cs wetk ` aci`telb rnbeon el tkn rnbeil. @hòs `lh ]nojc`t (:668)nopk`sezn tk`t iln murrnlmy rnbeon ipteil es ti `hipt ` aci`telb rnbeon wetk elac`teilt`rbntelb. Aicciwelb tkes ̀ rbuonlt, ]uss`lbd`rl ̀ lh Qemky`lilh (:662) onlteil tk`t ò`l`bnh-aci`telb rnbeon, miojelnh wetk elac`teil t`rbntelb, suets `l nonrbelb o`rdntnlverilonlt sumk `s tk`t el Xkèc`lh. ]eoec`rcy, Uiskeli, D`ge, `lh @siluo` (:668)aelh tk`t ` aci`telb rnbeon es `csi ` pissejcn ipteil air N`st @se`l miultrens, tibntknrwetk ` j`sdnt-pnb rnbeon. Ael`ccy, Deo `lh Cnn (:66;) skiw tk`t nxmk`lbn r`tnacnxejecety privehns brn`tnr oilnt`ry picemy elhnpnlhnlmn j`snh il tkner noperem`caelhelbs.

:. ]O@CC IVNL NMILIOU OIHNC

El tkes snmteil, wn privehn ` hylòem stimk`stem bnlnr`c nquecejreuo (H]BN) oihnc ia `so`cc ipnl nmilioy. Iur oihnc mcisncy aicciws Uiskeli, D`ge, `lh ]uzude (:66:) `lhHirljusmk (0521), `lh wn `l`cyzn et el ` hylòem miltnxt. @ctkiubk wn hi lit hnrevnnquecejreuo milheteils hernmtcy ario tkn ipteo`c jnk`veir ia kiusnkichs `lh aeros, iurnquecejreuo milheteils `rn tkn sòn `s tkisn el Uiskeli, D`ge `lh @siluo` (:60:),wkemk `rn j`snh il oemri aiulh`teils. Xknrn `rn tkrnn miultrens el tkes oihnc7 tknN`st @se`l miultry, G`p`l, `lh tkn ^]. Rn `ssuon tkn N`st @se`l miultry ti jn tknKion miultry `lh G`p`l `lh tkn ^] ti jn tkn rnst ia tkn wirch (ZIR). Xkn ^] hicc`r”ynl nxmk`lbn r`tn es nxibnlius ti tkn N`st @se`l miultry.

2 Xkny hnaeln –tkerh murrnlmy pknlionlil‟ `s prijcnos air nonrbelb o`rdnt miultrens tk`t `resn ario

acumtu`teils el tkn v`cuns ia tkn murrnlmens ia tkner o`gir tr`helb p`rtlnrs `bèlst n`mk itknr. El tkesrnb`rh, tkny `csi litn tk`t tkn miopiseteil ia ` j`sdnt ia murrnlmens `lh wnebkts `tt`mknh ti elhevehu`c

murrnlmens wecc lnnh ti mk`lbn `s mermuost`lmns `ctnr `lh `s tkn sebleaem`lmn ia o`gir wirch murrnlmensti ` hnvncipelb miultry―s j`c`lmn ia p`yonlts mk`lbns.

>


8/46


Aeburn 07 ]o`cc Ipnl Nmilioy Oihnc

]iurmn7 @utkirs― eccustr`teil.

X`jcn 07 Hnsmrepteil ia Q`re`jcns

Q`re`jcn Hnsmrepteil

]timd ia oilny suppcy

Vremn cnvnc el Kion

Nxpnmtnh hionstem premn cnvnc

Vremn cnvnc el tkn ^]

Vremn cnvnc el G`p`l

Kion eltnrnst r`tn

^] eltnrnst r`tn

Hionstem BHV

�

Vitnlte`c BHV

/

N`st @se`l murrnlmy”^] hicc`r nxmk`lbn r`tn

/ N`st @se`l murrnlmy”ynl nxmk`lbn r`tn/

^] hicc`r”ynl nxmk`lbn r`tn

Rnebkt ia tkn ^] hicc`r r`tn el ` murrnlmy j`sdnt

Xit`c prihumtvetey ia Kion

/ ^] hicc`r nxmk`lbn r`tn resd/ Unl nxmk`lbn r`tn resd

BHV ? briss hionstem prihumt.

Litn7 @cc tkn v`re`jcns, nxmnpt eltnrnst r`tns, `rn hnaelnh el l`tur`c cibs.

1


9/46


Rn `ssuon tk`t hionstem `lh airnebl `ssnts `rn eopnranmt sujstetutns, wknrn`sG`p`lnsn `lh ^] `ssnts `rn pnranmt sujstetutns air hionstem elvnstirs. @l eltnrnst

p`rety milheteil es skiwl `s7+0 ? + +0/ / / (0)wknrn hnlitns tkn `hgustonlt spnnh ia tkn hionstem eltnrnst r`tn, wkemk `csim`pturns tkn hnbrnn ia m`pet`c miltric. Ea es mcisn ti 6, et eopcens tk`t tkn hionstemeltnrnst r`tn hins lit rnspilh ti `l eltnrnst r`tn heaanrnlte`c. Xkes on`ls tk`t tknhionstem eltnrnst r`tn es nxibnlius `lh tit`ccy elhnpnlhnlt. Rn rnb`rh tkes `s ` m`snia stremt m`pet`c miltric. Il tkn miltr`ry, ea `ppri`mkns 0, et eopcens tk`t tkn hionstemeltnrnst r`tn rnspilhs miopcntncy ti tkn airnebl eltnrnst r`tn, wkemk wn milsehnr ti jn `

m`sn wetkiut m`pet`c miltrics. Aurtknroirn,

/

hnlitns ` resd prnoeuo wkemk

hnpnlhs il tkn ^] hicc`r nxmk`lbn r`tn. Ea ? 0, nqu`teil (0) m`l jn rnwrettnl `s7+0 ? + +0/ / / (0―) @s wn nxpc`el el ]nmteil =.0, ulhnr ` hicc`r-pnb rnbeon wetk m`pet`c miltrics, nqu`teil(0) hins lit kich. Xkn nquecejreuo milheteil air tkn oilny o`rdnt es7 ? +0 + ( �) (:)Xkn hno`lh air biihs hnpnlhs il tkn rn`c nxmk`lbn r`tns, tkn rn`c eltnrnst r`tn `lhtkn nxmk`lbn r`tn resds wrettnl `s7

� ? /+ + ›+0/, + /+ + ›+0/, {+0 (+0 )}/ / (=)wknrn tkn tnro (+0 ) skiws tkn nxpnmtnh r`tn ia elac`teil. Xkn c`st twi tnrosmirrnspilh ti nxmk`lbn r`tn resds.

]elmn iln ia tkn tkrnn nxmk`lbn r`tns es lit elhnpnlhnlt, tkn ynl r`tn m`l jnnxprnssnh ̀ s7

/

?

/

+

/

(8)

2


10/46


Xkn elac`teil r`tn hnpnlhs il tit`c prihumtevety, nxmnss hno`lh air biihs, tkn rn`c ^]hicc`r r`tn, tkn rn`c ynl r`tn, `lh tkn nxpnmtnh r`tn ia elac`teil, skiwl `s7

+0 ? +( �) + /+ + ›/, + /GV+GV + ›/, + (+0 ) + / + /

(>)

wknrn tkn aerst tnro il tkn rebkt-k`lh sehn skiws tkn tit`c prihumtevety ia tkn Kionmiultry `lh tkn c`st twi tnros hnlitn tkn hicc`r nxmk`lbn r`tn resd `lh tkn ynlnxmk`lbn r`tn resd. Rn `ssuon `bbrnb`tn prihumteil hnpnlhs il tit`c prihumtevety,eopirtnh o`tnre`cs ario G`p`l `lh tkn ^], `lh tkn elac`teil r`tn. Xkn N`st @se`lmiultry es `ssuonh ti eopirt o`tnre`cs ario G`p`l `lh tkn ^] `lh nxpirt ael`c biihsti G`p`l `lh tkn ^]. Jitk `bbrnb`tn hno`lh `lh `bbrnb`tn suppcy hnpnlh `csi il

tkn nxmk`lbn r`tn nxpnmt`teil, `s nxpirtelb `lh eopirtelb aeros `rn milmnrlnh wetksebleaem`lt hnve`teils ia tkn nxmk`lbn r`tn air tkn lnxt pnreih ario tkn murrnlt cnvnc.

@oilb tkn v`re`jcns, , � , , , / , / , `lh / `rn miooilnxibnlius v`re`jcns ulhnr `ly nxmk`lbn r`tn rnbeon. Rn `ssuon tk`t `cc nxibnlius

v`re`jcns nxmnpt /, /, /, , `lh `rn milst`lt (? 6) el tkn `l`cysesjnciw. @cc tkn minaaemenlts `jivn `rn pisetevn.

=. N[MK@LBN Z@XN ZNBEON

El tkes snmteil, wn hnrevn tkn cilb-tnro nquecejreuo tibntknr wetk nquecejreuo v`cuns `tpnreih t. Rn milsehnr aevn m`sns7

(@) hicc`r-pnb rnbeon wetk stremt m`pet`c miltrics,

(J) j`sdnt-pnb rnbeon wetk wn`d m`pet`c miltrics,

(M) j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics,

(H) aci`telb rnbeon wetkiut m`pet`c miltrics, `lh

(N) hicc`r-pnb rnbeon ulhnr pnranmt m`pet`c oijecety.

=.0 Hicc`r-Vnb Znbeon wetk ]tremt M`pet`c Miltrics (@)

^lhnr ` hicc`r-pnb rnbeon, tkn hicc`r r`tn (

/

) jnmions nxibnlius (

/

? 6).

Xkus, tkn nxpnmt`teil ia tkn nxmk`lbn r`tn el tkn lnxt pnreih es ehnltem`c ti tkn murrnltnxmk`lbn r`tn. Aurtknroirn, el tkes m`sn, tkn oilny suppcy ( ) jnmionsnlhibnlius, eopcyelb tk`t tkn oilnt`ry `utkirety eopcnonlts m`pet`c miltrics el irhnrti dnnp tkn ^] hicc`r r`tn milst`lt. ]elmn tkn oilnt`ry `utkirety rnstremts hionstemrnsehnlts― kichelbs ia airnebl `ssnts, nqu`teil (0) hins lit nxest. Hionstem eltnrnst r`tn(+0) es ` picemy elstruonlt (nxibnlius) el tkes m`sn. @s tkn N`st @se`l murrnlmy”^]hicc`r r`tn es aexnh, ario nqu`teil (8)7

/ ? / (8―)

;


11/46


Xkn nlhibnlius v`re`jcns el tkes m`sn `rn , , `lh . ]icvelb nqu`teils (:), (=),(8―), `lh (>) air tkn premn cnvnc `lh oilny suppcy, tkn aicciwelb snoe-rnhumnh aironqu`teils `rn ijtèlnh7

+0 ? T( + ) + ( + )_ + /

+ ( + ›)+0/

,

+ (0 + )(+0 ) + ( )/ +0

(1)

? T0 ( + ) + ( + )_ + / + ›+0/, + (+0 ) / ( +)+0 (2)

Xkn cilb-rul nquecejreuo v`cuns air tkn premn cnvnc `lh oilny suppcy ulhnr tkn ^]

hicc`r-pnb rnbeon `rn7;

̎ ? 00 {( + ›) + ›}̎/ ̎ � (;)

? 00 {( + ›) + ›} + ( + ›) ̎/ 00 � 0

0 + ( +) ̎ (5)

wknrn 0 ? ( + ) + ( + ) `lh 0 ? 0 ( + ) + ( + ). ? � nxprnssns tkn hnve`teil ario tkn cilb-rul nquecejreuo v`cun. Rn `ssuontk`t tkn ^] hicc`r”ynl r`tn oivns ario ets elete`c nquecejreuo v`cun (? 6) ti ̊/ `tteon t `lh rnoèls `t tkn lnw nquecejreuo àtnr teon t + 0 (? ̊/). @s tkn premn cnvnces stemdy ivnr tkn skirt rul, 6 ? 6 `t teon 6. Rn `ssuon tkn elete`c nquecejreuo v`cuns̎6 ? ̎6 ? 6. Xkn lnw nquecejreuo v`cun àtnr tkn ^] hicc`r”ynl r`tn mk`lbn es7

̎ ? 00 ̊/ + (›+ ›)̊+0/, + (0 +)(̊+0 ̊) + ( )̊/

+0 (06)

wknrn wn `ssuon tk`t tit`c prihumtevety rnoèls ulmk`lbnh jy nxmk`lbn r`tn skimds,e.n., ? 6.

; Rn `ssuon tk`t +0 ? `lh / ? 6 `t tkn cilb-ruo nquecejreuo.

5


12/46


Rn sicvn air tkn r`teil`c nxpnmt`teil `lh ijtèl nxprnsseils air yt y�@ `lh pt p�@ sumk tk`t75

y�@ ? 0()̊̂ ]/ + :()̊/ + =()+0 (00) p�@ ? 0()̊̂ ]/ + :()̊/ + =()+0 (00`)

Aurtknroirn, wn hnlitn tkn hnve`teil ia iutput `lh tkn premn cnvnc ario tkn lnw cilb-rul nquecejreuo v`cun ulhnr ` j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics (M) `s7

› ? �›+ �› ›? { 0() + 0 ()}̊/ + :()̊/ + : ()̊/ + =()+0

(00―)

̹› ? ̎›+ ̎› ̹›? 0() + 0()̊/ + :()̊/ + :()̊/ + =()+0

(00―`)

Litn tk`t ≠ `lh ̹ ≠ ̹ . @ mcn`r skirtmioelb ia ` hicc`r-pnb rnbeon wetk m`pet`cmiltrics es tk`t m`pet`c elaciw es rnstremtnh, wkemk cn`hs ti ` ciwnr cilb-rul nquecejreuov`cun, miop`rnh wetk tk`t ulhnr ` j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics.

=.: J`sdnt-Vnb Znbeon wetk Rn`d M`pet`c Miltrics (J)

@s ` j`sdnt pnb es `l nxmnpteil`c m`sn ia ` aexnh rnbeon, nlhibnlius v`re`jcns `rntkn sòn `s ulhnr ` ^] hicc`r-pnb rnbeon. El tkes m`sn, tkn oilnt`ry ùtkirety `hguststkn oilny suppcy jy eltnrvnlelb el tkn airnebl nxmk`lbn o`rdnt el irhnr ti oèltèltkn v`cun ia tkn j`sdnt. Xkus, tkn eop`mts ia tkn airnebl o`rdnt eltnrvnlteil k`vn jnnlmilsehnrnh el tkes m`sn `s wncc. @s onlteilnh `jivn, ` j`sdnt es ` wnebktnh `vnr`bn iatkn ^] hicc`r r`tn `lh ynl r`tn. Nqu`teil (:) tibntknr wetk tkn j`sdnt nqu`teil, wkemkjnmions7

/ + (0 )/ ? (0:)wknrn Ν es tkn v`cun ia j`sdnt. Ario tkes nqu`teil `lh nqu`teil (8), wn m`l ijtèl7

/ ? (0 )/ , / ? / (0:`)

5 Nxprnsseils 0(), :(), =(), 0(), :(), =() `rn skiwl el @ppnlhex @:.

06


13/46


]icvelb nqu`teil (0), (=), (>), `lh (0:`) air tkn premn cnvnc `lh eltnrnst r`tn, tknaicciwelb snoe-rnhumnh airo nqu`teils `rn ijtèlnh7

+0 ? + 0 + T{(0 )} + (0 )_/+ T{››(0 )} + › ›(0 )_/, +0+ ( )/ + ( )/ + (0 + )(+0 )

(0=)

+0 ? (0 )+0/, + (0 + )(0 )/ (08) @s el ]nmteil =.0, wn `ssuon tkn sòn nxibnlius ^] hicc`r”ynl r`tn mk`lbn. Xknlnw nquecejreuo v`cun àtnr tkn ^] hicc`r”ynl r`tn mk`lbn es7

̎ ? 00 T{ ( + + )(0 )} + (0 )_̊/ + ( )̊+ ( )̊ +0 + (0 +)(̊+0 ̊)+ T{›+ (0 )( ›)} + › ›(0 )_̊ ,

(0>)

̎ ? (0 ) (0 + )̊/ ̊+0/, (01)Rn sicvn air tkn r`teil`c nxpnmt`teil `lh ijtèl nxprnsseils air � , ̎ , `lh ̎ 5A06 � ? 0()̊/ + :()̊/ + =()̊ (02)

̎ ? 0()̊/ + :()̊/ + =()̊ (02`)

̎?

(0

)T(0 +

)(0

8)_(0

)

̊/

(02j)

wknrn =()̊ `lh =()̊ miopresns jitk ̊/ `lh ̊/.=.= J`sdnt-Vnb Znbeon wetkiut M`pet`c Miltrics (M)

@s el ]nmteil =.:, wn usn nqu`teil (0:`) el tkes m`sn. ]elmn wn `ssuon pnranmt m`pet`coijecety, wn usn nqu`teil (0―) wetk ? 0. ]icvelb nqu`teils (:), (=), (>), `lh (0:`) air06

Rn skiw kiw ti sicvn air tkn r`teil`c nxpnmt`teil `lh hnrevn nqu`teils (02) `lh (02`) `lh nxprnsseils

0(), :(), =(), 0(), :(), =() el @ppnlhex @.:.00


14/46


tkn premn cnvnc `lh oilny suppcy, wn k`vn `l ehnltem`c snoe-rnhumnh airo `s elnqu`teil (0=) `lh tkn aicciwelb nqu`teil7

+0 ? (0 )+0/, +(0+ )(0 )/ (08―) @s el ]nmteil =.0, wn `ssuon tkn sòn nxibnlius ^] hicc`r”ynl r`tn mk`lbn. Xknlnw nquecejreuo v`cun àtnr tkn ^] hicc`r”ynl r`tn mk`lbn es � ? � `lh ̎ ? ̎ . Rnsicvn air tkn r`teil`c nxpnmt`teil `lh ijtèl nxprnsseils air � `lh ̎ `lhsumk `s700

� ? 0()̊/ + :()̊/ + =()̊ (0;) ̎ ? 0()̊/ + :()̊/ + =()̊ (0;`)

=.8 Aci`telb Znbeon wetkiut M`pet`c Miltrics (H)

^lhnr ` aci`telb rnbeon, tkn oilny suppcy ( ) jnmions nxibnlius. ]icvelbnqu`teils (0―), (=), `lh (>), wn ijtèl tkn aicciwelb twi nqu`teils7

/ ? 0: ( + ) +/ + (+0 ) + ›+0/,+ { + + (›+ ›)}+0/, / /

(05)

+0 ? = + 8 + >/

+ 1(+0 ) + 2+0/

,

+ ;+0/

,

+ 5/ + 06/

(:6)

wknrn : ? (0 + )( + )( + ).

00 Rn skiw kiw ti sicvn air tkn r`teil`c nxpnmt`teil `lh hnrevn nqu`teils (0;) `lh (0;`) `lh nxprnsseils

0(), :(), =(), 0(), :(), =() el @ppnlhex @.=.0:


15/46


Cilb-rul nquecejreuo v`cuns m`l jn ijtèlnh ario tkn nqu`teils jnciw7

̎H/ ? 0 8 ( + ) 8 ̎ (:0)

̎ ? 1 > + 2 > ̎/ 0 > � (::)

wknrn 8 ? ( +) :( + ). @s el ]nmteil =.0, wn `ssuon tkn sòn nxibnlius ^] hicc`r”ynl r`tn skimd. Xkn lnwnquecejreuo v`cuns àtnr tkn skimd `rn7

̎ ? = + 0( + ) + = + 0( + ) ̊/ + 0(̊+0 ̊) + :̊/ + =̊/ (:=)

̎/ ? 8 + :( +) + = +0( +) ̊/ + 0 (̊+0 ̊) + :̊/+ =̊/

(:8)

]icvelb air tkn tkn r`teil`c nxpnmt`teil yenchs nxprnsseils air � `lh ̎ 00A0: � ? 0()̊/ + :()̊ + =() (:>) ̎ ? 0()̊/ + :()̊ +=() (:>`)

=.> Hicc`r-Vnb Znbeon ulhnr Vnranmt M`pet`c Oijecety (N)

@s el ]nmteil =.0, tkn N`st @se`l murrnlmy”^] hicc r̀ r`tn (

/

) es tit`ccy nxibnlius

(/ ? 6) wknrn`s oilny suppcy es nlhibnlius. ^lhnr arnn m`pet`c oijecety, wnk`vn nqu`teil (0'), `lh tkn hionstem eltnrnst r`tn (+0) es aexnh `t tkn cnvnc ia tkn ^]eltnrnst r`tn (nlhibnlius), e.n., +0 ? .Xkn cilb-rul nquecejreuo v`cuns air tkn premn cnvnc `lh tkn oilny suppcy ulhnr tkesrnbeon `rn tkn sòn `s el nqu`teils (;) `lh (5)7 � ? � `lh ̎ ? ̎ . @s el tknprnveius sujsnmteil, wn `ssuon tkn sòn nxibnlius ^] hicc`r”ynl r`tn skimd. Lnwnquecejreuo v`cuns àtnr tkn skimd `rn tkn sòn ulhnr ` ^] hicc`r pnb wetk m`pet`cmiltrics7 ̎ ? ̎.0:

Rn skiw kiw ti sicvn air tkn r`teil`c nxpnmt`teil `lh hnrevn nqu`teils (:>) `lh (:>`) `lh nxprnsseil

0(), :(), =(), 0(), :(), =() el @ppnlhex @.8.0=


16/46


]icvelb air tkn r`teil`c nxpnmt`teil yenchs nxprnsseils air � `lh ̎ 7 � ? 0()̊/ + :()̊/ (:1)

̎?

0(

)

̊/

+

:(

)

̊/

(:1`)

8. XKN XZ@L]EXEIL V@XK XI IXKNZ N[MK@LBNZ@XN ZNBEON]

El tkes snmteil, wn hnaeln aiur tr`lseteil picemens `lh iln air oèltèlelb tkn murrnltrnbeon. Uiskeli, D`ge, `lh ]uzude (:668) aelh tk`t wknl miop`rnh wetk ` iln-pnreihciss, et wiuch jn hnser`jcn air ` so`cc ipnl nmilioy, cedn Xkèc`lh, ti `hipt ` j`sdntpnb ir ` aci`telb rnbeon r`tknr tk`l ` hicc`r-pnb rnbeon. El iur miltnxt, tkes eopcens tk`ttkn hnser`jcn rnbeon es netknr ` j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics (M) ir `

aci`telb rnbeon wetkiut m`pet`c miltrics (H) ivnr tkn cilb rul. 0= Rn milsehnr tknaicciwelb aiur tr`lseteil p`tks ti tkn prnanrrnh rnbeons `lh oèltèlelb tkn st`tus qui,sumk `s ` ^] hicc`r-pnb rnbeon wetk m`pet`c miltrics (@).

(0) Oèltèlelb ` hicc`r-pnb rnbeon (wetk stremt m`pet`c miltrics)7 (@) ” (@) ” (@)

(:) @ br`hu`c skeat ario ` hicc`r-pnb ti ` j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics(br`hu`c `hgustonlts ia jitk m`pet`c miltrics `lh j`sdnt wnebkt)7 (@) ” (J) ” (M)

(=) @ suhhnl skeat ario ` hicc`r-pnb ti ` j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics (`suhhnl rnoiv`c ia m`pet`c miltrics `lh ` suhhnl skeat ia j`sdnt wnebkts)7 (@) ” (M) ”(M)

(8) @ suhhnl skeat ario ` hicc`r-pnb ti ` aci`telb rnbeon (` suhhnl rnoiv`c ia m`pet`c

miltrics `lh ` suhhnl elmrn`sn ia acnxejecety el tkn nxmk`lbn r`tn)7 (@) ” (H) ” (H)

(>) @ suhhnl skeat ario ` hicc`r pnb ti ` o`l`bnh-aci`telb rnbeon (` suhhnl rnoiv`c iam`pet`c miltrics `lh ` suhhnl elmrn`sn ia acnxejecety el tkn nxmk`lbn r`tn wetk imm`seil`celtnrvnlteil)7 (@) ” (H) ” (N) ” (H).

0= Uiskeli, D`ge, `lh @siluo` (:668) milaero tk`t et es `csi tkn m`sn air twi eltnrhnpnlhnlt so`cc ipnl

nmilioens tk`t tkn hnser`jcn rnbeon es netknr ` j`sdnt pnb wetkiut m`pet`c miltrics (M) ir ` aci`telbrnbeon wetkiut m`pet`c miltrics.

08


17/46


Aeburn :7 Xr`lseteil Vicemens Xiw`rh tkn Hnsernh Znbeon

]iurmn7 @utkirs― eccustr`teil.

Xkn aerst picemy es sustèlelb ` hicc`r-pnb rnbeon. Xkn oilnt`ry ùtkirety eopisnsm`pet`c miltrics `lh aexns ` wnebkt il tkn hicc`r r`tn `t 0. Xkn snmilh picemy elmcuhns `tr`lseteil pnreih (J), wkemk rnacnmts `l `hgustonlt pnreih ia m`pet`c miltrics `lh j`sdntwnebkts. Xkes picemy st`rts ario ` hicc`r-pnb rnbeon `lh ulhnrbins ` tr`lseteil pnreih(J) `lh `rrevns `t ` j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics (M). Xkn tkerh picemyhins lit elmcuhn ` tr`lseteil pnreih (J)4 tknrnairn, tkn oilnt`ry ùtkirety skeats ario `hicc`r-pnb rnbeon ti ` j`sdnt-pnb rnbeon wetkiut `ly eltnreo pnreih, eopcyelb tknnmilioy wecc guop ti tkn hnsernh j`sdnt-pnb rnbeon. Xkn aiurtk es tk`t tkn oilnt`ryùtkirety skeats ario ` hicc`r pnb ti ` aci`telb rnbeon wetkiut ` tr`lseteil pnreih,eopcyelb tk`t tkn nmilioy wecc suhhnlcy guop ti ` aci`telb rnbeon. Xkn aeatk picemy estk`t tkn oilnt`ry ùtkirety skeats ario ` hicc`r-pnb rnbeon ti ` o`l`bnh-aci`telbrnbeon wetkiut ` tr`lseteil pnreih. ^lhnr ` o`l`bnh-aci`telb rnbeon, ea tkn nxmk`lbnr`tn acumtu`teil es sebleaem`lt, tkn oilnt`ry ùtkirety eltnrvnlns el tkn airnebl nxmk`lbno`rdnt ti oèltèl tkn nxmk`lbn r`tn `t ` milst`lt r`tn (N). Itknrwesn, tkn oilnt`ry

ùtkirety `cciws tkn nxmk`lbn r`tn ti acumtu`tn `s cilb `s tkn nxmk`lbn r`tn hins lithnve`tn sujst`lte`ccy ario ets hnsernh cnvnc.

Rn `ssuon tk`t tkn teon eltnrv`c air tkn elete`c hicc`r-pnb rnbeon es 6. Aurtknroirn, wnrnb`rh tkn tr`lseteil pnreih `s 0 `lh tkn teon eltnrv`c àtnr tkn ùtkirety rn`mkns tknt`rbnt rnbeon `s :. Rn snt ` hesmiult a`mtir `s . Aeburn : hespc`ys tkn aevn picemens.

0>


18/46


Xkriubkiut tkes snmteil, wn milsehnr tkn m`sn ia tkn oilnt`ry ùtkirety èoelb tioeleoezn iutput acumtu`teils, skiwl ̀ s7 08

(

0,

:) ?

√0++

?0(

�›)

:

(:2)

Litn tk`t ` rnhumnh airo �› v`rens hnpnlhelb il tkn nxmk`lbn r`tn rnbeons, `snxpcèlnh el ]nmteil =.

8.0 Oèltèlelb ` Hicc`r-Vnb Znbeon (0)

Xkn miultry milteluns ` hicc`r-pnb rnbeon air tkn nltern teon pnreih 6 + 0 + :, `lhets muouc`tevn ciss, bevnl ipteo`c eltnrnst r`tn e−, es nxprnssnh `s aicciws70>

0(−,0 + :) ? √0 �@› : +?0 √0 @› :++

?+0

? √0( �@› ): +?0 √0

{ 0() + 0 ()}̊/ + :()̊/+ : ()̊/ + =()−

:++?+0

(:;)

−?

0(

−,

0+

:)

(:;―)

wknrn � ? 0()̊̂ ]/ + :()̊/ + =()− . Litn tk`t − es mkisnl tioeleoezn tkn muouc`tevn ciss el tnros ia hnve`teil ario ets st`jcn nquecejreuo v`cunulhnr ` hicc`r-pnb rnbeon.

08 El tkn m`sn ia premn cnvnc st`jecety, tkn muouc`tevn ciss m`l jn skiwl `s

(0,:) ? √0++?0 ( ̎›): (:2`)

0> Xkn muouc`tevn ciss nv`cu`tnh el tnros ia hnve`teil ia tkn premn cnvnc ario tkn stn`hy st`tn es skiwl `s

aicciws7

0− ,0 + : ? √0 ̎› : + √0( ̹ ):++?

?0

(:;`)− ? 0− ,0 + : (:;―`)

wknrn p�@ ? 0()̊̂ ]/ + :()̊/ + =()−. 01


19/46


8.: Br`hu`c @hgustonlt ti ` J`sdnt Vnb wetkiut M`pet`cMiltrics (:)

Aerst, wn hnlitn `l ipteo`c j`sdnt wnebkt `s

− `ssuoelb 6

≨ − ≨

0. @s nxpcèlnh

`jivn, tkn oilnt`ry ùtkirety st`rts jy `hiptelb ` hicc`r-pnb rnbeon wetk m`pet`cmiltrics (@), elhem`telb tk`t ets j`sdnt wnebkt es nqu`c ti 0. Xknl et skeats ti ` j`sdnt-pnbrnbeon `lh br`hu`ccy cisns ` hnbrnn ia m`pet`c miltric ulhnr rnbeon (J). ]eouct`liuscy,tkn ùtkirety hnmrn`sns ets j`sdnt wnebkt jy (0 −)/0 n`mk pnreih hurelb etstr`lseteil pnreih el irhnr ti `rrevn `t ` j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics. Ilmntkn oilnt`ry ùtkirety `hipts tkn t`rbntnh j`sdnt-pnb rnbeon, et oèltèls ets ipteo`cj`sdnt wnebkt `t −. Xkn muouc`tevn ciss ia tr`lseteil picemy (:) wetk `l ipteo`c j`sdntwnebkt − m`l jn nxprnssnh `s01 :(−,0,:) ? √0( � ): + √0( � ): ++

?+0

?0

√0++

?++0

( � ):

? √0( � ): +?0 √0 0()()̊/ + :()̊/ + =()̊ :+

?+0

+ √0 0()−̊/ + :()̊/ + =()̊ :++?++0

(:5)

wknrn � ? 0()̊/

+ :()̊/ + =()− `lh () ? 0 0√− ( 6).

01 Xkn muouc`tevn ciss nv`cu`tnh el tnros ia tkn hnve`teil ia tkn premn cnvnc ario ets stn`hy st`tn es hnaelnh

`s aicciws7:− ,0 + : ? ∐ √0( ̎ ): +∐ √0( ̎ ): ++?+0?0 ∐ √0++?++0 ( ̎ ): (:5`)

wknrn ̎›

? 0()̊̂ ]/

GV + :()̊N@/

GV + =()− `lh − es tkn ipteo`c j`sdnt wnebkt air tkntr`lseteil picemy ia st`jecezelb tkn premn cnvnc.02


20/46


Litn tk`t tkn snmilh `lh tkn tkerh tnros il tkn rebkt-k`lh sehn ia nqu`teil (:5) skiwcissns ulhnr tr`lseteil pnreihs `lh ulhnr tkn j`sdnt-pnb rnbeon (M), rnspnmtevncy. Xknipteo`c wnebkt es hnrevnh jy oeleoezelb tkn muouc`tevn ciss :(−,0 + :) wetk rnspnmtti tkn wnebkt

−7

− ? 00 √00()̊/ :()̊/ + =()̊++?++0+ √00() 60 ̊/ 0()

60 ̊/+:()̊/ + =()̊

+?+0

(:5―)

wknrn 0 ? ∐ √0 0() √ ̊/ : ++?+0 ∐ √0 0()̊/:++?++0 .8.= ]uhhnl ]keat ti ` J`sdnt Vnb wetkiut M`pet`c Miltrics (=)

@s onlteilnh, tkn oilnt`ry `utkirety st`rts wetk ` hicc`r-pnb rnbeon wetk m`pet`cmiltrics (@), eopcyelb tk`t ets j`sdnt wnebkt es aexnh `t 0, `lh suhhnlcy skeats ti `j`sdnt-pnb rnbeon eopcnonltelb `l ipteo`c wnebkt (−−) wetkiut m`pet`c miltrics (M).Xkn muouc`tevn ciss air picemy (=) wetk tkn ipteo`c j`sdnt wnebkt −− `lh t`rbnt rnbeonpnreih 0 + : es skiwl `s702

=−−,0 + :, /,: ? √0( � ): +

?0 √0+

+

?+0 ( � ): ? √0( � ): +

?0 √0 0()−−̊/ + :()̊/ + =()̊

:++?+0

(=6)

−− ? 0

: √0

0(

)

̊/

:(

)

̊/

+

=(

)

̊

++

?+0

(=6―)

02 Xkn muouc`tevn ciss air st`jecezelb tkn premn cnvnc es skiwl `s aicciws7

=−−,0 + :, ̍/,: ? √0( ̎ ): +?0 √0

++?+0

(̎ ): (=6`)

wknrn ̎ ? 0()̊̂ ]/

+ :()̊/

+ =()− `lh −− es tkn ipteo`c wnebkt air st`jecezelbtkn premn cnvnc.0;


21/46


Rknrn � ? 0()̊̂ ]/ + :()̊/ + =()− `lh: ? ∐ √0 0()̊/:++?++0 . ̍/,: ? ∐ 0 / :6+0+:?6+0 hnlitns ` suo ia hesmiultnh squ`rns ia tkn ^] hicc`r r`tn. Xkn eop`mts ia nxmk`lbn

r`tn vic`tecety àtnr tkn skeat `rn elmcuhnh el tkn snmilh tnros il tkn rebkt-k`lh sehn ianqu`teil (=6). Rknl miop`rnh wetk tkn j`sdnt wnebkt ijtèlnh el snmteil 8.:, −− esheaanrnlt ario − `s cilb `s tkn tr`lseteil pnreih nxests, 0 ≦ 6.8.8 ]uhhnl ]keat ario ` Hicc`r-Vnb ti ` Aci`telb Znbeon (8)

Xkn oilnt`ry ùtkirety st`rts jy `hiptelb ` hicc`r-pnb rnbeon wetk m`pet`c miltrics (@),`lh et suhhnlcy guops ti ` aci`telb rnbeon wetkiut m`pet`c miltrics. Xkn muouc`tevn cissulhnr picemy (8) wetk `l ipteo`c oilny suppcy − `lh tkn t`rbnt rnbeon pnreih X0 + X: es skiwl `s aicciws70;

8−,0 + :, /,: ? √0( � ): +?0 √0++?+0 ( � ): ? √0( � ): +

?0 √0 0()̊/ + :()̊ + =()−

:++?+0

(=0)

− ? 0

= √0=

(

)

̊/

0(

)

̊/

+

:(

)

̊++

?+0

(=0―)

wknrn � ? 0()̊/ + :()̊/ + =()− `lh= ? ∐ √0=():++?++0 .Xkn eop`mts ia nxmk`lbn r`tn vic`tecety `ssime`tnh wetk tkn skeat `rn elmcuhnh el tknsnmilh tnro il tkn rebkt-k`lh sehn ia nqu`teil (=0).

0; Xkn muouc`tevn ciss air st`jecezelb tkn premn cnvnc es hnaelnh `s aicciws7

8− ,0 + :, ̍/,: ? √0 ̎› : +?0 √0

++?+0

̎› : (=0`)

wknrn

̎

› ?

0(

)

̊/

+

:(

)

̊/ +

=(

)

− `lh

− es `l ipteo`c oilny suppcy air st`jecezelb

tkn premn cnvnc.

05


22/46


8.> ]uhhnl ]keat ario ` Hicc`r-Vnb ti ` O`l`bnh-Aci`telbZnbeon (>)

Aicciwelb tkn prnveius snmteil, wn hnlitn `l ipteo`c oilny suppcy ulhnr tkn aci`telb

rnbeon `s −− . Xkn oilnt`ry ùtkirety st`rts jy `hiptelb ` hicc`r-pnb rnbeon wetkm`pet`c miltrics (@), `lh et suhhnlcy skeats ti ` aci`telb rnbeon wetkiut m`pet`c miltrics.Imm`seil`ccy, wknl tkn ^] hicc`r r`tn acumtu`tns sebleaem`ltcy, et eltnrvnlns el tknairnebl nxmk`lbn o`rdnt ti oèltèl tkn ^] hicc`r r`tn `t ` milst`lt cnvnc ulhnrpnranmt m`pet`c oijecety (N). @atnr tkn vic`tecety ia tkn hicc`r r`tn oihnr`tns, et `hipts àci`telb rnbeon. Xknsn eltnrvnlteils `rn eopcnonltnh ilcy tnopir`recy ti `vieh c`rbnacumtu`teils ia tkn nxmk`lbn r`tn. Xkn muouc`tevn ciss ulhnr picemy (>) wetk wkicnpnreih 0 + :, pnreih ia ` aci`telb XH, `lh tnopir`c pnreih ia ` hicc`r pnb XN es skiwl`s705

> −−,0 + :, , , ̍,/$,:? √0( � ): +?0 √0

+?+0

( � ): + √0++?++0 ( � ):

+ √0++?+++0 ( � ): (=:)

−− ? 0

8 √0=()0()̊/ +:()̊+

?+0

+ √0=() 0()̊/ + :()̊++

?+++0

(=:―)

05 Xkn muouc`tevn ciss air st`jecezelb tkn premn cnvnc es hnaelnh `s aicciws7> −−,0 + :,, , ̍,/$,:

? √0( ̎ ): +?0 √0

+?+0

( ̎ ): + √0++?++0

( ̎ ):+ √0++?+++0 ( ̎ ):

(=:`)

wknrn ̎›

? 0()̊̂ ]/

GV + :()̊N@/

GV + =()− `lh −− es `l ipteo`c oilny suppcy airst`jecezelb tkn premn cnvnc.:6


23/46


wknrn � ? 0()̊/ + :()̊/ + =()− , � ? 0()̊/ + :()̊/ `lh 8 ? ∐ √0=(): ++?+0 ∐ √0=():++?+++0 .̍,/,: ? ∐ √0̊,/,:++?++0 es hnaelnh `s ` suo ia hesmiultnh squ`rns ia tkn hicc`r r`tns hurelb tkn eltnrvnlteilpnreihs. Xkn eop`mts ia tkn nxmk`lbn r`tn vic`tecety `ssime`tnh wetk tkn skeat `rnelmcuhnh el tkn snmilh tnro il tkn rebkt-k`lh sehn ia nqu`teil (=:). Rknl miop`rnhwetk `l ipteo`c oilny suppcy ijtèlnh el ]nmteil 8.8, −− es heaanrnlt ario − `s cilb`s tkn eltnrvnlteil pnreih nxests ≦ 6.>. MIOV@ZE]IL IA XZ@L]EXEIL VICEMEN]

El tkes snmteil, wn milsehnr tkn ipteo`c picemy air tkn oilnt`ry ùtkirety el irhnr tist`jecezn iutput a cumtu`teils.:6 Iur hesmusseil mnltnrs il twi qunsteils tkriubkiut tkessnmteil7 (e) Es et hnser`jcn air tkn oilnt`ry ùtkirety ti oèltèl ` hicc`r-pnb rnbeonivnr tkn cilb rul9 (ee) Rk`t wiuch jn `l ipteo`c picemy, bevnl tk`t tkn ùtkirety hnmehnsti hnve`tn ario tkn st`tus qui9 Rn `hv`lmn iur `rbuonlt el tkrnn stnps. Aerst, wn`ppcy sion eopcem`teils ario st`tem `l`cyses elti tkes hylòem miltnxt. Xknl, wnmiop`rn tkn muouc`tevn ciss ia tkn murrnlt picemy, picemy (0), wetk itknr tr`lseteilpicemens ti prnanrrnh rnbeons. @atnr wn aelh tk`t oèltèlelb ` hicc`r-pnb es lit tkn`ppripre`tn sicuteil ivnr tkn cilb rul, wn ciid air `l ipteo`c iutmion air tkn ùtkiretyario òilb tkn aiur tr`lseteil`c picemens.

>.0 Eopcem`teils air ]t`tem @l`cyses

Aerst, wn rnacnmt il sion eopcem`teils ario st`tem `l`cyses. ^selb ` st`tem so`cc ipnl-nmilioy bnlnr`c nquecejreuo oihnc, Uiskeli, D`ge, `lh ]uzude (:668) skiw tk`t et eslit hnser`jcn air tkn miultry ti `hipt ` hicc`r pnb miop`rnh wetk ` j`sdnt-pnb ir àci`telb rnbeon4:0 tkn v`cun ia tkn wnca`rn ciss ulhnr ` hicc`r pnb es kebknr tk`l tk`tulhnr ` j`sdnt pnb ir ` aci`telb rnbeon `t tkn stn`hy st`tn air iln pnreih. Rn m`lnxprnss tknsn eopcem`teils jy uselb ` iln-pnreih ciss el tkes oihnc `s aicciws7 ::

( ) < ( � ) (==)(

) < (

� ) (==―)

Litn tk`t tknsn rnsucts kich ulhnr rnbeons tk`t k`vn jnnl oèltèlnh air snvnr`cpnreihs.

:6 @ hesmusseil milmnrlelb st`jecezelb tkn premn cnvnc es `csi privehnh el tkn aiitlitns ia tkes p`pnr.

:0 Aurtknroirn, Uiskeli, D`ge, `lh @siluo` (:668) aelh tk`t tkes es `csi tkn m`sn air twi so`cc ipnl

nmilioens, wkemk `rn outu`ccy hnpnlhnlt el ` st`tem `l`cyses.::

]eoec`rcy, wn m`l nxprnss tknsn eopcem`teils jy uselb ` iln-pnreih ciss el tnros ia tkn hnve`teil ia tkn

premn cnvnc ario tkn stn`hy st`tn `s aicciws7

̹›

<

̎›

(==`)

̹›


24/46


>.: Miop`resil ia Vicemy (0) `lh Itknr Xr`lseteil Vicemens

Rn hesmuss tkn hnser`jecety ia ` hicc`r pnb ivnr tkn cilb rul jy miop`relb picemy (0)`lh itknr tr`lseteil picemens ti ` j`sdnt pnb ir ` aci`telb rnbeon. Rn st`rt wetk `

miop`resil jntwnnl oèltèlelb ` hicc`r pnb, picemy (0), `lh ` suhhnl skeat ti `j`sdnt-pnb rnbeon wetkiut m`pet`c miltrics, picemy (=). Rn hnaeln ` tkrnskich teonpnreih XM− sumk tk`t7 0(−,−) ? =−−,−, /,: nxprnsselb ` teon eltnrv`c ulhnr wkemk tkn muouc`tevn ciss ia oèltèlelb ` hicc`r pnbes nqu`c ti iln ia skeatelb ti ` j`sdnt pnb. X`delb elti `mmiult tk`t tkn `jivn nqu`teilkichs ulhnr tkn t`rbnt rnbeon pnreih, wn ijtèl tkn aicciwelb st`tnonlts7:=

0(−, ) 3 =−−, , /,: 3 − (=8)

0(

−,

) <

=−−,

,

/,:

<

−

(=8―)

Xkes on`ls tk`t ea t es skirtnr tk`l tkn tkrnskich teon pnreih −, tknl tkn muouc`tevnciss ia oèltèlelb ` hicc`r pnb es so`ccnr tk`l tk`t ia tr`lseteilelb ti ` j`sdnt pnb. Xkes miuch k`ppnl ilcy ea tkn nxmk`lbn r`tn vic`tecety lnb`tevncy àanmts tkn nmilioy. :8 Kiwnvnr, ea t es cilbnr tk`l tkn tkrnskich teon pnreih −, tknl ` muouc`tevn ciss iaoèltèlelb ` hicc`r-pnb rnbeon es kebknr tk`l ` suhhnl skeat ti ` hnsernh j`sdnt-pnbrnbeon. Xkn cilbnr tkn teon pnreih ia `hiptelb ` j`sdnt pnb, tkn oirn jnlnaets tknmiultry m`l ijtèl ario skeatelb ti ` j`sdnt-pnb rnbeon `s skiwl el nqu`teil (=8―).

Lnxt, wn miop`rn tkn cissns ulhnr oèltèlelb ` hicc`r-pnb, picemy (0), ti skeatelb ti àci`telb rnbeon, picemy (8). Rn hnaeln ` tkrnskich teon pnreih

− sumk tk`t7

0(−,−) ? 8−,− , /,: hnlitelb tkn teon eltnrv`c ulhnr wkemk ` muouc`tevn ciss ia oèltèlelb ` hicc`r pnb esnqu`c ti tk`t ia skeatelb ti ` aci`telb rnbeon. Znacnmtelb tk`t tkn `jivn nqu`teil kichsulhnr tkn t`rbnt rnbeon pnreih àtnr tkn skeat, tkn aicciwelb milheteils kich7

0(−, ) 3 8−, , /,: 3 − (=>)0(−, )


25/46


Xknsn eopcy tk`t tkn cilbnr tkn pnreih ia `hiptelb ` aci`telb rnbeon, tkn c`rbnr tknjnlnaets tkn miultry m`l ijtèl ario skeatelb ti ` aci`telb rnbeon `s skiwl el nqu`teil(=>―).

]uoo`rezelb tkn rnsucts onlteilnh `jivn, oèltèlelb ` hicc`r-pnb rnbeon es hnser`jcn

ilcy el tkn skirt tnro, e.n., 3 T,−,−_.:>

@s tkn t`rbnt teon pnreih bnts cilbnr, tknmiultry m`l ijtèl brn`tnr jnlnaets ario skeatelb suhhnlcy ti netknr ` j`sdnt pnb ir àci`telb rnbeon.

>.= Miop`resil òilb Xr`lseteil Vicemens

Rn tknl nxòeln `l ipteo`c picemy òilb tkrnn tr`lseteil picemens. Xknrn `rn jnlnaets`lh mists air tkn tkrnn tr`lseteil picemens (:), (=), `lh (8), `s skiwl el X`jcn :. Airmiopilnlts ia mists, nsteo`tns j`snh il luonrem`c `l`cyses `rn privehnh el X`jcn =.

X`jcn :7 Jnlnaets `lh Mists ia Xr`lseteil Vicemens

Vicemy Jnlnaets Mists

(0) Oèltèlelb `hicc`r pnb

`. Li vic`tecety ia / `. Ceoetnh m`pet`c elaciws(:) Br`hu`ccyskeatelb ti ` j`sdntpnb

`. ]o`cc vic`tecety ia j. ]o`cc vic`tecety ia /, / m. ]o`cc hnve`teils ia /,, /,

`. Xeon ti rn`mk st`jcnrnbeonj. @hgustonlt mists

(=) ]uhhnlcy skeatelbti ` j`sdnt pnb

`. Zn`mkelb st`jcn rnbeon `t ilmn(kebknr jnlnaets ulhnr st`jcn rnbeon)j. Li `hgustonlt mists

m. ]o`cc hnve`teil ia

/

,

,

/

,

`. Kebk vic`tecety ia .j. Kebk vic`tecety ia /,/

(8) ]uhhnlcy skeatelbti ` arnn aci`telbrnbeon

`. Zn`mkelb st`jcn rnbeon `t ilmn(kebknr jnlnaets ulhnr hnser`jcn rnbeon)j. Li `hgustonlt mists

`. Kebk vic`tecety ia e

j. Kebk vic`tecety ia /,/ m. C`rbn hnve`teils ia/,, /,

(>) ]uhhnlcy skeatelbti ` o`l`bnhaci`telb rnbeon

`. Zn`mkelb st`jcn rnbeon `t ilmn(kebknr jnlnaets ulhnr hnser`jcn rnbeon)j. Li `hgustonlt mistsm. Ceoetnh nxmk`lbn r`tn acumtu`teils

`. Kebk vic`tecety ia j. Li oilnt`ry picemyùtilioy hurelbeltnrvnlteils

]iurmn7 @utkirs― miopec`teil.

:> Air tkn m`sn ia premn st`jecety, 3 ,−,−. :=


26/46


X`jcn =7 Nsteo`tns ia Mists ulhnr tkn Aevn Vicemens

Vicemy Mists Nsteo`tns

VZM Xkèc`lh

(0) Oèltèlelb `

hicc`r pnb

`. Ceoetnh m`pet`c elaciws 6.6==` 6.66=

`

(:) Br`hu`ccy skeatelbti ` j`sdnt pnb

`. Xeon ti rn`mk st`jcn rnbeonj. @hgustonlt mists

6.66=6.6611

m

6.6666516.66666625

m

(=) ]uhhnlcy skeatelbti ` j`sdnt pnb

`. Kebk vic`tecety ia .j. Kebk vic`tecety ia /,/ 6.66:;h 6.66=6n 6.666666=2h 6.6660;n

(8) ]uhhnlcy skeatelbti ` arnn aci`telbrnbeon

`. Kebk vic`tecety ia j. Kebk vic`tecety ia /,/ m. C`rbn hnve`teils ia /,, /,

6.66=86.6=8

n

6.660=a

6.66666=;6.66>6

n

6.6666:8a

(>) ]uhhnlcy skeatelb

ti ` o`l`bnhaci`telb rnbeon

`. Kebk vic`tecety ia

j. Li oilnt`ry picemy ùtilioy hurelbeltnrvnlteils

6.66=8

6.6:=b

6.66666=;

6.666=;b

VZM ? Vnipcn―s Znpujcem ia Mkel`.

` Xkn nsteo`tn es tkn muouc`tevn ciss ivnr 5 qu`rtnrs (iln elete`c pnreih `lh : yn`rs).

j Xkn nsteo`tn es tkn heaanrnlmn jntwnnl muouc`tevn cissns ulhnr ` tr`lseteil pnreih ia 08 qu`rtnrs `lh iln ia

0; qu`rtnrs.m Xkn nsteo`tn es tkn heaanrnlmn jntwnnl muouc`tevn cissns j`snh il j`snceln `lh il ` :6% hnve`teil ario

tkn j`snceln .h Xkn nsteo`tn es tkn mk`lbn el muouc`tevn cissns hun ti `l elmrn`sn el eltnrnst r`tns irebel`ccy hrevnl jy `

6.660-ulet hnve`teil / skimd.n Xkn nsteo`tn es ` mk`lbn el muouc`tevn cissns hun ti ` 6.660-ulet / skimd.

a Xkn nsteo`tn es ` mk`lbn el muouc`tevn cissns hun ti ` 6.660-ulet /, skimd.

b Xkn nsteo`tn es ` ar`mteil ia muouc`tevn cissns hurelb eltnrvnlteil pnreihs.

]iurmn7 @utkirs― m`cmuc`teils.

Xknsn jnlnaets `lh mists `rn t`dnl elti `mmiult jy nv`cu`telb tkn muouc`tevn cissnsnxprnssnh jy nqu`teils (:5), (=6), `lh (=0). Jy miop`relb muouc`tevn cissns, wn m`l`l`cyzn `l ipteo`c tr`lseteil picemy skiuch tkn oilnt`ry ùtkirety hnmehn ti skeat ario `hicc`r-pnb rnbeon.

Rn st`rt jy miop`relb ` br`hu`c `hgustonlt ti ` j`sdnt pnb, picemy (:), `lh ` suhhnlskeat ti ` j`sdnt pnb, picemy (=). Bevnl teon pnreih X:, wn hnaeln 0− sumk tk`t:(−,0−,:) ? =−−,0− + :, /,: rnacnmtelb ` teon eltnrv`c air tkn tr`lseteil pnreih ulhnr wkemk tkn muouc`tevn ciss ia `

br`hu`c `hgustonlt picemy es nqu`c ti ` suhhnl skeat ti ` j`sdnt pnb.

:8


27/46


J`snh il tkn a`mt tk`t tnros el =−−,0− + :, /,: elmcuhn ` kebkcy vic`tecnnxmk`lbn r`tn `lh eltnrnst r`tn hun ti tkn skeat, et es `pp`rnlt tk`t tkn aicciwelb rnsuctswecc kich7:1

:(

−,

0,

:) 3

=−−,

0+

:,

/

,:

03

0− (=1)

:(−,0,:)


28/46


Ael`ccy, wn milsehnr wkntknr et es hnser`jcn ti skeat ti ` o`l`bnh-aci`telb rnbeon, picemy(>), r`tknr tk`l ` arnn-aci`telb rnbeon, picemy (8). Bevnl teon pnreih 0 + : , , ,oilny suppcy − `lh −−, `lh nxmk`lbn r`tn vic`tecety air tkn wkicn pnreih ̍/,:, wnhnaeln tkn nxmk`lbn r`tn vic`tecety air eltnrvnlteil pnreihs

̍,

/,:−−

4

> −−,0 + :, , , ̍,/,:−− ? 8−,0 + :, /,:−− rnacnmtelb ` suo ia hesmiultnh squ`rns ia tkn ^] hicc`r r`tn hurelb eltnrvnlteil pnreihsel wkemk tkn muouc`tevn ciss ia skeatelb ti ` o`l`bnh-aci`telb rnbeon es nqu`c ti tk`t ia` skeat ti ` arnn-aci`telb rnbeon. Ea tkn nxmk`lbn r`tn acumtu`tns sebleaem`ltcy hurelb tknskirt pnreihs, tkn miultry wecc jn jnttnr iaa eltnrvnlelb ti `vieh tkn lnb`tevn eop`mts iatkn nxmk`lbn r`tn swelb il tr`hn `lh m`pet`c aciws. Xkes m`l jn nxprnssnh `s7

> −−,0 + :, , , ̍,/,: 3 8−,0 + :, /,: ̍,/,: −−,0 + :, , , ̍,/,: ), `lh ti ` arnn-aci`telb rnbeon, picemy (8), tknmiultry wecc jn jnttnr iaa skeatelb ti ` o`l`bnh-aci`telb rnbeon, bevnl tkn c`rbn

nxmk`lbn r`tn acumtu`teils hurelb tkn skirt pnreihs.

:1


29/46


1. ]EO^C@XEIL N[NZME]N]7 XKN VZM @LH

XK@EC@LHEl tkes snmteil, wn rnpirt seouc`teil nxnrmesns uselb VZM `lh Xkè h`t`. ^selbnsteo`tnh p`ròntnrs air tkn twi miultrens, wn qu`lteay muouc`tevn cissns airtr`lseteil`c picemens. Iur qu`ltet`tevn rnsucts suppirt tkn tknirntem`c aelhelbs nxpcèlnhel ]nmteils >.: `lh >.=4 aerst, òilb tkn aevn picemens, oèltèlelb ` hicc`r pnb, picemy(0), cn`hs ti tkn kebknst cissns el jitk tkn VZM `lh Xkè m`sns. ]nmilh, wknlmiltr`stelb twi tr`lseteil picemens ti ` j`sdnt-pnb rnbeon, ` br`hu`c `hgustonlt r`tknrtk`l ` suhhnl skeat es hnser`jcn el jitk miultrens. Ael`ccy, wknl miop`relb ` skeat ti `j`sdnt pnb wetk ` skeat ti ` aci`telb rnbeon, air Xkèc`lh et es jnttnr ti skeat ti ` j`sdntpnb. Air tkn VZM, tkn rnsucts hnpnlh il picemy bi`cs7 air st`jecezelb iutput, ` skeat ti `j`sdnt pnb es prnanr`jcn, wkecn air st`jecezelb tkn premn cnvnc, ` skeat ti ` aci`telb rnbeon

es jnttnr.

1.0 H`t` `lh Znbrnsseil Znsucts

Rn usn VZM `lh Xkè qu`rtnrcy h`t` ario EOA Eltnrl`teil`c Ael`lme`c ]t`testems (EA]).Oist v`re`jcns, nxmnpt eltnrnst r`tns, `rn hnaelnh el l`tur`c cibs. Air nxmk`lbn r`tnresds, wn usn tkn v`re`lmn ia oiltkcy nxmk`lbn r`tn h`t` `s ` prixy. @ppcyelb tknHemdy-Auccnr bnlnr`ceznh cn`st squ`rns (HA-BC]) ulet riit tnsts, wn aelh sion v`re`jcnsk`vn ulet riits. Xknl wn oivn ilti Gik`lsnl mieltnbr`teil tnsts (Gik`lsnl 055:,055>) `lh privn tk`t `cc v`re`jcns el jitk tkn VZM `lh Xkè sòpcns `rn st`teil`ry. :2 Rn `ppcy tkn elstruonlt`c v`re`jcn (EQ) ontkih ti nsteo`tn p`ròntnrs seouct`lniuscy.Rn heaanrnlte`tn twi sòpcn pnreihs j`snh il rnbeon7 air tkn VZM m`sn (e) P0 0555”

P: :66> air ` hicc`r pnb rnbeon `lh (ee) P= :66>”P8 :606 air ` aci`telb rnbeon. :; @s

tkn VZM k`s lnvnr `hiptnh ` hn a`mti aci`telb rnbeon, wn usn nsteo`tnh minaaemenltsijtèlnh air ` j`sdnt-pnb rnbeon (ee). Air tkn Xkè m`sn, wn snt (e) P0 055=”P: 0552air ` hicc`r pnb `lh ` j`sdnt pnb `lh (ee) P= 0552”P0 :661 air ` aci`telb rnbeon. @huooy v`re`jcn es usnh ti nxmcuhn eop`mts ia tkn @se`l murrnlmy mreses pnreih P=0552”P: 055; air tkn Xkè m`sn (>tk micuol el X`jcn 8).

:2 Znsucts ia ulet-riit tnsts `lh mieltnbr`teil tnsts `rn rnpirtnh el @ppnlhex M.

:;

Uiskeli, D`ge, `lh @siluo` (:608) aelh noperem`ccy tk`t tkn nsteo`tnh wnebkt ia tkn ^] hicc`r r`tn el tknmurrnlmy j`sdnt ia tkn VZM hnmrn`snh ario 0.6 ti 6.;: ivnr tkn sòpcn pnreih.

:2


30/46


X`jcn 87 Nsteo`teil Znsucts

Minaaemenlt VZM Xkèc`lh

Aexnh,j`sdnt pnb

Aci`telb` Aexnh,

j`sdnt pnbAci`telb

]òpcn P0 0555”P: :66>

P= :66>”P8 :606

P0 055=”P: 0552

P= 0552”P0 :661 - 6.:1*** (6.65) - 6.>0** (6.62) - 6.6>** (6.6=) - 6.661 (6.6:) =.:6*** (6.;5) 06.0=*** (0.;5) 6.6> (6.6;) 0.26** (6.;:) 6.:=*** (6.6>) 6.>6*** (6.06) 6.58*** (6.05) 6.88 (6.=1), › -0.:6 (:.>0) 0.:2* (6.15) -6.2=*** (6.6;) 6.60 (6.06),› 6.26** (6.==) -6.662 (6.8:) 6.:2*** (6.62) -6.66> (6.6;)

-6.>: (6.=;) 6.1=** (6.:>) -=.2=*** (6.>6) 0.0=*** (6.=8) -=1.00 (81.2;) -6.08 (6.22) 6.6> (6.::) 6.66: (6.665) 6.86 (0.>6) ;.11 (0>.50) -:.66 (:.>>) 6.>= (6.58) 6.01*** (6.6:) 6.0=*** (6.68) 6.60*** (6.66=) 6.662*** (6.660) -6.68* (6.6:) 6.60:** (6.66>) -6.:>*** (6.68) 6.:6*** (6.6>), › -6.61* (6.6=) -6.0>** (6.62) -6.05*** (6.6=) 6.6: (6.6:),› -0.=:*** (6.:1) -6.=>*** (6.00) 6.62*** (6.6:) 6.6: (6.6:)

-2.:;*** (=.0=) -6.660 (6.08) 6.60 (6.61) 6.66: (6.66:)

->.;2*** (6.;;) -2.;6*** (:.;6) -6.>> (6.11) -6.=6 (6.:=)8, 8 6.20*** (6.01) 6.85*** (6.05) 6.20*** (6.08) 6.28*** (6.00)> - 6.5;*** (6.62) - 6.=;** (6.01)1 - 6.8;*** (6.61) - 6.=0*** (6.0:)κ 6.55 6.55 6.55 6.55VZM ? Vnipcn―s Znpujcem ia Mkel`.

Litn7 Xkn v`cuns el p`rnltknsns hnlitn tkn st`lh`rh nrrirs ia tkn minaaemenlts. ***, **, `lh * elhem`tn 0%, >%,`lh 06% cnvncs ia sebleaem`lmn, rnspnmtevncy.

` @s tkn VZM k`s lnvnr `hiptnh ` hn a`mti aci`telb rnbeon wn usn nsteo`tnh minaaemenlts air ` j`sdnt-pnb

pnreih.


1.: ]eouc`teil Znsucts uselb Nsteo`tnh V`ròntnrs

Rn qu`lteay ipteo`c v`cuns ia elstruonlts `lh v`cuns ia muouc`tevn cissns `mmirhelb titkn tr`lseteil picemens. Air tkn nxmk`lbn r`tns `lh nxmk`lbn r`tn resds, wn usn tkn`mtu`c h`t` air tkn pnreih P0 0555”P8 :606 air tkn VZM `lh pnreih P0 055=”P0 :661air Xkèc`lh, rnspnmtevncy. @s wn hnaeln nxibnlius skimds `lh itknr v`re`jcns `shnve`teils ario tkn cilb-rul v`cns, wn usn tkn hnve`teil ario tkn Kihremd Vrnsmitt (K-V) aectnrnh trnlh v`cuns. Rn `ssuon tkn teon pnreih air tkn hicc`r pnb `s 0 qu`rtnr

(6 ? 0), tkn eltnrv`c air tkn tr`lseteil pnreih `s 0; qu`rtnrs (0 ? 0;), `lh tkn pnreih:;


31/46


air tkn t`rbnt rnbeon `s 0; (: ? 0; ) qu`rtnrs. X`jcn > `lh 1 rnpirt v`cuns iamuouc`tevn cissns `lh ipteo`c elstruonlts ia aevn picemens air st`jecezelb iutput `lh tknpremn cnvncs, rnspnmtevncy.

X`jcn >7 Muouc`t`tevn Cissns air Iutput ]t`jecety

@. Vnipcn―s Znpujcem ia Mkel`

Vicemy (0) Vicemy (:) Vicemy (=) Vicemy (8) Vicemy (>)

( ? >) j]t`jcn rnbeon Hicc`r

pnbJ`sdnt

pnbJ`sdnt

pnbAci`telb O`l`bnh

aci`telb

@hgustonlt - Br`hu`c ]uhhnl ]uhhnl ]uhhnl

Elstruonlt v`cun − ? 8.=8 − ? 6.>; −− ? 6.1; − ? 6.601 −− ? 6.602 Muouc`tevn ciss

(v`cun)02.68 0.;6 0.50 :.12 :.=0

Muouc`tevn ciss

(% ia �:) ` :=.8 :.8 :.1 =.2 =.:`Rn m`cmu`tn tkn v`cun ia �: skiwl el snmteil = `lh ijtèl �: ? 2:.;.

j Air ? 2, tkn muouc`tevn ciss es =.>8 (−− ? 6.602).

J. Xkèc`lh


(

? >) j

]t`jcn rnbeon Hicc`r pnb J`sdntpnb

J`sdntpnb

Aci`telb O`l`bnhaci`telb


Elstruonlt v`cun − ? 6.66= − ? 6.1; −− ? 6.1: − ? 6.6;: −− ? 6.66;: Muouc`tevn ciss

(v`cun)6.6688 6.661 6.66:1 6.66>: 6.66>=

Muouc`tevn ciss

(% ia �:)/0

0>.6 0.= >.2 00.= 00.>

`Rn m`cmuc`tn tkn v`cun ia �: skiwl el ]nmteil = `lh ijtèl �: ? 6.681.

j Air ? >, tkn muouc`tevn ciss es 6.66>2 (−− ? 6.6;:).

:5


32/46


X`jcn 17 Muouc`t`tevn Cissns air Vremn ]t`jecety



( ? >)j

]t`jcn rnbeon Hicc`r pnb J`sdntpnb

J`sdntpnb

Aci`telb O`l`bnhaci`telb


Elstruonlt v`cun − ? 0.08 − ? 6.1> −− ? 6.2; − ? 6.00 −− ? 6.60 Muouc`tevn ciss

(v`cun)6.=6 6.6:6 6.6:0 6.60= 6.6==

Muouc`tevn ciss

(% ia ̎:) `==.6 :.: :.= 0.8 =.=

`Rn m`cmuc`tn tkn v`cun ia ̎: skiwl el snmteil = `lh ijtèl ̎: ? 6.50.

j Air ? 2, tkn muouc`tevn ciss es 6.>6 (o−− ? 6.60>).

J. Xkèc`lh


( ? >) j]t`jcn rnbeon Hicc`r pnb J`sdnt

pnbJ`sdnt

pnbAci`telb O`l`bnh

aci`telb


Elstruonlt v`cun − ? 6.6666> − ? 6.08 −− ? 6.>5 − ? 6.6600 −− ? 6.6605 Muouc`tevn ciss

(v`cun)6.6688 6.66:: 6.66:; 6.66=; 6.66==

Muouc`tevn ciss

(% ia ̎: ) /0 >.1 :.; =.1 8.; 8.:`Rn m`cmuc`tn tkn v`cun ia p�: skiwl el ]nmteil = `lh ijtèl ̎: ? 6.625.

j Air

? >, tkn muouc`tevn ciss es 6.66== (

−− ? 6.66:8).

X`jcns > `lh 1 milaero tkn tknirntem`c aelhelbs hesmussnh el ]nmteil >. Aerst, òilb tknaiur picemens, oèltèlelb tkn hicc`r pnb, picemy (0), cn`hs ti tkn kebknst cissns el jitkst`jecezelb iutput `lh tkn premn cnvnc air tkn VZM `lh Xkèc`lh. Et eopcens tk`t tknmiultry wecc jn jnttnr iaa skeatelb ti tkn t`rbnt j`sdnt pnb ir aci`telb rnbeon.

]nmilh, miop`relb tkn twi tr`lseteil picemens ti ` j`sdnt-pnb rnbeon, et es hnser`jcn airtkn miultry ti `hipt ` br`hu`c `hgustonlt r`tknr tk`l ` suhhnl skeat el jitk st`jecezelbiutput `lh tkn premn cnvnc air tknsn twi miultrens. Xkes es jnmùsn tkn eltnrv`c iatr`lseteil pnreihs es lit cilb nliubk air tkn miultry ti bèl tkn jnlnaets ia skeatelbsuhhnlcy ti tkn t`rbnt rnbeon. Oirnivnr, tkn ipteo`c wnebkts ia picemy (:) `lh picemy (=)`rn heaanrnlt, `s nxpcèlnh el ]nmteils 8.: `lh 8.=.

Xkerh, wknl miop`relb skeatelb ti ` j`sdnt pnb wetk skeatelb ti ` aci`telb rnbeon, airXkèc`lh, skeatelb ti ` aci`telb rnbeon cn`hs ti kebknr cissns, skiwelb tk`t tkn miultry

=6


33/46


wecc jn jnttnr iaa skeatelb ti tkn hnsernh j`sdnt-pnb rnbeon air jitk st`jecezelb iutput`lh tkn premn cnvnc. @s onlteilnh el ]nmteil >.=, tkes es ` m`sn wknrn tkn miultry m`lrnmnevn tkn jnlnaets ia miooettelb ti ` j`sdnt pnb tkriubk soiitkelb tkn lnb`tevneop`mts ia nxmk`lbn r`tn acumtu`teils `lh aicciwelb nxmk`lbn r`tn nxpnmt`teils. El tknm`sn ia tkn VZM, tkn rnsucts `rn oexnh `lh hnpnlh il picemy bi`cs. Ea tkn ùtkiretyprnanrs ti st`jecezn iutput, et wecc jn jnttnr iaa skeatelb ti tkn hnsernh j`sdnt-pnb rnbeon.Kiwnvnr, ea tkn ùtkirety mkiisns premn st`jecety, ets hnmeseil wecc jn ti skeat ti ` aci`telbrnbeon. Xkes es jnmùsn, ulcedn tkn mkiemn ti st`jecezn iutput, tknrn `rn anwnr lnb`tevneop`mts `ssime`tnh wetk nxmk`lbn r`tn acumtu`teils il hionstem premns. Ael`ccy, ` skeatti ` o`l`bnh-aci`telb rnbeon es cnss `ttr`mtevn tk`l ` oivn ti ` j`sdnt pnb. AirXkèc`lh, skeatelb ti ` j`sdnt pnb es oirn hnser`jcn tk`l oivelb ti ` o`l`bnh-aci`telbrnbeon el tnros ia jitk iutput `lh premn cnvnc st`jecety. Xkes es tkn m`sn air tkn VZM `swncc7 skeatelb ti ` o`l`bnh-aci`telb rnbeon rnsucts el kebknr cissns tk`l skeatelb ti `j`sdnt pnb. Xknsn rnsucts `rn jnmùsn eltnrvnlteils el tkn airnebl nxmk`lbn o`rdnt airmnrtèl pnreihs cn`h ti kebknr cissns `s tkn ùtkirety c`mds oilnt`ry picemy ùtilioy.

1.= Xeon Eltnrv`cs `lh Ipteo`c J`sdnt Rnebkts

Rn `l`cyzn ipteo`c j`sdnt wnebkts ulhnr ` j`sdnt pnb ulhnr heaanrnlt teon eltnrv`csuselb Xkè h`t` ti nxòeln tkn rnc`teilskep jntwnnl tkn twi. Aerst, wn milsehnr tknm`sn ia ` br`hu`c `hgustonlt ti ` j`sdnt-pnb rnbeon, picemy (:). Bevnl ` aexnh teoneltnrv`c air tr`lseteil pnreihs 0 (air elst`lmn 0 ? 0; ), `l ipteo`c j`sdnt wnebktelmrn`sns `s teon eltnrv`cs ulhnr tkn hnsernh j`sdnt pnb elmrn`sn. @l elmrn`sn el tkncnlbtk ia tkn pnreihs ulhnr tkn hnsernh j`sdnt pnb cn`hs ti `l elmrn`sn el tkn sk`rn iamuouc`tevn cissns ulhnr tkn hnsernh j`sdnt pnb el tit`c muouc`tevn cissns. El tkn m`snia Xkèc`lh, tkes elmrn`sn el tkn cnlbtk ia pnreihs rnsucts el `l elmrn`sn el tkn wnebkt iltkn ^] hicc`r r`tn. Kiwnvnr, bevnl ` aexnh teon eltnrv`c ulhnr tkn hnsernh j`sdnt-pnb : (air elst`lmn

:? 0;), tkn cilbnr tkn teon eltnrv`cs air tr`lseteil jnmion, tkn kebknr `l

iptoe`c j`sdnt wnebkt es. @l elmrn`sn el tkn cnlbtk ia tkn tr`lseteil pnreih cn`hs ti `lelmrn`sn el tkn sk`rn ia muouc`tevn cissns hurelb tr`lseteil el tit`c muouc`tevn cissns.Xkes rnsucts el `l elmrn`sn el ipteo`c j`sdnt wnebkts air Xkèc`lh.

=0


34/46


Aeburn =7 Ipteo`c J`sdnt Rnebkts `lh Xeon Eltnrv`cs ulhnr Vicemy (:)

]iurmn7 @utkirs.

Lnxt, el tkn m`sn ia ` suhhnl skeat ti ` j`sdnt-pnb rnbeon, picemy (=), tkn cilbnr tknteon eltnrv`cs ulhnr tkn hnsernh j`sdnt pnb bnt, tkn kebknr `l ipteo`c j`sdnt wnebktjnmions. @s el tkn prnveius m`sn, ea tkn teon eltnrv`cs ulhnr tkn hnsernh j`sdnt pnbjnmion cilbnr, tkn sk`rn ia muouc`tevn cissns ulhnr tkn hnsernh j`sdnt-pnb rnbeon eltit`c muouc`tevn cissns elmrn`sns. @l elmrn`sn el tkn teon eltnrv`c ulhnr tkn hnsernhj`sdnt pnb `csi rnsucts el kebknr ipteo`c j`sdnt wnebkts el tkn m`sn ia Xk`ec`lh.

Aeburn 87 Ipteo`c J`sdnt Rnebkts `lh Xeon Eltnrv`cs ulhnr Vicemy (=)

]iurmn7 @utkirs.

=:


35/46


2. MILMC^]EIL

Xknrn es ` jri`h hnj`tn il hnser`jcn nxmk`lbn rnbeons air N`st @se`l miultrens. Xknhicc`r pnb w`s `hiptnh jy oist N`st @se`l miultrens `jnairn tkn @se`l murrnlmy mreses

`lh k`s jnnl jcònh `s iln ia tkn mucprets ia tkn mreses. ]nvnr`c nmilioests k`vn`hvim`tnh j`sdnt-pnb rnbeons air @se`. Xkn oèl rn`sil air `hiptelb ` j`sdnt-pnbrnbeon es tk`t air miultrens wetk mcisn nmilioem rnc`teilskeps wetk tkn Nuripn`l ^leil,G`p`l, `lh tkn ^letnh ]t`tns, nxmk`lbn r`tn st`jecez`teil tkriubk ` j`sdnt miopreselbtkn murrnlmens ia tknsn miultrens m`l jn jnlnaeme`c jnmùsn et rnoivns tkn prijcno iac`rbn acumtu`teils el nxmk`lbn r`tns. Uiskeli, D`ge, `lh @siluo` (:668) k`vn skiwltk`t tibntknr wetk ` j`sdnt-pnb rnbeon, ` aci`telb rnbeon es `l ipteil air N`st @se`lmiultrens.

Vrnveius rnsn`rmk k`s `l`cyznh tkn st`tn `l N`st @se`l miultry rn`mkns ilmn et k`s`hiptnh ` j`sdnt pnb ir ` aci`telb rnbeon. Air miultrens cedn tkn VZM `lh O`c`yse`,wkemk murrnltcy k`vn ` hn a`mti hicc`r pnb, tknrn es stecc tkn jeb qunsteil ia kiw tkny m`l

tr`lseteil ti tkn lnw rnbeon. Xkes p`pnr k`s `ttnoptnh ti mioputn tkn hylòem naanmtia mk`lbelb ario ` aexnh rnbeon ti ` st`jcn j`sdnt pnb ir ` st`jcn aci`telb rnbeon. Rnijtèlnh twi tr`lseteil p`tks ario ` hicc`r pnb ti ` j`sdnt-pnb rnbeon (` br`hu`c`hgustonlt ia j`sdnt wnebkts ir ` suhhnl skeat) `lh iln tr`lseteil p`tk ario ` hicc`rpnb ti ` aci`telb rnbeon.

Xkn o`gir aelhelbs `rn `s aicciws. Aerst, tkn v`cun ia tkn muouc`tevn cissns ia tkn aiurpicemens `rn ijtèlnh tknirntem`ccy `s wncc `s noperem`ccy. Rn aelh tk`t oèltèlelb `hicc`r-pnb rnbeon es hnser`jcn ilcy ivnr tkn skirt rul, elhem`telb tk`t tkn miultry wecc jnjnttnr iaa skeatelb ti netknr ` j`sdnt-pnb rnbeon ir ` aci`telb rnbeon ivnr tkn cilb rul.]nmilh, wknl milsehnrelb tkn mkiemn jntwnnl ` br`hu`c `hgustonlt tiw`rh tkn t`rbntj`sdnt-pnb rnbeon, picemy (:), ir ` suhhnl skeat ti tkn t`rbnt j`sdnt pnb, picemy (=), tkncilbnr tkn tr`lseteil pnreih, tkn brn`tnr tkn jnlnaets tkn miultry rnmnevns ario rn`mkelbtkn hnsernh rnbeon. Ael`ccy, el ` miop`resil jntwnnl ` suhhnl skeat ti ` j`sdnt-pnbrnbeon, picemy (=), `lh ` aci`telb rnbeon, picemy (8), tkn wnca`rn ia tkn miultry es kebknrulhnr ` skeat ti ` j`sdnt-pnb rnbeon ea tkn nxmk`lbn r`tn acumtu`tns sebleaem`ltcy. Xknmiultry wiuch jn `jcn lit ilcy ti st`jecezn tkn lnb`tevn eop`mts ia nxmk`lbn r`tnacumtu`teils il tr`hn `lh m`pet`c elaciws jut `csi ti kncp tkn prev`tn snmtir airouc`tnnxmk`lbn r`tn nxpnmt`teils prnmesncy jy miooettelb ti ` j`sdnt rnbeon air mnrtèlpnreihs. Iur `l`cyses uselb VZM `lh Xkè h`t` suppirts tknsn aelhelbs. Kiwnvnr, iur`l`cyses es stecc ceoetnh ti ` onheuo-tnro pnrspnmtevn miop`rnh wetk iln j`snh il `cilbnr teon sp`l, sumk `s :6 yn`rs ir oirn. Xknrn es ` pissejecety tk`t ` miultry o`yjn jnttnr iaa `hiptelb ` aci`telb rnbeon ivnr tkn cilb tnro (oirn tk`l :6 yn`rs). Ea tkeses tkn m`sn, tkn qunsteil milmnrlelb kiw ` miultry skeats ario ` j`sdnt-pnb rnbeon ti

` aci`telb rnbeon rnoèls ` auturn rnsn`rmk tipem.

==


36/46


@VVNLHE[ @. ]ICQELB AIZ Z@XEIL@CN[VNMX@XEIL]

@.0. Hicc`r-pnb rnbeon (@)

]ujstetutelb nqu`teil (06) elti nqu`teil (=), wn ijtèl aicciwelb nqu`teil sumk tk`t

�› ? √(+) ̊/ + (0 + )(̊+0 ̊) +0 ̊/ T0 {0 ( + ) }_ +̊/ + (̊+0 ̊)̊/ +0 (@0)

Rn t`dn tkn nxpnmt`teil ia jitk sehns ia nqu`teil (1):5

`lh sicvn air

̊+0 7

̊+0 ? 0̊/ + :̊ (@:)Xknl wn sujstetutn air ̊+0 el nqu`teil (1) `lh ijtèl `l nxprnsseil air ̊ sumk tk`t

̊ ? =̊/ (@=)]ujstetutelb nqu`teil (@:) `lh (@=) elti nqu`teil (@0) `lh (06) rnspnmtevncy, wn ijtèl

�

› ?

0(

)

̊/

+

:(

)

̊/ +

=(

)

+0 (00)

̎› ? 0()̊/ + :()̊/ + =()+0 (00`) 0() ? ( + )T + (0 + )(0 + := :)_ T0 {0 ( + ) }_ +

+ (0 + := :) :() ? ( + ) T0 {0 ( + ) }_

=() ? (

+

)

T0 {0 ( + ) }_ 0() ? T + (0 +)(0 + := :)_ T0 {0 ( + ) }_ :() ? T0 {0 ( + ) }_, =() ? T0 {0( + ) }_

:5

Rn `ssuon tk`t nxmk`lbn r`tn resd tnros k`vn ` on`l ia znri, eopcyelb NΘnN@/

^] ? 6 `lhNΘnN@/GV ? 6.=8


37/46


@.:. J`sdnt-pnb rnbeon wetk wn`d m`pet`c miltrics (J)

]ujstetutelb nqu`teil (0=) elti nqu`teil (=), wn ijtèl aicciwelb nqu`teil sumk `s

� ? √(+) ̎̊/

+ (0 +)(̊+0 ̊)()̊/ ̊/ T0 {0( + ) }_ +{(0 ) + }̊/ T0 (0 )_(0 )̊/ + (̊+0 ̊)̊/

̊/

(@8)

wknrn ̎ ? T{ (0 ) (0 + )(0 )} (0 )_.Rn t`dn tkn nxpnmt`teils ia jitk sehns ia nqu`teil (0=) `lh sicvn air ̊+0 7

̊+0 ? (0+ 0)̊/

+ :̊ (@>)Xknl wn sujstetutn air ̊+0 el nqu`teil (0=) `lh ijtèl nxprnsseil air ̊ sumk tk`t

̊ ? (=+ =)̊/ (@1)]ujstetutelb nqu`teil (@>) `lh (@1) elti nqu`teil (@8) `lh (0=), wn ijtèl

� ? 0()̊/ + :()̊/ + =()̊ (02)

̎?

0(

)

̊/

+

:(

)

̊/

+

=(

)

̊ (02`)

0() ? ( + ) + + + (0 + )+(0 +)(0 + := =) T0 {0( + ) }_ + ( + )+ T0 (0 )_ + (0 + := :)

:() ? ( + ) + (0 + )+(0 + )(0 + := = ) T0 {0 ( + ) }_ T0 (0 )_ + (0 + := = )

=()̊ ? ( + ) ( )̊+̊/ T0 {0 ( + ) }_̊/ ̊/ 0() ? 0 + + + (0 + )+(0 + )(0 + := =) {0 ( + ) } :() ? 0 + (0 + )+(0 + )(0 + := = ) {0 ( + ) }

=()̊ ? 0

()̊ ̊/

{0 ( + ) } =>


38/46


@.=. J`sdnt-pnb rnbeon wetkiut m`pet`c miltrics (M)

]eoec`r ti @.:., sujstetutelb nqu`teil (0=) elti nqu`teil (=), wn ijtèl aicciwelb nqu`teilsumk tk`t

� ? √(+) ̎›̊/

+ (0 + )(̊+0 ̊)( )̊/ ̊/ T0 {0 ( + ) }_ +{(0 ) + (0 + )(0 )}̊/ + (̊+0 ̊)̊/ ̊/

(@2)

wknrn ̎› ? T{(0 ) (0 + )(0 )} (0 )_.Rn t`dn tkn nxpnmt`teil ia jitk sehns ia nqu`teil (0=) `lh sicvn air ̊+0 7

̊+0 ? (0+ 0)̊/

+ :̊ (@;)Xknl wn sujstetutn air ̊+0 el nqu`teil (0=) `lh ijtèl nxprnsseil air ̊ sumk tk`t̊ ? (=+ = )̊/ (@5)

]ujstetutelb nqu`teil (@;) `lh (@5) elti nqu`teil (@2) `lh (0=), wn ijtèl

� ? 0()̊/ + :()̊/ + =()̊ (0;)

̎?

0()

̊/

+

:()

̊/

+

=()

̊ (0;`)

0() ? ( + ) + ( + + + )+(0 + )(0 + := =) T0 {0 ( + ) }_ + ( + )+ (0 + ) + (0 + := =)

:() ? ( + ) ( + + )+(0 +)(0 + := =) T0 {0( + ) }_ (0 + ) + (0 + := =)

=()̊ ? ( + ) ( )̊+̊/ T0 {0 ( + ) }_̊/ ̊/ 0() ? 0 + + + (0 + )+(0 +)(0 + := =) {0( + ) } :() ? 0 + + (0 + )+(0 + )(0 + := = ) {0( + ) }

=(

)

̊?

(

+

)

(

)

̊/

+

̊/

{0

(

+

)

}

=1


39/46


@.8. Aci`telb rnbeon wetkiut m`pet`c miltrics (H)

Lnw nquecejreuo v`cun àtnr tkn hicc`r”ynl r`tn mk`lbn es

̎ ? =+

0( + ) + =+

0( + ) ̊/ + 0(̊+0 ̊) + :̊/ + =̊/ (:=)

̎/ ? 8 + :( +) 8 + :( +) ̊/ + 0(̊+0 ̊) + :̊/+ =̊/

(:8)

wknrn 0 ? +0+0+ (+) , : ? √+√0+ (+) , = ? √0+ (+) ,0 ? +0+0+ (+) , : ? √+√0+

(+) , = ? √√0+ (+)

]ujstetutelb nqu`teils (:=) `lh (:8) elti nqu`teil (=), wn ijtèl tkn aicciwelb nqu`teil

sumk tk`t

� ? ̎ + ( + )ℌ0̎/ + + + ℌ:̊/ + ℌ:(̊+0 ̊) ℌ:̊/ ℌ:̊/ (@06)

wknrn ? ( + )(0: ) + 0+(+)+ ( + )ℌ0: , ℌ0 ? 0 + `lh ℌ: ? 0 ++.

Rn t`dn tkn nxpnmt`teil ia jitk sehns ia nqu`teil (:6) `lh sicvn air ̊+0 7̊+0 ? 0̊/ + :̊ (@00)Xknl wn sujstetutn air ̊+0 el nqu`teil (:6) `lh ijtèl `l nxprnsseil air ̊ sumk tk`t

̊ ? =̊/ (@0:)]ujstetutelb nqu`teils (@00) `lh (@0:) elti nqu`teils (@06) `lh (:6), wn ijtèl

� ? 0()̊/

+ :()̊ + =() (:>)=2


40/46


̎ ? 0()̊/ + :()̊ +=() (:>`)

0(

) ?

= + 0(

+

)

(

+

)8 +:(

+

)

ℌ0

+ T0 + ℌ00( + ) + ℌ:_(0 + := =) + ℌ: :()̊ ? {: + ℌ0: ( + ) ℌ:}̊/ + {= + ℌ0= ( + ) ℌ:}̊/,=() ? +(+) ( + )ℌ0 +(+)+ +, 0() ? : +(+) + 0(0 + := =), :() ? : :̊/ + =̊/, `lh =() ? : +(+).

=;


41/46


@VVNLHE[ J7 ]@HHCN V@XK ]X@JECEXU ^LHNZ @ACI@XELB ZNBEON

Mk`r`mtnrestem riits ia heaanrnlmn nqu`teils (05) `lh (:6) m`l jn hnrevnh jy sicvelb tknnqu`teil jnciw7 : (: + 0 + 8) + (0 + 0 + 8 + ) ? 6 (@0=)]ivelb tkes nqu`teil,

υ0,υ: ? 0: (: + 0 + 8) ° 0: (: + 0 + 8): 8(0 + 0 + 8 + ) (@08)Liw wn `ssuon sion `ssuopteils ti s`tesay s`hhcn p`tk st`jecety, sumk `s

(`) (: + 0 + 8): 8(0 + 0 + 8 + ) < 6,(j) 0 + 0 + 8 + < 6, `lh(m) : + 0 + 8 (: + 0 + 8): 8(0 + 0 + 8 + ) 3 :

Aerst, ulhnr (`), jitk 0,: `rn rn`c `lh hestelmt. Et es n`secy aiulh tk`t 0 < 0. Liwulhnr (j), 0: ? 0 + 0 + 8 + < 6 Xknrnairn, : < 6. C`stcy, ulhnr (m), et seopcy eopcens tk`t : 3 0. Xkn systno eshnsmrejnh jy tkn ulequn st`jcn s`hhcn p`tk. Rn m`l nxprnss tkn sicuteil air tknirebel`c v`re`jcns `s

/ ̎/ ? (6 ̎ ): (@0>) ̎ ? (6 ̎ ): (@01)Ario tknsn nqu`teils `jivn, tkn s`hhcn p`tk es

/ ̎/ ? ( ̎ ) (@02)Rknrn ? √0√ .

=5


42/46


@VVNLHE[ M7 ^LEX ZIIX @LH MIELXNBZ@XEILXN]X]

Xkes snmteil hesmussns tkn rnsucts ia tkn ulet riit `lh mieltnbr`teil tnsts. Rn st`rt jy`ppcyelb tkn Hemdy-Auccnr bnlnr`ceznh cn`st squ`rns (HA-BC]) ulet riit tnsts. Xknrnsucts ia tkn ulet riit tnst `rn prnsnltnh el X`jcn @0. Znacnmtelb tkn 06% sebleaem`lmnmretem`c v`cun il HA-BC] st`testems, sion v`re`jcns, sumk `s tkn rn`c eltnrnst r`tns `lhtkn iutput b`p, k`vn ` ulet riit. Xknl wn oivn ilti Gik`lsnl mieltnbr`teil tnsts airtkn nqu`teils skiwl el X`jcn @:. ^selb tkn >% sebleaem`lmn mretem`c mretnre`, wn aelhmieltnbr`teil rnc`teilskeps `oilb tkn v`re`jcns el tknsn nqu`teils air jitk tkn VZM`lh Xk`ec`lh.

X`jcn @07 HA-BC] ^let-Ziit Xnsts


Q`re`jcns Hnbrnn Xrnlh C`b HA-BC] ]t`t.` Znsucts

/ Cnvnc 6 6 -:.12*** E(6)/ Cnvnc 6 0 -=.61*** E(6) Cnvnc 6 6 -0.1>* E(6) j (+0 ) Cnvnc 6 ; 6.020st heaa. 6 2 ->.=:*** E(0)

m Cnvnc 6 = -:.1;*** E(6) j Cnvnc 6 > -0.;;* E(6)

/

+ Cnvnc 6 6 -:.>2** E(6)/ + GV Cnvnc 6 : -=.::*** E(6) j / Cnvnc 6 6 -:.;6*** E(6)/ Cnvnc 6 6 -=.=0*** E(6)/ Cnvnc 6 6 6.02

0st heaa. 6 6 -6.1;8*** E(0)m +0 Cnvnc 6 ; 6.08

0st heaa. 6 = -8.5>*** E(0)m

� Cnvnc 6 8 -0.10* E(6)

86


43/46


J. Xk`ec`lh

Q`re`jcns Hnbrnn Xrnlh C`b HA-BC] ]t`t.` Znsucts

/

Cnvnc 6 6 -:.56*** E(6)j

/ Cnvnc 6 6 -=.:2*** E(6)j

Cnvnc 6 6 ->.:8*** E(6)

(+0 ) Cnvnc 6 6 -0.620st heaa. 6 6 ->.16*** E(0)

m

Cnvnc 6 6 -6.52

0st heaa. 6 6 -8.68*** E(0)m

Cnvnc 6 : -:.22*** E(6)

/

+

Cnvnc 6 6 -=.6=*** E(6)

/ + GV Cnvnc 6 6 -:.:0** E(6)/

Cnvnc 6 6 -:.:6** E(6)

/ Cnvnc 6 6 -=.;0*** E(6) j /

Cnvnc 6 6 ->.;0*** E(6)

+0 Cnvnc 6 6 -=.:=*** E(6) � Cnvnc 6 : -6.520st heaa. 6 = -0.;=* E(0)

m

` Xkn mretem`c v`cuns air tkn HA-BC] st`testems `rn >%, ”0.5;4 `lh 06%, ”6.1:. Iur rnsucts ia tkn ulet riit `rnj`snh il ` 06% mretem`c v`cun.

j E(6) skiws tk`t tkn v`re`jcn aicciws tkn st`teil`ry primnss ̀ t tk`t cnvnc.

m E(0) skiws tk`t tkn v`re`jcn k`s ` ulet riit ia hnbrnn 0.


80


44/46


X`jcn @:7 Gik`lsnl Mieltnbr`teil Xnsts


Nqu`teil Q`re`jcns Xrnlh Kypitknses Xr`mn

]t`testems

`

V-v`cuns

@bbrnb`tn

hno`lhh

� Hntnroelestem Liln m 01:.=*** 6.66/ + @t oist 0 m 00;.5*** 6.66/ + @t oist : m 2>.;*** 6.66 (+0 ) @t oist = m =1.5*** 6.66/ @t oist 8 m 08.6* 6.6;/ @t oist > m :.2* 6.65 @bbrnb`tn

suppcyn +0 Hntnroelestem

Liln

m020.=*** 6.66

� @t oist 0 m 0:0.;*** 6.66/ + @t oist : m 2;.;*** 6.66/ + @t oist = m =2.;*** 6.66/ @t oist 8 m 08.;* 6.68/ @t oist > m :.2* 6.65

J. Xk`ec`lh

Nqu`teil Q`re`jcns Xrnlh Kypitknses Xr`mn

]t`testems `

V-v`cuns

@bbrnb`tn

hno`lha

� Hntnroelestem Liln m 01:.=*** 6.66/ + @t oist 0 m 00;.5*** 6.66/ + @t oist : m 2>.;*** 6.66 (+0 ) @t oist = m =1.5*** 6.66/ @t oist 8 m 08.6* 6.6;ΘnN@/GV @t oist > m :.2* 6.65` Hnlitns >% mretem`c v`cuns.

j

Hnlitns O`mDellil, K`ub, ̀ lh Oemknces (0555) p-v`cuns.m Hnlitns rngnmteil ia tkn kypitknses ̀ t tkn >% sebleaem`lmn cnvnc.

h Xr`mn tnst elhem`tns = mieltnbr`telb nqu`teils ̀ t tkn >% sebleae`lmn cnvnc.

n Xr`mn tnst elhem`tns = mieltnbr`telb nqu`teils ̀ t tkn >% sebleaem`lmn cnvnc.

a Xr`mn tnst elhem`tns = mieltnbr`telb nqu`teils ̀ t tkn >% sebleaem`lmn cnvnc.


8:


45/46


ZNANZNLMN]

@hòs, M. `lh Z. ]nojc`t. :668. Ipteils air Murrnlmy @rr`lbnonlts `lh tkner VicemyEopcem`teils. El Nxmk`lbn Z`tn Znbeons el N`st @se`, nhetnh jy B. Hn Jriuwnr`lh O. D`wè. Cilhil `lh Lnw Uird7 Ziutcnhbn Mirzil.

Jerh, B. `lh Z. Z`g`l. :66:. Ipteo`c Murrnlmy J`sdnts `lh tkn Xkerh MurrnlmyVknlionlil7 Nxmk`lbn Z`tn Vicemy air ]iutkn`st @se`. Giurl`c iaEltnrl`teil`c Hnvnciponlt 087 06>=”062=.

Hirljusmk, Z. 0521. Nxpnmt`teils `lh Nxmk`lbn Z`tn Hylòems. Giurl`c ia Vicetem`cNmilioy ;8(1)7 0010”0021.

Eltnrl`teil`c Oilnt`ry Aulh. :662. Eltnrl`teil`c Ael`lme`c ]t`testems. R`skelbtil, HM7Eltnrl`teil`c Oilnt`ry Aulh.

Eti, X., N. Ib`w`, `lh U. L. ]`s`de. 055;. Kiw heh tkn Hicc`r Vnb Aèc el @se`9 Giurl`cia tkn G`p`lnsn ̀ lh Eltnrl`teil`c Nmilioens 0:(8)7 :>1”=68.

Eti, X., `lh U. M. V`rd. :66=. Nxmk`lbn Z`tn Znbeons el N`st @se`. El Oilnt`ry `lhAel`lme`c Eltnbr`teil el N`st @se`7 Xkn R`y @kn`h Qic. 0. Lnw Uird7 V`cbr`vnO`moecc`l.

Gik`lsnl, ]. 055:. ]t`testem`c @l`cyses ia Mieltnbr`teil Qnmtirs. Giurl`c ia NmilioemHylòems `lh Miltric 0:(:-=)7 :=0”:>8.

Gik`lsnl, ]. 055>. Cedncekiih-J`snh Elanrnlmn el Mieltnbr`tnh Qnmtir @utirnbrnssevnOihncs. Ixairh, ^D7 Ixairh ^levnrsety Vrnss.

D`wè, O. :668. Xkn M`sn air ` Xre-Vic`r Murrnlmy J`sdnt ]ystno air Nonrbelb N`st @se`. El Nxmk`lbn Z`tn Znbeons el N`st @se`, nhetnh jy B. Hn Jriuwnr, B `lh

O. D`wè. Cilhil `lh Lnw Uird7 Ziutcnhbn Mirzil.Deo, M., `lh G. R. Cnn. :66;. Nxmk`lbn

Dynamic Effect of a Change in the Exchange Rate System: From a Fixed Regime to a Basket-Peg or a...

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