venables (2003)

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Xpltdl` Edsplrdtdcs da Ecvc`bpdai Hbuatrdcs; Hdtdcs,

]cidbas lae Datcraltdbal` Urlec

Latjbay K. Vcalm`cs

Abvcgmcr =??8

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Lmstrlht Xpltdl` dacqul`dty da ecvc`bpdai hbuatrdcs ds euc tb tjc alturl` levlatlics bf sbgc rcidbas

rc`ltdvc tb btjcrs lae tb tjc prcscahc bf lii`bgcrltdba fbrhcs, `cledai tb h`ustcrdai bflhtdvdty. Ujds plpcr rcvdcws lae ecvc`bps sbgc sdgp`c gbec`s tjlt hlpturc tjcsc fdrst lae

schbae alturc chbabgdh icbirlpjdcs. Ujc prcscahc bf dahrclsdai rcturas tb shl`c da hdtdcs

`cles tb urmla struhturcs tjlt lrc abt bptdgl``y sdzce. Ujds ecprcsscs tjc rctura tb kbmhrcltdba, pbssdm`y rctlredai ecvc`bpgcat. @bbndai lt tjc wdecr rcidbal` struhturc,

ecvc`bpgcat hla mc lssbhdltce wdtj `lric sjdfts da tjc `bhltdba bf lhtdvdty ls daeustry ibcsfrbg mcdai dawlre `bbndai tb mcdai cxpbrt brdcatce.

Ncy Ybres; hdtdcs, spltdl` edsplrdtdcs, urmladsltdba, ecvc`bpdai hbuatrdcs.

KC@ h`lssdfdhltdba; ]<, ]<=, B<:

Ujds plpcr wls prbeuhce ls plrt bf tjc Hcatrc—s I`bml`dsltdba _rbirlggc

Ujc Hcatrc fbr Chbabgdh _crfbrglahc ds fdalahce my tjc Chbabgdh lae Xbhdl` ]csclrhj

Hbuahd`

Lhnabw`ceicgcats

Ujds plpcr wls prbeuhce ls plrt bf tjc SAS-YDEC] prbkcht ba Xpltdl` dacqul`dtdcs daecvc`bpdai hbuatrdcs.

_rbfcssbr Vcalm`cs ds Edrchtbr bf tjc I`bml`dsltdba _rbirlggc lt tjc Hcatrc fbrChbabgdh _crfbrglahc lae _rbfcssbr bf Datcraltdbal` Chbabgdhs, @baeba Xhjbb` bfChbabgdhs lae _b`dtdhl` Xhdcahc. Jc ds l`sb l ]csclrhj Fc``bw lt tjc Hcatrc fbr Chbabgdh

_b`dhy ]csclrhj.Hbatlht ectld`s; L.K. Vcalm`cs, @baeba Xhjbb` bf Chbabgdhs, Jbuijtba Xtrcct, @baeba

YH=L =LC, SN.Cgld`; l.k.vcalm`csO`sc.lh.un > Ycm dafbrgltdba; jttp;//chba.`sc.lh.un/stlff/lkv/

_um`dsjce my

Hcatrc fbr Chbabgdh _crfbrglahc@baeba Xhjbb` bf Chbabgdhs lae _b`dtdhl` XhdcahcJbuijtba Xtrcct

@baeba YH=L =LC

L`` rdijts rcscrvce. Ab plrt bf tjds pum`dhltdba gly mc rcprbeuhce, stbrce da l rctrdcvl`

systcg br trlasgdttce da lay fbrg br my lay gclas wdtjbut tjc prdbr pcrgdssdba da wrdtdai bftjc pum`dsjcr abr mc dssuce tb tjc pum`dh br hdrhu`ltce da lay fbrg btjcr tjla tjlt da wjdhj dt

ds pum`dsjce.

]cqucsts fbr pcrgdssdba tb rcprbeuhc lay lrtdh`c br plrt bf tjc Ybrndai _lpcr sjbu`e mc scattb tjc cedtbr lt tjc lmbvc leercss.

DXMA ? 938? <69< ?

Daedvdeul` hbpy prdhc; £3

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<. Datrbeuhtdba

Ujcrc lrc abw augcrbus stuedcs hjlrtdai tjc cvb`utdba bf spltdl` edsplrdtdcs eurdai chbabgdh

ecvc`bpgcat. Da glay hbuatrdcs l sumsct bf rcidbas `cles da glauflhturdai lhtdvdty, hrcltdai

kbms lae erlwdai da pbpu`ltdba frbg btjcr rcidbas. Ujds hla mc scca gbst h`clr`y da tjc

cxpcrdcahc bf sbgc bf tjc `lric ecvc`bpdai hbuatrdcs, suhj ls Hjdal, Gcxdhb, Mrlzd` lae

Daedl mut l`sb bhhurs da sgl``cr hbuatrdcs. Da Gcxdhb glauflhturdai jls mchbgc jdij`y

hbahcatrltce da rcidbas tjlt mbrecr tjc SX, lae spltdl` vlrdltdba da pcr hlpdtl dahbgcs jls

dahrclsce erlgltdhl``y sdahc tjc gde <4:?s (Hdnurc` =??=). Da Hjdal, Ecguricr ct l` (=??=)

hjlrt dahrclsdai spltdl` dacqul`dtdcs da pcr hlpdtl IE_ frbg tjc gde <4:?s; hblstl` prbvdahcs

cxpcrdcahce tjc ircltcst ech`dac da tjc sjlrc bf lirdhu`turc da cgp`bygcat lae butput, lae tjc

flstcst irbwtj bf pcr hlpdtl dahbgc. Da Daedl, sbutjcra stltcs jlvc hbgc tb prbgdacahc da

glauflhturdai lae trlelm`c scrvdhcs (Mcs`cy lae Muricss =??=).

Ujc spltdl` hbahcatrltdba bf acw lhtdvdtdcs l`sb bhhurs lt l guhj fdacr `cvc` bf

edsliirciltdba tjla suiicstce my stltc br prbvdahc `cvc` eltl. Da vdrtul``y l`` hbuatrdcs

ecvc`bpgcat ds lssbhdltce wdtj urmladsltdba lae tjc irbwtj bf prdgc hdtdcs, bftca flr gbrc

ebgdalat da gbecra ecvc`bpdai hbuatrdcs tjla lrc (br wcrc) suhj hdtdcs da tjc ecvc`bpce

wbr`e. Ujc augmcr bf hdtdcs da tjc wbr`e wdtj l pbpu`ltdba bf gbrc tjla < gd``dba wcat frbg

<<3 da <46? tb 5<6 da =???> fbr hdtdcs bf gbrc tjla 5 gd``dba tjc dahrclsc wls frbg <: tb 38,

lae fbr gbrc tjla <= gd``dba frbg < tb << (Jcaecrsba lae Ylai =??8). Da sbgc hlscs tjc

gbst suhhcssfu` hdtdcs cxjdmdt l jdij ecircc bf schtbrl` spchdl`dsltdba -- fbr cxlgp`c,

Mlail`brc—s sbftwlrc spchdl`dsg. Ujc irbwtj bf hdtdcs tc``s us tjlt, ecspdtc edschbabgdcs

lssbhdltce wdtj ecvc`bpdai hbuatry gcil-hdtdcs, tjcrc lrc cvca gbrc pbwcrfu` chbabgdcs bf

shl`c glndai dt wbrtjwjd`c fbr fdrgs tb hbatdauc tb `bhltc da tjcsc hdtdcs.

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Ujcsc hjlaics da spltdl` struhturc daedhltc l ‚`ugpdacss— da chbabgdh ecvc`bpgcat.

Flr frbg mcdai l prbhcss bf sgbbtj hbavcricahc, ecvc`bpgcat ds jdij`y spltdl``y

edffcrcatdltce. Ujds pbscs l augmcr bf qucstdbas fbr chbabgdh tjcbry. Ujc fdrst ds, wjy eb

tjcsc spltdl` edsplrdtdcs ecvc`bp2 Ujds qucstdba hla mc leercssce my erlwdai ba tjc

chbabgdh icbirlpjcr—s edstdahtdba mctwcca fdrst alturc lae schbae alturc icbirlpjy. Fdrst

alturc sdgp`y slys tjlt sbgc rcidbas lrc flvburce my vdrtuc bf caebwgcats br prbxdgdty tb

rdvcrs, hblsts, pbrts lae mbrecrs. Cvdecat`y, tjcsc flhtbrs lhhbuat fbr guhj bf tjc suhhcss bf

hblstl` Hjdal rc`ltdvc tb tjc abrtj-wcst, br mbrecr stltcs bf Gcxdhb rc`ltdvc tb tjc sbutj.

Xchbae alturc cgpjlsdscs tjc datcrlhtdbas mctwcca chbabgdh licats, lae da plrtdhu`lr tjc

dahrclsdai rcturas tb shl`c tjlt hla mc hrcltce my ecasc datcrlhtdbas. Ujus, hdtdcs tcae tb jlvc

jdij prbeuhtdvdty, lae lii`bgcrltdba fbrhcs lht tb icacrltc vdrtubus hdrh`cs bf sc`f-

rcdafbrhdai ecvc`bpgcat. Ujcsc fbrhcs jlvc mcca cxtcasdvc`y rcsclrhjce da rchcat yclrs

l`tjbuij guhj rcgldas tb mc ebac, plrtdhu`lr`y da tjc hbatcxt bf ecvc`bpdai hbuatrdcs.< Yjlt

ectcrgdacs tjc strcaitj bf tjcsc fbrhcs2 Jbw eb tjcy ecpcae ba lspchts bf tjc chbabgdh

cavdrbagcat suhj ls bpcaacss tb trlec, tjc stbhn bf `lmbur snd``s, lae tjc pb`dhy

cavdrbagcat2

Ujc schbae qucstdba ds; jbw eb spltdl` edsplrdtdcs cvb`vc eurdai ecvc`bpgcat, lae tb

wjlt lrc cxtcat lrc tjcy sc`f-hbrrchtdai br pcrsdstcat2 Cgpdrdhl``y, wc nabw frbg tjc wbrn

bf Yd``dlgsba (<463) lae btjcrs tjlt tjcrc ds l tcaecahy fbr spltdl` dacqul`dtdcs tb dahrclsc

lae tjca echrclsc. Mut frbg tjc stlaepbdat bf tjcbry, wjlt flhtbrs lrc hbaeuhdvc tb sprcle bf

lhtdvdty br tb pcrsdstcahc bf edsplrdtdcs2 Ds tjcrc l ‚abrgl`— plttcra tjlt hbuatrdcs gdijt mc

cxpchtce tb fb``bw2 Ls ecvc`bpgcat prbhcces tb wjlt cxtcat ebcs lhtdvdty sprcle but bf

cxdstdai lii`bgcrltdbas, lae tb wjlt cxtcat ds `lmbur erlwa datb tjcsc hcatrcs2 Ujcsc

qucstdbas lrc plrtdhu`lr`y dgpbrtlat da tjc hbatcxt bf urmladsltdba. Ujc ecvc`bpgcat bf acw

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urmla hcatrcs `dnc`y davb`vcs dahrclsdai rcturas, lrdsdai frbg mbtj dafrlstruhturc davcstgcats

lae h`ustcrdai cxtcral`dtdcs mctwcca fdrgs. Jbw clsy ds dt fbr acw hcatrcs bf lhtdvdty tb

mchbgc cstlm`dsjce, br ebcs lhtdvdty tcae tb mc `bhnce da tb cxdstdai hcatrcs2 Yjlt

dastdtutdbal` struhturcs lrc hbaeuhdvc tb tjc mdrtj bf acw hcatrcs lae tjc hbascqucat sprcle bf

lhtdvdty2

Ujc tjdre sct bf qucstdbas lrc tb eb wdtj rcl` dahbgc lae wc`flrc, da mbtj tjc sjbrt-

lae tjc `bai-rua. Xchbae alturc lii`bgcrltdba fbrhcs lrc dajcrcat`y lssbhdltce wdtj glrnct

fld`urc sb cqud`dmrdug hdty struhturcs lrc `dnc`y tb mc dacffdhdcat. Lrc ecvc`bpdai hbuaty hdtdcs

tbb `lric br tbb sgl``, lae lrc tjcrc tbb glay br tbb fcw bf tjcg2 Xjbu`e acw hdty

ecvc`bpgcat mc prbgbtce br aci`chtce2 Gbst dgpbrtlat`y, kust ls irbwtj sjlpcs tjc spltdl`

struhturc bf tjc chbabgy, sb l`sb tjc spltdl` struhturc sjlpcs tjc irbwtj prbhcss. Df l

hbuatry—s spltdl` struhturcs lrc wrbai tjca tjds gly rceuhc tjc rcturas tb gbecra schtbr

davcstgcat lae tjcrcmy elglic `bai rua irbwtj.

Ujds plpcr tlncs sbgc stcps tbwlres leercssdai tjcsc dssucs, davcstdiltdai tjc spltdl`

pltj tjlt l irbwtj prbhcss gdijt tlnc lae tjc wc`flrc prbpcrtdcs bf tjds pltj. Yc fdrst

(schtdba =) erlw ba stlaelre gbec`s bf urmla chbabgdhs, cxtcaedai tjcsc gbec`s tb

dahbrpbrltc mbtj fdrst lae schbae alturc icbirlpjy, lae usdai tjcg tb davcstdiltc tjc

hbascqucahcs bf l`tcraltdvc urmla dastdtutdbal` struhturcs. Yc sjbw tjlt glrnct fld`urcs `cle

tb sum-bptdgl` hdty sdzc struhturcs lae, my ecprcssdai tjc rctura tb kbm hrcltdba, hla rctlre

ecvc`bpgcat lae pcrjlps l`sb hrcltc tjc pbssdmd`dty bf mcdai stuhn da l `bw `cvc` cqud`dmrdug

trlp. Yc tjca (schtdba 8) gbvc ba tb tjc mrblecr pdhturc bf rcidbal` ecvc`bpgcat. Yjcrcls

da tjc urmla gbec`s l`` spltdl` `danlics lrc wdtjda hdtdcs, da tjds schtdba wc erlw ba ‚acw

chbabgdh icbirlpjy— gbec`s tb hlpturc mrblecr spltdl` datcrlhtdbas. Ujcsc gbec`s d``ustrltc

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jbw tjcrc hla mc erlgltdh sjdfts da hbuatrdcs— datcral` chbabgdh icbirlpjy eurdai tjc

prbhcss bf ecvc`bpgcat.

=. Hdtdcs

Yc stlrt my scttdai but l sdgp`y lal`ytdhl` frlgbrn wdtjda wjdhj tjc rc`ltdbasjdp mctwcca

hdty struhturc lae chbabgdh irbwtj hla mc cxlgdace. Yc suppbsc tjlt, da l idvca hbuatry,

tjcrc lrc l `lric augmcr bf pbtcatdl` hdty `bhltdbas, `lmc`ce my sumshrdpt d. Ujcsc lrc abt l``

‚irccafdc`e— lae gly dah`uec cxdstdai tbwas br hdtdcs wjdhj lrc pbtcatdl` jbsts fbr tjc

ecvc`bpgcat bf gbecra schtbr lhtdvdty.= Ujc augmcr bf wbrncrs da suhj schtbrs da hdty d ds ad.

Ujcsc hla mc tjbuijt bf ls ‚wbrncr-fdrgs—, wjbsc prbeuhtdvdty da hdty d ds idvca my qdl(ad) sb

tjc tbtl` butput bf tjc hdty ds adqdl(ad). Ujds prbeuhtdvdty fuahtdba jls twb hbgpbacats. Ujc

fdrst, qd, hlpturcs tjc ‚fdrst alturc— hjlrlhtcrdstdhs bf tjc hdty. Ujcsc dah`uec hdty ‚caebwgcats—

‘ suhj ls `bhltdba, h`dgltc, lae musdacss cavdrbagcat -- lae l`sb spltdl` vlrdltdbas da prdhcs.

Fbr cxlgp`c, bac wly tb tjdan bf qd ds da tcrgs bf hdtdcs prbeuhdai la cxpbrt ibbe, tjc prdhc

bf wjdhj (act bf trlec hbsts) ecpcaes ba edstlahc frbg l hblst br mbrecr. Yc brecr hdtdcs suhj

tjlt d 7 < ds tjc mcst `bhltdba lae qd ds echrclsdai wdtj d.

Ujc schbae hbgpbacat, l(ad), hlpturcs tjc decl tjlt prbeuhtdvdty ecpcaes ba tjc

augmcr bf wbrncrs da tjc slgc hdty, ad. Yc icacrl``y tlnc l(ad) tb mc dahrclsdai, lt `clst up tb

sbgc pbdat, lae hbahlvc. Ujus tjcrc lrc dadtdl``y dahrclsdai rcturas tb cxplaedai clhj hdty,

l`tjbuij mcybae sbgc pbdat aciltdvc cxtcral`dtdcs gly hbgc tb ebgdaltc sb furtjcr dahrclscs

da hdty sdzc rceuhc prbeuhtdvdty. Dgpbrtlat`y, tjcsc rcturas tb shl`c bpcrltc lt tjc hdty `cvc`, sb

lrc cxtcral` tb tjc lhtdbas bf daedvdeul` wbrncr-fdrgs. Yjcacvcr l—(a) … ? cxtcral`dtdcs lrc

prcscat, hrcltdai glrnct fld`urc, ua`css sbgc dastdtutdba cxdsts tb datcral`dsc tjcg. Ujc sburhc

bf tjc rcturas tb shl`c gly mc nabw`ceic spd``bvcrs br tjdhn glrnct cffchts, mut da tjds schtdba

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bf tjc plpcr wc wd`` abt gbec` tjc uaecr`ydai fbrhcs erdvdai tjcsc rcturas tb shl`c, sdgp`y

tlndai tjcdr prcscahc ls l flht.8

Xhlrhdty bf `lae da clhj `bhltdba gclas tjlt `lae prdhcs lrc dahrclsdai wdtj

pbpu`ltdba. Erlwdai ba tjc urmla chbabgdhs trledtdba tb gbec` tjds, hdty wbrncrs ply l

hbggutdai hbst, (`daclr da edstlahc) tb rclhj tjc hcatrl` musdacss edstrdht da clhj hdty. Yc

lssugc tjlt hdtdcs bhhupy l `daclr splhc lae clhj wbrncr bhhupdcs bac uadt bf `lae.5 Df

hbggutdai hbsts lrc =t pcr uadt edstlahc, tjca l hdty wdtj a wbrncrs jls tbtl` hbggutdai

hbsts bf , hrcltcs rcats bf , lae jls rcat p`us hbggutdai hbsts pcr wbrncr bf .

Da leedtdba tb dts hdtdcs, clhj chbabgy jls la lirdhu`turl` schtbr prbeuhdai butput

wjcrc @ ds tjc chbabgy—s tbtl` `lmbur fbrhc, lae A ds tbtl` urmla cgp`bygcat,

. Ujc prbeuhtdba fuahtdba T (.) ds strdht`y hbahlvc, sb la dahrclsc da tjc tbtl` urmla

pbpu`ltdba, A , rldscs tjc glridal` prbeuht lae tjc wlic da lirdhu`turc, , w—

1 ?. Ujc chbabgy ds bpca tb trlec lae flhcs hbastlat wbr`e prdhcs fbr dts butput. Fbr

sdgp`dhdty wc lssugc tjlt hbasugcr ibbes (lplrt frbg `lae) jlvc tjc slgc prdhc (uadty) da

l`` `bhltdbas. Jbusdai lae lirdhu`turl` rcats lrc edstrdmutce cqul``y lgbaist tjc pbpu`ltdba da

l `ugp sug glaacr.

Ujc prdvltc rctura tb l kbm da hdty d wd`` mc ecabtce M(ad , qd ) lae tlncs tjc fbrg

Ujds ds tjc vl`uc bf butput icacrltce my tjc kbm, gdaus tjc hbsts bf cgp`bygcat. Ujcsc lrc

tjc lirdhu`turl` wlic, w( A ), lae tjc hbggutdai hbst p`us rcat bf wbrncrs (cqul` tb tjc

hbggutdai hbsts bf tjc glridal` wbrncr). Bur ncy lssugptdba ds tjlt M(ad , qd ) ds dahrclsdai

da ad up tb sbgc vl`uc, edgdadsjdai tjcrclftcr, lae hbahlvc. Ujds lrdscs ls dahrclsdai rcturas

da tjc tchjab`biy, l— 1 ?, lrc bffsct my hbggutdai hbsts, t > lt `bw vl`ucs bf cgp`bygcat qd l—

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1 t , mut hbahlvdty bf l(ad) gclas tjlt mcybae sbgc pbdat tjds dacqul`dty ds rcvcrsce. Yc l`sb

lssugc tjlt lt `bw vl`ucs bf A tjcrc lrc spltdl` edstrdmutdbas bf ad fbr wjdhj sbgc Md lrc

strdht`y pbsdtdvc ‘ dc, tjc tchjab`biy qdl(ad) ds ibbe cabuij fbr tjds chbabgy tb mc lm`c tb

ecvc`bp la urmla struhturc.

=.< Fdrst alturc, schbae alturc lae urmla irbwtj

Ujc frlgcwbrn wc jlvc sct but dahbrpbrltcs mbtj fdrst lae schbae alturc icbirlpjy. Yjlt eb

tjcsc fbrhcs dgp`y fbr tjc spltdl` plttcra bf irbwtj lae ecvc`bpgcat2 Mcfbrc turadai tb l

ectld`ce lal`ysds bf tjc ectcrgdalats bf hdty struhturc wc gbtdvltc tjc edshussdba my

d``ustrltdai sbgc pbssdm`c ecvc`bpgcat pltjs.

Ls but`dace lmbvc, `bhltdbas lrc rlance lhhbredai tb prbeuhtdvdty plrlgctcr qd.

Xuppbsc fdrst tjlt tjcrc lrc ab dahrclsdai rcturas br cxtcral`dtdcs, sb l—(a) 7 ? fbr l`` a. Ydtj

tjds lssugptdba M(ad , qd ) ds echrclsdai da ad Yjlt ebcs irbwtj `bbn ̀ dnc da tjds chbabgy2

Fdiurc <l idvcs la d``ustrltdvc cxlgp`c. Ujc jbrdzbatl` lxds ds A , tjc tbtl` cgp`bygcat da

glauflhturdai, lae wc lssugc tjlt tjds dahrclscs lt l rltc tjlt ds cxbicabus`y idvca. (Yc

rctura tb fu``cr trcltgcat bf tjds da schtdbas =.8 lae =.5). Ujc vcrtdhl` lxds ds cgp`bygcat da

clhj `bhltdba, lae tjc hurvcs idvc cgp`bygcat fbr tjc mcst `bhltdba, a<, schbae mcst, a= lae

sb ba. Ybrncr-fdrgs lrc pcrfcht`y gbmd`c, lae ib wjcrcvcr tjc rcturas tb l kbm lrc jdijcst.

Cqud`dmrdug ad ds tjcrcfbrc ectcrgdace my tjc hbaedtdba tjlt l`` lhtdvc hdtdcs jlvc tjc slgc

vl`uc bf M(ad , qd ), l vl`uc wjdhj cxhcces tjlt da lay `bhltdba tjlt ds abt lhtdvc.3 Ujc irbwtj

plttcra ds ls wbu`e mc cxpchtce. Lt lay pbdat da tdgc (lay vl`uc bf A ) ba`y l sumsct bf

pbtcatdl` `bhltdbas lrc lhtdvc, tjds ectcrgdace my tjcdr fdrst alturc levlatlic. Dahrclsdai A

hluscs mbtj datcasdvc lae cxtcasdvc irbwtj. Cxdstdai hdtdcs ict `lricr mut tjcy cahbuatcr

edgdadsjdai rcturas tb shl`c mchlusc bf tjc prcscahc bf hbggutdai hbsts. Ujds rceuhcs tjc

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rcturas tb l kbm da tjc hdty, M(ad , qd ), glndai dt wbrtjwjd`c tb stlrt lhtdvdty da tjc acxt hdty,

lae sb ba.

Cvdecat`y, tjds chbabgy jls l spltdl` struhturc tjlt cvb`vcs eurdai ecvc`bpgcat, lae

tjcrc ds dahrclsdai tjca echrclsdai spltdl` edsplrdty ls lhtdvdty ds dadtdl``y hbahcatrltce da l

fcw `bhltdbas, tjca sprcles but. Ujc spltdl` struhturc ecshrdmce ds l edstrdmutdba bf

cgp`bygcat, mut wjlt lmbut tjc edstrdmutdba bf dahbgc2 Srmla wbrncrs rchcdvc l abgdal`

dahbgc ircltcr tjla tjc lirdhu`turl` wlic da brecr tb hbvcr tjcdr rcat lae hbggutdai hbsts,

lae, idvca l vl`uc bf A, tjcrc gly l`sb mc surp`us clrace ba clhj urmla kbm, M(ad , qd ) 1 ?.

Yjctjcr urmla wbrncrs jlvc jdijcr rcl` dahbgc tjla lirdhu`turl` ecpcaes ba tjc edstrdmutdba

bf tjds surp`us mctwcca wbrncrs lae fdrgs, wjdhj gly da tura ecpcae ba `bhl` `lmbur glrnct

hbaedtdbas lae tjc wd``daiacss bf wbrncrs tb gdirltc. Yc davcstdiltc tjcsc dssucs ab furtjcr

da tjc prcscat plpcr, mut scc Nlamur lae ]lppbpbrt =??8.

Jbw lrc tjdais edffcrcat wjca schbae alturc icbirlpjy ds l`sb prcscat2 L aba-

hbavcxdty lrdscs mchlusc M(ad , qd ) ds dahrclsdai da cgp`bygcat fbr sgl`` vl`ucs ad, mcfbrc dt

stlrts echrclsdai. Ujc dahcatdvc tb stlrt l acw hdty abw ecpcaes ba tjc glss bf wbrncrs wjb

hla hbbredaltc tjcdr echdsdbas. Yc edshuss tjds da gbrc ectld` da schtdba =.= mc`bw, lae abw

sdgp`y lssugc tjlt lhtdvc hdtdcs cxplae up tb tjc pbdat lt wjdhj dt mchbgcs prbfdtlm`c fbr l

sdai`c sgl`` wbrncr-fdrg tb sct up da l acw `bhltdba. Ujus, cgp`bygcat `cvc`s lrc suhj tjlt

clhj lhtdvc hdty jls tjc slgc rctura tb kbms, M(ad , qd ). Cxplasdba cvcatul``y mrdais l ech`dac

da tjds rctura, lae l acw hdty ds mbra wjca dt rclhjcs tjc `cvc` lt wjdhj dt cqul`s tjc rctura tb

cstlm`dsjdai l kbm da l acw `bhltdba. La d``ustrltdba bf tjc lssbhdltce irbwtj prbhcss ds idvca

da fdiurc <m.

Ujc irbwtj prbhcss ds abw guhj ‚`ugpdcr—, wdtj hdtdcs ecvc`bpdai da scqucahc, rltjcr

tjla da plrl``c`. Fdrst alturc ectcrgdacs tjc brecr bf ecvc`bpgcat lae, lt lay pbdat da tdgc,

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prcedhts wjdhj `bhltdbas lrc suhhcssfu` lae wjdhj lrc abt. Jbwcvcr, tjc ecpcaecahc bf

pcrfbrglahc ba fdrst alturc ds abt hbatdaubus. Vcry sgl`` edffcrcahcs da fdrst alturc hla

trlas`ltc datb `lric edffcrcahcs da buthbgcs fbr `bhltdbas lt tjc glrida bf ecvc`bpgcat.

Hbavcrsc`y, dgprbvdai l `bhltdba—s fdrst alturc ebcs abt achcsslrd`y hbafcr lay dggcedltc

plybff da tcrgs bf lttrlhtdai tjc lhtdvdty, ls tjc `bhltdba gly rcglda mc`bw tjc hurrcat

tjrcsjb`e. Lae lgbaist tjc sct bf lhtdvc `bhltdbas, edffcrcahcs da fdrst alturc jlvc `dtt`c cffcht

ba cgp`bygcat, ls tjcy lrc ebgdaltce my lhqudrce schbae alturc levlatlics. Furtjcrgbrc,

ecvc`bpgcat ds gbrc spltdl``y hbahcatrltce wdtj (fbr lay idvca vl`uc bf A ) lhtdvdty

hbahcatrltce da fcwcr lae ̀ lricr `bhltdbas. Ujds ds hbasdstcat wdtj tjc sty`dsce flhts ls wc

but`dace tjcg da tjc datrbeuhtdba. Yc sjbu`e l`sb abtc tjlt dt ds `dnc`y tjlt lt `clst sbgc bf

dahrclsdai rcturas lrc schtbr, ls wc`` ls `bhltdba spchdfdh. Irbwtj ds tjca lssbhdltce wdtj tjc

ecvc`bpgcat bf schtbrl``y spchdl`dsce hdtdcs, lae tjds tbb ds hbasdstcat wdtj cvdecahc. Xdahc

prbeuhtdvdty fuahtdbas lrc da tjds hlsc schtbr spchdfdh, qudtc edffcrcat hdty sdzc struhturcs gdijt

mc bmscrvce (Jcaecrsba <495).

Ydtj tjds bvcrvdcw bf tjc gbec` wc abw tura tb gbrc ectld`ce lal`ysds. Yc fdrst

(schtdba =.=) lsn tjc qucstdba> wjlt ectcrgdacs tjc sdzc lae augmcr bf hdtdcs, lae wjlt

dacffdhdcahdcs lrc prcscat lt cqud`dmrdug2 Ujc laswcr tb tjds qucstdba ds scasdtdvc tb tjc

hdtdcs— dastdtutdbal` struhturc -- tjc `lae glrnct lae tjc cxtcat tb wjdhj licats lrc lm`c tb

datcral`dsc tjc cxtcral`dty. Ujds dssuc jls mcca leercssce da tjc `dtcrlturc (scc Lmec`-]ljgla

lae Lals =??8 fbr l survcy). Yc lriuc tjlt sbgc bf tjc dastdtutdbal` lssugptdbas cgp`byce

da tjds `dtcrlturc lrc dalpprbprdltc, plrtdhu`lr`y fbr ecvc`bpdai hbuatrdcs, lae prcscat sbgc

acw rcsu`ts. Yc tjca tura tb l schbae qucstdba (schtdba =.8)> jbw ebcs urmla struhturc lffcht

tjc dahcatdvc tb hrcltc kbms lae jcahc `cvc`s bf gbecra schtbr cgp`bygcat, A 2 Edffcrcat

dastdtutdbal` struhturcs dgp`y edffcrcat vl`ucs bf kbm hrcltdba, M, sb df A rcspbaes

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caebicabus`y tb M, tjcy wd`` l`sb dgp`y edffcrcat `cvc`s bf gbecra schtbr cgp`bygcat lae

wlics. Yjd`c schtdba =.8 idvcs l ̀ bai rua lal`ysds, schtdba =.5 sncthjcs l eyalgdh vcrsdba bf

tjc gbec`, da wjdhj tjc glrnct fld`urcs lssbhdltce wdtj urmla ecvc`bpgcat hla `cle tb

gu`tdp`c cqud`dmrdl lae tjc pbssdmd`dty bf la chbabgy mcdai stuhn da l `bw `cvc` cqud`dmrdug.

=.= Bptdgl` lae cqud`dmrdug urmla struhturcs

Idvca tjc bvcrl`` `cvc` bf gbecra schtbr cgp`bygcat, A , lrc cqud`dmrdug hdty sdzcs `lricr br

sgl``cr tjla sbhdl``y bptdgl`2 Ujc laswcr tb tjds qucstdba ecpcaes ba tjc cxtcat tb wjdhj

cxtcral`dtdcs lrc datcral`dsce, lae wc hbgplrc tjrcc edffcrcat pbssdmd`dtdcs. Ujc mcahjglrn

hlsc ds tjc sbhdl``y cffdhdcat buthbgc. Fbr sdgp`dhdty, wc lmstrlht frbg fdrst alturc fbr tjc

rcgldaecr bf tjds schtdba, glndai l`` `bhltdbas cx latc decatdhl` (qd 7 q) lae erbppdai tjc

sumshrdpt d. Ub fdae tjc sbhdl``y bptdgl` buthbgc wc glxdgdsc tjc fb``bwdai cxprcssdba,

da wjdhj tjcrc lrc n lhtdvc hdtdcs clhj wdtj pbpu`ltdba a. Ujc fdrst tcrg ds tjc vl`uc bf butput

gdaus rcsburhcs usce da hbggutdai da tjcsc n hdtdcs, lae tjc schbae ds tjc vl`uc bf butput da

tjc lirdhu`turl` schtbr. Ujc `lst tcrg hlpturcs tjc flht tjlt tbtl` urmla cgp`bygcat ds fdxce lt

A , sb : ds tjc `lirlaic gu`tdp`dcr ba tjc hbastrldat tjlt an sjbu`e abt cxhcce A . Diabrdai

datcicr hbastrldats, tjc fdrst brecr hbaedtdbas fbr wc`flrc glxdgdsltdba wdtj rcspcht tb tjc sdzc

bf clhj hdty, a, lae tjc augmcr bf hdtdcs, n , lrc,

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Ujcsc twb cqultdbas, tbictjcr wdtj A 7 an , ectcrgdac tjc bptdgl` hdty sdzc, ab, augmcr bf

hdtdcs, n b, lae tjc sbhdl` vl`uc bf la dahrclsc da tjc augmcr bf kbms :.6

Ujds ds d``ustrltce da fdiurc =l. Ujc jbrdzbatl` lxds ds a, tjc sdzc bf l sdai`c hdty, lae

tjc vcrtdhl` ds butput pcr wbrncr da tjc hdty. Ujc sb`de hbahlvc hurvc (tjc slgc da fdiurcs =l-

=h) ds butput pcr wbrncr, ql(a). Glridal` butput, dah`uedai tjc cxtcral`dty, ds rcprcscatce my

hurvc q^l(a) + al—(a)W. Cqultdba (8) ds d``ustrltce lt pbdat L, wjcrc tjc glridal` mcacfdt bf

cxplaedai tjc hdty cqul`s tjc glridal` hbst bf tjc kbm, rcprcscatce my tjc `dac idvdai tjc

hbggutdai hbst bf tjc glridal` wbrncr (ta), butput fbrcibac, T—, lae sjlebw prdhc ba kbms,

:. Ujc augmcr bf hdtdcs ds sct suhj tjlt tjc lvcrlic vl`uc bf l kbm cqul`s dts lvcrlic hbst> tjds

ds pbdat M, hbrrcspbaedai tb cqultdba (5) lt wjdhj lvcrlic vl`uc ql(a) cqul`s tjc hbggutdai

hbst bf tjc lvcrlic wbrncr, (ta/=), p`us butput fbrcibac lae sjlebw prdhc :.9

Cqud`dmrdug buthbgcs ecpcae ba tjc cxtcat tb wjdhj licats lrc lm`c tb hbbredaltc da

brecr tb datcral`dsc tjc cxtcral`dtdcs tjlt lrc prcscat da tjds gbec`> wc rcfcr tb tjds ls tjc

chbabgy—s ‚dastdtutdbal` struhturc—. Ujc hlsc ecvc`bpce da guhj bf tjc `dtcrlturc ds bac da

wjdhj urmla ecvc`bpgcat ds uaecrtlnca my ‚`lric ecvc`bpcrs—.: Ujcsc lrc licats wjb lrc

lm`c tb hlpturc tjc catdrc `lae rcat lae hbatrb` tjc augmcr bf wbrncrs da tjc hdty. Ls ds wc``

nabwa, l hbgpctdtdvc supp`y bf tjcsc ecvc`bpcrs gclas tjlt tjc cqud`dmrdug ds tjc slgc ls

tjc sbhdl` bptdgug. Lt tjds cqud`dmrdug tjc `lae ecvc`bpcrs ply but tjc catdrc hdty rcat ls

sumsdedcs tb wbrncrs da tjc hdty, casurdai tjlt tjc u`tdgltc hrcltbrs bf tjc cxtcral`dty

(wbrncrs) flhc tjc hbrrcht dahcatdvcs lae tjlt l`` cxtcral`dtdcs lrc datcral`dsce. Ujds hlsc ds

mrdcf`y but`dace da tjc lppcaedx.

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Ecspdtc tjc wdecsprcle usc bf tjds ls l gbec``dai lpprblhj, dt sccgs jlre tb dglidac

tjlt tjc `lric ecvc`bpcr hlsc ds la lpprbprdltc ecshrdptdba bf `lae glrncts lae hdty irbwtj da

ecvc`bpdai hbuatrdcs, rcqudrdai, ls dt ebcs, tjlt l sdai`c ecvc`bpcr hbatrb`s hdty cgp`bygcat

my sumsdedsdai tjc bptdgl` augmcr bf wbrncrs tb catcr. Yc tjcrcfbrc davcstdiltc twb

l`tcraltdvcs tb tjc `lric ecvc`bpcr gbec`. Da mbtj bf tjcsc wc lssugc tjlt `bhltdba echdsdbas

lrc tlnca my wbrncr-fdrgs wjb lrc abt l`sb `laebwacrs, sb eb abt hlpturc l`` tjc rcat

lssbhdltce wdtj urmla ecvc`bpgcat. Ujc twb hlscs edffcr jbwcvcr, da tjc cxtcat tb wjdhj tjc

wbrncr-fdrgs hla hbbredaltc tjcdr echdsdbas, sb datcral`dsdai rchdprbhl` cxtcral`dtdcs da

prbeuhtdba.

Da tjc fdrst hlsc wc `bbn lt tjcrc ds ab suhj hbbredaltdba, sb l`` licats lrc sgl``. Ujc

rctura tb l kbm da l hdty wdtj a wbrncrs ds, ls da cqultdba (<),

wjcrc, sdahc q ds tjc slgc da l` `bhltdbas, M(ad , qd ) ds rcp`lhce my M(a). Df l glss , bf fdrgs

scts up da l acw `bhltdba, tjca tjc pcr wbrncr rctura ds

Da cqud`dmrdug tjcsc rcturas gust mc cqul`, wdtj hbggba vl`uc ecabtce M c, sb

. ]clrrlaidai,

Ujc fdrst bf tjcsc idvcs cqud`dmrdug hdty sdzc, ac, lae tjc schbae tjc lssbhdltce vl`uc bf M c.

Ujc augmcr bf hdtdcs hbgcs frbg tjc bvcrl`` `cvc` bf glauflhturdai cgp`bygcat, n c 7 A /ac.

Fdiurc =m d``ustrltcs tjds sgl`` licats hlsc. Ujc ilp mctwcca tjc sb`de hurvc lae tjc elsjce

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`dac ds tjc pcr wbrncr rctura, lae tjds cqul`s tjc hbggba vl`uc M c

lt pbdats L lae M, rcspchtdvc`y l hdty bf sdzc ac lae l hdty bf sdzc , 7 ?. Ujus, hdtdcs cxplae

uptb sdzc ac, mcybae wjdhj dt ds prbfdtlm`c tb stlrt l acw hdty.

Df l`` licats lrc sgl``, tjca , 7 ? da tjc cqultdbas lmbvc. Jbwcvcr, l furtjcr

pbssdmd`dty ds tjlt l hbl`dtdba bf prbeuhcrs ds lm`c tb hbbredaltc echdsdbas tb stlrt prbeuhtdba

da tjc hdty, l`tjbuij abt lm`c tb hlpturc tjc `lae rcats tjlt lrc icacrltce my hdty irbwtj. Df l

prbeuhcr hbl`dtdba bf lay sdzc , hla fbrg l acw hdty tjca dt wd`` eb sb df M(,) ds ircltcr tjla

br cqul` tb tjc rctura da la cstlm`dsjce `bhltdba, M(a). Yc ecabtc lriglx M(,) / ah, lae frbg

daspchtdba bf (6) scc tjlt tjc fdrst brecr hbaedtdba ds Ujc cqud`dmrdug hdty sdzc

lae rcturas tb l kbm lrc tjcrcfbrc,

Ub uaecrstlae tjds hlsc hbasdecr fdrst tjc vcrtdhl` `dac ah ba fdiurc =m. Catry lt tjds shl`c

wbu`e h`clr`y ydc`e rcturas pcr kbm ircltcr tjla M

. Hbl`dtdbas lrc lm`c tb cxp`bdt tjds, da l

wly tjlt sgl`` licats hlaabt, lae mde lwly tjds lrcl bf surp`us. Ujc buthbgc ds ls d``ustrltce

da fdiurc =h, wdtj cqud`dmrdug sdzc ah lae prbfdt `cvc` M h. Ujds ds tjc jdijcst lttldalm`c `cvc`

bf M my prbeuhcrs flhce wdtj idvca w( A ) lae fbr wjbg tjc wjb`c bf hbggutdai hbsts p`us

rcat (ta) ds l hbst.

Hbgplrdsba bf cqud`dmrdug lae bptdgug hdty sdzc

Uwb glrnct fld`urcs lrc prcscat, hrcltdai tjc edffcrcahcs mctwcca hlscs. Ujc fdrst ds tjc

cxtcral`dty da prbeuhtdba ls clhj wbrncr-fdrg lffchts tjc prbeuhtdvdty bf l`` btjcrs> sdahc tjds

ds l rchdprbhl` cxtcral`dty dt icacrltcs l pbtcatdl` hbbredaltdba fld`urc lgbaist wbrncr-fdrgs.

Ujc schbae lrdscs ls surp`us ds edvdece mctwcca wbrncr-fdrgs lae `lae`bres> tjds datcral`

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‚tcrgs bf trlec— gclas tjlt licats eb abt achcsslrd`y rchcdvc tjc fu`` glridal` mcacfdt bf tjcdr

lhtdbas.

Ujcsc fld`urcs hla mc scca my `bbndai lt tjc sdzc bf hdtdcs wjca tjcrc ds l hbl`dtdba bf

prbeuhcrs. Dt ds ualgmdiubus`y tjc hlsc tjlt ah 0 ac (scc fdiurcs =m lae =h). Ujc prbeuhcr

hbl`dtdba bvcrhbgcs tjc hbbredaltdba fld`urc, glndai dt clsdcr tb cstlm`dsj acw hdtdcs lae

jcahc hlusdai hdtdcs tb mc sgl``cr tjla da tjc sgl`` licat hlsc. Dt ds l`sb ualgmdiubus`y tjc

hlsc tjlt ah 0 ab. Hbgplrdai tjc tlaicahdcs lt M lae H ba fdiurcs =l lae =h rcspchtdvc`y, tjc

vl`uc bf cxtrl butput pcr wbrncr, ql—(a), ds cqultce tb tjc dahrclsc da hbggutdai hbsts p`us

rcat, t , da tjc hlsc bf tjc prbeuhcr hbl`dtdba, lae tb tjc dahrclsc da hbggutdai hbsts, t /=, da tjc

hlsc bf tjc bptdgug (tjds mcdai lhjdcvce my sumsdedsdai cgp`bygcat df tjc bptdgug ds

echcatrl`dsce my `lric ecvc`bpcrs). Datudtdvc`y, tjc prbeuhcr hbl`dtdba fld`s tb hlpturc tjc

leedtdbal` `lae rcat hrcltce my hdty ca`lricgcat, sb hdtdcs lrc sgl``cr tjla bptdgl`.

Mbtj glrnct fld`urcs hbgc datb p`ly da tjc hbgplrdsba bf tjc sbhdl` bptdgug lae tjc

sgl`` licats hlsc. Xgl`` licats lrc abt fu``y rcwlrece fbr hdty ca`lricgcat, mut l`sb fdae dt

edffdhu`t tb stlrt l acw hdty. Hbascqucat`y, tjc hbgplrdsba bf ac wdtj ab ds lgmdiubus. Xbgc

`dijt hla mc sjce my `bbndai lt tjc hlsc wjcrc tjc prbeuhtdvdty fuahtdba ds qulerltdh, idvca my

Cqultdbas (8) ‘ (:) tjca dgp`y

Hbgplrdai tjc bptdgug wdtj tjc sgl`` licats hlsc, wc scc tjlt df $q 1 8t/ = tjca ac 1 ab, tjc

hlsc d``ustrltce da tjc fdiurcs. Da tjds hlsc `lric prbeuhtdba cxtcral`dtdcs, $, rc`ltdvc tb

hbggutdai hbsts, t , gcla tjlt tjc hbbredaltdba fld`urc ds `lric rc`ltdvc tb `lae rcats. Ujc

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`lric hbbredaltdba fld`urc idvcs rdsc tb `lricr lae fcwcr hdtdcs tjla ds sbhdl``y bptdgl`.

Jbwcvcr, df tjc dacqul`dty ds rcvcrsce tjca sgl`` licats gly idvc rdsc tb l struhturc wdtj tbb

glay lae tbb sgl`` hdtdcs.4

=.8 Srmladsltdba lae tjc rltc bf ecvc`bpgcat

Yc slw da tjc prchcedai sumschtdba tjlt cqud`dmrdug lae bptdgl` buthbgcs edffcr da tjc sdzc

lae augmcr bf hdtdcs tjcy suppbrt, idvca tjc tbtl` augmcr bf urmla kbms, A. Ujcy l`sb edffcr da

tjc vl`uc bf kbm hrcltdba, (: lae M). Jcahc, da l `bai rua cqud`dmrdug da wjdhj A ds l fuahtdba

bf tjc vl`uc bf l kbm, tjcy wd`` edffcr da tjc `cvc` bf urmla cgp`bygcat, A , lae tjc wlic w( A ).

Fdiurcs =l-=h idvc l`` tjc dafbrgltdba wc acce tb lal`ysc tjc vl`uc bf kbm hrcltdba lae jcahc

hbgplrc tjc cffchts bf edffcrcat dastdtutdbal` struhturcs ba `bai rua gbecra schtbr

cgp`bygcat.

Ujc vcrtdhl` datcrhcpts glrnce ba fdiurcs = idvc tjc wlic p`us tjc vl`uc (sbhdl`, :, br

prdvltc, M) bf la urmla kbm. Xuppbsc tjlt suhj l kbm hla mc hrcltce lt hbastlat hbst, wjdhj hla

mc sct lt zcrb. Da tjc ‚`bai rua— dt wd`` tjcrcfbrc mc tjc hlsc tjlt : 7 Mc 7 Mh 7 ?, ls tjc

augmcr bf kbms ds uahbastrldace lae lay rcat lssbhdltce wdtj l kbm ds mde ebwa tb zcrb. Ujc

jcdijt bf tjc datcrhcpt tjca kust gclsurcs tjc cqud`dmrdug wlic da tjc chbabgy, T—( @ - A ) 7

w( A ), lae jcahc l`sb daedhltcs tjc gliadtuec bf tbtl` urmla cgp`bygcat.

Ujc rlandai ds ualgmdiubus lae, ls daedhltce ba fdiurcs =, tlncs tjc fbrg w( A b) 1

w( A h) 1 w( A c ) lae jcahc A b 1 A h 1 A c . Ujc fdrst bf tjcsc, A b 1 A h , hbgcs frbg hbgplrdsba

bf fdiurcs =l lae =h. Da clhj bf tjcsc fdiurcs bptdgdsdai mcjlvdbur idvcs l tlaicahy mctwcca

tjc glridal` prbeuhtdvdty ilda lae tjc glridal` hbst bf cxplaedai l hdty. Da tjc hlsc bf

hbbredaltce prbeuhcrs glridal` hbggutdai hbst lae rcat ds pcrhcdvce ls l hbst bf hdty

cxplasdba, wjcrcls da tjc bptdgug (lae tjc hlsc bf `lric ecvc`bpcrs) glridal` rcat acts but.

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Ujds dahrclscs tjc rctura tb cstlm`dsjdai l hdty, lae jcahc tjc rctura tb urmla cgp`bygcat.

Ujc rlandai bf tjc hbbredaltce prbeuhcrs lae sgl`` licats hlscs ds l`sb ualgmdiubus, wdtj

A h 1 A c. Ujds ds l edrcht hbascqucahc bf tjc flht tjlt rcturas tb kbm hrcltdba ds bptdgdsce da tjc

fdrst bf tjcsc hlscs, mut abt da tjc schbae. Ydtj sgl`` licats tjcrc ds la chbabgdh surp`us tjlt

ds abt mcdai cxp`bdtce, mchlusc bf hbbredaltdba fld`urc, lae tjds rceuhcs tjc vl`uc bf kbm

hrcltdba.

Ujc dgp`dhltdba bf tjcsc fdaedais lrc tjlt edffcrcat dastdtutdbas lffcht abt ba`y hdty

sdzcs, mut l`sb tjc vl`uc bf hrcltdai urmla kbms. Fld`urc tb datcral`dsc tjc cxtcral`dtdcs

lssbhdltce wdtj urmla ecvc`bpgcat rceuhcs tjc rcturas tb kbm hrcltdba, sb ‘ ecpcaedai ba tjc

gchjladsg ectcrgdadai A ‘ rctlredai ecvc`bpgcat lae `bwcrdai tjc wlic.

=.5 Drrcvcrsdm`c echdsdbas lae fbrwlre `bbndai mcjlvdbur

Xb flr wc jlvc lssugce tjlt echdsdbas lrc glec ba tjc mlsds bf dastlatlacbus rcturas, ls wd``

mc tjc hlsc df l`` echdsdbas lrc hbst`css`y rcvcrsdm`c. Yc abw mrdcf`y cxp`brc tjc pb`lr

bppbsdtc hlsc, da wjdhj l wbrncr-fdrg hbggdts tb l `bhltdba da pcrpctudty.

Ujc augmcr bf wbrncrs lhtdvc da l plrtdhu`lr hdty, d, lt eltc z wc ecabtc ad( z). Ujc

dastlatlacbus rcturas tb l kbm da tjds hdty lrc,

wjcrc, fbr sdgp`dhdty, wc abw lssugc tjlt tjc wlic ds hbastlat. Ybrncr-fdrgs lrc hrcltce lt

hbastlat rltc bf 0 pcr uadt tdgc. Hbasdecr l acw hdty mbra lt eltc ?> dt rchcdvcs wbrncrs lt rltc

0 uatd` sbgc (caebicabus`y ectcrgdace) eltc U , lt wjdhj pbdat wbrncrs dastcle stlrt tb catcr

tjc acxt hdty. Ujc tdgc pltj bf rcturas tb kbms da tjc hdty ds idvca da fdiurc 8. Dt rdscs lae tjca

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fl``s ls tjc hdty irbws, mcacfdttdai frbg dahrclsdai rcturas tb shl`c lae tjca ruaadai datb

edgdadsjdai rcturas. Mcybae eltc U tjc hdty mchbgcs stltdbalry lae M (ad( z)) hbastlat.

Ydtj sgl`` licats, tjc cqud`dmrdug wd`` jlvc tjc prbpcrty tjlt tjc prcscat vl`uc bf tjds

pltj lt eltc ? ds cqul` tb dts prcscat vl`uc lt eltc U . Ujcsc lrc tjc eltcs lt wjdhj wbrncr-fdrgs

lrc daedffcrcat mctwcca stlrtdai l acw hdty (eltc ?) br stlydai da la b`e lae stltdbalry bac

(eltc U ). Ujc swdthj eltc ds tjcrcfbrc dgp`dhdt`y ecfdace my tjc fb``bwdai cqultdba, da wjdhj *

ds tjc edshbuat rltc>

Fbr z , (?, U ) l`` acw kbms ib tjc hdty, sb ad( z) 7 0 z, wjd`c fbr fbr z 1 U tjc hdty ds stltdbalry,

wdtj ad( z) 7 0U . Ujc `cft jlae sdec bf tjds cqultdba idvcs tjc vl`uc bf ibdai datb l acw hdty lt

eltc ?. Ujc rdijt jlae sdec ds tjc vl`uc bf mcdai tjc `lst wbrncr-fdrg da, mcybae wjdhj tjc

f`bw bf prbfdts ds stltdbalry.

Ujds sdgp`c frlgcwbrn idvcs l hbup`c bf dasdijts. Ujc fdrst ds tjlt l flstcr irbwdai

chbabgy -- wdtj l jdijcr vl`uc bf 0 ‘ wd`` jlvc sgl``cr hdtdcs, btjcr tjdais mcdai cqul`.<?

Ujc rclsba ds tjlt prbeuhtdvdty irbwtj da l acw hdty bhhurs flstcr, ls gbrc acw kbms lrc mcdai

hrcltce. Da fdiurc 8, l jdijcr vl`uc 0 ds d``ustrltce my tjc elsjce `dac, lae wc scc tjlt tjc

mcacfdts bf tjc h`ustcr hbgc sbbacr, dahrclsdai tjc rctura tb hrcltdai l acw hdty, lae rceuhdai

U . Yjd`c tjc cffcht bf hdty sdzc ba irbwtj jls mcca davcstdiltce da tjc ̀ dtcrlturc (ci

Jcaecrsba =??8) tjds suiicsts tjlt hlusl`dty l`sb ruas da tjc bppbsdtc edrchtdba, wdtj irbwtj

ectcrgdadai hdty sdzc.

Xchbae, tjc flstcr irbwdai chbabgy jls tjc jdijcr rctura tb kbm hrcltdba, ls

d``ustrltce my tjc jcdijt bf M(0U) fbr tjc edffcrcat vl`ucs bf 0 da fdiurc 8. Ujds da tura

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suiicsts tjlt, df tjc rltc bf kbm hrcltdba ds la dahrclsdai fuahtdba bf tjc rcturas tb hrcltdai l

kbm, sb 0 7 0(M), 0— 1 ?, tjca tjcrc gly mc gu`tdp`c cqud`dmrdl. Da l s`bw irbwdai chbabgy dt

ds rc`ltdvc`y edffdhu`t tb stlrt acw hdtdcs> tjds rceuhcs tjc rctura tb kbm hrcltdba, M, rceuhdai 0,

lae hbafdrgdai tjc s`bw irbwtj bf tjc chbabgy. Hbavcrsc`y, flst irbwdai chbabgdcs hla

ecvc`bp la urmla struhturc tjlt bffcrs jdijcr rcturas tb kbm hrcltdba, hbafdrgdai tjc rlpde

irbwtj bf tjc chbabgy.

8. ]cidbas (lae Datcraltdbal` Urlec)

Ujc gbec`s ecvc`bpce lmbvc dgp`y tjlt ecvc`bpgcat ds spltdl``y hbahcatrltce, mut tjc rcl`

icbirlpjdhl` struhturc bf tjc gbec`s ds rltjcr wcln, csscatdl``y mchlusc l`` tjc `danlics

jlppca wdtjda hdtdcs. Ujc ba`y datcrlhtdba mctwcca tjcsc `bhltdbas ds tjrbuij glrncts wjdhj

lrc pcrfcht`y hbgpctdtdvc lae pcrfcht`y frdhtdba`css. Ub ict l rdhjcr stbry bf rcidbal`

edsplrdtdcs datcrlhtdbas mctwcca ls wc`` ls wdtjda hdtdcs acce tb mc leece. Bac lpprblhj tb

tjds ds tb wbrn wdtj l h`lss bf gbec`s da wjdhj tjc lii`bgcrltdba fbrhc ds trlaspbrt hbsts ba

ibbes wjdhj lrc prbeuhce sumkcht tb dahrclsdai rcturas tb shl`c (datcral` tb tjc fdrg).

Dahrclsdai rcturas gclas tjlt l plrtdhu`lr vlrdcty bf ibbe wd`` typdhl``y ba`y mc prbeuhce da l

sdai`c p`lhc, lae trlaspbrt hbsts gcla tjlt tjcrc lrc ildas tb prbeuhdai h`bsc tb `lric

glrncts. Lii`bgcrltdba hla lrdsc df tjcrc ds `lmbur gbmd`dty (sb l `lric glrnct hrcltcs kbms

lae tjc cxpcaedturc bf tjcsc wbrncrs glncs tjc glrnct `lric, Nruigla <44<) br daput-butput

`danlics, sb fdrgs hrcltc tjc glrnct fbr btjcr fdrgs, (Vcalm`cs <446).

L gbec` bf tjds ds sncthjce da tjc lppcaedx (dt erlws ba Fukdtl ct l` <444), lae wc eb

abt c`lmbrltc dt da tjc tcxt. Jbwcvcr, tjc ncy tb uaecrstlaedai tjc fbrhcs bpcrltdai da tjds

frlgcwbrn hla mc uaecrstbbe my `bbndai lt tjc wlic cqultdba ‘ tjc glxdgug wlic tjlt l

fdrg hla lffbre tb ply da `bhltdba d lae mrcln cvca. Ujds wlic, wd, ds dgp`dhdt`y ecfdace my

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wjcrc Id ds l prdhc daecx lt `bhltdba d, ecfdace ls

Ujc rdijt jlae sdec bf (<=) ds tjc ‚glrnct lhhcss— bf `bhltdba d, lae ds l tjcbrctdhl``y wc``

fbuaece vcrsdba bf glrnct pbtcatdl`. Dt ds tjc sug bf cxpcaedturcs, C k, da l`` `bhltdbas,

wcdijtce my l trlec hbst flhtbr lae ecf`ltce my l prdhc daecx. Ujc trlec hbst flhtbr, U dk, ds l

gclsurc bf tjc hbst flhce my hbuatry d prbeuhcrs da sc``dai da glrnct k. Ujc hbst bf ̀ dvdai

daecx, Id ds ecfdace da (<8) ls l HCX liirciltbr (wdtj c`lstdhdty bf sumstdtutdba F) bf tjc

prdhcs pd (trlec hbst lekustce) bf clhj bf tjc ad vlrdctdcs bf ibbes prbeuhce da clhj `bhltdba.

Hrbss hbuatry vlrdltdba da Id lrdscs ls hbuatrdcs h`bsc tb `lric sburhcs bf supp`y jlvc `bwcr

vl`uc bf tjc prdhc daecx.

Ujc `cft jlae sdec bf (<=) ds tjc uadt hbsts bf l rcprcscatltdvc fdrg lt `bhltdba d. " lae

$ lrc daput sjlrcs, sb df `lmbur ds tjc ba`y daput tb prbeuhtdba " 7 ? lae $ 7 <. Df

datcrgcedltcs lrc usce tjca " 1 ? gclsurcs tjcdr sjlrc, lae tjc prdhc bf l rcprcscatltdvc

muae`c bf datcrgcedltcs ds gclsurce my tjc prdhc daecx. Ujds prdhc daecx hla l`sb mc

datcrprctce ls tjc ‚supp`dcr lhhcss— bf `bhltdba d, tlndai l `bw vl`uc lt `bhltdbas tjlt lrc h`bsc

tb sburhcs bf supp`y bf glauflhturce datcrgcedltcs.

_u``dai tjds tbictjcr, wc scc tjlt tjc glxdgug wlic tjlt l fdrg hla lffbre tb ply lae

mrcln cvca ds ircltcr tjc mcttcr dts glrnct lhhcss ‘ tjc h`bscr dt ds tb sburhcs bf ecglae ‘ lae

tjc mcttcr dts supp`dcr lhhcss ‘ `bwcr I gcladai hjclpcr daputs. Ujds ds l fbrhc fbr spltdl`

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h`ustcrdai bf lhtdvdty, lae pu``dai lildast tjds ds sbgc edspcrsdba fbrhc, suhj ls `lae rcats.

Yjlt `dijt hla tjds frlgcwbrn sjce ba spltdl` dacqul`dtdcs da ecvc`bpdai hbuatrdcs2

8.< = rcidba gbec`s

_uil (<44:), usdai l frlgcwbrn sdgd`lr tb tjlt but`dace lmbvc, hbasdecrce twb rcidbas da l

h`bsce chbabgy. Jc sjbwce tjlt df trlaspbrt hbsts lrc jdij, tjcrc gust mc l ‚ml`lahce— urmla

systcg, wdtj l hdty da clhj rcidba. Ujc datudtdba hbgcs frbg tjdandai bf rcidbal` lutlrny, da

wjdhj clhj rcidba jls tb prbeuhc l`` ibbes tb gcct `bhl` ecglae. Jbwcvcr, lt `bwcr

trlaspbrt hbsts hbasugcr ecglaes hla mc gct my dgpbrts, sb lii`bgcrltdba fbrhcs idvc rdsc

tb l prdgltc-hdty struhturc. Glauflhturdai cgp`bygcat hbahcatrltcs da l sdai`c hdty, wjdhj ds

lm`c tb ply jdij wlics mchlusc bf dts ibbe glrnct lhhcss (jdij vl`uc bf tjc rdijt-jlae sdec

bf (<=)). _uil lriucs tjlt tjds ds bac bf tjc rclsbas wjy ecvc`bpdai hbuatrdcs ‘ urmladsdai

`ltcr lae wdtj mcttcr trlaspbrt tchjab`bidcs ‘ jlvc l `css ml`lahce urmla struhturc tjla eb

prcscat ecvc`bpce hbuatrdcs.

Ybrndai da l sdgd`lr frlgcwbrn, Nruigla lae @dvls (<446) sjbw jbw bpcaacss tb

datcraltdbal` trlec glncs l gbrc ml`lahce hdty struhturc gbrc `dnc`y. Ujc datudtdba ds tjlt da l

gbrc bpca chbabgy fdrgs lrc `css ecpcaecat ba `bhl` glrncts lae `bhl` sburhcs bf supp`y, sb

wdtjda hdty lii`bgcrltdba fbrhcs lrc wclncr. Idvca tjc prcscahc bf sbgc edspcrsdba fbrhcs,

trlec hla `cle tb l echbahcatrltdba bf lhtdvdty.

8.= L gu`td-rcidba gbec`

Furtjcr dasdijts hla mc ildace my gbvdai tb l gu`td-rcidba cavdrbagcat. L fu`` vcrsdba bf

suhj l gbec` hbu`e mc hl`dmrltce tb l plrtdhu`lr hbuatry da brecr tb sjbw jbw tjc dahcatdvcs

tb `bhltc da edffcrcat rcidbas cvb`vcs. Jcrc wc hbatdauc tb bpcrltc wdtj sbgctjdai gbrc

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sty`dsce, lae lal`ysc l `daclr chbabgy wdtj l wc`` ecfdace gde-pbdat lae twb cae-pbdats. Da

`dac wdtj tjc gbec`dai bf schtdba =, wc hbatdauc tb lssugc la cxbicabus irbwtj prbhcss>

wdtj tjc tbtl` augmcr bf glauflhturdai kbms, A, dahrclsdai tjrbuij tdgc. Yjcrc, da suhj la

chbabgy, eb tjcy `bhltc2

Daeustrdl`dsltdba uaecr lutlrny; Yc usc augcrdhl` gctjbes tb cxp`brc cqud`dmrdl bf tjds

gbec`, lae prcscat rcsu`ts da l scrdcs bf hbatbur p`bts.<< Da fdiurc 5l lae sumscqucat fdiurcs

tjc vcrtdhl` lxds rcprcscats `bhltdbas da tjc chbabgy> tjus, tjc tbp lae mbttbg bf tjc vcrtdhl`

lxds lrc tjc twb caes bf tjc `daclr chbabgy. Ujc jbrdzbatl` lxds ds tjc sjlrc bf tjc `lmbur

fbrhc tjlt ds da glauflhturdai ( A ), vlrydai frbg <% tb 8?%. Ujc hbatbur `dacs ba tjc fdiurcs

idvc glauflhturdai lhtdvdty `cvc`s da clhj `bhltdba.

Clhj pbdat ba tjc jbrdzbatl` lxds hbrrcspbaes tb la cxbicabus`y idvca augmcr bf

glauflhturdai fdrgs da tjc hbuatry ls l wjb`c, lae tjc gbec` hbgputcs tjc cqud`dmrdug

`bhltdba bf tjcsc fdrgs. Gbec`s bf tjds typc typdhl``y cxjdmdt pltj ecpcaecahc, sb tjc prbhcss

my wjdhj gbrc fdrgs lrc leece tb tjc chbabgy acces tb mc spchdfdce. Da tjc rcsu`ts sjbwa wc

hbgputc la dadtdl` cqud`dmrdug (lt tjc ̀ cft jlae cae bf clhj fdiurc). Acw fdrgs lrc tjca

leece tb l`` `bhltdbas, ba tbp bf tjc prcvdbus cqud`dmrdug plttcra. Fdrgs gly rc`bhltc tb tjc

gbst prbfdtlm`c `bhltdbas, idvdai tjc acw cqud`dmrdug. Ujc prbhcss ds rcpcltce, gbvdai tb tjc

rdijt l`bai tjc fdiurc.

Ujc h`bsce chbabgy ds d``ustrltce da fdiurc 5l. Lt `bw `cvc`s bf glauflhturdai

ecvc`bpgcat tjcrc lrc twb glauflhturdai rcidbas, `bhltce lpprbxdgltc`y </8 lae =/8 bf tjc

wly l`bai tjc `caitj bf tjc chbabgy. Ujds `bhltdbal` plttcra cxjdmdts h`ustcrdai, mchlusc bf

tjc ecglae lae hbst `danlics da tjc gbec`. Jbwcvcr, wbrndai lildast h`ustcrdai ds tjc

prcscahc bf ecglae fbr glauflhturcs da l`` `bhltdbas. Ujc edstrdmutdba bf `lae lhrbss

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`bhltdbas gclas tjlt dahbgc lae cxpcaedturc ba glauflhturcs bhhurs cvcrywjcrc, lae

hbgp`ctc lii`bgcrltdba bf glauflhturdai da l sdai`c hcatrl` h`ustcr wbu`e `clvc

bppbrtuadtdcs tb prbfdt frbg catry da pcrdpjcrl` rcidbas. Lt `bw `cvc`s bf bvcrl``

glauflhturdai lhtdvdty tjc tcasdba mctwcca tjc lii`bgcrltdba lae edspcrsdba fbrhcs prbeuhcs

la buthbgc wdtj twb edstdaht glauflhturdai rcidbas.

Ls tjc chbabgy mchbgcs gbrc ecvc`bpce, sb wc scc tjlt tjc twb glauflhturdai

rcidba struhturc mrclns ebwa lae l sdai`c rcidba fbrgs, glndai tjc spltdl` edstrdmutdba bf

lhtdvdty gbrc hbahcatrltce. Yjy ebcs tjds jlppca2 Ujc twb rcidba struhturc mchbgcs

uastlm`c mchlusc ls tjc chbabgy mchbgcs gbrc daeustrdl`dsce sb lii`bgcrltdba fbrhcs

mchbgc strbaicr. Da plrtdhu`lr, ls glauflhturdai irbws rc`ltdvc tb lirdhu`turc tjc prbpbrtdba

bf ecglae fbr glauflhturcs hbgdai frbg tjc daeustrdl` rcidbas mchbgcs ircltcr. Ujds ds l

fbrhc fbr gbvdai tjc daeustrdl` hcatrcs dawlres lae lwly frbg tjc ceics bf tjc chbabgy.

Jbwcvcr, mchlusc bf tjc `bhn-da cffcht hrcltce my lii`bgcrltdba, tjds ebcs abt jlppca

sgbbtj`y. Dastcle, tjc twb-hcatrc struhturc rcgldas la cqud`dmrdug up tb sbgc pbdat lt wjdhj

tjcrc ds l mdfurhltdba da tjc systcg, lae l acw struhturc ecvc`bps, wdtj l sdai`c hcatrl`

daeustrdl` rcidba. Furtjcr irbwtj bf glauflhturdai dahrclscs tjc augmcr bf fdrgs da tjds

rcidba lae l`sb (mchlusc bf tjc edschbabgdcs tb hdty sdzc tjlt lrc prcscat da tjc gbec`) hluscs

sbgc sprcle bf tjc rcidba tb cdtjcr sdec bf tjc hcatrl` `bhltdba. Yjlt wc scc tjca, ds tjc

h`bsce chbabgy ecvc`bpdai l gbabhcatrdh struhturc, wdtj l `lric hcatrl` glauflhturdai

rcidba.

Daeustrdl`dsltdba wdtj twb pbrts. Jbw eb tjdais edffcr da l gbrc bpca chbabgy2 Xuppbsc

tjlt tjc icbirlpjy bf tjc chbabgy rcgldas syggctrdh, wdtj bac pbrt lt clhj cae bf tjc

hbuatry. Buthbgcs lrc d``ustrltce da fdiurc 5m.

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Lt `bw `cvc`s bf daeustrdl`dsltdba, tjcrc ds abw l sdai`c daeustrdl` rcidba, `bhltce da

tjc hcatrc bf tjc chbabgy. Ujc rclsba ds tjc prcscahc bf fbrcdia hbgpctdtdba, glndai

pcrdpjcrl` `bhltdbas uaprbfdtlm`c. Fdrgs ecrdvc alturl` prbtchtdba frbg `bhltdai da tjc hcatrc

bf tjc chbabgy. Ls tjc augmcr bf fdrgs dahrclscs, sb twb tjdais jlppca. Fdrst, hcatrl`

rcidbas bf tjc chbabgy mchbgc dahrclsdai wc`` supp`dce wdtj glauflhturcs, erdvdai ebwa

tjcdr prdhcs. Lae schbae, hbst `danlics strcaitjca, rceuhdai hbsts lae glndai glauflhturdai

mcttcr lm`c tb hbgpctc wdtj rcst bf tjc wbr`e prbeuhtdba. Mbtj bf tjcsc fbrhcs cahburlic l

edspcrsdba bf lhtdvdty frbg tjc hcatrl` rcidba tbwlres tjc ceics bf tjc chbabgy. Bahc lilda,

tjcrc ds l mdfurhltdba pbdat, mut abw tjc sdai`c h`ustcr bf lhtdvdty edvdecs datb twb h`ustcrs

h`bscr tb tjc pbrts. Ecspdtc tjc `bhn-da fbrhcs euc tb lii`bgcrltdba, tjcsc hcatrcs cxjdmdt

sbgc gbvcgcat tbwlres tjc ceic bf tjc chbabgy, mchbgdai gbrc ecpcaecat ba cxpbrt

glrncts ls l ecstdaltdba fbr tjc irbwdai vb`ugc bf butput. Lt sbgc pbdat tjc h`ustcrs rclhj

lae hbahcatrltc lt tjc pbrt `bhltdbas.

Ujc mrble pdhturc ds tjcrcfbrc bac da wjdhj daeustrdl` ecvc`bpgcat da tjc bpca

chbabgy ds lssbhdltce wdtj trlasdtdba frbg l sgl`` hcatrl``y `bhltce lae dawlres brdcatce

glauflhturdai schtbr tb dts rcp`lhcgcat my `lric cxpbrt brdcatce h`ustcrs lt tjc pbrts -- tjc

bppbsdtc bf tjc lutlrny hlsc. Uwb qul`dfdhltdbas acce tb mc glec tb tjds. Df tjc ebgcstdh

chbabgy wcrc glec l ibbe ecl` `lricr, tjca tjc hcatrl` h`ustcr ecvbtce `lric`y tb supp`ydai

tjc ebgcstdh glrnct hbu`e l`sb survdvc, idvdai tjrcc glauflhturdai rcidbas. Lae df rcturas

tb h`ustcrdai wcrc glec strbaicr tjca dt ds pbssdm`c tjlt glauflhturdai wbu`e lii`bgcrltc lt

l sdai`c pbrt. Ujc ildas tb lii`bgcrltdba lt kust bac bf tjc pbrts wbu`e butwcdij lay

edschbabgdcs euc tb hbaicstdba br hbsts bf supp`ydai ebgcstdh hbasugcrs ba tjc btjcr sdec

bf tjc chbabgy.

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Daeustrdl`dsltdba wdtj l sdai`c pbrt. Fdal``y wc `bbn lt l hlsc wjcrc icbirlpjy ds suhj tjlt

trlec hla bhhur ba`y tjrbuij bac cae bf tjc chbabgy ‘ l pbrt `bhltce lt tjc mbttbg ceic bf

fdiurc 5h.

@dnc tjc prcvdbus hlsc, lt `bw `cvc`s bf daeustrdl`dsltdba tjcrc ds l sdai`c daeustrdl`

h`ustcr. Ujds ds abw `bhltce gbrc tjla jl`f tjc `caitj bf tjc chbabgy lwly frbg tjc pbrt, da

brecr tb mcacfdt frbg tjc alturl` prbtchtdba bf edstlahc. Daeustrdl`dsltdba glncs daeustry gbrc

butwlre brdcatce lae hluscs gbvcgcat bf tjds h`ustcr tbwlres tjc pbrt. Ujds gbvcgcat

gclas tjlt datcrdbr rcidbas bf tjc chbabgy mchbgc prbircssdvc`y `css wc`` scrvce my

glauflhturdai daeustry, lae tjc chbabgy rclhjcs l mdfurhltdba pbdat lt wjdhj l acw spltdl`

struhturc cgcrics. L acw daeustrdl` h`ustcr fbrgs da tjc datcrdbr bf tjc chbabgy, brdcatce

tbwlres gcctdai `bhl` ecglaes, lae tjc brdidal` h`ustcr ds rcp`lhce my l h`ustcr bf

glauflhturdai da tjc pbrt hdty. Ujcrc ds tjcrcfbrc l rledhl` hjlaic da datcral` chbabgdh

icbirlpjy, wdtj tjc brdidal` gbabhcatrdh struhturc mcdai rcp`lhce my twb daeustrdl` h`ustcrs,

bac cxpbrt brdcatce lae tjc btjcr prcebgdalat`y supp`ydai tjc ebgcstdh glrnct.

Furtjcr irbwtj da tjc augmcr bf fdrgs ds hbahcatrltce da tjc cxpbrt brdcatce h`ustcr,

ls edgdadsjdai rcturas (da tjc prbeuht glrnct) lrc cahbuatcrce `css rlpde`y da cxpbrt sl`cs

tjla da ebgcstdh sl`cs. Mut ls tjds bhhurs, sb tjc hblstl` h`ustcr ildas la dahrclsdai hbst

levlatlic, euc tb tjc eccpcadai bf hbst `danlics. Ujds uaecrgdacs tjc hbgpctdtdvcacss bf tjc

datcral` h`ustcr wjdhj ‘ da tjds cxlgp`c ‘ stlrts tb ech`dac lae cvcatul``y edslppclrs.

Hbgplrdsba. Ujcsc hlscs lrc suiicstdvc bf tjc fbrhcs lt wbrn da ectcrgdadai tjc hjlaidai

plttcra bf daeustrdl` `bhltdba eurdai ecvc`bpgcat. Ujcy sjbw jbw ‘ da bpca chbabgdcs ‘

ecvc`bpgcat hla mc lssbhdltce wdtj l echbahcatrltdba bf lhtdvdty. Lae da l hrbss-schtdba bf

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hbuatrdcs, tjcy lrc hbasdstcat wdtj tjc Lecs lae I`lcscr (<443) fdaedai tjlt gbrc bpca

chbabgdcs jlvc `css spltdl``y hbahcatrltce chbabgdh lhtdvdty.

Bf hbursc, tjc hlscs idvca jcrc lrc cxlgp`cs rltjcr tjla icacrl` fdaedais, lae tjc

`dtcrlturc rcgldas sjbrt bf jlvdai fdaedais tjlt lrc rbmust cabuij tb mc tjc mlsds fbr pb`dhy

levdhc. ]csu`ts lrc scasdtdvc tb ectld`s bf tjc icbirlpjy bf hbuatrdcs, dah`uedai mbtj cxtcral`

trlec bppbrtuadtdcs lae datcral` dafrlstruhturc (tjc cxlgp`c jcrc jb`es trlaspbrt hbsts

hbastlat). ]csu`ts l`sb ecpcae ba tjc strcaitjs bf `danlics wdtjda daeustrdcs lae ‘ wdtj glay

glauflhturdai schtbrs ‘ tjc strcaitj bf `danlics mctwcca daeustrdcs. Ujc gbec` but`dace jcrc

ds stltdh, lae wjd`c lii`bgcrltdba tcaes tb `bhn-da la cxdstdai daeustrdl` struhturc, btjcr

fbrhcs fbr `bhn-da, suhj ls suan hbsts, lrc diabrce. Ujus, wjd`c sbgc bf tjc hlscs but`dace

lmbvc jle tjc prbpcrty tjlt daeustrdl` struhturc ba`y hjlaice tjrbuij tjc mdrtj lae ecltj bf

daeustrdl` hcatrcs, btjcrs jle tjc `css sltdsflhtbry prbpcrty bf daeustrdl` hcatrcs gbvdai

hbatdaubus`y wdtj plrlgctcrs bf tjc gbec`. L`` bf tjds pbdats tb tjc acce fbr furtjcr wbrn,

mbtj tjcbrctdhl` lae cgpdrdhl`, tb pda ebwa tjcsc cffchts.

5. Hbah`uedai Hbggcats

Ujds plpcr jls but`dace sbgc sdgp`c gbec`s tjlt sccn tb d``ugdaltc spltdl` plttcras bf

ecvc`bpgcat. Ujc gbec`s ecgbastrltc jbw fdrst lae schbae alturc icbirlpjdcs datcrlht da

ectcrgdadai tjc `bhltdba bf lhtdvdty, lae tjcy hlpturc sbgc bf tjc sty`dsce flhts lmbut tjc

cvb`utdba bf spltdl` edsplrdtdcs da ecvc`bpdai hbuatrdcs.

Bac dgpbrtlat gcsslic frbg tjds gbec`dai cxcrhdsc ds tjlt glrnct fld`urcs lssbhdltce

wdtj hdty ecvc`bpgcat hla mc elglidai fbr rcl` dahbgc da mbtj tjc sjbrt-rua lae tjc `bai-

rua. Ujc glrnct fld`urcs hrcltc hdty struhturcs tjlt lrc `css tjla sbhdl``y cffdhdcat. Jbwcvcr,

tjc dgp`dhltdbas bf tjds ecpcae ba tjc cxtcat tb wjdhj chbabgdh licats ‘ mc tjcy prbeuhcr

8/3/2019 Venables (2003)

hbl`dtdbas, `lric ecvc`bpcrs br hdty ibvcragcats ‘ lrc lm`c tb datcral`dsc sbgc bf tjc

cxtcral`dtdcs. Idvca l `cvc` bf gbecra schtbr cgp`bygcat, dt ds abt l prdbrd h`clr wjctjcr

hdtdcs lrc `lricr br sgl``cr tjla ds bptdgl`. Gbrc dgpbrtlat jbwcvcr, ds tjc flht tjlt tjcsc

cxtcral`dtdcs ualgmdiubus`y rceuhc tjc rcturas tb kbm hrcltdba lae tjcrcmy gly rctlre

irbwtj. @bw `cvc` cqud`dmrdug trlps lrc pbssdm`c> `bw rltcs bf kbm hrcltdba rceuhc tjc

dahcatdvcs tb hrcltc acw hdtdcs, tjds da tura idvdai l hdty struhturc da wjdhj rcturas tb kbm

hrcltdba lrc ecprcssce.

Ujc u`tdgltc bmkchtdvc bf tjds `dac bf rcsclrhj gust mc tb dafbrg lae dgprbvc pb`dhy

fbrgu`ltdba. Ujc rlpde plhc bf urmladsltdba lae bf hjlaidai chbabgdh icbirlpjdcs da

ecvc`bpdai hbuatrdcs idvc tjds tlsn sbgc uricahy. Df dt ds lhhcptce tjlt hdtdcs lrc lssbhdltce

wdtj ‚schbae alturc— dahrclsdai rcturas tb shl`c tjca dt ds pbssdm`c, ls wc slw da schtdba 8, tjlt

tjcrc gly mc rledhl` sjdfts da hbuatrdcs— icbirlpjdcs. _b`dhy datcrvcatdbas ilda l plrtdhu`lr

dgpbrtlahc ls tjcy hla sjdft ecvc`bpgcat batb l`tcraltdvc pltjs. Saecrstlaedai tjc fbrhcs

sjlpdai hbuatrdcs— chbabgdh icbirlpjy lae tjc glrnct fld`urcs lssbhdltce wdtj tjcg ds l

achcsslry, df vcry prc`dgdalry, stcp tb fbrgu`ltdba bf suhj pb`dhdcs.

8/3/2019 Venables (2003)

Lppcaedx <

L rcprcscatltdvc ecvc`bpcr glxdgdscs tjc tbtl` hdty rcat act bf lay pcr wbrncr sumsdedcs (lt

rltc s), sb jls glxdglae . Jc flhcs tjc hbastrldat tjlt, tb lttrlht wbrncrs,

clradais act bf hbggutdai hbsts lae rcat, ta, lae dah`usdvc bf lay sumsdey plygcat, s, gust

mc lt `clst ls irclt ls sbgc butsdec bptdba u, sb . Glxdgdsdai tjds lae

scttdai ] 7 ?, (frcc catry bf `lric ecvc`bpcrs) idvcs tjc slgc buthbgc ls tjc wc`flrc

glxdgug, prbvdedai tjc butsdec vl`uc bf l kbm ds tjc slgc da mbtj hlscs (v 7 T— + :). Ujds

`lric ecvc`bpcr buthbgc davb`vcs plydai l sumsdey tb wbrncrs tb catcr tjc hdty, sdahc ] 7 ?.

Ujds ds tjc ‚Jcary Icbric tjcbrcg—, slydai tjlt l`` tjc rcats clrace da tjc hdty gust mc

trlasfcrrce tb tjc licats wjb hrcltc tjc cxtcral`dty.

Lppcaedx =

L fdxce frlhtdba bf dahbgc ds spcat ba daeustry, tjc rcgldaecr ba lirdhu`turc. Ecglae fbr l

sdai`c daeustrdl` prbeuht prbeuhce da `bhltdba d lae sb`e da k ds

_rdhc ds l fdxce plrn up n bvcr glridal` hbst, wjdhj ds l Hbmm-Ebui`ls fuahtdba bf wlic lae

prdhc daecx bf datcrgcedltcs, sb , " + $ 7 <. Fdrgs jlvc l fdxce hbst, sb tjcy

mrcln cvca wjca tbtl` sl`cs (suggce bvcr l`` glrncts) rclhj l `cvc` tjlt ecpcae kust ba

plrlgctcrs bf tchjab`biy lae tjc glrn up), dc. wjca

Ujc tcrg ds tjc ‚glrnct lhhcss— bf hbuatry d. Ssdai tjc prdhdai cqultdba da

tjds mrcln cvca cxprcssdba idvcs tjc wlic cqultdba (<=) bf tjc tcxt.

8/3/2019 Venables (2003)

<. Xcc Eurlatba lae _uil (=??8) lae ]bscatjl` lae Xtrlaic (=??8) fbr survcys bf tjcbry lae

cgpdrdhs rcspchtdvc`y. Ujcsc survcys lrc mbtj hbatldace da tjc `ltcst Jlaembbn bf Srmla lae

]cidbal` Chbabgdhs. Dt ds abtcwbrtjy tjlt tjds twcaty-bac hjlptcr vb`ugc ebcs abt hbatlda l

sdai`c hjlptcr ecvbtce tb ecvc`bpdai hbuatry dssucs.

=. Yc hbahcatrltc ba ‚gbecra schtbr— cgp`bygcat> leedai btjcr urmla lhtdvdtdcs glncs ab

qul`dtltdvc edffcrcahc.

8. Ujc survcy bf ]bscatjl` lae Xtrlaic (=??8) suiicsts tjlt tjc c`lstdhdty bf .prbeuhtdvdty wdtj

rcspcht tb cgp`bygcat ds da tjc rlaic ?.?5-?.<<.

5. Cqudvl`cat`y, tjc hdty bhhupdcs l twb-edgcasdbal` splhc lae `lae bhhupdce my clhj wbrncr

(dc, `bt sdzc) dahrclscs wdtj tjc squlrc bf edstlahc frbg tjc hcatrc.

3. Ujds cqud`dmrdug ds _lrctb cffdhdcat, sdahc tjcrc lrc ab glrnct fld`urcs da tjds mcahjglrn hlsc.

6. Dastcle bf scttdai up tjc @lirlaicla, tjc hbastrldat hbu`e jlvc mcca usce tb sumstdtutc but bac

bf tjc hjbdhc vlrdlm`cs. Jbwcvcr, tjc vl`uc bf tjc @lirlaic gu`tdp`dcr turas but tb mc bf datcrcst

da tjc acxt sum-schtdba.

9. Cqultdbas (8) lae (5) dgp`y tjc tlaicahy ql—(a) 7 t /=. : ds caebicabus l``bwdai mbtj L lae

M tb bhhur lt tjc slgc vl`uc bf a.

:. Ujc ̀ lric ecvc`bpcr hlsc ds frcqucat`y cgp`byce da tjc ̀ dtcrlturc, scc ci M`lhn lae Jcaecrsba

(<444), Cltba lae Chnstcda (<449), Jcaecrsba lae Ylai (=??8).

4. Ujds rcsu`t ds da hbatrlst tb tjlt da l augmcr bf plpcrs da tjc `dtcrlturc (fbr cxlgp`c, Lals

<44=, Jcaecrsba lae Mchncr =???). Ujcsc plpcrs lssugc tjlt da tjc sgl`` licats hlsc tjc wjb`c

bf hdty rcats lrc edvdece mctwcca wbrncr-fdrgs, lae catdt`cgcat tb tjcsc rcats ds fbrfcdt my

gbvdai tb l acw hdty. Ujc rclsba wjy tjcy lrc fbrfcdt ds abt l`wlys h`clr. Bac gchjladsg

wbu`e mc tjlt l hdty ibvcragcat hb``chts rcats lae rcedstrdmutcs tjcg ls l `ugp sug sumsdey tb

dajlmdtlats> tjds sccgs dgp`lusdm`c, plrtdhu`lr`y da tjc ecvc`bpdai hbuatry hbatcxt. Df tjds

lssugptdba ds glec tjca tjc sgl``-licat hlsc prbeuhcs rc`ltdvc`y `lric hdtdcs> hdty sdzc da tjds

hlsc ds ^$ - t /=qW/(.

<?. Edffcrcatdltdai cqultdba (<<), eU/e 0 0 ?.

<<. Ectld`s bf tjc sdgu`ltdbas lrc lvld`lm`c frbg tjc lutjbr ba rcqucst.

Caeabtcs

]cfcrcahcs

Lmec`-]ljgla, J.G. lae L. Lals (=??8), ‚Ujcbrdcs bf systcgs bf hdtdcs— da Jlaembbn bf

Srmla lae ]cidbal` Chbabgdhs, ces K.V. Jcaecrsba lae K-F Ujdssc, fbrtjhbgdai.

8/3/2019 Venables (2003)

Lmec`-]ljgla, J.G. lae _. Ylai (<443), ‚Ubwlre l icacrl` cqud`dmrdug tjcbry bf l hbrc-

pcrdpjcry systcg bf hdtdcs—, ]cidbal` Xhdcahc lae Srmla Chbabgdhs, =3, 3=4-356.

Lecs, L.F. lae C.@. I`lcscr (<443), ‚Urlec lae Hdrhuscs; Cxp`ldadai Srmla Idlats,—

\ulrtcr`y Kbural` bf Chbabgdhs, <<?, <43-==9.

Lals, L. (<44=) ‚Ba tjc mdrtj lae irbwtj bf hdtdcs> `ldsscz-fldrc lae p`laadai hbgplrce—,

]cidbal` Xhdcahc lae Srmla Chbabgdhs, ==, =58-=3:.

Mchncr, ]. lae K.V. Jcaecrsba, (=???) ‚Datrl Daeustry Xpchdl`dzltdba lae Srmla

Ecvc`bpgcat—da Ujc Chbabgdhs bf Hdtdcs, K-G Jurdbt lae K. Ujdssc (ces.), Hlgmrdeic

Sadvcrsdty _rcss.

Mcs`cy, U. lae ]. Muricss (=??=) ‚Hla `lmbur rciu`ltdba jdaecr chbabgdh pcrfbrglahc>

cvdecahc frbg Daedl—, HC_] ep ab 8=6?.

M`lhn, E. lae V. Jcaecrsba (<444) ‚L tjcbry bf urmla irbwtj—, Kbural` bf _b`dtdhl`

Chbabgy, <?9, =3=-=:5.

Hdnurc`, E, (=??=), ‚Yjy Gcxdhb—s rcidbal` hbavcricahc mrbnc ebwa—, prbhcssce Sadvcrsdty

bf Hl`dfbradl, Xla Edcib lae lt, jttp;//www.wdecr.uau.ceu/hbafcrcahc/hbafcrcahc-

=??=-3/hbafcrcahc=??=-3.jtg.

Ecguricr, X, K. Xlhjs, Y.Ybb, X. Mlb, I. Hjlaic lae L. Gc``daicr, ‚Icbirlpjy, Chbabgdh

_b`dhy lae rcidbal` ecvc`bpgcat da Hjdal— prbhcssce Sadvcrsdty bf Hl`dfbradl, Elvds

lae lt jttp;//www.wdecr.uau.ceu/hbafcrcahc/hbafcrcahc-=??=-=/hbafcrcahc=??=-

Eurlatba I. lae E. _uil, (=??8). ‚Gdhrb-fbuaeltdbas bf Srmla Lii`bgcrltdba Chbabgdcs—

da Jlaembbn bf Srmla lae ]cidbal` Chbabgdhs, ces K.V. Jcaecrsba lae K-F Ujdssc,

fbrtjhbgdai.

8/3/2019 Venables (2003)

Cltba, K. lae [. Chnstcda, (<449) ‚Hdtdcs lae irbwtj> tjcbry lae cvdecahc frbg Frlahc lae

Klpla—, ]cidbal` Xhdcahc lae Srmla Chbabgdhs, =9, 558-595.

Fukdtl, G, Nruigla, _, lae Vcalm`cs, L.K. (<444) Ujc Xpltdl` Chbabgy; Hdtdcs, ]cidbas, lae

Datcraltdbal` Urlec, GDU _rcss.

Fukdtl, G, lae Ujdssc, K. (=??<) Chbabgdhs bf lii`bgcrltdba, Hlgmrdeic Sadvcrsdty _rcss.

Jcaecrsba, K.V. (<495) ‚Ujc sdzcs lae typcs bf hdtdcs—, Lgcrdhla Chbabgdh ]cvdcw, 65, 65?-

Jcaecrsba, K.V. (=??8) ‚Ujc Srmladzltdba _rbhcss lae Chbabgdh Irbwtj; Ujc Xb-Yjlt

\ucstdba—, Kbural` bf Chbabgdh Irbwtj, :, 59-9<.

Jcaecrsba, K.V. lae ]. Mchncr, (=???) ‚_b`dtdhl` Chbabgy bf hdty sdzcs lae fbrgltdba—,

Kbural` bf Srmla Chbabgdhs, 5:, 538-5:5.

Jcaecrsba, K.V. lae J.I. Ylai (=??8) ‚Srmladzltdba lae hdty irbwtj—, prbhcssce, Mrbwa

Sadvcrsdty.

Jcaecrsba K.V., [. Xjl`dzd lae L.K. Vcalm`cs (=??<) ‚Icbirlpjy lae ecvc`bpgcat— Kbural`

bf Chbabgdh Icbirlpjy, <, :<-<?3.

Nruigla, _. (<44<) ‚Dahrclsdai ]cturas lae Chbabgdh Icbirlpjy—, Kbural` bf _b`dtdhl`

Chbabgy, 44(8), 5:8-44.

Nruigla, _.]. lae ]. @dvls C`dzbaeb (<446) ‚Urlec pb`dhy lae tjc tjdre wbr`e gctrbpb`ds—,

Kbural` bf Ecvc`bpgcat Chbabgdhs, 54, <89-3?.

Nruigla, _.]. lae Vcalm`cs, L.K. (<443) ‚I`bml`dsltdba lae tjc Dacqul`dty bf Altdbas—,

\ulrtcr`y Kbural` bf Chbabgdhs, <<?(5), :39-:?.

Bvcrgla, J I, ]ceedai, X, lae Vcalm`cs, L K (=??<) ‚Ujc Chbabgdh Icbirlpjy bf Urlec,

_rbeuhtdba, lae Dahbgc; L Xurvcy bf Cgpdrdhs—, HC_ Edshussdba _lpcr, 3?:,

fbrtjhbgdai da (ce) Jlrrdila, K, Jlaembbn bf Datcraltdbal` Urlec, Mlsd` M`lhnwc``.

8/3/2019 Venables (2003)

_uil, E. (<44:) ‚Srmladzltdba plttcrs> Curbpcla vcrsus `css ecvc`bpce hbuatrdcs—, Kbural` bf

]cidbal` Xhdcahc, 8:, =8<-=3=.

]bscatjl`, X.X. lae Y.H. Xtrlaic (=??8). ‚Cvdecahc ba tjc Alturc lae Xburhcs bf

Lii`bgcrltdba Chbabgdhs— da Jlaembbn bf Srmla lae ]cidbal` Chbabgdhs, ces K.V.

Jcaecrsba lae K-F Ujdssc, fbrtjhbgdai.

8/3/2019 Venables (2003)

Fdiurc <l; Hdty irbwtj wdtj fdrst levlatlic

Hdty cgp`bygcat,ad a<

Fdiurc <m; Cqud`dmrdug wdtj <st lae =ae alturc

Hdty cgp`bygcat,ad

8/3/2019 Venables (2003)

q^l(a) + al—(a)W

at + T— + :

T— + :

Butput

at/= + T— + :

Fdiurc =l; Bptdgug lae `lric ecvc`bpcrs

at + w + Mc

w + M c

Butput

Fdiurc =m; Xgl`` licats

8/3/2019 Venables (2003)

at + w + Mh

Butput

w + M h

Fdiurc =h; _rbeuhcr hbl`dtdbas

M (ad( z)) 7 M (0 z)

M (ad( z)) 7 M (0 U )

Udgc, z

Fdiurc 8; _rbfdt f`bws

8/3/2019 Venables (2003)

Fdiurc 5l; @bhltdba bf daeustry uaecr lutlrny

Glauflhturdai rcidbas

@cvc` bf daeustrdl`dzltdba

Datcral` `bhltdbas

Hcatrc

Fdiurc 5m; @bhltdba bf daeustry wdtj twb pbrts

Datcral` `bhltdbas

Hcatrc

8/3/2019 Venables (2003)

Fdiurc 5h; @bhltdba bf daeustry wdtj bac pbrt

Datcral` `bhltdbas

Hcatrc

8/3/2019 Venables (2003)

HCAU]C FB] CHBABGDH _C]FB]GLAHC

]chcat Edshussdba _lpcrs

34= Xy`vdc Hjlr`bt

Id``cs Eurlatba

Hbgguadhltdba Cxtcral`dtdcs da Hdtdcs

34< _lu` Yd``glaL`cx Mrysba

]lflc` Ibgcz

Yjy Eb Vbdhc ]cidgcs Edffcr2

34? Glrhb Glalhbrel Hjd`ehlrc lae tjc @lmbur Xupp`y bf Btjcr Jbuscjb`eGcgmcrs; Cvdecahc frbg <4=?s Lgcrdhl

3:4 L`cx Mrysba]lflc` Ibgcz

Yjy Jlvc Ybrncrs Xtbppce Kbdadai Sadbas2

3:: Jcary I. Bvcrgla

@. L`la Ydatcrs

Urlec Xjbhns lae Daeustrdl` @bhltdba; tjc Dgplht bf

CCH Lhhcssdba ba tjc SN

3:9 _dcrrc-_jd`dppc HbgmcsJcary I. Bvcrgla

Ujc Xpltdl` Edstrdmutdba bf Chbabgdh Lhtdvdtdcs da tjcCurbpcla Sadba

3:6 Jcary I. Bvcrgla Hla Yc @clra Laytjdai frbg Chbabgdh Icbirlpjy_rbpcr2

3:3 L. M. Mcralre

K. Mrlefbre Kcasca_. N. Xhjbtt

Fl``dai Urlec Hbsts, Jctcrbicacbus Fdrgs lae

Daeustry Eyalgdhs

3:5 L. M. Mcralre

K. Mrlefbre Kcasca_. N. Xhjbtt

Xurvdvl` bf tjc Mcst Fdt; Cxpbsurc tb @bw-Ylic

Hbuatrdcs lae tjc (Sacvca) Irbwtj bf S.X.Glauflhturdai _`lats

3:8 X. YbbeX. Gbbrc ]cvdcwdai tjc Xtltutbry Sadba ]chbiadtdba (C]L<444)

3:= U. Ndrhjgldcr Hbrpbrltc ]cstruhturdai lae Fdrg _crfbrglahc bfMrdtdsj lae Icrgla Aba-Fdalahdl` Fdrgs

3:< H. Ebuijcrty Yjy Ds tjc ]ltc bf ]ctura tb Xhjbb`dai Jdijcr fbrYbgca tjla fbr Gca2

3:? X. Muricss

E. Glwsba

Liirciltc Irbwtj lae tjc Cffdhdcahy bf @lmbur

]cl``bhltdba

8/3/2019 Venables (2003)

394 X. Adhnc`` _bvcrty lae Ybrn`cssacss da Mrdtlda

39: E. Glrseca ]cacibtdltdai _crfbrglahc; tjc ]b`c bf _crfbrglahc

_ly da ]cacibtdltdai tjc Cffbrt Mlrilda

399 X. Adhnc`` L _dhturc bf Curbpcla Sacgp`bygcat; Xuhhcss lae

Fld`urc

396 L. ec Hbu`baG. _drlhjl

Xc`f-Xc`chtdba lae tjc _crfbrglahc bf ]cturaGdirlats; tjc Xburhc Hbuatry _crspchtdvc

393 J. Xtccegla

N. YliacrK. Fbrcgla

Ujc Dgplht ba Fdrgs bf DHU Xnd``-Xupp`y Xtrltcidcs;

La Lai`b-Icrgla Hbgplrdsba

395 X. Idmmbas Ujc Hbsts bf Srmla _rbpcrty Hrdgc

398 ]. Irdffdtj

X. ]ceedaiJ. Xdgpsba

_rbeuhtdvdty Hbavcricahc lae Fbrcdia Bwacrsjdp lt

tjc Cstlm`dsjgcat @cvc`

39= X. ]ceedai_. N. Xhjbtt

Edstlahc, Xnd`` Eccpcadai lae Ecvc`bpgcat; Yd``_crdpjcrl` Hbuatrdcs Cvcr Ict ]dhj2

39< M. _ctrbaib`b

H. L. _dsslrdecs

Xhl`c Cffchts da Glrncts wdtj Xclrhj

39? G. Hb`csM. _ctrbaib`b

L Ucst Mctwcca Sacgp`bygcat Ujcbrdcs SsdaiGlthjdai Eltl

364 L. Mrysba

@. Hlppc``lrdH. @uhdfbrl

Ebcs Sadba Gcgmcrsjdp ]cl``y ]ceuhc Kbm

Xltdsflhtdba2

36: L. Mrysba

]. Ibgcz

Xcigcatltdba, Xwdthjdai Hbsts lae tjc Ecglae fbr

Sadbadzltdba da Mrdtlda

Ub brecr l edshussdba plpcr, p`clsc hbatlht tjc _um`dhltdbas Sadt

venables (2003)

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