Kvantitativ metode - Hjemmeeksamen 1 (2014)

7/21/2019 Kvantitativ metode - Hjemmeeksamen 1 (2014)

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=4.=:.4:=0 HLP 0:< -

Kvmbtetmtevl hlti`lOnlhhllksmhlb = Oÿstlb 4:=0

Dnÿrbl Anlccoleh ßlb

Icl Forestemb Kvlrbdlrg



Onlhhllksmhlb = ‖ Oÿstlb 4:=0 HLP 0:< Kvmbtetmtevl hlti`lr :4.:4.4:=<

=

Airir`

Airhìclt hl` `lbbl ippgmvlb lr ì aì lb `yplrl airstìlcsl mv plbsuhlt e kvmbtetmtevl

hlti`lr sih ihomb`clr rlgrlsnibsmbmcysl ig hi`lrmtirmbmcysl. Mbmcyslbl lr utaÿrt e VZVV

pì lt `mtmsltt arm lb ub`lrsÿklcsl tmtt ih iutsiurfebg ois birskl dusslcskmplr.

Ippgmvlb lr skrlvlt mv trl hmstlrgrm`sstu`lbtlr vl` Oÿgskiclb e Dusklru` ig Qlstaic`. Zì

lb gruppl pì trl dcer `lt lb `lc pì èskusnib rub`t tickbebg ig cÿsbebg mv ippgmvl. @lt omr

várt lb `lc se`lspir ig dceb`vlelr ub`lrvles e ippgmvlcÿsbebglb, scek `lt gnlrbl lr e lb

cárebgsprislss. @lt ì kidcl tlirelb e kvmbtetmtev hlti`l ipp hit lt dlstlht prmktesk

lkslhplc, omr gett lb gi` cárebgslaalkt.

Qe vec rlttl lb tmkk tec Kìrl Vmb`vek air vlecl`bebg ig Mbbl Vÿrldÿ air ippareskbebg e

hlti`lkubbskmplbl.




4

Ebboic`sairtlgblcslIppgmvl = ................................................................................................................................................ 0

Zridclhsteccebg> .................................................................................................................................... 0

Oypitlslr> ........................................................................................................................................... 0

O=> Peccet tec clvlrmb`ÿrlb omr lb pisetev laalkt pì ytlcsl. (PECCEP) .......................................... 0

O4> Kihpltmbslbárolt omr lb pisetev laalkt pì ytlcsl. (FZF) ............................................... 0

O6> Dl`reatlbs trmbsmksnibssplseaekkl ebvlstlrebglr omr lb pisetev laalkt pì ytlcsl (DPVE) ... 0

Tmsnibmcl> ............................................................................................................................................ 0

O= ............................................................................................................................................ 0

O4 ............................................................................................................................................ 0

O6 ............................................................................................................................................ <

Hi`lcc> ................................................................................................................................................ <

Ippgmvl 4 ................................................................................................................................................ 1

Tlgrlsnibsairutsltbebg 4 .................................................................................................................... 1

Tlgrlsnibsairutsltbebg 6 .................................................................................................................... 1

Tlgrlsnibsmbmcysl ............................................................................................................................... 7

O=> Peccet tec clvlrmb`ÿrlb omr lb pisetev laalkt pì clvlrmb`ÿrlbs ytlcsl (PECCEP). - Vtÿttlt. ... ?

O4> Kihpltmbslbárolt omr lb pisetev laalkt pì clvlrmb`ÿrlbs ytlcsl (FZF) - Vtÿttlt. ........ ?

O6> Dl`reatlbs trmbsmksnibsplseaekkl ebvlstlrebglr omr lb pisetev laalkt pì clvlrmb`ÿrlbs

ytlcsl (DPVE) - Airkmstlt. .................................................................................................................. ?

@eskutlr rlsuctmt ig cl`lcslshlssegl ehpcekmsniblr ........................................................................... 5

Ippgmvl 6 .............................................................................................................................................. =:

Oypitlslr .......................................................................................................................................... =:

O0 .......................................................................................................................................... =:

O< .......................................................................................................................................... =:

Tmsnibmcl ........................................................................................................................................... =:

O0 .......................................................................................................................................... =: O< .......................................................................................................................................... =:

Plstebg mv hi`lcclb .......................................................................................................................... =:

Oihicigezlrtlst hl` Peccet sih hi`lrmtir ...................................................................................... ==

Oihicigezlrtlst hl` FZF sih hi`lrmtir....................................................................................... =4

Cl`lcslshlssegl ehpcekmsniblr ......................................................................................................... =4

Ippgmvl 0 .............................................................................................................................................. =0

Ippgmvl < .............................................................................................................................................. =?

@rÿat rlsuctmtlbl ig ehpcekmsniblr air prmkses.................................................................................. =5




6

Ippgmvl 1 .............................................................................................................................................. 4:

Zmrtelcc kirrlcmsnib hl` kibtriccvmremdclr - ippgmvl 4 .................................................................... 4:

Tlgrlsnibsmbmcysl hl` kibtriccvmremdclr ‖ ippgmvl 4 .................................................................... 4=

Zmrtelcc kirrlcmsnib hl` kibtriccvmremdclr - ippgmvl 0 .................................................................... 44

Tlgrlsnibsmbmcysl hl` kibtriccvmremdclr ‖ ippgmvl 0 .................................................................... 44

Cettlrmturcestl ......................................................................................................................................... 40

Kec`lr> ................................................................................................................................................ 40

Mb`rl kec`lr> ...................................................................................................................................... 40

Ebtlrblttse`lr> ................................................................................................................................... 40

Ql`clgg .................................................................................................................................................. 4<

Vybtmks............................................................................................................................................... 45

/* Ippgmvl 4 */ ............................................................................................................................. 45/* Ippgmvl 6 */ ............................................................................................................................. 6:

/* Ippgmvl 0 */ ............................................................................................................................. 64

/* Ippgmvl < */ ............................................................................................................................. 66

/* Ippgmvl 1 */ ............................................................................................................................. 66




0

Ippgmvl =

Zridclhsteccebg>

Qe skmc ub`lrsÿkl laalktlbl mv iutsiurfebg ois birskl dusslcskmplr air ì sl pì ovir`mb `lt

pìverklr dusslcskmplbls ytlcsl air ì ge ÿkt grubbcmg air ì dlscuttl e ovecklb grm` dl`reatlb

skmc iutsiurfl.

Vpÿrshìclbl sih ihomb`clr ytlcsl e spÿrrlsknlhmlt gìr pì ih clvlrmb`ÿrlbs clvlrmbslr ig

utaÿrlcsl mv mktevetltlr lr byttegl air dl`reatlb. Qe`lrl tlbklr ve mt dl`reatlbs ytlcsl ÿklr hl`

byttlvlrèlb pì clvlrmb`ÿrlbs clvlrmbslr ig utaÿrlcsl mv mktevetltlr.

Zridclhsteccebg airhuclrt sih spÿrshìc>

Aÿrlr teccet tec clvlrmb`ÿrlb, grm`lb mv kihpltmbslbárolt ig trmbsmksnibssplseaekkl

ebvlstlrebglr tec ÿkt ytlcsl9

Oypitlslr>

O=> Peccet tec clvlrmb`ÿrlb omr lb pisetev laalkt pì ytlcsl. (PECCEP)

O4> Kihpltmbslbárolt omr lb pisetev laalkt pì ytlcsl. (FZF)

O6> Dl`reatlbs trmbsmksnibssplseaekkl ebvlstlrebglr omr lb pisetev laalkt pì ytlcsl

(DPVE)

Tmsnibmcl>

O=

Ni heb`rl teccet tec clvlrmb`ÿrlb, ni hlr te` ig rlssurslr drukls pì ì kibtricclrl clvlrmb`ÿrlbair ì sl tec mt ippgmvlr dcer utaÿrt hl` tecarl`sstecclb`l kvmcetlt. @lttl vec egnlb splecl blgmtevt

pì dl`reatlbs tecarl`solt hl` clvlrmb`ÿrlbs ytlcsl. @lrehit ih `lt lr oÿy teccet tec

clvlrmb`ÿrlb sì aÿrlr `lt tec mt clvlrmb`ÿrlb dcer e stÿrrl grm` slcvgìlb`l ig ger `lh rih tec ì

tm lgbl vmcg. @lttl trir ve vec várl hl` pì ì ÿkl laalktlb mv iutsiurfebg.

O4

Lb dl`reat kmb air lkslhplc ipp`mgl mt `lclr mv kihpltmbslb sih trlbgs air ì utaÿrl lb

tnlblstl sih clvlrls arm lb slcglr, mcclrl`l lksestlrlr ebblbair dl`reatlbs irgmbesmsnib.

@lrhl` kmb dl`reatlb prÿvl ì teclgbl slg kihpltmbslb ig alrègoltlbl sih gnlbstìr air ì

kubbl utaÿrl tnlblstlb ebblbair dl`reatlbs grlbslr (Gucdrmb`slb lt mc., 4::5).

Ni hlr druk mv kubbskmp dl`reatlb mcclrl`l omr mv lb mktevetlt clvlrmb`ÿrlb utaÿrlr, ni stÿrrl

smbbsybcegolt lr `lt air mt `lt airhe`cls e dl`rl grm` ovm sih airvlbtls mv mktevetltlb

clvlrmb`ÿrlb skmc utaÿrl. Zì `lbbl hìtlb vec clvlrmb`ÿrlb om hucegolt tec ì tecpmssl slg

dl`reatlb sih egnlb vec ge ÿkt laalkt mv iutsiurfebg.




<

O6

Hl` knÿplrs trmbsmksnibssplseaekkl ebvlstlrebglr sbmkklr ve olr ih ebvlstlrebglr e lglb

dl`reat air ì tecpmssl slg clvlrmb`ÿrlb. Qe trir mt ni hlr dl`reatlb tecpmsslr slg clvlrmb`ÿrlb,

ni dl`rl smhmrdle` skmpls sih egnlb vec olvl kvmcetltlb pì mktevetltlb clvlrmb`ÿrlb utaÿrlr.

Ni hlr dl`reatlb tecpmsslr slg clvlrmb`ÿrlb, ni hlr laalktevt vec mktevetltlb utaÿrls mv

clvlrmb`ÿrlb sih egnlb pìverklr laalktlb mv iutsiurfebg.

Lt lkslhplc pì `lt, kmb várl vl`cekloic` mv duss, ovir `lt dur`l aÿcgls lb vl`cekloic`spcmb

air e dlst huceg grm` tm vmrl pì dusslb smhteèg sih mt dusslb lr tecgnlbglceg bìr `lt lr

dloiv. Ni hlr dl`reatlb tecpmsslr slg scek mt vl`cekloic`lt mv duss aÿcglr vl`cekloic`spcmblb,

ni hlr iptehmct vl`cekloic` vec dce utaÿrt pì dusslb. @lttl vec ge ÿkt laalkt mv iutsiurfebg.

Hi`lcc>




1

Ippgmvl 4Zì ippgmvl 4 skuccl ve tlstl hi`lcclb arm ippgmvl = vl` druk mv rlgrlsnibsmbmcysl, smht ì

èskutlrl rlsuctmtlbl mv tlstlb ig ehpcekmsniblr air cl`lcsl. Aÿrst eb`lkslrtl ve mccl vmremdclbl

arm hi`lcclb smhhlb hl` 0 hìc air ovlr mv vmremdclbl. @lttl gnir`l ve gnlbbih "fihputl-

trmbsairh", scek mt ve aekk = vmremdlc air ovlr gruppl.

Bìr hmb skmc knÿrl lb rlgrlsnibsmbmcysl ig/lcclr mb`rl stmtesteskl mbmcyslr lr `lt vekteg mt

tmcchmtlremclt ippaycclr vessl krmv. @essl krmvlbl kmccls air rlgrlsnibsairutsltbebglr, ig dur`l

snlkkls aÿr mbmcyslr gnlbbihaÿrls scek mt airsklrlb kmb gnÿrl bÿ`vlbègl tectmk air ì ippbì

tecarl`sstecclb`l mbmcyslr ig hi`lcclr (Dlrry =556>=4). Qe omr sltt pì airutsltbebg buhhlr 4, 6

ig < sih stìr cestlt ipp e diklb "\b`lrstmbèbg Tlgrlsseib Mssuhpteibs" (Dlrry =556>=4).

Dcmbt èssl airutsltbebglbl skmc tmcchmtlremclt dcmbt mbblt tlstls air ì snlkkl ih `lt omr gi`

vmrembs, ig ih `lt lr birhmcair`lct. E tecclgg snlkklt ve igsì ih `lt ambtls plralkt

huctekiccebmretlt. Mct `lttl tlstlt ve gnlbbih ucekl mbmcyslr e VZVV. Ve`lb ve aekk vetl gnlbbih

lpist mt hìcvmce`lrebg gnlbbih amktirmbmcyslr ekkl lr plbsuh, omr ve vmcgt ì ekkl

gnlbbihaÿrl èssl (Vmb`vek, hmec).

Tlgrlsnibsairutsltbebg 4

Airutsltbebg buhhlr 4 gìr ut mt mccl umvolbgegl vmremdclr omr vmrembs ivlr :, mctsì mt `l

umvolbgegl vmremdclbl omr vmrelrtl vlrèlr (Dlrry =556> =4). @lttl snlkklt ve vl` ì gì pì

"mbmcyzl-`lsfreptevl stmtestefs-`lsfreptevls", ig sì krysslt ve mv air kurtises (sknlvolt) ig

sklwblss (spessolt). Tlgrlsnibsairutsltbebglb slr kub pì vmrembslb, hlb ve vmcgtl igsì ì sl

pì sknlvolt ig spessolt air ì snlkkl mt tmcchmtlremcl vmr birhmcair`lct.

Vih ve slr mv tmdlcclb

ivlr, sì omr mccl `l trlumvolbgegl vmremdclbl

lb vmrembs pì gi`t ivlr

:. FZF ig DPVE omr

blstlb cek vmrembs, hlbs

teccet omr cett cmvlrl. @lt

dltyr mt mccl `l trl

umvolbgegl vmremdclbl ippaycclr rlgrlsnibsairutsltbebg buhhlr 4 hl` gi` hmrgeb `m ebglb

omr sìkmct "bibzlri vmrembfl", ig lr `m lgblt air ve`lrl mbmcyslr. E smhhl tmdlcc slr ve mt

sknlvoltlb lr ub`lr 4 ig spessoltlb lr ub`lr 0 ois mccl `l trl vmremdclbl ve tlstlt, bil sih

tecselr mt `mtmhmtlremcl lr birhmcair`lct. Tlglclb selr mt bìr sknlvolt ig spessolt lr bár lb

vlrè pì : sì lr `mtmhmtlremcl gi`t birhmcair`lct (Vÿrldÿ 4:=4> 45). Mccl spÿrshìclbl ve omr

tlstlt olr, lr mccl spÿrshìc sih lr e airdeb`lcsl hl` mt dl`reatlb druklr lkstlrbl mktÿrlr. E

spÿrrlsknlhmlt stìr `lt mt mccl sih svmrtl nm pì ih dusslcskmplt druklr lkstlrbl mktÿrlr skmc

svmrl pì rlstlb mv spÿrrlsknlhmlt. E tmdlcclb vmr `lt 607 sih om``l svmrt, bil sih dltyr mt

?? ekkl om``l svmrt pì èssl spÿrshìclbl, ig `lrair ekkl druklr lkstlrbl clvlrmb`ÿrlr tec ì

utaÿrl mktevetltlr.

Tlgrlsnibsairutsltbebg 6

Airutsltbebg buhhlr 6 gìr pì mt `lt ekkl skmc várl plralkt huctekicceblmretlt, mctsì mt `lt

ekkl lr bil plralkt ceblárt airoic` hlccih ti lcclr aclrl mv `l umvolbgegl vmremdclbl (Dlrry=556> =4). Oves `lt aebbls plralkt huctekiccebmretlt sì kmb ve ekkl aebbl ut mkkurmt ovir stir




7

laalkt lb umvolbgeg vmremdlc omr pì `lb mvolbgegl vmremdlclb `m `lb dcer pìverklt mv lb

mbblb umvolbgeg vmremdlc (Dlrry =556> 40). Armvár mv plralkt huctekiccebmretlt snlkklr ve vl` ì

tlstl mccl `l umvolbgegl vmremdclbl hit ovlrmb`rl e lb devmremt kirrlcmsnibsmbmcysl. @lbbl

aebblr hmb e VZVV vl` ì trykkl pì "Mbmcyzl-Firrlcmtl-Devmremtl", ig sì puttlr hmb ebb mccl

vmremdclbl hmb vec tlstl hit ovlrmb`rl. E `lbbl mbmcyslb vmr `lt `m teccet, fpf ig dtse sih lr

`l trl umvolbgegl vmremdclbl e hi`lcclb vìr.

Oves kirrlcmsniblbl lr ivlr :.?, sì kmb

`lt várl plralkt huctekiccebmretlt ig

`mtmhmtlremclt vec ekkl ippayccl

rlgrlsnibsairutsltbebglb. Ql` shì

utvmcg (34::) ippstìr pridclhlt

mcclrl`l vl` kirrlcmsniblr ivlr :.1

(Vmb`vek 4:=0>?=). Vih ve slr e tmdlcclb

ivlbair lr kirrlcmsniblbl gi`t ub`lr :.?

ig hl` lt sì stirt utvmcg sih ve omr e`lbbl mbmcyslb, sì ty`lr ekkl `lttl pì mt

ve omr huctekicceblmretltspridclh. @lt

dltyr mt mccl trl vmremdclbl ippaycclr

rlgrlsnibsairutsltbebg buhhlr trl, ig

ve kmb drukl vmremdclbl tec ve`lrl

mbmcyslr.

Om``l kirrlcmsniblb `lrehit om``l várt ivlr :.?, sì veccl ve tlstlt vmremdclbl yttlrceglrl vl`

ì sl pì ticlrmbfl ig QEA (Qmrembfl Ebacmteib Amftir). @lttl aìr ve armh vl` ì knÿrl lb

rlgrlsnibsmbmcysl ovir ve krysslr mv air mt ve skmc om hl` èssl ti lkstrm vlrèlbl.

Qe slr mv tmdlcclb mt ticlrmbfl lr gi`t ivlr : ig mt QEA ekkl

lr ivlr =: air mccl trl vmremdclbl. Mccl vlrèlbl pì QEA lr

gmbskl bárl =.:, ig om``l `lt várt huctekiccebmretlt veccl ve

mc`re aìtt QEA sì bárl =.:, bil sih dlkrlatlr mt ve ekkl omr

huctekiccebmretlt hlccih èssl vmremdclbl. Oves QEA `lrehit

om``l várt ivlr =:, sì dltyr `lt mt 5:% mv vmrembslb mv

`lb umvolbgegl vmremdlclb veccl várt airkcmrt mv mb`rl

umvolbgegl vmremdclr (Vmb`vek 4:=0> ?6).

Tlgrlsnibsmbmcysl

Lttlr mt ve omr snlkklt mt tmcchmtlremclt ippaycclr krmvlbl tec rlgrlsnibsairutsltbebg 4 ig 6, sì

knÿrtl ve lb rlgrlsnibsmbmcysl air ì tlstl `l ucekl oypitlslbl (Pmdmfobefk & Ae`lcc 4::7>==7).

Ve`lb ve omr aclrl umvolbgegl vmremdclr, sì druklr ve lb huctevmremt rlgrlsnibsmbmcysl (Vÿrldÿ

4:=4>07). E tlstlb slr ve pì smhhlbolbglb hlccih `l umvolbgegl ig `lb mvolbgegl

vmremdlclb, ig ih slcvl hi`lcclb lr segbeaekmbt. Air ì knÿrl rlgrlsnibsmbmcyslb gekk ve pì

–Mbmcyzl ↔ Tlgrlsseib ↔ Ceblmr", ig sì smtt ve `lb mvolbgegl vmremdlclb ytlcsl pì

–`lplb`lbt‘, ig `l umvolbgegl vmremdclbl DPVE, FZF ig PECCEP e –eb`lplb`lbt‘ dikslb.




?

Vih ve slr mv tmdlcclb tec vlbstrl sì lr T Vqumrl pì :,=<4. @lt

veslr tec airkcmrebgskrmatlb, ig dltyr mt DPVE, FZF ig PECCEP

airkcmrlr =<,4% mv idslrvlrt lb`rebg pì ytlcslb. @lttl rlgbls

sih lb svmk airkcmrebgskrmat se`lb T4 lr ub`lr :,4 (Nmfidslb

4:::> 666).

Ql` ì sl pì MBIQM tmdlcclb sih tmr air slg

airskbebgshi`lcclb sih lb olcolt, sì slr ve mt segbeaekmbslb

lr pì :,:::, mctsì lr `lb segbeaekmbt pì lt <% bevì sih dltyr

mt `lt ekkl lr bil smbbsybcegolt air mt aubblbl sih lr gnirt

lr tecalcègl (Vÿrldÿ 4:=4> 07).

@lb bl`lrstl tmdlcclb e rlgrlsnibsmbmcyslb lr lb

kilaaeselbt tmdlcc. Ql` ì sl pì `lbbl tmdlcclb,

kmb ve sl pì airkcmrebgskrmatlb ovlr mv `l

umvolbgegl vmremdclbl omr tec hi`lcclb (Vÿrldÿ4:=4> 0?). Lb rlgrlsnibsmbmcysl lr sih skrlvlt

te`ceglrl, air ì tlstl oypitlslbl, ig ve kmb `m ut

earm kilaaeselbttmdlcclb ivlbair sl oveckl mv

oypitlslbl sih kmb dÿr airkmstls lcclr ekkl.

O=> Peccet tec clvlrmb`ÿrlb omr lb pisetev laalkt pì clvlrmb`ÿrlbs ytlcsl (PECCEP). -

Vtÿttlt.

E Dltm kicibblb slr ve mt teccet omr lb vlrè pì .61:, sih dltyr mt `lb kirrlclrlr pisetevt, mctsì mt

lb lb`rebg e teccet vec aÿrl tec lb ÿkbebg e ytlcsl. Vlr ve pì Veg. kicibblb, slr ve mt segbeaekmbslb

air teccet lr pì .:::, sih lr olct segbeaekmbt ig ve kmb `lrair sticl pì mt aubblt lr gycèg. Qe kmbpì dmkgrubb mv `lttl dloic`l oypitlslb `m `lb stlhhlr ivlrlbs hl` aubblt e tmdlcclb.

O4> Kihpltmbslbárolt omr lb pisetev laalkt pì clvlrmb`ÿrlbs ytlcsl (FZF) - Vtÿttlt.

Omr lb vlrè pì .:7=, bil sih igsì veslr tec lb pisetev rltbebg e airoic` tec ytlcsl, ig stlhhlr

ivlrlbs hl` oypitlslbs rltbebg. Veg. kicibblb veslr lt segbeaekmbsbevì pì .:61, sih lr ub`lr

.:< sì `lt dltyr mt aubblbl lr segbeaekmbt pì lt <% bevì. @lttl dltyr mt ve igsì dloic`lr `lbbl

oypitlslb.

O6> Dl`reatlbs trmbsmksnibsplseaekkl ebvlstlrebglr omr lb pisetev laalkt pì

clvlrmb`ÿrlbs ytlcsl (DPVE) - Airkmstlt.

Dltm vlrèlb lr pì -.:75 sih lr lb blgmtev vlrè sih dltyr mt lb ÿkbebg e dtse, vec om lb

blgmtev ebbverkbebg pì ytlcslb. @lttl hitselr oypitlslb sih pìstìr lb pisetev smhhlbolbg

hlccih dtse ig ytlcsl. Dtse omr lb segbeaekmbsvlrè pì .:=4 sih lr tecarl`sstecclb`l, hlb se`lb

rltbebglb lr alec sì hì ve airkmstl oypitlslb. \t earm aubblbl e rlgrlsnibsmbmcyslb sì kmb ve `m

kibkcu`lrl hl` mt ve ambt stÿttl air oypitlsl = ig 4, hlbs ve hìttl airkmstl oypitlsl 6 `m

stegbebgsairoic`lt vmr alec. Qe slr igsì mt teccet omr `lt stÿrstl stegbebgstmcclt sih dltyr mt `lt

pìverklr ytlcsl hlst.




5

@eskutlr rlsuctmt ig cl`lcslshlssegl ehpcekmsniblr

Pmcchmtlremclt ve omr aìtt lr `lc mv lb stir ub`lrsÿklcsl sih gnlbbihaÿrt mv birskl

dusslcskmplr air ì airstì laalktlr mv iutsiurfebg. Qe omr tlstlt tmcchmtlremclt e airoic` tec

rlgrlsnibsairutsltbebg 4 ig 6, ig ve ambt ut mt dlggl airutsltbebglb dcl tecarl`sstect sì ve

kubbl drukl tmcchmtlremclt ve`lrl. Qe omr igsì gnlbbihaÿrt hìcvmce`lrebg air ì snlkkl ovlrt

dlgrlp sett hìc gnlbbih amktirmbmcyslr air ì sl ih bilb etlh dur`l várt anlrblt airè `l

ekkl hìclr dlgrlplt gi`t bik. Qe ambt `m ut mt `lt vmr etlh pì mccl `l trl dlgrlplbl sih ekkl

tecarl`sstectl krmvlbl e amktirmbmcyslbl, ig sih ivlrcmpplt ovlrmb`rl. Zì dmkgrubb mv `lttl

dur`l `l `lrair ekkl várt drukt ve`lrl e ub`lrsÿklcslb, hlb pì hmec arm cárlr aekk ve dlsknl`

ih mt hìcvmce`lrebg ekkl vmr plbsuh sì `lrair omr ekkl ve lb`rlt bil pì tmcchmtlremclt air

ve`lrl mbmcyslr, ig ve airutslttlr mt tmcchmtlremclt lr gi`t bik air ve`lrl druk. Zì grubb mv

aubblbl e hìcvmce`lrebglb, cm ve hl` `lttl sih vl`clgg.

Qe skmc bì èskutlrl rlsuctmtlbl ig `l cl`lcslshlssegl ehpcekmsniblr, mctsì oveckl

kibslkvlbslr `l rlsuctmtlbl ig aubblbl sih lr aubblt omr ì se air dl`reatlbl. Oves ve stmrtlr

hl` ì sl pì rlsuctmtlbl arm rlgrlsnibsmbmcysl igsì kmct hi`lcctlstlb, sì ambt ve ut mt DPVE,FZF ig PECCEP kub airkcmrlr =<,4% mv `lb airkcmrtl vmrembslb e ytlcsl. @lt dltyr mt fm ?0,?% mv

lb`rebg e ytlcsl lr airkcmrt mv mb`rl vmremdclr. Pec scutt e tlstlb sì ve mt ve aekk stÿttl air

oypitlsl = ig 4, hlbs ve hìttl airkmstl oypitlsl 6 airè `lb om``l lt blgmtevt stegbebgstmcc

sih hitsm pìstmb`lb ih mt DPVE skuccl om lb pisetev ebbverkbebg pì ytlcsl.

E airoic` tec cl`lcslshlssegl ehpcekmsniblr sì sybtls ve `lttl aubblt aÿrst vmr vlcèg

ivlrrmsklb`l airè hmb iatl tlbklr mt `lt ì tecpmssl slg clvlrmb`ÿrlb e airh mv ebvlstlrebglr

rlgbls sih pisetevt, hlb lttlr cett èskusnib kih ve arlh tec mt `lt kmbsknl ekkl vmr sì

ivlrrmsklb`l mcceklvlc. @lt kmb ni air lkslhplc tlbkls mt lb dl`reat omr tecpmsslt slg hyl tec

åb clvlrmb`ÿr, ig `m vec dcmbt mbblt clvlrmb`ÿrlb lbklct kubbl slttl ipp preslb airè `l vltmt dl`reatlb kihhlr tec ì drukl `lh blstlb umbsltt. Dl`reatlb lr pì lb hìtl cett dub`lt tec

clvlrmb`ÿrlb. @lt kmb dce kistdmrt, ig vec smbbsybcegves om lb blgmtev ebbverkbebg pì ytlcsl

ivlr te`. Plbklr ve `m hitsmtt, sì kmb `lt ì om cmv tecpmsbebg ebbverkl pisetevt pì ytlcsl airè

dl`reatlb `m ekkl lr splselct tecpmsslt tec kub åb clvlrmb`ÿr, ig omr `m gi`l hucegoltlr air ì

drukl mbdu`. Mbdu` vec iatl aÿrl tec lb cmvlrl pres, sih egnlb `m vec om lb pisetevt ebbverkbebg

pì ytlcslb e airh mv rlùslrtl kistbm`lr dcmbt mbblt. Vì ut earm tmcclbl ve aekk e

rlgrlsnibsmbmcyslb, sì vec `lt bik cÿbbl slg ì ekkl tecpmssl slg air hyl tec kub åb clvlrmb`ÿr

`m `lttl air lkslhplc kmb aÿrl tec ÿktl kistbm`lr, ig lb `ìrceglrl laalkt mv iutsiurfebglb.

Qe sì igsì mt teccet vmr `lb vmremdlclb mv `l trl hl` stÿrst ebbverkbebg pì ytlcsl. @lt ì om oÿyteccet tec clvlrmb`ÿrlb vec pìverkl laalktlb mv iutsiurfebglb pì lb pisetev hìtl. Ih hmb ekkl

omr bil teccet tec lcclr sticlr pì mt clvlrmb`ÿrlb gnÿr sih `l skmc ig tmr `l rektegl

dlscutbebglbl sì vec hmb ekkl ippbì lb gi` laalkt pì iutsiurfebglb mv mktevetltlb. Hmb dÿr

`m kmbsknl aebbl lb mbblb clvlrmb`ÿr sih hmb sticlr pì mt gnÿr `l rektegl tebglbl, utlb ì

várl dlkyhrlt air mt tebg ekkl dcer gnirt sih `l skmc. @lt vec aÿrl tec lb dl`rl laalkt ig lb

stÿrrl byttlvlrè mv iutsiurfebglb.

Kihpltmbslbárolt omr lb svmk pisetevt ebbverkbebg pì ytlcsl, sih dltyr mt `lt vec cÿbbl slg ì

om kihpltmbsl ig alrègoltlr sih lr e bároltlb mv `lt clvlrmb`ÿrlb tecdyr. Vì `lt ì om

oÿylrl grm` mv kihpltmbslbárolt vec air lkslhplc aÿrl tec dl`rl kihhubekmsnib ig

airstìlcsl hlccih dl`reatlb ig clvlrmb`ÿrlb airè `l `m sbmkklr smhhl –sprìk‘, ig hitsmttvl` lb cmvlrl grm`.




=:

Ippgmvl 6E `lbbl ippgmvlb slr ve pì ovecklb laalkt hi`lrmtirlbl omr pì rlcmsniblb hlccih DPVE ig

Utlcsl, gnlbbih lb kvmsehi`lrmtirtlst ig oihicigezlrtlst, ig oveckl cl`lcslshlssegl

ehpcekmsniblr `lbbl laalktlb aÿrlr hl` slg.

Lb hi`lrmtir lr lb vmremdlc sih pìverklr laalktlb mv _ pì U (Vmb`vek 4:=0), `lr _ lr lb

umvolbgeg vmremdlc ig U lr lb mvolbgeg vmremdlc.

E ippgmvltlkstlb stìr `lt –Plst smhhl hi`lcc sih e ippgmvl =, hlb druk DPVE sih

umvolbgeg ig FZF ig Peccet sih hi`lrmtirlr‘. Qe ticklr `lttl sih mt ve skmc dloic`l mccl

rlcmsniblr arm ippgmvl = ig clggl tec FZF ig Peccet sih hi`lrmtirlr.

Qe aìr mctsì ti byl rlcmsniblr ig hi`lcclb vec `m sl scek ut>

Oypitlslr>

Pi byl rlcmsniblr ger ti byl

oypitlslr. O0> Peccet tec clvlrmb`ÿrlb

hi`lrlrlr pisetevt pì

rlcmsniblb hlccih

dusslcskmplts

trmbsmksnibssplseaekkl

ebvlstlrebglr ig clvlrmb`ÿrlbs

ytlcsl pì lb mktevetlt.

O<> Kihpltmbslbárolt

hi`lrlrlr pisetevt pì rlcmsniblb

hlccih dusslcskmpltstrmbsmksnibssplseaekkl

ebvlstlrebglr ig clvlrmb`ÿrlbs

ytlcsl pì lb mktevetlt.

Tmsnibmcl

O0> Ni oÿylrl teccet tec mt clvlrmb`ÿrlb utaÿrlr lb mktevetlt pì lb iptehmc hìtl, ni stÿrrl

smbbsybcegolt lr `lt air mt dl`reatlb vec clggl dl`rl ebbsmts e ì tecpmssl slg ovir`mb

lb gett mktevetlt utaÿrls mv clvlrmb`ÿrlb. Mktevetltlb sih lr iptehmceslrt mv

clvlrmb`ÿrlb kmb stì ulb`rlt ig `lrhl` clvlrl seb clvlrmbsl hlr laalktevt ig ge ÿkt

laalkt mv iutsiurfebg air dl`reatlb. O<> Ni hlr kubbskmp dl`reatlb mcclrl`l dlsettlr ih clvlrmb`ÿrlbs mktevetltlr, ni dl`rl

vlt dl`reatlb ovir`mb `l kmb tecpmssl slg clvlrmb`ÿrlb scek mt lb gett mktevetlt kmb

uaÿrls hlr laalktevt.

Plstebg mv hi`lcclb

Qe tlstlr `lb byl hi`lcclb hl` hi`lrmtirlr pì bytt hl` ceblár rlgrlsnibsmbmcysl e VZVV.

Air ì sl laalktlb mv hi`lrmtirlbl e rlgrlsnibsmbmcyslbl omr ve cmg` lt ebtlrmksnibscl`` air

ovlr mv hi`lrmtirlbl. Lt ebtlrmksnibscl`` lr `lb umvolbgegl vmremdlclb gmbglt hl`

hi`lrmtir. @lt dcer `lrhl` ti ebtlrmksnibscl`` e tecclgg tec `l umvolbgegl> DPVE hl` Peccet igDPVE hl` FZF.




==

E ippgmvltlkstlb stìr `lt

aÿcglb`l> –@eskutlr oveckl

mv `l ti hlti`lbl sih lr

hlst rektegl ì drukl e

`lbbl setumsniblb.‘

E dlsvmrlcslb tms `ltutgmbgspubkt e mt `lt olr

hlbls ih `lt lr hlst rekteg ì drukl kvmsehi`lrmtirtlst lcclr oihicigezlrtlst. Air ì aebbl ut

mv ovecklb typl `lt lr aÿcglr ve rmhhlvlrklt air e`lbteaeslrebg mv hi`lrmtirvmremdclr (Vomrhm,

=5?=> 451)

Airhlclb air ì sl hi`lrmtirlaalktlb lr aÿcglb`l>

U 8 d: + d=x= + d4x4 + d6x=x4 (Vmb`vek, 4:=0)

Hl` Peccet sih hi`lrmtir dcer

d: 8 6,071 (Dltm-vlrèlb tec kibstmbtlb)

d= 8 -:,:7? (Dltm-vlrèlb tec DPVE)d4 8 :,617 (Dltm-vlrèlb tec Peccet)

d6 8 :,=5= (Dltm-vlrèlb tec DPVEYHi`lrmtirYPeccet)

@lt aebbls trl typlr hi`lrmtirlr> Zurl hi`lrmtir, kvmsehi`lrmtir ig oihicigezlr (Vomrhm

=5?=> 454). Ve`lb dì`l d4 ig d6 lr segbeaekmbtl lr Peccet lb kvmsehi`lrmtir (Vmb`vek, 4:=0>6).

Hl` FZF sih hi`lrmtir dyttls d4 ig d6 ut hl` olboic`sves FZF ig DPVEYHi`lrmtirYFZF.

Kilaaeselbt-tmdlcclb veslr mt dì`l d4 ig d6 lr segbeaekmbtl. FZF lr mv `lb grubb igsì lb

kvmsehi`lrmtir.

Dlggl hi`lrmtirlbl lr kvmsehi`lrmtirlr ig lb kvmsehi`lrmtirtlst lr `lrair hlst rekteg ì

drukl. Lb oihicigezlrtlst veccl várt hlst rekteg ì drukl `lrsih dì`l d6 ig d4 ekkl lr

segbeaekmbtl (Vmb`vek, 4:=0>6). Om``l `lt ekkl várt air mt ippgmvltlkstlb splseaekt dlr ih ì

tlstl hi`lcclb sih oihicigezlr, sì veccl `lt ekkl dcett gnirt bilb oihicigezlrtlst dmslrt pì

aubblbl ivlr.

Oihicigezlrtlst hl` Peccet sih hi`lrmtir

E VZVV knÿrlr ve devmremt kirrlcmsnib ti gmbglr air ovlr hi`lrmtir, hl` ovlrt sett aectlr.

Aectlrlbl lr scek> Hi`lrmtir 2 Gnlbbihsbett(Hi`lrmtir) ig Hi`lrmtir 38

Gnlbbihsbettlt(Hi`lrmtir).Hi`lrmtirYPeccet 2 Hi`lrmtirYPeccetYhlmb Hi`lrmtirYPeccet 38 Hi`lrmtirYPeccetYhlmb

Druklr Aesolr-^ kmckucmtir (ottp>//amfucty.vmssmr.lù/ciwry/rèaa.othc) ig aìr aÿcglb`l rlsuctmt>^ 8 6.40. Ibl-tmecl`> :.:::1. Pwi-tmecl`> :.::=4.

http://faculty.vassar.edu/lowry/rdiff.html







=4

Peccet sih hi`lrmtirvmremdlc tecarl`stecclr krmvlt tec oihicigezlr pì =% bevì (p 3 :.:=).

Vlcv ih `lt ekkl omr bil ì se air rlsuctmtlt, kmb ve sl pì p-vlrèlb tec ibl-tmecl`, se`lb ve vlt

rltbebglb.

Oihicigezlrtlst hl` FZF sih hi`lrmtir

FZFYHi`lrmtir 2 FZFYHi`lrmtirYhlmb FZFYHi`lrmtir 38 FZFYHi`lrmtirYhlmb

^ 8 1.=0. Ibl-tmecl`> :. Pwi-tmecl`> :

FZF sih hi`lrmtirvmremdlc tecarl`sstecclr krmvlt tec oihicigezlr pì =% bevì (p 3 :.:=).

Cl`lcslshlssegl ehpcekmsniblr

Ve`lb `lt skmc tms oÿy`l air mt `lt lr ti hi`lrmtirlr, dcer airhlclb air ì rlgbl ut

clvlrmb`ÿrlbs ytlcsl aÿcglb`l> U 8 d: + d=_= + d4_4 + d6_6 + d0_=_4 + d<_=_6

Zrÿvlr ì gì gnlbbih lt pmr sflbmreilr hl` airsknlccegl sehuclrebglr mv ucekl vlrèlr mv FZF,

teccet ig DPVE. Ni oÿylrl sfirl pì DPVE, ni hlr ebbverkbebg omr hi`lrmtirlbl pì rlcmsniblb

hlccih DPVE ig ytlcsl. E tecalcclr ovir dl`reatlr omr tecpmsslt slg clvlrmb`ÿrlb e oÿy grm` air lbmktevetlt, omr `lt mctsì hyl ig se e ovecklb grm` hmb omr teccet tec clvlrmb`ÿrlb ig lglb

kubbskmp ih mktevetltlb air ytlcslb.

Cm iss se mt lb dl`reat ÿbsklr ì iutsiurfl lb mktevetlt ig mt `l hl` `lt selr slg veccegl tec ì

tecpmssl slg clvlrmb`ÿrlb e oÿy grm`. @lttl air ì aucct ut utbyttl laalktlb mv iutsiurfebg.

Zì dmkgrubb mv `lttl lr `lt vekteg mt cl`lrlb tmr steccebg tec, lcclr aebblr ut mv ti spÿrshìc aÿr

`l lvlbtulct tecpmsslr slg lb clvlrmb`ÿr>

=. Omr dl`reatlb teccet tec mt clvlrmb`ÿrlb `l vur`lrlr, vec utaÿrl mktevetltlb

tecarl`sstecclb`l utlb bil sárceg ebbdcmbèbg arm dl`reatlb9

Ve`lb hi`lrmtirvmremdlclb Peccet omr stÿrrl airkcmrebgskrmat lbb FZF lr `lt bmturceg ì svmrl pì

`lttl spÿrshìclt aÿrst. Air hl` oÿy grm` mv DPVE ig cmv grm` mv teccet vec ekkl FZF-bevìlt

pìverkl ytlcslb e bilb sárceg grm`. Qe tlbklr iss mt dl`reatlb kibkcu`lrlr hl` mt `l omr gi`

teccet tec mt clvlrmb`ÿrlb tmr gi`l dlscutbebglr slcv, utlb mt dl`reatlb hì dcmb`l slg ebb.

4. Ovir stir grm` omr dl`reatlb hucegolt tec ì gnlbbihaÿrl mktevetltlb slcv9

Dl`reatlb ger slg slcv lb sfirl pì cett ub`lr he``lcs.

Vehuclrebglr mv vlrèlr mv sflbmreilt ivlr vesls e tmdlcclb ÿvlrst pì blstl se`l.




=6

Vih ve slr mv hi`lcclb dcl

ytlcsls-sfirlb pì 1, bil sih

kmb mbsls sih lb gi` sfirl.

Dl`reatlb vec aì lb gi` laalkt mv

iutsiurfebg tec clvlrmb`ÿrlb

sih lr vur`lrt e `lttl tecalcclt. Air ì utbyttl laalktlb mv iutsiurfebg yttlrceglrl kmb `l niddlhit ì aì hlr kubbskmp ig kihpltmbsl ih mktevetltlb ebbm` e dl`reatlb (Oÿylrl FZF-bevì).

Air ì slttl sfirlb e plrsplktev lr cmvlstl huceg sfirl :,4 ig oÿylstl sfirl ?,?. Qe omr tmtt

utgmbgspubkt e mt lb ytlcsls-sfirl ivlr < rlgbls sih gi` laalkt mv iutsiurfebg. Qe omr cmgt

ebb < sih fut airè ve ekkl hlblr laalkteveslrebgsglvebstlb mv iutsiurfebglb pì mktevetltlb, vec

várl stir bik hl` lb ytlcsl ub`lr <, mctsì mt iutsiurfebglb ekkl vec várl vlr`t te` ig

rlssurslr `lt lvlbtulct hlàÿrlr.

E `lttl lkslhplclt lr `lt vmcgt

cett lkstrlhl, huceglbs

urlmcesteskl, vlrèlr air ì

eccustrlrl ovir`mb ytlcsl-sfirlblb`rlr slg. E `lttl tecalccl omr

dl`reatlb tecpmsslt slg clvlrmb`ÿrlb sì hyl sih ivlroi`lt huceg, smhteèg sih `l omr cmv

teccet ig FZF. Egnlb lr `lt teccet sih tlcclr hlst olr ig gnÿr ytlcsl-sfirlb cmv. @lttl kmb

airkcmrls hl` mt bìr dl`reatlb omr tecpmsslt slg vlcèg hyl lttlr lb clvlrmb`ÿr ig ekkl omr

gi` teccet tec mt clvlrmb`ÿrlb gnÿr lb gi` nidd.

Vmhteèg sì dcer `l lkstrm mvolbgeg mv clvlrmb`ÿrlb bìr `l ekkl omr kubbskmp lcclr

kihpltmbsl ebbm` e dl`reatlb tec ì olcclr utaÿrl mktevetltlb slcv. @lt lb`lr hl` mt

clvlrmb`ÿrlb kmb tm slg gi`t dltmct air ì utaÿrl mktevetltlb, smhteèg sih dl`reatlb druklr

hyl te` ig rlssurslr pì ì tecpmssl slg clvlrmb`ÿrlb ig kibtricclrl kibtebulrceg mtclvlrmb`ÿrlb utaÿrlr mktevetltlb gi`t bik.

Hl` tmbkl pì te` ig rlssurslr drukt titmct air ì utaÿrl mktevetltlb, sì dcer titmcl kistbm`lr air

iutsiurfebg hlglt oÿy. Cl`lrlb omr `m ti vmcg air ì ÿkl ytlcslb, sih `lt hì tms steccebg tec e

ovlrt lbklct tecalccl> Lbtlb gì bl` pì DPVE lcclr oÿybl dì`l teccet ig FZF bevì.

Hìtlb dl`reatlb kmb oÿybl teccet pì lr ig aÿrst skmaal slg kihpltmbsl/kubbskmp ih lb

mktevetlt sih skmc iutsiurfls, scek mt dl`reatlb vlt ovir`mb lb mktevetlt skmc utaÿrls. @lrlttlr

kmb `lt ebvlstlrls e clvlrmb`ÿrlb, scek mt clvlrmb`ÿrlb ÿklr kubbskmp ig kihpltmbsl ih `lb

gettl mktevetltlb. Zì `lb hìtlb kmb `l dce hlr slcvgìlb`l ig dl`reatlb kmb sticl pì mt

clvlrmb`ÿrlb gnÿr gi`l vmcg utlb hlr mv dl`reatlbs ebbdcmb`ls.

@lt kmb cÿbbl slg air lb

dl`reat ì gnÿrl slg heb`rl

mvolbgeg mv lb clvlrmb`ÿr

(cmvlrl DPVE-bevì) air `m lr

`lt lbkclrl ì aebbl mb`rl

clvlrmb`ÿrlr sih gnÿr smhhl mktevetltlb, hlb tec lb decceglrl plbgl. Clvlrmb`ÿrlr hì

kibkurrlrl ih ì aì dl`reatlb sih kub`l ig `lrhl` slbkl preslb. Oves `l gnÿr slg titmct

umvolbgegl ger `lttl lb ytlcsls-sfirl pì 1,4, sih vest e tmdlcclb ivlr.




=0

Ippgmvl 0Zì ippgmvl 0 skuccl ve sl pì ovecklb laalkt vmrelrlb`l grm` mv iutsiurfebg pì mktevetltlb omr

pì ytlcsl, ig ih ceblmretlt lr tecstl`l. Air ì aebbl ut `lttl, sì snlkklr ve rlgrlsnibsairutsltbebg

0 air ì sl ih `lt lr ceblár rlgrlsnib ve omr hl` ì gnÿrl. Airutsltbebg 0 lr `laeblrt sih –air

ovlrt sltt mv vlrèlr air k umvolbgegl vmremdclr, (_=n, _4n, .., _kn), L(ѐn| _=n, _4n, .., _kn) 8 :‘. @ltvec mctsì se mt ve skmc snlkkl ih gnlbbihsbettsvlrèlb mv alectlrhlb lr : (Dlrry =556>=4). @lb

vlrtekmcl sprl`bebglb rub`t rlgrlsnibscebnm skmc om cekl stirt mvvek ivlr sih ub`lr, sih egnlb

ger lb gnlbbihsbettceg alectlrh pì bucc. Qe snlkklr airutsltbebg 0 gnlbbih rlseùmc pcit e

rlgrlsnibsmbmcyslb, sfmttlrpcit ig furvl lstehmteib, ovir ucekl ekkl-ceblmrl mctlrbmtev kmb

vur`lrlr ut arm ucekl T4 - laalktlr (Vmb`vek 4:=0> 6). @lbbl airutsltbebglb lr vekteg bìr hmb

druklr ICV mbmcysl, se`lb ve slr pì ceblárl smhhlbolbglr. Oves gnlbbihsbettlt tec alectlrhlb

ekkl lr :, sì hì ve gnÿrl lb`rebglb pì vmremdclbl scek mt ve kmb drukl `lh ve`lrl e mbmcyslb

(Dlrry =556).

Qe dlgybblr hl` ì sl pì sprl`bebglb e lt stmb`mrèslrt rlseùmc pcit sih vest ivlbair. Qe

knÿrlr `m lb rlgrlsnibsmbmcysl, ovir ve slttlr ytlcsl sih mvolbgeg vmremdlc ig ve slttlr –grm`

mv iutsiurebg‘ sih lr `lb umvolbgegl vmremdlclb ebb e dikslb air umvolbgegl vmremdclr. Vìkrysslr ve mv air mt ve skmc om hl` –birhmc pridmdecety pcit‘ ig –oestigrmh‘, ig `m aìr ve

pcittlbl sih vest dì`l ivlbair. Vih ve slr pì pcittlt ivlbair, sì lr rlgrlsnibscebnlb tec –mb`lc

mv iutsiurfebg‘ mvveklb`l, ig veslr ekkl tec bilb gi` ceblár smhhlbolbg. E oestigrmhhlt aìr

ve igsì vetl mt gnlbbihsbettlt pì alectlrhlb lr ivlr :. @lttl dltyr mt ve kmbsknl omr lb

picybihesk rlgrlsnib ovir ve igsì hì sl pì ekkl-ceblárl mctlrbmtevlr sih kvm`rmtesk ig

kudesk. Qe utvekclr `m lb bucc oypitlsl sih selr mt kvm`rmteskl cegbebglb ekkl pmsslr `mtmlbl

segbeaekmbt dl`rl lbb `lb ceblárl cegbebglb, ig sì omr ve lb mbblb bucc oypitlsl sih selr mt

`lb kudeskl cegbebglb ekkl pmsslr `mtmlbl segbeaekmbt dl`rl lbb `lb kvm`rmteskl cegbebglb

(Vikmc ig Tioca =55<> 11<-17:).




=<

@lttl lr lt sfmttlr pcit ve cmg`l vl` ì drukl "grmpo duec`lr" ovir ve pcittlt ebb ytlcsl pì y-

mkslb ig grm` mv iutsiurfebg pì x-mkslb. Olr slr ve mt airkcmrebgskrmatlb air ceblmr rlgrlsnib

lr pì kub =%, bil sih lr vlcèg cmvt. @lrehit sì veslr kvm`rmtesk ig kudesk tec lb hyl oÿylrl

airkcmrebgskrmat pì =7% ig =?,5%.

Olr omr ve lb pmrmhltlr lstehmtls tmdlcc sih ve

aìr vl` ì knÿrl lb furvl lstehmteib. E tmdlcclb aìrve dlkrlatlt mt airkcmrebgskrmatlb tec `lb ceblmrl

cebnlb kub lr pì =% scek sih e grmalbl ivlbair.

@lt dltyr mt ve omr cetlb laalkt mv ceblmr

rlgrlsnib. Qlrèlb tec ceblár lr olcclr ekkl

segbeaekmbt se`lb segbeaekmbslb lr ivlr :,:<, ig

`lt dltyr mt ve ekkl kmb sticl pì aubblt se`lb `lt

kmbsknl lr tecalcèg. Qe slr igsì mt airkcmrebgskrmatlb air kvm`rmtesk ig kudesk rlgrlsnib lr

vlslbtceg oÿylrl sih vest e sfmttlrpcittlt ivlbair, bil sih igsì ty`lr pì `lt lr cetl ceblmretlt

tecstl`l. Ve`lb ve omr gnlbbihsbett vlrè pì alectlrhlb ivlr :, ig ve omr lb hyl oÿylrl

airkcmrebgskrmat pì kvm`rmtesk ig kudesk rlgrlsnib, sì lr ve bÿ`t tec ì lb`rl vmremdlchmtlhmtesk air ì kubbl drukl `lb ve`lrl e ICV mbmcyslb. Airkcmrebgskrmatlb pì `l airsknlccegl

rlgrlsniblbl dÿr várl ivlr :,:4 oÿylrl lbb `l mb`rl air ì dltrmktls sih sudstmbselcc

(Vmb`vek 4:=0>=?). @lb kudeskl lr ekkl ivlr :,:4 oÿylrl lbb `lb kvm`rmteskl, ig `lb lr egnlb

hyl oÿylrl lbb `lb ceblárl bil sih ty`lr pì mt ve omr hl` kvm`rmtesk rlgrlsnib ì gnÿrl. \t

earm `lbbl tmdlcclb sì aìr bucc oypitlslb ekkl stÿttl, se`lb kvm`rmtesk rlgrlsnib pmsslr

`mtmlbl dl`rl lbb ceblár, hlbs `lb mb`rl bucc oypitlslb aìr stÿttl `m `lb kudeskl

rlgrlsniblb ekkl lr segbeaekmbt oÿylrl lbb `lb kvm`rmteskl. Kvm`rmtesk rlgrlsnib dltyr ni mt ve

omr åb lb`rebg e cebnlbs rltbebg sih dltyr mt `lt lr lb mb`rlgrm`saubksnib (Aelc` 4::5).

@lrair hì ve cmgl picybihcl``lt vl` ì gmbgl grm` mv iutsiurfebg hl` slg slcv scek mt ve aìr

grm` mv iutsiurfebg ippoÿy` e mb`rl (Vmb`vek 4:=0>=?).




=1

E te`ceglrl mbmcyslr, sì vmr gnlbbihsbettlt pì alectlrhlb ivlr :, ig kvm`rmtesk ig kudesk om``l

lb vlslbtceg oÿylrl airkcmrebgskrmat lbb ceblár. Qe cmg`l `lrair lt picybihcl`` se`lb ve

kmbsknl omr picybihesk rlgrlsnib sih pmsslr `mtmlbl dlst. Qe snlkklt `lrlttlr `lb vmbcegl

vmremdlclb grm` mv iutsiurfebg hit picybihcl``lt air ì utlcukkl huctekiccebmretlt.

Vih ve slr ve kirlccmsnibshmtreslb ivlr, sì lr _=(grmÌutsiurfebg)ig _=R4

(grmìutsiurfebg4) oÿyt kirrlclrt ig vec `m drytl krmvlt ih armvár mv huctekiccebmretlt.

Cÿsbebglb lr `m mt ve hì gnlbbihsbettsslbtrlrl picybihcl``lt vl` ì trlkkl arm

gnlbbihsbettlt tec grm` mv iutsiurfebg air sì ì gmbgl vmremdlclb hl` slg slcv (Vmb`vek,

4:=0). Gnlbbihsbettlt ambt ve hl` `lskreptev stmtestekk, ig airhlclb dcle `m

grmÌutsiurfebg(grmÌutsiurfebgY48(grmÌutsiurfebg - 6,677<)*(grmÌutsiurfebg -

6,677<)). Airhlclb dcl sì knÿrt hl` –fihputl vmremdcl‘ scek mt ve aekk `lb

gnlbbihsbettsslbtrlrtl vmremdlclb grmÌutsiurfebgY4.

Vih ve bì slr sì lr kirrlcmsniblb hyl cmvlrl. Kirrlcmsniblb lr pì -.141 ig lr `m ub`lr :.?

sih ty`lr pì mt ve ekkl omr huctekiccebmretlt bì. Qe kmb bì drukl vmremdlclb e ve`lrl mbmcyslr air

ì sl ih airkcmrebgskrmatlb air ceblmretlt lb`rlr slg.




=7

Bìr ve `m knÿrlr furvl lstehmteib pì bytt hl` `lb byl gnlbbihsbettsslbtrlrtl vmremdlclb, sì

slr ve mt airkcmrebgskrmatlb air ceblár omr ÿkt arm =% tec =0% sih lr lb dlty`lceg ÿkbebg. E

tecclgg omr `lb bì dcett olct segbeaekmbt sih ty`lr pì mt ve kmb sticl pì mt ve omr lb hlr ceblár

smhhlbolbg bì. Kudesk `lrehit mvtik cett, hlbs kvm`rmtesk ÿktl hl` =,<%. Ih ve `m slr

egnlb pì ih èaalrmbslb hlccih `l airsknlccegl rlgrlsniblbl, sì slr ve mt èaalrmbslb lr

airtsmtt gi`t ivlr .:4 hlccih ceblár ig kvm`rmtesk. @lt dlkrlatlr aubblbl e airregl hi`lcc, mt

`lb aÿrstl bucc oypitlslb ih ceblmretlt ekkl aìr bil stÿttl. @eaalrmbslb `lrehit hlccihkvm`rmtesk ig kudesk lr pì .:=5, bil sih ekkl tecarl`sstecclr krmvlt ih ì várl ivlr .:4, sih

dltyr mt `lb mb`rl bucc oypitlslb ih kvm`rmtesk rlgrlsnib aìr stÿttl. Vlcv ih `lb

gnlbbihsbettsslbtrlrtl vmremdlclb airtsmtt omr air oÿy èaalrmbsl hlccih ceblár ig kvm`rmtesk,

sì lr `lb vlslbtceg airdl`rlt e airoic` tec ovm `lb vmr aÿr ve lb`rlt pì vmremdlclb.

Zì dmkgrubb mv aubblbl gnirt e mbmcyslbl ve omr gnlbbihaÿrt, ig `l tectmklbl ve omr gnirt air ì

rlttl pì mvvek, sì kibkcu`lrlr ve hl` mt rlgrlsnibsairutsltbebg 0 ekkl lr tecarl`sstect se`lb

rlgrlsnibscebnlb ekkl dltlgbls sih ceblár. @eaalrmbslb hlccih `lb kudeskl ig kvm`rmteskl

airkcmrebgskrmatlb lr ub`lr .:4, ig se`lb `l lr ihtrlbt cekl laalktevl sì vlcglr ve mt `lt lr

kvm`rmtesk rlgrlsnib sih pmsslr `mtmlbl dlst airè `lb lr heb`rl kihpclks. Kudesk sebairkcmrebgskrmat amct igsì cett lttlr mt ve gnlbbihsbettsslbtrlrtl, sih igsì gìr e amvÿr

kvm`rmtesk rlgrlsnib.

Kibkcusniblb lr `m mt `lb aÿrstl bucc oypitlslb sih omb`clr ih mt kvm`rmtesk rlgrlsnib ekkl

pmsslr segbeaekmbt dl`rl lbb ceblár rlgrlsnib ekkl stÿttls, hlbs `lb mb`rl bucc oypitlslb ih

mt `lb kudeskl rlgrlsniblb ekkl pmsslr segbeaekmbt dl`rl lbb `lb kvm`rmteskl stÿttls. @lttl

omr ve kihhlt armh tec vl` ì mbmcyslrl rlgrlsnibsairutsltbebg 0 gnlbbih aclrl stmtesteskl

mbmcyslr.




=?

Ippgmvl <Vltt ipp lbklc Lxflchi`lcc air prlèksniblr mv lstehmtlbl arm ippgmvl 0 air lstehlrt

plrairhmbfl vl` ucekl vlrèlr air grm` mv iutsiurfebg. @rÿat rlsuctmtlbl ig ehpcekmsniblr air

prmkses.

E spÿrrlsknlhmlt dcer dl`reatlb dl`t ih ì rmbglrl e ovir stir grm` mv `lb vmcgtl mktevetltlb

sih utaÿrls mv clvlrmb`ÿrlb arm =-<, `lr = lr =-4:% ig < lr ?=-=::%. Qe smtt ipp lb

lxflchi`lcc dmslrt pì tmcc ve aekk arm rlgrlsnibsmbmcyslb. Ve`lb ve omr hl` kvm`rmtesk rlgrlsnib

ì gnÿrl sì om``l ve hl` ytlcsl sih `lb mvolbgegl vmremdlclb, ig grm` mv iutsiurfebg ig

picybihcl``lt sih `l umvolbgegl. E hi`lccippsuhhlrebglb ig mbmcyslr gnlbbihaÿrt e

ippgmvl 0 aekk ve lb airkcmrebgskrmat pì =7% sih dltyr mt ucek grm` mv iutsiurfebg omr =7% ì

se air ytlcslb. Mccl vlrèlbl e tmdlcclb ub`lr vmr segbeaekmbtl sì `lt dltyr mt `lt ekkl lr

airìrsmklt mv tecalcègoltlr.

Airhlclb ve druktl air ì lstehlrl ytlcsl ut earm airsknlcceg grm` mv iutsiurfebg slr scek ut>

y 8 d: + d=_= + d4_=R4 (Vmb`vek 4:=0> =<). @lttl lr airhlclb air kvm`rmtesk rlgrlsnib.




=5

@rÿat rlsuctmtlbl ig ehpcekmsniblr air prmkses

\t e arm grmalb ivlr slr ve mt `lt ger ihtrlbt smhhl ytlcsl ih hmb iutsiurflr lb stir `lc mv

lb mktevetlt, kibtrm lb cetlb `lc mv lb mktevetlt. Ni bárhlrl dl`reatlb cegglr 0=-1:%

iutsiurfebg, ni `ìrceglrl ytlcsl aìr `l.

Dl`reatlb dur`l om lt cett –mct lcclr ebglbtebg‘ heb`slt bìr `lt kihhlr tec ovir hyl sih skmc

iutsiurfls mv lb mktevetlt. Ih dl`reatlb vur`lrlr ì iutsiurfl lb gett mktevetlt, hlb aebblr ut

mt ekkl hlr lbb omcvpmrtlb kmb iutsiurfls mv prmkteskl grubblr, sì vec `lt ut e arm hi`lcclb

cÿbbl slg ì cm várl, ig olcclr utaÿrl lb stÿrrl mb`lc mv mktevetltlb slcv.

Lt mbblt sflbmrei kmb várl mt dl`reatlb lr mvolbgeg mv mt clvlrmb`ÿrlb utaÿrlr ivlr 4:% mv

mktevetltlb, airè clvlrmb`ÿrlb dlsettlr lb splselcc kihpltmbsl. Lt lkslhplc kmb várl

rutlpcmbclggebg. Lb clvlrmb`ÿr omr utvekclt lt rutlpcmbclggebgsprigrmh sih lr sìpmss gi`t

mt dl`reatlb ekkl kmb kcmrl slg utlb. E `lttl sflbmreilt dur`l dl`reatlb sl ih `lt lr huceg ih

clvlrmb`ÿrlb kmb stì air utaÿrlcslb mv rutlpcmbclggebglb e seb olcolt. Oves ve `lrehit tlbklr

iss tol hitsmttl sflbmreilt, mt dl`reatlb gnÿr hebst 4:% slcv, sì vec `lt cÿbbl slg ì olcclr

gnÿrl mct slcv lbb mt clvlrmb`ÿrlb gnÿr ?:% mv iutsiurfebglb ih `lt lr gnlbbihaÿrdmrt e

prmkses.

\mbsltt vmrelrlr ytlcslb e cetlb grm` dmslrt pì kub mb`lc mv iutsiurfebg, smhteèg sih

airkcmrebgskrmatlb cegglr pì fm =7%, bil sih lr gmbskl cmvt. @lt dltyr ni mt ?6% mv ytlcsl

airkcmrls mv mb`rl vmremdclr. Oves lb dl`reat tmr dlscutbebglr kub dmslrt pì `lttl, lr `lt `lrair

vekteg ì várl kcmr ivlr mt mb`lc mv iutsiurfebg ekkl omr sì hyl ì se air ytlcslb e `lt stirl

dec`lt. Vih ve slr e èmgrmhhlt ig tmdlcclb, sì vmrelrlr ytlcslb lt stl` hlccih <,7 pì `lthlstl ig 0,? pì `lt hebstl. @lt dltyr ni mt slcv ih hmb omr iutsiurflt lt stl` hlccih 0=-

1:% scek mt hmb omr `lb cmvlstl ytlcsls sfirlb, sì lr `lt mcceklvlc ekkl sì hyl `ìrceglrl ytlcsl

ih hmb omr iutsiurflt ebglbtebg lcclr mct. Vì ih `lt hì gnÿrls hyl lb`rebglr air ì lbtlb

ÿkl lcclr slbkl grm` mv iutsiurfebg mv lb mktevetlt, kmb `lttl pìverkl ytlcslb blgmtevt. @m kmb

`lt mbtmklceg várl curt ì cm `lt várl sih `lt lr.




4:

Ippgmvl 1

@lt vec e hmbgl tecalcclr várl mktulct ì kibtricclrl air mctlrbmtevl airkcmrebglr pì

smhhlbolbglr e `mtmhmtlremclt. @lttl gnÿr hmb air ì mv`lkkl lvlbtulccl spureÿsl

smhhlbolbglr (Vÿrldÿ 4:=4). Vpureÿsetlt lr amcskl smhhlbolbglr, sih vec se mt

smhhlbolbglb hlccih ti vmremdclr airkcmrls mv mb`rl vmremdclr. Vcekl smhhlbolbglr aebblr

ve vl` ì kibtricclrl air mctlrbmtevl airkcmrebglr hl` sìkmctl kibtriccvmremdclr.

E tri ih mt `lt kmbsknl aebbls spureÿsl smhhlbolbglr, kmb hmb egnlb knÿrl

kirrlcmsnibsmbmcyslbl ig rlgrlsnibsmbmcyslbl vl` ì igsì tm hl` kibtriccvmremdclr. @lrlttlr

smhhlbcegblr hmb rlsuctmtlbl mv mbmcyslbl hl` kibtriccvmremdclr hit `l smhhl tlstlbl

utlb kibtriccvmremdclr. Oves hmb slr airsknlcclr e rlsuctmtlbl mv tlstlbl, sì kmb hmb se mt

tecstl`lvárlcsl mv èssl kibtriccvmremdclr pìverklr rlsuctmtlbl. Ih rlsuctmtlt mv tlstlbl lr

airsknlccegl sì dltyr `lt `l smhhlbolbglbl lr spureÿsl, mctsì mt `l pìverkls mv mb`rl

vmremdclr. Oves `lt ekkl lr bilb airsknlcc pì rlsuctmtlbl, vec ekkl armvár lcclr tecstl`lvárlcsl mv

kibtriccvmremdclr e mbmcyslbl speccl bilb riccl. @l ipprebblcegl rlsuctmtlbl lr `lrair ekklspureÿsl.

Qe ambt hucegl kibtriccvmremdclr air vmremdclbl drukt e hi`lcclbl vl` ì knÿrl lb

kirrlcmsnibsmbmcyslb hl` mccl vmremdclbl e `mtmslttlt. Qe snlkklt air `l vmremdclbl sih vmr

segbeaekmbtl (4-tmecl`) dì`l hl` `lb mvolbgegl vmremdlclb ig lb lcclr aclrl umvolbgegl

vmremdclr drukt e hi`lcclb. Zitlbselccl kibtriccvmremdclr air ippgmvl 4 ig 0 lr vest e tmdlcclbl

1.4.4 ig 1.0.4 e vl`clgg.

@lrlttlr knÿrtl ve pmrtelcc kirrlcmsnibsmbmcysl air lb ig lb kibtriccvmremdlc. @lttl dcl gnirt air

dlggl ti hi`lcclbl e ippgmvl 4 ig 0. Tlsuctmtlbl lr vest e tmdlcclbl a.i.h 1.4.6 t.i.h 1.4.1 airippgmvl 4 ig e tmdlcclbl a.i.h 1.0.6 t.i.h 1.0.1 air ippgmvl 0 e vl`clgg.

Qe knÿrtl igsì rlgrlsnibsmbmcyslr hl` kibtriccvmremdclr. @lttl dcl gnirt air dlggl ti

hi`lcclbl e ippgmvl 4 ig 0. Tlsuctmtlbl lr vest e tmdlcclbl a.i.h 1.4.7 t.i.h 1.4.? air ippgmvl

4 ig e tmdlcclbl a.i.h 1.0.7 t.i.h 1.0.? air ippgmvl 0 e vl`clgg.

Zmrtelcc kirrlcmsnib hl` kibtriccvmremdclr - ippgmvl 4

Zmrtelcc kirrlcmsnibs air ì snlkkl pìverkbebg mv kibtriccvmremdclr pì rlsuctmtlbl e ippgmvl 4.

E tmdlcclb ivlr omr ve smhclt kirrlcmsnibs ig segbeaekmbt vlrèlbl arm tmdlcclbl 1.4.= ig a.i.h

1.4.6 t.i.h 1.4.1 e vl`clgg. Peccet, FZF ig DPVE lr umvolbgegl vmremdclr. Utlcsl lr `lb mvolbgeg

vmremdlc. Zrigrmhhlrdmrolt, Ippirtubeshl, Prmbskist ig ClvYresekimv lr kibtriccvmremdclr.




4=

Tm` = veslr kirrlcmsnib ig segbeaekmbtl vlrèlr hlccih ytlcsl ig `l mb`rl trl umvolbgegl

vmremdclr drukt e hi`lcclb e ippgmvl 4 arm lb irèbár kirrlcmsnibsmbmcysl. Tm` 4 tec Tm` <

veslr rlsuctmtlbl arm pmrtelcc kirrlcmsnibsmbmcyslr ig pìverkbebg mv kibtriccvmremdclr pì

kirrlcmsnib ig segbeaekmbt vlrèlbl hlccih ytlcsl ig `l trl mb`rl umvolbgegl vmremdclbl.

Qe slr mt `l rmppirtlrtl kirrlcmsnibs- ig segbeaekmbsbevìlbl pì `l trl vmremdclbl teccet, FZF ig

DPVE ekkl omr smhhl segbeaekmbs- ig kirrlcmsnibsbevì bìr ve tlstlt hl` kibtriccvmremdclr (knÿrtovlr air slg). Kibkcusniblb lr `lrair mt Zrigrmhhlrdmrolt, Ippirtubeshl, Prmbskist ig

ClvYresekimv omr dlty`bebg air smhvmremsnib hlccih ytlcsl ig `l trl mb`rl umvolbgegl

vmremdclr drukt e hi`lcclb.

Tlgrlsnibsmbmcysl hl` kibtriccvmremdclr ‖ ippgmvl 4

Tlgrlsnibsmbmcysl tlst air ì snlkkl pìverkbebg mv kibtriccvmremdclr pì rlsuctmtlbl e ippgmvl 4.

@lt lr vest ti rlgrlsnibscegbebglr ivlr air ippgmvl 4. Qlrèlbl lr olbtlt arm tmdlcclbl 1.4.7

ig 1.4.? e vl`clgg. Peccet, FZF ig DPVE lr umvolbgegl vmremdclr. Utlcsl lr mvolbgeg vmremdlc.

Zrigrmhhlrdmrolt, Ippirtubeshl, Prmbskist ig ClvYresekimv lr kibtriccvmremdclbl. ßvrl

cegbebglb lr utlb kibtriccvmremdclr ig bl`rl cegbebglb lr hl` kibtriccvmremdclr.

Qe slr mt `l rmppirtlrtl vlrèlbl pì kibstmbt cl``lt ig `l trl vmremdclbl Peccet, FZF ig DPVE

omr airmb`rlt slg e cegbebg 4 pì grubb mv tecstl`lvárlcsl mv kibtriccvmremdclr.

Hi`lccippsuhhlrebg utlb kibtriccvmremdclr arm ippgmvl 4

Hi`lccippsuhhlrebg hl` kibtriccvmremdclr arm ippgmvl 4

Oves ve `m smhhlbcegblr hi`lccippsuhhlrebglbl arm ippgmvl 4 hl` ig utlb

kibtriccvmremdclr, sì slr ve mt airkcmrebgskrmatlb ÿklr dlty`lceg arm =<,4% tec 04,6%. @lt

dlkrlatlr mt smhhlbolbglbl e hi`lcclb e ippgmvl 4 omr spureÿsl smhhlbolbglr, ig lr

airkcmrt mv kibtriccvmremdclbl ve omr tmtt hl`. Kibkcusniblb lr `lrair mt Zrigrmhhlrdmrolt,

Ippirtubeshl, Prmbskist ig ClvYresekimv omr dlty`bebg air smhvmremsnib hlccih ytlcsl ig `l

mb`rl trl umvolbgegl vmremdclr drukt e hi`lcclb.




44

Zmrtelcc kirrlcmsnib hl` kibtriccvmremdclr - ippgmvl 0

Zmrtelcc kirrlcmsnib air ì snlkkl pìverkbebg mv kibtriccvmremdclr pì rlsuctmtlbl e ippgmvl 0.

E tmdlcclb ivlr omr ve smhclt kirrlcmsnibs ig segbeaekmbt vlrèlbl arm tmdlcclbl 1.0.= ig a.i.h1.0.6 t.i.h 1.0.1 e vl`clgg. Mb`lc lr umvolbgeg vmremdlc ig ytlcsl lr mvolbgeg vmremdlc. Peccet,

Zrigrmhhlrdmrolt, \taÿrl mktevetltlb slcv ig ClvYresekimv lr kibtriccvmremdclr.

Tm` = veslr kirrlcmsnibs ig segbeaekmbt vlrèlr hlccih ytlcsl ig mb`lc drukt e hi`lcclb e

ippgmvl 0 arm lb irèbár kirrlcmsnibsmbmcysl. Tm` 4 tec Tm` < veslr rlsuctmtlbl arm pmrtelcc

kirrlcmsnibsmbmcyslr ig pìverkbebg mv kibtriccvmremdclr pì kirrlcmsnib ig segbeaekmbt vlrèlbl

hlccih ytlcsl ig mb`lc.

Qe slr mt `l rmppirtlrtl kirrlcmsnibs ig segbeaekmbt vlrèlb pì mb`lc ekkl omr smhhl

segbeaekmbt- ig kirrlcmsnib vlrè bìr `lt dcl knÿrt pmrtelcc kirrlcmsnib hl` kibtriccvmremdclr

(knÿrt ovlr air slg). Kibkcusniblb lr `lrair mt Peccet, Zrigrmhhlrdmrolt, \taÿrl mktevetltlb slcv

ig ClvYresekimv omr dlty`bebg air smhvmremsnib hlccih ytlcsl ig mb`lc drukt e hi`lcclb.

Tlgrlsnibsmbmcysl hl` kibtriccvmremdclr ‖ ippgmvl 0

Tlgrlsnibsmbmcysl tlst air ì snlkkl pìverkbebg mv kibtriccvmremdclr pì rlsuctmtlbl e ippgmvl 0.

@lt lr vest ti rlgrlsnibscegbebglr ivlr. Qlrèlbl lr olbtlt arm tmdlcclbl 1.0.7 ig 1.0.? e

vl`clgg. Mb`lc lr `lb umvolbgeg vmremdlc ig ytlcsl lr `lb mvolbgegl vmremdlc. Peccet,Zrigrmhhlrdmrolt, ClvYTesekimv ig \taÿrl mktevetltlb slcv lr kibtriccvmremdclr. ßvrl

cegbebglb lr utlb kibtriccvmremdclr ig bl`rl cegbebglb lr hl` kibtriccvmremdclr.

Qe slr mt `l rmppirtlrtl vlrèlbl pì kibstmbtcl``lt ig mb`lc, omr airmb`rlt slg e cegbebg 4 pì

grubb mv tecstl`lvárlcsl mv kibtriccvmremdclr.




46

Ceblár rlgrlsnibstlst e ippgmvl 0 utlb kibtriccvmremdclr.

Ceblár rlgrlsnibstlst e ippgmvl 0 hl` kibtriccvmremdclr.

Oves ve smhhlbcegblr hi`lccrlsuctmtlbl air ceblár rlgrlsnib arm ippgmvl 0 hl` ig utlb

kibtriccvmremdclr, sì slr ve mt `lt lr stirl airsknlcclr. \tlb kibtriccvmremdclr sì om``l hi`lcclb

lb airkcmrebgskrmat pì =% sih olcclr ekkl vmr segbeaekmbt, hlbs pì hi`lcclb hl`

kibtriccvmremdclr sì om``l hi`lcclb lb airkcmrebgskrmat pì 4?,1% sih igsì vmr olct

segbeaekmbt. @lt dltyr mt ve kmb trygt se mt smhhlbolbglb hlccih mb`lc mv iutsiurfebg ig

ytlcsl vmr spureÿs, ig mt airoic`lt lr pìverklt mv kibtriccvmremdclbl ve vmcgtl ut. Kibkcusniblb

lr `lrair mt Peccet, Zrigrmhhlrdmrolt, ClvYresekimv ig \taÿrl mktevetltlb slcv omr dlty`bebg air

smhvmremsnib hlccih ytlcsl ig mb`lc e hi`lcclb.

Kibtriccvmremdclbl ve vmcgtl ut air ì tlstl rlsuctmtlbl arm ippgmvl 4 ig 0 vmr mccl hl` ì

pìverkl rlsuctmtlt arm mbmcyslbl. @lt dltyr mt ve om``l spureÿsl smhhlbolbglr hlccih `l

umvolbgegl ig `lb mvolbgegl vmremdlclb, sih dcl airkcmrt hl` kibtriccvmremdclbl ve vmcgtl.

Kibtriccvmremdclbl pìverklt rlsuctmtlbl airè `l lr vmremdclr sih pìverklr dì`l hit `lb

umvolbgegl ig `lb mvolbgegl vmremdlclb smhteèg (Vÿrldÿ 4:=4). Bìr ve `m clgglr ebb èssl

vmremdclbl e tecclgg tec `l ipprebblcegl vmremdclbl, sì vec rlsuctmtlt dce airsknlcceg, ig ve aìr

mv`lkklt lvlbtulccl spureÿsl smhhlbolbglr.




40

Cettlrmturcestl

Kec`lr>

Dlrry, W.@. (=556)> \b`lrstmbèbg rlgrlsseib mssuhpteibs, Vmgl pudcefmteibs, \K

Aelc`, M. Z. (4::5)> @esivlrebg stmtestefs usebg VZVV> mb` slx mb` `rugs mb` rifk 'b' ricc (toer`

lèteib). Vmgl pudcefmteibs, \K

Nmfidslb, @.E. (4:::)> ‘Ovir`mb gnlbbihaÿrl ub`lrsÿklcslr‘, Oÿyskiclaircmglt

Vomrhm, V., @urmb`, T.H., Gur-Mrel, I. (=5?=)> E`lbteaefmteib mb` Mbmcyses ia Hi`lrmtir

Qmremdcls. Niurbmc ia Hmrkltebg Tlslmrfo, Qic. _QEEE (Mugust), 45=-6::.

Vikmc, T. T, A. N. Tioca. (=55<)> Pol prebfepcls mb` prmftefl ia stmtestefs eb deicigefmc rlslmrfo,

6r` l`. W.O.Arllhmb & Fi Ct`> Blw Uirk, 11<-17:.

Vÿrldÿ M.(4:=4) Lb ebbaÿrebg e kvmbtetmtev `mtmmbmcysl hl` VZVV ‖ =7.:

Pmdmfobefk, D. G., & Ae`lcc, C. V. (4::7)> \sebg huctevmremtl stmtestefs. Zlmrsib/Mccyb & Dmfib>

Distib

Air ippgmvl 4>

Vmb`vek, K. (4:=0)> Ziwlrpiebt arm airlclsbebg, TlgrlsnibY@lcY= ==/:5/4:=0

Air ippgmvl 6>

Vmb`vek, K. (4:=0)> Ziwlrpiebt arm airlclsbebg, Hi`lrmtirmbmcysl ==/:5/4:=0

Air ippgmvl 0>

Vmb`vek, K. (4:=0)> Ziwlrpiebt arm airlclsbebg, Ekkl-ceblmrl laalktlr ==/:5/4:=0

Mb`rl kec`lr>

Gucdrmb`slb, D., Vmb`vek, K. & Omugcmb`, V.M. (4::5)> Mbtlfl`lbts ia vlrtefmc ebtlgrmteib>

Prmbsmfteib fist lfibihefs mb` rlsiurfl-dmsl` lxpcmbmteibs. Niurbmc ia Zursfomsebg &

Vuppcy hmbmglhlbt =<. Lcslvelr Ct`.

Ebtlrblttse`lr>

Aesolr-^ fmcfucmtir, Vegbeaefmbfl ia tol @eaalrlbfl Dltwllb Pwi Firrlcmteib Filaaefelbts>

ottp>//vmssmrstmts.blt/rèaa.othc

http://vassarstats.net/rdiff.html






4<

Ql`clgg

Pmdlcc 1.4.=> Kirrlcmsnibsmbmcyslb mv vmremdclbl drukt e ippgmvl 4

Pmdlcc 1.4.4> Kibtriccvmremdclr air vmremdclbl drukt e ippgmvl 4

Pmdlcc 1.4.6> Zmrtemc kirrlcmsnib tlst hl` Zrigrmhhlrdmrolt sih kibtriccvmremdlc air

ippgmvl 4

Pmdlcc 1.4.0> Zmrtemc kirrlcmsnib tlst hl` Ippirtubeshl sih kibtriccvmremdlc air ippgmvl 4

Pmdlcc 1.4.<> Zmrtemc kirrlcmsnib tlst hl` Prmbskist sih kibtriccvmremdlc air ippgmvl 4




41

Pmdlcc 1.4.1> Zmrtemc kirrlcmsnib tlst hl` ClvYresekimv sih kibtriccvmremdlc air ippgmvl 4

Pmdlcc 1.4.7> Tlgrlsnibsmbmcyslb utlb kibtriccvmremdclr air ippgmvl 4

Pmdlcc 1.4.?> Tlgrlsnibsmbmcyslb hl` kibtriccvmremdclr air ippgmvl 4

Pmdlcc 1.0.=> Kirrlcmsnibsmbmcyslb mv vmremdclbl drukt e ippgmvl 0




47

Pmdlcc 1.0.4> Kibtricc vmremdclr air vmremdclbl drukt e ippgmvl 0

Pmdlcc 1.0.6> Zmrtemc kirrlcmsnib tlst hl` Peccet sih kibtricc vmremdlc air ippgmvl 0

Pmdlcc 1.0.0> Zmrtemc kirrlcmsnib tlst hl` Zrigrmhhlrdmrolt sih kibtricc vmremdlc air

ippgmvl 0

Pmdlcc 1.0.<> Zmrtemc kirrlcmsnib tlst hl` CevYresekimv sih kibtricc vmremdlc air ippgmvl 0

Pmdlcc 1.0.1> Zmrtemc kirrlcmsnib tlst hl` \taÿrl mktevetltlb slcv sih kibtricc vmremdlc air

ippgmvl 0




4?

Pmdlcc 1.0.7> Tlgrlsnibsmbmcyslb utlb kibtricc vmremdclr air ippgmvl 0

Pmdlcc 1.0.? - Tlgrlsnibsmbmcyslb hl` kibtricc vmremdclr air ippgmvl 0




45

Vybtmks

/* Ippgmvl 4 */

@MPMVLP MFPEQMPL @mtmVlt=.

FIHZ\PL FZF8HLMB(`4fpf=,`4fpf4,`4fpf6,`4fpf0).

L_LF\PL.

FIHZ\PL PECCEP8HLMB(f4t=,f4t4,f4t6,f4t0).L_LF\PL.

FIHZ\PL DPVE8HLMB(`=dtse=,`=dtse4,`=dtse6,`=dtse0).L_LF\PL.

FIHZ\PL Utlcsl8HLMB(f=p5,f=p=:,f=p==,f=p=4).L_LF\PL.

@LVFTEZPEQLV QMTEMDCLV8PECCEP FZF DPVE

/VPMPEVPEFV8HLMB VP@@LQ QMTEMBFL HEB HM_ K\TPIVEV VKLWBLVV.

FITTLCMPEIBV/QMTEMDCLV8 PECCEP FZF DPVE/ZTEBP8PWIPMEC BIVEG/HEVVEBG8ZMETWEVL.

TLGTLVVEIB/HEVVEBG CEVPWEVL/VPMPEVPEFV PIC FILAA I\PV T MBIQM/FTEPLTEM8ZEB(.:<) ZI\P(.=:)

/BIITEGEB/@LZLB@LBP UPLCVL/HLPOI@8LBPLT PECCEP FZF DPVE.




6:

/* Ippgmvl 6 */

FIHZ\PL Hi`lrmtirYFZF8FZF.L_LF\PL.FIHZ\PL Hi`lrmtirYPECCEP8PECCEP.L_LF\PL.

FIHZ\PL \MQOLBGEGYDPVE8DPVE.L_LF\PL.

MGGTLGMPL/I\PAECL8* HI@L8M@@QMTEMDCLV/DTLMK8/Hi`lrmtirYFZFYhlmb8 HLMB(Hi`lrmtirYFZF)/Hi`lrmtirYPECCEPY hlmb 8HLMB(Hi`lrmtirYPECCEP)/\MQOLBGEGYDPVEY hlmb 8HLMB(\MQOLBGEGYDPVE).

FIHZ\PL DPVEYHI@LTMPITYPECCEP8(\MQOLBGEGYDPVE-\MQOLBGEGYDPVEYhlmb)*(Hi`lrmtirYPECCEP-Hi`lrmtirYPECCEPYgn).

L_LF\PL.

FIHZ\PL DPVEYHI@LTMPITYFZF8(\MQOLBGEGYDPVE-\MQOLBGEGYDPVEYhlmb)*(Hi`lrmtirYFZF-Hi`lrmtirYFZFYgn).

L_LF\PL.

TLGTLVVEIB/HEVVEBG CEVPWEVL/VPMPEVPEFV FILAA I\PV T MBIQM/FTEPLTEM8ZEB(.:<) ZI\P(.=:)/BIITEGEB/@LZLB@LBP UPLCVL/HLPOI@8LBPLT \MQOLBGEGYDPVE Hi`lrmtirYFZF Hi`lrmtirYPECCEP

DPVEYHI@LTMPITYPECCEP DPVEYHI@LTMPITYFZF




6=

/* Oihicigezlrtlstlb*/\VL MCC.FIHZ\PL aectlrY$8(Hi`lrmtirYPECCEP 2 Hi`lrmtirYPECCEPYhlmb).QMTEMDCL CMDLCV aectlrY$ 'Hi`lrmtirYPECCEP 2Hi`lrmtirYPECCEPYhlmb(AECPLT)'.QMC\L CMDLCV aectlrY$ : 'Bit Vlclftl`' = 'Vlclftl`'.

AITHMPV aectlrY$ (a=.:).AECPLT DU aectlrY$.L_LF\PL.

FITTLCMPEIBV/QMTEMDCLV8UPLCVL \MQOLBGEGYDPVE/ZTEBP8PWIPMEC BIVEG/HEVVEBG8ZMETWEVL.

\VL MCC.FIHZ\PL aectlrY$8(Hi`lrmtirYPECCEP 38 Hi`lrmtirYPECCEPYhlmb).QMTEMDCL CMDLCV aectlrY$ 'Hi`lrmtirYPECCEP 38Hi`lrmtirYPECCEPYhlmb(AECPLT)'.QMC\L CMDLCV aectlrY$ : 'Bit Vlclftl`' = 'Vlclftl`'.AITHMPV aectlrY$ (a=.:).AECPLT DU aectlrY$.L_LF\PL.


\VL MCC.FIHZ\PL aectlrY$8(Hi`lrmtirYFZF 2 Hi`lrmtirYFZFYhlmb).QMTEMDCL CMDLCV aectlrY$ ' Hi`lrmtirYFZF 2Hi`lrmtirYFZFYhlmb(AECPLT)'.QMC\L CMDLCV aectlrY$ : 'Bit Vlclftl`' = 'Vlclftl`'.AITHMPV aectlrY$ (a=.:).AECPLT DU aectlrY$.L_LF\PL.


\VL MCC.FIHZ\PL aectlrY$8(Hi`lrmtirYFZF 2 Hi`lrmtirYFZFYhlmb).QMTEMDCL CMDLCV aectlrY$ ' Hi`lrmtirYFZF 2Hi`lrmtirYFZFYhlmb(AECPLT)'.QMC\L CMDLCV aectlrY$ : 'Bit Vlclftl`' = 'Vlclftl`'.AITHMPV aectlrY$ (a=.:).AECPLT DU aectlrY$.L_LF\PL.

FITTLCMPEIBV

/QMTEMDCLV8UPLCVL \MQOLBGEGYDPVE/ZTEBP8PWIPMEC BIVEG/HEVVEBG8ZMETWEVL.




64

/* Ippgmvl 0 */

AECPLT IAA.\VL MCC.L_LF\PL.

@MPMVLP MFPEQMPL @mtmVlt=.FIHZ\PL grmÌutsiurfebg8m7.L_LF\PL.

TLGTLVVEIB/HEVVEBG CEVPWEVL/VPMPEVPEFV FILAA I\PV T MBIQM/FTEPLTEM8ZEB(.:<) ZI\P(.=:)/BIITEGEB/@LZLB@LBP UPLCVL/HLPOI@8LBPLT grmÌutsiurfebg/TLVE@\MCV OEVPIGTMH(^TLVE@) BITHZTID(^TLVE@).

* Fomrt Duec`lr.GGTMZO/GTMZO@MPMVLP BMHL8"grmpo`mtmslt" QMTEMDCLV8grmÌutsiurfebg UPLCVL

HEVVEBG8CEVPWEVLTLZITPHEVVEBG8BI

/GTMZOVZLF VI\TFL8EBCEBL.DLGEB GZCVI\TFL> s8uslrViurfl(e`("grmpo`mtmslt"))@MPM> grmÌutsiurfebg8fic(siurfl(s), bmhl("grmÌutsiurfebg"))@MPM> UPLCVL8fic(siurfl(s), bmhl("UPLCVL"))G\E@L> mxes(èh(=), cmdlc("grmÌutsiurfebg"))G\E@L> mxes(èh(4), cmdlc("UPLCVL"))LCLHLBP> piebt(piseteib(grmÌutsiurfebg*UPLCVL))

LB@ GZC.

* Furvl Lstehmteib.PVLP BLWQMT8BIBL.F\TQLAEP/QMTEMDCLV8UPLCVL WEPO grmÌutsiurfebg/FIBVPMBP/HI@LC8CEBLMT ]\M@TMPEF F\DEF/ZCIP AEP.

MGGTLGMPL/I\PAECL8* HI@L8M@@QMTEMDCLV/DTLMK8/grmÌutsiurfebgYhlmb8HLMB(grmÌutsiurfebg).

FIHZ\PL grmÌutsiurfebgY48(grmÌutsirfebg-grmÌutsiurfebgYhlmb) *(grmÌutsirfebg-grmÌutsiurfebgYhlmb).

L_LF\PL.




66

/* Ippgmvl < */

TLGTLVVEIB/HEVVEBG CEVPWEVL/VPMPEVPEFV FILAA I\PV T MBIQM/FTEPLTEM8ZEB(.:<) ZI\P(.=:)

/BIITEGEB/@LZLB@LBP UPLCVL/HLPOI@8LBPLT grmÌutsiurfebg grmÌutsiurfebgY4

/* Ippgmvl 1 */

FIHZ\PL Zrigrmhhlrdmrolt8HLMB(d4p=,d4p4,d4p6,d4p0).

L_LF\PL.

FIHZ\PL Ippirtubeshl8HLMB(f=im=,f=im4,f=im6,f=im0).

L_LF\PL.

FIHZ\PL Prmbskist8HLMB(f=tk<,f=tk1,f=tk7,f=tk?).L_LF\PL.

FIHZ\PL ClvYresekimv8HLMB(f6cr=).

L_LF\PL.

FIHZ\PL \taÿrlYmktYslcv8HLMB(m?).

L_LF\PL.

FIHZ\PL FZF8HLMB(`4fpf=,`4fpf4,`4fpf6,`4fpf0).

L_LF\PL.

FIHZ\PL PECCEP8HLMB(f4t=,f4t4,f4t6,f4t0).

L_LF\PL.

FIHZ\PL DPVE8HLMB(`=dtse=,`=dtse4,`=dtse6,`=dtse0).

L_LF\PL.

FIHZ\PL Utlcsl8HLMB(f=p5,f=p=:,f=p==,f=p=4).

L_LF\PL.

FIHZ\PL Zrigrmhhlrdmrolt8HLMB(d4p=,d4p4,d4p6,d4p0).

L_LF\PL.

FIHZ\PL Ippirtubeshl8HLMB(f=im=,f=im4,f=im6,f=im0).

L_LF\PL.

FIHZ\PL Prmbskist8HLMB(f=tk<,f=tk1,f=tk7,f=tk?).

L_LF\PL.

FIHZ\PL ClvYresekimv8HLMB(f6cr=).

L_LF\PL.

FIHZ\PL \taÿrlYmktYslcv8HLMB(m?).

L_LF\PL.




60

FIHZ\PL Mb`lcYgrmÌutsiurfebg8HLMB(m7).

L_LF\PL.

FITTLCMPEIBV

/QMTEMDCLV8UPLCVL PECCEP FZF DPVE Zrigrmhhlrdmrolt Ippirtubeshl

Prmbskist ClvYresekimv/ZTEBP8PWIPMEC BIVEG

/HEVVEBG8ZMETWEVL.

ZMTPEMC FITT

/QMTEMDCLV8UPLCVL PECCEP FZF DPVE DU Zrigrmhhlrdmrolt

/VEGBEAEFMBFL8PWIPMEC

/HEVVEBG8CEVPWEVL.

ZMTPEMC FITT

/QMTEMDCLV8UPLCVL PECCEP FZF DPVE DU Ippirtubeshl

/VEGBEAEFMBFL8PWIPMEC/HEVVEBG8CEVPWEVL.

ZMTPEMC FITT

/QMTEMDCLV8UPLCVL PECCEP FZF DPVE DU Prmbskist


/HEVVEBG8CEVPWEVL.

ZMTPEMC FITT

/QMTEMDCLV8UPLCVL PECCEP FZF DPVE DU ClvYresekimv


/HEVVEBG8CEVPWEVL.

TLGTLVVEIB

/HEVVEBG CEVPWEVL

/VPMPEVPEFV FILAA I\PV T MBIQM

/FTEPLTEM8ZEB(.:<) ZI\P(.=:)

/BIITEGEB

/@LZLB@LBP UPLCVL

/HLPOI@8LBPLT PECCEP FZF DPVE.

TLGTLVVEIB

/HEVVEBG CEVPWEVL



/BIITEGEB

/@LZLB@LBP UPLCVL

/HLPOI@8LBPLT PECCEP FZF DPVE Zrigrmhhlrdmrolt Ippirtubeshl

Prmbskist ClvYresekimv.

FITTLCMPEIBV

/QMTEMDCLV8UPLCVL Mb`lcYgrmÌutsiurfebg PECCEP Zrigrmhhlrdmrolt

\taÿrlYmktYslcv ClvYresekimv

/ZTEBP8PWIPMEC BIVEG

/HEVVEBG8ZMETWEVL.




ZMTPEMC FITT

/QMTEMDCLV8UPLCVL Mb`lcYgrmÌutsiurfebg DU PECCEP


/HEVVEBG8CEVPWEVL.

ZMTPEMC FITT/QMTEMDCLV8UPLCVL Mb`lcYgrmÌutsiurfebg DU Zrigrmhhlrdmrolt


/HEVVEBG8CEVPWEVL.

ZMTPEMC FITT

/QMTEMDCLV8UPLCVL Mb`lcYgrmÌutsiurfebg DU ClvYresekimv


/HEVVEBG8CEVPWEVL.

ZMTPEMC FITT

/QMTEMDCLV8UPLCVL Mb`lcYgrmÌutsiurfebg DU \taÿrlYmktYslcv/VEGBEAEFMBFL8PWIPMEC

/HEVVEBG8CEVPWEVL.

TLGTLVVEIB

/HEVVEBG CEVPWEVL



/BIITEGEB

/@LZLB@LBP UPLCVL

/HLPOI@8LBPLT Mb`lcYgrmÌutsiurfebg.

TLGTLVVEIB

/HEVVEBG CEVPWEVL



/BIITEGEB

/@LZLB@LBP UPLCVL

/HLPOI@8LBPLT Mb`lcYgrmÌutsiurfebg PECCEP Zrigrmhhlrdmrolt

ClvYresekimv \taÿrlYmktYslcv.

Documents

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