Nonlinear Disjunctive Kriging For The Estimating and Modeling

 

 

   

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 F rjefje rjefje L aurejd aurejd am G jrtb jrtb [ kfgekgs kfgekgs ]ad. ::, Ea. ;, ?>:6, ??=-?;=.

 

Eaedfegjr hfsluektfvg crfifei mar tbg gstf`jtfei jeh `ahgdfei am j vgfe kappgr hgpasft Jdf Jcojr Hjyj*   Hgpjrt`gett am @fefei G  Hgpjrt`ge Geifeggrfe eifeggrfei, i, Wefvgrsfty a amm [fstje je jeh h Ojdukbgstje, Ojdukbgstje, \jbghj \jbghje, e, Frje _gkgfvgh :? Juiust ?>:23 jkkgptgh : Ludy ?>:6

Jostrjkt Gstf`jtfae am `fegrjd rgsaurkgs jeh rgsgrvgs rgsgrvgs wftb daw vjdugs am grrar fs gssgetfjd fe `fegrjd gxpdarjtfae. Xbg jf` am tbfs st uhy fs ta gstf`jtg jeh `ahgd j vgfe typg hgpasft usfei hfsluektfvg crfifei `gtbah. Hfsluektfvg Crfifei (HC) js je jppraprfjtg eaedfegjr gstf`jtfae `gtbah bjs ogge usgh mar gstf`jtfae am Ku vjdugs. Mar gstf`jtfae am Ku vjdugs jeh `ahgdfei am tbg hfstrfoutfae am Ku fe Kbgdcurgb, sj`pdgs bjvg ogge tjcge mra` 82 hrfdd badgs fe Kbgdcurgb, jeh tbg vjdugs am Ku bjvg ogge jejdyzgh. _gsudtfei hjtj mra` jejdyzfei Ku vjdugs wgrg kaevgrtgh ta stjehjrh ear`jd vjdugs usfei Bgr`ftg padyea`fjds. ]jrfairjpby bjs ogge haeg fe tbg Kbgdcurgb hgpasft. Jmtgr stuhyfei vjrfairj`s fe hfmmgrget hfrgktfaes, ft wjs maueh aut tbjt tbg arg hgpasft bjs j `fdh jefsatrapy. Xbg  ogst-mfttgh vjrfairj` vjrfairj` `ahgd wjs kaesfhgrgh mar hfsluektfvg crfifei crfifei gstf`jtfae. Xbg `ahgd kaesfsts am j purg euiigt gmmgkt wftb >.8 = j`pdftuhg pdus j spbgrfkjd skbg`g wftb sfdd :.?> jeh rjeig :8> `. Kaesgqugetdy, j tbrgg-hf`gesfaejd `ahgd am gstf`jtgh vjdug jeh grrar gstf`jtgh vjdug wjs pravfhgh oy hfsluektfvg crfifei ta hfvfhg tbg arg feta je gkaea`fk jeh uegkaea`fk pjrt. Xbg `ahgds ojsgh ae tbg gstf`jtg am tbg HC `gtbah fe tbg stuhy jrgj gxbfoftgh je fekrgjsfei trgeh am kaekgetrjtfae mra` tbg kgetgr ta Eartb. Mfejddy, vjdfhjtfae ogtwgge ogtwgge tbg hfsluektfvg crfifei kjrrfgh aut oy usfei krass-vjdfhjtfae. Xbg rgsudt sbawgh tbjt tbg karrgdjtfae am gstf`jtgh vjdugs jeh rgjd vjdugs wjs straei (=;.8%).  Cgywarhs ygjrs. Bawgvgr, tbg sgg`feidy ka`pdgx tbgary `jcgs ft uejppgjdfei mar `ast prjktftfaegrs (Artfz gt jd. ?>>8). HC fs j tgkbefqug tbjt pravfhgs jhvjetjigs fe `jey jppdfkjtfaes. Ft kje og usgh ta gstf`jtg tbg vjdug am jey muektfae am tbg vjrfjodg am fetgrgst (Artfz gt jd. ?>>8). HC pravfhgs j sadutfae spjkg djrigr tbje tbg kaevgetfaejd crfifei tgkbefqugs tbjt aedy rgdy ae dfegjr ka`ofejtfaes am tbg hjtj. HC fs `arg prjktfkjd tbje tbg kaehftfaejd gxpgktjtfae, sfekg ft aedy rgqufrgs ceawdghig am tbg ofvjrfjtg djw, festgjh am tbg mudd `udtfvjrfjtg praojofdfty djw am tbg hjtj dakjtfaes jeh dakjtfae ogfei gstf`jtgh (Artfz gt jd. ?>>8). Fe

fehfkjtar crfifei (Hgutskb jeh Lauregd :662). Kaesfhgrfei tbfs kjpjofdfty, HC bjs ogge usgh fe gjrtb skfgekg3 tbg warcs am sa`g am tbg rgsgjrkbgrs kje og `getfaegh. J dat am rgsgjrkbgrs bjvg usgh HC fe hfmmgrget kjsgs sukb js @fefei, Gevfrae`get fssugs, ^gtradgu`, Igatgkbefqug jeh sa ae, ta pgrmar` tbg gstf`jtfaes (Lauregd jeh Buflorgits :6923 @jtbgrae :6283 Ygostgr jeh Adfvgr ?>>:3 Hjyj ?>:8). Mar festjekg, fe G`gry (?>>=), tbfs `gtbah fs usgh mar hgskrfofei tbg hfstrfoutfae am paddutfae fe tbg gjrtb jeh sa`g atbgr pjrj`gtgrs fe jirfkudturg (G`gry ?>>7). Fe tbfs stuhy, G`gry bjs maueh `arg rgjdfstfk rgsudts mra` HC vgrsus Arhfejry Crfifei (AC). Xbfs pjpgr jf`s ta

dfegjr gstf`jtars, tbg wgfibts jrg aptf`fzgh ta gesurg tbg `fef`jd gstf`jtfae vjrfjekg, wbge aeg egghs bjvg j dakjd gxpgktgh vjdug, sa tbg prf`ftfvg jssu`ptfae fs tbjt j ear`jd (mrgqugeky) hfstrfoutfae muektfae fs jvjfdjodg. Out wbge fs egghgh ta kjdkudjtg tbg praojofdfty am vjdugs joavg j tbrgsbadh, tbgsg praojofdftfgs jrg eat j sf`pdg

gstf`jtg jeh `ahgd tbg Ku vjdugs fe Kbgdcurgb usfei HC `gtbah js j eae-dfegjr igastjtfstfkjd gstf`jtar,  ojsgh ae fsa-mjktarfjd `ahgd jeh Bgr`ft padyea`fjds.

dfegjr mar` am hjtj, jeh tbgrg sbaudh og jhjptgh tgkbefqugs ta kjdkudjtg tbgsg praojofdftfgs (Ygostgr jeh Adfvgr ?>>:). Aeg am tbgsg tgkbefqugs fs Hfsluektfvg Crfifei (HC). Atbgr igastjtfstfkjd `gtbahs usgh ta kjdkudjtg tbg praojofdfty tbjt tbg trug vjdug gxkgghs tbg tbrgsbadh jrg kaehftfaejd sf`udjtfaes (Kbfdgs jeh Hgdmfegr :666), `udtf-Ijussfje crfifei (]grdy :62;3 G`gry ?>>= ) ar eaepjrj`gtrfk gstf`jtars sukb js ---------------------

hgka`pasgh feta j su` am hfslafet (uekarrgdjtgh) ka`paegets am sj`pdg vjdugs. Ybge crfifei am tbg sgpjrjtg ka`paegets fs passfodg, tbg prakghurg fs aewjrhs< f.g., wbge tbg lafet praojofdfty hgesfty muektfaes am \ (ar j trjesmar` am ft, V) jeh gjkb sj`pdg zj (ar Vj) fs am fsamjktarfjd typg (@jtbgrae :628). Fe  prjktfkg, j kaetfeuaus vjrfjodg dfcg tbg irjhg am je arg hgpasft kje jdwjys og trjesmar`gh oy jej`arpbasfs feta j Ijussfje gqufvjdget V, jeh tbge aedy j lafet Ijussfje bypatbgsfs mar tbg praojofdfty hgesfty muektfae (^HM) am sj`pdgs fs rgqufrgh, mar wbfkb tbgrg

*Karrgspaehfei jutbar.  G-`jfd jhhrgss< jhhrgss:6, ??=-?;=.

gxfsts je fsamjktarfjd rgprgsgetjtfae ojsgh ae Bgr`ftg  padyea`fjds (_fvafrjrh :668). Xbg mfrst stgp fs ta trjesmar` aosgrvjtfaes ae tbg rjeha` mfgdh, \(x), ta aosgrvjtfaes ae V(x) sukb tbjt<  \ ( x)      SV ( x)P(:)   Ybgrg V(x) fs E (>, :). Xbg muektfae    fs gxprgssgh fe tgr`s am Bgr`ftg padyea`fjds, wbfkb jrg rgdjtgh ta tbg ear`jd hfstrfoutfae oy _ahrfiug‖s mar`udj<

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(2) Fe pjrtfkudjr, tbg prakghurg gejodgs gstf`jtfae am \(x>) oy   c   \ ( x> )  {V ( x> )}    >   :S B : { y ( x> )}P  ˍ

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Fe wbfkb i(y) fs tbg ear`jd praojofdfty hgesfty muektfae, c fs tbg hgirgg am tbg padyea`fjd tjcfei vjdugs >, :, ?,… jeh :  fs j stjehjrhfzfei mjktar. Xbg mfrst twa Bgr`ftg

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(6) Xbg crfifei vjrfjekg am  B c {V ( x)}  fs ˍ

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Aekg tbg Bgr`ftg padyea`fjds bjvg ogge gstf`jtgh jt x> wg kje gstf`jtg tbg kaehftfaejd praojofdfty tbjt tbg

Xbgrgjmtgr tbg bfibgr arhgr padyea`fjds jrg aotjfegh usfei tbg rgkurrgekg rgdjtfae<

c   :    B c ? ( y ) c  c    Xbg Bgr`ftg padyea`fjds jrg artbaiaejd wftb rgspgkt ta tbg wgfibtfei muektfae gxp (-y?/?) ae tbg fetgrvjd mra`     ta      . @jey muektfaes am j Ijussfje mfgdh V(x) kje og rgprgsgetgh js tbg su` am Bgr`ftg  padyea`fjds (_fvafrjrh :668)<   m  {V ( x)}    m  a B a{V ( x)}   m  : B  :{V ( x)}   m    ? B ?{V ( x)}   (;)  B c  ( y )  

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trug vjdug tbgrg gxkgghs tbg krftfkjd vjdug, \k. Xbg trjesmar`jtfae  \ ( x)      SV ( x)P   `gjes tbjt \k bjs je gqufvjdget yk ae tbg stjehjrh ear`jd skjdg. [fekg tbg twa skjdgs jrg `aeataefkjddy rgdjtgh tbgfr fehfkjtars jrg tbg sj`g (_fvafrjrh :668)< S \ ( x)   z k P    SV    ( x)  yk P(:?)   wbgrg  fs je fehfkjtar. Mar SV ( x  )   yk P , wbfkb fs tbg ka`pdg`get am  SV ( x  )   yk P , tbg ctb Bgr`ftg kagmmfkfget fs 

 Ogkjusg tbg padyea`fjds jrg artbaiaejd wg kje kjdkudjtg tbg kagmmfkfgets rgqufrgh mar Gq. (:) js< 

 \ ( x)  SV ( x)P   > B >{V ( x)}      c  B c {V ( x)}(8) c  >

  Xbg trjesmar` fs fevgrtfodg, jeh sa wg kje gxprgss tbg rgsudts fe tbg arfifejd uefts am `gjsurg`get. Xa crfig tbg vjrfjodg am fetgrgst, \(x), tbg Bgr`ftg  padyea`fjds jrg crfigh sgpjrjtgdy jeh tbgfr gstf`jtgs jrg su``gh ta ifvg tbg hfsluektfvg crfifei gstf`jtar< c 

  c   \  HC  ( x)   >  : B  : {V (  x)}   ? B ? {V ( x)}  ˍ

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 [a mra` e hjtj pafets (x:,… xe) fe tbg egfiboarbaah am x> wbgrg wg wjet je gstf`jtg wg gstf`jtg tbg Bgr`ftg padyea`fjds oy

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  (:;) Xbg kagmmfkfget mar c0> fs tbg hfstrfoutfae muektfae am V(x) jt yk , f.g.,

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Xbg fehfkjtar kje og gxprgssgh fe tgr`s am tbg ku`udjtfvg hfstrfoutfae jeh tbg Bgr`ftg padyea`fjds< 

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  (:7) Fts hfsluektfvg crfifei gstf`jtg fs aotjfegh oy

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wgfibts, wbfkb jrg maueh oy sadvfei tbg sf`pdg crfifei gqujtfaes< e

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??2  Hjyj / F rjefje rjefje L aurejd aurejd am G jrtb jrtb [ kfgekgs, kfgekgs, ]ad. ::, Ea. ;, ?>:6, ??=-?;=.

Fe tbfs festjekg, wg jrg fetgrgstgh fe tbg praojofdfty am gxkgss, jeh sa wg ka`putg  D

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  (:9) ;. Kjsg stuhy Xbg Kbgbgdcurgb hgpasft fs dakjtgh fe tbg EgbojehjeCbjsb zaeg (gjstgre Frje) ogtwgge tbg Jmibje odakc ta tbg gjst, tbg Egb Mjudt ta tbg wgst, jeh tbg Ojsbjijrh Mjudt ta tbg sautb ([takcdfe :699) (Mfi :). Xbfs zaeg, jdsa ceawe js tbg [fstje suturg zaeg am gjstgre Frje (Xfrrud gt jd. :62;), rgprgsgets j ejrraw, sbart-dfvgh strfp am akgjefk dftbaspbgrg tbjt wjs kaesu`gh fe tbg [geeaefje jeh ^jdgaigeg jeh, fe pjrt, aohuktgh hurfei tbg Gakgeg kaetfegetjd kaddfsfae (Xfrrud gt jd. :62;). Hfcgs jeh djvjs mra` tbg Kbgbgdcurgb apbfadftfk `ædjeig jrg pdjifakdjsg-pbyrfk ojsjdts wftb kbg`fkjd ka`pasftfaes tbjt fehfkjtg tbjt tbgy wgrg `fh-akgje rfhig jeh `jrifejd ojsfe tbadgfftgs (Hgs`aes jeh Ogkkjduvj :62;).

Xbg E-[ ‛ trgehfei trgehfei Duecj-@jdusje @auetjfe _jeig fs tbg bfibgst fe tbg rgifae, wftb Cub-g-Duecj (?,;>>-` gdgvjtfae) ka`prfsfei `gtjturofhftgs (Mfi ?) jeh Cub-g@jdusje (?,8?7-` gdgvjtfae) ka`prfsfei ijoora (@jjeflau gt jd. (?>:?). Xbg stuhy jrgj fs hfvfhgh feta tbrgg dftbatypgs ae tbg ojsfs am rakc ka`paegets< fiegaus rakcs (yaueigr tbje apbfadftgs), sghf`getjry rakcs, jeh tbg apbfadftfk `ædjeig (Mfi ?). Gjkb am tbgsg dftbatypgs fs hgskrfogh ogdaw, rgdjtfvg ta fts jig (f.g., mra` tbg adhgst ta tbg yaueigst ueft). [ghf`getjry djygrs, wbfkb kaesfst am irgywjkcg, sbjdg, jeh df`gstaeg, jrg tfibtdy madhgh, stggpdy hfppfei, jeh mjudtgh (@jjeflau gt jd. ?>:?). Krgtjkgaus turofhftgs bjvg mjudtgh kaetjkts wftb tbg apbfadftfk ka`pdgx jeh jrg ka`pasgh am pbyddftg jeh s`jdd dgesgs am `jrodg (@jjeflau gt jd. ?>:?). ^jdgakgeg turofhftgs jrg ka`pasgh am sbjdg jeh sjehstaeg wftb rjrg df`gstaeg djygrs (Mfi ?). Gakgeg turofhftgs jrg up ta : c` tbfkc jeh wfhgsprgjh. Fe `gtj`arpbasgh turofhftgs, tbg ojsjd kaeida`grjtg fs tbg adhgst ueft.

Mfi :. Igadaifk `jp am tbg Kbgbgdcurgb arg hgpasft (@jjeflau gt jd. ?>>2).

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??6  Hjyj / F rjefje rjefje L aurejd aurejd am G jrtb jrtb [ kfgekgs, kfgekgs, ]ad. ::, Ea. ;, ?>:6, ??=-?;=.

Mfi ?. Oargbadg dakjtfae `jp am Kbgdcurgb hgpasft

Xbg wgstgre turofhftgs, wbfkb jrg jdtgrgh, bast tbg Kbgbgdcurgb arg hgpasfts (@jjeflau gt jd. ?>:?). [gvgrjd irjeftafh stakcs jeh hfcgs fetruhgh tbg sghf`getjry sgqugekg wbgrg tbgy jrg arfgetgh pjrjddgd ta tbg `jlar EY[G ‛   trgehfei mjudt sgt (Mfi ?). ^dutaefk rakcs krap aut `astdy ta tbg wgst am tbg Kbgbgdcurgb Mjudt fe tbg Duecj-@jdusje @auetjfe _jeig (]jdgb jeh [jgghf :626). Fetrusfvg oahfgs kaesfst am qujrtz`aezahfarftg jeh irjeahfarftg jt tbg Kbgbgdcurgb hgpasft. Gxpasurgs am rakc fe tbg vfkfefty am tbg Kbgbgdcurgb hgpasft jrg kaetraddgh oy `jlar E-[ ‛   jeh  EY-[G ‛ trgehfei trgehfei mjudts, ojsgh ae jfr pbata dfegj`gets, surmjkg trjkgs, jeh ammsgts am igadaifk mgjturgs (@jjeflau gt jd. ?>:?).

hada`ftg, jecgrftg, sfhgrftg, kbjdkapyrftg, spbjdgrftg,  pyrftg, ijdgej, sgdgefje ijdgej, `jrkjsftg, egvscft egvscftg, g, jeh  pjrjiujejlujtftg. Xbg ijeiug `fegrjds jrg ha`fejtgh oy qujrtz jeh vjrfaus kjroaejtgs, dakjddy jssakfjtgh wftb kbdarftg. Bypaigeg jdtgrjtfae kaesfsts am sfdfkfmfkjtfae, kjroaejtfzjtfae (jecgrftg, `jiegsftg, sfhgrftg, jeh hada`ftg), kbdarftfzjtfae, cjadfeftfzjtfae, sudmfhjtfae, jeh, dgss ka``aedy, sgrfkftfzjtfae (@jjeflau ?>>9, @jjeflau gt jd. ?>:?).

8. [tjtfstfkjd jejdysfs ae hjtj Xbfs hgpasft wjs gxpdargh prfekfpjddy oy 82 oargbadgs (Mfi ?) wftb tatjd ?69= ` am hrfddfei. Fe igegrjd, tbg hrfddfei irfh fs frrgiudjr3 tbg hfstjekg ogtwgge tbg twa

Xbg Kbgbgdcurgb hgpasft ka`prfsgs eu`graus dgesgs jeh vgfes. Xbgrg wgrg twa stjigs am `fegrjdfzjtfae, tbg mfrst am wbfkb kaesfsts am `gtjddfk `fegrjdfzjtfae kaekgetrjtgh jdaei tbg orfttdg, mfegdy mrjkturgh pjrts am

 oargbadgs vjrfgs mra` 7>` ta :>>` (Mfi ?). Oargbadg sj`pdgs wgrg jejdyzgh oy FK^@[ `gtbah. Xbgy wgrg am uegqujd dgeitb. Ft fs vgry f`partjet fe gstf`jtfae ta warc wftb gqujd suppart sj`pdgs jeh tbgrgmarg tbg hjtj

tbg oghs am sjehstaeg, sfdtstaeg, jeh sbjdg. Xbg sgkaeh stjig am `fegrjdfzjtfae mar`gh jdaei mrjkturgs tbjt krasskut sjehstaeg, sfdtstaeg, jeh sbjdg, hfspdjkfei tbg`  oy sgvgrjd `fddf`gtgrs. Xbg mfrst stjig fekduhgs qujrtz, kjdkftg, hada`ftg, jecgrftg, sfhgrftg, fd`geftg, rutfdg, `adyohgeftg, pyrrbatftg, jrsgeapyrftg, pyrftg, jeh kbjdkapyrftg. Xbg sgkaeh stjig kaesfsts am qujrtz,

wgrg ka`pasftgh ta gqujd dgeitbs (Hjyj ?>:?3 Jmzjd gt jd ?>:;3 Hjyj ?>:7j jeh o3 Hjyj jeh Ogljrf ?>:73 Hjyj jeh Bassgfefejsjo ?>:6). [tjtfstfkjd stuhfgs wgrg pgrmar`gh ae tbg rjw hjtj, jeh tbg rgsudts jrg sbawe fe Mfiurg ; mar Ku (%) kaekgetrjtfae.

Mfi ;. Bfstairj` am tbg hjtj mar Kbgdcurgb hgpasft 

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?;>  Hjyj / F rjefje rjefje L aurejd aurejd am G jrtb jrtb [ kfgekgs, kfgekgs, ]ad. ::, Ea. ;, ?>:6, ??=-?;=.

Mfiurg 8 jdsa sbaws tbg bfstairj` am ear`jd trjesmar`gh hjtj. Daijrftb`fk trjesmar`jtfae wjs usgh mar ear`jdfzfei tbg rjw hjtj. [tjtfstfkjd jejdysfs wjs haeg usfei tbg I[DFO [amtwjrg (Hgutskb jeh Lauregd :662).

kaesfsts am j spbgrfkjd `ahgd wftb sfdd :.?> jeh rjeig :8>` pdus j euiigt am >.8= (Mfi 7). Xbfs `ahgd wjs rgqufrgh sfekg HC gstf`jtfae wfdd og ojsgh ae ft.

=. Gstf`jtfae oy hfsluektfvg crfifei Xa gstf`jtg tbg Ku kaekgetrjtfae, tbg hfsluektfvg crfifei `gtbah wjs usgh ta rgkgfvg gstf`jtgs jt pafets

7. ]jrfairj` @ahgddfei Jmtgr ka`putfei jeh hrjwfei tbg gxpgrf`getjd vjrfairj`, j tbgargtfkjd `ahgd wjs mfttgh ae rgsudtgh gxpgrf`getjd vjrfairj`. Xbfs wjs haeg oy j sgrfgs am kahgs fe @JXDJO samtwjrg. Xbg gxpgrf`getjd vjrfairj`, λ(b) wjs mfttgh ta j tb tbgargtfkjd gargtfkjd `ahgd ta mfeh tbrgg pjrj`gtgrs, sukb js tbg euiigt (k>), tbg sfdd (k) jeh tbg rjeig rjeig (j). Jmtgr tbg gxpgrf`getjd vjrfairj` wj wjss kjdkudjtgh mra` tbg rgiudjrfzgh hjtj, j egstgh strukturg

ae j irfh ?>` x ?>` x :?.7`. Xbgsg pafets `jy og tjcge js tbg kgetgr-pafets am kuogs am hf`gesfae ?>` x ?>`x :?.7`. Xbg gstf`jtfae jeh ;-H `ahgdfei prakgss ka``gekgh mra` tbg gdgvjtfae am =7>` joavg tbg sgj dgvgd ta :?7>` joavg tbg sgj dgvgd fe tbg `feg. Mar tbg jppdfkjtfae am HC, @JXDJO [amtwjrg bjs ogge usgh. Mfiurg = jeh 9 sbaw gstf`jtgs jeh crfifei grrars am Ku kaekgetrjtfae fe hfmmgrget gdgvjtfaes ka`putgh oy HC.

wftb j euiigt jeh j spbgrfkjd vjrfairj` wjs usgh. Ft

Mfi 8. Xrjesmar`gh bfstairj` am tbg hjtj mar Kbgdcurgb hgpasft

Mfi 7. Gxpgrf`getjd a`efhfrgktfaejd vjrfairj` jeh fts mfttgh `ahgd fe Kbgdcurgb hgpasft

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?;:  Hjyj / F rjefje rjefje L aurejd aurejd am G jrtb jrtb [ kfgekgs, kfgekgs, ]ad. ::, Ea. ;, ?>:6, ??=-?;=.

Mfi =. Gstf`jtgs am Ku kaekgetrjtfae oy hfsluektfvg crfifei fe hfmmgrget gdgvjtfaes (J0:;>>`, O0:8>>`, K0:7>>`, H0:=>>` joavg tbg sgj dgvgd) fe Kbgbgdcurgb hgpasft

Mfiurgs 2 jeh 6 sbaw tbg tbrgg-hf`gesfaejd `ahgd am HC gstf`jtgs jeh HC grrars am Ku kaekgetrjtfae fe Kbgdcurgb hgpasft. Ojsgh ae tbg hfsluektfvg crfifei `gtbah, tbg gxtrg`gdy jeh bfibdy Ku kaekgetrjtfae bjppgegh fe tbg eartbgre jeh kgetrjd pjrts am tbg Kbgdcurgb hgpasft (Mfi 2).   Xbg gstf`jtg am tbg irjhg jt je uesj`pdgh dakjtfae fs eat geauib. Ft fs egkgssjry ta aotjfe je gstf`jtg am tbg  praojofdfty tbjt gxkgghs j ifvge tbrgsbadh, sjy >.7 %.

Mfiurg :> sbaws praojofdftfgs ta gxkggh tbg kbasge tbrgsbadh vjdug am >.7% fe hfmmgrget gdgvjtfaes ka`putgh oy HC. Mfiurg :: jdsa sbaws sbaws tbg tbrgg hf`gesfaejd `ahgd am praojofdftfgs ta gxkggh tbg kbasge tbrgsbadh vjdug am >.7%. Mfejddy, vjdfhjtfae am tbg hfsluektfvg crfifei fs kjrrfgh aut oy usfei krassvjdfhjtfae. Krass-vjdfhjtfae usgs jdd tbg hjtj ta gstf`jtg tbg trgeh jeh jutakarrgdjtfae `ahgds. Ft rg`avgs gjkb hjtj dakjtfae aeg jt j tf`g jeh prghfkts tbg jssakfjtgh

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 rkbfvg am [FH

?;?  Hjyj / F rjefje rjefje L aurejd aurejd am G jrtb jrtb [ kfgekgs, kfgekgs, ]ad. ::, Ea. ;, ?>:6, ??=-?;=.

hjtj vjdug. _gsudts sbaw tbjt tbg karrgdjtfae ogtwgge tbg gstf`jtgh vjdugs jeh tbg rgjd vjdugs fs =;.8% (Mfi :?). Fm wg wfsb ta djogd tbg strgeitb am tbg karrgdjtfae, >>.:6 fs rgijrhgh js vgry wgjc, >.?->.;6 js wgjc, >.8>>.76 js `ahgrjtg, >.=->.96 js straei jeh >.2-: js vgry

straei karrgdjtfae (Bjssjefpjc jeh [bjrjmjhhfe ?>>:, ]urjd ?>:8). Jkkarhfei ta tbg joavg kdjssfmfkjtfae, tbg karrgdjtfae ogtwgge tbg rgjd vjdugs jeh tbg gstf`jtgh vjdug fe tbfs stuhy fs straei.

Mfi 9. Hfsluektfvg crfifei grrars am Ku kaekgetrjtfae fe hfmmgrget gdgvjtfaes (J0:;>>`, O0:8>>`, K0:7>>`, H0:=>>` joavg tbg sgj dgvgd) fe Kbgbgdcurgb hgpasft

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 rkbfvg am [FH

?;;  Hjyj / F rjefje rjefje L aurejd aurejd am G jrtb jrtb [ kfgekgs, kfgekgs, ]ad. ::, Ea. ;, ?>:6, ??=-?;=.

Mfi 2. ;H `ahgd am Gstf`jtgs am Ku kaekgetrjtfae oy hfsluektfvg crfifei

Mfi 6. ;H `ahgd am hfsluektfvg crfifei vjrfjekg am Ku kaekgetrjtfae

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 rkbfvg am [FH

?;8  Hjyj / F rjefje rjefje L aurejd aurejd am G jrtb jrtb [ kfgekgs, kfgekgs, ]ad. ::, Ea. ;, ?>:6, ??=-?;=.