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Page 1: OL +i} L?t ˇL? ih}ifm oldweb/BlineMacro/howregions.pdfNV/ PL/ PQ/ PR/ QG/ QH/ RK/ VG/ ZL1 Vwdwhv lq wkh Zhvw duh= D]/ FD/ FR/ LG/ PW/ QY/ QP/ RU/ XW/ ZD/ Z\1 5 Vhh/ h1j1/ wkh Kdqgerrn

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Page 2: OL +i} L?t ˇL? ih}ifm oldweb/BlineMacro/howregions.pdfNV/ PL/ PQ/ PR/ QG/ QH/ RK/ VG/ ZL1 Vwdwhv lq wkh Zhvw duh= D]/ FD/ FR/ LG/ PW/ QY/ QP/ RU/ XW/ ZD/ Z\1 5 Vhh/ h1j1/ wkh Kdqgerrn

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of6|/ ofe|/ Os|/ O6|/ Oe|/ dqg ��|1 Dvvxph wkdw doo h{rjhqrxv yduldeohv hyroyh dffruglqj wr wlph0lqyduldqw

uhfxuvlyh odzv ri prwlrq1 Wkh vrfldo sodqqhu*v sureohp fdq eh vroyhg dv d g|qdplf surjudp1 Ohw d

kdw ghqrwh d ydoxh ri d yduldeoh lq wkh suhylrxv shulrg1 Wkh vwdwh yduldeohv frqvlvw ri Ds / D6/ N/

�/ aOs / dqg aO6. aOe1 Wkh vwdwlrqdu| uhfxuvlyh vroxwlrq wr wkh h�flhqw doorfdwlrq sureohp frqvlvwv ri

wlph0lqyduldqw srolf| ixqfwlrqv wkdw duh ixqfwlrqv ri wkh vwdwh ri wkh v|vwhp1 Wkh srolf| ixqfwlrqv

duh iru fs / f6/ N�/ Ns / N6/ Ws / W6/ ofs / o

f6/ ofe / Os / O6/ Oe/ dqg ��1 Wkh ydoxh ixqfwlrq y dqg srolf|

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ixqfwlrqv pxvw vdwlvi| wkh Ehoopdq htxdwlrq

y+Ds > D6> N> �> aOs > aO6 . aOe, @ pd{ix+fs > f6, . �y+D�

s > D�

6>N �> ��> Os > O6 . Oe,j>

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dssursuldwh ~ wr +5,0+9,/ +4<,0+56,1 Vwdqgdug wkhruhpv rq vroxwlrqv wr frqfdyh g|qdplf surjudp0

plqj sureohpv fdq eh xvhg wr suryh wkh h{lvwhqfh dqg xqltxhqhvv ri d vroxwlrq wr wklv sureohp1

E| frpsxwlqj �uvw0rughu dqg hqyhorsh frqglwlrqv wkh vroxwlrq lv vkrzq wr vdwlvi| +57,/

x�+fs > f6,I�+Ws > Os > Ns > Ds , @ x2+fs > f6,P�+W6> O6> N6> D6,> +5<,

dqg

x�+fs > f6,I�+Ws > Os > Ns > Ds , @ x2+fs > f6,P�+W6> O6> N6> D6,= +63,

Ghqrwh e| *s wkh pxowlsolhu iru ht1 +54, dqg ghqrwh e| *6 wkh pxowlsolhu iru ht1 +55,> erwk pxo0

wlsolhuv duh ixqfwlrqv ri wkh vwdwh yhfwru +Ds > D6>N> �> aOs > aO6 . aOe,1 Wkhvh ixqfwlrqv pxvw vdwlvi|

wkh wzr htxdwlrqv=

*s @ x�+fs > f6,I2+Ws > Os > Ns > Ds , . ��*�s > +64,

*6 @ x2+fs > f6,P2+W6> O6>N6> D6, . ��*�6= +65,

Qrwh wkdw � hqwhuv wkhvh htxdwlrqv ehfdxvh ri lwv uroh lq ghwhuplqlqj wkh hyroxwlrq ri idup dqg

pdqxidfwxuh zrunhuv ryhu wlph1 Ilqdoo|/ xvlqj wkh Ixqgdphqwdo Wkhruhp ri Fdofxoxv/ wkh vroxwlrq

pxvw dovr vdwlvi| wkh htxdwlrq

�� @4

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x2+fs > f6,P2+W6> O6>N6> D6,= +66,

D qhfhvvdu| dqg vx�flhqw frqglwlrq iru d vroxwlrq wr eh d vrfldo rswlpxp lv li wkh fkrlfhv fs / f6/

N/ Ns / N6/ Ws / W6/ Os / O6/ Oe/ dqg �� vdwlvi| +5,0+9,/ +4<,0+57,/ +BB,0+66,1

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doorfdwlrqv lq d frpshwlwlyh htxloleulxp pxvw vdwlvi| ht1 +5<, dqg frpelqh htv1 +<,/ +46,/ dqg +49,

wr vkrz wkdw wkh doorfdwlrqv lq d frpshwlwlyh htxloleulxp pxvw vdwlvi| ht1 +63,1 Dovr/ qrwh wkdw wkh

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dv wkh odwwhu uhihu wr wkh idup vkduh lq jurvv JGS1 Gdwd= Klvwrulfdo Vwdwlvwlfv ri wkh Xqlwhg Vwdwhv/

Vhulhv I458 dqg I45:> Pdgglvrq +4<<4,/ Wdeoh 51611

�= Zh dvvxph orj xwlolw|/ zklfk lpsolhv � @ 4=31

�= Ghqrwh wkh uhdo uhwxuq wr fdslwdo e| U/ dqg ghqrwh wkh uhdo shu0fdslwd frqvxpswlrq

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Vhfxulw| Sulfhv1

�= �A / �u/ �A / �u duh fkrvhq dv iroorzv1 Mrujhqvhq dqg Jroors uhsruw gdwd rq wkh uhodwlyh

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qrq0idup vhfwru1 Gdwd= Mrujhqvrq dqg Jroors/ lqihuuhg iurp Wdeohv <15 dqg <17/ dqg EOV/ Wdeohv

QIE8d dqg I8d1

�= Fkulvwhqvhq dqg Mrujhqvrq/ flwlqj wkh Fdslwdo Vwrfn Vwxg|/ uhsruw wkh iroorzlqj dqqxdo

ghsuhfldwlrq udwhv +Wdeoh 8144, dqg uhodwlyh ydoxhv ri wkh fdslwdo vwrfn +Wdeoh 8145,= Frqvxphu

Gxudeohv +ghsu1 @ 1533/ zhljkw @ 154,/ Qrquhvlghqwldo Vwuxfwxuhv +ghsu1 @ 1389/ zhljkw @ 155,/

Surgxfhu Gxudeohv +ghsu1 @ 146;/ zhljkw @ 153,/ dqg Uhvlghqwldo Vwuxfwxuhv +ghsu1 @ 136</ zhljkw

@ 16:,1 Wkh zhljkwhg dyhudjh ghsuhfldwlrq udwh lv 13<971 Wklv lpsolhv d ydoxh ri � @ =692ghfdgh1

Gdwd= Fkulvwhqvhq dqg Mrujhqvrq/ Wdeohv 8144 dqg 81451

j6= Dffruglqj wr Mrujhqvrq dqg Jroors/ wkh dyhudjh wrwdo idfwru surgxfwlylw| +wis, jurzwk

udwh lq wkh qrq0idup vhfwru iurp 4<7:0;8 zdv 133;42|hdu +wklv ydoxh lv qrw dgmxvwhg iru wkh fkdqjlqj

txdolw| ri lqsxwv> dgmxvwhg iru txdolw| wklv hvwlpdwh lv 13377,1 Dv uhsruwhg lq wkh Klvwrulfdo Vwdwlvwlfv

ri wkh X1V1/ wkh dyhudjh wis jurzwk udwh lq wkh qrq0idup vhfwru iurp 4<5< wr 4<7; zdv 13494/ dqg

wkh dyhudjh wis jurzwk udwh iurp 4;;< wr 4<5< zdv 134961 Wkh hduolhu wis jurzwk udwhv duh odujhu

wkdq wkh odwhu rqhv/ exw dv dujxhg e| Mrujhqvrq dqg Jroors/ hvwlpdwhv vxfk dv wkhvh ryhuvwdwh

wkh wis jurzwk udwh +gxh wr ydulrxv huuruv ri djjuhjdwlrq,1 Jhwwlqj d uhdvrqdeo| dffxudwh hvwlpdwh

ri dyhudjh wis jurzwk iurp 4;;3 wr 4<<3 lv vrphzkdw fkdoohqjlqj1 Lq wkh hqg zh fkrvh wr xvh

wkh Mrujhqvrq0Jroors hvwlpdwh ri 133;4 iru wkh hqwluh 4;;304<<3 shulrg/ zklfk lpsolhv dq dyhudjh

jurzwk udwh ri 13;732ghfdgh +j6 @ =3;73,1 Gdwd= Mrujhqvrq dqg Jroors/ Wdeohv <15 dqg <17/ dqg

Klvwrulfdo Vwdwlvwlfv ri wkh X1V1/ Vhulhv Z;1

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jsf= Dv hvwlpdwhg e| Mrujhqvrq dqg Jroors/ wkh dyhudjh wis jurzwk udwh lq wkh idup vhfwru

iurp 4<7:0;8 zdv 135392|hdu +dv deryh/ wklv qxpehu lv qrw dgmxvwhg iru wkh fkdqjlqj txdolw| ri

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wis jurzwk udwhv,/ dqg lqghhg wkhlu hvwlpdwh lv pxfk kljkhu wkdq wkh hvwlpdwhv ri idup wis jurzwk

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ri idup hpsor|phqw/ zklfk duh kljko| vxvshfw iru wkh hduo| shulrg +vhh iq1 44,1 Lqvwhdg ri wrwdoo|

glvfrxqwlqj wkh hduolhu hvwlpdwhv ri wis jurzwk/ zh wrrn wkhp lqwr dffrxqw dqg fkrvh d idup wis

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wkh qrq0idup wis jurzwk udwh,1 Gdwd= Jroors dqg Mrujhqvrq/ Wdeohv <15 dqg <17/ dqg wkh Klvwrulfdo

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�f= Vhw wr pdwfk wkh idup2qrq0idup zdjh udwlr lq 4;;3/ zklfk lv =531 Gdwd= Wdeoh 41

��= Vhw wr pdwfk wkh idup2qrq0idup zdjh udwlrq lq 4<;3/ zklfk lv =9<1 Gdwd= Wdeoh 41

�= Wkh h{shfwhg olihwlph ri shrsoh lv 4@+4��,1 Lq wkh gdwd/ wkh olih h{shfwdqf| dw eluwk iru

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dqg khqfh h{shfw wr olyh dqrwkhu 7 ghfdghv1 Wklv lpsolhv d ydoxh ri � @ =:81 Klvwrulfdo Vwdwlvwlfv ri

wkh Xqlwhg Vwdwhv/ Vhulhv E459 dqg E43:> Vwdwlvwlfdo Devwudfw ri wkh Xqlwhg Vwdwhv +4<<:,/ Wdeoh

44:1

Nf= Wkh lqlwldo fdslwdo vwrfn/ Nf/ lv vhw vr wkdw wkh lqlwldo uhwxuq wr fdslwdo htxdov wkh uhwxuq

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4;;3/ zklfk lv =831 Gdwd= Wdeoh 41

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wkh whup lq wkh wklug olqh1 Dxwkruv* fdofxodwlrqv1 Gdwd vrxufhv= +4;;304<83/ vhuylfh lqfrph shu zrunhu, Ohh

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