Suri1 Ghqlv Jurpe Wkh h {dp lv e hwzhhq 3;=43dp Prqgd / Qryhpe hu </ 4<<; 3<=83dp1 rnv dqg ohfwxuh qrwhv duh qrw doorzhg1 Rqh grxeoh0 vlgh g vkhhw ri s huvrqdo qrwhv zulwwhq uhdvrqdeo odujh lv doorzhg1 Wkh uh duh 8 lqghs hqghqw txh vwlrqv1 Gr qrw olqh xs htxdwlrqv zlwkrxw h{sodqdwlrq= Qr rwkhuzlvh vsh flhg,1 zulwh rxu qdph dw wkh wrs ri hdfk hdfk txh vwlrq lq wkh f ruuhvsrqglqj vsdfh s wkh sdfndjh vwdsohg wrjhwkhu Li rx qlvk e hiruh 3<=68dp/ rx fdq kdqg lq rxu h{dp dqg ohdyh wkh ur rp QD PH = 4 P1L1W1 Idoo 4<<; Vordq Vfkrro ri Pdqdjhphqw 481748 PLGWHUP 5 Vhfwlrq E dqg Er Qr Srlqwv +xqohvv H{sodqdwlrqv/ Sohdvh/ sdjh QRZ$ Dqvzhu Nhh Wr dyrlg fkdrv dqg hqvxuh htxlw dprqj wkh vwxghqwv= Li rx qlvk diwhu 3<=68dp/ sohdvh VWD\ VHDWHG XQWLO \RXU H[DP LV FROOHFWHG DW \RXU GHVN Rqfh rxu h{dp lv froohfwhg/ sohdvh ohdyh wkh urrp lq vlohqfh JRRG OXFN$ Txhvwlrq 4 +53 swv, Txhvwlrq 5 +53 swv, Txhvwlrq 6 +53 swv, Txhvwlrq 7 +53 swv, Txhvwlrq 8 +53 swv, Wrwdo +433 swv,
srlqwv` Qr h{sodqdwlrqv qhh ghg1 Flufoh rqh d txhvwlrq rqo li rx f lufoh doo fruuh fw dqvzhuv1 41 Zklfk ri wkh iroorzlqj vwdwhphqwv duh fruuhfwb uv s hu txhvwlrq1 \rx zloo jhw f uhglw iru +d, Wkh uhwxuqv ri vwr fn D dqg d sxw rq vwr fn D duh dozd v s rvlwlyho fruuhodwhg +e, Wkh uhwxuqv ri vwr fn D dqg d sxw rq vwr fn D duh dozd v qh jdwlyho f ruuhodwh g +f, Wkh uhwxuqv ri vwr fn D dqg d fdoo rq vwr fn D duh dozd v s rvlwlyho f ruuhodwh g +g, Wkh uhwxuqv ri vwr fn D dqg d fdoo rq vwr fn D duh dozd v qhjdwlyho fruuhodwhg +h, Qrqh ri wkh de ryh 51 Vxs s rv h w kd w l qy h v wruv f d q i ru p s ru w irolrv zlwk rqo wzr ulvn dvvhwv wkh uh wxuq ri zklfk duh qrw s huihfwo srvlwlyho ru qhjdwlyho fruuhodwhg1 Wkhuh lv qr ulvnohvv dvvhw1 Zklfk ri wkh iroorzlqj vwdwhph qwv duh fruuhfw df fruglqj wr Rswlpdo Sruw irolr Wkhru B +d, Wkh uhodwlyh zhljkwv rq D dqg E duh wkh vdph iru doo lqyhvwruv +e, Wkh uhodwlyh zhljkwv sxw e dq lqyhvwru rq D dqg E ghs hqg rq khu ulvn dyhuvlrq +f, Dq sruwirolr ri D dqg E lv rq wkh Sruwirolr Iurqwlh u +g, Dq sruwirolr ri D dqg E lv rq wkh H!flhqw Sruwirolr Iurqwlhu +h, Qrqh ri wkh de ryh 61 Vxs s rv h wk d w l qy h v wruv f d q i ru p s ru w irolrv z lwk wkh ulvnohvv dvvhw dqg rqo wzr ulvn dvvh wv wkh uhwxuq ri zklf k duh qrw s huihfwo s rvlwlyho ru qhjdwlyho fruuhodwhg1 Zklfk ri wkh iroorz lqj vwdwhphqwv duh fruuhfw dffruglqj wr Rswlpdo Sruwirolr Wkhru B +d, Wkh uhodwlyh zhljkwv rq D dqg E duh wkh vdph iru doo lqyhvwruv +e, Wkh uhodwlyh zhljkwv sxw e dq lqyhvwru rq D dqg E ghs hqg rq khu ulvn dyhuvlrq +f, Dq sruwirolr ri D dqg E lv rq wkh Sruwirolr Iurqwlh u +g, Dq sruwirolr ri D dqg E lv rq wkh H!flhqw Sruwirolr Iurqwlhu +h, Qrqh ri wkh de ryh 71 Zklfk ri wkh iroorzlqj vwdwhphqwv duh fruuhfwb +d, Htxlw lv jhqhudoo mxqlru zlwk uhvs hfw wr ghew +e, Htxlw lv jhqhudoo vhqlru zlwk uhvs hfw wr ghew +f, Wkh Sxw0 fdoo sdulw uhodwlrq krogv iru Hxurs hdq dqg Dphulf dq rswlrqv +g, Sxw fdoo sdul w k r og v r q o iru Dphulfdq rswlrqv +h, Qrqh ri wkh de ryh QD PH = 5 Txhvwlrq 4 ^53 wkh ru vhyhudo dqvzh
srlqwv` Vwd wh 4 5 6 Suredelolw 4@6 Dvvhw D*v uh wxuq 43( Dvvhw E*v uh wxuq 43( duh wkh h {sh fwhg uhwxuqv dqg wkh yduldqfh0fryduldqfh pdwul{ ri dvvhwv D dqg EB QD PH = 6 Txhvwlrq 5 ^53 4@6 4@6 ;( 9( 7( :( d, Zkdw
^Txhvwlrq 51d1 f rqwlqxhg` QD PH = 7
rx lqyh vw doo rxu zhdowk lq wkh s ruwirolr ri dvvh wv D dqg E zlwk h{s hfwhg uh wxuq zr xo g1 hv/ h {sodlq zk 1 Li qr/ h {sodlq zk 1 Li pd e h/ h{sodlq xqghu zklfk frqglwlrqv rx QD PH = 8 e, Zrxog :=8(B Li
srlqwv` [\] Lqf1 kdv mxvw e hh q irxqghg wrgd +Mdq xdu 4 / 4< < <, 1 Lw v ex vl qh vv zloo jhqhudwh d s hushwxdo '43 hduqlqjv0s hu0vkduh dw hdu h qg1 Wkdw lv/ wkh hduqlqjv zloo uvw dffuxh rq Mdqxdu 4/ 5333/ wkhq rq Mdqxdu 4/ 5334/ h wf1 [\]*v pdunhw fdslwdol}dwlrq udwh lv dqg zloo uhpdlq f rqvwdqw dw 43(1 [\] lv frpplwwhg wr sd lqj d frqvwdqw glylghqg G lq s hus hwxlw dw wkh hqg ri hyhu t xduwhu1 Wkdw lv/ wkh glylgh qg zloo uvw e h sdlg rq Dsulo 4/ 4<<</ wkhq rq Mxo 4/ 4<<</ hwf 1 lv wkh ydoxh ri G B Z kd w lv [\ ]* v S YJRB QD PH = 9 Txhvwlrq 6 ^53 dqqxdo Pruhryhu/ d, Zkdw
rvh lqvwhdg wkdw [\] ghf lghg qrw wr sd dq glylgh qg iru wkh qh{w 8 hduv +l1h1/ xqwlo dqg lqfoxglqj Mdq xdu 4 / 5337, dqg wkhq wr sd d uvw glylghqg ri ': Dsulo 4/ 5337 dqg ohw lw jurz dw d udwh j hyh u txduwhu lq s hus hwxlw 1 Zkdw zrxog j kdyh wr e hb Zklfk glylgh qg s rolf lv suhihuuhg e [\]*v vkduhkrogh uvb QD PH = : e, Vxss rq
srlqwv` Wkh dqqxdo ulvn0iuhh udwh lv dw dw 43(1 Lqf 1 kdv 833> idfh ydoxh dqg d 50 hdu pdwxulw 1 Wkh sur f hvv jryhuqlqj wkh ydoxh ri [\]*v dvvhwv ryhu wkh qh{w wzr hduv lv ghvfule hg e wkh iroorzlqj elqrpldo wuhh lq zklfk hdfk s hulr g uh suh vhqwv rqh hdu1 lq wkh eodqnv lq wkh iroorzlqj wuh h gh vfulelqj wkh sur fh vv jryhuqlqj wkh sulfh ri rqh vkduh ri [\] +jlyh wkh ydoxhv ri V / VÄ V @ V_ VÄÄ g V QD PH = ; Txhvwlrq 7 ^53 [\] 333 vkduhv1 Lwv ghew kdv d '73P [ÄÄ @ '445=8P [Ä @ ':8P [ @'83P [Ä_ @ '6:=8P [_ @'58P [ @'45=8P d, Iloo / / / VÄ_ dq,1 VÄÄ @ === VÄ @ === === VÄ_ @ === V_ @ === V @ ===
^Txhvwlrq 71d1 f rqwlqxhg` QD PH = <
duh wkh suhpld rq d Hxurs hdq dqg dq Dphulf dq sxw rswlrq rq rqh vkduh ri [\] QD PH = 43 e, Zkdw zlwk d 50 hdu pdwxulw dqg vwulnh sulfh '83B
^Txhvwlrq 71e1 frqwlqxhg` QD PH = 44
srlqwv` Qr h{sodqdwlrqv duh qhh ghg wr dqvzhu wkh iroorzlqj txhvwlrqv1 Qr sduwldo fuhglw zloo e h jlyhq1 Lq wkh iroorzlqj txhvwlrqv/ wkh xqgh uo lqj dvvhw lv rqh vkduh ri [\] Lqf 1*v vwr fn 1 iroorz lqj gldjudp uhsuhvhqwv d s ruwirolr*v sd r 5 prqwkv iurp wr gd ghs hqglqj rq [\]*v vwr f n sulfh dw wkdw gdwh1 Gh vfuleh dv suhflvh o dv s rvvleoh rqh vxf k s ruwirolr1 QD PH = 45 Txhvwlrq 8 ^53 d, Wkh
iroorzlqj gldjudp uhsuhvh qwv d sruwirolr*v sd r 5 prq wk v i u rp w r gd gh s h q gl q j r q [\]*v vwr f n sulfh dw wkdw gdwh1 Gh vfuleh dv suhflvh o dv s rvvleoh rqh vxf k s ruwirolr1 QD PH = 46 e, Wkh
rq d judsk wkh sd r 6 prqwkv iurp wr gd ri wkh s ruwirolr frpelqlqj= h [\ ] v kduh Lqglf dwh wkh fr ruglqdwhv ri hdfk s rlqw dw zklfk wkh judsk*v vorsh fkdqjh v1 QD PH = 47 f, Uhsuhvhqw Rqh orqj Hxursh dq fdoo rq rqh [\] v kduh z l wk 60 prq wk pd wx ul w d q g v wu l nh '73 Rq h vk ru w H xu rs h d q sx w r q rq h [\ ] vkdu h z l wk 6 0 pr qwk pd wx ul w dq g vwu l nh '73 Rq
rq d judsk wkh sd r 6 prqwkv iurp wr gd ri wkh s ruwirolr frpelqlqj= h [\ ] v kduh Lqglf dwh wkh fr ruglqdwhv ri hdfk s rlqw dw zklfk wkh judsk*v vorsh fkdqjh v1 QD PH = 48 g, Uhsuhvhqw Rqh ulvniuh h e rqg zlwk 60prqwk pdwxulw dqg idfh ydoxh '43 Rqh vkruw H xurs hdq fdoo rq rqh [\] vkduh zlwk 60prqwk pdwxulw dqg vwulnh '73 W zr v kruw H xursh dq fdoov rq rqh [\] vkduh/ zlwk 60prqwk pdwxulw dqg vwulnh ':3 Rq