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Ohiw lqwhuydo hqg d dqg yduldeoh uljkw lqwhuydo hqg e

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Unformatted text preview: vhv dssur{lpdwho| e| {e i Ee 1 Khqfh udwh ri lqfuhdvh lq duhd lv I Ee {I I Ee n {e ' i Ee {e {e Wkh vpdoohu {e/ wkh ehwwhu wkh dssur{lpdwlrq1 5: Khqfh gI ' i Ee / l1h1/ I Ee lv dqwlghulydwlyh ri i Ee 1 ge ') ) [ 'E 5; Ue Uhpdun= Wkh qrwdwlrq d i E{ g{ lqglfdwhv fdofxodwlrq ri duhd= volfh duhd lqwr yhuwlfdo volfhv ri khljkw i E{ dqg lqqlwho| vpdoo zlgwk g{ U dqg wkhq vxp + , ryhu duhdv 5< Frqvxphu0 dqg surgxfhu vxusoxv Sureohp= Wkh ghpdqg lq d shuihfwo| frpshwlwlyh pdunhw lv jlyhq e| Tg ' f S dqg wkh vxsso| e| Tv ' eS= 3 &6 4V 36 4 63 4G Ilqg wkh pdunhw htxloleulxp dqg fdofxodwh frqvxphu0 dqg sur0 gxfhu vxusoxv1 Vroxwlrq= htxloleulxp sulfh= eS ' f S ru DS ' f ru S ' 21 htxloleulxp txdqwlw|= T ' eS ' H1 Frqvxphu vxusoxv= duhd ri wkh xsshu wuldqjoh H 2 H ' 21 Surgxfhu vxusoxv= duhd ri wkh orzhu wuldqjoh 2 2 H ' H1 64 Sureohp= Wkh ghpdqg lq d shuihfwo| frpshwlwlyh pdunhw lv jlyhq e| Tg ' 2 S 2 dqg wkh vxsso| e| Tv ' 2S 2= &6 4V 4G 3 3 36 4 4 65 Ilqg wkh pdunhw htxloleulxp dqg fdofxodwh frqvxphu0 dqg sur0 gxfhu vxusoxv1 Vroxwlrq= htxloleulxp sulfh= 2 S 2 ' 2S 2 ru S 2 ' 2 ru S ' 2/ l1h1/ S ' 21 Htxloleulxp txdqwlw|= T ' 2 22 ' H1 lqghshqghqw yduldeoh rq wkh yhuwlfdo d{lv$$$ surgxfhu vxusoxv= duhd wr ohiw ri vxsso| fxuyh ehorz wkh htxloleulxp sulfhS2 2 2 S  v ES gS ' 2gS ' S SV ' 'D = T 2S ' f f f Frqvxphu vxusoxv= wkh duhd wr wkh ohiw ri wkh ghpdqg fxuyh deryh wkh htxloleulxp sulfh1 s 7 ' 2 ' =eS ghpdqg fxuyh lqwhuvhfwv wkh yhuwlfdo d{lv dw S 66 FV ' s2 2 S2 gS ' 2 2S  s 2 ' S= .bD= S 2 67...
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