sol_ch4

sol_ch4 - .kdswhu 7 Pdwulfhv dqg .orvxuhv ri Uhodwlrqv 714...

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Fkdswhu 7 Pdwulfhv dqg Forvxuhv ri Uhodwlrqv 714 Pdwulfhv 41 +d, d 44 @: / +e, d 56 @< / +f, e 46 @ 7 / +g, e 55 @ 7< / +h, e 57 grhv qrw h{lvw/ +i, f 45 grhv qrw h{lvw/ +j, f 54 @56 1 61 +d, D . E grhv qrw h{lvw/ +e, 8 D @ 5 7 53 48 8 6 8 +f, D 6 G @ 5 7 4: < 4 6 8 / +g, 5 D 9 G @ 5 7 67 4; 5 6 8 > +h, 7 E .: F @ 5 7 58 43 5: 55 49 93 49 6< :4 6 8 81 Khuh d .5 e @8 > 5 d e @3 >f . g @ 7 > dqg f 5 g @4: = Vroylqj zh jhw d @4 >e @5 @6 > dqg g @ : 1 :1 +d, DE @ 4 5 45 49 / +e, ED @ 4 ; 6 49 / +f, DF @ 7 69 / +g, FD grhv qrw h{lvw/ +h, EG @ 3 47 4: 5 5; 6: / +i, D 5 . E 5 @ ;4 3 48 6; <1 +d, DE grhv qrw h{lvw/ +e, EF @ 5 7 43 : 5; 4< 79 64 6 8 / +f, GD grhv qrw h{lvw/ +g, GD 8 grhv qrw h{lvw/ +h, G 5 . H 5 @ 85 7 49 4< / +i, FH . FG @ 5 7 6; 4: 67 4 45 43 6 8 / +j, F + H . G , @ 5 7 6; 4: 67 4 45 43 6 8 1 441 +d, L 6 D @ 5 7 433 343 334 6 8 5 7 65 4 38 3 5: < 6 8 @ 5 7 4 6 8 @ D= Vlploduo|/ DL 6 @ D 1 +e, D . ! $ @ 5 7 4 6 8 . 5 7 333 6 8 @ 5 7 4 6 8 @ D= Vlploduo|/ ! $ . D @ D 1 86
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87 71 Pdwulfhv dqg Forvxuhv ri Uhodwlrqv +f, ! $ E @ 5 7 333 6 8 5 7 45 6 78 9 3<8 6 8 @ 5 7 6 8 @ ! $ = Vlploduo|/ E ! $ @ ! $ 1 461 +d, Wkh vl}h ri F lv 6 6 dqg wkdw ri G lv 5 5 1 +e, Qrz/ F @ DE @ 5 7 3 :5 36 43 37 6 4 7 6 8 dqg G @ ED @ <5 3 53 ; = +l, f 55 @6 / +ll, f 65 @76 / +lll, g 44 @< / +ly, g 54 @ 53 > +y, g 65 grhv qrw h{lvw1 481 DE m @ ^ d lm ` p q 5 9 9 9 7 e 4 m e 5 m 1 1 1 e qm 6 : : : 8 @ 5 9 9 9 7 S d 4 n e nm S d 5 n e nm 1 1 1 S d pn e nm 6 : : : 8 @ 5 9 9 9 7 f 4 m f 5 m 1 1 1 f pm 6 : : : 8 @ F m 4:1 Khuh/ D + E . F , @ 5 7 56 7 7: 3 49 < 6 8 5 7 9 6 3< ;4 4 6 8 @ 5 7 53 98 57 84 :; 7; 6 8 = Dovr DE . DF @ 5 7 55 < 45 8 54 7< 6 8 . 5 7 4; 69 45 79 8: 4 6 8 @ 5 7 53 98 57 84 :; 7; 6 8 = Khqfh/ D + E . F ,@ DE . DF 1 4<1 +d, D +5 D 6 E ,.6 E + D . E , 5 D 5 6 E 5 .7 DE @5 D 5 6 DE .6 E 5 5 D 5 6 E 5 DE @ DE ED= +e, + D . E , 5 + D . E ,+ D E , @ D 5 . DE . . E 5 + D 5 DE . E 5 , @ D 5 . DE . . E 5 + D 5 DE . E 5 ,@5 E 5 .5 DE= 541 Ohw F @ DE dqg G @ 1 Wkhq f lm @ S d ln e nm @3 li l 9 @ m dqg f lm @ S d ln e nm @ d ll e ll iru l @ m 1 Dovr g lm @ S e ln d nm li l 9 @ m dqg g lm @ S e ln d nm @ e ll d ll @ d ll e ll iru l @ m 1Wkx v / f lm @ g lm iru doo l> m 5i 4 > 5 >=== >q j 1 Khqfh/ F @ G 1 561 Qrz D 5 @ 5 7 433 334 6 8 5 7 6 8 @ 5 7 6 8 @ D= Wkxv/ D lv lghpsrwhqw1 581 de 3 f lv lghpsrwhqw li 3 f 3 f @ 3 f > l1h1/ d 5 de . ef 3 f 5 @ 3 f = Wklv lpsolhv wkdw d 5 @ d> de . ef @ e> dqg f 5 @ f= Qrz d 5 @ d lpsolhv wkdw d ru 4 = Vlploduo|/ f 5 @ f lpsolhv wkdw f ru 4 = Vxssrvh d dqg f = Wkhq de . ef @ e lpsolhv wkdw e = Wkxv/ lq wklv fdvh wkh rqo| lghpsrwhqw pdwul{ lv 33 1
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7141 Pdwulfhv 88 Vxssrvh d @3 dqg f @4 = Wkhq wkh htxdwlrq de . ef @ e lv wuxh iru dq| uhdo qxpehu e= Vr lq wklv fdvh lghpsrwhqw pdwulfhv duh ri wkh irup 3 e 34 > zkhuh e lv dq| uhdo qxpehu1 Vxssrvh d dqg f = Wkhq dv lq wkh suhylrxv fdvh/ lghpsrwhqw pdwulfhv duh ri wkh irup 4 e 33 > zkhuh e lv dq| uhdo qxpehu1 Vxssrvh d dqg f = Wkhq de . ef @ e lpsolhv 5 e @ e> l1h1/ e = Wkxv lq wklv fdvh/ wkh rqo| lghpsrwhqw pdwul{ lv 43 = 5:1 Zh suryh wkh uhvxow e| lqgxfwlrq rq p= Edvlv Vwhs= Li p > wkhq D p @ D 4 @ D= Wkxv/ wkh uhvxow lv wuxh iru p = Lqgxfwlyh K|srwkhvlv= Vxssrvh D n @ D iru vrph srvlwlyh lqwhjhu1 Lqgxfwlyh Vwhs= Zh vkrz wkdw D n .4 @ D> zkhuh n 4
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This note was uploaded on 11/11/2009 for the course CSE 2353 taught by Professor Bhanukapoor during the Spring '09 term at SMU.

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sol_ch4 - .kdswhu 7 Pdwulfhv dqg .orvxuhv ri Uhodwlrqv 714...

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