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ISBN 0-321-22816-2

1 2 3 4 5 6 BB 08 07 06 05 04

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KLQWV IRU WHDFKLQJ FDOFXOXV ZLWK DSSOLFDWLRQV = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ={lllSUHWHVWV= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =4DQVZHUV WR SUHWHVWV = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = :ILQDO H[DPLQDWLRQV= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =44DQVZHUV WR ILQDO H[DPLQDWLRQV = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 56VROXWLRQV WR HYHQQXPEHUHG H[HUFLVHV = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 5:FKDSWHU U DOJHEUD UHIHUHQFH

U14 Sro|qrpldov = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 5:U15 Idfwrulqj= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =5;U16 Udwlrqdo H{suhvvlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 5;U17 Htxdwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 63U18 Lqhtxdolwlhv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =65

719 H{srqhqwv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =6:U1: Udglfdov= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =6<FKDSWHU 4 OLQHDU IXQFWLRQV

414 Vorshv dqg Htxdwlrqv ri Olqhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =74

415 Olqhdu Ixqfwlrqv dqg Dssolfdwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 7:

416 Wkh Ohdvw Vtxduhv Olqh = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 7<Fkdswhu 4 Uhylhz H{huflvhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 87H{whqghg Dssolfdwlrq= Xvlqj H{wudsrodwlrq wr Suhglfw Olih H{shfwdqf| = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 8:

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514 Surshuwlhv ri Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 8<

515 Txdgudwlf Ixqfwlrqv> Wudqvodwlrq dqg Uh hfwlrq = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 97

516 Sro|qrpldo dqg Udwlrqdo Ixqfwlrqv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =:3

517 H{srqhqwldo Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ::

518 Orjdulwkplf Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ;4

519 Dssolfdwlrqv= Jurzwk dqg Ghfd|> Pdwkhpdwlfv ri Ilqdqfh = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ;7Fkdswhu 5 Uhylhz H{huflvhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ;;H{whqghg Dssolfdwlrq= Fkdudfwhulvwlfv ri wkh Prqnh|idfh Sulfnohedfn = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <9FKDSWHU 6 GHULYDWLYH

714 Whfkqltxhv iru Ilqglqj Ghulydwlyhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 454

715 Ghulydwlyhv ri Surgxfwv dqg Txrwlhqwv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =458

716 Wkh Fkdlq Uxoh= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =45;

717 Ghulydwlyhv ri H{srqhqwldo Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 465

718 Ghulydwlyhv ri Orjdulwkplf Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 469Fkdswhu 7 Uhylhz H{huflvhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 46<FKDSWHU 8 JUDSKV DQG WKH GHULYDWLYH

814 Lqfuhdvlqj dqg Ghfuhdvlqj Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 478

815 Uhodwlyh H{wuhpd = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 47<

816 Kljkhu Ghulydwlyhv/ Frqfdylw|/ dqg wkh Vhfrqg Ghulydwlyh Whvw = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 487ly

817 Fxuyh Vnhwfklqj = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 493Fkdswhu 8 Uhylhz H{huflvhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 49;FKDSWHU 9 DSSOLFDWLRQV RI WKH GHULYDWLYH

:14 Dqwlghulydwlyhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 534:15 Vxevwlwxwlrq = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 538:16 Duhd dqg wkh Ghqlwh Lqwhjudo= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =53;:17 Wkh Ixqgdphqwdo Wkhruhp ri Fdofxoxv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =547:18 Wkh Duhd Ehwzhhq Wzr Fxuyhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 553:19 Qxphulfdo Lqwhjudwlrq= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =559Fkdswhu : Uhylhz H{huflvhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =564H{whqghg Dssolfdwlrq= Hvwlpdwlqj Ghsohwlrq Gdwhv iru Plqhudov = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 56:

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<14 Ixqfwlrqv ri Vhyhudo Yduldeohv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =589

4314 Vroxwlrqv ri Hohphqwdu| dqg Vhsdudeoh Glhuhqwldo Htxdwlrqv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =5<7

4315 Olqhdu IluvwRughu Glhuhqwldo Htxdwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 633

4316 Hxohu*v Phwkrg = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 637

4317 Dssolfdwlrqv ri Glhuhqwldo Htxdwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 63:Fkdswhu 43 Uhylhz H{huflvhv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =645H{whqghg Dssolfdwlrq= Srooxwlrq ri wkh Juhdw Odnhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 64:FKDSWHU 44 SUREDELOLW\ DQG FDOFXOXV

4414 Frqwlqxrxv Suredelolw| Prghov= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =64<

4415 H{shfwhg Ydoxh dqg Yduldqfh ri Frqwlqxrxv Udqgrp Yduldeohv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 655

4416 Vshfldo Suredelolw| Ghqvlw| Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 659Fkdswhu 44 Uhylhz H{huflvhv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =664H{whqghg Dssolfdwlrq= H{srqhqwldo Zdlwlqj Wlphv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 669FKDSWHU 45 VHTXHQFHV DQG VHULHV

4514 Jhrphwulf Vhulhv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =66:

4515 Dqqxlwlhv= Dq Dssolfdwlrq ri Vhtxhqfhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 674

4516 Wd|oru Sro|qrpldov dw 3= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =679yl

4517 Lqqlwh Vhulhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =685

4518 Wd|oru Vhulhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 688

4519 Qhzwrq*v Phwkrg = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =695451: O*Krvslwdo*v Uxoh = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 69:Fkdswhu 45 Uhylhz H{huflvhv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 69<FKDSWHU 46 WKH WULJRQRPHWULF IXQFWLRQV

4614 Ghqlwlrqv ri wkh Wuljrqrphwulf Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 6:8

4615 Ghulydwlyhv ri Wuljrqrphwulf Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 6:<

4616 Lqwhjudov ri Wuljrqrphwulf Ixqfwlrqv = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 6;;Fkdswhu 46 Uhylhz H{huflvhv= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =6;;H{whqghg Dssolfdwlrq= Wkh Vkruwhvw Wlph dqg wkh Fkhdshvw Sdwk = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 6<5

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Vhfwlrq 514

Diwhu ohduqlqj derxw olqhdu ixqfwlrqv lq wkh suhylrxv fkdswhu/ vwxghqwv qrz ohduq derxw ixqfwlrqv lq jhqhudo1 Wklvfrqfhsw lv fulwlfdo iru vxffhvv lq fdofxoxv1 Xqohvv vx!flhqw wlph lv ghyrwhg wr wklv vhfwlrq/ wkh uhvxowv zloo ehfrph

{ly Klqwv iru Whdfklqj Fdofxoxv zlwk Dssolfdwlrqv

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vr zh uho| rq txdgudwlfv ohvv wkdq lq suhylrxv hglwlrqv1

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H{huflvhv 6673 fryhu vwuhwfklqj dqg vkulqnlqj ri judskv lq wkh yhuwlfdo dqg krul}rqwdo gluhfwlrqv1 Fryhulqj wkhvhh{huflvhv fduhixoo| zloo qrw rqo| jlyh vwxghqwv d ehwwhu judvs ri ixqfwlrqv/ exw zloo khos wkhp odwhu wr lqwhusuhw wkhfkdlq uxoh1

Vhfwlrq 516

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Wkh wzr pdlq jrdov ri wklv vhfwlrq duh wr kdyh dq xqghuvwdqglqj ri zkdw dq q0wk ghjuhh sro|qrpldo orrnv olnh/dqg wr eh deoh wr qg wkh dv|pswrwhv ri d udwlrqdo ixqfwlrq1 Vwxghqwv zkr pdvwhu wkhvh lghdv zloo eh ehwwhu suhsduhgiru wkh fkdswhu rq fxuyh vnhwfklqj1

H{huflvh 8< lv wkh uvw ri vhyhudo lq wklv fkdswhu dvnlqj vwxghqwv wr qg zkdw w|sh ri ixqfwlrq ehvw wv d vhw rigdwd1 +Vhh dovr Vhfwlrq 517/ H{huflvhv 7< dqg 83/ dqg wkh Uhylhz H{huflvhv <5 dqg 4381, Wkh fodvv fdq hdvlo| jhwerjjhg grzq lq wkhvh h{huflvhv/ sduwlfxoduo| li |rx ghflgh wr h{soruh wkh uhjuhvvlrq ihdwxuhv lq d fdofxodwru vxfk dvwkh WL0;62;7 Soxv1 Exw wkhuh lv d srzhuixo sd|r lq whupv ri pdvwhu| ri ixqfwlrqv iru wkh vwxghqw zkr vxffhhgv dwwkhvh h{huflvhv1

Vhfwlrq 517

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Vhfwlrq 518

Orjdulwkpv duh d yhu| gl!fxow wrslf iru pdq| vwxghqwv1 Lw*v hdv| wr vd| wkdw d orjdulwkp lv mxvw dq h{srqhqw/exw wkh idfw wkdw lw lv wkh h{srqhqw wr zklfk rqh pxvw udlvh wkh edvh wr jhw wkh qxpehu zkrvh orjdulwkp zh duhfdofxodwlqj lv d udwkhu rewxvh frqfhsw1 Wkhuhiruh/ vshqg orwv ri wlph jrlqj ryhu h{dpsohv wkdw fdq eh grqh zlwkrxw

d fdofxodwru/ vxfk dv orj#;1 Vwxghqwv zloo dovr whqg wr frph xs zlwk pdq| lqfruuhfw svhxgrsurshuwlhv ri orjdulwkpv/

Klqwv iru Whdfklqj Fdofxoxv zlwk Dssolfdwlrqv {y

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Vhfwlrq 519

Wklv vhfwlrq jlyhv vwxghqwv pxfk qhhghg sudfwlfh zlwk h{srqhqwldov dqg orjdulwkpv/ dqg wkh dssolfdwlrqv nhhsvwxghqwv lqwhuhvwhg dqg prwlydwhg1 Lqvwuxfwruv vkrxog nhhs wklv lq plqg dqg qrw zruu| derxw kdylqj vwxghqwvphprul}h irupxodv1 Zh kdyh uhpryhg wkh irupxodv iru suhvhqw ydoxh lq wklv hglwlrq/ kdylqj ghflghg wkdw lw*v ehwwhuiru vwxghqwv wr mxvw vroyh wkh frpsrxqg dprxqw irupxod iru S1 Wklv uhgxfhv e| wzr wkh qxpehu ri irupxodv wkdwvwxghqwv qhhg wr uhphpehu1

Wkhuh lv d vxppdu| ri judskv ri edvlf ixqfwlrqv lq wkh hqg0ri0fkdswhu uhylhz1

Vhfwlrq 614

Wklv lv wkh uvw vhfwlrq rq fdofxoxv/ dqg shukdsv wkh prvw lpsruwdqw/ vlqfh olplwv duh zkdw uhdoo| glvwlqjxlvkfdofxoxv iurp dojheud1 Vwxghqwv zloo kdyh wkh ehvw xqghuvwdqglqj ri olplwv li wkh| kdyh vwxglhg wkhp judsklfdoo|+dv lq H{huflvhv 845,/ qxphulfdoo| +dv lq H{huflvhv 4853,/ dqg dqdo|wlfdoo| +dv lq H{huflvhv 6485,1 Wkh judsklqjfdofxodwru lv d srzhuixo wrro iru vwxg|lqj olplwv1 Qrwlfh lq H{dpsoh < +f, dqg +g, wkdw zh kdyh prglhg wkh phwkrg

ri qglqj olplwv dw lqqlw| e| glylglqj e| wkh kljkhvw srzhu ri { lq wkh ghqrplqdwru/ zklfk dyrlg wkh sureohp riglylvlrq e| 31

Vhfwlrq 615

Wkh vhfwlrq rq frqwlqxlw| vkrxog eh vwudljkwiruzdug li vwxghqwv kdyh pdvwhuhg olplwv iurp wkh suhylrxv vhfwlrq1Vhfwlrq 616

Wklv vhfwlrq lqwurgxfhv wkh ghulydwlyh/ hyhq wkrxjk wkdw whup grhvq*w dsshdu xqwlo wkh qh{w vhfwlrq1 Lq d fodvv ixoo

ri exvlqhvv dqg vrfldo vflhqfh pdmruv/ dq lqvwuxfwru pd| zlvk wr sodfh ohvv hpskdvlv rq yhorflw|/ dq dssurdfk pruhvxlwhg wr sk|vlfv pdmruv1 Exw zh kdyh irxqg yhorflw| wr eh wkh pdqlihvwdwlrq ri wkh ghulydwlyh wkdw lv prvw lqwxlwlyh

wr doo vwxghqwv/ uhjdugohvv ri wkhlu pdmru1

Lqvwuxfwruv lq d kxuu| fdq vnls wkh pdwhuldo rq hvwlpdwlqj wkh lqvwdqwdqhrxv udwh ri fkdqjh iurp d vhw ri gdwd/exw lw khosv vrolgli| vwxghqwv* xqghuvwdqglqj ri wkh ghulydwlyh e| jlylqj wkhp rqh pruh srlqw ri ylhz1

Vhfwlrq 617

Vwxghqwv zkr kdyh ohduqhg glhuhqwldwlrq irupxodv lq kljk vfkrro xvxdoo| zdqw +dqg ghvhuyh, vrph h{sodqdwlrq

ri zk| wkh| qhhg wr ohduq wr wdnh ghulydwlyhv xvlqj wkh ghqlwlrq1 \rx pljkw wu| h{sodlqlqj wr |rxu vwxghqwv wkdwjhwwlqj wkh uljkw irupxod lv qrw wkh rqo| jrdo> judsklqj fdofxodwruv fdq jlyh ghulydwlyhv qxphulfdoo|1 Wkh prvwlpsruwdqw wklqj iru vwxghqwv wr ohduq lv wkh frqfhsw ri wkh ghulydwlyh/ zklfk wkh| grq*w ohduq li wkh| rqo| phprul}hglhuhqwldwlrq irupxodv1

]rrplqj lq rq d ixqfwlrq zlwk d judsklqj fdofxodwru xqwlo wkh judsk dsshduv wr eh d vwudljkw olqh jlyhv vwxghqwv

d yhu| frqfuhwh lpdjh ri zkdw wkh ghulydwlyh phdqv1

Diwhu vwxghqwv kdyh ohduqhg wkh glhuhqwldwlrq irupxodv/ wkh| pd| irujhw derxw wkh ghqlwlrq ri ghulydwlyh1 Zhkdyh irxqg wkdw li zh zdqw wkhp wr xvh wkh ghqlwlrq rq d whvw/ lw lv lpsruwdqw wr vd| vr fohduo| dqg hpskdwlfdoo|/

ru wkh| zloo vlpso| xvh wkh vkruwfxw irupxodv1

Vhfwlrq 618

Rqh zd| wr jhw vwxghqwv wr irfxv rq wkh frqfhsw ri wkh ghulydwlyh/ udwkhu wkdq wkh phfkdqlfv/ lv wr hpskdvl}hjudsklfdo glhuhqwldwlrq1 Zh kdyh wkhuhiruh ghyrwhg dq hqwluh vhfwlrq wr wklv wrslf1 Judsklfdo glhuhqwldwlrq lv

{yl Klqwv iru Whdfklqj Fdofxoxv zlwk Dssolfdwlrqv

gl!fxow iru pdq| vwxghqwv ehfdxvh wkhuh duh qr irupxodv wr uho| rq1 Rqh pxvw wkrurxjko| xqghuvwdqg zkdw*v jrlqj

rq wr gr dq|wklqj1 Rq wkh rwkhu kdqg/ zh kdyh vhhq vwxghqwv zkr duh zhdn lq dojheud exw zkr srvvhvv d jrrglqwxlwlyh judvs ri jhrphwu| qg wklv wrslf txlwh vlpsoh1

d nh| irupxod xqghu wkh suhvvxuh ri dq h{dp1

Vhfwlrq 716

Qr pdwwhu krz pdq| wlphv dq lqvwuxfwru fulhv rxw wr klv ru khu vwxghqwv/ Uhphpehu wkh fkdlq uxoh$/ pdq|zloo vwloo irujhw wklv uxoh dw vrph wlph odwhu lq wkh frxuvh1 Exw li d ihz pruh vwxghqwv uhphpehu wkh uxoh ehfdxvh wkhlqvwuxfwru uhplqgv wkhp vr riwhq/ vxfk uhplqghuv duh zruwkzkloh1

Vwxghqwv riwhq frqixvh frqfdyh grzqzdug dqg xszdug zlwk lqfuhdvlqj dqg ghfuhdvlqj> fduhixoo| jr ryhu Iljxuh

64 ru wkh htxlydohqw zlwk |rxu fodvv1

Vhfwlrq 817

Judsklqj fdofxodwruv kdyh pdgh fxuyh vnhwfklqj whfkqltxhv ohvv hvvhqwldo/ exw fxuyh vnhwfklqj lv vwloo rqh ri wkhehvw zd|v wr xqli| wkh ydulrxv frqfhswv lqwurgxfhg lq wklv dqg wkh suhylrxv wzr fkdswhuv1 Vwxghqwv vkrxog xvhjudsklqj fdofxodwruv wr fkhfn wkhlu zrun1

Ehfdxvh wklv vhfwlrq lv wkh fxoplqdwlrq ri pdq| lghdv/ vwxghqwv riwhq qg lw gl!fxow dqg vwduw wr irujhw wklqjvwkh| suhylrxvo| nqhz1 Iru h{dpsoh/ d vwxghqw pljkw vwdwh wkdw d ixqfwlrq lv lqfuhdvlqj rq dq lqwhuydo dqg wkhq gudz

lw ghfuhdvlqj1 Wkh ehvw vroxwlrq vhhpv wr eh orwv ri sudfwlfh zlwk lpphgldwh khos dqg ihhgedfn iurp wkh lqvwuxfwru1Vwxghqwv vrphwlphv vwxpeoh ryhu wklv wrslf ehfdxvh wkh| xvh wkh uxohv iru glhuhqwldwlrq lqfruuhfwo|/ ru ehfdxvhwkh| pdnh plvwdnhv lq dojheud zkhq vlpsoli|lqj1 H{huflvhv vxfk dv 686< duh h{fhoohqw iru whvwlqj zkhwkhu vwxghqwvuhdoo| judvs wkh frqfhswv1

Vhfwlrq 914

Wklv vhfwlrq vkrxog qrw eh frqfhswxdoo| gl!fxow/ exw vwxghqwv qhhg frqvwdqw uhplqghuv wr fkhfn wkh hqgsrlqwv ri

dq lqwhuydo zkhq qglqj wkh devroxwh pd{lpd dqg plqlpd1

Klqwv iru Whdfklqj Fdofxoxv zlwk Dssolfdwlrqv {yll

Vhfwlrq 915

Wklv vhfwlrq lv rqh ri wkh kljk srlqwv ri wkh frxuvh1 Vrph ri wkh ehvw dssolfdwlrqv ri fdofxoxv lqyroyh pd{lpd dqgplqlpd1 Qrwlfh wkdw vrph h{huflvhv kdyh d pd{lpxp ru plqlpxp dw wkh hqgsrlqw ri dq lqwhuydo/ vr vwxghqwv fdqqrwljqruh fkhfnlqj hqgsrlqwv1

Doprvw hyhu|rqh qgv wklv pdwhuldo gl!fxow ehfdxvh prvw shrsoh duh qrw vnloohg dw zrug sureohpv1 Uhplqg |rxuvwxghqwv wkdw li wkh| hyhu zrqghu zkhwkhu pdwkhpdwlfv lv ri dq| xvh/ wklv vhfwlrq zloo vkrz wkhp1

Zk| duh zrug sureohpv vr gl!fxowB Rqh wkhru| lv wkdw zrug sureohpv uhtxluh wkh xvh ri wzr glhuhqw prghv riwklqnlqj/ zklfk vwxghqwv duh xvlqj vlpxowdqhrxvo| iru wkh uvw wlph1 Shrsoh xvh zrugv lq gdlo| olih zlwkrxw gl!fxow|/exw zkhq wkh| vwxg| pdwkhpdwlfv/ wkh| riwhq wxuq r wkdw sduw ri wkhlu eudlq dqg ehjlq wklqnlqj lq d yhu| irupdo/phfkdqlfdo zd|1 Lq zrug sureohpv/ erwk prghv ri wklqnlqj pxvw eh dfwlyh1 Li dqg zkhq wkh QFWP Vwdqgdugv ehfrphzlgho| dffhswhg lq wkh vfkrrov/ fkloguhq zloo jhw pruh sudfwlfh dw dq hduo| djh lq vxfk zd|v ri wklqnlqj1 Phdqzkloh/wkh vwhsv iru vroylqj dssolhg sureohpv jlyhq lq wklv errn pljkw pdnh wkh surfhvv d olwwoh pruh vwudljkwiruzdug/ dqgkhqfh dfklhydeoh e| wkh dyhudjh vwxghqw1

Vhfwlrq 916

Wklv vhfwlrq frqwlqxhv wkh lghdv ri wkh suhylrxv rqh1 Wkh srlqw ri vwxg|lqj hfrqrplf orw vl}h vkrxog qrw eh wrdsso| Htxdwlrq +6,/ exw wr ohduq krz wr dsso| fdofxoxv wr vroyh vxfk sureohpv1 Zh wkhuhiruh xujh |rx wr fryhuH{huflvhv 4346/ lq zklfk zh ydu| wkh dvvxpswlrqv/ vr Htxdwlrq +6, grhv qrw qhfhvvdulo| dsso|1 Lq wklv hglwlrq/ zhkdyh fkdqjhg wkh suhvhqwdwlrq wr eh frqvlvwhqw zlwk wkdw ri exvlqhvv wh{wv1

Wkh pdwhuldo rq hodvwlflw| fdq eh vnlsshg/ exw lw lv dq lpsruwdqw dssolfdwlrq wkdw vkrxog lqwhuhvw vwxghqwv zkrkdyh vwxglhg hyhq d olwwoh hfrqrplfv1

Vhfwlrq 917

Wkhuh duh wzr pdlq uhdvrqv iru fryhulqj lpsolflw glhuhqwldwlrq1 Iluvw/ lw uhlqirufhv wkh fkdlq uxoh1 Vhfrqg/ lw

lv qhhghg iru grlqj uhodwhg udwh sureohpv1 Li |rx vnls uhodwhg udwhv gxh wr odfn ri wlph/ lw lv qrw hvvhqwldo wr fryhulpsolflw glhuhqwldwlrq/ hlwkhu1

Vhfwlrq 918

Uhodwhg udwh dssolfdwlrqv duh ohvv lpsruwdqw wkdq dssolhg h{wuhpd sureohpv/ exw wkh| xvh vrph ri wkh vdph vnloov

lq vhwwlqj xs zrug sureohpv/ dqg iru wkdw uhdvrq duh zruwk fryhulqj1 Wkh ehvw dssolfdwlrq h{huflvhv duh xqghu wkhkhdglqj Sk|vlfdo Vflhqfhv/ehfdxvh wkrvh duh wkh h{huflvhv lq zklfk qr irupxod lv jlyhq wr wkh vwxghqw> wkh vwxghqwpxvw frqvwuxfw d irupxod iurp wkh zrugv1 Wkh jhrphwulfdo irupxodv qhhghg duh nhsw wr d plqlpxp= wkh S|wkdjruhdqwkhruhp/ wkh duhd ri d flufoh/ wkh yroxph ri d vskhuh/ wkh yroxph ri d frqh/ dqg wkh yroxph ri d f|olqghu zlwk dwuldqjxodu furvv vhfwlrq1 Vrph lqvwuxfwruv doorz wkhlu vwxghqwv wr xvh d fdug zlwk vxfk irupxodv rq wkh h{dp1 Wkhvhirupxodv duh vxppdul}hg lq d wdeoh lq wkh edfn ri wkh errn1

Vhfwlrq 919

Glhuhqwldov pd| eh vnlsshg e| lqvwuxfwruv lq d kxuu|> |rx qhhg qrw ihdu wkdw wklv rplvvlrq zloo kdpshu |rxuvwxghqwv lq wkh fkdswhu rq lqwhjudwlrq1 Wkh glhuhqwldov xvhg wkhuh duh qrw wkh vdph dv wkrvh xvhg khuh/ dqg wkhuhtxluhg whfkqltxhv duh hdvlo| slfnhg xs zkhq lqwhjudwlrq e| vxevwlwxwlrq lv fryhuhg1 Wkh h{fhswlrq lv iru lqvwuxfwruvzkr lqwhqg wr fryhu Vhfwlrq 4316 rq Hxohu*v Phwkrg/ vlqfh glhuhqwldov duh xvhg wr prwlydwh dqg ghulyh wkdw phwkrg1

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Vhfwlrq :14

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Vhfwlrq :18

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Vhfwlrq :19

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Vhfwlrq ;14

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Vhfwlrq <17

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Vhfwlrq 4314

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Vhfwlrq 4315

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Vhfwlrq 4316

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Vhfwlrq 4317

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Vhfwlrq 4515

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Vhfwlrq 4519

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