%$& amp lt;6,&6
10
0
0
Pełen tekst
(2) % ,1752'8&7,21729(&7256 6FDODUDQGYHFWRUTXDQWLWLHV5HVXOWDQW*UDSKLFDODGGLWLRQRIYHFWRUV SRO\JRQPHWKRGDQGSDUDOOHORJUDP PHWKRG
(3) &RPSRQHQWVRIDYHFWRUDQGFRPSRQHQWPHWKRGRIDGGLQJYHFWRUV8QLWYHFWRUV3URGXFWVRIYHFWRUV 027,21,1$3/$1( 9HORFLW\$YHUDJHYHORFLW\,QVWDQWDQHRXVYHORFLW\$FFHOHUDWLRQ8QLIRUPO\DFFHOHUDWHGPRWLRQDORQJDVWUDLJKW OLQH$FFHOHUDWLRQGXHWRJUDYLW\ 1(:721¶6/$:6 )RUFH0RPHQWXP1HZWRQ¶VILUVWODZ1HZWRQ¶VVHFRQGODZ1HZWRQ¶VWKLUGODZ7HQVLOHIULFWLRQDQGQRUPDO IRUFHV&RHIILFLHQWRINLQHWLFIULFWLRQ &216(59$7,212)(1(5*<$1'/,1($5020(1780 (QHUJ\.LQHWLFHQHUJ\*UDYLWDWLRQDOSRWHQWLDOHQHUJ\&RQVHUYDWLRQRIHQHUJ\/LQHDUPRPHQWXP,PSXOVH &RQVHUYDWLRQRIPRPHQWXP&ROOLVLRQVDQGLPSORVLRQV $1*8/$5027,21,1$3/$1( $QJXODUGLVSODFHPHQW$QJXODUVSHHG$QJXODUDFFHOHUDWLRQ&HQWULSHWDOIRUFHDQGDFFHOHUDWLRQ&RQVHUYDWLRQRI DQJXODUPRPHQWXP 7+(502'<1$0,&6 ,GHDO*DV/DZ)LUVW/DZRI7KHUPRG\QDPLFV,VREDULFSURFHVV,VRYROXPLF LVRFKRULF
(4) SURFHVV,VRWKHUPDO SURFHVV$GLDEDWLFSURFHVV6SHFLILFKHDWVRIJDVHV6SHFLILFKHDWUDWLR 7HVW (/(&75,&),(/' &RXORPE¶V/DZ&RQVHUYDWLRQRIFKDUJH(OHFWULFILHOGGXHWRDFKDUJHGSDUWLFOH6XSHUSRVLWLRQSULQFLSOH *$866¶/$: (OHFWULFIOX[*DXVVLDQVXUIDFH*DXVV¶/DZ &$3$&,7256 3RWHQWLDOGLIIHUHQFH(OHFWULFDOSRWHQWLDOHQHUJ\&DSDFLWDQFH3DUDOOHOSODWHFDSDFLWRU&DSDFLWRUVLQSDUDOOHO DQGVHULHV(QHUJ\VWRUHGLQDFDSDFLWRU &855(175(6,67$1&($1'2+0¶6/$: 3RWHQWLDOGLIIHUHQFH&XUUHQW5HVLVWDQFHDQG2KP¶V/DZ5HVLVWLYLW\5HVLVWRUVLQVHULHVDQGSDUDOOHO 0$*1(7,&),(/' &KDUJHPRYLQJWKURXJKDPDJQHWLFILHOG'LUHFWLRQDQGPDJQLWXGHRIWKHIRUFH)RUFHRQDFXUUHQWLQDPDJQHWLF ILHOG 7+(%2+502'(/ +\GURJHQDWRP(OHFWURQRUELWV(QHUJ\OHYHOGLDJUDPV(PLVVLRQDQGDEVRUSWLRQRIOLJKW6SHFWUDOOLQHV 3+272(/(&75,&())(&7$1'&203721())(&7 4XDQWDRIUDGLDWLRQ3KRWRHOHFWULFHIIHFW0RPHQWXPRIDSKRWRQ&RPSWRQHIIHFW 7HVW
(5)
(6) . .
(7) . .
(8) ,QWURGXFWLRQWR9HFWRUV . $6&$/$548$17,7<RUVFDODULVRQHWKDWKDVQRWKLQJWRGRZLWKVSDWLDOGLUHFWLRQ0DQ\SK\VLFDOFRQFHSWVVXFKDVOHQJWKWLPH WHPSHUDWXUHPDVVGHQVLW\FKDUJHDQGYROXPHDUHVFDODUV HDFKKDVDVFDOHRUVL]HEXWQRDVVRFLDWHGGLUHFWLRQ 6FDODUVDUHVSHFLILHGE\RUGLQDU\QXPEHUVDQGDGGDQGVXEWUDFWLQWKHXVXDOZD\ $9(&72548$17,7<LVRQHWKDWFDQEHVSHFLILHGFRPSOHWHO\RQO\LIZHSURYLGHERWKLWVPDJQLWXGH VL]H
(9) DQGGLUHFWLRQ0DQ\ SK\VLFDOFRQFHSWVVXFKDVGLVSODFHPHQWYHORFLW\DFFHOHUDWLRQIRUFHDQGPRPHQWXPDUHYHFWRUTXDQWLWLHV $YHFWRUTXDQWLW\FDQEHUHSUHVHQWHGE\DQDUURZGUDZQWRVFDOH7KHOHQJWKRIWKHDUURZLVSURSRUWLRQDOWRWKHPDJQLWXGHRIWKHYHFWRU TXDQWLW\ FP1NPK
(10) 7KHGLUHFWLRQRIWKHDUURZUHSUHVHQWVWKHGLUHFWLRQRIWKHYHFWRUTXDQWLW\. ,QSULQWHGPDWHULDOYHFWRUVDUHRIWHQUHSUHVHQWHGE\EROGIDFHW\SHVXFKDV):KHQZULWWHQE\KDQGWKHGHVLJQDWLRQ ) LVFRPPRQO\ XVHG$YHFWRULVQRWFRPSOHWHO\GHILQHGXQWLOZHHVWDEOLVKVRPHUXOHVIRULWVEHKDYLRU 7+(5(68/7$17RUVXPRIDQXPEHURIYHFWRUVRIDSDUWLFXODUW\SH IRUFHYHFWRUVIRUH[DPSOH
(11) LVWKDWVLQJOHYHFWRUWKDWZRXOG & KDYHWKHVDPHHIIHFWDVDOOWKHRULJLQDOYHFWRUVWDNHQWRJHWKHU & *5$3+,&$/$'',7,212)9(&7256 32/<*210(7+2'
(12) & & & & 7KLVPHWKRGIRUILQGLQJWKHUHVXOWDQW 5 RIVHYHUDOYHFWRUV $ % DQG &
(13) FRQVLVWVLQEHJLQQLQJDW & & DQ\FRQYHQLHQWSRLQWDQGGUDZLQJ WRVFDOHDQGLQWKHSURSHUGLUHFWLRQV
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
(16)
(17) . &. \. &. 5* 5FRVT5+ 5VLQT . .
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Â 0 DQGGHILQHGDV & $ 6 0 Â 0 $%FRVT ZKHUHTLVDQDQJOHEHWZHHQGLUHFWLRQVRIYHFWRUV ILJ
(19) 6 ,IZHNQRZWKHFRPSRQHQWVRI 0 DQG 0 ZHFDQFDOFXODWHWKHVFDODUSURGXFWXVLQJWKH T & IRUPXOD % 6 0 Â 0 $7 %7 $8 %8 $9 %9 )LJ $S %S $T %T $U %U
(20) 7KXVWKHDQJOHTFDQEHFDOFXODWHGDVIROORZV FRVT $% 6 6 : 9(&725352'8&7DOVRFDOOHGDFURVVSURGXFWRIYHFWRUV 0 DQG 0 LVGHQRWHGE\ 0 u 0 DQGGHILQHGDV 6 : _ 0 u 0 _ $%VLQT O :HGHILQHDYHFWRUSURGXFWWREHDYHFWRUTXDQWLW\ZLWKWKHGLUHFWLRQSHUSHQGLFXODUWRWKH N u N G I SODQHGHWHUPLQHGE\YHFWRUV F DQG H ILJ
(21) J I & :HPHDVXUHWKHDQJOHTIURP H WRZDUG H DQGWDNHLWDOZD\VWREHEHWZHHQDQG % 7KHGLUHFWLRQRIWKHYHFWRUSURGXFWLVJLYHQE\WKHULJKWKDQGUXOH K I I I H LQWR H
(22) $VLWLVVKRZQLQILJ H u H LVRSSRVLWHWR H u H URWDWLQJ T K K I I H u H H u H
(23) & $ ZKLFKPHDQVWKDWWKHYHFWRUSURGXFWLVDQWLFRPPXQLWDWLYH V O N u N M O 7KHFRPSRQHQWVRIWKHFURVVSURGXFW L u N DUHJLYHQE\ )LJ O N u N >$P %Q $Q %P $Q %R $R %Q $R %P $P %R @ 3UREOHPV ; $FKLOGSXOOVRQWKHURSHDWWDFKHGWRDVOHGZLWKDIRUFHRI17KHURSHPDNHVDQDQJOHRI WRWKHJURXQG D
(24) &RPSXWHWKH HIIHFWLYHYDOXHRIWKHSXOOWHQGLQJWRPRYHWKHVOHGDORQJWKHJURXQG E
(25) &RPSXWHWKHIRUFHWHQGLQJWROLIWWKHVOHGYHUWLFDOO\ ; $FDUZKRVHZHLJKWLV) < LVRQWKHUDPSZKLFKPDNHVDQDQJOHRI WRWKHKRUL]RQWDO+RZODUJHDSHUSHQGLFXODUIRUFHPXVWWKH UDPSZLWKVWDQGLILWLVQRWWREUHDNXQGHUWKHFDU¶VZHLJKW" $ERDWFDQWUDYHODWDVSHHGRINPKLQVWLOOZDWHURQDODNH,QWKHIORZLQJZDWHURIWKHVWUHDPLWPRYHVDWNPKUHODWLYHWRWKH WUHHVRQWKHVKRUH+RZIDVWZRXOGWKHERDWWUDYHOLQWKHRSSRVLWHGLUHFWLRQ" +LQW ILQGWKHVSHHGRIWKHVWUHDPILUVW
(26) $SODQHLVWUDYHOOLQJHDVWZDUGDWDQDLUVSHHGRINPK%XWD NPKZLQGLVEORZLQJVRXWKZDUG:KDWDUHWKHGLUHFWLRQDQG VSHHGRIWKHSODQHUHODWLYHWRWKHJURXQG",QZKDWGLUHFWLRQPXVWWKHSODQHKHDGLQRUGHUWRPRYHGXHHDVWUHODWLYHWRWKH(DUWK" = $VKLSLVWUDYHOOLQJGXHHDVWDWNPK:KDWPXVWEHWKHVSHHGRIWKHVHFRQGVKLSKHDGLQJ HDVWRIQRUWKLILWLVDOZD\VGXHQRUWK RIWKHILUVWVKLS" ? $FRQVWDQWIRUFH > >@ 1
(27) FDXVHVDGLVSODFHPHQW A @ >@ P
(28) )LQGWKHZRUNGRQHE\WKLVIRUFHDQGDQDQJOHEHWZHHQ C WKHWZRYHFWRUV +LQW : B Â E D
(29) = $FKLOGLVKROGLQJDZDJRQIURPUROOLQJVWUDLJKWEDFNGRZQDGULYHZD\WKDWLVLQFOLQHGDW WRWKHKRUL]RQWDO,IWKHZDJRQ ZHLJKWV1ZLWKZKDWIRUFHPXVWWKHFKLOGSXOORQWKHKDQGOHLIWKHKDQGOHLVSDUDOOHOWRWKHLQFOLQH" . .
(30) 8QLIRUPO\$FFHOHUDWHG0RWLRQ 63(('LVDVFDODUTXDQWLW\,IDQREMHFWWDNHVDWLPHLQWHUYDOWWRWUDYHODGLVWDQFHWKHQ O WRWDOGLVWDQFHWUDYHOOHG $YHUDJHVSHHG RU Yhi WLPHWDNHQ W +HUHWKHGLVWDQFHLVWKHWRWDO DORQJWKHSDWK
(31) OHQJWKWUDYHOOHG7KLVLVZKDWDFDU¶VRGRPHWHUUHDGV & 9(/2&,7<LVDYHFWRUTXDQWLW\,IDQREMHFWXQGHUJRHVDYHFWRUGLVSODFHPHQW V LQDWLPHLQWHUYDOWWKHQ . . V & YHFWRUGLVSODFHPHQW $YHUDJHYHORFLW\ RU Yjk WLPHWDNHQ W 7KHGLUHFWLRQRIWKHYHORFLW\YHFWRULVWKHVDPHDVWKDWRIWKHGLVSODFHPHQWYHFWRU7KHXQLWVRIYHORFLW\ DQGVSHHG
(32) DUHWKRVHRI GLVWDQFHGLYLGHGE\WLPHVXFKDVUQVRUNPK $&&(/(5$7,21PHDVXUHVWKHWLPHUDWHRIFKDQJHRIYHORFLW\ &. . . . $YHUDJHDFFHOHUDWLRQ FKDQJHLQYHORFLW\YHFWRU RU WLPHWDNHQ. & D lm. & & Yn Yo W. . & & ZKHUH Yp LVWKHLQLWLDOYHORFLW\ Yq LVWKHILQDOYHORFLW\DQGWLVWKHWLPHLQWHUYDORYHUZKLFKWKHFKDQJHRFFXUUHG7KHXQLWVRI r. DFFHOHUDWLRQDUHWKRVHRIYHORFLW\GLYLGHGE\WLPH7\SLFDOH[DPSOHVDUH PV
(33) V RUPV
(34) DQG NPK
(35) V1RWLFHWKDWDFFHOHUDWLRQLVD & & YHFWRUTXDQWLW\,WKDVWKHGLUHFWLRQRI Yq Ys WKHFKDQJHLQYHORFLW\. 81,)250/<$&&(/(5$7('027,21$/21*$675$,*+7/,1(LVDQLPSRUWDQWVLWXDWLRQ,QWKLVFDVHWKHDFFHOHUDWLRQ & & YHFWRULVFRQVWDQWDQGOLHVDORQJWKHOLQHRIWKHGLVSODFHPHQWYHFWRUVRWKDWWKHGLUHFWLRQVRI D DQG Y FDQEHVSHFLILHGZLWKSOXVDQG PLQXVVLJQV,IZHUHSUHVHQWWKHGLVSODFHPHQWE\V SRVLWLYHLILQWKHSRVLWLYHGLUHFWLRQDQGQHJDWLYHLILQWKHQHJDWLYHGLUHFWLRQ
(36) WKHQ WKHPRWLRQFDQEHGHVFULEHGZLWKWKHIROORZLQJHTXDWLRQV . V Ytu W . V Y x W. . Ytu. DW . D. y. Yv Yw. . z Y Y{. W. . . 5HPHPEHU DFDQEHQHJDWLYHZKHQ Y| Y}
(37) LVQHJDWLYH,QWKLVFDVHLWLVDGHFHOHUDWHGPRWLRQ ,167$17$1(2869(/2&,7<LVWKHYHORFLW\RIDQREMHFWDWDQ\RQHVSHFLILFLQVWDQWRIWLPHRUDWRQHVSHFLILFSRLQWLQLWVSDWK,WLV GHILQHGDVGHULYDWLYHRIGLVSODFHPHQW[ZLWKUHVSHFWWRWLPHW . Y~ . '[. OLP 'W. G[ GW. 3UREOHPV $QREMHFWVWDUWVIURPUHVWZLWKDFRQVWDQWDFFHOHUDWLRQRIPV DORQJDVWUDLJKWOLQH)LQG D
(38) WKHVSHHGDWWKHHQGRIV E
(39) WKH DYHUDJHVSHHGIRUWKHVLQWHUYDODQG F
(40) WKHGLVWDQFHWUDYHOOHGLQWKHILIWKVHFRQGRILWVPRWLRQ 7KH VSHHG RIWUDLQLVUHGXFHGXQLIRUPO\IURPPVWRPVZKLOHWUDYHOOLQJDGLVWDQFHRI P)LQGWKHDFFHOHUDWLRQ+RZPXFK IDUWKHUZLOOWKHWUDLQWUDYHOEHIRUHFRPLQJWRUHVWSURYLGHGWKHDFFHOHUDWLRQUHPDLQVFRQVWDQW" $ EDOODVW LV GURSSHG IURP D EDOORRQ WKDW LV P DERYH WKH JURXQG DQG ULVLQJ DW PV )RU WKH EDJ ILQG WKH PD[LPXP KHLJKW UHDFKHGLWVSRVLWLRQDQGYHORFLW\VDIWHULWLVUHOHDVHGDQGWKHWLPHDWZKLFKLWKLWVWKHJURXQG 7KH EDOO LV GURSSHG IURPUHVWDWDKHLJKWRIP DERYHWKHJURXQG D
(41) :KDW LV LWVVSHHGMXVWEHIRUHLW KLWV WKHJURXQG" E
(42) +RZ ORQJGRHVLWWDNHWRUHDFKWKHJURXQG" $EXVPRYLQJDWDVSHHGRIPVEHJLQVWRVORZGRZQDWFRQVWDQWUDWHRIPVHDFKVHFRQG)LQGKRZIDULWJRHVEHIRUHVWRSSLQJ DQGKRZORQJLWZLOOWDNH $FDUPRYLQJDWPVVORZVXQLIRUPO\WRDVSHHGRIPVLQDWLPHRIV'HWHUPLQH D
(43) WKHDFFHOHUDWLRQRIWKHFDUDQG E
(44) WKH GLVWDQFHLWPRYHVLQWKHWKLUGVHFRQG $EDVHEDOOLVWKURZQVWUDLJKWXSZDUGRQWKH0RRQZLWKDQLQLWLDOVSHHGRIPV&RPSXWH D
(45) WKHPD[LPXPKHLJKWUHDFKHGE\WKH EDOO E
(46) WKHWLPHWDNHQWRUHDFKWKDWKHLJKW F
(47) LWVYHORFLW\VDIWHULWLVWKURZQDQG G
(48) ZKHQWKHEDOO¶VKHLJKWLVP WXYX. TZ [. W\
(49) ]. [ ^_ ^`ab. \
(50) cddef cddg. .
(51) 1HZWRQ¶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
(52) 1(:721¶6),567 /$: $QREMHFWDW UHVW ZLOOUHPDLQ DWUHVW DQREMHFWLQPRWLRQZLOOFRQWLQXHLQPRWLRQZLWKFRQVWDQWYHORFLW\ H[FHSWLQVRIDUDVLWLVDFWHGXSRQE\DQH[WHUQDOIRUFH)RUFHLVWKHFKDQJHURIPRWLRQ . 1(:721¶66(&21'/$: ,IWKHUHVXOWDQW RUQHW
(53) IRUFH ) DFWLQJRQDQREMHFWRIPDVVPLVQRW]HURWKHREMHFWDFFHOHUDWHVLQWKH & GLUHFWLRQRIWKHIRUFH7KHDFFHOHUDWLRQ D LVSURSRUWLRQDOWRWKHIRUFHDQGLQYHUVHO\SURSRUWLRQDOWRWKHPDVVRIWKHREMHFW7KLVFDQEH ZULWWHQDV &. &. & ) P D & & 7KHDFFHOHUDWLRQ D KDVWKHVDPHGLUHFWLRQDVWKHUHVXOWDQWIRUFH ) . . 1(:721¶67+,5'/$: 0DWWHULQWHUDFWVZLWKPDWWHUIRUFHVFRPHLQSDLUV)RUHDFKIRUFHH[HUWHGRQRQHERG\WKHUHLVDQHTXDO EXWRSSRVLWHO\GLUHFWHGIRUFHRQVRPHRWKHUERG\LQWHUDFWLQJZLWKLW7KLVLVRIWHQFDOOHGWKH/DZRI$FWLRQDQG5HDFWLRQ1RWLFHWKDW WKHDFWLRQDQGUHDFWLRQIRUFHVDFWRQWKHWZRGLIIHUHQWLQWHUDFWLQJREMHFWV & 7+(7(16,/()25&( )
(54) DFWLQJRQDVWULQJRUFKDLQRUWHQGRQLVWKHDSSOLHGIRUFHWHQGLQJWRVWUHWFKLW7KHPDJQLWXGHRIWKH WHQVLOHIRUFHLVWKHWHQVLRQ )
(55) &. 7+()5,&7,21)25&( )
(56) LVDWDQJHQWLDOIRUFHDFWLQJRQDQREMHFWWKDWRSSRVHVWKHVOLGLQJRIWKDWREMHFWRQDQDGMDFHQWVXUIDFH ZLWKZKLFKLWLVLQFRQWDFW7KHIULFWLRQIRUFHLVSDUDOOHOWRWKHVXUIDFHDQGRSSRVLWHWRWKHGLUHFWLRQRIPRWLRQRURILPSHQGLQJ PRWLRQ2QO\ZKHQWKHDSSOLHGIRUFHH[FHHGVWKHPD[LPXPVWDWLFIULFWLRQIRUFHZLOODQREMHFWEHJLQWRVOLGH &. 7+(1250$/)25&( )
(57) RQDQREMHFWWKDWLVEHLQJVXSSRUWHGE\DVXUIDFHLVWKHFRPSRQHQWRIWKHVXSSRUWLQJIRUFHWKDWLV SHUSHQGLFXODUWRWKHVXUIDFH 7+(&2()),&,(172).,1(7,&)5,&7,21 P
(58) LVGHILQHGIRUWKHFDVHLQZKLFKRQHVXUIDFHLVVOLGLQJDFURVVDQRWKHUDW FRQVWDQWVSHHG,WLV IULFWLRQIRUFH P QRUPDOIRUFH ) ) 3UREOHPV & ) $ NJ FDU LV PRYLQJ RQ D OHYHO URDG DW PV D
(59) +RZ ODUJH D UHWDUGLQJ IRUFH DVVXPHG FRQVWDQW
(60) LV UHTXLUHG WR VWRS LW LQ D GLVWDQFH RI P" E
(61) :KDW LV WKH PLQLPXP FRHIILFLHQW RI P D IULFWLRQEHWZHHQWLUHVDQGURDGZD\LIWKLVLVWREHSRVVLEOH"$VVXPHWKHZKHHOVDUHQRWORFNHGLQ ZKLFKFDVHZHDUHGHDOLQJZLWKVWDWLFIULFWLRQWKHUHLVQRVOLGLQJ $NJER[LV D±ILJ
(62) SXOOHGDQG E±ILJ
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
(64) &RQVHUYDWLRQRIHQHUJ\DQGOLQHDUPRPHQWXP. (1(5*<LVDPHDVXUHRIWKHFKDQJHLPSDUWHGWRDV\VWHP,WLVJLYHQWRDQREMHFWZKHQDIRUFHGRHVZRUNRQWKHREMHFW7KHDPRXQW RIHQHUJ\WUDQVIHUUHGWRWKHREMHFWHTXDOVWKHZRUNGRQH)XUWKHUZKHQDQREMHFWGRHVZRUNLWORVHVDQDPRXQWRIHQHUJ\HTXDOWRWKH. ZRUNLWGRHV,IDQREMHFWXQGHUJRHVWKHGLVSODFHPHQW ´ ³ XQGHUWKHDFWLRQRIWKHFRQVWDQWIRUFH ) WKHZRUNGRQHE\WKHIRUFHLVGHILQHG ¶µ DVDVFDODUSURGXFWRIWZRYHFWRUV ´ ³ : (QHUJ\DQGZRUNKDYHWKHVDPHXQLWVMRXOHV -
(65) (QHUJ\OLNHZRUNLVDVFDODUTXDQWLW\ .,1(7,&(1(5*< (·
(66) ,IDQREMHFWRIPDVVPLVPRYLQJZLWKDVSHHGYLWKDVWUDQVODWLRQDO(· JLYHQE\ . &. ¸. . . . . . . . PY (· . . *5$9,7$7,21$/327(17,$/(1(5*< (¹º
(67) ,QIDOOLQJWKURXJKDYHUWLFDOGLVWDQFHKDPDVVPFDQGRZRUNLQWKHDPRXQW (¹º PJK. :KHUHJLVDFFHOHUDWLRQGXHWRJUDYLW\K±LVWKHSRVLWLRQRIDQREMHFWUHODWLYHWRDUHIHUHQFHOHYHORIWHQWKH(DUWK¶VVXUIDFH &216(59$7,212)(1(5*< ,QDQLVRODWHGV\VWHPLWVWRWDOPHFKDQLFDOHQHUJ\ (» (¼ RIDOOHOHPHQWVRIWKHV\VWHP
(68) LVFRQVWDQW & & 7+(/,1($5020(1780 S
(69) RIDERG\LVWKHSURGXFWRILWVPDVV P
(70) DQGYHORFLW\ Y
(71) . & & S P Y . 0RPHQWXPLVDYHFWRUTXDQWLW\ZKRVHGLUHFWLRQLVWKDWRIWKHYHORFLW\7KHXQLWVRIPRPHQWXPDUHNJPVLQWKH6, &216(59$7,212)/,1($5020(1780 ,IWKHQHWH[WHUQDOIRUFHDFWLQJRQDV\VWHPRIREMHFWVLV]HURWKHYHFWRUVXPRIWKH PRPHQWDRIWKHREMHFWVZLOOUHPDLQFRQVWDQW :KHQ )½¿¾ÁÀ. P. GY GW. WKHQ. G PY
(72) GW. GS GW. & o S. FRQVW . ,1&2//,6,216$1'(;3/26,216WKHYHFWRUVXPRIWKHPRPHQWDMXVWEHIRUHWKHHYHQWHTXDOVWKHYHFWRUVXPRIWKHPRPHQWD MXVWDIWHUWKHHYHQW7KHYHFWRUVXPRIWKHPRPHQWDRIWKHREMHFWVLQYROYHGGRHVQRWFKDQJHGXULQJWKHFROOLVLRQRUH[SORVLRQ 7KXVZKHQWZRERGLHVRIPDVVHVP Â DQGPÃ FROOLGH 7RWDOPRPHQWXPEHIRUHLPSDFW WRWDOPRPHQWXPDIWHULPSDFW & & & & P Â X Ä PÃ X Å P Â Y Æ PÃ Y Ç ZKHUH X È DQG X Ç DUHWKHYHORFLWLHVEHIRUHLPSDFWDQG Y È DQG Y Ç DUHWKHYHORFLWLHVDIWHU,QRQHGLPHQVLRQLQFRPSRQHQWIRUP P Â X Â É PÃ XÃ É P Â Y Â É PÃ YÃ É DQGVLPLODUO\IRUWKH\DQG]FRPSRQHQWV5HPHPEHUWKDWYHFWRUFRPSRQHQWVDUHVFDODUTXDQWLWLHVDQGFDQEHSRVLWLYHRUQHJDWLYH GHSHQGLQJRQWKHLQLWLDOO\VHOHFWHGGLUHFWLRQ ,13(5)(&7/<(/$67,&&2//,6,21WKHWRWDOPHFKDQLFHQHUJ\LVFRQVHUYHGLHLQFDVHRIWZRERGLHVFROOLVLRQ . &. &. &. &. Ó. PÊË X ÊÌ P XÌ PÐÑ Y ÐÒ PÓÔY Ó PJ+ Í ÌÎÌ PJ+Ï PJK Í PJKÏ . EHIRUHWKHFROOLVLRQ DIWHUWKHFROOLVLRQ 3UREOHPV $SURMHFWLOHLVVKRWXSZDUGIURPWKHHDUWKZLWKDVSHHGRIPV+RZKLJKLVLWZKHQLWVVSHHGLVPV,JQRUHDLUIULFWLRQ $EDOODWWKHHQGRIFPORQJVWULQJVZLQJVDVDSHQGXOXPDVVKRZQLQILJ7KHEDOO¶VVSHHGLQ LWVORZHVWSRVLWLRQLVFPV D
(73) 7RZKDWKHLJKWKDERYHWKLVSRVLWLRQZLOOLWULVHEHIRUHVWRSSLQJ" E
(74) :KDWDQJOHGRHVWKHSHQGXOXPWKHQPDNHWRWKHYHUWLFDO" Õ $JLUOMXPSVRIIDERDWZLWKKRUL]RQWDOVSHHGRIPV$VVXPLQJWKHERDWLVRULJLQDOO\DWUHVWDQGIUHHWR PRYHLQWKHZDWHUILQGDVSHHGRIWKHERDW7KHPDVVRIDJLUOP NJ ERDW¶VPDVV0 NJ × $JPDVVLVPRYLQJLQWKH[GLUHFWLRQDWFPVZKLOHDJPDVVLVPRYLQJLQWKH[GLUHFWLRQDW FPV7KH\FROOLGHKHDGRQDQGVWLFNWRJHWKHU)LQGWKHLUYHORFLW\DIWHUWKHFROOLVLRQ Ö 7ZRLGHQWLFDOEDOOVFROOLGHKHDGRQ7KHLQLWLDOYHORFLW\RIRQHLVPVHDVWZKLOHWKDWRIWKHRWKHULV PVZHVW,IWKHFROOLVLRQLVSHUIHFWO\HODVWLFZKDWLVWKHILQDOYHORFLW\RIHDFKEDOO" )LJVKRZVDEHDGVOLGLQJRQWKHZLUH,IIULFWLRQIRUFHVDUHQHJOLJLEOHDQGDEHDGKDVDVSHHGRI )LJ FPV DW $ ZKDW ZLOO EH LWV VSHHG D
(75) DW SRLQW %" E
(76) $WSRLQW&" $JLUORIDPDVVP NJLVUXQQLQJDWDVSHHG $ RI PV ZKHQ VKH MXPSV RQWR D VOHG WKDW LV LQLWLDOO\DWUHVWRQWKH IUR]HQVXUIDFHRIDODNH ,IWKHJLUOVOHGV\VWHPEHJLQVWRVOHGDWDVSHHG FP RIPVZKDWLVWKHPDVVRIWKHVOHG" % ° ± ² ¡
(77) ¢ £¤ £¥¦§¡
(78) ¨©©ª« ¨©©¬. & ®¯ . .
(79) 5LJLG%RG\5RWDWLRQ $1*8/$5',63/$&(0(17 D
(80) LVXVXDOO\H[SUHVVHGLQUDGLDQVLQGHJUHHVRULQUHYROXWLRQV UHY SUDG RU UDG 2QHUDGLDQLVWKHDQJOHVXEWHQGHGDWWKHFHQWHURIDFLUFOHE\DQDUFHTXDOLQOHQJWKWRWKHUDGLXVRIWKHFLUFOH7KXVDQDQJOHDLQUDGLDQV LVJLYHQE\HTXDWLRQ DU O ZKHUHOLVWKHDUFOHQJWKDQGULVWKHUDGLXVRIDFLUFOH 7+($1*8/$563((' Z
(81) RIDQREMHFWZKRVHD[LVRIURWDWLRQLVIL[HGLVWKHUDWHDWZKLFKLWVDQJXODUFRRUGLQDWHWKHDQJXODU GLVSODFHPHQWDFKDQJHVZLWKWLPH,IDFKDQJHVIURPD WRD LQDWLPH'WWKHQWKHDYHUDJHDQJXODUVSHHGLV Z!#" D$ D%
(82) 'W (*) DQGDQLQVWDQWDQHRXVYDOXHRIDQJXODUVSHHG WLPHGHULYDWLYHRIDQJOH
(83) Z% &#' . (
(84) + . 7KHXQLWVRIZ DUHH[FOXVLYHO\UDGV:HFDQDVVRFLDWHDGLUHFWLRQZLWKZDQGWKHUHE\FUHDWHDYHFWRUTXDQWLW\ Y 7KXVLIWKHILQJHUVRI. &. WKHULJKWKDQGFXUYHDURXQGLQWKHGLUHFWLRQRIURWDWLRQWKHWKXPESRLQWVDORQJWKHD[LVRIURWDWLRQLQWKHGLUHFWLRQRI Y WKHDQJXODU YHORFLW\YHFWRU 7+()5(48(1&<LVWKHQXPEHURIUHYROXWLRQVSHUVHFRQGURWDWLRQVSHUVHFRQGRUF\FOHVSHUVHFRQG,WLVUHODWHGWRWKHDQJXODU Z SI VSHHGE\DVLPSOHIRUPXOD - 7KH6,XQLWIRUIUHTXHQF\LV+HU] +] V,
(85) 7+($1*8/$5$&&(/(5$7,21 H
(86) RIDQREMHFWZKRVHD[LVRIURWDWLRQLVIL[HGLVWKHUDWHDWZKLFKLWVDQJXODUVSHHGFKDQJHV ZLWKWLPH,IWKHDQJXODUVSHHGFKDQJHVXQLIRUPO\IURPZ WRZ LQDWLPH'WWKHQWKHDQJXODUDFFHOHUDWLRQLVFRQVWDQWDQG H!." Z$ Z%
(87) 'W (*/ . &. % &#' (
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
(89) DERXWDQD[LVGXHWRDIRUFHLVDPHDVXUHRIHIIHFWLYHQHVVRIWKHIRUFHLQSURGXFLQJURWDWLRQDERXW WKDWD[LV,WLVGHILQHGLQWKHIROORZLQJZD\ 7 U u) 7+(020(172),1(57,$ ,
(90) RIWKHERG\LVWKHPHDVXUHRIWKHURWDWLRQDOLQHUWLDRIWKHERG\,IDQREMHFWWKDWLVIUHHWRURWDWH DERXWDQD[LVLVGLIILFXOWWRVHWLQWRURWDWLRQLWVPRPHQWRILQHUWLDDERXWWKDWD[LVLVODUJH ,IDERG\FRQVLVWVRIWLQ\PDVVHVP - P0 P = DWUHVSHFWLYHGLVWDQFHU - U0 U= IURPDQD[LVLWVPRPHQWRILQHUWLDDERXWWKHD[LVLV . &. &. &. ,. P @AU@ PBCUB PDEUD B. B. B. ¦ P>?U>. B. 7KHPRPHQWVRILQHUWLD DERXWDQD[LVWKURXJKWKHFHQWHURIPDVV
(91) RIWKHPRVWW\SLFDOREMHFWVHDFKRIPDVV0 ØÙÚ úüûûåýþûÿ Ö û û óûÿ
(92) ÿ ÛÝÜÞ ß àá âãá àåäçæéè ê ë ì ì ÛÝÜÞ ß àá âñðóòôöõá õæéè ì ë ÷ ê ìíïî íùø & $1*8/$5020(17802)$5,*,'2%-(&7 /
(93) LVDYHFWRUTXDQWLW\GLUHFWHGDORQJWKHD[LVRIURWDWLRQDQGLVGHILQHGDQGLV & & & UHODWHGWRDQDQJXODUVSHHGE\WKHHTXDWLRQV / U u S & & / ,Y %\FRPSDULVRQZLWKOLQHDUPRPHQWXP ,,1(:721¶6/$:)25527$7,21$/027,21 DWRUTXH7DFWLQJRQDERG\RIPRPHQWRILQHUWLD,SURGXFHVLQLWDQDQJXODU DFFHOHUDWLRQHJLYHQE\ 7 ,H , . GY G ,Y
(94) GW GW. G/ GW. .
(95) &216(59$7,212)$1*8/$5020(1780 ,IWKHH[WHUQDOQHWWRUTXHRQDV\VWHPLV]HURLWVDQJXODUPRPHQWXPZLOOUHPDLQ XQFKDQJHGLQERWKPDJQLWXGHDQGGLUHFWLRQ . . . . 7_` a Æ. G/ Æ/ FRQVWÆ/b /c Æ,b Zb ,c Zc GW. 7+(.,1(7,&(1(5*<2)527$7,21 (d
(96) RIDPDVVZKRVHPRPHQWRILQHUWLDDERXWDQD[LVLV,DQGZKLFKLVURWDWLQJZLWKWKH DQJXODUYHORFLW\ZLV. . . . ( f. e. ,Y . 3UREOHPV $V VKRZQ LQ ILJ D PDVV P NJ KDQJV IURP WKH ULP RI D GLVN RI UDGLXV U P :KHQ UHOHDVHGIURPUHVWWKHPDVVIDOOVPLQV)LQGWKHPRPHQWRILQHUWLDRIWKHGLVN 7KHVSLQGULHURIDZDVKLQJPDFKLQHUHYROYLQJDW USPVORZVGRZQXQLIRUPO\WRUSPZKLOH PDNLQJUHYROXWLRQV)LQGWKHDQJXODUDFFHOHUDWLRQDQGWKHWLPHUHTXLUHGWRWXUQWKURXJKWKHVH UHY $ J ODG\ELUG VWDQGV KDOIZD\ EHWZHHQ WKH FHQWHU DQG WKHHGJHRIWKHSKRQRJUDSKUHFRUG WKDWLV URWDWLQJDWDQDQJXODUVSHHGRIUDGV D
(97) :KDWLVWKHDQJXODUVSHHGRIWKHUHFRUGDIWHUWKHODG\ELUG ZDONVWRLWVHGJH" E
(98) ZKDWLVWKHFKDQJHLQNLQHWLFHQHUJ\RIWKHV\VWHP"7KHUDGLXVRIWKHUHFRUGLV FPDQGLWVPDVVZKHQHPSW\LVNJ P g $ ZKHHO KDV D PRPHQW RI LQHUWLD RI NJP :KDW FRQVWDQW WRUTXH LV UHTXLUHG WR LQFUHDVH LWV IUHTXHQF\IURPWRUHYVLQFLUFOHV" $XQLIRUPEDOOLQLWLDOO\DW UHVWVWDUWVWRURWDWHXQGHUWKHLQIOXHQFHRIFRQVWDQWIRUFH) 1DFWLQJ )LJ WDQJHQWLDOO\+RZORQJGRHVLWWDNHWRDFFHOHUDWHWKHEDOOWRWKHIUHTXHQF\I +]*LYHQWKHPDVVRI WKHEDOOP NJDQGLWVUDGLXVU P $GLVNRIPRPHQWRILQHUWLD, h LVURWDWLQJIUHHO\ZLWKDQJXODUVSHHGZ h ZKHQDVHFRQGQRQURWDWLQJ ,q GLVNZLWKDPRPHQWRILQHUWLD,g LVGURSSHGRQLW ILJ
(99) 7KHWZRWKHQURWDWHDVDXQLW)LQGWKH ILQDODQJXODUVSHHG Zh $GLVNOLNHWKHORZHURQHLQILJ 0 NJ
(100) LVWXUQLQJDWUHYV$WULFNOHRIVDQGIDOOVRQWRWKH h g GLVNDWDGLVWDQFHU h UDQGEXLOGVDULQJRIVDQGRQLW+RZPXFKVDQGPXVWIDOORQWKHGLVNIRULW g WRVORZWRUHYV" +LQW FRQVLGHUDQDGGLWLRQDOPRPHQWRILQHUWLDRIWKHULQJ,d PU h
(101) )LJ 7KHUPRG\QDPLFV ,'($/*$6/$: 7KHDEVROXWHSUHVVXUHSRIQPROHVRIJDVFRQWDLQHGLQDYROXPH9LVUHODWHGWRWKHDEVROXWHWHPSHUDWXUH7E\. . . . . . . . ,r . S9 Q57. ZKHUH5 - PRO.
(102) LVFDOOHGWKHXQLYHUVDOJDVFRQVWDQW,IWKHYROXPHFRQWDLQVPNLORJUDPVRIJDVWKDWKDVDPROHFXODU RU i. DWRPLF
(103) PDVV0WKHQQ j 63(&,$/&$6(6RIWKH,GHDO*DV/DZREWDLQHGE\KROGLQJWZRRILWVSDUDPHWHUVFRQVWDQWDUH %R\OH¶V/DZLVRWKHUPDOSURFHVV Q7FRQVWDQW
(104) S9 FRQVWDQW k &KDUOHV¶/DZLVREDULFSURFHVV QSFRQVWDQW
(105) . . l FRQVWDQW m. *D\/XVVDF¶V/DZLVRFKRULF LVRYROXPLF
(106) SURFHVV Q9FRQVWDQW
(107) l FRQVWDQW +($7 '4
(108) LV WKH WKHUPDO HQHUJ\ WKDW IORZV IURP RQH ERG\ RU V\VWHP WR DQRWKHU ZKLFK LV LQ FRQWDFW ZLWK LW EHFDXVH RI WKHLU WHPSHUDWXUHGLIIHUHQFH+HDWDOZD\VIORZVIURPKRWWRFROG)RUWZRREMHFWVLQFRQWDFWWREHLQWKHUPDOHTXLOLEULXPZLWKHDFKRWKHU LH IRUQRQHWKHDWWUDQVIHUIURPRQHWRWKHRWKHU
(109) WKHLUWHPSHUDWXUHVPXVWEHWKHVDPH,IHDFKRIWZRREMHFWVLVLQWKHUPDOHTXLOLEULXPZLWK D WKLUG ERG\ WKHQ WKH WZR DUH LQ WKHUPDO HTXLOLEULXP ZLWK HDFK RWKHU 7KLV IDFW LV RIWHQ UHIHUUHG WR DV WKH =HURWK /DZ RI 7KHUPRG\QDPLFV
(110) 7+(,17(51$/(1(5*< 8
(111) RIDV\VWHPLVWKHWRWDOHQHUJ\FRQWHQWRIWKHV\VWHP,WLVWKHVXPRIDOOIRUPVRIHQHUJ\SRVVHVVHG E\WKHDWRPVDQGPROHFXOHVRIWKHV\VWHP7KHFKDQJHLQWKHLQWHUQDOHQHUJ\LVDOZD\VUHODWHGWRWKHWHPSHUDWXUHRIWKHERG\ '8 QF n '7. 7+(:25.'21(%<$6<67(0 ':
(112) LVSRVLWLYHLIWKHV\VWHPWKHUHE\ORVHVHQHUJ\WRLWVVXUURXQGLQJV:KHQWKHVXUURXQGLQJV GRZRUNRQWKHV\VWHPVRDVWRJLYHLWHQHUJ\':LVDQHJDWLYHTXDQWLW\. 7+(),567/$:2)7+(502'<1$0,&6LVDVWDWHPHQWRIWKHODZRIFRQVHUYDWLRQRIHQHUJ\,WVWDWHVWKDWLIDQDPRXQWRIKHDW '4 IORZV LQWR D V\VWHP WKHQ WKLV HQHUJ\ PXVW DSSHDU DV LQFUHDVHG LQWHUQDO HQHUJ\ '8 IRU WKH V\VWHP DQGRU ZRUN ' : GRQH E\ WKH V\VWHPRQLWVVXUURXQGLQJV$VDQHTXDWLRQWKH)LUVW/DZLV '4 '8': ,1$1,62%$5,&352&(66 FRQVWDQWSUHVVXUH
(113) ':o 3'9 3 9g 9 h
(114) '4o QFo '7 ZKHUHFo PRODUVSHFLILFKHDWDWFRQVWDQWSUHVVXUH '8 QF p '7 ZKHUHF p PRODUVSHFLILFKHDWDWFRQVWDQWYROXPH ,1$1,6292/80,&352&(66 FRQVWDQWYROXPH
(115) ': p Æ '4 p '8 '4 p QF p '7 FGIH*G JKML FNPOQL RS R.TVU#WNPXZYY\[] XZYY\^ .
(116) ,1$1,627+(50$/352&(66 FRQVWDQWWHPSHUDWXUH
(117) '8 Æ . . . . . ': s . . ³ 3G9 t³u. t v. t v. t u. '4 s ': s. G9 Q57 ³ t u 9 t v. Q57 G9 9. 9 Q57 OQ 9x w. ,1$1$',$%$7,&352&(66 WKHRQHLQZKLFKQRKHDWLVWUDQVIHUUHGWRRUIURPWKHV\VWHP
(118) '4 Æ'8 ':y )RUDQLGHDOJDVFKDQJLQJIURPFRQGLWLRQV 3 h 9 h 7 h
(119) WR 3g 9g 7g
(120) LQDQDGLDEDWLFSURFHVV |}| 39 . 3~ 9 ~ DQG7|} 9| . |. 7~ 9~. |. ZKHUHN. Fz. F{. LVGLVFXVVHGEHORZ. 63(&,),&+($762)*$6(6 :KHQDJDVLVKHDWHGDWFRQVWDQWYROXPHWKHKHDWVXSSOLHGJRHVWRLQFUHDVHWKHLQWHUQDOHQHUJ\RIWKH JDVPROHFXOHV%XWZKHQDJDVLVKHDWHGDWFRQVWDQWSUHVVXUHWKHKHDWVXSSOLHGQRWRQO\LQFUHDVHVWKHLQWHUQDOHQHUJ\RIWKHPROHFXOHV EXWDOVRGRHVPHFKDQLFDOZRUNLQH[SDQGLQJWKHJDVDJDLQVWWKHRSSRVLQJFRQVWDQWSUHVVXUH+HQFHWKHVSHFLILFKHDWRIDJDVDWFRQVWDQW SUHVVXUHFo LVJUHDWHUWKDQLWVVSHFLILFKHDWDWFRQVWDQWYROXPHF p ,WFDQEHVKRZQWKDWIRUDQLGHDOJDVRIPROHFXODUPDVV0 Fo F p 5. ZKHUH5LVWKHXQLYHUVDOJDVFRQVWDQW%RWKFo DQGF p DUHGLUHFWO\UHODWHGZLWKWKHFRQFHSWRIGHJUHHVRIIUHHGRPLLHQXPEHUVRI . YHORFLW\FRPSRQHQWVQHHGHGWRGHVFULEHWKHPRWLRQRISDUWLFOHVRIJDV)RUPROHRIWKHJDVF p ZKHUHL IRUDPRQDWRPLFJDV DQGL IRUDGLDWRPLFJDV 63(&,),&+($75$7,2 N Fo F p 7KH NLQHWLF WKHRU\ RI JDVHVLQGLFDWHVWKDWIRUPRQDWRPLFJDVHV VXFK DV +H1H$U
(121) N )RUGLDWRPLFJDVHV VXFKDV 2 1
(122) N DWRUGLQDU\WHPSHUDWXUHV 3UREOHPV Q NLORPROHV RI PROHFXODU K\GURJHQ DW LQLWLDO FRQGLWLRQV S h 9 h 7 h H[SDQGV LVREDULFDOO\ WR SUHFLVHO\ WZLFH LWV YROXPH :KDW LV WKH ILQDOWHPSHUDWXUHRIWKHJDV":KDWLVWKHH[SDQVLRQZRUNGRQHE\WKHJDVDQGKRZPXFKKHDWHQWHUVWKHJDVGXULQJWKHH[SDQVLRQ" 6XSSRVH IRU VRPH PRQRDWRPLF JDV FRQWDLQHG LQ D F\OLQGHU WKH DQG ILQDO WHPSHUDWXUHVDUH.DQG. UHVSHFWLYHO\DQG LQLWLDO WKDWLWVLQLWLDOSUHVVXUHLVN3DDQGLWVLQLWLDOYROXPHLV P )LQG'8':DQG'4LIWKHJDVLVKHDWHGDW D
(123) FRQVWDQWYROXPH E
(124) FRQVWDQWSUHVVXUH F
(125) DGLDEDWLFDOO\ 7KHS9GLDJUDPLQILJDEDSSOLHVWRDJDVXQGHUJRLQJDF\FOLFFKDQJHLQDSLVWRQF\OLQGHUDUUDQJHPHQW:KDWLVWKHZRUNGRQH E\WKHJDVLQWKHF\FOH" D
(126) S E
(127) S $ ' S h Sh $ 7 FRQVW Sg Sg % & % & 9 9 9 h 9g 9 h 9g )LJ g. $ F\OLQGHU RI LGHDO JDV LV FORVHG E\ DQ NJ PRYDEOH SLVWRQ DUHD FP
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
(129)
Powiązane dokumenty
[r]
IJKLMNOPNQLRST LUVOLWNOXNWYUNSZO[KZN\O]]^TT^OPNOPNQLRSNVOZ^\_
[r]
[r]
[r]
[r]
[r]
[r]
