)UHT *+] 3R XW G %P )UHT *+] 3R XW G %P 3RX W G% P )UHT *+] 3RX W G% P )UHT *+]
$QDO\VLVRI2GG0RGH3DUDPHWULF2VFLOODWLRQVLQ
+%70XOWL6WDJH3RZHU$PSOLILHUV
$$QDNDEH
-0&ROODQWHV
-3RUWLOOD
--XJR
60RQV
$0DOOHW
//DSLHUUH
8QLYHUVLW\RIWKH%DVTXH&RXQWU\(OHFWULFLW\DQG(OHFWURQLFV'HSDUWPHQW$SGR%LOEDR6SDLQ 3KRQH )D[ HPDLODDL#ZHOFHKXHV ,5&208QLYHUVLW\RI/LPRJHV$Y7KRPDV/LPRJHV)UDQFH HPDLOPRQV#LUFRPXQLOLPIU &1(6$Y(GRXDUG%HOLQ7RXORXVH)UDQFH HPDLODODLQPDOOHW#FQHVIU $EVWUDFW²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
,,1752'8&7,21
6HYHUDO RVFLOODWLRQ PHFKDQLVPV FDQ DIIHFW PXOWLVWDJH SRZHU DPSOLILHUV >@ ,Q SDUWLFXODU +%7 PXOWLVWDJH SRZHU DPSOLILHUV KDYH D WHQGHQF\ WR H[KLELW SDUDPHWULF IUHTXHQF\ GLYLVLRQV WKH VWDUWXS RI WKH VXEKDUPRQLF IUHTXHQF\FRPSRQHQWEHLQJIXQFWLRQRIWKHLQSXWSRZHU IRULQVWDQFH,QRUGHUWRGHWHFWDQGDYRLGWKHSUHVHQFHRI WKHVHXQGHVLUHGUHVSRQVHVDQGHQVXUHVXFFHVVIXOGHVLJQV DFDUHIXOVWDELOLW\DQDO\VLVLVUHTXLUHG
7KH V\PPHWU\ LQ WKH WRSRORJ\ RI PXOWLVWDJH SRZHU DPSOLILHUV DQG WKH SUHVHQFH RI SRZHU FRPELQLQJ EORFNV LQWURGXFHWKHSRVVLELOLW\RIRGGPRGHV RI RVFLOODWLRQ > @6PDOOVLJQDODQDO\VLVWHFKQLTXHV>@IRUSUHGLFWLQJWKH H[LVWHQFH RI RGGPRGH RVFLOODWLRQV DUH QRW DSSOLFDEOH WR SDUDPHWULF RVFLOODWLRQV ,Q DGGLWLRQ WLPHGRPDLQ VLPXODWLRQVDUHRIWHQLPSUDFWLFDOGXHWRWKHFRQVLGHUDEOH SUHVHQFHRIHOHPHQWVGHILQHGLQWKHIUHTXHQF\GRPDLQDQG WKHODUJHWUDQVLHQWVLQYROYHG
6WDELOL]DWLRQWHFKQLTXHVVKRXOGEHEDVHGRQDQLQGHSWK NQRZOHGJH RI WKH QDWXUH DQG RULJLQ RI WKH RVFLOODWLRQ PHFKDQLVP,JQRULQJWKHW\SHRIWKHRVFLOODWLRQPRGHFDQ OHDG WR WKH LQVHUWLRQ RI QRQRSWLPDO VWDELOL]DWLRQ QHWZRUNV$VDQH[DPSOHXVXDOVWDELOL]DWLRQVWUDWHJLHVIRU SDUDPHWULFRVFLOODWLRQVDSSO\5&QHWZRUNVDWWKHLQSXWRI WKHWUDQVLVWRUV>@>@>@+RZHYHUWKLVPD\QRWEHWKH PRVW VXLWDEOH VROXWLRQ ZKHQ GHDOLQJ ZLWK RGGPRGH RVFLOODWLRQV>@
,Q WKLV SDSHU D WHFKQLTXH IRU SUHGLFWLQJ RGGPRGH RVFLOODWLRQV IURP WKH DQDO\VLV RI H[DFW SROH]HUR FDQFHOODWLRQV WKDW WDNH SODFH LQ WKH IUHTXHQF\ UHVSRQVH REWDLQHGDWVRPHVSHFLILFQRGHVRIWKHFLUFXLWLVUHSRUWHG 7KHVWDELOLW\DQDO\VLVPHWKRGSURSRVHGLQ>@LVDGDSWHG KHUH WR SURYLGH D VWUDLJKWIRUZDUG PHWKRGRORJ\ WR FRQFOXGHWKHRVFLOODWLRQPRGH7KLVVWDELOLW\DQDO\VLVZDV EDVHG RQ WKH FDOFXODWLRQ RI WKH V\VWHP SROHV DQG ]HURHV
DVVRFLDWHG WR WKH OLQHDUL]DWLRQ RI WKH VLPXODWHG ODUJH VLJQDOVWHDG\VWDWH>@7KHPHWKRGORZWLPHFRQVXPLQJ DQGHDVLO\FRPELQDEOHZLWKDQ\VWDQGDUG&$'SDFNDJHLV SDUWLFXODUO\ZHOODGDSWHGWRWKHULJRURXVLQYHVWLJDWLRQRI SDUDPHWULFVWDELOLW\LQFRPSOH[FLUFXLWV
7KH SURSRVHG PHWKRGRORJ\ IRU DQDO\VLQJ DQG HOLPLQDWLQJ RGGPRGH SDUDPHWULF RVFLOODWLRQV KDV EHHQ DSSOLHGKHUHWRD00,&SRZHUDPSOLILHU
,,/$5*(6,*1$/67$%,/,7<$1$/<6,62)$1;%$1'
32:(5$03/,),(5
7KH DQDO\VLV PHWKRGRORJ\ LV DSSOLHG WR D 00,& ; EDQG WZRVWDJH SRZHU DPSOLILHU 7KH FLUFXLW LV EXLOW LQ +%7 WHFKQRORJ\ EDVHG RQ $V*D*D,Q3 SURFHVV 'HVLJQ JRDOV ZHUH :DWW RXWSXW SRZHU ZLWK PD[LPXP SRZHU DGGHG HIILFLHQF\ 7KH OD\RXW RI WKH FLUFXLW LV VKRZQ LQ )LJ )LJ /D\RXWRIWKH;EDQGSRZHUDPSOLILHU
$ SDUDPHWULF IUHTXHQF\ GLYLVLRQ KDV EHHQ H[SHULPHQWDOO\ IRXQG LQ WKLV DPSOLILHU )LJ VKRZV WKH RXWSXW VSHFWUXP PHDVXUHG DURXQG WKH IXQGDPHQWDO DQG GLYLGHG IUHTXHQFLHV IRU ILQ *+] DQG 3LQ
G%P
)LJ 6SHFWUXP PHDVXUHPHQWV QHDU ILQ DQG ILQ RI ;EDQG SRZHUDPSOLILHUILQ *+]3LQ G%P
,P 5H SSSSHuuuu uuuu SSSSH ,P 5H SSSSHuuuu uuuu SSSSH ,P 5H SSSSHuuuu uuuu SSSSH ,P 5H SSSSHuuuu uuuu SSSSH ,P 5H SSSSHuuuu uuuu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
REWDLQHG XVLQJ IUHTXHQF\ GRPDLQ LGHQWLILFDWLRQ PHWKRGV >@$VDQH[DPSOHLQ)LJWKHHYROXWLRQRIILQSROHV
ZLWK WKH LQSXW SRZHU YDOXH LV UHSUHVHQWHG IRU ILQ
*+] 7KHVH SROHV EHFRPH XQVWDEOH ZLWK SRVLWLYH UHDO SDUW DV LQSXW SRZHU LQFUHDVHV )RU ILQ *+] D
IUHTXHQF\GLYLVLRQLQVWDELOLW\ZDVGHWHFWHGIRU3LQKLJKHU WKDQG%P 5H ,P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P SHu u SH 5H ,P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P 3LQ G%P SHu u SH
)LJ (YROXWLRQ RI ILQ SROHV ZLWK WKH LQSXW SRZHU YDOXH ILQ *+]
%'HWHUPLQDWLRQRIWKHRVFLOODWLRQPRGH
,QRUGHUWRVWXG\WKHRULJLQRIWKHSDUDPHWULFIUHTXHQF\ GLYLVLRQOHWXVLOOXVWUDWHWKHDQDO\VLVWKURXJKDVLPSOLILHG FLUFXLW )LJ WKDW TXDOLWDWLYHO\ H[KLELWV WKH VDPH XQVWDEOHEHKDYLRXUDVWKHZKROHDPSOLILHU7KLVEDVLFFHOO LV RQO\ FRPSRVHG RI WZR +%7 WUDQVLVWRUV ZLWK D VLPSOLILHGSRZHUVSOLWWHUQHWZRUNDWWKHLQSXWDQGZLWKRXW SRZHUFRPELQLQJQHWZRUNDWWKHRXWSXW 56 ILQ3LQ 5/ 5/ F D E
)LJ %DVLF FHOO WKDW TXDOLWDWLYHO\ H[KLELWV WKH VDPH EHKDYLRXUDVWKHRULJLQDODPSOLILHUFLUFXLW
7KHLQMHFWLRQRIDFXUUHQWSHUWXUEDWLRQLQWRWKHFLUFXLW DOORZV WKH H[FLWDWLRQ RI RGG DQGRU HYHQ PRGHV GHSHQGLQJ RQ WKH QRGH RI WKH FLUFXLW ZKHUH WKH SHUWXUEDWLRQLVLQWURGXFHG
,QWR WKH EDVH RI RQH WUDQVLVWRU QRGHV µD¶ RU µE¶ WKH FXUUHQWSHUWXUEDWLRQH[FLWHVERWKRGGDQGHYHQPRGHV RI WKH FLUFXLW 7KXV WKH SUHVHQFH RI RGG DQG HYHQ PRGHRVFLOODWLRQVFDQEHSUHGLFWHG
,QMHFWLQJ WZR FXUUHQW SHUWXUEDWLRQV ZLWK LGHQWLFDO DPSOLWXGHDQGDSKDVHGLIIHUHQFHRIDWWKHEDVHV RIERWKWUDQVLVWRUVQRGHVµD¶DQGµE¶H[FLWHVRQO\WKH RGG PRGH DQG WKHUHIRUH RQO\ RGGPRGH LQVWDELOLWLHV ZLOOEHGHWHFWHG
$WWKHFRPELQLQJQRGHRIWKHSRZHUVSOLWWHUQRGHµF¶ RU LQWURGXFLQJ WZR LGHQWLFDO FXUUHQW SHUWXUEDWLRQV DW WKHEDVHVRIERWKWUDQVLVWRUVQRGHVµD¶DQG µE¶ RQO\ WKH HYHQ PRGH LV H[FLWHG WKXV RQO\ HYHQPRGH LQVWDELOLWLHVZLOOEHGHWHFWHG
([DPSOHVRIWKHVHSURFHGXUHVDSSOLHGWRWKHEDVLFFHOO RI)LJILQ *+]3LQ G%PDUHVKRZQLQ
ILJXUHVWR)LJ VKRZV WKH IUHTXHQF\ UHVSRQVH DQG WKHLGHQWLILFDWLRQUHVXOWVREWDLQHGZKHQRQO\RQHFXUUHQW SHUWXUEDWLRQ LV DSSOLHG WR QRGH µD¶ 7KH SUHVHQFH RI DQ XQVWDEOHSDLURIFRPSOH[FRQMXJDWHSROHVDWILQLQGLFDWHV
WKHVWDUWXSRIDIUHTXHQF\GLYLVLRQ1RFRQFOXVLRQDERXW WKH QDWXUH RI WKH RVFLOODWLRQ PRGH FDQ EH H[WUDFWHG \HW )LJVKRZVWKHUHVXOWVFRUUHVSRQGLQJWRWKHFRQQHFWLRQ RI WZR SHUWXUEDWLRQV ZLWK D SKDVH GLIIHUHQFH RI DW QRGHVµD¶DQGµE¶7KHREWDLQHGXQVWDEOHSROHVVXJJHVWDQ RGGPRGH RVFLOODWLRQ 7KLV LV FRQILUPHG E\ WKH UHVXOWV VKRZQ LQ )LJ LQ ZKLFK WKH FXUUHQW SHUWXUEDWLRQ ZDV FRQQHFWHGDWWKHQRGHµF¶FRPELQLQJQRGHRIWKHSRZHU VSOLWWHU1RXQVWDEOHSROHVDUHGHWHFWHGEHFDXVHDQH[DFW SROH]HUR FDQFHOODWLRQ RFFXUV LQ WKH IUHTXHQF\ UHVSRQVH REWDLQHG DW WKH V\PPHWU\ OLQH RI WKH SRZHU VSOLWWHU :H FDQ WKXV FRQILUP WKDW WKH LQVWDELOLW\ FRUUHVSRQGV WR DQ RGGPRGHIUHTXHQF\GLYLVLRQ
)LJ )UHTXHQF\ UHVSRQVH DQG LGHQWLILFDWLRQ UHVXOWV ZKHQ H[FLWLQJ RGG DQG HYHQ PRGHV 8QVWDEOH SROHV DW ILQ DUH REWDLQHGILQ *+]3LQ G%P
)LJ )UHTXHQF\ UHVSRQVH DQG LGHQWLILFDWLRQ UHVXOWV ZKHQ H[FLWLQJRQO\WKHRGGPRGH8QVWDEOHSROHVDWILQDUHREWDLQHG ILQ *+]3LQ G%P ( ( ( 0D J G % $Q J )UHT +] ( ( ( ( 0D J G % $Q J )UHT +] ( ( ( ( 0D J G % $Q J )UHT +] ( ( ( ( 0D J G % $Q J )UHT +] (
11th GAAS Symposium - Munich 2003 534
,P 5H SSSSHuuuu uuuu SSSSH ,P 5H SSSSHuuuu uuuu SSSSH 5/ = =
)LJ )UHTXHQF\ UHVSRQVH DQG LGHQWLILFDWLRQ UHVXOWV ZKHQ H[FLWLQJ RQO\ WKH HYHQ PRGH 1R XQVWDEOH SROHV DUH REWDLQHG ILQ *+]3LQ G%P
,QWKHRGGPRGHVLJQDOVLQERWKEUDQFKHVRIWKHEDVLF FHOO )LJ DUH RXW RI SKDVH DW WKH RVFLOODWLRQ IUHTXHQF\&RQVHTXHQWO\DYLUWXDOJURXQGFDQEHDVVXPHG DWWKHV\PPHWU\OLQHRIWKHSRZHUVSOLWWHU)LJD,QWKH HYHQPRGHWKHVLJQDOVLQERWKEUDQFKHVDUHLQSKDVHVRD YLUWXDO RSHQ FLUFXLW FDQ EH DVVXPHG EHWZHHQ WKH WZR KDOYHVRIWKHFLUFXLW)LJE D E
)LJ D 2GGPRGH HTXLYDOHQW FLUFXLW E (YHQPRGH HTXLYDOHQWFLUFXLW
)URPRGGDQGHYHQPRGHHTXLYDOHQWFLUFXLWVRI)LJ WKH RVFLOODWLRQ VWDUWXS FRQGLWLRQV IRU HDFK PRGH FDQ EH VWDWHGDV 2GGPRGH 5HDO= DQG ,P= (YHQPRGH 5HDO=56 DQG ,P=
(YHQPRGH RVFLOODWLRQ FRQGLWLRQV DUH PRUH UHVWULFWLYH WKDWWKHRGGPRGHRQHVZKLFKDUHVDWLVILHGDWWKHGLYLGHG IUHTXHQF\IRUFHUWDLQLQSXWSRZHUYDOXHV
$VWDELOLW\DQDO\VLVRIWKHRGGPRGHHTXLYDOHQWFLUFXLW FDQ DOVR EH SHUIRUPHG WR YHULI\ WKDW WKH IUHTXHQF\ GLYLVLRQ LV DQ RGGPRGH RVFLOODWLRQ ,Q RUGHU WR GR WKLV WKH ODUJH VLJQDO VWHDG\ VWDWH KDV WR EH PDLQWDLQHG ZKLOH SUHVHQWLQJDYLUWXDOJURXQGDWWKHV\PPHWU\OLQH$VLPSOH SURFHGXUH WR REWDLQ WKH RGGPRGH HTXLYDOHQW FLUFXLW DURXQGDJLYHQODUJHVLJQDOVWHDG\VWDWHLVWRLQWURGXFHDQ LGHDOVWRSEDQGILOWHUDWILQDQGLWVKDUPRQLFVEHWZHHQWKH
FRPELQLQJQRGHDQGWKHYLUWXDOJURXQG)LJ7KXVWKH ODUJH VLJQDO VWHDG\ VWDWH RI WKH FLUFXLW LV QRW GLVWRUWHG 7KLVDSSURDFKLVDJHQHUDOL]DWLRQRIWKHVPDOOVLJQDORGG PRGH DQDO\VLV WR WKH ODUJHVLJQDO FDVH 7KH IUHTXHQF\ GLYLVLRQLQVWDELOLW\GHWHFWHGLQWKHEDVLFFHOO)LJKDV DOVREHHQREVHUYHGXVLQJWKHRGGPRGHHTXLYDOHQWFLUFXLW RI )LJ FRQILUPLQJ DJDLQ WKH RGG QDWXUH RI WKH RVFLOODWLRQ
5/
6WRSEDQGHILOWHUDW
ILQILQILQILQª
56 ILQ3LQ )LJ 2GGPRGHHTXLYDOHQWFLUFXLWXVHGIRUWKHODUJHVLJQDO VWDELOLW\DQDO\VLV
)LQDOO\ WKH VWDELOLW\ RI WKH ZKROH FLUFXLW KDV EHHQ VWXGLHGLQRUGHUWRGHWHUPLQHWKHRVFLOODWLRQPRGHLQWKH ZKROHDPSOLILHU7KHSRZHUDPSOLILHUVFKHPHLVVKRZQLQ )LJ ,Q >@ WKH IUHTXHQF\ UHVSRQVH ZDV REWDLQHG E\ LQWURGXFLQJ D FXUUHQW SHUWXUEDWLRQ DW WKH EDVH RI RQH WUDQVLVWRURIWKHVHFRQGVWDJHQRGHVDDƍDƍƍRUDƍƍƍDQG XQVWDEOH SROHV DW ILQ ZHUH GHWHFWHG ,Q GRLQJ VR ERWK
RGG DQG HYHQ PRGHV RI WKH DPSOLILHU DUH H[FLWHG VR WKH QDWXUHRIWKHRVFLOODWLRQFDQQRWEHGHWHUPLQHG\HW:LWK WKH DLP RI GHWHUPLQLQJ WKH QDWXUH RI WKH RVFLOODWLRQ WKH IUHTXHQF\ UHVSRQVH RI WKH DPSOLILHU KDV EHHQ REWDLQHG KHUHXVLQJSXUHRGGRUHYHQH[FLWDWLRQV D 56 ILQ3LQ 3RZ HU V SOL WWHU 3RZ HU F RPE LQ HU 5RGG 5RGG 5/ 3RZ HU FRPE LQ HU Dµµ Dµµµ Dµµµµ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
GHWHFWHG LQ WKLV DPSOLILHU ,Q IDFW DQ H[DFW SROH]HUR FDQFHOODWLRQRFFXUVLQWKHIUHTXHQF\UHVSRQVHREWDLQHGE\ LQWURGXFLQJ WKH FXUUHQW SHUWXUEDWLRQ DW WKH FRPELQLQJ QRGHV RI SRZHU VSOLWWHUV DQG FRPELQHUV 7KH SDUDPHWULF IUHTXHQF\GLYLVLRQRIWKLVDPSOLILHULVWKXVDQRGGPRGH RVFLOODWLRQ
$VH[SODLQHGLQ>@GLIIHUHQWRGGPRGHRVFLOODWLRQVFDQ EHIRXQGLQDFLUFXLWZLWKPXOWLSOHFRPELQHGGHYLFHV,Q SDUWLFXODU WKUHH RGGPRGH RVFLOODWLRQV >@ FDQ EH IRXQG LQDFLUFXLWZLWKFRPELQHGGHYLFHVOLNHWKHRQHXQGHU DQDO\VLV$VWKHLQVWDELOLW\LVQRWGHWHFWHGDWQRGHVERUEƍ ZH FDQ FRQFOXGH WKDW 4 DQG 4 RSHUDWH ZLWK D SKDVH GLIIHUHQFH RI DW ILQ DQG 4 DQG 4 RSHUDWH DOVR
ZLWKDSKDVHGLIIHUHQFHRIDWILQ,IWKHLQVWDELOLW\ ZHUHGHWHFWHGDWQRGHVERUEƍEXWQRWDWQRGHF4DQG 0D J G % $Q J )UHT +] ( ( ( ( 0D J G % $Q J )UHT +] ( ( ( ( 56 5/ = =
4ZRXOGRSHUDWHLQSKDVHZLWKHDFKRWKHUEXWRXW RISKDVHZLWK4DQG4DWILQ
%)UHTXHQF\GLYLGHGVWHDG\VWDWHVROXWLRQZLWKKDUPRQLF EDODQFH
7LPHGRPDLQ VLPXODWLRQV ZHUH QRW DSSOLFDEOH WR WKH SRZHUDPSOLILHUXQGHUVWXG\EHFDXVHRILWVODUJHDPRXQW RI GLVWULEXWHG SDUDPHWHU FRPSRQHQWV 7KHUHIRUH D PHWKRG WR REWDLQ WKH IUHTXHQF\ GLYLGHG VWHDG\VWDWH LQ KDUPRQLF EDODQFH +% RULJLQDOO\ GHYHORSHG IRU IUHTXHQF\GLYLGHUV>@KDVEHHQDGDSWHGDQGVXFFHVVIXOO\ DSSOLHGWRWKHDQDO\VLVRISRZHU DPSOLILHUV 7KH YROWDJH WLPH ZDYHIRUPV DQG VSHFWUXP REWDLQHG LQ WKH EDVHV RI WUDQVLVWRUV 4 DQG 4 IRU ILQ *+] DQG 3LQ
G%P DUH UHSUHVHQWHG LQ )LJ 2EVHUYH WKDW WKH RGG KDUPRQLFV RI WKH RVFLOODWLRQ IUHTXHQF\ ILQ ILQ
ILQKDYHDSKDVHGLIIHUHQFHRIFRQILUPLQJWKH RGGPRGHRVFLOODWLRQ )LJ 9ROWDJHWLPHZDYHIRUPVDQGVSHFWUXPREWDLQHGLQWKH EDVHVRI4DQG4WKURXJK+% VLPXODWLRQV ILQ *+] 3LQ G%P ,,,&,5&8,767$%,/,=$7,21
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
WKH DPSOLILHU LV QRW DIIHFWHG VLQFH QR FXUUHQW ZLOO IORZ WKURXJKWKHVHUHVLVWDQFHVSURYLGHGWKDWLGHDOO\V\PPHWULF FLUFXLWLVFRQVLGHUHG
9,&21&/86,21
$ WHFKQLTXH IRU SUHGLFWLQJ SDUDPHWULF RGGPRGH RVFLOODWLRQVLQSRZHUDPSOLILHUVKDVEHHQSUHVHQWHG7KLV WHFKQLTXH LV EDVHG RQ WKH DQDO\VLV RI H[DFW SROH]HUR FDQFHOODWLRQV WKDW WDNH SODFH LQ WKH IUHTXHQF\ UHVSRQVH REWDLQHG DW VRPH VSHFLILF QRGHV RI WKH FLUFXLW 7KH NQRZOHGJH RI WKH RVFLOODWLRQ PRGH DOORZV ILQGLQJ D VXLWDEOH VWUDWHJ\ IRU FLUFXLW VWDELOL]DWLRQ 7KH PHWKRGRORJ\KDVEHHQVXFFHVVIXOO\DSSOLHGWRWKHDQDO\VLV DQGHOLPLQDWLRQRISDUDPHWULFRGGPRGHRVFLOODWLRQVLQDQ ;EDQGWZRVWDJH00,&SRZHUDPSOLILHU
$&.12:/('*(0(17
7KHDXWKRUVIURPWKH8QLYHUVLW\RIWKH%DVTXH&RXQWU\ ZLVK WR DFNQRZOHGJH WKH ILQDQFLDO VXSSRUW RI WKH &1(6 FRQWUDFW WKH 6SDQLVK &RPPLVVLRQ RI 6FLHQFH DQG 7HFKQRORJ\ 5HVHDUFK 3URMHFW 7,& DQG WKH SDUWLDO VXSSRUW RI WKH 839(+8 839
5()(5(1&(6
>@ 3 GH +HN ³'HVLJQ DQG UHVXOWV RI VWDWHRIWKHDUW PLFURZDYH PRQROLWKLF LQWHJUDWHG KLJKSRZHU DPSOLILHUV´ 3URFHHGLQJVRI6$)(SS
>@ -* .DVVDNLDQ ' /DX ³$Q DQDO\VLV DQG H[SHULPHQWDO YHULILFDWLRQ RI SDUDVLWLF RVFLOODWLRQV LQ SDUDOOHOHG SRZHU 026)(7V´ ,((( 7UDQVDFWLRQV RQ (OHFWURQLF 'HYLFHV YRO('QRSS-XO\
>@ 5* )UHLWDJ ³$ XQLILHG DQDO\VLV RI 00,& SRZHU DPSOLILHU VWDELOLW\´ ,((( 0776 'LJHVW SS
>@ ' 7HHWHU $ 3ODW]NHU 5 %RXUTXH ³$ FRPSDFW QHWZRUN IRU HOLPLQDWLQJ SDUDPHWULF RVFLOODWLRQV LQ KLJK SRZHU 00,& DPSOLILHUV´ ,((( 0776 'LJHVW SS
>@ $$QDNDEH-0&ROODQWHV-3RUWLOOD--XJR$0DOOHW / /DSLHUUH -3 )UD\VVH $QDO\VLV DQG HOLPLQDWLRQ RI SDUDPHWULF RVFLOODWLRQV LQ PRQROLWKLF SRZHU DPSOLILHUV ,(((0776'LJHVWSS
>@ --XJR-3RUWLOOD$$QDNDEH$6XDUH]-0&ROODQWHV ³&ORVHGORRS VWDELOLW\ DQDO\VLV RI PLFURZDYH DPSOLILHUV´ ,(((OHFW/HWWHUV9RO1RSS)HE >@ $ $QDNDEH 6 0RQV 7 *DVVHOLQJ 3 &DVDV 5 4XHUH -0 &ROODQWHV $ 0DOOHW ³(IILFLHQW QRQOLQHDU VWDELOLW\ DQDO\VLV RI PLFURZDYH FLUFXLWV XVLQJ FRPPHUFLDOO\ DYDLODEOH WRROV´ 3URFHHGLQJV RI WKH QG (XURSHDQ 0LFURZDYH&RQIHUHQFHSS
>@ 6 0RQV -& 1DOODWDPE\ 5 4XpUp 3 6DYDU\ - 2EUHJRQ´$XQLILHGDSSURDFKIRUWKHOLQHDUDQGQRQOLQHDU VWDELOLW\DQDO\VLVRIPLFURZDYHFLUFXLWVXVLQJFRPPHUFLDOO\ DYDLODEOHWRROV´,(((7UDQVDFWLRQVRQ0LFURZDYH7KHRU\ DQG7HFKQLTXHV9ROQ'HFHPEHUSS
>@ $ $QDNDEH -3 3DVFXDO - 3RUWLOOD - -XJR -0 &ROODQWHV´+DUPRQLFEDODQFHDQDO\VLVRIGLJLWDOIUHTXHQF\ GLYLGHUV´ ,((( 0LFURZDYH DQG :LUHOHVV &RPSRQHQW /HWWHUVYROQRSS$XJXVW IUHT*+] PD J 9 E PD J 9 E IUHT*+] PD J 9 E PD J 9 E IUHT*+] SKDVH 9E SKDVH 9E IUHT*+] SKDVH 9E SKDVH 9E 7LPHQVHF 9E 9E 7LPHQVHF 9E 9E
11th GAAS Symposium - Munich 2003 536