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Imperial College Londonpavl/rpithes.pdf · 2002. 6. 18. · z nl78{/ 2:3659kjg 9 8 9 s / 1$243658792:3;78< =?>a@cbedaf63;7 gh3;< =?f6f ]a3;58khgh

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Page 1: Imperial College Londonpavl/rpithes.pdf · 2002. 6. 18. · z nl78{/ 2:3659kjg 9 8 9 s / 1$243658792:3;78< =?>a@cbedaf63;7 gh3;< =?f6f ]a3;58khgh

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B8_NW�MO<cGH36TUB�GOM � � >6§9§8B � \k78F6F;7E�"<:>I�7h59M4G"MO<�GO36TUB�GOM � � >6§8§9S � �ÌM$36_HGHMO592:BzGHM�GHKRM$MO_NMO2:5 / 36WRMi_jGO3VG / � � >6§8¦ � 3;_XGH36TUMuGO778S9GOB836_Ny

î » Û¿ÙÚ$ÛzÜ¡^ðV Á�Á K D ÁíÁ ¼ ÓAò^ï ½ § À � F ¸ î

¡^ðV � � Å D � Ó ò ï ½ § À â Ý Î� Á�Á D ÁíÁ ¼ Óvò�ï ½ § À � �9� ¹ Ý Î� Á�Á D ÁíÁ ¼ ÓAò�ï ½ § À � F V �

õ îWF V Á�Á � ÁíÁ Ó î ïíï V e ¡fð�Àíñ Ó ò ï ½ § ÀíÀ ÁíÁ D Á�Á Ó î ï�ï V e ¡^ð�À�ñ Ó ò ï ½ § À�À â Ý Î� î ¼ ÁíÁ P Á�Á ¼ ÓAò�ï ½ § Àõ î ¼ ¤ â F V

Ý Î F V ô ÁíÁ � Á�Á Ó î ïíï V e ¡^ð�Àíñ Ó ò ï ½ § ÀíÀ â Ý Î� î ¼ Á�Á P ÁíÁ ¼ Óvò�ï ½ § Àõ î ¼ Ý Î� â ¤ â F V

Ý Î ô ¼ � � >6§ ² �

v QRF[GH36{NF / 36_R5�_R7E� � � >6§ ² � S /������< ô���öB9_RW�GHB9�¶3;_R5�GHKRML<4f¶QNB82:M�2:7¥7zGÌ79\AS�7�GOK�<:3;WRMO<��?MaB92:2:3[D|MLB�G � � >6§9§8S � >

ILKRM${R247¥78\q78\eGHKRM$F;MOThTUB�3;<LZO78TU{RF;M4GHMO>�?7E���?M"B92:M�2:MOB9W / GH7U{R247ÆD|M�GOKRM�KR79Th7958MO_N36¨OBzGH3679_UGOKRMO7824MOTU>aILKRM${RF;B8_��"36F6FsS�MÞGH7UF67¥78��\k792

B�<478F6QÈGH3679_�3;_(GHKRM�\k7824Tþ78\uB�TQRF[GH36{NF6M$<:ZOB9F6MO<-M ~ {NB8_R<43678_N>h¡?<436_R5"GHKRMO_!F;MOTUThB ¤ �ÌM<4KRB8F;FC78SÈGHB83;_MOfgQRB�GO3679_R<\k782-GOKRM�dR2:<cGhGb�Ì7(GOMO2:TU<�3;_­GHKRM�M ~ {RB8_N<:3679_R>�ILKNMO_��?M�<:KRB9F6FL79S9GHB936_�S�79QR_RWR<U\k782-GOKRMMO242:782qZOB9QR<:MiW�S / _NMO58F;MOZ4GH3;_R5?KR3;58KRMi2�7824WRMO2�GHMi2:TU<&3;_$GOKRM�M ~ {NB8_R<43678_N>L¡?<:3;_R5�GHKRMO<4MaS�79QR_RWR<0�?Ma<4KRB8F;FMO<cGH36TUB�GOM�GHKRMWR3;«�MO2:MO_NZOM$S|MxGx�?MOMO_XGHKNM�<:79F6Q9GO3679_ D �óÙ Å�F � GH7�GOKRM�792:365936_RB9F^Mif¶QRBzGH3;78_ � � > � ¤ � B8_RW(GOKRM<:QNTÇ79\�GHKRMdR24<�G�Gb�Ì7�GOMO2:TU< D B9_RW(�ÌM�<:KRB9F6FewxQR<�GO36\ / GHKRBzG�3VG�36<�<:TUB8F;F6��36_�GHKRM�B8{R{R2478{R2436BzGHM_R792:TU>=?<0�?M?KRBED|M?B8F;2:MOB9W / TUMO_HGH3679_RMOWR��3;_GOKR36<uZ�KNB8{9GOMO20�ÌM?B92:M$ZO79_RZOMO24_RMOW��"3[GHKXGHKRM-{RB824B8TUM4GHMO2L24MO583;ThM·�Ü � ¹ ¤ Å �8� Å ½ÁÂÌ>

¢�M"<4KRB8F;FsQR<:M�GOKRM$_R7�GOB�GH3;78_Ry

� < y6¸ Ý Î CC F â � � �óÙ Å�F � â î Ù ì � Ù î Å Fî Ú �:�I�K�¹ î » Û¿ÙÚ$Û Ü N � � >6§9® �

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¦ �

ILKRM$36_N3VGH3;B8F DNB9F6QRM${R2478SRF;MOT � � > � ¤ � ZOB8_�S�M��"243VG4GHMO_�B9< « y

� < D < �kÙ ÅZF � ¸ � ¬�­ R(S � � Å�U � � � >;¦ � B �

D < �óÙ Å�F ¸ �8� ¸ D ��¶ �kÙ ��® ­ R Å � � >6¦ � S �

=?ZOZi782:WN36_R5ÞGH7�GOKRM?24MOZO36{�M�78\sTQRF[GH3;{RF6ML<4ZOB8F;M?M ~ {RB8_R<43679_R<��?M?<:KRB9F6F GH2:MiB�G�GOKRM(n9<:F67E�9n-D¶B82436B9SRF6MO< Ù ÅEFB8_NW-GHKRMun8\kB8<cG§n�D¶B82436B8SNF6MO< í y;¸ × < Å ê y6¸ ¡<�� B9<C36_NWRMO{�MO_RWRMi_jGO>&ILKNMLWR36«�MO24MO_jGO36B9F¥78{�MO2:BzGH792:<�GO2:B8_N<:\k7824TB8<4y

CC F

C CC Fâ ¤î ÚCC ê � � >;¦ ¤ B �

K C K × â ¤îK û � � >6¦ ¤ S �

¡?<:3;_R5 � � >6¦ ¤ � �?M$2:M4�"243VGHM�� < 36_XGHKRM$\k79F6F67E�"3;_R5\k7824Thy� < ¸ Ý Î CC F â � �óÙ Å�F � â î Ù ì � Ù î Å Fî Ú

� I�K�¹ î » Û�ÙÚ$ÛzÜ N

¸ Ý Î CC Fâ ¤î ÚCC ê â � � �kÙ ÅZF � â î�Ù ì �óí Å ê �:� I � K × â ¤

îK û �

¹ î » Û�ÙÚ$ÛzÜ N × â �îK × K û"â ¤

î ¼NUû

¸ Ý Î ¤î ÚCC ê â

¤î » µ Ù

ì£I�K û�¹ ¤Ú$ÛzÜ NUû â ¤

î��I�K û

â î Ù ìcI�K × ¹ �Ú$Û Ü K × K û â Ý Î CC F â��YI�K × ¹ î Ù"Û »Ú$Û Ü N ×

y;¸ ¤î Ú

� V â ¤î »Zµ Ù

� » â¤î� ¼ â î Ù � ¾ â � ¸ â î Ù"Û » � ­ Å � � >6¦ �8�

�"KRMO24MOy

� V yO¸ Ý Î CC ê � � >;¦8§9B �

��� �[��+�����lü�������ú��]�����<ú°þ��¡ü þ��¾úàüZý!ÿ++������� ü���¡ü(�¡ü ÿ¢ü��+�:ü��+� ü&ú�Ld��¡üN�lú���,+����ú��<ú�L�ü �.,+������ú��DT"!�� !$#�Z�ú�� ��� ' ü(��+�����,+�lü$��¡ü��¡ú���������ú���% & T � ��VJZv���+ú°ÿ¡ÿbú��¾ü�� �¾ú&%(T � ��VJZv��+��� ' ü�+�|0°ü©û¢ü ü�� ,+�����+ ����:��¡üwÿ¡þlü�0.��ú�,+�%�lü�������ú��]�

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¦ ¤

� » yO¸*ì �óí Å ê � I�K[û$¹ ¤Ú$ÛzÜ NUû � � >6¦8§9S �

� ¼ yO¸�� �óÙ Å�F � I�K û � � >;¦8§8Z �

� ¾ yO¸�ì �kí Å ê � I�K ï ¹�Ú$Û Ü K ï K[û � � >6¦8§9W �

� ¸ yO¸ Ý Î CC F âH� �óÙ Å�F � I�K ï � � >;¦8§8M �

� ­ yO¸º¹ ¤Ú$ÛzÜ N × � � >6¦9§8\ �

ILKRML<�GO2:QRZxGHQR24ML78\çGHKRMLTQNFVGH3;{RF6Mq<4ZOB8F;MO<^M ~ {RB9_R<:3;78_UWRMO{�MO_RWN<CQR{�78_ÌGHKRM0D¶B9F6QRMO<078\¥½�B9_RWh·�>ñ¢ÄML<4KRB8F;F{R24MO<:MO_HG�GOKRM$WRM4GOB836F;MOW�WRMi2:3VD¶BzGH3679_�\k7820GHKNM"<436TU{RF6Mi<�GÌZiB8<:Mi�A_RB9ThMOF / \k792-·­¸�¹ »¼ B8_RWU½�¸ ¤ ¹�·Á¸ö¾¼B8_NW!GOKRMO_�M ~ {RF;B83;_�KR7E��GH7�{R2:7¥ZOMiMOW��"3VGOK�GHKNM�7�GOKRMO2ZOB9<:MO<4>�ILKR2:79QR58KN78Q9GUGHKRM(ZOB8F;ZOQRF6BzGH3;78_R<ÞGHKRBzG\k78F;F67E�*�ÌM$<:KRB9F6FsQR<4M$S|7zGHK�D|MOZ4GH792L_R7�GOB�GO3678_�B8< �ÌMOF;F�B8< GHKRM$<:QNThTUB�GO3678_�ZO78_HD|MO_HGH3;78_R>

æpÀM`pÀ¾¿ ¹87z½�� º�Æ�½ ·­¸Ë¹ »¼æpÀM`pÀ¾¿�Àl¿ ¹87z½�� ºÆ�½ ½!¸ ¾¼

`b_XGHKR3;<LZOB8<4M'� < S�MOZi78TUMO<� < ¸ ¤

î�(ò� V â ¤

î� » â î ôò � ¼ â)� ¾ â î ôò � ¸ � � >6¦9¦ �

�"KRMO24MOy

� V yO¸ � V â � » � � >;¦8³9B �

� » yO¸ � ¼ � � >6¦8³9S �

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¦ �

� ¼ yO¸ � ¾ � � >;¦8³8Z �

� ¾ yO¸ � ¸ � � >6¦8³9W �

� ¸ yO¸ � ­ � � >;¦8³8M �

¡?{�78_�QN<:36_N5 � � >6¦9¦ � �ÌMu�"243VGOM"Mif¶QRBzGH3;78_�\k782 � � >6¦ �9� 3;_�GHKNM"\k792:TUy

¤î ( ò

� V â ¤î� » â î ôò � ¼ â � ¾ â î ôò � ¸ D < �óÙ Å�F � ¸ � � � >6¦ ° �

Y 7820GOKRMO<:M-{RB82cGH36ZiQRF6B92�D¶B8F;QRMO<�79\0·�B8_RW½�3VG?36<LMO_R79QR58KXGO7ZO78_R<436WRMi2�B8_�M ~ {RB9_R<:3;78_�79\�GOKRM?\k78F;F67E�"36_N5\k7824Thy

D < �kÙ Å�F �+* D V �kÙ ÅZFiÅ í Å ê � â îqôò D » �kÙ ÅZFiÅ í Å ê � â î D ¼ �kÙ Å�F�Å í Å ê �â î (ò D ¾ �óÙ Å�F�Å í Å ê � â î ¼ D ¸ �óÙ Å�F�Å í Å ê � â æOæOæ � � >6¦ ± �

�"KRMO24M�GHKNM�\kQR_RZ4GO3679_R< D � Å ¬ ¸ � Å ¤ Å � Å æiæOæ B82:M({|Mi2:367¥WN36Z�3;_ í B9_RW ê >�¢�M�<:QNSR<�GO3VGHQÈGHM � � >6¦ ± � 3;_jGO7� � >6¦ ° � B8_NWR�sS / MOfgQRB�GO36_R5-GOKRM?ZO7¥M1�hZO3;MO_HGH<�79\^{�7E�ÌMi2:<L78\ î GO7 � �ÌM?79S9GHB936_XGHKNM"\k79F6F;7Æ�"3;_R5�<4MOfgQRMO_RZOM78\0MOf¶QNB�GH3;78_R<4y

; � î µ ( ò � y,� VWD V ¸ � � � >;¦ ² B �

; � î µR» � y,� VWD » â � » D/V ¸ � � � >6¦ ² S �

; � î µ ô ò � y,� VOD ¼ â � » D » â)� ¼ D/V ¸ � � � >;¦ ² Z �

; � ¤ � y,� V�D ¾ â)� » D ¼ â)� ¼ D » â � ¾ D/V ¸ � � � >6¦ ² W �

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¦8§

; � î%ôò � y,� V D ¸ â)� » D ¾ â � ¼ D ¼ â)� ¾ D » â)� ¸ D V ¸ � � � >;¦ ² M �

rsM4G"QR<�_R7E�¿B9_RB8F / ¨OM$MOfgQRBzGH3679_R< � � >6¦ ² � > ¢�M"dN2:<�G�78SN<:MO2cD|MuGHKRBzGXF;MOTUThB ¤ B8{R{RF;36MOWXGO7-GHKRM ; � î µ ( ò �MOfgQRB�GO3679_�583VD|Mi<�GHKRBzG�GHKRM!dR24<�G�GOMO2:T 36_ GOKRM!M ~ {RB8_R<43679_�36<�36_RWNMO{�MO_RWRMO_HG�78\�GOKRM!\kB8<cG�DNB92:3;B8SRF;MO<:yD/V ¸ D V �óÙ Å�F � >�nL79_R<:Mif¶QRMi_jGOF / � GHKRM$B8ZxGH3679_�79\-� » GH7 D V 593VD|MO<u¨OMO2:79y

� » D/V ¸��YI�K û D/V ¸ � � � >6¦9® �

ILKgQR<:� GHKRMQ; � î µN»:� S�MOZi78TUMO<&� VOD » ¸ � B8_RW��?MaZi78_RZOF;QRWRM0GOKRB�GuGHKRM�<:MOZi78_RWÌGHMO24T÷36_ÌGHKRM�M ~ {RB8_N<:3679_36<-B8F6<47�36_RWRMi{|Mi_RWRMO_HG�78\ñGHKRM\kB9<�G$D¶B82436B8SNF6MO<4� D » ¸ D » �kÙ Å�F � >¡?<:3;_R5�_R7E�JGOKRMU\kB8Z4G?GOKRB�G.� » D V ¸ �GHKNM�; � î µ ôò � <:3;Th{NF636dNMO<�GO78y

� VWD ¼ â)� ¼ D V ¸ � � � >6³ �8�

ILKRM$<:79FVD¶B8SN36F63[G / ZO79_RWR3[GH3679_�\k782 GHKR3;<LMOf¶QNB�GH3;78_�36<L3;ThTUMOWR3;B�GOMOF / <4B�GH3;<:dRMiW©<436_RZiM

� � ¼ D V�� ¸ � ì �kí Å ê � I�K × ¹ �Ú"ÛzÜ K × K û D/V �kÙ Å�F � �

¸ � ì �kí Å ê � � I�K × D V �kÙ Å�F � ¸ � Å � � >6³ ¤ �

78_�B9ZOZO78QN_jG"79\�GOKRM$B8<:<4QRTU{9GH3;78_XGHKRBzGLGHKRM�D|MOF;7¥ZO3VG / dRMOF6W�KRB9<LThMiB8_�¨OMO247�7ED|MO2�GOKRM${�MO2:3;7¥WR36ZO3[G / ZOMOF6F;>¢�MZOB8_!<478FVD|M � � >6³ ¤ � GHKN2:78QN58K�<:MO{RB92:BzGH3679_�79\�DNB92:3;B8SRF;MO<:>I�7�GHKN36<?MO_NWR���?MF67¥79��\k782-B�<:79F6Q9GO3678_!3;_GHKNM"\k792:T

D ¼ �kÙ Å�F�Å í Å ê � ¸àø �óÙ Å�F�Å í Å ê � I¢K × D/V �óÙ Å�F � � � >6³ �8�

PRQRSN<�GH3[GHQ9GO36_R5�_R7E� � � >6³ �8� 36_HGH7 � � >6³ ¤ � �ÌM�78SÈGHB83;_�MOfgQRBzGH3679_R<U\k782ÌGHKRM�B8Q ~ 3;F636B92 / D|MiZ4GH792�\kQR_RZxGH3679_ø�¸Å¹ ÷�Üfº RÜ g » ® >L`óG"36<0GOKRM$QR_R36fgQRM$TUMOB8_�¨OMO247<:79F6Q9GO3678_N<L78\�GOKRM$ZOMOF6F�{R2:79SRF6MiThy

� V ø �kí Å ê � ¸o¹Ìì �óí Å ê � � � >6³9§ �/ � �K��¡ü��lü þ¾ý����¡ú���ú� �1!ú�L"¡ú°ý!ú� hü��+����������ú�����¡üZúhþ�1�0�������¡ü2143�5 57641893�5;:<6=?>Ï�

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¦8¦

¢�M"{N2:7¥ZOMOMiW©_N7Æ�o�"3VGHKXGOKRM$B8_RB9F / <:36<L79\�GHKNM�; � ¤ � MOf¶QNB�GH3;78_R>LILKNM"<478F[DNB9SR36F;3VG / ZO78_RWN3VGH3;78_�2:MOB9WR<:y� � » D ¼ â)� ¼ D » â)� ¾ D/V1� ¸ � � � >6³9¦ �

PR3;_RZOM D » 36<�36_NWRMO{�MO_RWRMi_jG�78\çGHKNM�\kB8<cGCD¶B82436B8SNF6MO<CB9_RW�ì�36<�36_RZi78TU{R2:MO<4<:3;SRF6M�GHKNM�BED|MO2:B958ML79\9GHKRML<4MOZO79_RWGHMi2:Tÿ3;_�GHKRM$B9S|7ED|M�MOf¶QNB�GH3;78_XD¶B8_R3;<:KRMi<:>LILKgQR<:�N�?M"KNBÆD|Miy

¹ � � » D ¼ � ¸ ¹ � ��I¢K[û � øQI�K × D V � �¸ ¹ » � � C ÷�ÜC ä � �

CED VC5  Ü

¸ � ¸ � � ¾ D V �¸ Ý Î CED/VC F â�� �kÙ ÅZF � IbK × D V � � >6³9³ �

`b_�GOKRMLB8S�7ED|MLZOB8F;ZOQRF;B�GH3;78_Þ�ÌM�KNBÆD|MuQR<:MiW-GHKRMu\kB8Z4GCGOKRB�GO�R<:3;_RZOM�ø �óí Å ê � 36<C{�MO24367¥WR3;Z�36_ í �HGHKRMuBÆD|Mi2:B859M78\u3VGO<"592:B9WR36MO_HGh36<$¨OMO2478>�nL78_R<4MOf¶QNMO_jGOF / �|GHKRMUMOfgQRB�GO3678_�\k782ÞGHKRMUdR24<�G$GHMO24T+36_(GOKRMhM ~ {RB9_R<:3;78_�3;<$BGH24B8_R<4{�782�GMOf¶QNB�GH3;78_Ry

Ý Î CED VC F â�� �kÙ ÅZF � I�K × D/V ¸ � Å � � >6³ ° �

GH7958M4GOKRMO20�"3[GHKXGHKRM$3;_R3VGO36B8F�ZO78_NWR3VGO3678_Ny

D V �óÙ Å�F � ¸ D ��¶ �óÙ � � � >6³ ± �

ILKR3;<�2:Mi<:QRF[G&�?B8<0GO7�S�M?M ~ {�MOZ4GHMiWRyqPR36_RZiMqGOKRM?58F;78SRB9FA@CMiZOF6M4Ga_gQRTS�MO2q36<qB8_�; � î µR» µ Ù � fgQRB9_jGO3VG / �9GOKRM; � ¤ � MO«�MOZxG"78\+��â î Ù ì 36<0GOKRB�G"79\�GH24B8_R<4{|792�G�WNQRM�GH7-GHKNM"TUMOB9_�ÓR7E�">ILKRM$MOfgQRB�GO3679_©\k792 D ¾ S�MOZi78TUMO<:y

� VOD ¾ ¸Ë¹ » � C ÷ ÜC ä �CED VCE  Ü ¹ ´ Ü

CED »CE  Ü � � >6³ ² �

¢�M"<478F[D|MuGHKR3;<aMif¶QRBzGH3;78_XGHKR2478QR59K�<4MO{RB824B�GO3678_�78\�D¶B92:36B9SRF6Mi<:y

D ¾ ¸A@ �kÙ Å�F�Å í Å ê �CED VC5  Ü â�ø �kí Å ê � CED »CE  Ü � � >6³9® �

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¦8³

�"3VGOK

� V @�¸º¹<� �óÙ Å�F � I�K û ø �óí Å ê � � � > ° �8�

¢�M"24MOTUB82:�"GHKRBzGB@Ô3;<LB\kQR_RZ4GO3679_©79\CS�7�GOKUGHKNM"\kB9<�G�B8_RW�GHKRM$<4F67E�ºD¶B92:36B9SRF6Mi<:>�?7E�*�ÌM$<�GOQRW / GOKRM ; � î ôò � MOfgQRB�GO3679_R>LILKRM$<:79FVD¶B8SR3;F63[G / ZO79_RWR3VGO3679_©24MOB8WN<:y

� � » D ¾ â)� ¼ D ¼ â)� ¾ D » â � ¸ D/V1� ¸ � � � > °R¤ �

¢�M"<4KRB8F;FNGH24MOB�G"MOB9Z�KXGOMO2:Tÿ3;_ � � > °R¤ � <:MO{RB92:BzGHMOF / >0¢ÄM$KRBED|MOy

� � » D ¾ � ¸ � ��I�K û � ø_I¢K × D » âC@_I�K × D/V � � ¸ � � � > ° �8�

QR<436_R5ÌGHKRM$<4B8TUM"B92:59QRThMi_jG"B9<a3;_ � � >;³8³ � >aILKNM"<4MOZO79_RWXGHMO24Tÿ36_ � � > °R¤ � 583VD|Mi<:y

� � ¼ D ¼ � ¸ � ì �kí Å ê � I�K × ¹ �Ú"ÛzÜ K × K û øQI�K × D V��

¸ � ´ � ÷|Ü � C ¼ D/VCE  � C5 AÜ ¹�Ú$Û Ü �

C ÷|ÜC ä � �

C ¼ D VC5  � CE �Ü

¸ � ´ � ÷|Ü � C ¼ D VCE  � C5  Ü � � > ° § �

ILKRM�GHKN362:W�B9_RW�\k79QR2�GOKUGHMi2:T�36_ � � > °e¤ � B92:M$36_NWRMO{�MO_RWRMi_jG"79\�GOKRM$\kB8<�G�D¶B82436B8SNF6MO<LB9_RWUGOKRM / 3;ThTUMOWR3[¬B�GOMOF / 583VD|Miy

� � ¾ D » � ¸ Ý Î C5D »C F â�� �kÙ Å�F � IbK × D » � � > ° ¦ �

B8_NW

� � ¸ D V � ¸Ë¹ ¤Ú$ÛzÜ N × D V � � > ° ³ �

@qQ9G:GO36_R5UM4D|MO2 / GOKR36_N5LGO7859M4GHKRMi2q�?M"79S9GHB936_XGHKNM"Mif¶QRBzGH3;78_�\k782 D » �kÙ Å�F � y

CED » �óÙ Å�F �C Fâ�� �óÙ Å�F � I�K × D » �kÙ Å�F � ¸ ¤

Ú"ÛzÜ K × I u â Ø �kÙ Å�F � I�K × D V �kÙ ÅZF � Å � � > °9° �

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¦ °

GH7958M4GOKRMO20�"3[GHKXGHKRM$3;_R3VGO36B8F�ZO78_NWR3VGO3678_Ny

D » �kÙ Å�F ¸ �9� ¸ � � � > °9± �

ILKRM$MO_RKNB8_RZOMiThMO_HGÌ3;_XGHKRM$WR3;«|QN<:3VDA3VG / 36<LWRMidR_RMOW�B8<4y

Ø ��� ¸Ë¹�Ú$Û�Ü � ´ � ÷ � � Å � � > °9² �

B8_NWUGHKNM"Mi«|MiZ4GH3[D|MaWR3;«�QR<:3[D�3[G / 36<4y

Ø ���� ¸ u â Ø ��� � � > ° ® �

¢�M"KNBÆD|M-B8F624MOB8W / 79S9GHB936_RMiWGOKRM$MO«�MOZ4GO3VD|M�MOf¶QNB�GH3;78_R<�\k7820GOKRM$dR2:<cGaGb�?7-GHMO24Th<L3;_GOKRM$M ~ {RB8_9¬<:3;78_R>(p?7E�ÌM4D|MO24�^3;_!7824WRMO2�GH7�78SÈGHB83;_�GOKRM_RMOZiMO<:<4B82 / MO<�GO36TUB�GOMO<uGHKNB�G$�"36F;FCMO_RB9SRF6MQR<�GO7©{N2:7ED|M�GOKRMKR79Th7958MO_R3;¨OB�GO3679_UGHKNMO7824MOT��?M$<:KRB9F6Fs_RMOMiWGO7hZi78TU{RQ9GHM D ¸ >0¢�M"KNBÆD|Miy

� V D ¸ ¸ ¹ � � » D ¾ â � ¼ D ¼ â � ¾ D » â � ¸ D/V �¸ ¹ » � C ÷ ÜC ä �

CED »C5  Ü ¹ » � C ÿ ÜC ä �C5D VCE  Ü ¹ ´ � ÷|ÜN¹ � ´ � ÷�Ü � ¹ �

Ú$ÛzÜC ÷ ÜC ä �

C ¼ D VC5  Ü C5  � � � > ± �8�

¢�M"F;7¥78��\k782L<478F;Q9GH3;78_R<�78\ � � > ± �8� 3;_XGHKRM$\k7824Thy

D ¸ �kÙ Å�F�Å í Å ê � ¸ ß � Ü �óí Å ê �C ¼ D/VCE  Ü CE  � â ÿ Ü �kÙ Å�F�Å í Å ê � CED »C5  Ü âEDgÜ �kÙ Å�F�Å í Å ê �

CED/VCE  Ü � � > ±R¤ �

PRQRSN<�GH3[GHQ9GO3679_78\ � � > ±e¤ � 36_ � � > ± �8� 593VD|MO<eGHKRMLMif¶QRBzGH3;78_R<�GOKRB�G0GHKRMLB9Q ~ 3;F63;B82 / \kQR_RZ4GO3678_N<Aß � Ü Å DgÜ�<:BzGH3;<:\ / y

� V ß � Ü�¸o¹ ´ � ÷�Ügâ � ´ � ÷|Ü � â �Ú$ÛzÜ

C ÷|ÜC ä � Å�¸ÈÅ Ý ¸ ¤ Å æ;æ Å � � � > ± � B �

� V DgÜA¸Ë¹ » � �kÙ Å�F � C ÿ ÜC ä � �kÙ ÅZFiÅ í Å ê � Å Ý ¸ ¤ Å æ6æ Å � � � > ± � S �

B8_NWF@�36<�583[D|MO_�S / GHKNM"<478F;Q9GH3;78_�79\qMOf¶QNB�GH3;78_ � � > ° �9� >u¢�M�_R7zGHMÞGHKRBzGaGOKRM�243658KHG�KRB8_RW�<:3;WRMO<�78\�GOKRMB8S�7ED|M�MOfgQRB�GO3678_N<hKRBED|M�¨OMO247!BED|MO2:B958M�B8_RWÁGHKgQR<MOfgQRB�GO3679_R< � > ± � B�B8_RW � > ± � S KRBED|M©<4Th7¥7zGHK B8_RWQR_R3;f¶QNMO�RQR{�GO7$B�ZO79_R<�GOB8_HGH�A<478F;Q9GH3;78_R<4>0¢ÄM�MO_R<4QR2:M�QR_R3;f¶QRMi_RMO<:<qS / 24MOf¶QN362:3;_R5uGOKRMa<478F;Q9GH3;78_R<ñGH7�KNBÆD|M

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¦ ±

¨OMO247BED|MO2:B958MO>Y 2:79T*GHKNM�TQRF[GH36{NF6Mq<:ZOB9F6MuM ~ {NB8_R<43678_B9_RW-GHKNML<:78F[D¶B8SR3;F63VG / Zi78_RWR3[GH3;78_R<��?ML78S9GOB83;_RMOWB?<478F6QÈGH3679_

GH7U7824365936_RB9Fs36_R3[GH36B9FgD¶B8F;QRM${R2:79SRF6MiT � � > � ¤ � �"KR36Z�K�KRB8< GHKNM"\k792:TUy

D �óÙ Å�F � ¸ D V �kÙ ÅZF � â î ôò D » �óÙ Å�F � â î D ¼ �kÙ Å�F�ÅÙî Å

Fî�( ò�

â î ( ò D ¾ �óÙ Å�F�Å Ù î Å Fî (ò� â î ¼ D ¸ �óÙ Å�F�Å

Ùî Å

Fî (ò� â D �HG4G

¸ D/V �kÙ ÅZF � â î ôò D » �óÙ Å�F � â î ÷�Ü � Ù î Å Fî (ò� CED/VCE �Ü

â î ( ò ÿ Ü �kÙ Å�F�Å Ù î Å Fî ( ò� C5D/VCE  Ü âà÷|Ü � Ù

î ÅFî (ò� C5D »CE  Ü

â î ¼ ß � Ü �óí Å ê �C ¼ D VC5  Ü CE  � â ÿ Ü �kÙ ÅZFiÅ í Å ê � CED »C5  Ü âIDgÜ �kÙ Å�F�Å í Å ê �

CED VC5  Ü

â D �HG4G �óÙ Å�F � Å � � > ± § �

�"KRMO24M D/V �kÙ Å Í � B9_RW D » �kÙ Å Í � B92:M�593VD|MO_�S / � � >;³ ° � B9_RW � � > °9° � �a24MO<:{�MOZ4GO3VD|MOF / �eGH7859M4GHKNMO2��"3[GHK�GOKRMZO792:2:Mi<:{�78_RWN36_R5U36_R3[GH3;B8FAZi78_RWR3[GH3;78_R<4>

m$QR2?5978B8Fq_R7E�ù36<&GH7�<4KR7E�JGOKRB�G D �7G4G 36<-36_RWRMiMOW�<4ThB9F6FC3;_UGHKNMB8{R{R2478{R2436BzGHM_R792:TU>$¢�M�<4KRB8F;FB8ZiZO78TU{RF63;<:KXGHKN36<�S / 78SÈGHB83;_R36_N5�Bh{NB82:B9S�78F63;ZMOfgQRB�GO3678_�\k782 D �HG4G B8_RW(GOKRMO_�B9{R{RF / 3;_R5hF;MOTUThB � > � GO7GHKN36<LMOfgQRB�GO3679_R>LI^7ÌGHKN36<LMO_RWN�N�ÌM$B8{R{NF / GOKRM$78{�MO2:BzGH7922� < GO7 � � > ± § � y

� ¸J� < D < ¸ � < D V �kÙ Å�F � â î ôò � < D » �óÙ Å�F � â î � < D ¼ �kÙ ÅZFiÅ Ù î Å Fî ( ò�

â î (ò � < D ¾ �kÙ ÅZFiÅ Ù î Å Fî (ò� â

â î ¼ � < D ¸ �óÙ Å�F�Å Ù î Å Fî ( ò� â � < D �HG4G �kÙ ÅZF � � � > ± ¦ �

Y 7820GOKRM$36_R3[GH36B9FAZO79_RWR3[GH3679_R< �ÌM?KRBED|MOy

D ��¶ ¸ D < Á ¡ g V ¸ D/V �óÙ Å�F � Á ¡ g V â î%ôò D » �kÙ ÅZF � Á ¡ g V â î D ¼ �kÙ Å�F�ÅÙî ÅFî (ò� Á ¡ g V

â î ( ò D ¾ �kÙ Å�F�Å Ù î Å Fî�(ò� Á ¡ g V

â î ¼ D ¸ �kÙ Å�F�ÅÙî Å

Fî ( ò� Á ¡ g V â D �HG4G �óÙ Å�F � Á ¡ g V

¸ D ��¶ â î D ¼ Á ¡ g V â î ( ò D ¾ Á ¡ g V â î ¼ D ¸ Á ¡ g V â D �HG4G Á ¡ g V � � > ± ³ �

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¦ ²

Y 2:79TöGHKRM$B9S|7ED|M$MOfgQRB�GO3679_R<q�?M?78SÈGHB83;_�B9_�36_N3VGH3;B8F DNB9F6QRM${R2478SRF;MOTÿ\k792 D �HG4G y

� < D �HG4G ¸Ë¹ � < D/V â î ôò � < D » â î � < D ¼ â î ( ò � < D ¾ â î ¼ � < D ¸ � � > ±8° B �

D �7G4G �óÙ Å�F ¸ �8� ¸Ë¹ î D ¼ Á ¡ g V â î (ò D ¾ Á ¡ g V â î ¼ D ¸ Á ¡ g V � � > ±8° S �

rsM4G"QR<�<�GOQRW / MiB8Z�KGOMO2:Tµ36_XGHKRM$243658KHGÌKNB8_RW�<:36WNM"79\ � � > ±9° B � <:Mi{RB824B�GHMiF / >0¢�M$KRBED|MOy

� < D V ¸ � ¾ â î µ ôò ì�I�K�¹ ¤Ú$ÛzÜ î%ôò N D V

¸ î µ ôò ìcI�K D V ¹ ¤Ú$Û�Ü î ôò N D V � � > ±9± �

�"KRMO24M$MOf¶QNB�GH3;78_ � � >6³ ° � �ÌB8<�QR<4MOWR>LILKRM$B8ZxGH3679_�79\-� < 79_ D » 593VD|MO<4y� < D » ¸ � ¾ â î µ ôò ìXI¢K�¹ ¤

Ú$Û Ü î%ôò D »¸ ¤

Ú$ÛzÜ N D/V ¹ � ´ � ÷ � � C ¼ D/VC5  � CE  � â î µ ôò ì�I�K D » ¹ ¤Ú$ÛzÜ îqôò N D » � � > ±9² �

`b_�WRMO2:3[D�3;_R5 � � > ±9² � �ÌM$QR<:MiW � � > °9° � >��?7E���?M"{N2:7¥ZOMOMiW�"3[GHKXGHKNM�_RM ~ GLGHMi2:TU>0¢ÄM$KRBED|M�GH7UQR<:M�GOKRM\kB8ZxGLGHKRBzGUø�WNMO{�MO_RWR<L79_ Ù B8_RW F GHKN2:78QN58K í ¸ ï < B8_RW ê ¸ ¡< ( ò y

� < D ¼ ¸ ¤î (ò

� V â ¤î� » â î µ ôò � ¼ â � ¾ â îqôò � ¸ ÷|Ü �kí Å ê � C5D/VCE  Ü Á û gLK M2e Ô gINM

( ò¸ ¤î ( òCED VC5 �Ü � � V ÷ Ü � Á ð gPOM e Ô g NM

( òâ ¤î» � C5D/VCE �Ü C ÷�ÜC ä � Á û g K M e Ô g NM

( òâ î µ ôò C ¼ D VCE  Ü C5  � ´ � ÷�ܶ¹ �

Ú"ÛC ÷ ÜC ä � Á û gQK M2e Ô gINM

( òâ Ý Î÷�Ü C ¼ D VCE  � C F

â » � ÷|Ü C ¼ D VCE  Ü CE  � Á û gLK M2e Ô gINM( ò

â î%ôò ¹ ¤Ú$Û

C ¾ D VCE �Ü C5  ¼ � ÷�Ü Á û gLK M2e Ô gINM

( ò� � > ± ® �

`b_!ZO78TU{RQ9GO36_R5R� < D ¾ ���ÌM�KRBED|M-GH7�{RB / B�G:GOMO_HGH3679_(GH7�GOKRM\kB8ZxG?GHKRBzGS@ùWRMO{�MO_NWR<?78_�S�7�GOK�GOKRM\kB8<cG

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¦8®

B8_NWUGHKNM"<4F67E�*DNB92:3;B8SRF;MO<:>0¢�M$KRBED|MOy

� < D ¾ ¸ ¤î ( ò

C5D »CE  Ü � � V ÷|Ü � â CED VCE  Ü � � V ÿ Ü � Á û g K M.e Ô g NM

( òâ ¤î» � C5D »CE  Ü

C ÷ ÜC ä � â

CED VC5  Ü

C ÿ ÜC ä � Á û g K M+e Ô g NM( ò

â î µ ôò � C ¼ D »CE  Ü C5  � ´ � ÷|ÜN¹ �Ú$Û

C ÷�ÜC ä � â C ¼ D/V

CE  Ü C5  � ´ � ÿ Ü ¹ �Ú$Û�Ü

C ÿ ÜC ä �â CED V

C5  Ü ´ � C ÿ ÜC5  � ¹�Ú$ÛzÜ

C ¼ ÿ ÜCE  � C ä � � Á û gLK M2e Ô gINM( ò

â � Ý Î ÿ Ü C ¼ D/VCE  � C Fâ Ý Î C ÿ ÜC F

CED VC5  � â » � C ÿ ÜC5  �

C5D/VCE  Ü â » � ÿ Ü C ¼ D/VCE  Ü CE  �

â Ý Î ÷ Ü C ¼ D »C5  � C Fâ » �É÷ Ü C ¼ D »CE  Ü CE  � � Á û g K M e Ô g NM

( òâ îqôò ¹ ¤

Ú$ÛC ¾ D »CE  Ü CE  ¼ � ÷|Ü ¹

¤Ú"Û

C ¾ D VC5  Ü CE  ¼ � ÿ ÜN¹

¤Ú$ÛCED VC5  Ü N × ÿ Ü Á û gQK M.e Ô gENM

( ò� � > ² �8�

¢�M"Zi78TU{RQ9GHM$_R7E�T� < D ¸ y� < D ¸ ¸ ¤

î�( òCED »C5  Ü � � V ÿ Ü � â CED V

C5  Ü � � V DgÜ � âC ¼ D VCE  Ü C5  � � � V ß � Ü � Á û gQK M.e Ô gENM

( òâ ¤

î» Í CED »C5  Ü

C ÿ ÜC ä Í â C5D/VCE  Ü

C DgÜC ä Í â C ¼ D/V

C5  Ü CE  �C ß � ÜC ä Í Á û g K M2e Ô g NM

( òâ ¤

î ôò� C ¼ D »C5  Ü CE  � ´ � ÿ Ü ¹ �

Ú$ÛzÜC ÿ ÜC ä � â CED »C5  Ü ´ � C ÿ ÜC5  � ¹

�Ú$ÛzÜ

C ¼ ÿ ÜCE  � C ä �â C ¼ D/V

C5  Ü CE  � ´ � DgÜN¹ �Ú$ÛzÜ

C DgÜC ä � â CED V

C5  Ü ´ � C DgÜCE  � ¹�Ú$ÛzÜ

C ¼ DgÜCE  � C ä �

â C ¾ D/VC5 �Ü CE  Í CE  � ´ Í ß � ÜN¹ �

Ú$ÛC ß � ÜC ä Í � Á û g K M e Ô g NM

( òâ � Ý Î ÿ Ü C ¼ D »C5  � C F

â Ý Î C ÿ ÜC FC5D »CE  � â » � C ÿ ÜCE  �

CED »C5  Ü â » � ÿ Ü C ¼ D »C5  Ü CE  �â Ý Î�DgÜ C ¼ D/VC5  � C F

â Ý Î C DgÜC FCED VCE  � â » � C DgÜCE  �

CED/VCE  Ü â » � DgÜ C ¼ D VCE  Ü CE  �

â ß � Ü Ý Î C ¾ D/VCE  � C5  Ü C F

â » Í C ¾ D/VCE  Ü C5  � CE  Í Á û gLK M2e Ô gINM

( òâ î ôò � ¹ ¤

Ú$Û�ÜC ¾ D »CE  Ü CE  ¼ � ÿ Ü ¹

¤Ú"ÛzÜ

CED »C5  Ü N × ÿ ܹ ¤

Ú$Û ÜC ¾ D/VCE �Ü C5  ¼ � D Ü ¹

¤Ú$Û Ü

C5D/VCE �Ü N × D Ü ¹ ¤

Ú$Û Ü ßw� ÜC ¸ D/V

C5 AÜñCE �Ü CE  ¼ Í � Á û g K M e Ô g NM( ò

� � > ²R¤ �

�?7E���?MhB92:M�24MOB8W / GH7�Zi78TU{RQ9GHMÌGHKNMh243658KHGhKRB8_NW�<:3;WRMh79\ � � > ±8° B � >�¡?<436_R5XGOKRM�ZOMOF;FC{R2478SRF;MOTh<$\k792

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³ �

GHKNM"B9Q ~ 36F63;B82 / \kQR_RZ4GO3678_N<$ø Å @ ÅVU �?M?<:KNB8F6Fs<4KR7E�ºGOKRB�GLGOKRM$2:3;58KHGÌKRB9_RW�<436WRM?79\ � � > ±8° B � 3;<LB8_�; � î �fgQRB8_HGH3[G / >&`b_�792:WRMi2�GH7�<:3;Th{RF;36\ / GHKRM�_R7�GOB�GO3678_N�g�ÌM-WRMO_R7zGHM GHKRM?243659KjGaKRB9_RW�<:3;WRM?79\ � � > ±8° B � S / ]�p?PB8_NWU�ÌM��"243VGHM-3VG"36_XGOKRM$\k78F6F;7E�"36_R5\k792:TUy

°�W Ý ¸Ë¹ î µ ôò � » ¹÷� ¼ ¹ î ôò � ¾ ¹ î � ¸ â ® � î � � � > ² �8�

m$_RF / � < D V B9_RWX� < D ¼ ZO78_HGH2436SRQÈGHMuGO7$GOKRM ; � î µ ôò � GOMO2:TUy� » �óÙ Å�F � ¸ ì �  

î ÅFî (ò� I�K D V â C5D/V

CE  Ü � � V ÷ Ü � Á û g K M e Ô g NM( ò¸ � ì �kí Å ê � â � V ø �:� Á û g K M e Ô g NM

( òI�K D V

¸ � Å � � > ² § �

78_�B8ZOZi78QR_HG"78\eGHKRM$ZOMiF6FA{N2:78SNF6MOTÿ\k792$ø">�� < D » Å � < D ¼ B8_RWY� < D ¾ ZO79_jGO2:3;SRQ9GHM&GH7ÌGHKRM ; � ¤ � GOMO2:TUy� ¼ �kÙ Å�F � ¸ ì�I�K D » â » � CED VC5 �Ü C ÷�ÜC ä � â

C5D »CE �Ü � � V ÷|Ü � â C5D/VCE �Ü � � V ÿ Ü � Á û gLK M.e Ô gINM

( ò¸ ì�I�K D » â

C5D »CE  Ü � � V ÷�Ü � Á û gLK M.e Ô gINM( ò

â » � C5D VCE  Ü C ÷ ÜC ä � âCED VC5  Ü � � V ÿ Ü � Á û gLK M.e Ô gENM

( ò¸ � � � > ² ¦ �

�?7E� �ÌMLZO79_R<:3;WRMO2�GOKRMG; � î ôò � GHMO24Th>q=?<CS�MO\k792:MO��3[GÞ36<CQN_RWRMO24<�GH7¥7¥W"GHKRBzGC�ÌMLM4D¶B9F6QRBzGHM0GHKNMLM ~ {N2:MO<4<:3679_B�G í ¸ × < Å ê ¸ ¡< ( ò B8_NWU�ÌM��"3;F6FA_N7�G"2:Mi{|MiB�G�3VGHy

� ¾ �kÙ ÅZF � ¸ ¹ � ´ � ÷ � � C ¼ D VCE  � CE  � âC ¼ D/VCE �Ü C5  � ´ � ÷�ܶ¹ �

Ú$ÛC ÷�ÜC ä �

â » � C5D VCE  Ü

C ÿ ÜC ä � âC5D »CE  Ü

C ÷ ÜC ä � â C5D »CE  Ü � � V ÿ Ü � â C5D V

CE  Ü � � V DgÜ � âC ¼ D VC5  Ü CE  � � � V ß � Ü �

¸ CED »C5 AÜ � V ÿ Ü â » � C ÷�ÜC ä � â CED VC5 AÜ � V D Ü â » � C ÿ ÜC ä �

â C ¼ D VCE  Ü C5  � � V ß � Ü �óí Å ê � ¹ � ´ � ÷ � � â ´ � ÷�ܶ¹ �

Ú$ÛC ÷ ÜC ä �

¸ � Å � � > ² ³ �

�"KRMO24MuGHKNM"ZiMOF6F�{R2478SRF;MOTh<L\k792Z@ ÅV[ B8_NW U KRBED|M?S�MOMO_�QR<4MOWR>LILKRM-_RM ~ GLGHMO24Tù3;_ � � > ² �9� 3;<�GOKRM$dR2:<cG

Page 60: Imperial College Londonpavl/rpithes.pdf · 2002. 6. 18. · z nl78{/ 2:3659kjg 9 8 9 s / 1$243658792:3;78< =?>a@cbedaf63;7 gh3;< =?f6f ]a3;58khgh

³ ¤

_R79_R¨OMO247$GOMO2:TUy

� ¸ �kÙ Å�F � ¸ ¹ ¤Ú$ÛzÜ N D » â Ý Î÷�Ü C ¼ D VCE  � C F

â » � ÷|Ü C ¼ D VC5  Ü CE  � âC ¼ D »C5  Ü CE  � ´ � ÷�ܶ¹ �

Ú$ÛC ÷ ÜC ä �

â C ¼ D/VCE  Ü CE  � ´ � ÿ ÜN¹ �

Ú"ÛzÜC ÿ ÜC ä � â C5D/V

CE  Ü ´ � C ÿ ÜCE  � ¹�Ú"ÛzÜ

C ¼ ÿ ÜCE  � C ä �â » Í CED »CE  Ü

C ÿ ÜC ä Í âCED/VCE  Ü

C DgÜC ä Í â

C ¼ D/VCE  Ü CE  �

C ß � ÜC ä Í � � > ²9° �

PR3;_RZOM�GHKRMÞGb�Ì7UZO78TU{�78_RMO_HGH<-78\�GHKRMÞD|MOF67¥Zi3VG / dNMOF6W�B8<&�ÌMOF;FsB8<uGOKRM�3;_R3VGO36B8FsZi78_RWR3[GH3;78_R<�B824MB8<:<4QRTUMOWGH7�S�M�<:TU7¥7�GOKR�qGOKRMUdR2:<cG�Gb�Ì7�GHMO24Th<$36_©GHKRMUM ~ {RB8_R<43679_ D V B9_RW D » B824M�<:TU7¥7�GOKR> v 7824MO7ED|MO2:��GOKRM<:79F6Q9GO3679_R<L78\NGOKRM?ZOMOF;FR{R2478SRF;MOTh<uB824M?B8F;<:7�<4Th7¥7zGHK�\kQR_RZxGH3679_R<:>LnL79_R<:Mif¶QRMi_jGOF / ��� ¸ �kÙ Å�F � 36<uB�<:TU7¥7�GOKR�S�78QR_NWRMOW�\kQN_RZ4GH3;78_R>LILKNM"3;_R3VGO36B9FgD¶B8F;QRM${R2:79SRF6MOTµ\k782 D �HG4G S�MOZO78TUMO<4y

� < D �HG4G ¸º¹ î � ¸ �kÙ Å�F � ¬�­ R<S � � Å�U � � � > ²8± B �

D �HG4G �óÙ Å�F ¸ �9� ¸ î P �óÙ ��® ­ R � � > ²8± S �

.0/ B8{R{NF / 36_R5_R7E�ÔF;MOTUThB � GH7ÌGHKRM$36_N3VGH3;B8F DNB9F6QRM${R2478SRF;MOT � � > ²9± � �?M"79S9GHB936_�GHKRM$MO<cGH36TUB�GOMO<

ÁíÁ D �7G\G Á�Á Ó�î=ïíï V e ¡^ð�Àíñ Óvò�ï ½ § À�À õ î ¤ â F VÝ Î ô � � > ²8² B �

Á�Á K D �7G4G Á�Á Ó ò ïíï V e ¡^ð�Àíó ½ § À�À õ î ô] Ú"ÛzÜ Ý Î� â ¤ â F VÝ

ô � � > ²8² S �

\k782qM4D|Mi2 / F V  � >LrsM4GaQR<q_R7E�ËWRMOdN_RMqGOKRM�\kQR_RZ4GO3678_ D » e < y6¸ D/V â î ôò D » > Y 2:78ToGOKRM�B8S�7ED|MaMO<cGH3;ThBzGHMO<78_ D �7G4G �gGO7858MxGHKRMO20�"3[GHKXGHKNMuGH2436B8_N58F6M-36_RMOfgQRB9F63VG / �ç�?M?ZOB8_�MO<cGH3;ThBzGHMuGOKRM?WR3;«|Mi2:MO_RZiM?S�M4Gb�ÌMOMO_ D B8_RWD �HG4G 3;_GOKRM_^£y6¸ · £ �4� � ÅZF V � � · ¼ � R �:� _R792:TU�s\k782L<4Q��hZi36MO_HGHF / <:TUB8F6F î y

ÁíÁ D < ¹ D »e < ÁíÁ ` ¸ ÁíÁ î D ¼ â î (ò D ¾ â î ¼ D ¸ â D �HG4G Á�Á `

õ î ÁíÁ D ¼ ÁíÁ ` â î (ò ÁíÁ D ¾ Á�Á ` â î ¼ ÁíÁ D ¸ Á�Á ` â ÁíÁ D �7G\G Á�Áõ ô » î â ® � î � � � > ² ® �

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³ �

nL78TSN36_R3;_R5_R7E� � � >6³ ° � B8_NW � � > °9° � �ÌM$78S9GOB83;_�B8_�MOfgQRBzGH3679_�\k792 D » e < y

Ý Î CED »e <

C Fâ�� �kÙ Å�F � I�K D »

e < ¸ ¤Ú$ÛzÜ î ôò KeI Ø � I�K D » e < â ® � î ôò � ¬�­ R(S � � Å�U � � � >;® � B �

D » e < �óÙ Å�F ¸ �9� ¸ D ��¶ �kÙ ��® ­ R � � >6® � S �

�?MO59F6MOZxGH36_N5�_R7E��KR3659KRMO2L7824WRMO2 GHMO24Th<0�?M?78SÈGHB83;_UGOKRM$MO«�MOZ4GH3[D|MaMif¶QRBzGH3;78_Ry

Ý Î C DC F â�� �kÙ Å�F � I�K D ¸ ¤Ú$Û�Ü î%ôò KmI Ø�� I�K D ¬�­ R S � � Å�U � � � >;® ¤ B �

D �kÙ ÅZF ¸ �9� ¸ D ��¶ �óÙ ��® ­ R � � >6® ¤ S �

¨£½EÉ�º�Äba y Y 2478T¯GHKRM�B9S|7ED|M�B8_NB8F / <:3;<$�?M�WRMO2:3[D|MOW�B9_�MO«�MOZ4GO3VD|MUB8W9D|MiZ4GH3;78_bg�WR36«�QR<43678_ MOfgQRBzGH3679_�"3VGOK�BhZO79_R<�GOB8_HGXMi«|MiZ4GH3[D|MaWR3;«�QR<:3;78_UGOMO_R<4782 �"KR36Z�K�36<L36_NWRMO{�MO_RWRMi_jG?78\�GOKRM$ThMOB9_�ÓR7E�">aILKRM�MO«�MOZ4G78\NGOKRM�ThMOB9_hÓN7Æ�JQN{|79_�GHKNMaMO«�MOZxGH3VD|M0GO2:B9_R<:{�782cG"B8{R{�MOB92:<uB8<�B�KR3659KRMO2q7824WRMO2uMO«�MOZ4GH>uILK¶QN<:�ç�"2:3[GH36_N5D ¼ 36_"GHKRM$\k7824Thy

D ¼ �óÙ Å�F�Å í Å ê � ¸sø �kí Å ê � I�K × D V �óÙ Å�F � â D&V �óÙ Å�F � � � >6® �8�

B8_NW�B8QR59ThMi_jGO36_R5uGOKRM�M ~ {NB8_R<43678_ � � >6¦ ± � �"3[GHKÌGHKRMG; � îdc ò � GHMi2:T D ­ �?ML78S9GOB836_N�A\k2:79ToGHKRML<478F[DNB9SR36F;3VG /ZO79_RWR3VGO3679_©79\�GHKNM�; � î � MOfgQRB�GO3679_R�NGHKRM$\k79F6F67E�"3;_R5MOfgQRB�GO3678_�\k792 D ¼ yC D ¼ �óÙ Å�F �C F

âH� �óÙ Å�F � I�K D ¼ �kÙ Å�F � ¸�¹[KeI � � ì ¤ ø � I�K D » �kÙ Å�F �4� ¹_KmI � � ì ¤ @ � �kÙ Å�F � I�K D V �kÙ ÅZF �4� Å� � >;®8§ �

�"3VGOK�¨OMO247�3;_R3VGO36B8FqZO79_RWR3[GH3679_R<:> @q2:7¥ZiMOMOWR3;_R5!B8<S�MO\k792:MO�0�?M�ZOB8_ 78S9GOB836_ B9_ÉMif¶QRBzGH3;78_�\k792 D ¼ e < y;¸D V â î ôò D » â î D ¼ y

Ý Î CED ¼e <

C Fâ�� �kÙ Å�F � I�K D ¼

e < ¸ ¤Ú$ÛzÜ î ôò KmI Ø�� I�K D ¼ e < â ¤

Ú$ÛzÜ î KmI e �kÙ ÅZF � I�K D ¼ e < â ® � î � ¬�­ R S � � Å�U �� � >;®8¦9B �

Page 62: Imperial College Londonpavl/rpithes.pdf · 2002. 6. 18. · z nl78{/ 2:3659kjg 9 8 9 s / 1$243658792:3;78< =?>a@cbedaf63;7 gh3;< =?f6f ]a3;58khgh

³8§

D ¼ e < �óÙ Å�F ¸ �9� ¸ D ��¶ �kÙ ��® ­ R � � >6®8¦9S �

�"3VGOKfe �óÙ Å�F � ¸�¹ � ì ¤ @ � �kÙ Å�F � > ¢�M�MOTU{RKRB9<:36¨iMLGOKRB�G�@÷WRMO{�MO_RWN<a79_UGHKNM�TUB8ZO2478<:Zi78{R3;ZLD¶B92:36B9SRF6Mi<Ù Å�F GHKN2:78QN58K GHKNM©TUMOB9_ÉÓN7Æ�µ�"KR36Z�K�B8{N{|MiB82:<(78_�GOKRM�2:3;58KHG©KRB8_RW <:3;WRM�78\ GHKRM�ZOMOF;F�{R2478SRF;MOTý\k792@$>�ILK¶QN<:�0�ÌMU<:MiM�GHKRBzG©M4D|MO_ô�ÌMOB9��TUMOB9_�ÓR7E�"<4�aZO79Th{NB82:MiW�GH7�GHKRM�ÓNQRZ4GHQNB�GH3;78_R<4�LZO78_HGH2436SRQÈGHM�GO7GHKNM�<�GO2:QRZxGHQR24M"79\�GHKNM�MO«�MOZ4GO3VD|M�MOfgQRB�GO3678_N<:�eGH7UKR3659KRMO2�782:WNMO2:<4>?nL78_HGH3;_¶QR3;_R5-�"3VGOKUGOKR36<�{R2:7¥ZiMO<:<4�^79_RMZOB9_©79S9GHB936_�KR3;58KRMO2L792:WRMi2�ZO792:2:MiZ4GH3;78_R<0GOKRB�GL�"3;F6F�36_HD|78F[D|MaKR3;58KRMi2�7824WRMO2LWRMi2:3VD¶BzGH3VD|Mi<&79\�GOKRM$MO«�MOZ4GO3VD|M{RB9<:<:3[D|M$<:ZOB9F6B82LdNMOF6WR>0¢�M$<:KRB9F6Fs_R7zGX{NQR2:<4QRM�GHKR3;<L36<:<4QRM$\kQR2�GOKRMO24>

æpÀM`pÀ¾¿�À7æ ¹87z½�� ºÆ�½ ½ÁÀ�¾¼�?7E�ÿ�?MU�"36<4K GH7�{N2:MO<4MO_jGUGHKNM�WRMO243VD¶B�GO3679_�78\�GOKRM�MO«�MOZxGH3VD|M�MOfgQRBzGH3679_�B9<��ÌMOF;FLB8<�GOKRM!ZOMOF;F

{R2478SRF;MOT \k782q½�ø ¤ ¹�·ñ>�ILKNM�{R24MO<:MO_NZOM$78\�GHKRM�78{�MO24B�GH792 î µ Ú � V �"36F6FsF;MOB8WXGO7�GHMO24Th<�78\|GHKRM�\k782:Tîhg ò µ Ú � V D � Å)¸ ¸ � Å ¤ Å æOæOæ B8_RW"�ÌM?_RMiMOW�GH7B9QR58TUMO_HG�GOKRM?M ~ {RB8_N<:3679_ � � >;¦ ± � �"3VGHK(B8WRWR3[GH3;78_RB9FNGHMO24Th<GHKNB�G��"3;F6FRF;MOB8WÌGH7Þ�ÌMOF;FR{�78<4MOW�; � îhg ò µ Ú � MOfgQRB�GO3679_R<:>LnL79_R<:MOfgQRMO_HGHF / �9�?Ma_RMiMOW$GO7�3;_jGO2:7¥WRQRZiMqGOMO2:TU<q78\GHKNM�\k7824T î ( �igò�j � Åv¸ ¸ � Å ¤ Å æOæOæ >"m$_RM�ZOB8_�Z�KNMOZ��g�AKN7Æ�?M4D|MO24�gGHKNB�G�GHKR3;<aM ~ {RB9_R<:3;78_(�"36F;FAB958B83;_!F6MOB9WGH7U36F;FV¬:{�78<:MiW�MOfgQRB�GO3678_N<aQR_NF6MO<4<LTh792:M�GHMO24Th<uB824M"3;_jGO2:7¥WRQNZOMOWR>LILKRM$59MO_RMO24B8Fs\k7824Tÿ78\|GHKRM$M ~ {RB8_N<:3679_GHKNB�G��ÌM?<4KRB8F;F^_RMiMOW�KRB9<qGO7hS�M$B8QR59ThMi_jGOMOWX�"3VGHKXGOMO2:TU<L78\�GOKRM$\k7824Thy

î (ò µ Ú j V â î ¼ µ Ú j » â î c ò µ Ú j ¼ â æiæOæ î2Úlk V â î�Ú+Û$ôò k » â î�Ú+Û » k ¼ â æOæOæ Å � � >6®9³ �

GHKNM"\kQN_RZ4GH3;78_R< j � Å�k � Å ¬ ¸ ¤ Å � Å æOæiæ S�MO3;_R5U\kQR_RZ4GO3678_N<L78\CS�7�GOKUGOKRM$\kB8<�G�B8_NWUGHKNM"<4F67E��D¶B82436B9SRF6MO<4>L=WR3;<:ZOQR<4<:3;78_�78\�Bh24MOF6BzGHMOW({R2:79SRF6MOTµ36<�{N2:MO<4MO_jGOMOW�3;_ ? ¤ ¦9�s{R{R> � ° � g � ° ³bA6> Y 792LSR2:M4DA3VG / 78\�M ~ {|79<:3[GH3679_�ÌML<4KRB8F;F�78TU3VGCGOKRMLWRM4GOB836F;<CB8_NWh{R24MO<:Mi_jGCGOKRM�WRMO2:3[D¶B�GH3;78_79\gGHKNMLKR78TU7859MO_R36¨iMOWMOfgQRB�GO3678_U\k782�GOKRMLZOB8<4M�"KRMO24ML½�GHB9�¥MO<L36_HGHMi58MO2ñDNB9F6QRMi<:>�`x_"GHKR3;<aZOB9<:MO��_R7U\kQR2�GOKRMO2LTU7¥WR36dRZiB�GH3;78_�78\ � � >;¦ ± � 3;<L_RMOZOMO<4<:B92 / >

ILKgQR<:� �ÌM?<4M4G�½!¸ ¤ > ¢�Ma<4KRB8F;FA\kQR2cGHKRMO2uB8<4<:QRTUMuGHKNB�GLGHKNM?BED|MO2:B958M�78\eGHKRM D|MOF67¥Zi3VG / dRMiF6W�7ED|MO2GHKNMh<4{RB�GO36B8Fq{�MO24367¥W�36<$¨OMO2478� � ì � ð ¸ Ä���GHKRM<4{RB�GO36B9F&BED|MO24B859MhS�MO3;_R5�WRMOdR_RMiW!36_�MOf¶QNB�GH3;78_ � � > ¤ ®8B � >ILKR3;<?B8<4<:QRTU{9GH3;78_�36<$_R7zG�_RMOZOMi<:<:B92 / B8_RWô�ÌMTUB8�¥M�3VG�3;_!782:WNMO2�GH7�<436TU{RF63;\ / GOKRMZOB9F6ZOQRF;B�GO3678_N<:>U=qGGHKNM"Mi_RW�79\�GHKR3;<a<4QRSR<4MOZ4GH3;78_��ÌM$<:KRB9F6FsWRMi<:ZO2436S�M�SR2436MOÓ / KR7E��GH7U{R247¥ZOMOMOWX�"KRMO_�GHKR3;<aB9<:<4QRTh{ÈGH3679_�3;<2:MiTh7ED|MOWR>

ILKRM$MOfgQRB�GO3679_R< � � >;¦ ² � B824M$<�GH3;F6F DNB9F63;W©\k7920GHKRM$\k79F6F67E�"3;_R5WR36«�MO24MO_HGH36B9FA79{|Mi2:B�GO7824<:y

� V yO¸ � » � � >;® ° B �

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³8¦

� » yO¸ � V â � ¼ � � >6® ° S �

� ¼ yO¸ � ¾ � � >;® ° Z �

� ¾ yO¸ � ¸ � � >6® ° W �

� ¸ yO¸ � ­ � � >;® ° M �

ILKRM�TUB83;_ÉWN36«�MO2:Mi_RZOM�\k2478TÊGOKRM�{R2:M4DA3679QR<UZOB8<4M©3;<-GHKRBzGm� V 3;<h_N7Æ�þB8_ MOF6F;36{9GO36ZO�uB8<U78{R{�79<:MOW GO7{RB92:B8S�79F636Zi��78{�MO24B�GO782�B9_RW�GHKRM!\kB9<�G�GH3;ThM ê MO_jGOMO2:<(ThMO24MOF / B9<©B {RB824B8TUM4GHMO24>ÿnL78_N<:MOfgQRMO_HGHF / �$BD¶B82436B8_HGÞ79\¥GOKRM�<478F[DNB9SR36F;3VG / ZO78_NWR3VGO3678_�583[D|MO_�BzGÞF6MOTUTUB ¤ �9D¶B8F63;W�\k792CMOF6F;36{9GO36Zq78{�MO24B�GO782:<��"3[GHK�{�MO24367¥WR3;ZS�78QR_NWRB82 / Zi78_RWR3[GH3;78_R<�KRB8< GH7S�M�QR<:MOWN>L�?B8TUMOF / �¥GOKRM$36_RKN78TU7858Mi_RMO78QN<aMOfgQRBzGH3679_

� » P �óí Å ê � ¸ � �kí Å ê � � � >6® ± �

KRB9<�B�QN_R36fgQRMO��QR{�GO7�B�ZO78_R<cGHB9_jG?<:78F;Q9GH3;78_�3;\AB9_RW�78_RF / 36\gGOKRM?BED|MO24B858M�78\���7ED|MO2|GHKRM?<4{RB�GO36B9FA{�MO2:3;7¥W36<$MOfgQRB9F�GH7�¨OMO2478y � � � ð ¸ � > v 792:MO7ED|MO24��GHKNMh79_RF / <478F6QÈGH3679_R<�GH7XGHKNMhKR79Th7958MO_NMO78QR<�MOfgQRB�GO3678_�B824MZO79_R<�GOB8_HGH< �"3VGHK�24MO<:{�MOZ4GLGO7 í SRQ9G�GHKNM / ZiB8_�WNMO{�MO_RW�78_ ê >

¢J3VGOK�GHKNM?B8S�7ED|M?WR3;<:ZOQR<4<:3;78_�3;_�Th3;_RWR�ç�ÌM-{R2:7¥ZOMiMOW�GH7B9_RB8F / ¨iMuGHKRMK; � î µ ( ò � MOfgQRB�GO3679_R> Y 2:78TGHKNM�<:79FVD¶B8SN36F63[G / ZO78_NWR3VGO3678_N<q�?M�ZO79_RZOF6QNWRM�GHKRBzG D/V 36<�36_RWNMO{�MO_RWRMO_HG"78\ í y D V ¸ D/V �óÙ Å�F�Å ê � >?p?MO_RZiMO�GHKNM"<478F[DNB9SR36F;3VG / ZO78_RWN3VGH3;78_�\k782 GHKNM�; � î µR»:� MOfgQRBzGH3679_�S|MiZO78TUMO<:y

Ý Î CED VC ê ¸ � � � >6® ² �

\k2:79T¿�"KR36Z�KU�?M�36TUTUMOWR36BzGHMOF / WRMOWRQNZOM�GOKRB�G D V ¸ D/V �óÙ Å�F � >?�-7Æ�oGHKRM8; � î µR»Æ� S|MiZO78TUMO<B� VOD » ¸ �B8_NW��ÌM�ZO78_NZOF6QRWNM0GHKRBzG�GHKNMa<4MOZO78_NW�GHMO24T�3;_$GOKRMaM ~ {RB9_R<:3;78_�3;<q36_RWRMi{|Mi_RWRMO_HGÞ78\ í y D » ¸ D » �kÙ Å�F�Å ê � >

ILKRM$<:79FVD¶B8SN36F63[G / ZO79_RWR3[GH3679_�\k782 GHKRM ; � î µ ôò � MOf¶QNB�GH3;78_�583[D|MO<:y� � » D » â)� ¼ D V � ð ¸ � � � >6®9® �

Page 64: Imperial College Londonpavl/rpithes.pdf · 2002. 6. 18. · z nl78{/ 2:3659kjg 9 8 9 s / 1$243658792:3;78< =?>a@cbedaf63;7 gh3;< =?f6f ]a3;58khgh

³8³

nL78_N<:MOfgQRMO_HGHF / y

Ý Î C5D »C ê ¸º¹ � ì � ð I�K × D/V ¸ �

B8_NWU�ÌM$ZO79_RZOF;QRWRMuGOKRB�GO� D » ¸ D » �óÙ Å�F � >uILKRM$MOf¶QNB�GH3;78_�\k782 D ¼ S�MOZi78TUMO<:y

� VOD ¼ ¸Ë¹ÌìcI�K × D V � � > ¤ �9�8�

¢�M�<:79FVD|M � � > ¤ �8�8� GHKR2478QR59K!<:MO{RB92:BzGH3679_!78\�D¶B82436B8SNF6MO<4>u¢ÄM�F67¥79��\k782�BU<:78F;Q9GH3;78_!3;_UGHKNM"\k792:T � � >6³ �8�B8_NW��?M�78SÈGHB83;_!B8_�MOfgQRB�GO3678_!\k792uGHKNMZO78242:MOZ4GO782�dRMOF;W�ø��"KN36Z�K!36<�B8_�MOF6F;36{9GO36Z?MOfgQRBzGH3679_!36_ í �"3VGOK{�MO2:3;7¥WR36Z$S�78QN_RWRB82 / ZO78_RWN3VGH3;78_R<�36_X�"KR3;Z�K ê Mi_jGOMO2:<LB9<aB{RB92:B9ThM4GOMO2:y

ì�I�K û�øĹ ¤Ú$Û Ü NUû�ø�¸Ë¹$ì � � > ¤ � ¤ �

¢�M?MOTU{RKRB8<436¨OM GHKNB�G"MOfgQRB�GO3679_ � � > ¤ � ¤ � 3;<��ÌMiF6FV¬:{�78<4MOW�S�MOZOB9QR<:M��ÌM�KRBED|M?B9<:<:QNThMOW"GHKRBzGLGHKRM?<4{RB�GO36B9FBED|MO2:B958M79\sGOKRM-D|MOF;7¥ZO3VG / dRMOF6W(D¶B9_R36<4KRMO<:>Ì¢�M�MO_R<4QR2:MQN_R36fgQRMO_RMi<:<?79\&<478F;Q9GH3;78_R<?S / 24MOfgQR362436_R5�ø�GO7KRBED|M?¨OMi2:7BED|MO2:B958M$7ED|MO20GHKNM"<4{RB�GO36B9Fs{|Mi2:367¥W�ZOMOF;F6>

¢�M"_N7Æ�÷B8_RB9F / ¨OMuGHKNM�; � ¤ � MOfgQRBzGH3679_R>LILKRM$<:79FVD¶B8SN36F63[G / ZO79_RWR3[GH3679_�2:MOB9WR<:y� Ý Î C

C ê â�� �kÙ ÅZF � I�K û øQI�K × D/V âÉì£I�K × D » â Ý Î CC F âH� �kÙ Å�F � I�K × D V�� ð ¸ � � � > ¤ �9�8�

PR3;_RZOMKø÷B9_RWÁì KRBED|M�¨OMO2:7UBED|MO2:B958M3;_�<:{NB8ZOMB9_RW�øù3;<a{�MO24367¥WR3;Z36_�<4{RB8ZiM-GHKRM�dR2:<cG?Gb�Ì7�GOMO2:TU<a3;_GHKNM"BED|MO24B859MLD¶B9_R36<4K©B9_RWU�?M$B82:M$F;MO\ GL�"3VGOKRy

Ý Î CC F âH� �kÙ Å�F � I�K × D V ¸ � � � > ¤ � § �

ILKR3;<C36<4�|B9<qM ~ {�MOZxGHMOWR�gB�GH24B8_R<4{|792�G?MOf¶QNB�GH3;78_\k792 D/V �9GO7859M4GHKRMi2s�"3[GHK-GOKRML36_R3[GH3;B8FgZO78_RWN3VGH3;78_ D V �kÙ ÅZF ¸�8� ¸ D ��¶ > ¢�M�2:MOTUB824�­GHKRBzGhGOKRM�\kB9Z4GGHKRBzG��ÌM�KRBED|M�<:MxG � ø � ð ¸ � 36<_R7zGÁ_RMOZiMO<:<4B82 / \k782ÌGHKR3;<WRMO243VD¶B�GO3679_Ry�¢�M?ZO79QRF6W�GOB8�¥M GHKRM-BÆD|Mi2:B859M?36_ÌGH3;ThM�78\eGHKNMaMOfgQRBzGH3679_�GHKNB�G"2:Mi<:QRF[GH<�B9\ GHMO2qBED|MO24B8583;_R5�3;_<:{NB8ZOMO>

¢�M�ZOB9__R7E�o<478F[D|M�GHKNMLMOf¶QNB�GH3;78_�\k782 D ¾ GHKR2478QR59Kh<4MO{RB92:B�GO3679_h79\¥D¶B92:36B9SRF6Mi<^B9_RWh79S9GHB936_ � � >6³9® � >

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³ °

ILKRM$ZOMOF;FA{R2478SRF;MOTÿ\k792Z@�2:MOB9WR<:y

� V ÿ ÜA¸Ë¹ » � �óÙ Å�F � C ÷ ÜC ä � �kí Å ê � ¹ Ý Î C ÷ ÜC F Å Ý ¸ ¤ Å æ6æ Å � � � > ¤ � ¦ �

¢�M"<4KRB8F;Fs78S9GOB83;_�B8_�MOfgQRB�GO3678_�\k792 D » \k2:78TJGHKRM$<:79FVD¶B8SN36F63[G / ZO79_RWR3[GH3679_�\k7820GHKNM�; � î ( ò � MOfgQRB�GO3678_Ny� Ý Î C

C ê âH� �óÙ Å�F � I�K û � øQI�K D » ân@QI�K D V � â ì �kí Å ê � I�K × ¹ �Ú$ÛzÜ K × K û ø_I�K × D/V

â Ý Î CC F âH� �óÙ Å�F � I¢K × D » ¹¤Ú$ÛzÜ N × D/V1� ð ¸ � � � > ¤ � ³ �

nL78_N<:MOfgQRMO_HGHF / y

Ý Î CC ê � øQI�K × D » ân@QI�K D V � â Ý Î CC F âH� �kÙ Å�F � I�K × D » ¸

¤Ú$Û�Ü N × D/V ¹_KmI � � ì[ø � ð K × D/V �

� � > ¤ � ° �

¢�M"_N7Æ�*GHB9�¥M�GHMOTU{�782:B9FsBED|MO2:B958M � �"KR36Z�K�36<LWRMOdN_RMOW�3;_©Mif¶QRBzGH3;78_ � > ¤ ®8S � GO778S9GOB836_�B8_�36_RKR79Th7958M4¬_RMO79QR< GH2:B9_R<:{�792�G�MOf¶QNB�GH3;78_�\k782 D » y

C5D » �kÙ ÅZF �C Fâ�� �kÙ ÅZF � IbK × D » �óÙ Å�F � ¸ ¤

Ú$ÛzÜ KmI u â Ø �kÙ Å�F � K × D V �óÙ Å�F � Å � � > ¤ � ± �

GH7958M4GOKRMO20�"3[GHKXGHKRM$3;_R3VGO36B8F�ZO78_NWR3VGO3678_Ny

D » �kÙ Å�F � ¸ � � � > ¤ � ² �

ILKRM$MO_RKNB8_RZOMiThMO_HGÌ3;_XGHKRM$WR3;«|QN<:3VDA3VG / 36<LWRMidR_RMOW�B8<4y

Ø ��� ¸Ë¹�Ú$Û�Ü � ´ � ÷ � � Å � � > ¤ � ® �

B8_NWUGHKNM"Mi«|MiZ4GH3[D|MaWR3;«�QR<:3[D�3[G / 36<4y

Ø�� ¸ u â Ø � � > ¤8¤ �8�

`b_�GHKNM?B8S�7ED|M?WRMO243VD¶B�GO3679_��ÌM?KNBÆD|M-QR<:MOW"GHKRM?\kB9Z4G�GOKRB�G"3;_�7824WRMO2ñGH7ZO79Th{RQÈGHMuGOKRMuGH7zGHB9FsBÆD|Mi2:B859Mq�?M

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³ ±

ZOB9_©dN2:<�G�GHB9�¥M�GHKRM$<:{NB�GH3;B8FsBED|MO24B858M$B9_RWUGOKRMO_XGHKRM�GOMOTh{�792:B8FsBED|MO24B859MOy

� I � ¸ �o� I � ð � Ô ¸ ��� I � Ô � ð � � > ¤8¤9¤ �

@q2:7¥ZOMiMOWR36_N5©_N7Æ�ÿB8<$36_(GOKRMUZOB8<4M?½�¸ ¾¼ �?MhZi78_RZOF;QRWRMÞGHKRBzG"GOKRMUKR78TU7859MO_R36¨iMOW!MOfgQRB�GO3678_�36<-B858B936_� � > � § � �"3VGOK(GHKRM<4B8TUMh\k792:TQRF;B8<?\k792uGHKRMUMO«�MOZ4GO3VD|M$WR3;«|QN<:3VDA3VG / B8_NW�GOKRMZO78242:MOZxGH782-dRMOF6W!<4B�GO36<:\ / 36_N5GHKNM"MiF6F63;{9GH3;ZaZiMOF6F�{R2:79SRF6MOT � � > ¤ � ¤ � >

rsM4G�QN<?_R7E�ùWR36<4ZOQR<:<&�"KRB�G�KNB8{R{�MO_R<��"KRMi_ � ì � ð ø Ä�>ILKRMÓ; � î µ ( ò � B9_RWß; � î µN» � MOfgQRB�GO3678_N<583[D|M�QR<4�CB8<$S�MO\k792:MO��GOKRB�G D/V ¸ D/V �óÙ Å�F � B9_RW D » �óÙ Å�F�Å ê � >�p?7E�ÌMxD|MO2:�NGOKRM�<478FVD¶B9SR36F;3VG / ZO78_RWN3VGH3;78_!\k792GHKNM�; � î µ ôò � MOfgQRB�GO3679_©593VD|MO<4y

Ý Î C5D »C ê ¸º¹ � ì � ð I�K × D/V¢�M"<478F[D|MuGHKR3;<aMif¶QRBzGH3;78_�S / <:M4G4GH36_N5 D » �óÙ Å�F�Å ê � ¸ D » �kÙ ÅZF � â öD » �kÙ Å�F�Å ê � �"3[GHK

öD » �kÙ ÅZFiÅ ê � ¸º¹ ¤Ý Î

ÔV � ì � ð � ± � � ± I�K × D/V � � > ¤8¤ �8�

�?7E�*GHKRM$MOfgQRB�GO3679_©\k792 D ¼ S�MOZO78TUMO<4y

� V�D ¼ ¸Ë¹ � ìô¹ � ì � ð � I�K × D/V � � > ¤8¤ § �

¢�M"<478F[D|MuGHKR3;<aMif¶QRBzGH3;78_�QR<:3;_R5<:Mi{RB824B�GH3;78_�78\�D¶B82436B9SRF6MO<0GO7h79S9GHB936_Ry

D ¼ �kÙ Å�F�Å í Å ê � ¸©ø �kÙ ÅZFiÅ í Å ê � IbK × D V �óÙ Å�F � â öD ¼ �óÙ Å�F�Å ê � � � > ¤8¤ ¦ �

B8_NWUGHKNM"Zi782:24MOZ4GO782LdRMOF;WEø�<4B�GH3;<:dRMi<qGOKRM$ZOMOF6F�{R2:79SRF6MiThy

ì£I�K ûoø�¹ ¤Ú$ÛzÜ NUûoø�¸º¹ � 쩹 � ì � ð � � � > ¤8¤ ³ �

�?7E�*GHKRM$<:79FVD¶B8SN36F63[G / ZO79_RWR3[GH3679_�\k782 GHKRM ; � ¤ � MOfgQRBzGH3679_�583VD|Mi<�B8_�MOfgQRB�GO3678_�\k792 öD ¼ �kÙ ÅZFiÅ ê � y

Ý Î CöD ¼C ê ¸Ë¹ � ì � ð I�K × D » ¹�K × ¤

Ý Î � ì � ð �ëê �ÔV � ì � ð � ± � � ± I¢K × D/V â)� ¾ D V � � > ¤8¤z° �

ILKRM<478FVD¶B9SR36F;3VG / ZO79_RWR3VGO3679_!\k782uGOKR36<?Mif¶QRBzGH3;78_!583[D|MO< GHKRMÞGH2:B9_R<:{�792�GôMif¶QRBzGH3;78_!\k782 D V >-¢�M2:MiThB92:�

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³ ²

GHKNB�GH�s<436_RZiM � ì � ð �òê � 3;<aB{�MO24367¥WR3;Z$\kQR_RZ4GO3678_�79\ ê �g�?M$KRBED|MOy

�o� ´ � � ð �òê �ÔV � ´ � � ð � ± � � ± � Ô ¸ � Å ¬ Åh¸ ¸ ¤ Å æOæOæ � � � > ¤8¤z± �

�?7E�*�ÌM$ZOB8_�<478FVD|M$\k792 öD ¼ GH7U78S9GOB836_Ny

öD ¼ �kÙ Å�F�Å ê � ¸ [ �ëê � I�K × D » âQK × ¤Ý Î

ÔV �7o � ð � ± � � ± I�K × D V � � > ¤8¤z² �

�"KRMO24M [ �ëê � y6¸º¹ »ábp ÔV � ì � ð � ± � � ± B8_RW o �kÙ Å ê � y6¸ºì �kÙ Å ê �4¤ [ �ëê � >ILKRM$MOfgQRB�GO3679_©\k792 D ¾ S�MOZi78TUMO<:y

� V�D ¾ ¸º¹ Ý Î C øC ê âH��I¢K û ø I�K × D/V ¹ � ìô¹ � ì � ð � I�K × D » ¹�K × �:� o ¹ �7o � ð � I�K × D V �� � > ¤8¤ ® �

ILKRM$<:79F6Q9GO3679_�78\eGHKN36<LMOfgQRB�GO3679_�36<4y

D ¾ �óÙ Å�F�Å í Å ê � ¸ U I�K × D/V â ø�I�K × D » âQK × � @_I�K × D/V � â öD ¾ �óÙ Å�F�Å ê � � � > ¤ �9�8�

=?_RWXGOKRM$ZO78242:MOZ4GO782LdRMiF6WR< UhÅ @�<4B�GO36<:\ / GHKRM$\k78F;F67E�"36_N5ZOMOF6F�{R2:79SRF6MiTh<4y

IñK û U ¹ ¤Ú"ÛzÜ N û U ¸Ë¹ Ý Î C øC ê âH��I�K û ø � � > ¤ � ¤ B �

K ûq@Ĺ ¤Ú$ÛzÜ N[û$@�¸Ë¹ � o ¹ �\o!� ð � � � > ¤ � ¤ S �

¢�M?{R2:7¥ZiMOMOWÌ�"3VGHK"GHKRMQ; � î ôò � MOfgQRB�GO3679_R>LILKRM?<478FVD¶B9SR36F;3VG / ZO79_RWR3[GH3679_�\k782ñGHKR3;<�MOfgQRBzGH3679_h593VD|MO<qQR<LB9_MOfgQRB�GO3679_©\k792 öD ¾ �óÙ Å�F�Å ê � y

Ý Î CöD ¾C ê ¸Ë¹ � ì3ø � ð I�K × D V ¹ � ì [ � ð I�K × D V ¹ [ � ¾ K × D V ¹A� ¾ D » ¹A� ¸ D V � � > ¤ �9�8�

I�B8�g36_R5�_R7E�ùGOKRM�GHMiTh{�7824B8FuBÆD|Mi2:B859M�78\0GOKR36<�MOfgQRB�GO3678_©�ÌM�79S9GHB936_­GHKRM(MOf¶QNB�GH3;78_ � � > ¤ � ± � \k782 D » >nL78_HGH3;_¶QN36_R5�_R7E�¿B9<L36_XGHKRM-{R2:M4DA3679QR<�ZiB8<:Mi<0�ÌM?79S9GHB936_XGHKRM-MO«�MOZ4GH3[D|MaMif¶QRBzGH3;78_�\k792 D ¸ D V â î ôò D » >

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³8®

æpÀM`pÀ¾¿�À7ã ¹87z½�� ºÆ�½ ½ÁÂ�¾¼>�¢�M�_N7Æ�ùWR3;<:ZOQN<:<uGOKRM�ZOB9<:MÞ�"KRMO_�½� ¤ ¹�·ñ> Y 782�SR2:MxD�3[G / �ÌM�<4KRB8F;F^24MO<�GO2:3;Z4GX79QR2:<4MOFVD|Mi<qGO7

GHKNM"ZiB8<:ML½!¸ � >LILKRM�78{�MO2:BzGH7922� < GOB8�¥MO<0GOKRM$\k782:TUy� < ¸ ¤

î ¼� V â ¤

î ( ò� V â ¤

î� » â î ôò � ¼ â)� ¾ â î ôò � ¸ � � > ¤ � § �

�"KRMO24MOy

� V yO¸ � » � � > ¤ � ¦9B �

� » yO¸ � ¼ � � > ¤ � ¦9S �

� ¼ yO¸ � ¾ � � > ¤ � ¦9Z �

� ¾ yO¸ � ¸ � � > ¤ � ¦9W �

� ¸ yO¸ � ­ � � > ¤ � ¦9M �

PRQRSR<cGH3VGOQ9GH3;_R5U_R7E�ºGOKRM$M ~ {NB8_R<43678_ � � >6¦ ± � 3;_jGO7-GHKRM$MOfgQRBzGH3679_Y� < D < ¸ � �ÌM$78SÈGHB83;_XGHKRM$\k78F;F67E�"36_N5<:Mif¶QRMi_RZOM?79\CMOfgQRB�GO3678_N<:y

; � î µ ¼ � y � V D V ¸ � � � > ¤ � ³9B �

; � î µ ( ò � y � VOD » â � VOD/V ¸ � � � > ¤ � ³9S �

; � î µR» � y � V D ¼ â)� V D » â)� » D V ¸ � � � > ¤ � ³9Z �

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° �

; � î µ ôò � y � V D ¾ â)� V D ¼ â � » D » â)� ¼ D V ¸ � � � > ¤ � ³9W �

; � ¤ � y � V�D ¸ â � VOD ¾ â)� » D ¼ â)� ¼ D » â)� ¾ D V ¸ � � � > ¤ � ³9M �

; � îqôò � y � VOD ­ â � VOD ¸ â � » D ¾ â)� ¼ D ¼ â � ¾ D » â)� ¸ D/V ¸ � � � > ¤ � ³8\ �

Y 2478TËGHKRM ; � î µ ¼ � MOfgQRB�GO3679_�?M?58MxGLGHKRBzG D/V 36<L3;_RWRMO{�MO_NWRMO_HGÌ78\ ê y D/V ¸ D/V �óÙ Å�F�Å ê � >&`b_�7824WRMO2L\k792GHKNM�; � î µ ( ò � GH7US�M��ÌMOF;FA{�78<4MOWU�?M"_NMOMOWRy

� � V�D/V1� Ô ¸ �sr � � V¡� Ô D/V ¸ � � � > ¤ � ° �

�"KRMO24M

� � V � Ô yO¸ � ì �óí Å ê � � Ô I�K û ¹ ¤Ú$ÛzÜ N û � � > ¤ � ± �

nLF6MiB82:F / � � � > ¤ � ± � 3;<aB�QN_R36\k792:TUF / MOF6F;36{9GO36Z?79{�MO2:BzGH782-B8_RW!ZO79_R<:Mif¶QRMi_jGOF / � � > ¤ � ° � 3;Th{NF636Mi<0GHKRBzG D/V ¸D/V �kÙ Å�F � >LILKRMÓ; � î µ ( ò � S�MOZO78TUMO< � VOD » ¸ � \k2478Tö�"KN36Z�K�?M$WRMOWRQRZiMLGOKRB�G D » ¸ D » �óÙ Å�F�Å í � >�PN36_RZOMD/V 36<L3;_RWRMO{�MO_NWRMO_HGÌ78\ í GOKRM ; � î µR»:� MOfgQRB�GO3679_©S�MOZi78TUMO<:y

� V�D ¼ â)� VOD » ¸ � � � > ¤ � ² �

ILKRM�B8_NB8F / <:3;<\k782-GOKR36<�MOf¶QNB�GH3;78_ 36<-GOKRM�<4B8TUM©B9<\k782-GOKRM�; � î µ ( ò � B8_RWÁ�ÌM�ZO79_RZOF;QRWRM�GOKRB�G D » ¸D » �kÙ Å�F � B9_RW D ¼ ¸ D ¼ �óÙ Å�F�Å í � >

ILKRM ; � î µ ô ò � MOf¶QNB�GH3;78_�KRB9<aBU<:79F6Q9GO3678_�\k782 D ¾ 3;\sB8_RW�78_RF / 36\ky� � VOD ¼ â)� » D » â)� ¼ D V�� Ô ¸ � � � > ¤ � ® �

7824y

� � V¡� Ô D ¼ ¸º¹ � ì �óí Å ê � � Ô I�K × D/V � � > ¤ § �8�

ILKRMu<:78F;Q9GH3;78_ÞGH7uGOKR36<sMOfgQRBzGH3679_�KRB9<�GHKNM�\k7824T � � >;³ �9� D ¼ �kÙ Å�F�Å í � ¸Å÷ �kí � I D/V �kÙ Å�F � �H�"3VGOK ÷�<4B�GO36<:\ / 36_N5

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°e¤

GHKNM"\k79F6F;7�"3;_R58��ZOMOF;FA{R2478SRF;MOThy

� ì �óí Å ê � � Ô I�K û�øĹ ¤Ú$ÛzÜ NUû�ø�¸Ë¹ � ì �óí Å ê � � Ô � � > ¤ § ¤ �

¢�M�2:MiThB92:��GOKRB�G � � > ¤ § ¤ � 3;<aBÌ�ÌMiF6Fs{�78<4MOW!MOF6F;36{9GO36Z�MOfgQRB�GO3678_��"3VGOK�{�MO2:3;7¥WR36Z�S�78QR_RWNB82 / ZO78_NWR3VGO3678_N<<:3;_RZOMuGOKRM$<:{RBzGH3;B8F�BÆD|Mi2:B859M$78\eGHKRM$2:3;58KHG"KRB8_NW�<:3;WRM$36< � >a�?7E�*�ÌM?ZiB8_�M ~ {R24MO<:< D ¾ 36_XGHKNM"\k792:T

D ¾ �kÙ Å�F�Å í Å ê � ¸ öD ¾ �óÙ Å�F�Å í Å ê � âutD ¾ �kÙ Å�F�Å í � � � > ¤ § �8�

�"3VGOK

öD ¾ �óÙ Å�F�Å í Å ê � ¸¤Ý Î

ÔV è �óÙ Å�F�Å í Å ± � � ± � � > ¤ §9§ �

�"KRMO24MOy

è �kÙ Å�F�Å í Å ê �4� ¸ ¹ � � VOD ¼ â)� ¼ D/V �¸ ¹ � ì�¹ � ì � Ô � I � K[ûoøĹ u � I�K û D/V � � > ¤ §9¦ �

�?7E�*�ÌM${R2:7¥ZiMOMOWX�"3VGOKGOKRM ; � ¤ � MOfgQRB�GO3679_R>aILKNM"<478F[DNB9SR36F;3VG / ZO78_RWN3VGH3;78_�2:MiB8WR<4y� � VWD ¾ â � » D ¼ â)� ¼ D » â)� ¾ D V¡� Ô ¸ � � � > ¤ §9³ �

ILKR3;<L36<LB8_�MOF6F;36{9GO36Z�MOfgQRB�GO3678_�\k792 tD ¾ y

� � V � Ô tD ¾ ¸o¹ � � V öD ¾ â � » D ¼ â)� ¼ D » â � ¾ D V � Ô � � > ¤ § ° �

B8_NW�3VG?36<��ÌMOF;F�{|79<:MOW(36\sB8_NW�78_RF / 3;\gGOKRMa<4{RB�GO36B9FABED|MO2:B958M?79\NGHKRM�2:3;58KHGÌKRB9_RW�<436WRM?3;<q¨OMO2:79>0¢ÄM�KRBED|MOy

��� � V öD ¾ � Ô � ð ¸ �o� � V öD ¾ � ð � Ô ¸ � � � > ¤ § ± �

.0/ 36_HGHMi2:Z�KRB8_R5936_R5"GHKRM�792:WRMi2"79\0GHB9�¶3;_R5�BÆD|Mi2:B859MO<��?MB8F;<:7�79S9GHB936_�GOKRB�G �o� � » D ¼ � Ô � ð ¸ � >!¡-<:36_N5_R7E��GOKRML\kB8ZxG&GOKRB�G D » 36<q36_NWRMO{�MO_RWRMi_jG�78\ GHKRML\kB9<�G�D¶B92:36B9SRF6Mi<CB8_RWÌGHKNB�GqGHKRML<4{RB�GO367zGHMOTU{�782:B9F�BÆD|Mi2:B859M78\eGHKNMuD|MOF67¥Zi3VG / 79\^dRMiF6W�D¶B8_N36<:KNMO<0�ÌM?79S9GHB936_ �o� � ¼ D » � Ô � ð ¸ � >�ILK¶QR<4�g�?M?78S9GOB83;_GOKRB�G"3;_�7824WRMO2L\k792

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� � > ¤ § ° � GH7US�M��ÌMOF;FA{�78<4MOWU�?M"<4KR78QNF6W�KNBÆD|Miy

Ý Î C5D VC F â�� �óÙ Å�F � I�K D V ¸ � Å � � > ¤ § ² �

�"KR3;Z�K�36<:�NB8<qM ~ {|MiZ4GHMOWN�jGOKRM0GH24B8_R<4{|792�GaMOfgQRB�GO3679_\k782�GHKRMudR2:<cGqGHMO24TJ3;_-GHKRMuM ~ {RB8_R<43679_R>0¢ÄMuZOB8_U_R7E�<:79FVD|M � � > ¤ § ± � \k782 öD ¾ SRQ9G?<:3;_RZOMu�?Mq�?78_ d G"_RMOMOWÌGHKR3;<�\k7920GHKRM?WNMO2:3[DNBzGH3;78_�79\NGHKRM?Mif¶QRBzGH3;78_�\k792 D » �?M<:KNB8F6F078TU3VG�GHKRMWRMxGHB83;F6<4>�ILKRMO_N� D ¸ ZiB8_!S�M-�"2:3[G:GHMi_!B8< D ¸ �kÙ ÅZFiÅ í Å ê � ¸ öD ¸ �óÙ Å�F�Å í Å ê � âvtD ¸ �kÙ Å�F�Å í ��"3VGOKRy

öD ¸ �óÙ Å�F�Å í Å ê � ¸¤Ý Î

ÔV � � VOD ¾ â)� » D ¼ â � ¼ D » â � ¾ D V � � ê � � > ¤ §9® �

ILKRM ; � î ôò � Mif¶QRBzGH3;78_�ZOB8_�S�M�<478F[D|MOW�\k782 D ­ {N2:7ED�3;WRMOWXGHKNB�GHy� � VWD ¸ â � » D ¾ â)� ¼ D ¼ â)� ¾ D » â)� ¸ D/V1� Ô ¸ � � � > ¤ ¦ �8�

�"KR3;Z�K�F6MiB8WR<0GO78y

� � V¢� Ô tD ¸ ¸Ë¹ � � V öD ¸ â � » D ¾ â)� ¼ D ¼ â)� ¾ D » â � ¸ D/V¡� Ô ¸ � � � > ¤ ¦ ¤ �

ILKRM<478FVD¶B9SR36F;3VG / ZO79_RWR3VGO3679_!\k782 � � > ¤ ¦ �9� �"3;F6Fs593VD|M�QN<uGHKRMMif¶QRBzGH3;78_�\k792 D » y$S / GHB8�g36_N5�GHKRM<4{RB�GO36B9FBED|MO2:B958M?79\�GHKNM?2:3;58KHG"KRB8_RW�<:3;WRM?B8_NW�36_HGHMi2:Z�KRB8_R5936_R5ÞGHKRM-782:WNMO2L78\C<4{RB�GO36B9FsB8_RWXGHMiTh{�7824B8FsBED|MO24B858Mi<�ÌM$79S9GHB936_UGOKRB�G �o� � V öD ¸ � Ô � ð ¸ �o� � » D ¾ � Ô � ð ¸ � >0¢�M�24MOThB92:�ÌGHKRBzGX3;_�782:WNMO2qGO778S9GOB83;_UGHKN36<�2:MO<4QRFVG�ÌM-WR78_ d G"_RMOMOW"GHKRM?<4{�MOZO36dNZ?\k7824Tÿ78\s_RMi3VGHKNMO2 D ¾ _R782 D ¸ SRQ9G"78_NF / GHKRM?\kB9Z4GLGHKNB�GLGHKNM / B92:M?{�MO24367¥WR3;Z36_ í B9_RW ê >

ILKRM�GHKN362:WXGOMO2:Tÿ593VD|MO<4y

�o� � ¼ D ¼ � Ô � ð ¸eKeI � � ì[ø � IbK D/V � � � > ¤ ¦ �8�

ILKRM�F;B8<cG�Gb�Ì7XGHMi2:TU<�B824Mh3;_RWRMO{�MO_NWRMO_HG(79\0GHKRM(\kB8<�G�D¶B82:3;B8SRF;MO<�B9_RW�ZO79_R<:Mif¶QRMi_jGOF / GOKRM / B824M�MOfgQRB8FGH7(GOKRMO3;2BÆD|Mi2:B859MO>�@qQ9G4GH3;_R5�_N7Æ�þM4D|MO2 / GOKR36_N5UGH7958M4GOKRMO2-�?M©79S9GHB936_ MOfgQRB�GO3679_ � � > °8° � >ºILKNM©<4B8TUM\k7824TQRF6B9<?\k782&GHKRM�MO«�MOZ4GH3[D|M$WR36«�QR<43VDA3VG / KR79F6WR��GOKRMWR3;«|Mi2:MO_RZiM"_N7Æ�ùS�MO3;_R5�GHKNB�G?GOKRMZOMOF;Fs{R2:79SRF6MOT 3;<GHKNM"MiF6F63;{9GH3;ZaMif¶QRBzGH3;78_ � � > ¤ § ¤ � >

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{RF;36<:KNMOW <:7�\kB92:> Y 782h·ö¸ý¹­»¼ �?M�QR<:MOW B�TQNFVGH3;{RF6M(<:ZOB9F6MO<M ~ {RB9_R<:3;78_R�uGO2:MOBzGH3;_R5�\kB9<�GÁB9_RW�<4F67E�D¶B82436B8SNF6MO<LB9<L36_RWRMi{|Mi_RWRMO_HGH��36_�792:WRMO20GO7WRMO243VD|M�B<:MOfgQRMO_RZiMa79\^MOfgQRBzGH3679_R<L\k7820GOKRM�D¶B82:3;78QR<0GOMO2:TU<�3;_GHKNMaM ~ {RB9_R<:3;78_R>ñ¢ÄM�QR<:MiW$GOKRM3; � î µR» Û�Ù � B8_NWB; � î ¼ Ù � MOfgQRB�GO3679_R<�GH7�<4KR7E��GOKRB�GuGHKRMLdR24<�GuGx�?7�GHMO24Th<36_�GHKRM$M ~ {RB9_R<:3;78_�B92:M�36_RWRMiMOW�36_RWRMi{|Mi_RWRMO_HG"78\�GOKRM�\kB9<�G�D¶B82:3;B8SRF;MO<:>&¢ÄMÞGHKRMO_�QR<:MiWUGHKNM"<478F[DNB9SR36F;3VG /ZO79_RWR3VGO3679_R<L\k7820GOKRM$KR3659KRMO2L7824WRMO2LMOfgQRBzGH3679_R<0GH7UWRMO243VD|M GHKRM$MO«�MOZxGH3VD|M�MOfgQRB�GO3679_R<LB8<0�?MOF6F�B8< GHKRM$ZOMOF;F{R2478SRF;MOTh<4> ¢�MXGHKRMi_ÉQN<:MOWÁGHKRM�KR3;58KRMO2792:WRMi2$GOMO2:TU<36_­GHKNM©M ~ {RB9_R<:3;78_ 36_ 7824WRMO2-GH7�78SÈGHB83;_�GOKRM_RMOZiMO<:<4B82 / MO<�GO36TUB�GHMi<0GHKRBzG"MO_RB8SNF6MOW�QR< GH7{R247ED|MLGOKRM$KR78TU7859MO_R3;¨OB�GO3678_XGOKRMO7824MOTU>

ILKRM�KR3659KRMO<cG-792:WRMi2&Mif¶QRBzGH3;78_ÌGHKRBzG&�?MLKRB8W"GH7$<�GOQRW / �ÌB9<�GOKRMG; � î » Û�Ù � MOfgQRBzGH3679_h\k2478To�"KR3;Z�K�ÌM�79S9GHB936_RMOWÁGHKRM�MO«�MOZxGH3VD|MUMOfgQRB�GO3679_É\k792$GOKRM�<:MOZi78_RWÁGHMO24T�3;_!GOKRM�M ~ {RB8_R<43679_�B8_NW�GHKNM©M ~ {RF;36ZO3[GM ~ {R2:Mi<:<:3;78_�\k782�GOKRMLKR3659KRMO<cGÞ7824WRMO2eGHMO24T�GOKRB�G0�ÌMLKRB9W-GH7?ZO79_R<:3;WRMO2�36_792:WRMO2|GH7?79S9GHB936_-GHKNM�_RMOZiMO<:<4B82 /MO<cGH36TUB�GOMO<:>q�?MiMOWRF6Mi<¥GO7a<4B / �iGHKRMqKR3;58KRMi2s782:WNMO2sMOfgQRB�GO3678_N<NGHKRBzGs�ÌMq_RMO59F6MOZ4GOMOW?B92:Mq_R7�G&S�MO3;_R5L<:BzGH3;<:dRMOWN�<:3;_RZOMuGOKRM / 3;_jD|79FVD|M GHMO24Th<L3;_XGHKRM$M ~ {RB8_N<:3679_XGHKRBzGXKRBED|M$B8F;2:MOB9W / S�MOMO_�WRMxGHMO24Th3;_RMOWR>

ILKRMU<�GO2:QRZ4GOQR2:M79\�GOKRMhM ~ {RB9_R<:3;78_�36_ôGHKRM59MO_RMO24B8FqZOB9<:M<:KN78QRF;W�S�Mh<4QRZ�K(GOKRB�G�B8F;FCMOfgQRB�GO3678_N<QR{(GO7B; � î » Û�Ù � S|M-�?MOF6Fs{�79<:MOWR>Ì¢�MThB / B8F;<:7�_RMiMOW(GH7�Zi78_R<436WRMO2�B8F;<:7�KR3;58KRMO2�7824WRMO2?Mif¶QRBzGH3;78_R<?3;_7824WRMO2�GH7(S|MUB8SNF6M-GH7�79S9GHB936_ôGHKRMMO242:792"Mi<�GH3;ThBzGHMO<4>hILKNM58MO_RMi2:B8F0\k782:T+79\�GOKRMM ~ {RB8_R<43679_R�q\k782uGOKRMZOB9<:M"·�Ü � ¹ ¤ Å �9� �"3[GHK©·Éø˹ Ü

w �"3VGOK Ý Åx Ü 36<4y

D < ²Í¶�g V î

¶ ï » Û�Ù À k ¶aâͶ¿g V î » Û

¶ ï » Û�Ù Àly ¶?âͶ¿g V î ¼ Û

¶ ï » Û�Ù À N�¶aâ· Û »¶¿g » î

ï » µ ¶ Ù À j ¶ � � > ¤ ¦9§ �

�"3VGOK j ¶ Å�k ¶ Å y ¶ Å N ¶ S�MO36_R5U\kQR_RZxGH3679_R<�78\CS�7�GOK(GHKRM�<:F;7Æ�÷B8_RW�GHKRM�\kB8<�G-DNB92:3;B8SRF;MO<:>?ILKNM�D¶B8F;QRMO<�78\GHKNM"3;_jGOMO58Mi2:<�z Å \�WRMO{�MO_RW�QR{�78_(GOKRM�DNB9F6QRM$79\ ·�>-ILKR36<0�"3;F6FsS�MOZO79ThM$TU782:M$ZOF;MOB82LB9\ GHMO2 �ÌM${R24MO<:Mi_jGGHKNMhMOfgQRBzGH3679_R<�79\0D¶B82:3;78QR<�7824WRMO2:<4>!m$QR2�5978B8Fu36<�GH7�78S9GOB83;_�B8_�Mif¶QRBzGH3;78_�\k782�GOKRMUdR2:<cG�Gb�Ì7�GHMO24Th<k V â î » Û�Ù k » >"PNQRSR<�GO3VGOQ9GH3;_R5h_N7Æ� � � > ¤ ¦9§ � 3;_jGO7 � � >6¦ �8� �"3[GHKf� < 583VD|Mi_©S / � � >6¦ �9� �"3[GHKU½�¸ ¤ ¹º·�ÌM$79S9GHB936_UGOKRM$\k78F;F67E�"36_R5�MOfgQRB�GO3678_N<:y

; � î ï ¶ µR» À Û ï ¶ Û » À Ù � y,� V k ¶ ¸ � Å ­ ¸ ¤ Å æiæOæ Å z � � > ¤ ¦8¦9B �

; � î µR» � y,� » k V ¸ � � � > ¤ ¦8¦9S �

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; � î ¶ ï » Û¿Ù À Û�Ù � y,� V y ¶?â)� » k ¶ Û » â)� ¼ k ¶�¸ � Å ­ ¸ ¤ Å æOæOæ Å z � � > ¤ ¦8¦9Z �

; � ¤ � y,� V j » â � » y V â � ¾ k V ¸ � � � > ¤ ¦8¦9W �

; � î Ù ï »Zµ ¶ À � y,� V j ¶ Û » â � » j ¶ ¸ � Å ­ ¸ ¤ Å æOæOæ Å \�â ¤ � � > ¤ ¦8¦9M �

; � î ï ¶ Û » À ï » Û�Ù À � y,� V N ¶ â � » y ¶ Û » â)� ¼ y ¶ â � ¾ k ¶ Û » â)� ¸ k ¶ ¸ � Å ­ ¸ ¤ Å æOæiæ Å z � � > ¤ ¦9¦8\ �

¢ÄM�<:MiMGOKRB�GGOKRM�MOfgQRB�GO3678_N<h\k792 j ¶ WRMiZO78QR{NF6M�\k2:79TÊGHKRM�24MO<�G©79\qGOKRM�MOf¶QNB�GH3;78_R<4>�ILKR36<3;<_RB�G4¬QR24B8F�<436_RZiM-GHKRM�_gQRTS�MO2?79\ j ¶ GHMO24Th<�GOKRB�G��ÌMU<:KRB9F6Fq_RMOMOW�36<�WR36«�MO24MO_HG?GHKRB9_�GHKNM�_¶QNTS|Mi2?78\0GOKRMk ¶ Å y ¶ Å N ¶ GOMO2:TU<:> v 7824Ma<4{|MiZO36dRZiB8F6F / �RB9<Þ·�C � �?Ma_NMOMOWÌGH7�B9WRW�TU7824M j ¶ GHMO24Th<4>�m$_ÌGHKRM?7zGHKRMi2KRB9_RWR�NGHKNM�·?C ¹ ¤ F63;Th3[G-24MOfgQR3624MO<�TU7824M k ¶ Å y ¶ Å N�¶�GHMi2:TU<:>

rsM4G©QR<U_R7E� <478FVD|M(MOf¶QNB�GH3;78_R< � � > ¤ ¦8¦ � >�ILKNMl; � î ï ¶ µR» À Û ï ¶ Û » À Ù � GHMi2:TU<36TU{RF / GHKRBzGGHKRMXGOKRM\kQR_RZxGH3679_R< k ¶ B824M�36_NWRMO{�MO_RWRMi_jG"79\�GHKRM�\kB8<cGaD¶B82436B9SRF6MO<4y k ¶ ¸ k ¶ �kÙ Å�F � Å ­ ¸ ¤ Å æOæiæ zN>?ILKRM8; � î µN» �MOfgQRB�GO3679_�3;<uGH243VDA36B8F;F / <:BzGH3;<:dRMOWN>�PR36_NZOM-GHKRM\kQN_RZ4GH3;78_R< k ¶�B82:MU36_NWRMO{�MO_RWRMi_jG�79\�GOKRM\kB8<cG"D¶B92:36B9SRF6Mi<GHKNM�; � î ¶ ï » Û�Ù À Û�Ù � Mif¶QRBzGH3;78_R<LS�MOZO79ThMiy

� V y ¶?â)� ¼ k ¶�¸ � � � > ¤ ¦9³ �

¢�M�<:79FVD|M�GHKNMO<:M$MOfgQRB�GO3679_R<qGOKR2:79QR58K!<4MO{RB92:B�GO3679_!78\�D¶B82436B9SRF6MO< GH7U78SÈGHB83;_ y ¶ �kÙ Å�F�Å í Å ê � ¸ ø �kí Å ê � IK k ¶ �óÙ Å�F � �"KRMO24M�GHKRM$ZO792:2:MiZ4GH792LdRMOF6WOø�<4B�GO36<:dNMO<0GHKRM$ZOMiF6FA{N2:78SNF6MOT � � >;³8§ � >

ILKRM�<:79FVD¶B8SN36F63[G / ZO78_RWN3VGH3;78_�\k792-GHKRM�; � î »:� MOf¶QNB�GH3;78_ 583[D|MO<�GOKRM�GO2:B8_N<:{�782cG­MOfgQRBzGH3679_ � � >6³ ° �\k782 k V >��?7E�÷�ÌMUZOB8_�<478F[D|Mh\k792 j » GO7�78SÈGHB83;_ j V �óÙ Å�F�Å í Å ê � ¸{@ V �kÙ Å�F�Å í Å ê � I�K y V �kÙ Å�F � �"KRMO24M@ V <4B�GH3;<:dRMi<qGOKRM$ZOMOF6F�{R2478SRF;MOT � � > ° �8� >q¢�M$ZOB8_XGHKNMO_�{R2:7¥ZOMiMOWXGH7U<:78F[D|MuGHKNM�; � î Ù ï » µ ¶ À � Mif¶QRBzGH3;78_R<4>ILKRM$dR_RB9F^24MO<:QNFVGÌ3;<:y

j ¶ Û » �óÙ Å�F�Å í Å ê � ¸�@ ¶ Û »È�kÙ ÅZFiÅ í Å ê � I�K j ¶ �kÙ ÅZFiÅ í Å ê � � � > ¤ ¦ ° B �

� V ÿ ¶ Û »Ü ¸Ë¹ » � �óÙ Å�F � C ÿ¶Ü

C ä � �kÙ ÅZFiÅ í Å ê � Å Ý ¸ ¤ Å æ6æ Å � � � > ¤ ¦ ° S �

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C k ¶ Û » �óÙ Å�F �C FâH� �óÙ Å�F � I�K k ¶ Û » �óÙ Å�F � ¸

¤Ú$ÛzÜ KeI u â Ø �kÙ Å�F � I�K k ¶ �kÙ Å�F � Å � � > ¤ ¦ ± �

�"3VGOK | ��� ¸Ë¹�Ú"ÛzÜ � ´ � ÷ � �� V N ¶ ¸º¹ » � C ÷�ÜC ä �

C k ¶ Û »CE  Ü ¹ ´ � ÷|ÜN¹ � ´ � ÷|Ü � ¹ �Ú$Û�Ü

C ÷�ÜC ä �

C ¼ k ¶C5  Ü CE  � � � > ¤ ¦ ² �

ILKRM$<:79F6Q9GO3679_�78\eGHKN36<LMOfgQRB�GO3679_�36<4y

N ¶ �óÙ Å�F�Å í Å ê � ¸�ß � Ü �kí Å ê �C ¼ k ¶CE  Ü C5  � â ÿ VÜ �kÙ Å�F�Å í Å ê � C k ¶ Û »CE  Ü � � > ¤ ¦9® �

�"3VGOK U 593VD|MO_�S / MOfgQRBzGH3679_ � � > ± � B � >�?7E�*�ÌM$ZOB8_�78S9GOB83;_UGHKNM"Mi«|MiZ4GH3[D|MaMOfgQRBzGH3679_ � � > � § � \k782 D y;¸ k V â î}k » >aILKNM�KR3;58KRMO2L792:WRMi2

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v 7824MO7ED|MO2:�H�ÌML<4MOM0GHKNB�GqGHKRM�MO«�MOZ4GO3VD|MqWR3;«|QN<:3679_$GOMO_R<4782q36<C_N7Æ��B$\kQR_RZ4GO3678_79\A<4{RB8ZOM�B8_NW$GO36TUMO>ILKR3;<�<:{NB�GH3;7�GOMOTh{�792:B8F�WRMO{�MO_RWNMO_RZOM�78\ Ø � �kÙ ÅZF � 3;<&WNQRMuGH7�S�7�GHK"GHKRM?{N2:MO<4MO_RZOM�78\sB�_R78_HGH243VDA36B8FNThMOB9_ÓR7E� B9<$�?MOF6FLB9<h79\uGHKRM�<4F67E� TU7¥WRQRF6BzGH3;78_R<U78\uGOKRM�{�MO24367¥WR3;Z�ÓRQRZ4GOQRB�GO3678_N<:>�ILKR3;<h3;<B�<cGH2436�g36_R59F /WR3;«|Mi2:MO_HGa<:3VGOQRB�GO3679_GOKRB8_"GHKRM?79_RM$36_Ì�"KR36Z�K�GOKRM?TUMOB8_�ÓN7Æ�J3;<�MO3[GHKRMi2&Zi78_R<cGHB8_HG"782ñ�ÌMOB9�hZi78TU{RB824MOWGH7©GHKRM!ÓRQNZ4GHQRBzGH3;78_R<�B8_NW GOKRM�ÓRQNZ4GHQRBzGH3;78_R<�B824M!36_RWNMO{�MO_RWRMO_HG�78\�GOKRM!TUB8ZO2478<:Zi78{R3;ZUD¶B82436B8SNF6MO<�3;_�"KR3;Z�K�ZiB8<:M�GOKRM$MO«�MOZ4GH3[D|MaWN36«�QR<:3;78_�GHMO_R<4782L3;<LZO78_R<cGHB9_jG�B8_RWXGOKRM$MO«�MOZ4G"78\eGHKNM"ÓNQRZ4GHQNB�GH3;78_R<�78_XGOKRMMO«�MOZ4GO3VD|M GH24B8_R<4{|792�G�3;<L{RQR24MOF / WR36«�QR<43VD|MO>

¢�ML�"243VGOMLGOKRM$MO«�MOZ4GO3VD|M�MOf¶QNB�GH3;78_�36_�_R79_9¬:WR3VD|MO2458MO_NZOM?\k7824Thy

ÝC5D �óÙ Å�F �C F

âH� �kÙ Å�F � I�K D �óÙ Å�F � ¸ îÚ$ÛR�fe �hg »

Ø ���� �óÙ Å�F �C ¼ D �kÙ Å�F �C5  � C5  � â îÚ$Û

R�^g »

� � �kÙ Å�F �C5D �óÙ Å�F �C5  �

� §9> ± B �

D �kÙ ÅZF ¸ �8� ¸ D ��¶ �kÙ � Å � §9> ± S �

�"KNMO2:M � � y;¸µ¹ R�hg »L���h� � gï × e ¡�À

� ï g>�¢ÄMUQR<:MÌGHKNMh\k792:TUB8F63;<:TÔGHKRBzG��ÌMU36_HGH247¥WRQRZOMiW!36_�Z�KRB9{9GHMi2 ¤ y$�?M

<:{NF63VGLGOKRM$MO«�MOZ4GO3VD|M�WR36«�QR<43678_�GHMO_N<:782L3;_jGO73VGO<L< / ThTUM4GH2436Z?{NB82�G"B9_RW�B9_jGO36< / TUThMxGH2:3;Za{NB82�GOy

Ø � ¸_� â�� � §9> ² �

�"KRMO24MOy

� ��� ¸ ¤� � Ø[���� â Ø���l� � � §9>6®9B �

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� ��� ¸ ¤� � Ø ���� ¹ Ø ��l� � � §9>6®8S �

`óGÁ36<�MOB9< / GO7É<4KR7E� ? ° ®8�{N> � ³ � A�GOKRB�G�GOKRM!< / ThTUM4GO2:36Z�{RB82cGH<�ZOB8_*S�M!2:M4�"243VG:GOMO_�36_�GHKNM!\k782:T� ��� ¸ î ��� â¿Ú$Û � K û)÷ � I+K[ûA÷ � � > nL78_N<:MOfgQRMO_HGHF / �&�+3;<�{|79<:3[GH3VD|M!WNMOdR_R3[GHMOy WR36«�QR<43678_o36_�B8F[�ÌB / <MO_RKNB8_RZOMiWR>

PR3;Th3;F6B824F / �eGHKNMhMO«�MOZxGH3VD|M�WR2:3;\ G�ZOB9_�S�MUWRMOZO79Th{�78<4MOW�36_HGH7XGb�Ì7�{RB92�GO<:��Zi782:24MO<:{�79_RWR36_N5UGH7XGOKRMWR3[D|MO2:59MO_RZOM�78\�GOKRM$< / ThTUM4GO2:36Z�B8_NWUGHKNM"B9_jGO36< / TUThMxGH2:3;Za{NB82�GO<a79\ Ø � y

����¸Ë¹]KeI1� Å ���a¸Ë¹]KeI1� � §9> ¤ �8�

ILKRM$MO«�MOZ4GO3VD|M?Mif¶QRBzGH3;78_�ZOB8_�S�M��"243VG4GHMO_�3;_XGHKRM$\k7824Thy

ÝC D �óÙ Å�F �C F

â � � �kÙ Å�F � â îÚ$Û � � â îÚ$Û � � � IbK D �kÙ Å�F � ¸ îÚ"ÛR�fe �hg »

� ��� �óÙ Å�F �C ¼ D �óÙ Å�F �C5  � C5  � � §8> ¤8¤ B �

D �kÙ ÅZF ¸ �8� ¸ D ��¶ �kÙ � Å � §9> ¤8¤ S �

ILKRM MO«�MOZ4GH3[D|M�WR2436\ G�WNQRM­GH7�GHKRM B8_HGH3;< / ThTUM4GO2:36Z�{RB92�GÉ78\"GHKRM MO«�MOZ4GO3VD|M�WR36«�QR<43VDA3VG / GHMO_R<4782!3;<<:79F6MO_N7836WNB8F6y

R�^g »

C � ��CE  � ¸ ¹ R

�^g »R�Jg »

C � ���CE  � CE  �

¸ R�^g »

R�hg »

C �8�l�C5  � C5  �

¸ ¹ R�^g »

C � ��C5  � Å � §9> ¤ �8�

B8_NW�GHKgQR<9K IE� � ¸ � >�`x_�{RB92�GH3;ZOQRF;B82:�q\k792LGb�?7©WN36TUMO_R<:3;78_RB9FCÓR7E�"<��?MZOB8_ô�"2:3[GHM � � ¸ÕK���� ¼ »�"3VGOKJK � ¸ � C F CE  ¼ Å ¹ C F CE  » � B9_RW£� ¼ » 3;<uGHKRM�<�GO2:MOB9TÇ\kQN_RZ4GH3;78_!79\�GHKRMMiWRW / 36_RWNQRZOMOW�GH2:B9_R<:{�792�GD|MOF;7¥ZO3VG / >q`b_XGHKRM$58Mi_RMO2:B9FsW9ªeWN36TUMO_R<:3;78_RB9FsZOB8<4M!�þ3;<0GHKRM<0:6i§��.1� ��.�6i°24�$79\k� � >

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m$_XGHKRM$7�GOKRMO2�KRB8_NWR� � � ZO78_R<436<cGH<�78\�S|7zGHK�Bh<478F6Mi_R783;WRB8FsB9_RW�BU{�7�GHMi_jGO36B8Fs{NB82�GO>a=o<:Q��UZO36Mi_jGZO79_RWR3VGO3679_©\k792 � � GH7US|M${�7�GOMO_HGH36B9Fs36<L\k792=�ÄGO7hS�M$78\�GOKRM$\k7824T ? ²R¤ A6y

� ��� ¸J| �kÙ Å�F � Å � ��� ¸ � Å ¬ ø ¸ � §9> ¤ § �

1$MO_RMO24B8F�_RMOZOMO<4<:B92 / B8_NW©<4Q��UZO36MO_HGÞZO79_RWR3[GH3679_R<�GOKRB�G"Mi_R<:QR24MqGOKRB�GT� � 36<u{�7�GHMi_jGO36B8F�ZOB8_(S|M-78S9GOB836_NMOWS / GO2:B9_R<:\k792:TU36_R5<�*GO7�3VGO<L{R2:3;_RZO3;{RB8FsB ~ MO<-B8_RW�<�GHQNW / 3;_R5ÌGHKRM�{R2:79SRF6MOT 3;_GOKR36<�ZO7¥792:WR3;_RB�GOM\k2:B8TUMO>¢�M"<4KRB8F;Fs_R7�G�{RQR24<:QRM�GOKR36<L3;<:<:QNM"\kQN2�GHKNMO2:>

Y 2:79T GHKRMqB9S|7ED|MqZO79ThTUMO_HGH<g�?MqZO78_RZiF6QRWRM�GOKRB�G&B9_�B8F[GHMO24_RB�GO3VD|MC\k792:T�79\9GHKNM&Mi«|MiZ4GH3[D|M^MOfgQRBzGH3679_36<4y

ÝC D �óÙ Å�F �C F

â�� �H��� �óÙ Å�F � I�K D �óÙ Å�F � ¸¤Ú$Û Î

R�^e �Jg »

� ��� �kÙ ÅZF �C ¼ D �kÙ Å�F �CE  � CE  � � §8> ¤ ¦9B �

D �kÙ ÅZF ¸ �8� ¸ D ��¶ �kÙ � Å � §9> ¤ ¦9S �

�"3VGHK�� �H��� �kÙ ÅZF � ¸ � �kÙ Å�F � â <��� � � �kÙ ÅZF � â <�~� � � �kÙ ÅZF � B8_RWÁGHKRM�59F678SNB8F�@CMOZOF;M4Gô_gQRTS�MO2XÚ$Û ÎS�MO36_N5B8_²; � »< � fgQRB8_HGH3[G / >Y 2:79TÊGHKRM�B8S�7ED|M�WR3;<:ZOQN<:<:3;78_ 3VG�S�MOZO79ThMO<B9{R{RB92:MO_HGhGOKRB�GUGHKNM�B8_HGH3;< / ThTUM4GO2:36ZU{RB92�G�78\uGOKRM

MO«�MOZ4GO3VD|M�WR36«�QR<43678_ôGHMi_R<:792?36<$36TU{�782cGHB8_HG�\k792LGOKRMMO«�MOZ4GO3VD|MÞGH2:B9_R<:{�792�Gô79\�GOKRM{RB8<4<:3[D|M<:ZOB9F6B82$dRMiF6WR>ILKRM$<�GOQRW / 79\�GOKRM?< / TUThMxGH2 / {R2478{�MO2�GO36MO<L79\�GOKRM?MO«�MOZxGH3VD|M�WR3;«|QN<:3679_XGHMO_R<4782 �"36F;F|S�M$<�GOQRWR3;MOW�36_�GOKRM_RM ~ G"Z�KRB8{9GOMO2:>

×T��× ��k rw~Øt(âoyzs`b_�GHKN36<<:MiZ4GH3;78_��?M�M ~ KR36SR3[G$GHKRM�Zi78TU{RF63;ZOB�GOMOW�WRMO{�MO_NWRMO_RZOM(78\0GHKNM©Mi«|MiZ4GH3[D|MWR36«�QR<43VDA3VG / 79_

GHKNMhTUMOB8_!ÓN7Æ�ÿB8_RW©GHKRM<4F67E�"F / Th7¥WRQNF6B�GOMOW�ÓRQRZ4GOQRB�GO3678_N<�\k782$<478TUMh<436TU{RF6M�M ~ B9Th{NF6MO<4>�¢ÄM<cGHB92�G�"3VGOK�B�Gb�?7�ªeWN36TUMO_R<:3;78_RB9FAM ~ B8TU{RF;Mq�"KRMi2:M GHKRM?ÓNQRZ4GHQNB�GH3;78_R<LKNBÆD|M GHKNM?\k7824Tù79\sB<:KRMOB92�ÓR7E���"KR79<:MB8TU{RF;3VGHQNWRM?WRMO{�MO_NWR<a79_UGOKRM$ThB9ZO2:79<:ZO79{R36Z�D¶B82436B8SNF6MO<4y

ì �óÙ Å�F�Å í Å ê � ¸ � P �   ¼ Å�F �¢´ � ä ¼ Å ê � Å �9� � §9> ¤ ³ �

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ILKRM?ÓNQRZ4GHQNB�GH3;78_R<uB824M?78SHD�3;78QR<4F / 3;_RZO78TU{R24MO<:<436SRF;MO>q�?7�<4{|MiZO36dRZ�\k7824T÷78\NGOKRM?TUMOB8_UÓR7E�J36<uB8<:<4QRTUMOWB�G�GHKN36<�{|7936_HGHy&� �óÙ Å�F � ¸ � » » �kÙ ÅZF � Å » ¼ �kÙ ÅZF �4� �"3VGOKJK Ib�ʸ � >$m$<:ZO3;F6F6BzGH792 / <4KRMOB82 D|MOF;7¥ZO3VG / dRMOF6WN<KRBED|M�S�MOMi_QR<:MOW�S / D¶B82:3;78QR<0B8Q9GOKR7824<&B9<C<:3;Th{NF6M�TU7¥WRMOF;<C\k782036_HGHMO24_RB8Fi�?BÆD|Mi<^792�GH3;WRB8FRZiQR2:24MO_jGO<^3;_�GOKRM7¥ZOMOB9_ ?V� ¤ � °8° � ¤8¤z° A6>$ILKRM�<:36TU{RF;36ZO3[G / 79\�GHKRM�D|MOF;7¥ZO3VG / dRMOF6W�MO_RB9SRF6MO<�QR< GH7�<478F[D|MLGOKRM�ZiMOF6Fs{R2478SRF;MOT36_�ZOF;78<:MiW!\k782:TU> Y 2:78T � §8> ¤ ³ � 3VG�3;<$ZOF6MOB92uGHKNB�G$GHKRMU<:MiZO78_RW�ZO79Th{�78_NMO_jGh79\0GHKRMZO792:24MOZ4GH792$dRMOF6W�øD¶B8_R3;<:KRMi<:> ¢ÄM$<:79FVD|MuGOKRM$dR2:<cGXZiMOF6F�{R2478SRF;MOTÿS / F67¥79�¶3;_R5\k782�<:79F6Q9GO3678_N<a79\�GOKRM$\k782:TUy

÷ » ¸ ÷ »i� ä ¼ Å ê �   » Å   ¼ Å�F � � §9> ¤z° �

ILKRM$TUB8ZO2478<:Zi78{R3;ZLD¶B92:36B9SRF6Mi<   » Å   ¼ Å�F MO_HGHMO2LB9<a{NB82:B9ThMxGHMO24<:>LILKRM$ZOMOF;FA{R2478SRF;MOT�S|MiZO78TUMO<:y

ÝC ÷0»C ê â » ¼ �   » Å�F � C ÷0»C ä ¼

¹ ¤Ú"ÛC ¼ ÷^»C ä ¼¼

¸º¹[P �   ¼ Å�F �¢´ � ä ¼ Å ê � � §9> ¤z± �

¢�M"B9<:<4QRThMÞGHKRBzG ´ � ä ¼ Å ê � KRB9<qGOKRM$\k78F6F;7E�"36_R5 Y 78QN2:36Mi2�2:Mi{R2:MO<4MO_HGHB�GO3679_Ry

´ � ä ¼ Å ê � ¸ Í ò Û Ü ò �g Vö´ Í e Ü Û ¼ õ � ï Í ð ò Û Ü Ô À � §9> ¤z² �

¢�M"<478F[D|M?MOfgQRB�GO3678_ � §9> ¤�± � QN<:36_N5 Y 79QR2:3;MO2L<:Mi2:36Mi<:>=÷ » 36<:y÷ »H� ä ¼ Å ê �   » Å   ¼ Å�F � ¸Ë¹�Ú"Û Í ò Û Ü ò �g V

P �   ¼ Å�F �pö´ Í e Ü Û ¼ õ � ï Í ð ò Û Ü Ô À¦ ã ¼ z ¼ â ��ã ¬ Ú$Û � Ý Ý â)z » ¼ �   » Å   ¼ ÅZF �4� � §9> ¤ ® �

ILKRM$WR3;«|QN<:3VDA3VG / 36<LMO_NKRB8_RZiMOW�78_RF / B8F;78_R5ÌGHKRM öÛ » WR3624MOZ4GH3;78_Ry

Ø »b» �   » Å   ¼ Å�F � ¸ ¹�Ú$Û � P ´ ÷ » �¸ Ú$Û ¼ Í ò Û Ü ò �g V

z ¼ P ¼ �   ¼ Å�F � Á ö´ Í e Ü Á ¼¦ ã ¼ z ¸ â�Ú"Û ¼ � Ý Ý â)z » ¼ �   » Å   ¼ Å�F �:� ¼ � §9> �9�8�

¢�M78SR<4MO2�D|MÞGHKRBzG?GHKRMMi_RKRB8_NZOMOTUMO_jG"3;_(GHKRM�WR36«�QR<43VDA3VG / 36<�36_RWNMO{�MO_RWRMO_HG�78\�GHKRM » » ZO79Th{�78_NMO_jG78\GHKNM"TUMOB9_©ÓN7Æ�">

¢�MhZO79_R<:3;WRMO2?_N7Æ�öGHKRMU\k78F;F67E�"36_N5©<4{�MOZO36dNZM ~ B9Th{NF6MO>�ILKNMhÓRQNZ4GHQRBzGH3;78_R<$B824M$GOB8�¥MO_(GO7�S�MU78\GHKNM"\k792:TUy

´ » � ä ¼ Å ê �   ¼ ÅZF � ¸ � P �   ¼ Å�F � ZO78< � ��ã ê � ZO78< � ��ãsä ¼ � � §9> � ¤ �

Page 82: Imperial College Londonpavl/rpithes.pdf · 2002. 6. 18. · z nl78{/ 2:3659kjg 9 8 9 s / 1$243658792:3;78< =?>a@cbedaf63;7 gh3;< =?f6f ]a3;58khgh

± §

�?7E�*GHKRM$MO_RKNB8_RZOMiThMO_HGÌ3;_XGHKRM$WR3;«|QN<:3VDA3VG / B8F;78_R5ÌGHKRM öÛ » WR3624MOZ4GH3;78_�3;<:y

Ø »b» �   » Å   ¼ Å�F � ¸ Ú"Û ¼ P ¼ �   ¼ Å�F ��¤

¦ ã ¼ â�Ú"Û ¼ç� Ý â » ¼ �   » Å   ¼ Å�F �4� ¼ â¤

¦ ã ¼ â�Ú$Û ¼ç� Ý â » ¼ �   » Å   ¼ ÅZF �4� ¼� §8> �9�8�

ILKRM$78_NF / _R79_UD¶B8_N36<:KN36_R5UZO78TU{�78_RMi_jG"79\�GHKRM$MO«�MOZxGH3VD|M�WR2436\ G"36<4y

� �» �   » Å   ¼ Å�F � ¸ ¹ C Ø »b»CE  »¸ Ú$Û ¸ P ¼ �   ¼ Å�F �

C » ¼ �   » Å   ¼ Å�F �CE  »� Ý â » ¼ �   » Å   ¼ Å�F �� ¦ ã ¼ âÄÚ$Û ¼ � Ý â » ¼ �   » Å   ¼ ÅZF �4� ¼ � ¼

â Ý ¹ » ¼ �   » Å   ¼ ÅZF �� ¦ ã ¼ âÄÚ$Û ¼¥� Ý â » ¼ �   » Å   ¼ Å�F �:� ¼ � ¼ � � §9> � § �

I�B8�g36_R5�_R7E��GHKRM�ThMiB8_�ÓR7E��GO7�S�MaB�<:KRMiB82�ÓN7Æ�JB9F679_R5-GHKRM öÛ ¼ WR3;2:MOZxGH3679_[� ¸ � � Å » ¼ �   » Å�F �:� �?Ma<4MOMGHKNB�G�GHKRM$MO«�MOZ4GO3VD|M�WR2:3;\ GT� �7��� KRB9<qGOKRM$\k7824Thy

� �7��� �kÙ Å�F � ¸ îÚ$Û � �» �   » Å   ¼ Å�F � Å » ¼ �   » Å�F � � §9> � ¦ �

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Y 782U78QR2U<:MiZO78_RW M ~ B8TU{RF6MX�ÌM�Z�KN7¥78<:M�B�Gb�?7�ªeWN36TUMO_R<:3;78_RB9Fa<cGHMOB9W / ThMiB8_ ÓR7E� �"KR36Z�K 36<UBF63;_RMOB92L\kQR_RZ4GO3678_�79\^<4{RB8ZOM�B8_RW�\k792qGOKRM$ÓRQRZ4GOQRB�GO3678_N<q�?M"Z�KR7¥79<:M�GO36TUM?WRMO{�MO_NWRMO_HG"{|Mi2�GHQN2:SRBzGH3679_R<�78\ZOMOF;F6QRF;B82uÓR7E�"<:> v 782:M$<4{|MiZO36dRZiB8F6F / �çGHKRM$TUMOB8_�ÓR7E�Ô3;<:y

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B9> Ø »b» \k792s½!¸ �çæ � Å~� V ¸ ¤ �8æ;� SR> Ø » ¼ \k782s½!¸ �çæ;� Å~� V ¸ ¤ �çæ �

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for linear mean flow with γ = 5, ω0 = 10 with Pe

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B9> Ø »b» \k792s½!¸ ¤ �8æ;� Åh� V ¸ �8æ;� SR> Ø » ¼ \k782s½!¸ ¤ �çæ � Å~� V ¸ �çæ �` Ì¾Ê G Ä¡½eãpÀl¿�Á Ø �kÙ � È¥Ç�ÄÃÄ:Ç�Í�ºÍ�ÌlÇ�Ë(n8Æ�Í1Ä:ºÌlË ºËpÅ Æ27p½Eº�Ä�¼¾ÌlËz½#ºÄ�É�½#º�Ë ÎpÇEÏ Æ_º�ËzÅ Ú$Û�ܸ¤ � Å^Ý Ü�¸ ¤ À

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ÝCED VC F

â�� �kÙ Å�F � I�K D V ¸ � Å � §9>6§9³ �

GH7958M4GOKRMO2u�"3[GHK(GOKRM36_R3[GH3;B8F�ZO78_RWN3VGH3;78_ D V �kÙ ÅZF ¸ �8� ¸ D ��¶ �kÙ � >hILKN36<?3;<:�CB9<"M ~ {�MOZ4GOMOWR��BXGH2:B9_R<:{�792�G�JI�¡ü�� ' þ��������+ (��¡ü�ü �¢ü�������0°üuü��2,�������ú��+� ' ü���+����� ,+�lü���¡ü$�¡ú���������ú��S�����+ú°ÿ¡ÿbú��¾ü�� �¾ú��P� �

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±8²

MOfgQRB�GO3679_R>L¡?<:3;_R5_R7E� � §8>6§9³ � 36_HGH7-GOKRM ; � ¤ � MOfgQRB�GO3678_X�?M"79S9GHB936_�GHKRM$MOfgQRB�GO3679_©\k792 D » �óÙ Å�F � y� V�D » ¸Ë¹Ìì �óÙ Å�F�Å í Å ê � I�K × D V �kÙ Å�F � � §9>6§ ° �

I�7h{R247¥ZOMOMOW�\kQR2cGHKRMi2:�g�?M$WRMOZO79Th{�78<4M D » �kÙ ÅZF � 36_HGH73[GH<LÓRQRZxGHQRBzGH36_N5hB9_RW�TUMOB8_�{RB92�GOy

D » �kÙ Å�F�Å í Å ê � ¸©ø �kÙ Å�F�Å í Å ê � I�K × D V �kÙ Å�F � â D » �kÙ ÅZF � � §9>6§ ± �

�"KRMO24M � ÷ � ¸ Ä�>aPRQNSR<�GO3VGHQÈGH36_N5h_R7E� � §8>;§ ± � 36_HGH7UMOfgQRB�GO3679_ � §8>;§ ° � �ÌM$78S9GOB83;_UGHKNM"ZiMOF6Fs{R2478SRF;MOTÿ\k792ø$y

� V ø �kÙ Å í Å�F�Å ê � ¸º¹$ì �kÙ Å�F�Å í Å ê � Å � §9>6§ ² �

PR3;_RZOMÌGHKRM�BED|MO24B859M�78\0GOKRM�2:3;58KHGôKRB9_RW <:3;WRM�78\LMif¶QRBzGH3;78_ � §8>6§ ² � D¶B8_N36<:KNMO<B8_RW©�ÌM�KRBED|MUB8F;<:7!<:MxG� ø � ¸ÅÄ��sM ~ 36<�GOMO_RZOM-B8_RW�QR_R3;f¶QNMO_RMO<4<L78\C<478F6QÈGH3679_R<0GH7 � §9>6§ ² � 36<LMO_R<4QR2:MiWR>

¢�M©_N7Æ���"36<4K�GO7!78S9GOB836_ B8_ MOfgQRB�GO3679_É\k792 D » �óÙ Å�F � >Á¢ÄM�WRMO243VD|MÌGHKR3;<MOfgQRB�GO3678_ \k2478TÊGOKRM<:79FVD¶B8SN36F63[G / ZO79_RWR3[GH3679_�\k782 GHKRM ; � î � MOf¶QNB�GH3;78_Ry

� � » D » â)� ¼ D/V1� ¸ � Å � §9>6§9® �

\k2:79Tö�"KR3;Z�KR��B8\ GOMO2L<:79ThM�B8F659MOSR24B8�N�ÌM$79S9GHB936_Ry

C D » �óÙ Å�F �C FâH� �óÙ Å�F � I�K D » �kÙ Å�F � ¸

¤Ú"Û KeI u â Ø �kÙ ÅZF � I�K D V �kÙ ÅZF � Å � §9>6¦ �8�

GH7958M4GOKRMO2-�"3[GHK�KR79Th7958MO_NMO78QR<U36_N3VGH3;B8FqZO79_RWR3VGO3679_R< D » �kÙ Å�F ¸ �8� ¸ � > ILKRM�MO_RKRB9_RZOMOTUMO_HGh36_�GOKRMWR3;«|QN<:3VDA3VG / 36<4y

Ø ��� �óÙ Å�F � ¸Ë¹�Ú$Û � ´ ��÷�� � Å � §9>6¦ ¤ �

�?7E���?MZOB8_�<:79FVD|M-GOKRMý; � î � MOfgQRB�GO3678_�\k782 D ¼ >U¢�M<:QNSR<�GO3VGHQÈGHM � §8>;¦ �9� 36_(GOKRMD; � î � MOfgQRB�GO3679_�GO7

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± ®

78SÈGHB83;_UGOKRM$MOf¶QNB�GH3;78_�\k782 D ¼ y

� V D ¼ ¸ ¹ CCE  � � » � â ´ � � ÷�Ü ¹ �

Ú$ÛC ÷|ÜC ä � â

¤Ú$Û Ø � Ü

CED/VCE  Ü ¹ ´ Ü C D »C5  Ü ¹ Ý

CC F

÷|Ü C5D/VCE  ܸ ¹�D � Ü C ¼ D VC5  � C5  Ü ¹

C D � ÜC5  � â Ý

C ÷�ÜC F

C5D/VCE  Ü ¹ ´ Ü

C D »CE  Ü ¹ Ý ÷�Ü C ¼ D VC5  Ü C F� §9>6¦ �8�

�"KRMO24M

DE� Ü ¸ � » �Câ ´ � � ÷ Ü ¹ � C ÷�ÜC ä � â¤Ú$Û Ø � Ü � §9>6¦9§ �

¢�M!36_HGH2:7¥WNQRZOMôGHKRM!B9Q ~ 3;F63;B82 / \kQR_RZ4GO3679_R<B¹iß � Üfº R�Ye Ü g » Å ¹��zÜ�º RÜ g » Å ¹ ÿ Ü º RÜ g » GHKRBzG <4B�GO36<:\ / GOKRM!\k78F;F67E�"36_N5KR3;58KRMO2L792:WRMi2LZOMOF6F�{R2:79SRF6MiTh<4y

� V ß � Ü|¸�¹�D � Ü Å�¸ÈÅ Ý ¸ ¤ Å æ6æ Å � � §8>;¦8¦9B �

� V ÿ Ü�¸Ë¹ C D � ÜCE  � ¹ ÝC ÷|ÜC F Å

Ý ¸ ¤ Å æ;æ Å � � §9>6¦8¦9S �

� V �zÜA¸Ë¹ Ý ÷�Ü Å Ý ¸ ¤ Å æ6æ Å � � §8>;¦8¦8Z �

¢�M�_R7zGHM-GHKNB�G�<436_RZOM Ø ��� ¸�¹�Ú$Û � ´ � ÷ � � B9_RW � ÷ � � ¸ � GOKRM�243659KjG�KNB8_RW!<436WRMO<-78\�GHKRM�B8S�7ED|MMOfgQRB�GO3679_R<hKNBÆD|M�¨OMi2:7�BÆD|Mi2:B859M�B8_RW�ZO79_R<:Mif¶QRMi_jGOF / MOfgQRBzGH3679_R< � §8>;¦8¦ � KRBED|M�<:TU7¥7�GHK�B9_RW�QN_R36fgQRMO�QR{ôGH7�B�Zi78_R<cGHB8_HGH�q<478F6QÈGH3679_R<:>�¢ÄMMi_R<:QR24MhQN_R36fgQRMO_RMi<:<$S / 2:MOfgQR3;2:36_N5�GHKRMU<:79F6Q9GO3679_R<�GH7�KRBED|M¨OMO247BED|MO2:B958MO> D ¼ KRB8< GHKNM"\k792:TUy

D ¼ �kÙ Å�F�Å í Å ê � ¸�ß � Ü �kÙ Å�F�Å í Å ê �C ¼ D VCE  Ü CE  � â ÿ Ü �kÙ ÅZFiÅ í Å ê � CED VC5  Ü âà÷|Ü �kÙ Å�F�Å í Å ê � C D »CE  Ü â)�zÜ �kÙ ÅZFiÅ í Å ê �

C ¼ D/VCE  Ü C F� §9>6¦9³ �

�?7E���?ML�"3;<:K�GH7UMO<�GO36TUB�GHM�GOKRM$MO2:24782 GHKRBzGa�?M"B92:M�WR783;_R5�S / _RMO59F6MOZ4GO36_R5KN3658KNMO2L7824WRMO2 GHMO24Th<4>q¢�MWRMO_N7�GHM�S / D �HG4G GHKNMaWR3;<:ZO24MO{RB9_RZ / S�M4Gb�?MOMO_-GHKNMadR24<�GqGHKN2:MOM0GOMO2:TU<q36_ÌGHKRMLTQRF[GH3;{RF6Mu<:ZOB9F6MO<qM ~ {RB8_N<:3679_

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² �

B8_NWUGHKNM"<478F;Q9GH3;78_ D < 79\ � §8> ¤ � yD < �óÙ Å�F � ¸ D V �kÙ ÅZF � â î D » �óÙ Å�F�Å

Ùî ÅFî� â î ¼ D ¼ �kÙ Å�F�Å

Ùî ÅFî� â D �7G\G � §9>6¦ ° �

m$QR2$5879B8F�3;<uGH7�78S9GOB83;_�QR_N36\k7824T+MO<�GO36TUB�GOMO<?\k782ÞGHKRMMi2:2:792�GHMO24Tþ36_ � §9>6¦ ° � >�¢ÄMU<:KNB8F6FqB9ZOZO78TU{RF;36<:KGHKN36<LS / 78S9GOB83;_R36_R5UB{RB92:B8S�79F636Z�MOfgQRB�GO3678_�\k792 D �7G4G B9_RW�QN<:36_N5MO_RMO245 / MO<cGH3;ThBzGHMO<4>

¢�M"B9{R{RF / � < GH7 � §8>6¦ ° � GH7U78S9GOB83;_Ry� < D �HG4G ¸Ë¹S� < D V ¹ î � < D V ¹ î ¼ � < D ¼ � §8>;¦ ± B �

D �7G\G �kÙ ÅZF ¸ �8� ¸Ë¹ î ÷�Ü CED/VCE  Ü Á ¡ g V ¹ î ¼ D ¼ Á ¡ g V � §9>6¦ ± S �

¢�ML2:MOZOB9F6FiGOKRB�GCGOKRMLB8Q ~ 3;F636B92 / \kQR_RZxGH3679_R<%ø Å �0ÅVUôÅ @*B82:ML\kQN_RZ4GH3;78_R<078\�S�7�GHK Ù ÅEF B8_NWý× < Å ¡< > . MOB92:36_N5GHKN36<L36_�TU36_RWN�g�ÌM$ZO79Th{NQ9GHM�GHKNM"243659KjG"KRB9_RW�<436WRM-78\�GOKRM$B8S�7ED|M"Mif¶QRBzGH3;78_R>0¢�M$KRBED|MOy

� < D/V ¸ºì�I�K D V ¹ îÚ$Û N D V � §9>6¦ ² �

�?7E�*�ÌM��ÌB9_jGLGO7hZO79Th{NQ9GHM�GHKNM"<4MOZO79_RWXGHMO24Tù3;_GOKRM$2:3;58KHG"KRB8_RW�<:3;WRM$78\ � §8>6¦ ± B � > ¢ÄM$KRBED|MOy

� < D » ¸ ¤Ú$Û N D V â

¤Ú$Û KmI Ø I�K D/V â ìcI�K D » ¹ îÚ$Û N D » � §9>6¦9® �

B8_NWRy

� < ÷�Ü CED/VCE  Ü ¸ ¤î� � V ÷|Ü � Á û g K M+e Ô g NM CED/VCE  Ü

â ÝC ÷ ÜC F

â � » � â ´ � � C ÷ ÜCE  � ¹�Ú"Û

C ¼ ÷ ÜC5  � C ä � Á û gLK M2e Ô g}NM C5D VCE  Ü

â � » � â ´ � � ÷|ÜN¹ �Ú$ÛC ÷|ÜC ä � Á û g K M2e Ô g NM C ¼ D V

C5  Ü CE  � â Ý ÷�Ü C ¼ D/VC5 WV1C F¹ îÚ"Û

C5D/VCE  Ü N × ÷ Ü â � C ÷�ÜCE  �

C ¼ D VCE  Ü C5  � âà÷ Ü C ¾ D/V

CE  Ü C5  � CE  � Á û g K M e Ô g NM � §9>6³ �8�

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²e¤

�?7E�*�ÌM$ZO78TU{RQ9GOMs� < D ¼ >0¢ÄM$KRBED|MOy

� < D ¼ ¸ ¤î

� < ß � Ü C ¼ D/VCE  Ü CE  � â)� < ÿ Ü ÁCED VC5  Ü â)� < ÷�Ü C D »C5  Ü â)� < �zÜ C ¼ D VC5  Ü C F Á û g K M2e Ô g NM

â � » D ¼ â î � ¼ D ¼ � §9>6³ ¤ �

@qQ9G:GO36_R5ÌGHKNM"B9S�7ÆD|M$MOfgQRBzGH3679_R<0GH7958M4GOKRMO2 �ÌM?59M4GHy

� < D �HG4G ¸ ¹ � < D V â � < D » â)� < ÷ Ü C5D/VCE  Ü â î ¼ � < D ¼¸ ¹ � � < ÷|ܶ⠴ Ü � Á û g K M+e Ô g NM CED VCE  �¹ î �:� � < ß � ÜgâID � Ü � C ¼ D VCE  Ü C5  � â � � < ÿ Ügâ C D � Ü

CE  � â ÝC ÷�ÜC F� CED VC5  Ü â � � < ÷|ܶ⠴ Ü � C D »C5  Ü

â � � < �zܶâ Ý ÷|Ü � C ¼ D VC5  Ü C F� Á û g K M2e Ô g NM ¹ î ¼ � �kÙ ÅZF �

¸ ¹ î ¼ � �kÙ ÅZF � � §9>6³ �8�

�"KRMO24M

� �kÙ Å�F � ¸Ë¹ ¤Ú$Û N × D » â CED/V

CE  Ü N × ÷|ܶâ � C ÷|ÜCE  �C ¼ D/VCE  Ü C5  � â�÷�Ü C ¾ D/V

C5  Ü CE  � CE  � â)� » D ¼ â î � ¼ D ¼Y 7820GOKRM$36_R3[GH36B9FAZO79_RWR3[GH3679_R< �ÌM?KRBED|MOy

P �óÙ � ¸ú÷|Ü CED VCE  Ü Á ¡ g V â î D ¼ Á ¡ g ¼ � §9>6³9§ �

PR3;_RZOM-�ÌMKNBÆD|MB9<:<4QRThMiW�GHKRBzG$GHKRMÌD|MOF67¥Zi3VG / dRMOF6W!B9<��ÌMOF;FCB8<�GHKNMh3;_R3VGO36B8F0ZO78_RWN3VGH3;78_R<-B82:MU<:TU7¥7�GOKR�GHKNM<:78F;Q9GH3;78_R<$79\ � §8>;§ ° � B9_RW � §8>;¦ �8� B9<L�?MOF6FsB9<$78\�GOKRMZOMOF;Fs{R2:79SRF6MiTh<?B92:M<4Th7¥7zGHK�B9_RW�S�79QR_RWRMOWN>nL78_N<:MOfgQRMO_HGHF / �gGOKRM$\kQR_RZ4GO3678_N< � �kÙ ÅZF � Å P �kÙ Å�F � B92:M�B8F6<47<:TU7¥7�GOK!B8_RW�S|79QR_RWRMiWR>aILKgQR<4�s_RMO58F;MOZ4GO36_R5KR3;58KRMO2L792:WRMi20GHMO24Th<4� D �HG4G <:BzGH36<4dRMO<0GOKRM$\k78F6F;7E�"36_R53;_R3VGO36B8F D¶B8F6QNM"{N2:78SNF6MOTÿ{N2:78SNF6MOTUy

� < D �HG4G ¸Ë¹ î ¼ � �kÙ Å�F � � §8>;³8¦9B �

D �HG4G �   Å�F ¸ �9� ¸�¹ î P �kÙ � � §9>6³8¦9S �

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² �

�?7E���ÌM-ZOB8_�B8{N{RF / F6MOTUTUB � > � GO7-GHKRM?3;_R3VGO36B9F¥D¶B9F6QRM?{N2:78SNF6MOT � §8>6³9¦ � GO7MO<�GO36TUB�GHM D �HG4G >Lp?7E�ÌM4D|MO24�3VG�36<�ZOF;MOB820GOKRB�G?GOKRM�S�79QR_RW(GHKNB�G?�?M�<:KNB8F6F�78SÈGHB83;_�3;<a_R7zG�<:KNB82:{N>�ILKRM�2:MOB9<:78_!\k792uGHKN36<�36< GHKRBzGaGOKRM36_N3VGH3;B8FsZO79_RWR3[GH3679_ � §9>6³8¦9S � \k792 D �HG4G 36<U; � î � B8_NW!_R7�GO; � î ¼ � GHKRBzG?�ÌM�_RMOMOW!3;_�7824WRMO2uGO7�S�M�B9SRF6M-GO778SÈGHB83;_�BU<:KRB92:{�MO2�S�78QR_RWN>?]aMiThMOTS�MO2436_R5ÞGHKRBzG P �kÙ � ¸ ÷ Ü � Ö ð� ï � Á ¡

g V â ® � î � �ÌM$<4MOM�GHKRBzGX3;_©792:WRMi2qGO7<:79FVD|M-GOKR36<${R2478SRF;MOT��?MhKRBED|M-GO7©B9QR58TUMO_HG$GHKRMTQRF[GH3;{RF6M�<:ZOB9F6MO<$M ~ {RB8_N<:3679_��"3[GHK(GOMO2:TU<�GHKRBzG"�"3;F6FZO79Th{�MO_R<4B�GOMh\k792LGOKRM ; � î � GOMO2:T 3;_ � §8>6³9¦8S � B9_RW��"3;F6FeD¶B8_R3;<:K�M ~ {�79_RMO_HGH36B9F6F / \kB9<�G�BÆ�?B / \k2:79T�GOKRM7824365936_�<47�GHKNB�GLGHKNM / �"36F;F|_N7�GÌ3;_jGO2:7¥WRQNZOMU; � î � GOMO2:TU<�3;_ � §8>;³8¦8B � > Y 78F6F;7E�"36_R5 ? ¤�² Aç�ÌM?3;_jGO2:7¥WRQRZiMqGOKRM\k78F;F67E�"36_N5TQRFVGO36{RF;Ma<4ZOB8F;MO<LM ~ {RB8_R<43679_Ry

D < �kÙ Å�F �+* D V �kÙ ÅZF � â î D » �óÙ Å�F�Å í Å ê � â î ¼ D ¼ �kÙ ÅZFiÅ í Å ê � ââ î D

��¶» �kÙ ÅZFiÅ í Å ê Å ê � � â î ¼ D

��¶¼ �kÙ ÅZFiÅ í Å ê Å ê � � â æiæOæ � §9>6³9³ �

�"3VGOK D ��¶» Å D ��¶¼ S|Mi36_R5${�MO2:3;7¥WR36Z�36_ í B8_NW ê >0¢�MaKRBED|M�B8F;<:7�3;_jGO2:7¥WRQNZOMOWÌGHKRM�_RM4� GH36TUM4ªRF636�¥MñD¶B82:3;B8SRF;Mê � ¸ ¡< >�¢ÄM24MOTUB82:��GHKRBzG?GHKNMO<:M-Gb�Ì7XGOMO2:TU<aWNMO{�MO_RW�78_ ¡< 36_(Gb�Ì7��?B / <?B9_RWô�ÌMKRBED|MM ~ {RF63;ZO3VGOF /GHB9�¥MO_�GOKR36<�36_HGH7�B9ZOZO79QR_jGO> D/V Å D » <4B�GH3;<:\ / Mif¶QRBzGH3;78_R< � §8>;§ ° � B8_RW � §9>6¦ �8� ��2:Mi<:{�MOZ4GO3VD|MOF / B8_NW D ¼ 3;<583[D|MO_�S / \k792:TQRF;B � §9>6¦9³ � >LPNQRSR<�GO3VGOQ9GH3;_R5?_R7E� GHKRMLM ~ {RB9_R<:3;78_ � §9>6³8³ � 36_HGH7-MOf¶QNB�GH3;78_ � §8> ¤ � �ÌML78SÈGHB83;_MOfgQRB�GO3679_R<L\k782 GHKRM�GOMO2:TU< D ��¶» Å D ��¶¼ y

� ��¶ D ��¶» ¸ � � §8>;³ ° B �

D ��¶» �óÙ Å�F ¸ � Å í Å ê Å ê � ¸ �9� ¸Ë¹3ø �óÙ Å í Å ê Å�F ¸ �9� IbK × D ��¶ �kÙ � Å � §9>6³ ° S �

B8_RW

� ��¶ D ��¶¼ ¸º¹S� » D ��¶» � §8>;³ ± B �

D ��¶¼ �óÙ Å�F ¸ � Å í Å ê Å ê � ¸ �9� ¸Ë¹ ß � Ü C ¼ D VC5  Ü C5  � â ÿ Ü C5D/VCE  Ü âà÷|Ü C D »C5  Ü â ��Ü C ¼ D VCE  Ü C F Á ¡ g V � §9>6³ ± S �

�"KRMO2:M

� ��¶ yO¸ ÝCC ê � â Ý

CC ê â � � �kÙ ÅZF � âÉì �kÙ Å�F�Å í Å ê �4� I�K û�¹ ¤

Ú$Û NUû � §9>6³ ² �

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² §

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Standing waves, irrational ratio, k −vs |V| for various S

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K

Pe

Kanti

K11

10−3

10−2

10−1

100

101

102

103

10−7

10−6

10−5

10−4

10−3

10−2

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100

101

102

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K vs Pe for vCS

(y) + A(τ)

Kanti

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K vs S for vCS

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Kanti

Pe = 100

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100

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Kanti

K vs S for vCS

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