Ð ne such run is referred to as apd multi w al k er f simulation , and w e ...... U#` Vb UWr' V X¦ Rh EÐw B4Ф 0 ежРB` 0¦ 1"6 U#`8V2 UW 8B¦T8V§0 ¡ v8w¨0¦w BФ 0 ...
! " # $% & (')**,+ $#$ (-" ./ 0 # $#$ 1 - ! ,$# 2 3 !$ 46578 9;:?"@ :BACAD8 EFADG/A;78HI2J >"K AML G2N OQP 8SR 8 K*TVU :BW8 P 9C:BAML ?L X "7 9;I UZY I ?? I DP [ I2E8\7 : U^] I P AD:_I K N >KB`"KBK_@ 8 U AVG2NaA;7"8 P 8 b > : P 8 @ 8 U AD9(NcG P A;78E8\d P 8\8 G2N O G JSA;G P GeNfg7: K G9CG ] 7 L Y>U 8 heiij
,hJ ei2i j X 7"9DI UFY I ?? I PD[ IE 8\74 KBK :Bd7A 9 #8 9C8 P W8 E
:B:
57: 8 A;% G E G/NcG P @ 8
:_:B:
(G >"K E K : 2 8
A;G ` P 9MA A;7I U @ L ] I P 8 U A 9QI U E 9;: P Ied8 @ 8 U A A;7 P G > d27G > A @ L d P IE > IeA;8 9MA > E :_8 9 (I9 NcG P A >"U I AD8 A; G (G P G U ? GeA;7/AD78\G P 8\A;:"? A;8#E K L A;7:?? 8 EF G G UF@ 8
L A;78#9C: A!A;78gA;78" (G P QI U E d > : A G2N QO P . P 8SA;A/. K I2J @ I U $ TVU :_W28 P 9;: AML G2N10Q: P d2: U : \J 8 E 9C8#J P 8SA;:_G U P I A;8 a:K 9;8 A;: @ 8 P 8 ] P G E > JS: U d AD78 P 8 9 >K AD9GeN + G9;7:U JSA;:_G U "> R^JSG U E : AD:BG U
j
= J 78 @ I A;: J\8 9 J 78 @ GI A;A P I2JSADI U A :BA;7 P I AD8 GeN*i i2i @ d eJ @ 9 NcG P i2ii 9gI U E A;7"8 P 8 I N AD8 P E G 8 9 U G2A ] P G E > JS8 57"8/J\G U J\8 U A P I AD:BG U :K I AD8 E I A IZE : P J\8 K G J\IeA;8#EFIeA A;78 SJ 8 U AD8 P G2N A;7"8 E G @ Ie: U ] P G E > J\: U d^ J 7"8 @ GIeACA P I2JSADI U A JSG U AD: U > G > 9 K L :BA;7 P IeA;8 GeNi i2i2ii @ d eJ @ 9 * ,: G > 9 K L $ ? & = I @ 8I9 $I &(8SRJS8 ] A : AD7 ]">K 9;8 E P I U EG @ ] P G E > JSA;:_G U I29 E 8#9;J P : ? 8#E : U A;78 AD8SR A 8#I U A;: @ 8 ADG JSG U A I2JSA9) ; W 9 J 78 @ GI A;A P I2JSADI U A E : > 9;:BG U JSG 8= JS:_8 U A 9 ?3 NcG P W I P :_G > 9 J 7"8 @ G ADIJ AD:_J\: AMLFJSG 8= JS:_8 U A 9 6 78 U A;7"8 ] G: U AV9;G > P JS8 ] P G E > JS8#9 J 78 @ GIeACA P IJ ADI U A(: U^]>K 9C8#9
578 ] IeA;7 A (G^J\8 K_K 9 ADI 84 7: K 8 $I & ? G2A;7&I P 8%9C8#J P 8SAD: U d J 78 @ GI A;A P I2JSADI U A JSG U AD: U > G > 9 K L I U E 9C:_d U I K : U d 8#I2J 7 GeAD78 P : AD7 9;I @ 8 9MA P 8 U deAD7 578\L^JSG >K E U GeA P 8 IJ 7^GeA;7"8 P IeN A;8 P ii 7 $ ? &.(GeA;7 I P 8 9;8 J P 8SAD: U d J 78 @ GI ACA P IJ A I U A JSG U AD: U > G > 9 K LZI U E 9;:Bd U I K : U d%8 IJ 7FG2A;78 P ?> A :BA;7 E : 8 P 8 U A 9CA P 8 U d2A;7 8 @;4CBF: JS: U d i i @ d6 J @ D 9 7: A P I U E G @ AD: @ 8(: U AD8 P W I K 9 ? 8SA (8\8 U 9 (8\:_d27A;8#E hei ] 8 P JS8 U A 578\L P 8 IJ 78 E 8 IJ 70GeA;7"8 P IeN A;8 P h ^7 578 ]>K 9;8 9 % 78 @ GeA I2JSA;: P JS8 ] G P 8 ? G >U EI P :_8 9 P 8 K 8 I29;8 0 X H : U 9;:_E8A;78VEG @ Ie: U NcG P $ E & h EI L 9 3$8 & EI L 92I U E $ N & i EI L 9 I U E G @/K L 9;7"I ] 8 E G ? 9MA I2J K 8 9 I P 8 9;7G U : U^?K I2J j
0
X H \J G U J\8 U A P I AD:BG U ] P G `"K 8 IeAA;: @ 8 7 P $I & = A P I AD8\d2L $ ? & = A P IeA;8 d2L h I U E $J& = A P IeA;8 d2L 57"8 W I KB> 8 9 I AAD78 ? I P 9 P 8 ] P 8 9;8 U AD9 J\G U \J 8 U A P I AD:BG U $ i 5 d ! & i 5!GeADI K W8 9D9C8 KK 8 U ed AD7 I29 I N >U J A;:_G U G2N)A;: @ 8NcG P E : 8 P 8 U A : U AD8 P U I K P 8 K 8 I9C8E > P IeA;:_G U 9 $ I'& = A P IeA;8 d2L h $ ? & = A P IeA;8 d2L
R :BW
5!GeADI K K 8 U deAD7 GeN8 IJ 7 d28 U 8 P I AD:BG U GeNaW8 9D9C8 K 9gNcG P A (G P 8 K 8 I9C8VE > P IeA;:_G U 9(G2N? 6h I U E #i EI L 9 "$ I'& = A P IeA;8\dLZh $ ? & = A P I AD8\d2L
h /I U E #i E"I L 9 $ I & = A P I AD8\d2L h $ ? & = A P IeA;8\dL
j
h
#
:U JSA;:_G U G2NE 8 ] A;7 : U 0E: P 8 JSA;:_G U NcG P AD7 P 8 8 P 8 K 8 I9C8 E > P I AD:BG U 9 G2N
)
G P @ I K : [ 8#EZJ\G W28 P 8 EZI P 8 I I29 I N >U JSA;:_G U GeN): U AD8 P U I K P 8 K 8 I9C8 E > P I AD:BG U NcG P 9MA P IeA;8 d2:_8 9 h I U E
5!GeADI K W8 9D9C8 KaK 8 U d2A;7 I9VI N >U J AD:BG U GeN AD: @ 8 NcG P M9 A P IeA;8\d:B8#9 O 8 d P I2EIeA;:_G U P I A;8 : I K A;G h I U E iFEI L 9 I P 8 J\G U 9;:_E8 P 8 E cN G P 9MA P IeA;8\d:B8#9 h [ 8 P G $ O I i'& 5; (G P 8 K 8 I9C8 E > P I AD:BG U 9VG2N Z IUE
# :"U J AD:BG U G2N!E 8 ] A;7F: U ^E: P 8 JSA;:_G U NcG P 9MA P IeA;8\d:B8#9 O \8 d P IEI AD:BG U P I A;8 2: I K A;G [ 8 P G4$ O I i'& 5; (G P 8 K 8#I29;8 E > P I A;:_G U 9)GeN> h I U E i EI L 9 I P 8 SJ G U 9C: G P 8#9;J\8 U A 9MA Ie: U : U dZG2Nf X (4 '$ O & G U 7 >@ I U 8 U E GeAD78 K :_I K JS8 K_K 9 J >K A > P 8 E NcG P EI L 9 G U f!a4 49;: U A;8 P 8#E @ : J K 8 :!JSG >U A;8 P 9CADI2: U 8#E : AD7 O 4Vf$ ?K_> 8 & @ Ied8 9 I P 8 JSG @/] G9C8#E GeN(9C8#J A;:_G U 9QG2N A;7"8/9DJ\I G K E"9 @ G W : U d AD7 P G > d27 : A 9 A;7: 9(E 8 ] A;7 G2N!h2h @ AD7"I AI P 8VJSG KBK I ] 9;8 E/G U 8 IJ 7%GeA;7"8 P "$ I'& Ied U : ` J I AD:BG U #i $ ? & I2d U : ` J\IeA;:_G U
j LA;G98 K 8SADI K I2JSA;: U E : A;:_G U I U E G P dI U : [ IeA;:_G U G2N(8 U E GeAD78 K :"K A > P 8#E NcG P EI L 9 G U f !4 4 9C: U A;8 P 8 E @ :_J P G9 ] 7"8 P 8 9DJ\I G K E9 X U E GeAD78 K :_I K JS8 K_K 9 9CADI2: U 8 E :BA;7 P 7G EI @ : U 8 ] 7"I KBK G2: J K 8 :J\G >U A;8 P 9CADI2: U 8 E% : AD7 O 4Vf$ ?K_> 8 & @ I2d28#9 I P 8 JSG @/] G9;8 E GeN 9;8 JSA;:_G U 9 G2NA;78 9DJ\I G K E9 @ G W : U d AD7 P G > d7Z:BAD9AD7: 9 E 8 ] A;7^GeN h @ AD7"I AVI P 8 J\G K_K I ] 9C8#E G U 8#I2J 7FGeAD78 P $I'& Ied U : ` J I AD:BG U #i $ ? & Ied U : ` J I AD:BG U
j X R ] P 8 9D9;:BG U G2N$I'&W H ;$ ? &f X (4 ;$J & X 9;8 K 8 JSA;: U I U E($ E& (4 GeN 8 U EGeA;7"8 K :_I K J\8 K_K 9 J >"K A > P 8#E G U 5 (f = I U E f!a4 4 9;: U AD8 P 8 E @ :K A > P 8 E NcG P #i EI L 9 G U f !4 4 9C: U A;8 P 8 E @ :_J P G9 ] 78 P 8F9DJ\I G K E"9 4 O = (9 9CADI2: U 8#E :BA;7 I U AD: ? G E L E: P 8 JSA;8 E/I2dIe: U 9CA0 X H $cd P 8 8 U &)I U E U> J K 8\:"J\G >U A;8 P 9CADI2: U 8 E : AD7 O 4Vf"$ ?KB> 8 & @ Ied8 9 I P 8 JSG @/] G9;8 E GeN!9;8 JSA;:_G U 9(GeNaA;78 9DJ\I G K E9 @ G W: U d A;7 P G > d7 :BAD9(AD7:_J U 8#9;9(I A E 8 ] A;7F: U J P 8 @ 8 U A 9gG2N @ I U EFI NcG J > 9 E 8 ] A;7^GeN h2h @ A;7"IeAVI P 8 J\G K_K I ] 9;8 EZG U 8 I2J 7FGeAD78 P h
] P G K :BNc8 P I AD:BG U G U JSG J >K A > P 8 I29 9VJ\G U ADI2: U : U d X I K G U 8 X U G U A P I U 9CNc8 JSA;8#EF4 O = (9 I U E X A P I U 9MNc8#J A;8#E 4 O = (9 O IeADI 8 P 8 P 8 ] P 8 9;8 U ADIeA;:_W28gG2N Q: U E 8 ] 8 U E8 U A 8SR ] 8 P : @ 8 U A 9I U E I KBK E"I ADI ] G2: U A 9 8 P 8 ]K GeA;A;8 E I29 @ 8 I U = O $ U & E 8 U GeAD8 9 IF9C:_d U : ` J I U A K L $ ] i i &V7:_d278 P X ] P G K : Nc8 P IeA;:_G U : U I X (9 U G U A P I U 9MNc8#J A;8#E/4 O = (9J\G J >K A > P 8 9;L 9MAD8 @ I9 JSG @/] I P 8 E A;G X I K G U 8 E 8 U GeAD8 9 I^9C:_d U : ` J I U A K L $ ] i i &V7:_d278 P X ] P G K :BNc8 P I AD:BG U : U I X (9 A P I U 9MNc8#J A;8#E 4 O = (9J\G J >"K A > P 89;L 9MAD8 @ I9 JSG @ ] I P 8 E A;G X (9 U G U A P I U 9CNc8 JSA;8#EF4 O = (9 8 ] P 8#9C8 U ADI AD:BW8 # : P 8 U J\: U O fg7 O 578 ` 8 K EFGeN!A;: 8 8 U d2: U 8\8 P : U d/Ie: @ 9(A;G P 8 d28 U 8 P I AD8 U IeA > P I K DA :_9D9 > 8 9 I U EZJ P 8#I A;8 U 8 AD:_9D9 > 8 9 > 9;: U d/J\G @ ? : U I A;:_G U 9 GeN K :_W: U d JS8 K_K 9 ? :_G @ IeA;8 P :"K 8#9 Q U 8 2G N ;A 78Z: @/] G P ADI U A P 8#b > : P 8 @ 8 U A 9NcG P ? :BG @ IeA;8 P :K AD9G2N A;7: E L0: U J K_> E 8#E&A;7"8 NcG K_K G : U d $c: & J 78 @ GI A;A P I2J A I U A 9C8#J P 8SA;:_G UF] P G `"K 8 9 E8SA;8 P @ : U 8 EZAD788 8 JSA;:_W28 U 8 9D9GeN JS8 KBK*@ G2A;: K :BAMLZI U EZJ\8 K_K A;G J\8 K_K
P d P G AD7 : U DA G A P I U 9C:_8 U JS8 : U
9C:_d U I K : U d $c:_: &
A >"U : U d/A;78 ] G P 8 9 > P NI2J\8 P 8 IJ AD:BW :BAML/A;G%I U d :BGd28 U _: JVNI2JSA;G P 9(G 8 P 8 EFI ] G 9;9;: ?K 8 @ 8 J 7I U : P I AD:BG U 9)GeNI U I U d2:_G2d28 U : JS8#E E 8 8 ] 8 P W I29DJ >K I P d P G AD7 : U A;G A;789DJ\I G K E 578 8\R ] 8 P : @ 8 U ADI K"] I P AgG2NA;7: J\8 W I29DJ >"K I P : U d P G A;7 = G @ 8 GeN A;7"8
7:_d27 K :_d27A P 8 9 >K AD9 G2N A;7: PDP 8 U A K L > 9;8 E : U J K_> E 8 I > A;Gd P I N AD9 I U E I K_K G2d P I N A 9 h 7: K 8 I > A;G K G2dG > 9 ? G U 8 9C8\AD9 AD78%d2G K E09CADI U EI P E NcG P J K : U :_J I K ? G U 8 P 8 ] Ie: P a : A 9I ]]"K :K E @ 8\8\A 9 > J 7 I29 ] P G W:]"] G P ANcG P AD78 JS8 K_K 9I U E/A;7"8 J 78 @ :_J I K I U E ? :_G K G2d:_J I K J > 8#9 NcG P
NcG P @ : U dQN >"U J AD:BG U I K DA :_9D9 > 8 9 = 8\W28 P I K ] G K L @ 8 P 9 9 > J 7 I 9 ] G K L $ K I2JSA;: 9 NI ? P : 9;8 G2N A;78 : P ? :BG JSG @/] I AD: ? : K : AML *I U E A;78 : P > 9;8SN >K P I U d8%GeN @ 8#J 7"I U :_J I K ] P G ] 8 P A;:_8 9!A;78#9C8 ] G K L @ 8 P 9 7"I W28 P 8 J\8\:_W28#E 9 >? 9CADI U AD:_I K IeACA;8 U A;:_G U NcG P 98 K 8SADI K P 8 ] I2: P I U E P 8\d28 U 8 P I AD:BG U = A > E :_8 9 7"I W28%9;7G U 7:_d27 I K I K : U 8 ] 7G9 ] 7"IeADI9C8 $ 4af"& I2JSA;:_W : AML I U E @ : U 8 P I K : [ 8 E 8SR A P IJS8 K_K_>K I P
h
@ I A P :BR E 8 ] G9C:BA;:_G U ? L G9CA;8\G ?K I29CA J\8 K_K 9 J >K A > P 8 E G U f a4 4 D9 J\I G K E9 U I2EE :BA;:_G U af !4 4 J I U ? P 8 I E G U ADG K I2JSA;: P I K_K L : U A;7 8 ? G E L : AD7,I SJ G U A P G KBK I ?K 8 E 8 d P I2EIeA;:_G U P IeA;8 ;A 7"IeA @ I A J 78 9 U 8 GeAD:_9D9 > 8QNcG P @ IeA;:_G U #i 4 U >@ ? 8 P G2N NI ? P :_J I AD:BG U @ 8\A;7G E9Q7"I W8 ? 8 8 U > 9;8 E A;GZJ\G U 9CA P > JSA O 9DJ\I G K E9 N P G @ E 8\d P IEI ?K 8 ] G K L @ 8 P : J 7 I29/9;I K A K 8 IJ 7: U d ] 7"I29;8Z: U W28 P 9;:BG U 9;G K W28 U A/J I29CA;: U d ] P G2A;G2AML ] : U d gI U E @ P 8 U J\: U/K I ? G P I ADG P L 7I29 > AD: K : [ 8 E/I 9;: U AD8 P : U d AD8 J 7 U : 8A;GE8\W28 K G ] O f a4 49DJ\I G K E"9 :BA;7 I ] G P G > 9 : U A;8 P JSG UU 8#J A;8#E 9CA P > JSA > P 8/NcG P ? G U 8/A;: 8%8 U d2: U 8\8 P : U d Z578#9C8 9DJ\I G K E9 7I W28 ? 8 8 U 9;7G U A;G 7"I W8 I J\G U A P G K_K I ?K 8 E 8\d P IEI AD:BG U P IeA;8FI U E @ 8#J 7"I U :_J I K(] P G ] 8 P AD:B8#9 :BA;7: U A;78 P I U d28 eG NV7 >@ I U L 7 >"@ I U ? G U 8 U IEE :BA;:_G U A;7"8 9;8 9DJ\I G K E"99 >]] G P AAD78 : U W : A P G d P G A;7 I U EF9 ] P 8 IE%GeN ] P : @ I P / 7: E :B8#9 9C7G (8 E A;7"IeA AD78/
f a4 4 9;: U A;8 P 8#E @
A P I ? 8 J >"K I P G9MAD8\G ?K I9MA 9
: JSA;:_W28 d P G A;7FNIJ A;G P 9QJ\I U 9C:_d U : ` J I U A K L 8 U "7 I U JS8 ? G U 8 78 I K : U d : U I J P :BA;: E :_8 9)ADG2d28\A;78 P : U E : J 7
I29 ] P G K :BNc8 P I A;:_G U @ :_d P I A;:_G U I U EZE : 8 P 8 U DA :_IeA;:_G U ! 8 K_K 9: U A;8 P IJ A; : AD7Zd P G AD7 NI2JSA;G P 9 > 9;: U d ;A 7"8\: P 9 > P NI2J\8 P 8 JS8 ] A;G P 9 578#9C8%: U A;8 P I2JSA;:_G U 9 : U :BA;:K I P ;9 :Bd U I K : U d ] I A;72 I L 9 A;7"IeA A P :Bdd28 P AD78 8\R ] P 8#9;9;:BG U G PP 8 ] P 8 9D9C:_G U GeN d8 U 8#9 I U E ] P GeAD8\: U 9 I U E P 8\d >K I A;8FJS8 KBK(? 8 7"I W :BG P 9 U E 8 9;:Bd U : U d AD:_9D9 > 8 8 U d2: U 8\8 P 8#E JSG U 9MA P > J AD9 )A P 8 @ 8 U E G > 9
8 G P AZ7I29Zd2G U 8 A;G,: U J\G P ] G P IeA;8 d P G AD7 NI2J ADG P 9 9;8 K 8 JSA;:_W28 K L ;A G ] P G @ GeA;8 ;A : 8 : U d P G AD7 U G U 8 I ]] P GIJ 7 9;L U AD78SAD:_J G P U I A > P I K] G K L @ 8 P 97"I W8 ? 8 8 U 8 @/]K G L28#EZA;G%8 U J\I ] 9 >K I AD8 I U E P 8 K 8 I29;8 d P G A;7ZNI2JSA;G P 9: U I 9 > 9CADI2: U 8#E I U E JSG U A P G KBK 8 EFNI9C7":BG U h2 i h h2h h 4 U G2A;78 P 9CA P I A;8 d2L ] P G @ GeAD8 9 AD78 IE9;G P ] A;:_G U G2N d P G A;7FNI2JSA;G P 9 G U A;7"8 9 > P NIJS8QGeN*: @ ]"K I U A 9g: U G P E8 P ADG 8 U "7 I U JS8QJ\8 K_K IeACA I2J 7 @ 8 U AI U E d P G A;7 h h h hj h HG P : U 9CADI U JS8 A;G7 8\A I K hj a9;7G (8 E A;7"IeA J\GIeA;: U d%I 7 L E P G R LI ] I A;:BA;8 9 > P NIJS8 : AD7 I O $ I P d2: U : U 8 d K L JS: U 8 I29 ] I P A;: DA d P G A;7 GeN U *8 ?K G G E 2W 8#9;9;8 K 9N P G @ 8SR :"K IeA > P 8 A : U J K_> E 8 9: U A;8 P @ 8 E:_IeA;8 9MAD8 ] 9 9 > J 7^I29(8 U EGeA;7"8 K :_I K J\8 K_K I2JSA;:_W IeA;:_G U : U P 8#9 ] G U C9 8QA;G%I U d2:_G2d28 U :K :
@ :Bd P IeA;:_G U I U E ] P G K : Nc8 P IeA;:_G U GeN 8 U E G2A;78 K : P IeA;:_G U h i 4 N A;8 P 9MAD: @ > K IeA;:_G U 28 U E G2A;78 K : :B8#9;J\8 U A 9MA I A;8 ADG^I U IJ AD:BW I AD8 E 9MA I AD8/I U E 8 U 7"I U SJ 8 @ I A P :BR @ 8SA I K_K G ] P G2A;8 : U I9C8 $ fg9 & ] P G E > J AD:BG U 57:] P 8\d >K I A;8#E I U E 8 U E G2A;78 K : :_8 9DJS8 U A 9CADI AD8 h
= G KB>?"K 8%d P G AD7 N I2JSA;G P 9 P 8\d >K IeA;8/JS8 KBK ] P G K :BNc8 P I AD:BG U @ B: d P IeA;:_G U !I U E JS8 KBK J\8 K_K : U AD8 P I2J AD:BG U 9 E > P : U d I U d:BGd28 U 8 9;:_9 8 W I9;J >K I P 8 U E G2;A 78 K :K I AD8 8 U E GeAD78 K :_I K JS8 K_K ] P G K : Nc8 P IeA;:_G U I U E @ :_d P I AD:BG U )f O H :_9 9;7G U DA G : U> 8 U J\8 U 8* K L NcG P @ 8 E W28 9D9;8 K @ I A > P IeA;:_G U ? L P 8 J P > :BA;: U d ] 8 P :_J\LAD8 9 5 H :_9 I @ >K A;:BN >U J AD:BG U I K d P G A;7 NI2JSA;G P AD7"I A: J\8 E ? L W I P :B8\AML GeN JS8 KBK AML ] 8#9 9 > J 7FI9 `"? P G ?K I29CAD9I U EF8 U E G2A;78 K : 9J\I ] 9 >"K 8 J 7"I P I2JSA;8 P : J AC # G (8\W8 P A;7: I K_K L K : @ :BA;8#E/A;G I E 8 ] AD7 GeN*9;8\W8 P I K 7 >U E P 8#E @ P NI2JS8G2NAD78 : @ ]"K I U A 9 h U IEE :BA;:_G U W28#9;9;8 K : U `"K A P I AD:BG U NcG P K I P d28 P 9DJ\I G K E9 G J J > P 9)G W28 P K G U d28 P A;: @ 8 N P I @ #8 9 7: I AD8 ] 8 P N > 9C:_G U : U A;78 A;: @ 8 N P I @ 8 JSG U 9C: 8 d P G A;7 578 P 8\NcG P 8 ;A 78 P 8 7"I29 ? 8 8 U I%A P 8 @ 8 U E G > 9V8* G P A : U E 8 9;:Bd U GeN(9MA P IeA;8\d:B8#9 ADG ] P G @ GeAD8 I U d2:_G2d28 U 8 9;: E : U d%$: & I U d2:_G2d28 U : 9MA Ie: U 8 E I U E JSG U A P G KBK 8 EFNI9C7:_G U Q U 8 I ]] P GI2J 7 : U E 8 W28 K G "] @ 8 U AQGeNgE8 K :BW8 P LZW8\7: A;: K : [ : U d 9;L U A;78\A;: P I K] G K L @ 8 P 9 hei i
?
4 U eG A;7"8 P 9CA P I AD8\dL :_9V8 @/]K G L : U d/W8\7: J 7 I 9 W : P > ;9 8 9 G P d28 U 8SAD:_J I K_K LZ8 U d: U 8 8 P 8 EFJS8 KBK 9 AD7"I AQJ I U^? 8 E : J 7/JSG @ ]"K 8\R ? :_G K G2d2:"U E 78 I K : U d !8 @ ? P LG2d8 U 8#9C: K I AD: U d AD7"I AVJ\8 K_K 9 @ eG A;: K : AML& 578#9C8/E L U I @ :"U EI @ 8 U A I K_K L ? I29;8 E G U JS8 KBK JS8 K_K I U E JS8 K_K X : U AD8 P I2J AD:BG U 9 U A;8 U ;9 8 P 8 9;8 I P J 7
8 G P AD97"I W28 ? 8\d > U A;G 8 KB> JS:K AD: U d N P G @ A;7: : P 8#9 I N >U E"I @ 8 U ADI K >U E 8 P 9CADI U E : U d0GeNQI U 2d :_G2d8 U 8#9C: JSAD9 I2: U : U d A;7:"U E 8 P 9CADI U E : U dN P G @ 8SR ] 8 P : @ 8 U ADIeA;:_G U I K G U 8 :@ 8 U ADI K A I29 P 8 b > : P : U d DA 78Q8\R ] K G P IeA;:_G U G2N!I K I P d28 ] I P I @ S8 AD8 P 9 ] IJS8 4 U d2:_G2d8 U #8 9C:U A GeN : U NcG P @ I AD:BG U A;"7 IeA J I U&? 8 :U E : U d 8* 8#J AD9 U I2EE :BA;:_G U : U AD78 NI JS8ZGeN A;"7 8 W I P :B8\AML G2N @ IeA;8 P : P : U d ] P G2A;G JSG K ] P _: G P A;G :BAD9 NI ? P : I AD:BG U G E 8 K : U d I BK K G 9 NcG P 8\R ]K G P : U d,W I P : J 7 @ G E 8 K 9(I P 8 ? I9C8#E/G U AD78QG ? 9;8 P W IeA;:_G U
A;7I A: U AD78/I ? 9;8 U J\8 G2N 8SR A;8 P U I K J 7"8 @ :_J I K 9C:_d U I K 9 JS8 KBK 9 7 :_J 7 J\I U @;J P I K B/G U 9 >? 9MA P IeA;8 9 E GF9CGZ: U I @ G P 8 G P K 8 9D9 P I U E G @ @ I U"U 8 P O : 8 P 8 U A @ I AD78 @ I AD:_J I K @ G E 8 K 9 : U JSG P ] G P I A;8/J 78 @ G2ADIeR :>@ @ G E8 K 9 )I U E($:B:_: & E :] :_8 E !G P :BA;7 I JSG @/]> ADIeA;:_G U I K JS8 KBK U 8 I2J 7&9;: @ >K I A;:_G U0] I9;9G P AD: @ 8 9CA;8 ] !8#I2J 70G \J J >"] :B8#E&JS8 KBK 9;8 E (4 : U JSG U >U J AD:BG U :BA;7 9;: @/]K 8 A P I U 9 ] G P A @ G E 8 K 9 ADG ] P G ? 8 A;78 8 8 J A 9QJ\8 K_K A;G J\8 K_K 9;:Bd U I K : U d%: U AD78 E 8 W28 K G ]@ 8 U A GeN @ :K I P 9CA P > J A > P 8#9
EC U JSG U AD: U >>@ @ G E 8 K 9 A;7"8FG ? 9;8 P W I ?K 8 9
IPZ 8 JS8 KBK E8 U 9;: AML I U E I U d2:_G2d8 U : G > 9 W I P :_I ?K 8 9(A;7I A 8\WG K W28 I2J JSG P E : U d ;A G I%9;8SA G2N P 8 IJ AD:BG U E: > 9;:BG U #8 b > I A;:_G U 9 gH"G P 8\R I @/]K 8 : U A;78 ] G "] >K IeA;:_G U "> R @ G E 8 K GeN 5 8 K_K 8 P I U E = 8 d28 K JS8 KBK E 8 U 9;: AML%: G > 9W I P :_I ?K 8QG ? 8\L : U d IA P I U 9 ] G P A8 b > IeA;:_G U I U E A;7"8 P I A;8%G2NVJS8 KBK E :_9 ] 8 P 9C:_G U N P G @ 9CG @ 8 : U : AD:_I K JSG U JS8 U A P I A;:_G U0] P G `K 8 : 9 ADG
j
E : > 9C:_W : AML/I U E/E P :BN Ag: U%@ G K 8#J >K I P 9;L 9MAD8 @ 9 j = 8\W8 P I K GeAD78 P @ G E 8 K 9 ? I29;8 E G U AD785 8 K_K 8 P = 8 d28 K I ]] P GIJ 7 (8 P 8 E 8 W28 K G ] 8 E
gj i j 2j h j gj j : U J\G P ] G P IeA;: U d ? : 9d28 G @ S8 A P L > 9CAQI29(AD78\LF8 8 JSA;:_W28 K LFI W28 P Ied8QG > VA E 8\ADIe: K 9 eG N)A;7"8 P I U E G @ (I K 9(AD7"I AVd:BW8 P : J 7 I J I29;8 G U 8 : @ 2I d2: U 8 9 IFSJ G U AD: U > G > 9 @ G E 8 K : U 7:_J 7 A;78 A P I U 9 ] G P A ] I P I @ 8\A;8 P 9 $8 d "JS8 KBK E : > 9;:BW :BA;:_8 9 & I P 8 P 8 U G P @ I K : [ 8 E ;A G P 8 8 J A AD78 : U"> 8 U SJ 8G2N)A;78 ] G P G > V9 E G @ eI : U - 7": K 8 ;A 7"8 I2JSA > I K E G @ I2: U G U 7: A;:_G U :_9 G ? A Ie: U 8 EZ:_9 >"U : NcG P @
G U AD: U > G > 9 @ G E8 K 9 7G (8\W28 P I P 8 K : @ :BA;8#E^: U A;7"IeA A;78 : U> 8 U J\8GeN E G @ eI : U U G U >U :BcN G P @ : AMLZG U 9 @ I KBK!K 8 U deDA 7
9DJ\I K 8 9Q:]] G9;8 E U I2EE :BA;:_G U AD78\L I P 8 : U I ]] P G ] P : U E8 P 9MA I U E^AD78 @ G P ] 7 G K G2dL GeN JS8 K_K@ :Bd P IeA;:_G U ] IeA;7"9 4V9/I U 8SRI @ ]"K 8 ;A 78 L&7"I W28 U GeA ? 8\8 U I ?K 8ZA;G S8 R ]K Ie: U 2I E8 b > I AD8 K L A;78FG W28 P I BK K E 8 U E 8 P :BA;:>@ @ G E 8 K 9NIe: K A;G : U JSG P ] G P I A;8 ] P G ] 8 P K L A;7"8
JSG U A P : ?> A;:_G U GeN): U E:BW : I K J\8 K_K J 7"I P IJ A;8 P : IeA;:_G U 9 GeN @ GeA;:_G U : U J K_> E 8FA;8 P @ 9 A;7I A JSG >] K 8ZAD78 (I K
W28 K G J\: AML : AD7 K G J\I K d P I2E:B8 U A 9): U J 7"8 @ GIeACA P I2JSADI U A J\G U J\8 U A P I AD:BG U ! 4 9;:_d U : ` J\I U AgI2E W I U JS8 : U E :_9DJ P 8SAD8 @ G E 8 K : U d GeN
I U 2d :_G2d28 U 8 9;: 8 U?"> P d8 P 7G E 8#9;J P : ? 8#EAD78 d P G A;7 eG N @ :_J P G W8 9D9C8 K 8#9!I9I U : U AD8 P ]K I L%GeN P I U E G @ @ eG AD:BG U G2N!: U E :_W : I K JS8 KBK 9 I U E ;A 7"8 E: P 8 JSA;:_G U I K ? :_I9G2N @ G W28 @ 8 U AE > 8 A;% G J 78 @ G2ADI R : A DA : ] 9VI29/ 8 KBK I9A;7"8 K : U 8 E 8 U 9;: AMLFGeN J\8 K_K 9 : U I K_K 9 ] P G > A 9 I K_K G : U d NcG P $: & ? : 8 U JS8#E ? L AD78 J\8 K_K 9 /.(8 J\I > 9;8 GeN A;7":_9QI29D9 >@/] AD:BG U A;7: P 8 DA 78 8\R ] 8 P : E @ ? P > 9;7 ? G P E 8 P B *8 8#J A : U 7: 9C:_G U > K AD: @ IeA;8 K L P 8SA I P E : U d A;7"8 ] P G J\8 9D9G2N)I U d2:_G2d8 U 8#9C:"@ ] ;A :_G U G U 9;8 b > 8 U A K L : U J\G P ] G P IeA;: U d d P G AD70NI2J ADG P E : > ;9 :_G U "7 G @ G2d8 U 8 G > 9 E 8\d P IEI AD:BG U I U E >"] ADI 28 ? L JS8 KBK 9aAD78\L 8 P 8 I ?K 8%A;G IEE P 8 9D9 A;78 P G K 8%G2Nd P G AD7 N IJ ADG P E L U I @ :_J 9G U d P G AD7 G2N(W I9;J >K I P U 8\A G P 9 T C9 : U d A;7":_9 @ G E 8 K 5!G U d%I U E + > I U 9 > J JS8 9D9CN >KBK L J\I ] A > P 8#E I U E \8 R ]"K I2: U 8#E AD78 ? P > 9C7 ? G P E 8 P 8 8 JSA : U I&;@ J\G P U 8 I ] G J 28\A I29D9DI L B @ G E8 K : U d 9;: @ >K I AD8 EFI U d:BGd28 U 8 9;:_9
?
578 J\8 U A P I K d2GI K GeN(A;7":_9 ] P G ] G 9;8 E C9 A > E L :_9 AD7"I A AD7 P G > d270I^J K G9;8%JSG G ] 8 P I AD:BG U ? 8SA (8\8 U S8 R ] 8 P : @ 8 U A I AD:BG U I U E 9;: @ >K IeA;:_G U " (8FdIe: U I ? 8SA;A;8 P > U E 8 P 9CADI U E : U d0GeNVAD78 P 8 K 8\W I U A >U E 8 P K L : U d @ 8#J 7"I U : 9!9DJ\I G K E"9 5aG I2J 7:_8\W8gAD7:K I P : U W I9C:_G U : U ADG 9;J I G K E9*9 > J 7 I29 *9;J I G K E9 @ :_J P G9MA P > J A > P 8
A;7"8A P I U 9 ] G P A)GeN 9C:_d U I K : U d @ G K 8 J >K 8#9 eJ\8 K_K@ GeAD: K : AML I U E JS8 KBK P 8 9 ] G U 9;8gADG 9;:_d U I K : U d @ G K 8#J >K 8 9 U/] I P I KBK 8 K e9;8\W28 P I K 9CA P I A;8 d2:_8 9A;G 8 U 7"I U JS8ZW I9;J >K I P : U d P G A;7 9 > J 7 I9 I U d2:_G2d8 U :U E 8 P 9CADI U E : U dFeG N DA 7:_9 9;:Bd U I K : U d ] P G JS8#9;9 J\I U ? 8 G ? ADI2: U 8#E ? L > AD: K : [ : U d I >U : 8 @ I AD78 @ I AD:_J I K @ G E 8 K A;7"IeA J\I U : U A;8 d P I A;8 AD78 ? :_G J 78 @ : IeA;:_G U GeN I U d2:_G2d28 U 8 9;: : P 8#9I b > I U AD: A I A;:_W28 "> U E 8 P 9CADI U E : U d GeN A;7"8 9C8 U 9C:BA;:_W : AML GeN 8 U E G2A;78 K : AD:BG U 2G N d P G AD7NI2JSA;G P JSG U JS8 U A P I A;:_G U : AD7: U AD78 ] G P G > 9QJ\G U 9CA P > JSA 8/7 L ] GeAD78 9;: [ 8 A;7"IeA E:_9DJ P 8SAD8 9;: @ >K I A;:_G U GeN(8 U E G2A;78 K : 9)9DJ\I G K E9)J\I U @ I 2 8IQ9;:Bd U : ` J\I U A ] P G2d P 8#9;9*A;G I P E AD7:_9 >"U E 8 P 9CADI U E : U d 6 7I ] AD8 P e I U E E:_9 > 9D9 IVd8 U 8 P : # L ] GeAD78 9;:_9 = : U JS8^8 U EGeA;7"8 K :_I K JS8 K_K 9 ]K I L I 2 8 L P G K 8F: U I U d2:_G2d8 U 8#9C: P 8 & 2 A;78 ]> P ] G9C8 G2NA;7: E L/:_9 A;G 8\RI @ : U 8 7 >"@ I U 8 U E GeAD78 K :_I K J\8 K_K N >U JSA;:_G U G U f !4 4
9;: U A;8 P 8#E @ : !
L ] GeAD78 9;:_9 8 7 L ] 2G A;78#9C: [ 8 ;A 7"IeA ;A 78 P 8 K 8#I29;8FG2NI U d:BGd28 U :_JFd P G A;7 NIJ A;G P 9 I A I U G ] ;A : @ : [ 8 E K 8\W8 K N P G @ I JSG @/] G9C:BA;8^9CL 9CA;8 @ eG N 2d 8 U 8SA;: 8 U J\8 W I29DJ >K I P d P G AD7Z: U A;G%9C: U A;8 P 8#E @ : J 7%I29 J\LADG eJ 78 @ G : U 8 9 AD7"I AE: > ;9 8
A;7 P G > d27 AD78g: U A;8 P JS8 KBK_>K I P @ 8#E : >"@ e IeN A;8 P 7 : U E9 ? L J\8 P ADIe: U JS8 K_K 9J I U ? 8AD: @ 8 W I P L : U d j 4 ] I P AD:_J >K I P K L : U A;8 P 8#9MAD: U d/8\R I @/]K 8 :"U :_J I AD:BG U : U d K : 92B GeN (I 2i 57"8 U >@ 8 P G > 9 AML ] 8 9 GeN 9;:Bd U I K : U d JSG @ ] G >"U E9 C9 8#J P 8SA;:_G U P I AD8 ] P G `"K 8 9 I U E : K_K :K AADG I U 9 (8 P 8\R ] 8 P : @ 8 U ADI K_K L B: A;7 A;7: U E 8 P 9MA I U E ;A 78 8 8 JSAD9G2N!IAD: @ 8 W I P L : U d 9;8 J P 8SAD:BG U ] P G `"K 8 G U AD78 E 8 `"U 8 EZ8= J\IJSL B: A;7: 7":_J 7 A;78 JS8 KBK @ I L ? 8 8SR ] 8#J AD8 EZA;G ] P G ] I2dIeA;8 I @D9C:_d U I K B
1
f P 8\W :_G > 9 P 8 9;8 I P J 78 P 9V7"I W28 JSG U 9C: 9 C9 8#J P 8SAD8 9 I d28 U 8 P :"? 9MA I U J\8 E : > 9;8 9 I I L : U ADG I 7G @ G d28 U 8\G > 9 @ 8 E : >@ g 578 dG W28 P U : U dA P I U 9 ] G P A 8 b > IeA;:_G U NcG P AD78JSG U JS8 U A P IeA;:_G U GeNA;7:? 9CADI U JS8 $ & : 3 8 8 8 8
$ &
h
78 P 8 3 :_9QAD78%E : > 9;:BG U J\G 8= JS:_8 U A 578 J\G U E: AD:BG U 9 GeNgAD78%9CG KB> A;:_G U I P 8 $ Di'& i $% ' & i *I U E A;7"8 "> RFJ\G U E: AD:BG U IeA A;78J\8 K_K 9 > P NI2J\8 :_9
78 P 8
3$# &Q:_9
3 88 $ &
$ h'&
I ] P 8#9;J P : ? 8 E AD: @ 8 E 8 ] 8 U E 8 U A " > R $ @ G K 8 J >K 8 9 I P 8 I AD: @ 8 & 578%9CG KB> A;:_G U : : K : ? P : >@ ? : U E: U d JSG U 9MA I U A NcG P A;78 9;:_d U I K*@ G K 8 J >"K 8#9 ] P 8 E :U : : K : ? P : >@ ? : U E : U d,JSG U 9CADI U A 9 AD78 AD: @ 8 9DJ\I K 8#9 J 7"I P IJ A;8 P : [ : U d0AD78 ] 8 P :BG E :U E L 2+ G9C7":_EI 8SA I K > 9;8 E A;7:U : J\IeA;:_G U E : P : U d A;78 ]>K 9C8FI U E AD7 8 U @;9 : A J 78 9 G B )VGeAD8 A;7I AAD78 +* ,* (- . : U ]>"K 9;8 9;8 J P 8SAD:BG U P IeA;8 JSG U 9;:_E 8 P 8#E : U AD78 + G9;7: E L 2I 9 AD78Z9DI @ 8/NcG P I K_Kg]>K 9;8 E > P I AD:BG U 9 J\G U 9;:_E8 P 8 E)578 ] I P AD:_J >K I P 9;G _K > A;:_G U 2G N + G9;7:_E"I _: 9gG ? A Ie: U 8 E/: U A;8 P @ 9gGeN*E : @ 8 U 9;:BG UK 8#9;9JSG U JS8 U A P IeA;:_G U $ -& $ & "E: @ 8 U 9C:_G UK 8 9D9 E :U : JS8 - 9C:_d U I K : U d J\G @/] G >U E9 I P 8 @ G P 8 8* 8#J AD:BW8/IeA JSG @ @ >U : J\8 - 8 9CA;:_G U 9 $ I'& (I U I JS8 KBK JSG @/@ >U : A;: U d : A 9 ] P G E > J A;:_G U : U ADG P 8 K I A;:_W28 K L
9;7G P ;A 8 P @ G P 8 : U A;8 U 9C8 ]">K 9;8 9Q9C8 ] I P I AD8 E ? L K G U d%: U A;8 P W I K 9 G2N P 8#9MA $ ? & # G 6E G 8 9AD78 8* 8#J AD:BW8 SJ G @ @ >U :"] G U 9 > J 7 I ]>K 9C8#EZ9;8 J P 8\A;:_G U P eI A;8 ] P GeADG J\G K 8 @ G E : ` 8 E A;78 9;: U d K 8 JS8 K_K @ G E8 K E 8 W28 K G ] 8 E ? L+ G9;7:_E"IV8\A I K 6 P 8\:BA;8 P I AD8 E 7"8 P 8: U X b !H: P 9CA (8I29 9 >@ 8(I ] 8 P :_G E K 8 U deAD7 G2N ii2i $ 2 i2iQ9 &aI U E I ? I9C8 K : U 8(9C8#J P 8SA;:_G U> RGeN #ih$
i @ G K 8 J >K 8 J @ 9 &
578 U cN G P 8#I2J 76GeN%AD78 W I P :_G > 9 ]>K 9;8 K 8 U d2A;7"9 h j i i 2i ;A 78 : U ]">K 9;8,9;8 J P 8\A;:_G U "> R
" V:_9 > 9C8#E ;A G G ? A Ie: U A;78 C9 G KB> AD:BG U $ ? -&%N P G @ 8 b $ 2& 7: K 8 @ Ie: U A Ie: U : U d i $ U A;"7 8
G P :_d2: U I K 9CA > E L/GeN + G9;7:@ 8 E SJ G U 9MA I U Ag: P;P 8 9 ] 8#J AD:BW8 eG N & 578 P 8 E > JS8 E/8* 8#J AD:BW8 JSG @/@ > U : 8 GeN $ - &(:K 8 "I U E : d27 2AD78 U AD7 P G > d7 I @ I R : @ >@ 2AD78 U ? I2J /E G U A;7 P G > d27 = AD: ]">K IeA;: U d AD7"I A AD7:_9 @ I R : @ >@ : I P I U AD8\8 9 A;7"IeAVA;7"8 J\G U J\8 U A P I AD:BG U I AVAD7"I A E : 8 9 G2N NcG P 7:"K 8E :"@ 8 P : 8 9 NcG P E : 8 P 8 U A/9C8#J P 8SA;:_G U AD: @ 8 9 I P 8 ] P 8 9;8 U AD8 E : U !5 I ?K 8 H P G @ G > P P 8 9 >K A 9 (8 9;8\8 A;"7 IeA *8 8#J A;:_W28 JSG @ @ >U :K 8 J\G U J\8 U A P I AD:BG U ] P G `"K 8 9 NcG P AD78 \J G U 9;:_E8 P 8 E 9;8 J P 8SAD:BG U A;: @ 8 9 )4Q 9 (8 7"I W8 A;7"8Q9DI @ 8 A;G2ADI K I @ G >U AgGeNa9;:_d U I K"] P G E > JS8#E/G W28 P A;78QG U 8 E > AML/JSL J K 8 NcG P #8 I2J 7 ]>K 9;8
A;: @ 8 DA 78 I P 8 I9 >"U E 8 P AD78JSG U JS8 U A P I A;:_G U ] P G `"K 8 J > P W28 9I P 8 8 b > I K NcG P E : 8 P 8 U A 9;8 J P 8\A;:_G U A;: @ 8#9 I299C7"G U NcG P 2i/: U H!:_d '$ ? & # G (8\W8 P A;78 J\G U J\8 U A P I AD:BG UZ] P G `"K 8#9NcG P 9C7G P AD8 P 9;8 J P 8\A;:_G U A;: @ 8 9 7I W28 K I P d8 P ?> AQ9C7I P ] 8 P @ I R : @ I 7:"U :_J I AD:BG U E :
R ? G >U EI P LZJSG U E : AD:BG U
3 > $ &
$ &
78 P 8:U A(G2Na9C:_d U I K] P G E > J\8 E ] 8 P >U : A 9 > P NIJS8 I P 8 I G2N*A;78 SJ 8 KBK U GeAD8VAD7"I A$ & C )57"8 U G U E : @ 8 U 9;:BG U I K : [ 8 EF9CG KB> A;:_G U GeN X b 9 >? M8#J AD8 EZA;G I/E 8 K A I N >"U J AD:BG U9> R ? G >U EI P L SJ G U E :BA;:_G U :_9VI29(NcG K_K G 9
$ -&
$ &
$
F8\R ] $ &M8 P NJ h $ $
8SR ]
78 P 8
2
$ j &
I U E A;7"8 P 8#E > JS8#E \J G U J\8 U A P I AD:BG U $ -& E : IeA;:_G U DA 7"I AA;78VA;78 G P 8SA;:K 9;8%AD: @ 8ZI ? G W84 7_: J 70AD78 J\G U J\8 U A P I AD:BG U ] 8 I U 8 W28 PP 8#I2J 78#9 A;7"8 J P :BA;: A2BFIFJS8 K_K \J I U @ I 8 B: AD9 ]>K 9;8 GeN9;:_d U I K 9C8#J P 8SA;:_G U A;G @ Ie: U ADI2: U A;78I ? : K :BAML%A;G J\G @/@ >"U :_J I AD8 G W8 P K I P d28 E :_9CADI U JS8#9 U A;8 P 8#9MAD: U d K L g: U A;78 J I29;8FG2N >"U : NcG P @ ] P G E > J A;:_G U gAD78 8 8 JSA;:_W28 JSG @/@ >U :U :_J I A;:_G U E :U :BNcG P @ 9;8 J P 8\A;:_G U I29 I ? I9C8 K : U 8 ' 8 9;8\8(A;7I AI JS8 KBK J\I U : U J P 8 I9C8(A;7":_9 E:_9CADI U JS8 ? L I KB@ G9CA I NI2JSA;G P G2N h ? L ]>"K 9;: U d A;7"8 ] P G E > J AD:BG U G P 8\G W28 P :BAI ]] 8#I P 9): @/] G9D9C: ?K 8 A;G : U J P 8#I29;8A;7:K 9C8#E 9;8 J P 8\A;:_G U ] P G2A;G JSG K NIJS: K :BADIeA;8 9 9;:_d U I K A P I U 9 @ :K 9;8 ] 8 P :_G E"9 K 8 IE ADG K I P d28 P 8* 8#J A;:_W28/JSG @/@ >U :K E ? 8 ADI 8 U : U A;G IJ\JSG >U A : U @ G E 8 K 9VGeNgJ 78 @ GeADIeR :_9 578 ] P 8 9;8 U AQ9CA > ELF8\R ]K I2: U 9 7G
A;7"8 9;8 : @/] G P ADI U A b > I U AD: AD:B8#9 E 8 ] 8 U E >] G U I%9;: @/]K 8 J 7G2: IeA;:_G U 7":_J 7: P;P 8 U A K L I29 ? :_I9C8#E P I U E G @ I K 9 7: 8 U JS8 & AD7:_9(JSG U JS8 U A P I A;:_G U/` 8 K E I P 8 8SR 8#J > AD8 E QU 8 @ I L : U Nc8 P N P G @ AD7:_9! (G P AD7"I AJSG U JS8 U A P I AD:BG U ` 8 K E9 7 : P 8VI A K 8#I29CA(9;G @ 8 : @ ] G P ADI U A(I29 ] 8 J A 9gG2N ] P G J\8 9D9C8#9 d2G W8 P U 8 E ? L%J 78 @ G2ADI2JSA;: d27%: U A;8 P 8 9CA;: U d 2:BA:U J K 8 I P N P G @ AD7:U E ? L 8 @ ]"K G L : U d
I P I U E G @ AD: @ 8 W I P L : U d ;9 8 J P 8\A;:_G UF] P G2A;G JSG K 57:K I A;:_G U0] P GeADG JSG K 9
U = 8 J (8 E :_9DJ > 9;9 P 8 9 >K AD9 : U :BA;: 9D9;:BG U G2NJ 7G G9C: U dFA;78ZI ]] P G ] P :U EI P L JSG U E :BA;:_G U 9 H: U I KBK L (89 >@/@ I P : [ 8QA;7"8 @ I2: U I9 ] 8 JSAD9GeNA;7":_9 J 7I ] AD8 P : U = 8#J
1
Q> P @ G E8 K : U J K_> E 8 9"$ a& I N >K_K L AD: @ 8 P 8 9;G K W28 E `"U :BA;8E : 8 P 8 U JS89;G K_> AD:BG U
7:K ADI U 8\G > 9 K L 8\WG K W : U d J\G U J\8 U A P I AD:BG U ` 8 K E0G2NJ 78 @ GI A;A P I2JSADI U A 578 @ G E8 K J\G U 9;:U E"I @ 8 U ADI K 8 W28 U A 9 $: & P 8 K 8#I29;8 G2N % I J 78 @ GIeACA P IJ ADI U AN P G @ C9 G > P JS8 9G P JS8 KBK 9 $c:_: & E : > 9;:BG U GeN J 78 @ GI A;A P I2J A I U A : U AD78E G @ I2: U $c:_:B: & P I U E G @ U 8 9D9: U ;A 78E: P 8 JSA;:_G U GeN SJ 8 K_K*@ :_d P I A;:_G U ] P 8#9 >@ I ?K LZE > 8 ;A G/G2A;78 P >U E 8 P K L : U d/W I P : I ?"K 8#9 I ? G > A 7:_J 7 (8 E G U GeAV7"I W8 8 U G > d27^: U NcG P @ I AD:BG U $:B-W & J 7"8 @ GeA I2J AD:_J P 8 9 ] G U 9;8 GeN JS8 KBK 9 8 J\G U 9;:_E8 P A (G J\I9C89CA > E :B8#9A;G%: K_KB> 9CA P I AD8 7G A;G b > I U AD: NcL A;78 : @/] G P ADI U SJ 8 GeNA P I U 9C:_8 U \J 8 $ &I%9CADIeA;:_G U I P L ] 2G : U AQ9;G > P JS8 7: J\8 J 78 @ GI A;A P I2J A I U A JSG U AD: U > G > 9 K L G P P I U E G @ K L : U G P E 8 P ADG : U W8 9CA;:_dI AD8 K : @ :BA;: U d 9;:BA > IeA;:_G U 9 : U J 78 @ GI A;A P I2J A I U A JSG U JS8 U A P IeA;:_G U : U"> 8 U J\8 9 J\8 K_K@ 2G A;: K :BAML
1 6
7: I U A;:BAML-& 5 78 d2G W28 P U : U d A P I U 9 ] G P A #8 b > I AD:BG U 3 $ & $ & $ & 78 P 8 3 : 9;:_W:BAML^GeNgJ 78 @ GI A;A P I2JSADI U AQI U E :_9VA;78 K G J I AD:BG U GeN AD78 A;7 ] G2: U A 9;G > P JS8 Vf)G2: U A 9;G > P JS8#9 ] P G E > JS8IeAQI P I A;8 $# & :"@ 8 G2N I%JS8 K_K 9;G
P 8 ] P 8 9;8 U AD9(AD78 P I AD8I A/ 7: JS8#EFIeA I U L ] G2: U AV9;G > P J\8 ] G9;: AD:BG U $ &:_9 A;78 O : P I2J E 8 K A I N >U J AD:BG U
$ & i
:BN i :BN i
$ h'&
HG P C9 : @/]K :_J\: AML I A%A;7":_9 9CADI2d28^GeN @ G E 8 K E 8\W8 K G ]@ 8 U A (J\8 K_K E :_W:"] ADI 28 I U E,E 8 d P I2EIeA;:_G U GeN J 78 @ :@ 8 P :_J I K W I K_> 8 9G2N!AD78 P 8 K I A;:_W28 b > I U AD: AD:B8#9: U ;A 7":_9 @ G E 8 K I ]] 8 I P : U 4 ]"] 8 U E :BR^4 X b :_9 9CG K W8 E U >@ 8 P : 9;: U d^I `"U : AD8 E : 8 P 8 U JS8/A;8#J 7 U : 8 P 8\Nc8 PDP 8#E ADG^I9 A;78 ;@ 7G ] 9;J\GeADJ 7 @ 8SA;7"G E B
j 578/h O 7"G @ G2d8 U 8 G > 9 9;G K_> AD:BG U E G @ I2: U @ 8#I29 > P 8#9Qh @ @
h @ @ * I9V9;7G U : U H:Bd E :U 9 SJ G U ;9 :_E 8 P 8#E 78 P 8 *I [ 8 P G JSG U JS8 U A P I A;:_G U O : P : U EI P L JSG U E :BA;:_G U _: 9I ]"]K :_8 EZI K G U d I J\: P J K 8QG2N P I2E : > 9 ! / @ @ \J 8 U A;8 P 8#E%G U A;78 G P :Bd: U ;$ 8 E : 9Dg9 AD78 P I @ : ` J I A;:_G U 9 GeNA;7":_9 J 7G:_J\8 NcG P ! : U = 8 J & 578 7"G ] 9DJSG2ADJ 7 A;8#J 7 U : 8 I29 ] P 8 W:_G > 9 K L,9;7G U A;G ? 8 I0NI29CAZI U E 2I J J > P I AD8 (I L A;G,9;: @ > K I AD8 A P I U 9;:_8 U A E : > 9C:_G U 8 b > I AD:BG U 9!: U h O I U E O E G @ Ie: U 9 !57: ADIeA;:_G U 9 @ I 28#9 AD7: 8QN I29CA: U J\G @/] I P : J 7
I29 J K I9;9;: 9;:BG U 8 b > IeA;:_G U : U I >"U : NcG P @ h O E G @ Ie: U A (I9 U G2A J K 8#I P N P G @ AD78\: P G P 7G (8\W28 P 7G 6G U 8 J 7G G9C8#9 A;7"8 `"U : AD8 AD: @ 8/9MAD8 ] E 8 U GeAD8 E : U AD7:_9 G P I 9(* /,0 1 / : U/K :Bd7A G2N P 8 b > : P 8 @ 8 U AD9NcG P I2J\J > P I2JSLI U E/9 ] 8\8#E cN G P I d2:_W28 U ] P G ?K 8 @ ;9 : [ 8 )57:_9 : P I ]"] K : E $ $ & 8
$ &
J\I U : U d8 U 8 P I K? 8I U L K : U 8#I P 8 KBK : ] A;: P JS8 9 : U M8 JSA;: U d @ 2I 9D9 : U ADGZAD78 ;9 L 9CA;8 @ /5: @ 8%:_9 E:_9DJ P 8SAD: [ 8 E : U A;G 9 K : I P 8 d P :"U J AD:BG U B : I AD:BG UZ>"] EIeA;8#9 I/JS8 K_K*] G9;: AD:BG UZ? I29;8 EZG U : A 9 J > DP P 8 U A ] G9C:BA;:_G U $# (* /,+ & $ & - (* /,+
$ &
#
8 P 8 - :@ JS8 KBK W28 K G J\: AML I U E :@/] : U d A;Gd28SAD78 P GeNaI KBK >U E 8 P K L : U d ] P G JS8 9D9;8 9 dG W28 P U : U dJS8 KBK @ :Bd P IeA;:_G U NcG P 7: P ] G9;8 K L _: d U G P 8QNcG P ;9 : @ ]"K : ]K 8 E ADG ;A 78 A P I U 9 ] G P AG2NJ 7"8 @ GIeACA P I2JSADI U A ? 8 J I > 9;8 I K G J I K JSG U JS8 U A P IeA;:_G U d P I2E :_8 U A .(8 J I > 9;8 JS8 KBK ] G9;: AD:BG U 9gI P 8 G K IeACAD:_J\8 IJS8 KBK I AI U I P ? :BA P I
JS8 KBK@ > C9 A @ @ #8 I29 > P 8 BFI P L K G J I AD:BG U : U h O 9 ] I2J\8
? L K : U 8#I P : U AD8 P ] G K IeA;:_G U I @ G U d A;78 cN G > P U G E 8 9 U #8 I P 8 9CA(:BA 4(A 8 IJ 7ZJ\8 K_K] G9C:BA;:_G UZ>] E"I A;8 A;7"8 : U 9MA I U A W I K_> 8 9G2NI W8 P Ied28 I U E I P 8 > 9;8 EF: U DA 78E 8\;A 8 P @ : U I A;:_G U eG N 9DI @/]K 8 9EQI U E
4 U : @/] G P A I U AJSG @/] G U 8 U A 2G NAD78 @ G E 8 K :K I AD8 E J 7"8 @ GIeACA P I2J ADI U A d P I2E :_8 U A #i2i g578 P 8\NcG P 8 (8 ] P 8 9DJ P : ? 8 A;7"IeA A;78J\G 8= JS:_8 U A I K ;9 G/9;8 P W28 I29VI 9 :BADJ 7^G U A;7"8 J 78 @ G2ADI2JSA;: 8 G2N > 9C8#E A;G E 8\A;8 P @ : U 8 AD78%E : P 8#J A;:_G U GeNg:BAD9 U 8\RA%9CA;8 ] : E L0I P 8 C9 7G U : U 4 ]] 8 U E : R&4 578 9;8 W I K_> 8#9I P 8 8\:BA;7"8 P ? G PDP G (8 E N P G @ ] P 8\W :BG > 9 9CA > E :_ 8 9G P S8 R A P I2JSA;8#E N P G @ I W I2: K I ?K 8 8SR ] 8 P : @ 8 U A I K EIeADI
h
$# #1! ! * $ # . \$ # g $# 1a 2 578 ? I29;:_J%J 7"I P IJ AD8 P :_9CA;:K I AD:BG U E G @ Ie: U : U AD7 : E L : P J\8/IeAA;7"8 G P :Bd: U : U M8 JSA;: U dFJ 7"8 @ GIeACA P I2JSADI U AQ: U A;GZA;7"8 E G @ Ie: U I2J JSG P E : U d%ADGFI d2:_W28 U ] P G2A;G JSG K 578 ] P GeA;G2AML ] :_J I K 9C: @ >K I AD:BG U P >U :] EI AD8 I U E NcG P 8#I2J 7 J\8 K_K I >U : NcG P @ P I U EG @ W I P :_I ?K 8 ? 8\A 8 8 U i I U E :_9 J 7G9C8 U 8 > 9;8 A;7:"@ ? 8 P A;G^E 8 J\:_E8 78\A;78 P A;7"IeA J\8 K_K ADI 8 9 I C9 A;8 ] IeQA AD7"I A A;: @ 8 8 K_K 9 Ie:BAQNcG P I U I W8 P Ied28 GeNC(*,/,+ ? 8\A 8 8 U JS8 KBK 9CA;8 ] 9 Z578 @ ] P G ? I ? : K :BAML B A;7I A I U L JS8 K_K A I 28#9 I 9MAD8 ] eI A I U L @ 8 9;7 >] EI AD8 :@ ? 8 P :U :_b > 8 P I U E G @ SJ G U A P : ?> DA :BG U H"G P 8 I2J 7 ] G9;: AD:BG U >] EI AD8 I JS8 KBK 9;8 K 8 JSAD9 :BAD9 9MAD8 ] E : P 8#J A;:_G U ? I29;8 E G U A;78/: U 9MA I U ADI U \8 G > 9QW I KB> 8 9 GeNgA;78 K G J I K_K L I W8 P Ied8 E I U E 8%I K 9;G
J 7G G9;8QI 9MAD8 ]FK 8 U deAD7 P I U E G @/K L N P G @ I I > 9D9C: A;:_G U : AD7FI @ 8 I U GeNh2i 2i i @ I U E I 9CADI U EI P E E 8 W:U NcG P 8#I2J 7 QU 89 > J 7 P >U :_9 P 8SNc8 P;P 8 EA;G I29 F
GeN W I P :_G > 9QW I K_> 8 9QGeNgJ 7"8 @ GIeACA P I2JSADI U A E : > 9;:BW :BAML 3 *I U E J 78 @ eG A I2JSA;:K A;: (I K 8 P P >"U : I U A;:BAM8L 7: 9;8 : I P I U AD8\8 ;A 7"IeAA;7"8 9C8 8 E NcG P ] 9;8 > E G P I U E G @ d28 U 8 P I ADG P _: 9 E : 8 P 8 U A NcG P 8 I2J 7&J\8 K_K 5"7 8 ] 9;8 > EG P I U E G @ U >@ ? 8 P d28 U 8 P I ADG P > 9;8 EZ:_9AD78 @ 8 P 9C8 UU 8 5; :_9CA;8 P B GeN I A 9 >"@ G2A;G%I U E )V:_9;7: @ > P I4 #i K AD: I K 2 8 P P >U 9 NcG P A (G^9DJS8 U I P :_G9 $ I'& JSG U AD: U > G > 9 ] P G E > J AD:BG U
h
8 P I U ;9 8SAD9 G2N @ G2N(J 78 @ GI A;A P I2JSADI U A : AD7 P I A;8 G2N " i i2ii2i @ d J @ 9 $ JSG ;P P 8 9 ] G U E9(ADG ] d 7 NcG P I #i @ P I2E : > 9 J\8 K_K &$ ? & ]>"K 9;8 E ] P G E > J AD:BG U GeNaJ 7"8 @ GIeACA P I2JSADI U A :BA;7 P IeA;8 G2N + " i i2ii2i @ d J @ 9 ?> A! :B;A 7 P I U EG @ : U A;8 P W I K 9 ? 8\A 8 8 U 8#I2J 7 ]>K 9;8 578 ] P G E > J AD:BG U E > AML0JSL J K 8 : U ]>"K 9;8 E P I U E G @ ] P G E > J A;:_G U :_9 J 7"I P I2JSA;8 P : [ 8 E ? L >U :BNcG P @ E:_9CA P : ?"> A;:_G U 9
GeNVA G b > I U A;:BA;:_8 9 $ & AD78 ]">K 9;8ZA;: @ 8 021 g I U E $ h'& AD78Fb > :_8 9DJS8 U A AD: @ 8 0 & 4(A i g I ] I P A;:K I P W I KB> 8 NcG P 0 :U :BNcG P @/K L ? 8\A 8 8 U 0 1 i @ : U I U E 0 - i @ : U %4 N A;8 P A;7":_9 AD: @ 8%"7 I9 8 K I ] 9C8#E A;78 ] 2G : U A ;9 G > P J\8g: U M8 JSAD9 J 78 @ GI A;A P I2J A I U A!: U A;GQA;78 E G @ Ie: U cN G P I U : U AD8 P W I K 0 1 C9 : @ : K I P K LJ 7G9;8 U? S8 A (8\8 U 021 1 i @ : U I U E 0 1 - 2i @ : U I U E/I AI P I AD8 + " 5 7:_9 P I U E G @ G ? G U E > AML J\L J K 8 P 8 ] 8#I A 9)A;7 P G > 2d 7G > A
A;7"89C: @ >K I AD:BG U
$# #1! ! * $ 1^ &$# - ! - ' . . & ' F 2 $ U AD78 9;8 J\G U E J\I29;8 C9 A > EL 8 9MA > E :_8 E A;78 ? 8 7"I W :BG P eG N A (G @ G ? : K 8 J\8 K_K 9 8 IJ 7 J\I ] I ?K 8GeN ] P G E > SJ : U d J 78 @ GI A A P I2JSADI U A (4 9C: @ >K I AD:BG U :_9V: U :BA;: I K
E : I K JSG U JS8 U A P I A;:_G U JS8 KBK>] E IeA;8 9DJ 78 @ 8 : P 7 I W28 8 K I ] 9;8 E9 : AD7 U G ] 8 P J\8\:_W I ?K 8 E8 J P 8 I9C8 : U : U A;8 P J\8 K_KB>K I P E :K A GeN I 9;8SA G2N 9 > \J J\8 9D9MN >"K P >"U 9:_9 I2dI2: U A;78 @ 8#I U ;A : @ 8 ADG JSG U A I2JSA 9 ;
" " U G P E8 P A;G ] :_J I U I ]] P G ] P :_IeA;8 A;: @ 8/9CA;8 ] NcG P A;7"8 7"G ] 9DJSG2ADJ 7 9;G K W28 P (* /,0 1 / (8/JSG @/] I P 8#E 9CA;8 IE L 9CADIeA;8
h
JSG U
JS8 U A P I A;:_G UF] P G `"K 8 9VI29; (8 K_K 2I 9AD78 DA : @ 8 E 8 ] 8 U E 8 U AQE8 J\I LZJSG U JS8 U A P IeA;:_G U G ? A Ie: U 8 E ? L AD787G ] 9;J\GeA J 7 DA 8 J 7 U : 8 I U E 9 ADGFA;7G9C8/G ? ADIe: U 8#E > 9;: U d IF;9 : @ ]"K 8%8\R ]"K : 9;: U dFW I P :_G > 9QAD: @ 8 9CA;8 ] 9 ? \8 A 8 8 U % 9;8 P W IeA;:_W28 K L 9 @ I KBK AD: @ 8%9MAD8 ] GeN ( +.- i 9 578/9;G K_> A;:_G U G ? A Ie: U 8 E N P G @ A;78/8\R ]"K :U J A;:_G U GeN AD: @ 8/I AQA;78/E : P 94$ hei @ & ih *G > P 9MA > E L : U E : A U G2A U 8 JS8#9;9DI P : K L^AD78 9MAD8 IE L 9CADIeA;8 ] P G `"K 8 &QGeN(A;7"8 JSG U JS8 U A P I A;:_G U 1 7:K E ] 8 P 7"I ] 9 I K AD8 P A;78%AD8 @/] G P I Kg? 8\7I W:_G P GeN A;7"8\: P 9;L 9CA;8 @ : U I U&>U I U AD:_J\: ] IeA;8#E (I L 578%d P 8#I A;8#9MA 8 PDP G P G \J J > P 9 : U J I ] A > P : U dFAD78/A;8 @ ] G P I K @ eI R : @ >"@ W I K_> 8/GeN eI A I ` R 8 E ] G9C:BA;:_G U I N AD8 P I `"U : AD8 ]>K 9;8 IeA 9;G @ 8 GeA;7"8 P ] G9C:BA;:_G U .8#J\I > 9C8 A;7"8\L 8 @/]K G L28#E I ` R 8 E AD7 P 8 9;7G K E NcG P I J AD:BW I AD: U dFJ 78 @ GeADIJ AD:_J @ 2G A;:_G U
hj
9 > J 7Z: U IJ\J > P IJS:_8 9(: U JSG >K E P 8 9 >K A: U 9 ]"> P :_G > 9 J 78 @ GeA I R :"K IeA;:_G U P 8 9 >K A 9 3 8 ] P 8#9C8 U A : U H:_d %A;78 ] I A;79
ii i2ii'&!
GeN 9;: R P 8 ] P 8 9;8 U DA IeA;:_W28 JS8 KBK 98$G > QA GeN 7: G > 9 K L ] P G E > JS: U d J 78 @ GI A;A P I2JSADI U A ] G2: U AQ9CG > P JS8 "H G P AD78 9;88 I K 9 I
J 78 @ G2ADIJ A;: 9C8#E 4V9Q8SR ] 8#J AD8 E >U E 8 P JSG U AD: U > G > 9VJ 7"8 @ GIeACA P I2JSADI U A ] P G E > JSA;:_G U
: U J P 8 I9C: U d E 8 J P 8#I29;8 9 AD78 @ 8#I U ;A : @ 8 ADG JSG U A I2JSA>9 K IeA;:_G U ADI 2 8%: U J\I9C8 J 78 @ GI A;A P I2J A I U A E : > 9;:BW :BAML
U
J\8 K_K @;4"B
I P 8 ]K GeA;A;8 E ^ 57":_9 d8 U 8 P I K G ? 9C8 P W I AD:BG U :"U : NcG P @/K LFIeAVI%7:_d27 P I AD8 7": K 8 SJ 8 KBK @ .EB%I A I K G @;4"B 7"I P E K L @ G W28 9 7: K 8^JS8 K_K @ .EB E : 9CA " > J A > I AD8%I P G >U E A;7"8\: P : U :BA;: 9;8(A;78 L I P 8 C9 8 U 9C: U d 9;8 K N ] P G E > J\8 E J 7"8 @ GIeACA P I2JSADI U A !578 P 8 @ > 9MA ? 8 I E P I9MAD:_JE : 8 P 8 U J\8 ? 8SA (8\8 U JS8 KBK 9 ] P G E > J AD:BG U P IeA;8 NcG P 9 > J\J\8 9D9MN >K ADIeR : P : U A;7:K 9;8 9 : AD7 ] I P A;:K I P W I KB> 8#9GeN6 0 1 i @ : U 0 - i @ : U
@ : U ! I U E 0 1 - i
021 1 i
i
@ : U 5 7 > 9: U A;7":_9 J\I9C8 A;7"8/J\G U J\8 U A P I AD:BG U ] P G "` K 8 I P G >U E #8 I2J 7 JS8 K_K)?> : K E"9 >] I U E E 8 J I L 9 .(8#J\I > C9 8 AD78 9;8 J P 8\A;:_G U : 8 U A K L A;78 L P 8#JS8\:_W28Q9C:_d U I K N P G @ 8 IJ 7%GeAD78 P 9;G B: A @ > 9CA(E 8 ] 8 U E G U J 78 @ GIeACA P IJ ADI U AE : > 9;:_W:BAML I9 (8 E : 9D9 ? 8 K G H > P A;78 P @ G P 8 AD78 ;A : @ 8/: U ;A 8 P W I K I U E ?> P M9 A9CA P 8 U d2A;7 GeNJ 78 @ GI A;A P I2JSADI U A ] P G E > J A;:_G U K : 28 K L I K 9;G ]K I LF: @ ] G P ADI U A P G K 8#9 : U P 8 d >K I AD: U d JS8 K_Ka@ G2A;: K :BAML A;7G > d27 (87"I W8 L28\A A;GF9CL 9CA;8 @ IeA;: E :_8 E/AD78V: U"> 8 U J\8VGeN*J 78 @ GeDA IJ AD:_J\: AML/I U E%E: > 9;:BW :BAML G U JS8 KBK 9C:_d U I K : U d : U J I29;8 GeNAD78Z9CADIeA;:_G U I P L ] G2: U A 9;G > 8 I9C: K L eAD7 > 9 E 8#J P 8 I29;: U d A;78 : P
= : @
: K I P A;G AD78QJ I29;8 P JS8 a7:_d27"8 P J 7"8 @ GeA I2J AD:_J\: AML 78 K_] 9A;78FJS8 _K K 9 E 8\A;8 P @ : U 8%A;78ZJSG DP P 8 J A E: P 8 JSA;:_G U&@ G P 8 @ 8 8SA;: U d AD: @ 8 U H:_d j-$I & (8 9;7G AD78 8 8 JSAgGeN*J 78 @ GeADIJ AD:_J\: AMLG U%@ 8 I U AD: @ 8
A;G J\G U ADIJ A)NcG P E : 8 P 8 U AgE : > 9C:_W : AD:B8#9 7 8 P 8 #8 I2J 7 ] G: U Ag:K I AD:BG U 9 O : > 9;:BW :BAML : 9;:BW :BA;:_8 9 :BA A I 8 9 I P 8 K I A;:_W28 K L K G U d A;: @ 8 cN G P JS8 K_K 9ADG P 8 J\8\:_W28Z9;:_d U I K I U E E I ]] P G ] P : 9C:_W : AD8 9 @ I 28AD78VJ\G U J\8 U A P I AD:BG U ] P G `"K 8 E8 J\I L N I29CA;8 P K 8#I2E : U d ADG P 8 9 ] G U / - AD: @ 8 B: A;7G > A 9C:_d U I K \J G @/] I P 8#E/A;G K G (8 P E : > 9C:_W : AD:B8#9 8 : U E8\8 EZG ? 9C8 P W8VI U G ] AD: @ I K P I U d 8VG2NE : > 9C:_W : AML : U 7 : P 8 K L cN G P JSG @/]> ADI AD:BG U I K J\G U 2W 8 U :B8 U JS8 A;7"IeA 8 : @/] G9;8&I [ 8 P G JSG U SJ 8 U A P IeA;:_G U? G >U "E I P L SJ G U E : AD:BG U IeA ! @/@ 57":_9 I KBK G 9 > 9gADG > 9C8 I @ G E 8 P IeA;8 K L%9;: [ 8 E 9;8SA G2N U G E 8 9$ hei2i 2h i2i'& A;G P 8 ] P 8 9;8 U A I/h @ @ h @/@
P : U @ I : U d 9 > J 7 I%J 7G2: 9CA ? 8 JSG2d U : [ I U A GeNA;7"88 8 JSAVGeN)A;7"8 ? G >U E"I P LZJSG U E :BA;:_G U G U A;78 ? 8\7I W:_G P GeN)A;78 C9 G KB> AD:BG U J'$ A & Q578 E P J\8 $I AVA;78 G P :Bd: U &ADG%A;7"8 ;9 : U $ AD78QJ\: P J K 8VIeA! & ] I P A;: J 7 eG N I U 8 8 J A)AD7:_9 P 8 ] P 8#9C8 U AD9 : A : C9 8\N >K ADG J\G U 9;: A;:_G U A;G I 9C: @/]K : ` 8#E W28 P 9;:_G U G2N!AD78 A P I U 9 ] G P (A 8#b > I DA :BG U : U JSL K : U E P : 3 > 8 8 8
$ &
:BA;7FA;78 NcG KBK G : U d/: U :BA;:U EI P LZJSG U E : AD:BG U 9
i
$# ;i & $#! & i
$ & $ i &
4V9 % i AD7:_9 JSG DP P 8 9 ] G U E9VA;G^IF9;: U d K 8 ]">K 9;8/GeNJ 78 @ GIeACA P IJ ADI U A I A DA 78/G P :Bd: U 5 78%I U I K LAD:_J I K C9 G BK > A;:_G U eG N X b 7 : AD7 AD78FI ? G W8 ? G >U EI P L&I U E&: U :BA;: W : K_K 8 : U DA 8\d P I K
A P I U 9MNcG P @ ADG ? 8 $ :_J\8 O G &
$ $ & h !
78 P 8
$ & $)! $
&
&
8\R ] $ 3 &
$ &
I U E I P 8i AD7 I U E 9CAVG P E 8 P (. 8#9;9;8 K N >U J AD:BG U 9QGeN)A;78 ` P 9CA : U E P 8#9 ] 8 JSA;:_W28 K L 5 78 8\:_d28 U W I KB> 8#9
I P 8 A;78 P G GeA 9G2N!AD78 NcG K_K G : U d 8 b > IeA;:_G U
$ ! & i ] P G `"K 8$)! $ & 6 78 P 8!
$ #h'&
8 > 9;8 X b /A;G JSG @/] I P 8 A;78 E8 J\I L i ^@/@ )NcG P W I P :_G > 9 W I K_> 8 9 GeN A;7"8 [ 8 P G J\G U J\8 U A P I AD:BG U&? G >U EI P L P I2E : > 9 ! 8FA P >U J\IeA;8#E&A;7"8^9 >@ : U X b ZIeN A;8 P #iD7 A;8 P @ 9 :_9 A I 8 U A;G ? 8 i2i2i^6d J @ )I U E i @ U H:_d 1 (8 9;7G A;78FI U I K LDA :_J I K $)! $ & NcG P ? G >U E"I P L P I2E :_:!
8\dI P E K 8 9D9/GeN ! ] 8 I 9ZI A h2i&9 : U E : A;:_G U G2N ! @/@ E 8SAD8 P @ : U 8#9 AD78 AD: @ 8 : U A;8 P W I K VIeN A;8 P I ]>K 9C8 cN G P A;7 P 8#9C7G K EFI AVI KBK W I KB> 8#9Ge:N ! 78 P 8 JS8 K_K 9 P 8#9 ] G U E AD G
7:"K A 9 ;A G ? 8 : U E 8 ] 8 U E 8 U AGeN ;A 7"8 9;: [ 8 GeN*AD78E G @ I2: U I 9(G U 8 (G >K E K : 8 57: 8 U JS8 U GeA G U"K L%G2NaA;7"8 \J G @/]> A I AD:BG U I _K K L J\G U W28 U :_8 U A J 7G:_J\8 GeN I [ 8 P G JSG U JS8 U A P IeA;:_G U0? G >U EI P L J\G U E: AD:BG U I A ! ?> A I K 9;G E > Z 8 A;G ;A 7"8 "] > P ] G9;8SN >"KBK L 9C: @/]K : ` 8#E A P I U 9 ] G P A @ G E 8 K G2N)J 78 @ GI A;A P I2JSADI U A 8 P 8SNc8 P A;G/AD78 NIJ A A;7I AQE 8 d P I2EIeA;:_G U _: 9 U GeA : U J _K > E #8 E^: U AD78 A P I U 9 ] G P A
8 b > IeA;:_G U NcG P J 78 @ GI A;A P I2JSADI U A 57:@ 8J 7"I UU 8 K NcG PVP 8 @ G W I K GeN J 78 @ GI ACA P IJ A I U AN P G @ A;7"8 9CL C9 A;8 @ (G >K E P 8 E > J\8VAD78 `"U :BA;8 9;: [ 8Q*8 8#J A : U A P G E > J\8 E ? L/AD78 ? G >U EI P L ? 8 J I > 9;8 I @ > J 7Z9 @ I KBK 8 P I @ G >U AG2NJ 78 @ G I A;A P I2J A I U A (G
>K E G G > AVI AA;7: U E I P L
$
8E8\W28 K G ] 8#EI @ IeA;78 @ I A;:K I AD8(J 7"8 @ GeA I2J AD:_J(JS8 KBK @ GeAD:BG U : U I h O 7 G @ G d28 U 8\G > 9aE G @ Ie: U 7:U 9MAD8 I2EL J 78 @ GI A;A P I2JSADI U AJ\G U J\8 U A P I AD:BG U/] P G `"K 8 9 578Q7G ] 9;J\GeADJ 7 @ 8\;A 7G E I29I ]]K :_8 E/ADGG ? A Ie: U
N >K_K LZA P I U 9C:_8 U AQJ\G U J\8 U A P I AD:BG UZ] P G ` K 8#9 8 9 >K AD9Q9C7G (8 EZAD7"I A AD78 7"G ] 9DJSG2ADJ 7 @ 8SA;7"G E :BA;7 I U I ]] P G ] P : P I AD8 @ 8\A;7G EZA;G%I ]"]K LZ: U A P I U 9 ] G P A 9C: @ >K I AD:BG U 9GeN!A;7: d27 @ 8 I9 > P : U d^A;7"8 @ 8 I U A;: @ 8 ADG JSG U A I2JSAGeN
JS8 KBK 9^J P I K : U d&ADG (I P EI ] G2: U A 9;G > P JS8 eG N J 78 @ G I A;A P I2JSADI U A U A;78 ` P 9MA^J\I9C8 9MA > E ( L (8 G ? 9C8 P W8 E AD7"I A^A;7"8 E : > 9C:_W : AML^GeNgJ 7"8 @ GIeACA P I2JSADI U AQ7"I29 U G 8* #8 J A G U 7 G NI9MA J 78 @ GeA I2JSA;: P JS8 78 UF] P G E > JSA;:_G U :_9VJSG U AD: U > G > 9 # G 8 W28 P : U AD78 J\I9C8 G2N ]>K 9;8 E P I U E G @ J 78 @ GI ACA P IJ A I U A ] P G E > JSA;:_G U
7:_d278 P E: > 9;:BW :BAML 9 ] 8\8#E9 >] P 8 J\8\:_W : U d 9C:_d U I K ? L \J 8 K_K 9 ?> A :BAI K 9;G @ I 28 9gA;7"8 \J G U J\8 U A P I AD:BG U%] P G `"K 8 E8 J\I L N I9MAD8 P 578 P 8\NcG P 8 AD78 P 8%:_9 I U G ] AD: @ >@ P I U d8 NcG P E : > C9 :_W : AML GeN(J 7"8 @ GIeACA P I2JSADI U A : U 7 :_J 70JS8 KBK 9 P 8 J\8\:_W28/9C:_d U I K @ G 9CA 8 8 JSA;:_W28 K L I U E P 8#I2J 7^A;7"8 ] G2: U A 9CG > P SJ 8 A;7"8 NI9MAD8 9CA 8 I K 9;G I A;A P : ?"> A;8#E^A;78 JSG @ ]"K : 9;:BW :BAML A;G I U : U A;8 P ]K I L GeN"AD78 d P 2I E:B8 U A I U E SJ G U JS8 U A P I A;:_G U A;7 P 8 9;7G K E9 > 9;8 E : U AD7: P 9MA 9g: U AD78 9;8 J P 8\A;:_G U G2N!J 78 @ GI A;A P I2J A I U A I K_K G @ G ? : K 8 JS8 KBK 9%ADG E 8\A;8 JSAZ9;:Bd U I K N P G @ GeAD78 P @ G ? : K 8 J\8 K_K 9 6578 P 8SNcG P 8 : A^9C8 8 @ 9 >UK : 28 K L,A;7"IeA @ :Bd P IeA;: U d
JS8 KBK 9AD7"I AVI P 8QA P L : U / d ADG `"U EF8 IJ 7ZG2A;78 P 9C8#J P 8SAD8 9;:_d U I K : U d/JSG @/] G >U E9 JSG U A;: U> G > 9 K L = : @ : K I P A;G/AD78J\I9C8 GeNA;7"8 9CADI AD:BG U I P L ] G: U A 9CG > P JS8 :BA;7 P I U E G @ ] P G E > JSA;:_G U 7":Bd78 P E : > 9C:_W : AML9 ] 8 8 E9 >] 9;:Bd U I K A P I U 9 @ :_9D9;:BG U? L J\8 K_K 9 ?> A :BA I K 9;G P 8 9 >K AD9: U IVNI29CA;8 P E8 J\I L G2N"AD78 JSG U JS8 U A P IeA;:_G U] P G `K 8 # 8 U JS8 (8G ? 9C8 P W8I U G ] A;: @ I K P I U d28gNcG P E : > 9C:_W : AML :U
7:_J 7 JS8 K_K 9 E 8\A;8 JSA 8 IJ 7GeAD78 P 9 9C:_d U I K @ G9CA 8 8 JSA;:_W28 K L I U EJ\G U 9;8 b > 8 U A K L P 8 IJ 7 8#I2J 7 GeAD78 P A;78 NI29CA;8 9CA
8#9 >K AD9 : U,? GeAD7 J I29;8Z9CA > E:B8#9 P 8 ] P 8#9C8 U A K : @ : AD: U d09;:BA > IeA;:_G U 9 7: 9CA P I AD8Z7G >U 9CA;8 IE L J 78 @ G I A;A P I2J A I U A JSG U JS8 U A P I A;:_G U^] P G `K 8#9 : U-"> 8 U JS8 J\8 K_Ka@ :_d P I A;:_G U U ] I P A;:K I P - (87"I W28 G ? 9;8 P W28 E^J I29;8 9 : U 7: 9;:_W:BAMLFGeN J 78 @ GI A;A P I2J A I U A 9MA P G U d K L%: U-"> 8 U JS8 9VJS8 K_K@ GeAD: K : AML
YH 'U 4o& ")(0`$) 67$)3-% #"'&H")(0 5+ H,&QB5; i ? F424 @ )B ] !426& $)(*-% ! !,]")U ^ ! 3D"%$'& ")(0 5 6$) 10o & gV,G !$ 3n671*(0 (["k&! U7 56 -%3 !")'U 7([")27(93$) 7 ^423")U7 D7-`h([")U C!&H$)(0 ! -Z")(042^- ") 67- E - "'& ")(* !& $%g 6 !(*#" -% !7$) 2& " ")U ^ 3D")R$ !,]")U727 !4o&!(0 6$) D77 'U 42 5&H"%"%$'&!R"'&!#"Zh([")U $'&H")L !,? ?!?5=J42/ 4 -S,G H$2c58 ?5?!?+-k&HJ")U 3$) &H,")R$L # - H"S67$) D 5E2TU ^ ! 3D"%$'& ")(0 5 (0&H1*3 1*&H") &H"`&o7(0- "'&!7 !, `K i ?DE o424 , $) 54 ")U7 6 5(0#"`-% !7$) 5Ek;e B D") &5g - "'&H") ! 3D"%$'& ")(0 5V67$) 1058!5;H@" $#&% B ,$) !4 3n6 10(0 ([" ;(') +*-, i ?DE0c -'B&HFU 567-% !")'U ;(') ".0/+1. i32 -'B ([") 7( 93$) 7 - E
200
y (0.01 mm)
150
100
50
0 0
50
100
150
200
x (0.01 mm)
m(0/!$'&H")(0 !m6& ")U -O !,Y&S-% 10 3")(0 5F !, 31*10-]") h&H$'^")U -%(0 /!1*6 5(0#"]-% !7$) I10 #&H") & "]")U 3D")R$] H,")U7` 54o&H(* 67$) D (07/^RU7 42 Q& "%"%$'&!3"'&H#" 5#")(0D 57-%1[gFh([")Um$'& ")S !,O?DE ?!?5?!?!=F42/ H 4 - EOW (0-? 2 &! (*-Sc ?S 4 H- E
Contact time (105 s)
16 14 12
-9
2
40
1 × 10-8 cm2/s 1 × 10 cm /s 1 × 10-7 cm22/s -6 1 × 10-6 cm2/s 5 × 10 cm /s
D= = = = =
35
10 8 6 4 2
30
5
D= = = = =
Contact time (10 s)
18
25
0
-9
2
0.4
0.5
1 × 10-8 cm2/s 1 × 10 cm /s 1 × 10-7 cm22/s -6 1 × 10-6 cm2/s 5 × 10 cm /s
20 15 10 5
(a)
j
(b)
0 0.1
0.2
0.3
0.4
0.5
Chemotacticity
0.6
0.7
0.1
0.2
0.3
0.6
0.7
Chemotacticity
Y2;>&QB m &!V")(*42 ") 5#"'&!R"8 CD- ESRU7 42 !"'&H3")(0 ([" gJ3 #2 (0 #"8Wf89,G H$ C5& $)(0 5 -`RU7 42 Q& "%"%$'&!3"'&HD"Z7(9 -%(0 ! #^ (0 #")- 8 hU ")U ^6 !(0D" -% !7$) 26$) D7 3 -SRU7 42 Q& "%"%$'&!3"'&H#" 5#")(0D 57-%1[g#EJ;eB &!42^&H-o;>&QBZ3n 6"Sh(0")U 6 71*-% $'&! 7 !4 67$) D773")(0 5m&!-7 -%3$)(0eF(0m")U `")Rn"E
25
β = 0.2 = 0.3 = 0.4 = 0.5
20 5
Contact time (10 s)
15 10 5 0 10-4
(I)
(II)
-3
(III)
-2
(IV)
-1
10 10 10 100 Diffusivity (10-6 cm2/s)
101
9 m&! ")(042>") 5#"'&H3"8 CD- E RU7 42 Q& "%"%$'&!3"'&H#"27(97-%(* ! 3 #2 (0 #")- 8 8O,G H$2C!&H$)(0 57-^RU7 42 !"'&H3")(0 ([" g #^ (0 #")- 8 WO87hU7 m")U `6 5(0#"-% !7$) S6$) D77 -RU7 42 Q& "%"%$'&!3"'&H#"(* 6 71*-%3- E
200.0
200.0 (a)
Cell A
100.0 Cell B
Cell A
100.0 Cell B
50.0
50.0 0.0 0.0
(c)
150.0 y (0.01 mm)
150.0
0.0 0.0
50.0 100.0 150.0 200.0 x (0.01 mm)
200.0 (b)
y (0.01 mm)
y (0.01 mm)
150.0 Cell A
100.0 Cell B
50.0 0.0 0.0
50.0 100.0 150.0 200.0 x (0.01 mm)
115.5
50.0 100.0 150.0 200.0 x (0.01 mm)
110.0
115.0
114.5
114.0 79.5
80.0 80.5 x (0.01 mm)
81.0
y (0.01 mm)
y (0.01 mm)
y (0.01 mm)
115.0
112.0
109.0
106.0 79.5
105.0 100.0 95.0
82.0 84.5 87.0 x (0.01 mm)
89.5
90.0 90.0
95.0 100.0 105.0 110.0 x (0.01 mm)
Y STU7k6 &H")U+" h] 3 101*-"'&!aQ hU (010 ;>&5BIe H")U & $)L-% R$)3")(0 /oRU7 42 Q& "%"%$'&!3"'&H#"Z !D")(0D ! -%1[gJ&HJ-%(0/5 &!10(0 /m &!'U !")U73$h(0")U -)&H42O- "%$)3 /!")UE&QBZTU72 9 3" H,j'U 42 H"'&!3")(0 ([" g ! !D"'&H3" ")(042k,G H$k7(93$) #" 'U 42 5&H"%"%$'&!R"'&!#"I7(9 -%(0 !+ # 23(*3D")- EI;eBTU S 9 R" H,O7(9 -%(0CD([" go !+ 5#"'&H3"")(*42,G !$( 9R$) #"'U 342 !"'&!R")(*3(0")(0 - E
0.2
c(Rs,t) (g/cm3)
0.002
0.15
R
0.001
0.1 0 3 10
10
4
10
5
10
6
10
7
0.05
R 0 101
102
103
104 t (s)
105
106
107
FM ADG2d P IeN A ? G U 8 P 8 ]K I2J\8 @ 8 U AAD78 P I ] L 7"I29 9C7G U AD7"I A ] P 8SA P 8 IeA @ 8 U A8 :BA;7,I 0 X H P 8 J\8 ] DA G P $ H K A & J\I U : @/] 8 E 87"8 I K : U d%: U J\G P A;:U JSA;:_G U I K : [ : U d A;78 : U AD8 P :BG P 9 > P NIJS8#9 GeN ] G P G > 9 JSG U 9CA P > J A 96 : AD7/J\LA;G : U 8 P 8#JS8 ] A;G P 9: U"> 8 U JS8#9)A;: 8: U d P G A;7 QU 8 @ I L7 L ] GeAD78 9;: [ 8(A;7"IeAgI @ IMG P @ 8 J 7I U :U E8 P K L : U dVAD7: A;G2d P IeN AE :_9 P >] A;8#E AD78 E : P 8 J AD:BG U `"U E : U d I ? : K : AML G2N(7"G9CA U 8\G W I29DJ >"K IeA > P 8 ] G9CA : @ ]"K I U A I AD:BG U AD7"I A: g9 JSG U M9 A P > JSAD9 @ :_2d 7A ? 8QIJ 7:_8\W28#E ? L A >"U : U d
A;7"8 P 8 IJ A;:_W : AML0G2NV: U DA 8 P :BG P 9 > P NI2JS8#9ADG J\8 P ADIe: U J 7"8 @ G IeACA P I2JSADI U A 9 > 9;: U d : @/@ G ? : K : [ 8#E P 8 JS8 ] A;G P 9 U I P IeA;:_G U I K 8SR ]K G P I AD:BG U GeN A;7":_9 ] GeA;8 U A;:"K E J\G U 9;: 8 U JS8 GeNg9 ] I AD:_I K : U 7G @ Gd28 U 8SAD:B8#9 G U E : > 9;:BG U GeNJ 78 @ GI ACA P IJ A I U A I U E J\8 K_K K G JSG @ GeA;:_G U $c:_: &QAD78%J 78 @ : P NI2J\8 96$:B:_: &QA;78 : U 8SA;: P 8 G2NaA;7"8 J 7"8 @ GeA I2J AD:_J P 8 9 ] G U 9C8 GeN)JS8 KBK 9(A;G U G U JSG U JS8 U A P I A;:_G U 9(I U EFJSG U JS8 U A P IeA;:_G U d P IE :_8 U AD9G2NJ 78 @ GI A;A P I2J A I U A
4V9 I 9MAD8 ] ADG (I P E A;7:U E 8 P 9CADI U E : U d !G U 8 J\G >K E&E 8#9C:_d U I ;9 8 P :B8#9 eG N 8SR ] 8 P : @ 8 U A 9 ADG I29D9C8#9;9 AD78 E 8 d P 8\8/ADG 7: 8 U JS8/AD78Zh O K G JSG @ eG A;:_G U eG N JSG U ADI2JSA : U 7: ? : AD8 E0J 78 @ G2ADI2JSA;:K A > P 8 X W8 U ;A 7G > d27%9 > J 7/I 9;J\8 U I P :_GQ:_d U G P 8 9!A;78 J\G @/]K 8SR B: AML eG NI O ] G P G > 9 JSG U 9MA P > JSAe:BA U 8 W28 P A;7"8 K 8 9D9 ] P 8 9;8 U AD9)I 9C:_d U : ` J I U A U"> @ ? 8 P GeN W I P :_I ?K 8#9*AD7"I A @ > M9 A ? 8 JSG U A P G KBK 8 E I ? G 2W 8I U E ? 8 L2G U EAD7G9;8: U IVAML ] E 8 AD78 U >@ ? 8 P 9"9C7I ] 8 9"I U E^9;: [ 8 9G2NAD78 G ? 9MA I2J K 8 9 A;7"8\: P I PDP I U d28 @ 8 U A(G U A;7"8 J >K A > P 8 9 > P N I2J\8 :BA;7 P 8#9 ] 8 JSA A;G%AD78: U : AD:_I K 9;8\8 E: U d ] G9C:BA;:_G U GeN J\8 K_K 9 I U EFA;7"8 J 78 @ GI ACA P IJ A I U A9;G > P J\8 "I U E A;7"8\: P 9 > P NIJS8 P 8 IJ AD:BW :BAML :BW8 U AD7:_9 JSG @/]K 8\R : AML ":BAQ: A P I U E G @/K LZ: U A;7"8 E G @ I2: U V578 ? G >U EI P :B8#9 G2N)G ? 9CADI2J K 8#9VJ\G U 9 >@ 8 J 78 @ GI A;A P I2J A I U A : AD7 ] P 8 9DJ P : ? 8 E : U 8SA;: 8 U J\8 9)AD78VJS8 KBK 9eI ? : K :BAMLADG A P I W28 P 9;8:BA : U P 8#9 ] G U 9;8(A;G A;7"8 G W28 P I KBK J 78 @ GI A;A P I2J A I U A d P I2E:B8 U A
57: 9V9CA P > J A > P 8 9 NcG KBK G (8 E ? LFIZE : 9;9;:_G U GeN AD78 : U> 8 U J\8 G2N @ :_J P Gd28\G @ 8SA P LZI U E G ? 9CADI2J K 8 ? G >U EI P L P 8 I2JSA;:_W : AMLFG U J\8 K_K)@ G2A;:_G U H : U I K_K L (8 9 >@/@ I P : [ 8
A;7"8 @ I2: U I9 ] 8 JSAD9GeN!A;7: E 8 $ &*I N >K_K L A;: @ 8 P 8#9CG K W8 E `U : AD8 E : 8 P 8 U SJ 8 9;G K_> ;A :_G U 7 :"K A I U 8 G > 9 K L 8\WG K W : U d/JSG U JS8 U A P I A;:_G U ` 8 K EFeG N J 78 @ GI ACA P IJ A I U A
1 6
8 JSG U 9C:U JSA;:_G U GeN ] G9C:BA;:_G U I U E AD: @ 8 $ >$ & g578 d2G W8 P U : U dA P I U 9 ] G P A 8 b > IeA;:_G U :_9 I9(NcG K_K G 9
> 3 $ ? > & 8
78 P 8 3 :_9QAD78%E : > 9;:BW :BAML GeNJ 78 @ GIeACA P IJ ADI U A I U E
$
$ &
>$ &Q: P JS8 AD8 P @ H"G P 9C: @/]K :@ 8 P :_J I K_K L > 9;: U d A;78 7"G ] 9DJSG2ADJ 7 @ 8SA;7"G E
j 4 AD: @ 8V9CA;8 ] GeN ( h 9 : 9;8 E : U A;7: E L 5 78Vh O E G @ I2: U/@ 8 I9 > P 8#9 h @ @ h @/@ aI29 9C7"G U : U H:Bd I U E :_9 E :K I P @ 8#9C7 GeN i2i i2i U G E 8#9 57 > 9 A;7"8 K I ACAD:_J\89 ] 2I JS: U d
: I K_K L^: U M8 JSA J 78 @ GI A;A P I2J A I U A : U ADG%A;78 E G @ 2I : U eI A ] P 8 9DJ P : ? 8 E P IeA;8 9 -$ & P 8 ] P 8#9C8 U ADV9 A;78 P IeA;8 I A 7:_J 7 ;A 78%JSG U SJ 8 U A P I A;:_G U 2G NJ 78 @ GI A;A P I2J A I U AV: J\ 8 E eI A ] G9;: AD:BG U
7: & @ I L ? 8 P :BACAD8 U > 9;: U d%A;7"885 P G 8 U 8 J 8 P
$ ?
E 8 K A I N >U J AD:BG U I29 I/9 >"@ G W28 P ] G2: U AV9CG > P JS8 9 $
>$ & -$ &
78 P 8A;78 > U 9 >? ;9 J P : ] A;8#E U G E"I K ] G9C:BA;:_G U 9 *I U E E 8 U GeA;8 ] G9;: AD:BG U $ ? -& I U E ] P G E > J AD:BG U P I AD8 eG NA;78 AD7 ] G: U A 9CG > P JS8
$ h'&
-$ &E
8 U GeAD8 9!A;7"8AD: @ 8 E 8 ] 8 U E 8 U A
5!G%: U :BA;:U EI P :B8#9
3 6
$ &
78 P 8 : JSA6)J\I U A;78 P 8\NcG P 8 ? 8 AD7G > d27A*GeNI29aI JSG U W8 JSA;:_W28 "> RZGeN!J 78 @ GI A;A P I2JSADI U AA;7 P G > d7 AD78 ? G >U EI P :_8 9 A;7G > d27 9CA P :"@ ? 8 P f)8 3
$ &
78 P 8! 8(7"I W28J 7G9;8 U AD78 K IeACA;: R ? G >U E"I P :B8#9 & (8 7I W28 J 7G9;8 U A;G 9 8 8 ] W I K_> 8 9G2N N P G @ I K G f)8 GeN h i5 A;G I 7:_d27^f)8 G2N)i
8 @ G E 8 K 8 > I P :_GeA;: I AD:BG U 9VdG W28 P U : U d \J 8 K_K!] G9;:BA;:_G U >"] EIeA;8/I P 8 E : 9D9C8#E : U 7"I ] AD8 P = 8 J h h
! # #! $/V"')$\ # 2 $ 578QG ? 9CADIJ K 8 ` 8 K E9(I P 8VJSG @ ] G9;8 E G2N P I U E G @/K L E : A;8 E 9CG K : JS8 E ? L QO [ : >?K I i 8 ` P 9MAJSG U 9C: R P 8#I2JSA;:_W28 ? G >U EI P LFJSG U E :BA;:_G U 9 $ X b &(G U AD78G ? 9MA I2J K 8 ? G >U E"I P :B8#9 - (8 ] P 8 J\G @/]> AD8 A;7"8 ? G >U EI P L U G P @ I K W8 JSA;G P 9(NcG P I K_Ka? G >U E"I P L U G E 8#9 : U AD78 NcG KBK G : U d (I L N I @ I K_K B U G E8 ? 8 K G U d9 G UK L ADG G U 8 JS: P J K 8 AD78 ? G >U EI P L U G P @ I K W28#J A;G P : KBK? 8 JSG U 9C:U : A W28 JSA;G P A;7"IeA ] G2: U AD9 N P G @ ;A 7"8 U G E 8ADG%A;7"8 G P :_d2: U GeNA;78 JS: P J K 8 > 9;8 EA;G J P 8 IeA;8A;78 ] G P 8 N I I K_K U G E 8 ? 8 K G U d9!ADG @ G P 8A;7"I U G U 8(J\: P J K 8 AD78 U G P @ I K : [ 8 E 9 >@
GeN)AD78 U G P @ I K W28 JSA;G P 9 I9;9;G JS: 9;: U dE : 8 P 8 U A P I U E G @ 9C8 8 E9 G W28 P 7:K AD9 $57"8 ] 9;8 > E G P I U E G @ U >@ ? 8 P d8 U 8 P IeA;G P > 9;8 E%: G9;: AML-&g: U = 8#J
j
21! 1c . $ 1 8V: KBK_> 9CA P I A;8 A;7 8 JSG U J > PDP 8 U AgJ 78 @ GIeACA P IJ ADI U A A P I U 9 ] G P A ? :K A;: (I K 8 P 9;: @ > K I AD:BG U EG @ Ie: U : U H:Bd 8QJ\G U 9;:_E8 P AD78Q9DJS8 U I P :BG : U 7: P JS8 K : U 8 I U E K I >U J 7": U d ] G9C:BA;:_G U G2NgJS8 KBK 9 i2i i i2i/JS8 KBK 9 I P 8 K I >U J 78#E : U 8 IJ 7 9C: @ > K I AD:BG U NcG P W I P :BG > 9 W I K_> 8 9 GeN)G ? 9MA I2J K 8 ? G >U EI P L P 8 IJ AD:BW :BA;:_8 9 I U E ` 8 K E ] G P G9;: AD:B8#9 578 J K G J ^9MA I P AD9QI U E J\8 K_K 9QI P 8 9;: @ >K A I U 8 G > 9 K L K I >U J 78 EFN P G @ A;78 : P P 8 9 ] 8#J A;:_W28 ] G 9C:BA;:_G U 9VG U AD78 9CADI P A K : U 8 7: K 8 A;78 9CG > P J\8 K : U 8 : U 9CADI U A I U 8 G > 9 K L ? 8\d2: U 9 ] P G E > JS: U dJ 78 @ GI ACA P IJ A I U A 578 ] P : @ I P L G ? 9;8 P W I ?K 8 :_9 A;78VA;: @ 8 P 8 b > : P 8#EFNcG P AD78 J\8 K_K 9VA;G A P I W28 P 9;8 A;78/i @/@ E : P J\8 P 8SNc8 P;P 8 EFADGZI9
A;7"8 A P I U 9C:BA A;: @ 8 * E 8 U GeA;8#E
4Q9Q9;G @ 8/JS8 K_K 9 @ :_d27A d8SAQA P I ]] 8 E : U 9;: 9 I J\8 K_K "7 :_J 7 dG8#9 ? 8\LG U E^AD78 K : @ :BAD9 eG N AD78 EG @ Ie: U : U I U LZG U 8 E : @ 8 U 9;:_G U 8 U AD8 P 9 N P G @ A;78 GeAD78 P 9C:U EI P :_8 9I P 8 : @ ] 8 U 8SA P I ?"K 8 ADG/J\8 K_K 9
6
8FJ 7"I P IJ AD8 P : [ 8%G > P G ? 9CADIJ K 8 ` 8 K E9 ? L($I & ] G P G9;: AML $ ? & ] G P 8F9C: [ 8FE : AD:BG U 9 I U E $ J&A;G P A > G9;: AML !5 G G ? ADIe: U ] G P 8%9;: [ 8 E : A;:_G U 9 (8 @ #8 I29 > P 8 AD78/W28 P A;: P NI2J\8 9 4Q9 @ 8 U A;:_G U #8 E
: U = 8 J h ] G P G9C:BAML : : I U AD: ` 8 E&I29 ;A 78 P I AD:BG^G2NWG2:K AD9 NcG P 8#I2J 7 ] G P G9;: AML%G W8 P A;8 U P 8#I K : [ I A;:_G U 9! :BA;7 E : 8 P 8 U A P I U E G @ 9C8 8 E9 U H!:_d h-$I & (8 ] P 8#9C8 U A ] G P 8 9;: [ 8 E:_9CA P : ?"> A;:_G U 9 NcG P I K_K ] G P G9C:BA;:_8 9(JSG U 9C: AA :_J\8VAD78 P I2E : > 9 > 9;8 E A;G d28 U 8 P I A;8QA;7"8 ` 8 K E9 # G 8 W28 P I29^: U J P 8#I29;8 9 ( 8 G ? 9;8 P W28 I
? P GIE 8 P ] G P 8 C9 : [ 8E : A;:_G U U H!:_d h-$ ? & 3 89;7G A;78 I W8 P Ied8 ] G P 89C: [ 8 W 9C 4V9 8\R ] 8 JSA;8#EAD78 I W28 P I2d28 ] G P 8Q9;: [ 8QI K 9;G : U J P 8 I9C8#9gI29EF: U J P 8 I9C8#9 ;$ 8Q7I W28VJ\G U 9;:_E8 P 8 E I JSG U 9MA I U A P I2E : > 9 NcG P 9;: @ "] K : J A > P 8QJ P 8 I AD:BG % U ] P G J\8 9D9 G U 8 @ :_d27Ag7I W28 @ G P 8VJ\G U A P G K G W8 P AD78 ] G P 8V9;: [ 8 E : AD:BG U & U 2I EE: AD:BG U (8 7 I W28 NcG > U E AD7"I A G U I W28 P I2d28 ] G P 8/9C: [ 8/:K AD9 U G2A 9;7G U & U d28 U 8 P I K *9 @ I KBK 8 P d2:_W28#9 I ? P GIE 8 P E : AD:BG U GeN ] G P 8/9C: [ 8#9 # G (8\W8 P d8 U 8 P IeA;:_G U I29 8 KBK I29(I ]"]K :U E I P L%J\G U E :BA;:_G U 9 ? 8 J\G @ 8 \J G / @ ]> A I AD:BG U I _K K L @ G P 8 \8 R ] 8 U 9C:_W28 ? 8 J I > 9;8 :BA;7F9 @ I KBK 8 P G U 8 9;7G >K E > 9C8I @ G P 8 `"U 8 K L E:_9DJ P 8SAD: [ 8 E^E G @ I2: U
8FE 8 `"U 8FA;G P A > G 9;:BAML I29 A;78 ] IeA;7 K 8 U deAD7 P 8 b > : P 8#E G U I W28 P I2d28%ADG A P I W8 P 9C8%AD78^G ? 9CADIJ K 8 ` 8 K E,E :_W :_E8 E ? L :K E 8 b > I K AD78A;G P A > G9;:BAML @ >K A;: ]K :B8#E ? L A;78AD: @ 8 P 8 b > : P 8#EADG A P I W28 P 9;8(I U G ? M9 A I2J K 8 N P 8\8 ` 8 K E5aG @ 8 I29 > P 8ADG P A > G 9C:BAML 8 C9 8\A #i2i i i2i N >K_K L J 7"8 @ GeA I2J AD:_J ] P G ? 8 SJ 8 KBK 9$c: 8 : P SJ 8 IeA h @ @ 8 J\I KBK AD7"I A A;7"8 P I U E G @/K L^G U I K : U 8%I A A;78 ] G 9C:BA;:_G U R i j // G ? 9MA I2J K 8 ` 8 K E :_9 K G J\IeA;8 E ? 8SA (8\8 U R @ @ I U E R Q@ @ 4 9MA I U E"I P E @ >K AD: I K 28 P 9C: @ >K I AD:BG U :U EI P :B8#9 G P @ G E 8 P I AD8
` 8 K E%: U : U : AD:_I KBK L/8 9CADI ?K : 2d 7ZA;78 G ? 9MA I2J K 8 ` 8 K E! G U 9C8#b > 8 U A K L 2 (8 G ? ;9 8 P W28VA;7"IeAVI 9;:Bd U : ` \J I U A U >@ ? 8 P GeN)JS8 KBK 9 ? 8#JSG @ 8 A P I ]] 8#E I29 9;7G U : U H:Bd 57 > 9I N > P AD78 P E 8#J P 8 I9C8 : U EG 8#9 U GeA K 8 IE ADG/I K I P d28 J 7"I U d 8
: U 57:_9:"@ :B;A 7 A; G Z57: d2d8 9CAD9 A;7I A @ G E 8 P I AD8 P 8#I2J AD:BW :BA;:_8 9 i5 i5 !$J\G PDP 8#9 ] G U E : U dZADG f)8/GeN #i65 I P 8 9;G @ 8\7G NI W2G P I ?K 8 NcG P J 78 @ GeA I R :K A;: ]K 8%G ? 9CADI2J K 8 ? G >"U EI P _: 8 9 G U J 78 @ GeADIJ DA :_J P 8 9 ] G U 9C8 78 @ GI A;A P I2J A I U AJSG U JS8 U A P IeA;:_G U
d P I2E:B8 U A 9: U E : P 8#J A;:_G U 9 U G P @ I K ;A G ? G >U E"I P :B8#9!W I U :_9;7%I A U G U P 8 IJ AD:BW8 ? G >U "E I P :B8#9 7:U EI P :_8 9 P I2E:B8 U A 9 ] G2: U A I I L N P G @ P 8#I2JSA;:_W28 ? G > U EI P :B8#9 P 8 ] 8 K_K : U dZJ\8 K_K 9 8 I2JSA;:_W28 ? G "> U EI P :_8 9 G U
G ]"] G9C:BA;8 9;:_E 8#9 GeN)I%JS8 KBK AD7 > 9NcG P JS8 A;7"8JS8 K_K ADG AD78 @ :_E"E K 8 eG NaAD78 dI ] G P J 7"I U"U 8 K? 8SA (8\8 U AD78 @ g57"8 J\8 K_K 9 A;7"IeA @ :Bd P IeA;8Q: U A;78 @ :_E"E K 8 G2N!J 7"I U"U 8 K 9ADI 8Q9;7G P A;8 P ] I ;A 79gADG P 8 IJ 7%A;7"8 9;G > P J\8 K : U 8 : U J\G @/] I P : 9;8A;7"8 E 8\ADI2: K 8 E 9MA P > JSA > P 8 G2N A;7"8 ? G >U EI P :B8#9V: 9CA P I AD8 E ? L%AD78 P 8 ] P 8 9;8 U ADIeA;:_W28 I
K 9(: U H!:_d
7":_J 7 ( 8VJ\I KBK A;78@;J 7"I UU 8 K : U d 8 8 JSA B (8 @ 8#I29 > P 8 E A;7"8VI W28 P I2d28E :_9CADI U JS8VGeN*IJS8 KBK I A 8#I2J 77 I K 9CA;8 ] N P G @ AD78%J K G9;8 9CA ? G >"U EI P L U G E 8 NcG P W I P :_G > 9 I U A E /4Q9 9C7"G U : U H:_d *A;78%I W28 P I2d28 E :U EI P L U G E 8 U 8 I P 8#9MA : U J P 8 I9C8#9 I29 (8 : U J P 8 I9C8 : AD7 7:_d278 P eAD78 P 8 IJ A;:_W : AML 5!G W28 P :BNcL AD7:_9 ] G9MA >K I A;8
'
? 8\d2: U 9gA;G/E G @ : U I AD8QE : > 9C:_G U I U E d P I2E :_8 U DA 9 ] G: U AD: U d I (I L N P G @ ? G >U EI P :_8 9 ] 8 P 9;:@ eG NZI29gIN >U JSA;:_G U G2N P 8 9 >K A 9 N P G @ A;7"8Q: @/] G9C8#E J 78 @ G2ADI2JSA;: E L JS8 KBK 9gJ I U E 8\A;8#J AI ] 8 P JS8 U A E : 8 P 8 U JS8 : U JSG U JS8 U A P IeA;:_G U G2NJ 78 @ GI A;A P I2JSADI U AI K G U d A;7"8\: P K 8 U deAD7& 578J\G U J\8 U A P I AD:BG U GeN J 78 @ GI A P I2JSADIJ ADI U A I K G U d 9;G @ 8 ] G P A;:_G U G2N A;78 U G U P 8 IJ AD:BW8 ? G >U EI P :_8 9Q:K I AD8 " 7: U E A;7"8 P 8 d2:_G U 9): U A;7"8
78 P 8 d P IE :B8 U A A;7 P 8 9;7G K E9QI P 8W :BG K IeA;8#E U !H :_d j I 8 : K_KB> 9MA P IeA;8AD78 9;8 E8 I2E [ G U 8 9VNcG P I ] I P A;:"K I P P 8 I K : [ I AD:BG U NQI JS8 KBK 7"I ]"] 8 U 9ADG 8 U AD8 P I E 8#I2E [ G U 8 : A : K_KU GeA/E 8SAD8 JSA/I U L09;:Bd U I K I U E : K_K AD78 P 8SNcG P 8 @ G W8 P I U E G @/K L 6)VGeAD8 A;7"IeA A;78#9C8 [ G U 8#9 I P 8 U GeA K : @ :BA;8 EZADG/A;78 P 8\d:BG U E 8 `"U 8#EFI9: U 9C:U A GeN E 8 IE [ G U 8/I P 8#I W 9 NcG P A (G E : 8 P 8 U A 9 $I W8 P Ied28#E G W8 P i P 8 I K : [ IeA;:_G U 9(8#I2J 37 &(: U H:Bd j ? (HG P ? G2A;7 9 J\G U 9;:_E8 P 8 E @ G E 8 P IeA;8 P 8 I2JSA;:_W : AD:B8#9
h
78 KB] P 8#E > SJ 8 A;7"8 ADGeA I K I @ G >"U A GeNE8 I2E [ G U 8/I P 8 I 57":_9 : 9;8 : AD7 @ G E 8 P I AD8 P 8 IJ A;:_W : AML ? G >U EI P :_8 9 I2JSA I29 9C: U 9 P 8 E > JS: U d A;7"8 J 7 8 @ GI ACA P IJ A I U A JSG U JS8 U A P IeA;:_G U U 8 I P AD78 @ @ I : U d ;A 78 * - d P I2E :_8 U A 9 K I P d8 P # G (8\W8 P U G U P 8 IJ AD:BW8 ? G >U EI P :B8#9 I K_K G A;78ZJ 78 @ GIeACA P IJ ADI U A J\G U J\8 U A P I AD:BG U DA G ?> : K E >] J I > 9;: U d^9;7"I KBK G 8 P
U G P @ I K : [ 8 E^d P IE :_8 U AD9 Q578#9C8 U 8 I P ? G >U E"I P L P 8\d:BG U 9 ? 8 J\G @ 8 E 8#I2E [ G U 8#9 7"8 U AD78 9;8 9;7"I KBK G d P I2E :_8 U AD9QE P G ] ? 8 K G AD78 ] P 8 9DJ P : ? 8#E DA 7 P 8 9;77G K E H > A;78 P @ G P 8 2I 9C : U J P 8 I9C8#9 AD78ADGeA I KaK 8 U deA;7 G2N ? G >U EI P LFE 8 J P 8#I29;8 9; 7:U A GeNE8 I2E [ G U 8 I P 8 I
578 U I A > P I K b > 8 9CA;:_G U%? 8 J\G @ 8 9' "7 :_J 7%G2N AD78 9;8 A (G 8 8 JSAD9:_9 @ G P 8 : @/] G P ADI U Ag: U J I > 9;: U d A;78 @ : U : @ >@ : U W 9 F5!G I U 9 (8 P AD7:_9 b > 8#9MAD:BG U (8 ] 8 P NcG P @ 8 E 9C: @ >"K IeA;:_G U 9 :BA;7 @ > J 7 K G 8 P AD7 P 8#9C7"G K E9 8* 8#J AD:BW8 K L8 K : @ : U I AD: U d I K_K E 8 IE [ G U 8 9 8 @ 8 I9 > P 8 E A;78(E 8 ] AD7 G2NAD78 @ : U : @ > @ : U $-& 2E8 `"U 8#E I29*A;78E : 8 P 8 U JS8 ? 8\A 8 8 U $ i'& $ ,i & IUE
1-$-&
NcG P ;A 78 A GZJ\I29;8 9VGeN$ I'& E 8 I2E [ G U 8#9 I U E $ ? &VG UK L^J 7"I UU 8 K : U d 8 G ? 9C8 P W8 EZA;7I AQG U I W28 P I2d28 A;7"8 E 8 ] ;A 7 eG N AD78 @ : U : @ >@ E 8 J P 8#I29;8 9 ? L #i ] 8 P J\8 U A $E 8 ] 8 U E : U d G U & 7 8 U A;78 P ^ 8 I P 8 U G E 8#I2E [ G U 8 9 &57:_9 : U E :@ : U ^W 9 Z:U E I P L P 8 I2JSA;:_W : AML 7"8 K_] N >K 5aG&I U 9 (8 P AD7:_9 b > 8 9CA;:_G U " 8 @ 8 I9 > P 8#E ,NcG P 7:_d27 G ? 9MA I2J K 8 ? G >U EI P L P 8 IJ AD:BW :BA;:_8 9
i5 J @ 9
8VG ? 9;8 P W28 E AD7"I AJS8 K_K 9I P 8 U GeAI ?K 8VA;G I2J\b > : P 8 9C:_d U I K I9 7:_d278 PP 8 IJ AD:BW :BA;:_8 9 K 8 IE A;G @ G P 8QJSG U
9 >@/] A;:_G U G2NgJ 78 @ GI ACA P IJ A I U A A;7 P G > d27G > A DA 78 G ? 9MA I2J K 8 ` 8 K E 57":_9Q: @/] I2: P 9 AD78 E: > 9;:BG U GeNgJ 7"8 @ G IeACA P I2JSADI U A A;7 > 9 aJ\8 K_K 9 U 8 W28 P P 8 J\8\:_W28 9;:_d U I K G P ? 8 J\G @ 8 A P I ]] 8 E NcG P K G U dZA;: @ 8 9 ] I P A;:"K I P K L^: U 9;: AD: U d >U ? : U EI P L P 8 IJ AD:BW :BAML8 7 :"K E
? 8 ] G2: U A;8#E^G > AQA;7"IeAQ: U A;7: E L 8 7"I W28J\G U 9;: 8 9CA;:_G U 9 I Ie:BAN > P AD78 P : U W28#9MAD:BdI A;:_G U 9
$
87"I W8gE 8 W28 K G ] 8 E IV9;: @ >K I A;:_G U ? I9C8#E @ G E8 K GeNJ\8 K_KB>"K I P K G J\G @ eG AD:BG U : U P 8 9 ] G U 9C8gA;GVA;: @ 8 I U E9 ] IeA;: 8 U JS8 9 A;78 J 7"8 @ GeA I2J AD:_J P 8 9 ] G U 9;8 GeN)A;78 JS8 K_K 9 8 W28 U AD7G > d27 :BA : G > V9 8 U G > d27 DA GZ7: U E 8 P \J 8 K_K)K G JSG @ GeA;:_G U I K G U 8 8 JSAQG2N 7:_J 7 :U EI P L P 8#I2JSA;:_W:BAML (I9 G ? 9;8 P W28#E I U E 8SR ]K Ie: U 8 E U AD78 K : @ : A 9 GeN ? GeA;7 K G 6I U E 7:_d27 ? G >U E"I P L P 8 IJ A;:_W : AML $J\G @/] I P 8#E9 :BA;7 J 78 @ GIeACA P IJ ADI U AVE : > 9;:BW :BAML-& J 78 @ G2ADI R :U EI P L P 8 I2JSA;:_W : AML #J\8 K_K 9)I P 8 8* 8#J A;:_W28 K L IeACA P I2JSA;8#E A;G ? G >U EI P :_8 9 9 K G : U d A;78 : P
78 U P 8 I2JSA;:_W : AML E G @ : U I A;8#9 9CG @ > J 7^J 7"8 @ GIeACA P I2JSADI U A:"@ 8#EZA;7"IeAVJS8 K_K 9 C9 : @/]K L P 8 JS8 :BW8 U G 9;:Bd U I K "I U EZ7"8 U J\8 E G U G2AQJ 78 @ 2G ADI R 8 AD78 P 8SNcG P 8 G ? 9C8 P W8 I U G ] AD: @ I K U G U [ 8 P G ? G >U EI P L 9 > P NIJS8 P 8 IJ A;:_W : AML A;7I A78 KB] 9 AD78 JS8 KBK 9 E 8\A;8 JSA 9C:_d U I K)@ G9CA *8 8#J AD:BW8 K L I U E J\G U 9;8 b > 8 U A K L @ G9MA P I ] : d27
G U"K LJ I DP P :_8 E G > A)NcG P h O P I U E G @6] G P G > 9EG @ Ie: U 9 A;78 9;: @ >K I A;:_G U 9!G 8 P ] G9;9;: ?"K 8d > :_EI U JS8I29!ADG 7"G &A;G 8 U d2: U 8\8 P J 78 @ : P NI2J\8 9 GeNIF9DJ\I G K E A;G^8 U 7"I U JS8 A;78 K : 28 K :_7G G E I U E 9 ] 8 8 E GeN9 > J\JS8#9;9CN >K AD:_9D9 > 8 : U d P G A;7 AQ:K I AD:BG U 9 G2N A;7: P N > P A;78 P (G P : U E 8 W28 K G ] : U d ? G2A;7 @ G P 8 P 8#I K :_9CA;:K IeA;:_G U 9 I9; 8 KBK I98SR ] 8 P : @ 8 U A I K I29D9DI L 9(G2NJS8 KBKaK G JSG @ GeA;:_G U : U J\G @/]K 8SR O ] G P G > 9 9MA P > JSA > P 8 9
obstacle field
2
chemoattractant source line
cell launch line
1
chemoattractant sink line
y (mm)
overall gradient direction
0
1 x (mm)
2
'U 4o& ")(* $) 6$) -% #"'&H")(0 5 !,f")U 2 424 2 424 -%(04k 1*&H")(0 5 7 !4o&!(0YE) -% !7$) ^10(0 7- "Z") ")U7 $)(0/5U#"S H, ")U 6 H$) 5 -7 !4o&!(0J67$) D 3-'U 42 5&H"%"%$'&H3"'&!#"I")U&H"( 97-% -")U$) 57/5U !7"")U 54o&!(0V&Hm(0-$)342 HC5me#g+&^-%(07am10(0 k&H" KLi ?E0c2424+E ] 1010- &H$)21*&!7 'U J,$) !4 $'&! 54 6 !-%([")(* ! - 5 & 10(0 - "S") m")U7L103, "k H,]")U7^6 !$) ! - 7 !4o&!(0YE 3$)(0 D7(0 e 577&H$%gF 5 7([")(0 57-I !+e !")U RU7 42 Q& "%"%$'&!3"'&H#" 57 #"%$'&H")(0 5+&! 101Y10 # !42 !")(0 5V& $)S 7, !$) E
0.25
0.5
0.15
average pore size (mm)
φ = 0.80 φ = 0.85 φ = 0.90 φ = 0.95
0.2
normalaized count
0.1
0.05
1.2
0.4
1.15
0.3 1.1 0.2 1.05
0.1
0
0 0
0.1
0.2
0.3
pore size (mm)
0.4
0.5
tortuosity
0.8
0.85
0.9
1 0.95
φ
;>&5B !$)j-%( (*- "%$)(0e77")(0 57-., !$OC!&H$)(0 57-O6 H$) 5-%([")(0 - 8: E;eB m&!^6 H$)-%( S;-% 510(*^10(0 B &HL 54o&H(* ") !$%")7 5-%([" g ;> &H-%U F10(*7 BCD- E]: EOTU7Z$) -% 1[")-I&H$) &CQ3$'&H/5 HC53$ c?k$)&H10( &H")(0 57-` !,")U 7 !4o&!(0YE
0.5
1.0
y (mm)
1.0
0.9
2.5 3.0
2. 0
1.5
0.8 0.7 0.6
(a) 1.2 1.3 x (mm)
1.0
0.2
1.0
1.1
y (mm)
0.8
0.5
0.3
0.9
1.4
1.5
1.5 2.0 2.5
0.5 1.0
0.7 0.6
(b)
0.5 1.0
1.1
1.2 1.3 x (mm)
1.4
1.5
y (mm)
1.0 1.5
0.5
0.1
0.9
0.03
0.01
0.3
1.0
0.8 0.7 0.6
(c)
0.5 1.0
1.1
1.2
1.3
1.4
1.5
x (mm)
6$) -% #"'&H")(0CQ 10 # !42 !")(0 5V6& ")U - !,f&2-% 10 3")(0 5V !,f 1010-") h&H$'+")U 10(0 -% 57$)3k10 #& ") & "n i c!E 2424 67$) D (07/m'U 42 5&H"%"%$'&!R"'&!#"S !D")(0D ! -%1[gVh([")U $'&H")2 H, i P5?5?+67/HUE D 510(* $)CQ - &H$)k")U ^10 # !42 !")(0 5 6 &H")U7-S !,]")U7 -% 10 3") 1010- 8&! & $%$) h-o(0(0&H")+")U7m4o& !$F([$) 3")(0 5 H,Z")U 6& ")U - E Z&!-%U $)CQ -2& $)JRU7 42 Q& "%"%$'&!3"'&HD"^(*-% #3 5 #"%$'& ")(* ! !D") !7$)-&QB !e - "'&!31*me 5 & $%g $)&!3")(0CD([" g ; i ?5B k;eB m D7R$'&H") e 577&H$%go$)&!R")(*CD([" g ; i c ? 4 -'B ; B_`(0/5U e 5 & $%gF$) &!3")(0CD([" g ; i c? 4 H-'BRE
j
transit time (105 s)
10
φ = 0.8
7.5
0.85
5
0.87
0.82 0.92
0.90
2.5
0.95
0 0
0.25
0.5
0.75
1
-3
k (10 cm/s) 2 0.85
φ = 0.8
transit time (105 s)
1.8
1.6 0.82
0.87 0.90 0.92 0.95
1.4
1.2
1 0
0.05
0.1
0.15
0.2
-3
k (10 cm/s)
9 m&H+"%$'&!7-%(0"")(04258Y8CD- EO 5e7- "'&! 10Se 577&H$%go$)&!R")(*CD([" g#8 87, !$IC5& $)(0 5 -6 H$) 5-%([")(0 - 89: E
fraction of trapped cells
1
φ = 0.80
0.8
0.85 0.87
0.82 0.90
0.6
0.4 0.92
0.2 0.95
0 0
0.2
0.4
0.6
0.8
1
-3
k (10 cm/s)
I 7$'&H3")(0 5+ H, "%$'&!676 3 101*-ICD- E. 5e7- "'&! 10 e 57 & $%go$)&!3")(0CD([" g#8 98,G H$IC5& $)(* ! -6 !$) !-%([")(*3- 89: E
4
Distance from the pore wall (10 mm)
φ = 0.80
3
k=10-4 cm/s
k=10-5 cm/s
2 k=0 cm/s 1
3 k=10-4 cm/s k=10-5 cm/s 2 k=0 cm/s
1 1
1.25 x (mm)
1.5
1
1.25 x (mm)
1.5
6
Distance from the pore wall (10 mm)
5 φ = 0.90
φ = 0.95
-2
Distance from the pore wall (10-2 mm)
φ = 0.85
-2
Distance from the pore wall (10-2 mm)
4
4 k=10-4 cm/s 3
k=10-5 cm/s
k=0 cm/s 2
5 k=10-4 cm/s 4
k=10-5 cm/s
3
k=0 cm/s
2 1
1.25 x (mm)
1.5
1
1.25 x (mm)
1.5
TU7V& C53$'&!/! (0- "'&! 3J !, 1010-o,$) 54 ")U7+ 10 5-% - "m 5e7- "'&! 10Jhj&H1*1I,G H$mC!&H$)(0 57-o6 !$) 5-%([")(0 - 8`: 8&! 5e7- "'&! 10 e 577&H$%go$)&!R")(*CD([")(0 - 8 E
i
2.0
(a) y (mm)
1.5
1.0
0.5
0.5
1.0 x (mm)
1.5
2.0
5
-2
fractional dead zone area (10 )
0.0 0.0
(b) 4
3
2
1 0
0.2
0.4
0.6
0.8
1
k (10-3 cm/s) 9^;>&5B `&5 3 5 3-`(0V&^$) 67$) -%3D"'& ")(0CQ $) &!10(&H")(0 5 !,O")U : i ?E !?F !e - "'&!31* 31 +, !$`")U7 &!-%k !, i ?DEL;eB 7$'&H3")(0 5&H1Y") H"'&!1Y7&! 57 &H$)&kC- E 2,G H$Z: i ?E 5?2&H ?E ?DE
U
? :
6 C
1
!
G P E8 P DA G : U 2W 8 9CA;:_dIeA;8 AD78 W I9;J >K I P : [ IeA;:_G U 2G N I&A;: 8 8 U d: U 8\8 P 8 E JSG U 9MA P > JSA/ (8 U 8\8 EA;G >U E 8 P 9CADI U E A;7"8 P G K 8 GeN ] G P G > 9 @ :_J\GI P J 7:BA;8#J A > P 8 G U AD78 NcG P @ eI A;:_G U GeNVI J\I ] : K_K I P L U 8\A G P U ] I P AD:_J >K I P AD78 8 W I KB> I A;:_G U GeN I U d2:_G2d28 U 8 9;: : P 8#9 I,b > I U A;:BADIeA;:_W28 >"U E 8 P 9CADI U E : U d GeN AD7809C8 U 9C:BA;:_W : AML G2N8 U E G2A;78 K : A;:_G U G2N d P G A;7^NIJ A;G P J\G U J\8 U A P I AD:BG U : AD7: U A;7"8 ] G P G > 9/JSG U 9CA P > J A 5aG @ 8\8\A/A;7: A;8#E 8 I9;9;8 9D9!A;78 : U"> 8 U JS8 G2N 0 X H
K G2dLFG2N U 8 K L NcG P @ 8#E \J I ] : KBK I P L U 8SA (G P 9V: U A G K : @ : AD: U d^J I29;8 9 GeN(I P 8 K I AD:BW8 K L^7:Bd7 I U E [ 8 P G 0 X H E 8 d P I2EIeA;:_G U P IeA;8 98 @ ]"K G L : U dVAD7 P \8 8 9MA P IeA;8 d2:_8 9GeN 0 X H ] P G E > J AD:BG U $ &G UK L I K : U 8 9;G > P JS8 -$ h'& K : U 8%9;G > P JS8 ] K_> 9 JSG U A P G K_K 8#E P 8 K 8 I29;8 Ge!N 0 X H N P G @ 8 @ ? 8 EE8 E ] G: U A9;G > P JS8#9 7":_J 70I P 8 P I U E G @/K L E :_9CA P : ?> A;8#E
G U A;7"8^9;G K :U EI P :B8#9 (I U E $ & K : U 8 9CG > P JS8 ] KB> 9%JSG U A P G KBK 8 E P 8 K 8#I29;8ZG2N 0 X H N P G @ DA 78 9CG K :"U EI P :_8 9 = A P IeA;8\dL @ : @ : IeA;:_G U : U 7:U EI P :B8#9 P 8 K 8 I29;840 X H 1 8%: U W28#9MAD:BdI A;8 AD78 8 8 JSA G2NAD78%A;8 @/] G P I K P 8 K 8#I29;8 ] P G `"K 8%G U A;7"8 W28#9;9;8 K d P G AD7ZI U E : U `"K A P I AD:BG U : U A;G AD78 A;78 ] G P G > 9 @ 8 @ ? P I U 8
U
A;7: E L I ]]K L : U d0E: 8 P 8 U A ] P G @ eG AD:BG U 9CA P I AD8\d2:_8 9 (8 K G G I A/A;7"8 I U d:BGd28 U 8 9;:_9 ] P G JS8 9D9 : U 9C: d7 A;G @ Ie: U ADIe: U :BAD9
h
:BA;7"G > A 9;:_E8%8 8 J A 99 > J 7&I29 A >"@ G P d P G A;7 %4 K 9;G aA;78 P G K 8 9 G2NI U d2:_G2d8 U : E 8 9
I U I K d2G P :BA;7 @ NcG P d28 U 8 P I A;:_G U G2N I ] G P G > 9 9;: @ >K IeA;:_G U EG @ Ie: U $ h'&gIN >K_K L%AD: @ 8 P 8 9;G K W28#E `"U :BA;8 E : 8 P 8 U JS8 9CG KB> ;A :_G U 7: P @
$ &
JS8 KBK!@ GeA;:_G U ADG%A;78 9C: @ >K ADI U 8\G > 9 K LZ8\W2G K W : U d%JSG U JS8 U A P IeA;:_G UZ` 8 K E^GeN0 X H 578 @ G E 8 K J\G U 9;:_E8 P 9(A;78 cN G KBK G : U d N >U E"I @ 8 U ADI K 8 W28 U A 9 ;$c: & P 8 K 8#I29;8 GeNa8 I 0 X H N P G @ I K : U 8 9;G > P JS8 P I U EG @/K L/E : P JS8#9 G U ;A 78 9CG K :U E"I P :B8#9 I U E C9 G K :U EI P :_8 9 $c:_: & E: > 9;:BG U G2N"0 X H : U AD78 E G @ 2I : U $c:_:_: & P I U E G @/U 8#9;9 : U A;78 E: P 8 JSA;:_G U GeN JS8 KBK@ :_d P I AD:BG U $c:_W-&J 78 @ GeA I2JSA;: A 9$ ? P I U J 7": U d2&gN P G @ A;7"8 ] P : @ I P L W28#9;9;8 K G P G2A;78 P U *8 K L 8#9MA I ?K : 9C:_G U G2NaI 9 ] P G > A;A : ] A;G I U G2A;78 P 9 ] P G > A AD: ] G P I U G2A;78 P
9 ] P G > A$I U I29CA;G @ G 9C:K I P >] A I 28 I U E >"U : NcG P @ E 8\d P IEI AD:BG U G2N10 X H Q> P @ G E 8 K E G 8 9 U GeA \8 R ]"K E8 7"I ] A;GeA I R : J 7/I9 JS8 KBK I A;ADI2J 7
@ 8 U A ] G K I P :BAML ad P G A;7 I U E0E : 8 P 8 U AD:_IeA;:_G U I P 8 @ 8#E :K 8#9 #ij # i # G (8\W8 P : U A;7: EL (8 _: d U G P 8 DA 78 P G K 8 G2N JS8 K_K 8\RA P IJS8 KBK_>K I P @ I A P :BRZ: U DA 8 P I2JSA;:_G U 9NcG P 9;: @/]K :_J\: AML 8 I;9 9 >@ 8 A;7"IeAVG > P 9 >? 9CA P I A;8 ] P G W :_E8 9 9CA P > J A > P I K 8 K 8 @ 8 U A 9 P 8#b > : P 8 E cN G P ;A 78I U J 7G P Ied8 E 8 ] 8 U E 8 U AVJS8 K_K 9 9CG AD78\L^J\I U IeACADIJ 7FA;G/A;7"8 9 > P NIJS8 I U E @ :_d P I A;8 U G P @ I KBK L U d28 U 8 P I K U *8 K LZNcG P @ 8#E^W28 9D9;8 K 9VI P 8 K 8 I ^L I U E GeN A;8 U P 8 @ G E 8 K JSG U AD: U > G > 9 K L h U JSG P ] G P I AD:BG U G2N @ IeA > P I A;:_G U I U E P 8 @ G E 8 K : U dZGeN AD78 W I9;J >K IeA > P 8 P 8 b > : P 8 9Q: U J KB> E : U dZW I P :_G > Q9 9C:_d U I K : U d @ G K 8#J >K 8 9 9 > J 7 I9Q4 U d I U E 5:_8 h I9 ( 8 K_K I29 GeAD78 P J\8 K_K AML ] 8 9 9 > J 7 I9 ] 8 P : 8 U JS8#E ? L A;78 : U A P : 9 ] 7 L 9;:_G K G2d2:? 9;L 9MAD8 @ 9 V: U J KB> E : U d
I U d2:_G2d28 U : J 7 I29 ] 8 P : 9;J K 8 SJ 8 KBK 9 I U E%: U 7: ? : ADG P 9C h T U E 8 P 9CADI U E : U d/A;78 9;L U 8 P d2: 9C8#E : U J 7"8 @ eG A I R :_9(I29D9DI L 9 : AD7FI ] P : @ I P L/W28#9;9;8 K G U G U 8 9;:_E 8 8 I 0 X H K : U 8 ;9 G > P \J 8VG U ;A 78 GeAD78 P 9;:_E8
I U E I @ I J P G ] G P G > 9 @ 8 @ ? P I U 8 : U ? 8SA (8\8 U 8/JSG U 9C: 8 U ?> P d28 P j AD78 8SR : P JS8%: 9 @ 8 @ ? P I U 8 : U G P E8 P ADG @ :_d P I AD8 A;G I P E 7":Bd78 P 0 X H JSG U JS8 U A P I A;:_G U 9 Q> P dGI K :U E8 P 9MA I U EZ7G 0 X H0A P I U 9 ] G P A : U 9C: 9 @ 8 @ ? P I U 8 P 8 d >K I AD8 9JS8 KBK
@ :Bd P IeA;:_G U
578 ADI9^GeN(I `"U :BA;8%E : 8 P 8 U J\8 9;G K W28 P :U JSA;:_G U eG N ] G9;:BA;:_G U I U E A;: @ 8 $ ? 8 & 8/JSG U 9;:_E 8 P I `"U :BA;8 A G E : @ 8 U 9;:_G U I K E G @ I2: U GeNgI P 8 I : U "7 :_J 7 0 X H E : > 9C8#9 *E 8 d P I2E 8#9 I U E/:_9 ] P G E > JS8#E ? L/9;G > P JS8#9gI U E >] ADI 28 U%? L/8 U E GeAD78 K : 9)E 8 d P I2EI A;:_G U 578 9;G > P JS8#9!I P 8I ] P 8#9;J P : ? 8 E 9C8\AG2N U G E 8#96 7_: J 7 : U E :_W: I KBK L : U M8 JSA0 X H : U A;GQA;7"8 E G @ Ie: U IeA ] P 8#9;J P : ? 8 E P I A;8#9 $ ? 8 & : P JS8A;8 P @ P 8 ] P 8 9;8 U AD: U d 9;G > P J\8 9 G2N60 X H 578 U A;7"8
A;8 P @ $
>$ & @ I L ? 8 P :BACAD8 U^> 9;: U d AD785 P G8 U 8 J 8 P E 8 K ADI N >"U J AD:BG U I9 I/9 >@ G W28 P AD78 ] G2: U A 9;G > P JS8#9 $
>$ & -$ &
$ h'&
78 P 8QA;78 >U 9 >? 9;J P : ] A;8#E : U E :@ G W28 P AD78JS8 KBK 9 I29(NcG KBK G 9
82*& !
4$ ?
$ &
78 P 8 >U 9 >? D9 J P : ] ;A 8 E&I U E E 8 U G2A;8 A;7"8 ] G9;:BA;:_G U G2N ;A 7"8/J\8 K_K 9*I U E ! E 8 U G2A;8#9VAD78 > ] A I 28 P I A;8 JSG U 9MA I U A GeN A;7"8 JS8 K_K 6.(8#J\I > C9 8 JS8 K_K ] G9C:BA;:_G U 9(I P 8 G K IeACAD:_J\8 NcG P 9C: @/]K :_J\: AML (8V: @/]K 8 @ 8 U A;0 X H > ] ADI 8QIeAAD78 ] G9;: AD:BG U
GeN(A;7"8 JS8 K_K 9**J\8 U A;8 P ? L K : U 8#I P : U AD8 P ] G K IeA;:_G U G U K L I @ G U dFA;78/NcG > P U G E 8#9 U 8 I P 8#9MA A;7"8 @ 4 JS8 KBK K G J\IeA;8 E0IeA I U I P ? :BA P I P L ] G9;: AD:BG U "7"I9VIeA @ G9CA NcG > P U 8 I P 8#9MA U 8\:_d27 ? G P U G E 8#9 NcG P @ : U d/A;78 W28 P A;: I P 8JSG U ADIe: U : U d/A;7"8 JS8 KBK J\8 U A;8 P 8a8SA A;78/W8 P A;8SR ] G9;: AD:BG U 9 ? 8 K I ? 8 K 8 E JSG >"U P AD8 P J K G J 9 : ] ADI 28 ? L DA 78 \J 8 K_K*? 8*$i ;i'& $ DDi'& $i &I U E $ D & HG P 8SRI @/]K 8 A;78 K : U 8 I P K L : U A;8 P ] G K I A;8#EFW I KB> 8 GeN >] A I 8 U 0 X H ? L JS8 KBK IeA A;78 U G E 8 $ i i'&! : KBK*? 8J\I K J >K I A;8#EZI9 0
4$ i;i * &
6! $ iDi'&$(*
$ 2&
= : @ : K I P ADG a5 G U d I U E + > I U (8 I29D9 >"@ 8 0 X H E 8\d P IEI AD:BG U I9I ` P 9MA G P E 8 P P 8 IJ A;:_G U B: A;7 P I AD8 JSG U 9MA I U A : AD7 A;7"8 E : @ 8 U 9;:_G U G2N A;: @ 8F 57"8 ] P G E > J A J\I U A;78 P 8\NcG P 8 ? 8 : U A;8 P ] P S8 AD8 E I9QI P 8#I2J AD:BG U W28 K G J\: AML 4V9(: 9C:_G U ] P G ?K 8 @ 9 8 JSG U 9;:_E 8 P AD78 E : @ 8 U 9C:_G U"K 8#9;9 ] I P I @ 8\A;8 P 7: P 8 9" 78\A;78 P E : > 9C:_G U G PP 8 IJ A;:_G U E G @ : U IeA;8 9(ADG ? 8 O I @ 2G 7 K 8 P U >@ ? 8 P O I
3
$ &
78 P 8 8Q7"I W28 J 7G9;8 U A;78 E G @ I2: U C9 : [ 8 I9A;78 P 8 K 8 W I U A K 8 U deA;7F9;J I K 8 )HG P AD78 ] I P I @ 8SAD8 P 9gd:BW8 U : U 4 ] ] 8 U E :BR 4 $)3 6i 5>7 J @ e9 h #i65 J @ & ' (8 JSG U 9;:_E 8 P A GJ I29;8 9)G2N I 7:_d27 O I GeN (J\G PDP 8#9 ] G U E : U dQADG # i
7 P 5 I U E O I i $: 8 i & 5!G C9 G K W/ 8 NcG P $ ? 8 & 6 (8 I29D9 >"@ 8/AD7"I A A;78 : U :BA;:U E"I P L JSG U E :BA;:_G U 9 I9(NcG K_K G 9
8 8 U NcG P J\8 ] 8 P :_G E : 9C:_G U eG N 0 X H JSG @/]K 8\A;8 K L
i @/@ ! I9;9 >@ : U d
HG P : U AD8 P U I K 9;G K :_E ? G >U E"I P :B8#9 2 (8 : @/] G9;8QAD78 NcG K_K G : U d%I/JSG U 9CADI U A " > R ? G >U EI P L J\G U E: AD:BG U
3 $ *&
$ &
:"@ 8 P : 8#9 GeNAD78 P 8 K 8\W I U A(b > I U A;:BA;:_8 9g: U AD7: P 8 9h @/@ h @ @ 5 7 > 9 A;78 K I A;A;: A d28 U 8 P I A;:_G U A;8 P @ 8 E K I P L/IeAI U L AD: @ 8QA;7 P G > d27G > AgAD78 ) 8 69
@ ? P I U J 7: U d B J\I U G J\J > P N P G @ A;78 ] P : @ I P L W28#9;9;8 K G P I U L U 8* 9;: @ >K I AD:BG U HG K_K G : U d 5aG U d I U E + > I U 2 (8 A P 8 IeA9 ] P G > ANcG P @
K L NcG P @ 8 E J I ] : K I A;:_G U 9MADG J 7I29CA;:
J\I KBK L 578 ] P G ? I ? : K :BAMLA;7I A / I 9 ] P G > ANcG P @ 9N P G @ I 2W 8 9D9;8 K 9C8 d @ 8 U A: U I A;: @ 8 : U A;8 P W I K (*g:U J DA :BG U I29(NcG K_K G 9
*( $( 1 #$ *&
$ &
:@ ] P G ? I ? : K :BAMLGeN 9 ] P G > AFNcG P @ I AD:BG U ] 8 P > U B: AFAD: @ 8&I U E W28#9;9;8 K K 8 U 2d A;7 1 $#*& :_9 I ;A 7 P 8 9;7G K E N >U J A;:_G U 7:U A DA 78 : U"> 8 U J\8 G2N0 X H SJ G U JS8 U A P IeA;:_G U G U 9 ] P G > A NcG P @ IeA;:_G U ] P G JS8 9D9 9 > J 7 A;7I A ? 8 K G I^JS8 P ADI2: U JSG U JS8 U A P IeA;:_G U I U d2:_G2d8 U 8#9C: P I U E 7:_d27"8 P A;7"I U IFD9 I A > P IeA;:_G U
78 P 8
JSG U JS8 U A P I A;:_G U A;78 P I A;8 eG N I U 2d :_G2d8 U 8#9C: E > 8 A;G 9;IeA > P I AD:BG U GeN JS8 K_K P 8#JS8 ] ;A G P 9& #i #i HG KBK G : U d 5!G U d/I U E9+ > I U - 8 @ G E 8 K A;7:U JSA;:_G U I2(9 NcG KBK G 9
1
i i $)*& \8 R ] $# A &.
78 P 8 :_9 I AD7 P 8 9;7G K E0JSG U JS8 U A P IeA;:_G U ? 8 K G 9CA P 8 U d2A;7
7:_J 7&9 ] P G > A NcG P @ I AD:BG U E G 8#9 U GeAG J J > P I U E
j
$ i &
:U A;8#E cN G P ? L : U SJ G P ] G P I A;:_G U GeN I U I W28 P I2d28QJ\G U 9CADI U A J\8 K_K E 8 U 9C:BAML I K G U d ;A 7"8 K 8 U d2A;7 G2NaJ\I ] : K_K I P L $JS8 KBK K 8 U deA;7 & 7: K 8 Q8 I29D9 >@ V8 I JSG U 9MA I U A U >@ ? 8 P GeNaJ\8 K_K 9I K G U d AD78 ] P : @ I P L W 8 9D9C8 K A;7 P G > d27G > A A;7"8Z9;: @ >K IeA;:_G U !A;7"8 U >@ ? 8 P GeN JS8 KBK 9 I K G U d^A;7"8 U 8 J I ] : K_K I P :_8 9 : U J P 8#I29;8 9 I29A;78 L 8 K G U dIeA;8 ^5 7"8 K 8 U d2A;7%: U J P 8 I9C8GeN*I J I ] : KBK I P L J I U%? 8VE > 8 ADG ] P G K : Nc8 P IeA;:_G U I U E @ :_d P I A;:_G U G2N 8 U E GeAD78 K :K I AD8 E A;G%E 8\A;8 P @ : U 8 78SAD78 P I U I29CA;G @ G9;:_9(7"IE A I 28 UZ]"K IJS8 8 A P 8 IeA ? P I U J 7: U d NcG P I K_KU 8* K L NcG P @ 8#E W8 9D9C8 K 99;: @ : K I P A;GFAD78 ] P : @ I P L^W28 9D9;8 K 5 7 > 9A;78 U >@ ? 8 P G2N(9 ] P G > A 9 J 7I U d 8 9 : AD7 AD: @ 8%E > 8 ADGFd8 U 8 P IeA;:_G U $ ? P I U J 7: U d2&VI U E E 8#I A;7 $I U I29CA;G @ G9;:_9 & 8 A;8 P @ : U I AD8 AD78%9C: @ >K I AD:BG U IeAQAD: @ 8 # iZE"I L 9 57: P I AD:BG U I29 J 7G9;8 U A;G ? 8
K G U d/8 U G > d7 ADG P 8\W8 I K AD78 U 8\A G P 9CA P > JSA > P 8 I U EZW28#9;9;8 K : U `"K A P I AD:BG U : U A;G ;A 78 ] G P G > 9 @ 8 @ ? P I U 8 U I U d2:_G2d28 U 8 9;:K I P U 8SA (G P J\I U ? 8 b > I U A;: ` 8 E > 9C: U d ] I P I @ 8SA;8 P 9 9 > J 7 I29 U >@ ? 8 P G2N W28 9D9;8 K 9 ] 8 P >U :BAV9 > P NIJS8 I P 8 I @ 8#I U W28#9;9;8 K K 8 U d2A;7^I U E A;78 8\R A;8 U A G2NJ\I ] : KBK I P L%: U W I29;:_G U : U A;G A;7"89;J I G K E: 7 : 9 @ 8 @ ? P I U 8 > 9C: U d^E : 8 P 8 U A P I U E G @ 9;8\8#E9QI U E G W8 P 7 :_J 77 8/I W28 P I2d28 A;7"8 P 8 9 >K A 9
8 9CA > E L
1 - ! J\I ] : KBK I P L U 8SA (G P ] I A;A;8 P U 9 I ]]K L : U d
AD78 A;7 P 8\80 X H P 8 K 8 I29;8Q9CA P I AD8\d:B8#9 : U $ &gG U K L I W8 P A;: P JS8 /$ h & W28 P AD:_J I K(K : U 8^9CG > P JS8 ]"KB> 9 AD8 U P I U E G @/K L&E :_9CA P : ?> A;8#E ] 2G : U A/9;G > P JS8#9 G U AD78F9;G K :U E"I P :B8#9 I U E $ &QW28 P A;: P J\8 ]K_> 9 : U DA 8 P U I K 9;G K :_E ? G >U EI P :_8 9 P 8 K 8 I9C8 0 X H 78 @ G2ADIJ A;:K AD9 : U&U 8 W8 9D9C8 K 9 7: K I A;:_G U P 8 9 >K AD93 (8 ] P 8 9;8 U AV: U H!:_d h/8 @/]K G L : U d 9MA P IeA;8\dLFh/I U E HG P 8#I2J 7 9MA P IeA;8 d2L A;7 P 8\8 E:_9CA;: U J A 0 X H P 8 K 8#I29;8 E > P I A;:_G U 9 GeNVh )I U E i E"I L 9 I P 8 JSG U 9C: 9;8GeN)AD78 78\A;8 P Gd28 U 8\G > 9 9MA P > JSA > P 8G2NAD78 ] G P G > 9 E G @ I2: U /)VGeAD8
A;7I A! 7": K 8 A;7"8 @ IMG P :BAMLGeNaJ I ] : K_K I P :_8 9)d P G ,A;G I P EAD78 K : U 8Q9;G > P JS8 e : U 9CG @ 8 J\I29;8 9J\I ] : K_K I P :B8#9NcG P @ K G G ] 9I U E/: U
9;G @ 8VG2A;78 P J I29;8 9gA;78 L/J 7"GG9C8 I K A;8 P U IeA;8VE: P 8 JSA;:_G U 9 # G (8\W28 P 2A;78 W28#9;9;8 K U 8\A G P ] I A;A;8 P U 9(I P 8QJ K 8#I P K L/E : 8 P 8 U A NcG P 8#I2J 7^J\I9C8 9CA > E L
578J I ] : KBK I P L U 8\A G P ] I ACAD8 P U 9 : U H!:_d h-$I J &gNcG P 9CA P I AD8\d2LFh P 8 W28 I K A;7"IeA : AD7 9C7G P AD8 P P 8 K 8 I9C8 E > P I AD:BG U 9 Nc8* (8 P U *8 K L NcG P @ 8 F E W8 9D9C8 K 9(d P G : U A;/ G AD78 @ 8 @ ? P I U 8 : U J\G @/] I P : P I A;:_G U - 8 G ? 9;8 P W28QA;7"IeAVW28#9;9;8 K E 8 U 9;: AMLZ: U J P 8#I29;8 9 9;:Bd U : ` J\I U A K L U #8 I P A;7"8 8 U A P I U SJ 8GeN ;A 78 @ 8 @ ? P I U 8 QU AD78 GeAD78 P 7I U E' : AD7 K G U d28 P P 8 K 8#I29;8 ] 8 P :_G E9Nc8* (8 P W8 9D9C8 K 9A P I W8 P 9C8A;7"8 8 U AD: P 8 ] G P G > 9 @ 8 @ ? P I U 8 G @/] I P : P IeA;:_G U 9 NcG P 9CA P I A;8 d2L : U H:_d -h $ E N &(9C7G 9I/9;: @ : K I P A P 8 U E U 9 ] : AD8 G2NaAD7_: 9V9C: @ : K I P : AML 2 8 G ? 9C8 P W8QI/9C:_d U : ` J I U A: U J P 8#I29;8 : U U >@ ? 8 P eG N U 8 K L I2E"E : AD:BG U G U 8 J\I U : U I ]"]K L : U d 9CA P I A;8 d2L
NcG P @ 8 E/W28#9;9;8 K 9)NcG P 9CA P I A;8 d2L NcG P I K_K AD78 P 8 K 8 I9C8 ] P G `K 8#9 : U SJ G @/] I P :K I P U 8\A G P %: A;:_G U GeNg9;G > P JS8#9 I29 8 KBK I29 A;78 G W28 P I KBK*@ : J A > P 8 GeN A;7"8 ] G P G > 9 @ 8 @ ? P I U 8 5!G 8 K_> JS: 9;8VI AgA;7: 9;:BG U A;7 > 9 ;A 7"8Z7:_d27 P IeA;8FGeNQE8\d P I2E"I A;:_G U 9 I @/] 9 ;A 78^8 8 JSA 2G N 0 X H K : U 8^9;G > P JS8 7: K 8 A;78 ] P 8 9;8 U J\8 GeN)A;78 G ? 9CADIJ K 8 9 : U J P 8#I29;8 9AD78 E : > 9C:_G U A;: @ 8 9;J I K 8 ? 8#J\I > C9 8 GeN)A;78 7_: d27 E 8 d P I2EIeA;:_G U P IeA;8 0 X H J K 8 I P 9 P I ] :K A 9: U^U G U 8 W8 9D9C8 K NcG P @ IeA;:_G U
U
= A P I A;8 d2L h *9C: @ : K I P A;G^9MA P IeA;8 d2L P 8 IJ A;:_G U E G @ : U I AD8 9 E : > 9C:_G U I U E ? 8#J\I > 9C8 eG N(7:Bd7 E 8 d P I2EIeA;:_G U P I AD8 0 X H P 8 K 8#I29;8 E ? L K : U 8Q9;G > P JS8 J K 8#I P 9 P I ] : 9;8 NI P : U ADGA;7"8 @ 8 @ ? P I U 8 A;78 P 8\NcG P 8 A;78Q8 8 JSA GeN K G J\I K : [ 8#E P 8 K 8#I29;8 ? L^8 @ ? 8 EE 8#E 9;G > P JS8#9 :_9 ] P G U G >U J\8 E U H!:_d ? (8G ? 9;8 P W28 9C8 2W 8 P I K P 8 d2:_G U 9 : U 9;:_E8A;7"8 G ? 9MA I2J K 8 ` 8 K E I A/ 7":_J 7 ( 8 7I W28 I/7:_d27 JSG U JS8 U A P IeA;:_G U GeN60 X H 578 9;8 P 8 d2:_G U 9; 7":_J 7 I P 8 K G J I A;8#E^I P G >U E A;7"8 8 @ ? 8#EE 8#E ] G2: U A 9;G > P J\8 9Q7"I W28 @ I2E 8 A;7"8/J\G U J\8 U A P I AD:BG U ] P G `"K 8 : U "7 G @ G2d8 U 8 G > Q9 : U 9C: 9 @ 8 @ ? P I U 8 :_d27
H J\G U J\8 U A P I AD:BG U 9 U 8 I P A;789;G > P JS8#9 ?K : U EZA;7"8QAD: ] J\8 K_K 9(ADG A;78 G W8 P I K_K J\G U J\8 U A P I AD:BG U d P I2E:B8 U AADG (I P E X ;A 7"8 K : U 8%9CG > P SJ 8/I29QA;78%d P IE :_8 U AQAD7 P 8 9;7G K E : 9 7: K 8 A;7"8 9;8/9;G > P J\8 9 JSG U AD: U > 8 A;G ] P G E > J\8 0 X H A;78E8 U 9;: AML GeN!W8 9D9C8 K 9 U 8 I P AD78 @ : U J P 8#I29;8 9 # G (8\W28 P (8 G ? 9;8 P W28 U G N > P AD78 P W28 9D9;8 K : U`"K A P IeA;:_G U : AD7: U A;7"8 ] G P G > 9 @ 8 @ ? P I U 8 I29 9;7G U : U H:_d heJ #
0
7: K 8 8 9CA;: KBK G ? ;9 8 P W28 I U : U 7"G @ 2G d8 U 8 G > 9 J\G U J\8 U A P I AD:BG UQ] P G `K 8 : U H:Bd 2J \AD7:"U : NcG P @ :BAMLV7"I9 ? 8 JSG @ 8 @ : AD:BdI AD8 E 9C:_d U : ` J I U A K L E > 8/ADGZAD78 > U :BNcG P @ P 8 K 8 I29;8 GeN!0 X H ? L AD78 9;G K :_E ? G >U EI P :_8 9 U P 8\d2:_G U 9 7":_J 70I P 8 JSG U `"U 8#E ? L K I P d8 P 9CG K :U E"I P L K 8 U deA;7 A;78/JSG U JS8 U A P IeA;:_G U ?> : K E9 >] P I ] :_E K L = : @ : K I P A;G^9CA P I A;8 d2L h A;7"8 9;8
U ? L A;: ] SJ 8 KBK 9 7:_J 7^: U A > P U : U 7": ? :BAD9 N > P AD78 P W28 9D9;8 K : U W I9C:_G U # G 8 W28 P A;7"8 P 8\d2:_G U 9! : K_K 7: U E 8 P 9C:_d U I K E S8 AD8 JSA;:_G ^ >U :BNcG P @ P 8 K 8 I9C8QGeN10 X H ? L 9;G K :_E ? G >U EI P _: 8 9(78 KB] 9(A;78 JS8 KBK 9I W2G:_E ? 8 J\G @ : U d A P I ]] 8 EZ: U 9C: 9 @ 8 @ ? P I U 8 I29 9;7G U : U H:_d h-$ E N & 578 P 8 9 >K AD9 : U H!:_d hZI U E ^7": U A A;7I A U G2AG UK L AD78 I ]"]K :_8 E09CA P I AD8\d2L A;G P 8 K 8 I29;840 X H ?> A I K 9CGFA;7"8 E > P I AD:BG U I 1A 7":_J 7 (8 8 U d: U 8\8 P A;78g8 @ ? 8 E"E 8 E9;G > P J\8 9G P 9CG K :U E"I P :B8#9 A;G P 8 K 8 I9C8 E8SA;8 P @ : U 8 9*A;78 @ G P ] 7G K G2dL GeN)J\I ] : K_K I P L U 8SA (G P :BA;7": U A;7"8 ] G P G > 9 @ 8 @ ? P I U 8 U G P E 8 P ADG N > P AD78 P : U W28 9CA;:_dIeA;8VA;7: 9 @ 8 @ ? P I U 8
G U 9C8#b > 8 U A K L (8G ? 9;8 P W28A;7I A A;7"8A;GeA I K W8 9D9C8 K K 8 U deAD7 : U J P 8#I29;8 96 :BA;7 A;: @ 8 ) G2A;8(A;7"IeAgI K_K A;7"8 J > P W28#9I9;9;G JS: P IeA;:_G U 9 K G (8 P ;A 7"I U A;8 U EI L 9 9;7G 6I ? P 8 I ] 2G : U A 0 8 9D9C8 K d P G A;7 I U E ? P I U J 7: U d P IeA;8 9QE 8 ] 8 U E G U A;7890 X H \J G U J\8 U A P I AD:BG U I U E0AD78\L&E 8#J P 8 I29;8 P I ] 9 A;78 ? P 8 I ] G2: U A $cA;78 ] G2: U A A;7I A A;78^9 K G ] 8^E 8 J P 8#I29;8 9 & I A/8 IJ 7 J > P W28F9C:_d U : ` 8#9 A;78ZA;: @ 8FIeA
7: d 7 K I P 2d 8 E G9;8 9: U 9;7G P AE > P IeA;:_G U 9 9 > J 7FI9 A (G EI L 9 P I ] : 8 ADG E 8 d P I2EIeA;:_G U 57 > 9 AD78VAD: @ 8QN P I @ 8V: U 7: : P I AD:BG U 9 J\G U 9;:K A 9%: U I K I P d8 P A;G2ADI K W28#9;9;8 K K 8 U deA;7 AD7"I U 9CA P I AD8\dL,h QU 8 @ IMG P%P 8#I29;G U ? 8 7: U E A;7":_9ZE :_9CA;: U JSA;:_G U : : K E9 "> ]&U 8 I P A;78 ] P : @ I P L W8 9D9C8 K P I ] : d27,NcG P ? P I U J 7": U d ADG G J J > P N P G @ 0
] P : @ I P L 2W 8#9;9;8 K : U 9CA P I AD8\dL/h:_9 K G U d28 P AD7"I U C9 A P I AD8\dL 57: C9 :_G U A;: @ 8 K 8 I2E"9 A;G ] I P A;: ;9 8 Ge(N E 8\d P IEI AD:BG U E > P : U d ;A 78 A P I U 9 ] G P A ] P G JS8#9;9 578 P 8SNcG P 8 3 (8 G ? 9C8 P W8 A;7I A A;7840 X HJSG U JS8 U A P IeA;:_G U
j
U 8#I P ;A 78 ] P : @ I P L^W28#9;9;8 K : U 9MA P IeA;8\dL h%:K AD9 : U K G 8 P P I A;8 G2N ? P I U J 7": U d U I2EE: AD:BG U : U 9CA P I AD8\dLZh AD78 K G J I K : [ 8 EZ7:_d27 0 X H JSG U JS8 U A P I A;:_G U 8 U 7"I U J\8 9 ? P I U J 7: U d N P G @ W28 9D9;8 K 9 U 8 I P A;7"8 8 @ ? 8 EE8 E 9;G > P J\8 9(I U E A;78 U 8 W28#9;9;8 K 9 P I ] :_E K L/G P dI U : [ 8 AD78 @ 9;8 K W28 9gA;G I P E/AD78 A;78#9C8 9CG > P JS8 9! :BA;7ZI W28 P L
7:_d27 ] P G ? I ? : K : AML0G2NVI U I 9MADG @ G9;:_98 : AD7,G2A;78 P W8 9D9C8 K 9 I29 ;9 7G U : U H:Bd h &4V9 A;7"8ZW8 9D9C8 K E 8 U 9;: AML&: U J P 8 I9C8#9 ] P G2d P 8#9;9;:BW8 K LZJ K G9C8 P ADG DA 78/8 @ ? 8 E"E 8 E 9CG > P JS8 9I ? I P;P :_8 P ;A G 0 X H E : > 9;:BG U ? 8 J\G @ 8 9 8 9CADI ?K :_9;78 E E > 8 A;GZA;7"8 0 X H >] A I 8 ? L JS8 KBK 9 7:] A I 8 ? I PDP :_8 P G ? 9C8 P W8 EZ: U 9CA P I AD8\d2LFh U I2E"E : AD:BG U I9 9 ] P G > AD9 ? P I U J 7ZN P G @ 8SR :_9CA;: U d%W8 9D9C8 K 9E 8SAD8 JSA;:_G U GeNA;7"8 E : 9D9C8#E0: U,= 8 J
0
G W28 P I KBK J\G U J\8 U A P I AD:BG U d P IE B: 8 U A(ADG (I P E A;7"8W28 P AD:_J I KK : U 8 9CG > P J\8 ? L A;78A;: ] JS8 K_K 9 I _K K G 9(N > P AD78 P d P G AD7 ] P :_G P DA G I U I29CA;G @ G9C: P IeA;:_G U 9)A;G2ADI K(K 8 U deA;7,GeN K G (8 P 2d 8 U 8 P I A;:_G U W28 9D9;8 K 9 \8 R J\8\8#E9AD78^7:_d278 P d8 U 8 P IeA;:_G U 9 &57:_9 : U E : d27G > A A;7"8 9C: @ >K I AD:BG U 9*A;7"8 @ IMG P :BAML GeN W28#9;9;8 K 9 ? P I U J 7 N P G @ ] P : @ I P L W8 9D9C8 K 9 I U E0E : > 9;8 : U A;G^A;7"8 @ 8 @ ? P I U 8 4Q9VAD78 9;8 W28 9D9;8 K 9 ] P G2d P 8#9;9VI U E ] 8 U 8SA P IeA;8 : U A;GZA;7"8 @ 8 @ ? P I U 8 AD78\L ? P I U J 7 I U E NcG P @ IZE8 U E P :BA;: J A > P 8 # G (8\W8 P AD789 ] 2I J\8 : U 9;:_E8 A;78 @ 8 @ ? P I U 8 9 U 8* ? P I U J 78#9 7: 9 @ 8 @ ? P I U 8 (8 E _: W :_E8 AD78 ] G P G > 9 @ 8 @ ? P I U 8 : U ADG^h2i2i ? : U 9 : U A;78 ,E : P 8 JSA;:_G U I U E @ 8#I29 > P 8/A;78%ADGeA I K 8 U E G2A;78 K : P I AD:BG U 9GeNA (G 9;: R^I U EZA;8 U EI L 9(NcG P 9CA P I A;8 d2:_8 9 h I U E %I P 8 J\G U 9;:_E8 P 8 E 8 G ? 9;8 P W28QA;7I A NcG P
I 7:_d27&JS8 KBK E8 U 9;: AML U 8 I P A;G^A;7"8 ] G P G > 9 @ 8 @ ? P I U 8/8 U A P I U J\8 ? GeA;7&9CA P I AD8\d2:_8 9 K G U d P 8 K 8 I9C8%E > P I AD:BG U 9 K 8 I2E"9 A;G F NcG K_K G 8#E ? L^I%9C:_d U : ` J I U A P 8 E > J A;:_G U E 8 8 ] 8 P : U 9;: P eI A;:_G U 3 8G ? 9;8 P W28 I @ G P 8 J\G U 9CADI U AJ\8 K_K E 8 U 9;:BAML A;7 P G > d27G > AQAD78 @ 8 @ ? P I U 8 /4V9 E8 9DJ P : ? 8 E 8 I P K :B8 P : U&= 8 J K G U d28 P : U A;8 P U I K P 8 K 8 I29;8 E > P IeA;:_G U 9 J I > ;9 8 K G J\I K : [ 8#E P 8\d2:_G U 9 :BA;7": U ;A 78 ] G P G > 9 @ 8 @ ? P I U 8 : AD7 7":Bd7%0 X H J\G U J\8 U A P I AD:BG U 9 I9 9;7G U : U H :_d U DA 78 9;8 P 8 d2:_G U 9 J I ] : K_K I P L A;: ] SJ 8 K_K 9(I P 8 U GeA I "? K 8QA;G/E 8SAD8 JSA(AD78 G W28 P I K_K d P IE :_8 U AD9gA;G I P E/A;7"8 K : U 8/9;G > P JS8 A;7 > 9 A;78 L ? 8#JSG @ 8 A P I ]] 8 E : U 9C: P I AD:BG U 9 I N A;8 P A;7"8 8 @ ? 8 E"E 8 E/9;G > P JS8#9)G P 9;G K :_E ? G >U E"I P :B8#9 9MADG ] P 8 K 8#I29;: U d 0 X H U 8 K L NcG P @ 8 E 2W 8 9D9;8 K 9 ] P G2d P 8#9;9(I29(AD78\: P A;: ] SJ 8 KBK 9; 7:U EZAD78\: P I L/A;G I P E%A;7"8 K : U 8 9;G > P JS8 A P I W8 P 9C8VA;78 @ 8 @ ? P I U 8 578 P 8 E > JSA;:_G U : U DA 78 9 K G ] 8%GeN(7:_d278 P P 8 K 8#I29;8/E > P IeA;:_G U J > P W28#9 : U C9 A P I A;8 d2L hZU J AD:BG U G2N P 8 K 8#I29;8 E > P I AD:BG U : U H!_: d j 8 G ? C9 8 P W8 ;A 7"IeAQNcG P
? GeA;7 9MA P IeA;8 d2:_8 9 K G U d28 PaP 8 K 8 I29;8E > P IeA;:_G U 9 K 8 I2E A;G @ G P 8(9 > P NIJS8J\G W28 P I2d28 ? L W28 9D9;8 K 9 57:_9 P 8\W28#I K 9AD7"I A E 8#9 ] :BA;8A;7"8 NI2JSAA;7"IeA W28 9D9;8 K : U`"K A P IeA;:_G U E 8 J P 8#I29;8 9W8 9D9C8 K U>"@ ? 8 P I U E K 8 U d2A;7F: U J P 8 I29;8 9" :BA;7 K G U d28 P E > P I A;:_G U 9gAD7"I A K 8 IE ADG
I K I P d28I P 8 I G J\J >"] :B8#E ? L W28 9D9;8 K 9 # G (8\W28 P eH:_d jQ: K_KB> 9CA P I AD8 9AD7"I A DA 78V9;G K :_E ? G >U EI P L P 8 K 8#I29;89CA P I AD8\dL P 8#9 >"K A 9 : U I K I P d8 P 9 > P NI2JS8QJSG W28 P I2d28NcG P I K_K E > P I AD:BG U 9 J\G U 9;:_E8 P 8 E P 8 K IeA;:_W28ADG ;A 78Q8 @ ? 8#EE 8 E%9;G > P J\8 9MA P IeA;8\dL G U ;9 :K AD9 : U H:Bd I U E 2A;78 @ IMG P P 8 I9CG U 9 ? 8\7: U E%AD7: P I AD:BG U 9 K 8 IE9ADGZI%7:_d27"8 P U >@ ? 8 P G2N)W8 9D9C8 K 9QI U E K G U d28 P A;GeA I K W28 9D9;8 KaK 8 U deA;7 I9V9;7G U : U H:_d $c:_: &V9CG K :U E"I P L P 8 K 8 I9C8 7"8 K_] 9 ADG 8#9MA I ?K :_9;7 I @ G P 8 7"G @ G2d8 U 8 G > 9 J\G U J\8 U A P I AD:BG U%] P G `"K 8/ 7: 9;:BG U 9CA P I AD8\dL hFI U E
K 8 I2E ADGF8 U 7"I U JS8 @ 8 U AGeN W28#9;9;8 K ] P G2d P 8#9;9;:_G U I U E : U `K A P IeA;:_G U 4 K 9;G^N P G @ J\G @/] I P : U d^9MA P IeA;8\d:B8#9h^I U E FG U 8
: U Nc8 P 9 AD7"I A/E :_9CA P : ?> A;8#E P 8 K 8 I29;8/N P G @ 9CG K :U EI P :_8 9 P 8#9 >K AD9 : U I K I P d8 P U >@ ? 8 P 2G N(NcG P @ #8 E0W28 9D9;8 K 9 )I @ G P 8 7G @ Gd28 U 8\G > 9 K LQE:_9CA P : ?"> A;8#EW28#9;9;8 KU 8\A G P I U E I 7:_d278 P E 8 d P 8\8GeNW28#9;9;8 K : U d P G A;7: U SJ G @/] I P _: 9;G U :BA;7 K G J I K : [ 8 E P 8 K 8 I29;8 U A;7:&5B 2 & g- 8.;eB o7&g- 8&H ; B c ? & g- D"%$'&H")3/!g ;>=QB m&577([")(0 5m") ^10(0 S-% !7$) !8 6 H$)Se 5 & $)(*3-$)31* &!-% ZM (*7-%(*7Z")U 5 4o&H(*F,G H$k;> B 2 & g- 8Y; B & g- 8 &! ;G,'B`c?^7& g7- E.&! 7 !4210go-%U &!6 5e - "'&H 10 -&H$)S-%U h+(0+e71*&!'a9E
i
1
0.8
0.6
0.4
0.2
(a) 0 1
0.8
0.6
0.4
0.2
(b) 0 1
0.8
0.6
0.4
0.2
(c) 0
9 ZM 3 5 3 #"%$'&H")(0 5 67$) 10^& "`")(042) i =oU7$EL;>&QB #"%$'&H") /Hg c58.;eB # "%$'&H") /Hg 2 8Y&! ; B # "%$'&H") /HgV=E TU7 C!&!10 -I& "I")U7Ze& $)-j$) 67$) -%3D")- ! 3D"%$'& ")(0 5 ; c? Z/ BRE
40
40
rs = 2 days = 4 days = 6 days = 8 days 30 = 10 days
rs = 2 days = 4 days = 6 days = 8 days 30 = 10 days
total vessel length (mm)
total vessel length (mm)
20
10
20
10
(a)
(b)
0
0 0
50
100
150
time (hr)
200
250
0
50
100
150
time (hr)
200
250
T !"'&H1]CQ3-%-% 1]10 7/!")U &!-k&m,G7 3")(0 ! !,")(042^,G !$L7(93$)3D" (0#")3$)&H1f$) 10&H-%m7$'& ")(* ! - E ;>&5B # "%$'&H") /Hg 2 `;eB D"%$'& ") /!gm=E
140
160
rs = 2 days rs = 10 days
h
rs = 2 days rs = 10 days
140
120
120
100
vessel length (mm)
vessel length (mm)
80 60 40
100 80 60 40
20
20
(a)
(b)
0
0 1
2
3
4 generation
5
6
7
1
2
3
4 generation
5
6
7
T !"'&H110 7/!")Um H,>"@ `"K A P I AD:BG U 6 (I9C7"8 E : AD7 E 8 :_G U : [ 8#E($ O & I AD8 P Ie: P E P :_8 EZG W28 P U :_d27A I U EZA;78 U K LG ] 7: K : [ 8 EZNcG P IEE :BA;:_G U I K h %7 T 9;: U d 9MA Ie: UK 8#9;9 9CA;8 8 K 9C:_8\W8 9 @ :K AML-& I A ] I9;9DIed8Qh (8 P 8QI KBK G 8#E A;G/I A;ADI2J 7 A;G/9;J I G K E9 NcG P Q7G > P ? 8SNcG P 8 I U IE E B: A;:_G U I K h @/K GeN @ 8 E: >@ $ X h 0
>K_K 8\A : A &$ (I @ ? P 8\R G P ] G P I AD:BG U I K 28 P 9;W: K_K 8 O & I29VIEE 8#E^: U A;G 8 I2J 7 (8 K_K 8 K_K 9 8 P 8 @ 2I : U ADI2: U 8 E^: U I 7 >@ :_E: ` 8#E%: U J >? I A;G P I A j : AD7 U I K_K J I29;8 9JSG U A P G K 96 8 P 8VJ I PDP :_8 E G > A : AD7%A;7"8V9;I @ V8 JS8 KBK 9 d P G U .
G U A;: 8J >K A > P 8 ] G K L 9CAML P 8 U 84$ 5 (f =
&
K_K@ G P ] 7G K Gd2L I29)I29D9C8#9;9;8 E I A ] P 8 E8SA;8 P @ : U 8 E A;: @ 8 ] G: U A 9 > 9C: U d 9DJ\I U"U : U d 8 K 8#J A P G U @ :"U E 8 P = X $ Y X j ii'&
8 K_K d P G AD7 G U 9DJ\I G K E9 I U E65 (f = $ I29 I SJ G U A P G K & I29 I29D9C8#9;9;8 E ? L $ E : @ 8\A;7 L K :K NcG ] 7"8 U L K & h # A;8SA P I [ G K : >@ $ 5 = &J\G K G P : @ \8 A P :_JQI29D9;I L $ 8 KBK 5: AD8 P 4 > 8\G > 9 f P G @ 8 dI IE :_9;G U &I2J\J\G P E : U dADG AD78 @ I U > NIJ A > P 8 P 9E : P 8 JSA;:_G U 9 UZ? P _: 8SNIeA ] P 8#E 8SAD8 P @ : U 8#E AD: @ 8 ] 2G : U A 9 9DJ\I G K E9 (8 P 8 I29;78 E :BA;7 f . = A P I U 9CNc8 PDP 8#E : U A;G I U *8 8 KBK!]K I A;8J\G U ADI2: U : U d @/K GeN)N P 8#9C7 J >K A > P 8 @ 8 E : > @ I U EFh2i2i K 5 = 9;G K_> A;:_G U I U E : U J >? IeA;8#EZIeA j
NcG P h 7 4(AA;78 8 U E G2N*A;7"8 : U J >? I AD:BG U AD: @ 8 A;78 P 8 IJ A;:_G U (I9 9CA;G ]"] 8#E ? L/IEE : U d h i K GeN #i 9;G E: > @ E G E #8 JSL K 9 >K_] 7"IeA;8$ = O = &(9CG KB> A;:_G U 57 8 P 8#9 >K A;: U d 9;G K_> AD:BG U (I9gE : K_> A;8#E : U I P IeA;:_G > 9;: U d O I AD8 P I U E/AD78 I ? 9;G P ? I U JS8 I29 P 8 IE%I A
h U@ > 9;: U d I5!8 J\I UZ= ] 8 JSA P GH KB> G f K_> 9 P 8#I2E 8 P $5 X (4) T = 4 .(G9MADG U 4 &
,
C
K_K 9 d P G : U d G U 9;J I G K E9 (8 P 8 P : U 9C8#E( : AD7 f!. = ` R 8#E :BA;7 ] I P I NcG P @ I K E 8 7L E 8^NcG P &@ : U I A P G G @ A;8 @/] 8 P IeA > P 8 4 N A;8 P I29;7 :BA;7 f . = J\8 K_K 9 8 P 8 ] 8 P @ 8 I ? : K : [ 8 E :BA;7 i 5 P : ADG U #i2i NcG P i @ : U 8 K_K 9 (8 P 8 I29;78 E : AD7 f!. = *I U E . = 4 $ = :Bd @ I 4 K E P : :_9 & : U f!. = I29 I ]"]K :_8 E NcG P i @ : U I A P G G @ A;8 @/] 8 P IeA > P 8ZI9 I ?K G J : U d 9CG KB> AD:BG U 4 N AD8 P I29;7 : AD7 f . = ]K IeA;8 K 8\A 8 U E GeAD78 K :_I K J\8 K_K IE 78 9;:_G U
8
@ G K 8 J >K 8 4$f X (4 &gI U ;A : ? G E L7$ heii E : KB> A;:_G U & $ L @ 8#E9!I ? G P I A;G P :_8 9 = I U H P I U J\:_9DJSG (4 &" (I9I2EE 8#E I U E : U J >? I A;8#EG W8 P U :Bd7A!I A 5 7"8(9DJ\I G K E91 (8 P 8 A;7"8 U (I9C78#E B: A;7 f . = I U E AD78 C9 8#JSG U EI P L I U A;: ? G E L $ 22i i
I U AD: @ G > 9;8 4 K 8SRI H K_> G P &4$ G K 8#J >K I P f P G ? 8 9 X > 2d 8 U 8 & I29IEE #8 E&I U E0: U J >"? I AD8 E NcG P 7 I A P G G @ A;8 @/] 8 P IeA > P 8 57: d28 U 8 & @ : U 4 N AD8 P I29;77 :BA;70f . = 9DJ\I G K E9 8 P 8 ]K I2J\8 E : U I U A;:BNI2E 8 P 8 Ied8 U I U E%8SRI @ : U 8 E ? L%JSG U NcG J\I K"K I29;8 P 9DJ\I UU : U d @ :_J P G9;J\G ] 8 8 $ " = 7& 57 P 8 8VE : @ 8 U 9;:BG U I K : @ Ied8 9 8 P 8VJ P 8#I AD8 E ? L I U
I29D9;8 @ "? K L^GeN h O 9C8#J A;:_G U 9QG2N A;7"8/9DJ\I G K E"9 @ G W : U d AD7 P G > d7 : A 9 A;7: 9VE 8 ] AD7^GeN)hh @ 578 J\8 K_KB>"K I P JSLA;G98 K 8SA I K \J G @/] G U 8 U A IJ A;: U 6 I299CADI2: U 8#E > 9;: U d P 7G EI @ : U 8 ] 7I K_K G:_E : U 8 K_K 9 d P G : U dFG U 9DJ\I G K E 9 (8 P 8 P : U 9C8#E8 :BA;7/f . = ` R 8#E8 :BA;7 ] I P I cN G P @ I K E 8 7 L E8 NcG P @ : U I A P G G @ A;8 @/] 8 P I A > P 8 I29;78 E :BA;7 ! f . = "I U EFAD78 U ] 8 P @ 8 I ? : K : [ 8#E : AD7 i 5 P : ADG U ii NcG P i @ : U 4 N A;8 P I29;7 : AD7 f . = . = 4 : U f . = I29 I ]]K :B8#E I29QI ?K G J : U d 9;G K_> A;:_G U NcG P i @ : U IeA P GG @ AD8 @/] 8 P I A > P 8 4 P 7G EI @ : U 8 f 7"I KBK G2:K I (4 &: U f . = (I9IEE 8 EZI U E : U J >? IeA;8#E NcG P 7,I A P G G @ A;8 @ ] 8 P I A > P 8 H"G K_K G : U d (I 9C7 B: A;7,f . = )9;I @ ]"K 8#9 (8 P 8 @ G >U A;8#E : U I U AD: NIE 8 P 8 I2d28 U A I U E S8 RI @ : U 8#E ? L " = 57 P 8\8QE : @ 8 U 9C:_G U I K : @ Ied28#9 (8 P 8 I2J b > : P 8 E ? L I U I29D9C8 @ ?K L G2Nah O 9;8 J AD:BG U 9 G2N AD78Q9DJ\I G K E"9 9;G K_> A;:_G U $ iiE : KB> A;:_G U
& $ 7"8
@ G W : U d AD7 P G > d27Z: A 9A;7":_J U 8#9;9 IeAVE 8 ] AD7^: U J P 8 @ 8 U AD9G2N 0I U EFI NcG J > 9 E 8 ] A;7^G2N h @
" 6
HG P d 8 U 8Z8SR ] P 8 9D9C:_G U I U I K L 9C:"K 8 $ (4 O 2& X 9C8 K 8#J AD: U $ O h X & I U E,A;7"8 8 U E GeAD78 K :_I K JS8 KBK!>U :_W28 P 9DI K@ I P 28 P W2G U : K_K 8 ? P I U EFNI2JSA;G P $cW H & (8 P 89MA > E :_8 E > 9;: U d I P 8#I K AD: @ 8 P 8\W8 P 9C8 A P I U
9DJ P : ] AD:BG U] G K L @ 8 P I9C8gJ 7Ie: U P 8#I2JSA;:_G U $ 5 f" & $ 4 ]]K :_8 E8.(:_G9;L 9MAD8 @ 9 4 . !f P :_9 @ ej 2ii # 5 = 8 b > 8 U JS8 O 8SAD8 JSA;G P = L 9CA;8 @ TQ= 4 & 4(A ] P 8#E 8SAD8 P @ : U 8#E AD: @ 8 ] G2: U AD9 j I U E%h E"I L 9)IeN A;8 P J >K A > P 8 2A;78 9DJ\I G K "E 96 8 P 8; I29;78 E G U J\8 :BA;7 f!. = I U E A;78 ADGeA I K )V4N P G @ A;7"8QJS8 KBK 9 G U A;78 9;J I G K E9 (8 P 8 : 9;: U d I U
U J 0
)
8 I9CL @ : U : :BA $ Q : NI2JSA > P 8 P 57 P 8 8 d P G >] 9QGeNg9DJ\I G K E9VNI ?
i
P :_J I A;8#E: B: A;7^AD7 P 8\8E : 8 P 8 U A @ J AD94 I29 @ G U : ADG P 8 E I U E b > I U A;: ` 8 E > 9;: U d = +. P 8\8 U I U E AD78 JSG @/] I P IeA;:_W28 (5 @ 8SAD7G E : U 7:"@ >K I AD8 E/f" ,] P G E > J A 9)NcG P #8 I2J 7/GeN A;7 8 d8 U #8 9)8SRI @ : U 8 E : 9C828 8 ] : U d d28 U 8
4Vf O
# "578
] P : @ 8 P 9(NcG P 8 IJ 7Zd8 U 8 I P 8 K : 9C: U d/A;7"85 > 8\L%AD8 9CAVI U EF9CADI AD:_9CA;: JSA > P 8 GeN!A;789DJ\I G K E9 I U EFI2E G ] A;8#EFI/9CA P 8SA J 78 EF9C7I ] 8 P G A;7 GeN 8 U E GeAD78 K :K A > P 8 E G U 5 (f = I U E f !4 4 9DJ\I G K E9 N I ? P :_J I AD8 E E :K A;8 EZ: UFU G 9C:_d U : ` J I U AE: 8 P 8 U J\8 9 ? 8SA (8\8 U AD78 @ 8 I U 9
, /
578Z8SR ] P 8 9D9C:_G U G2NV9 > P NI2J\8 2I E78 9;:BG U&] P GeA;8 : U J 7"I P I2JSA;8 P : I A;8#E > 9;: U d%: @/@ >"U G "> G P 8 9DJS8 U JS8 @ _: J P G9;J\G ] L gH:_d j %9C7G 9(AD78 ] IeACAD8 P U eG N f X (4 \8 R ] P 8#9;9;:_G UF? L^JS8 KBK 9 d P G : U d G ? 9;8 P W28#E0A;7I A f X (4 Z9CADI2: U : U d GeNQJ\8 K_K 9 P 8 9 >K A/: U I C9 A P G U d K G J I K : [ 8 E 9CADIe: U : U d ] IeACAD8 P U I AQA;78 > U J AD:BG U G2NgI2E CIJS8 U AQJ\8 K_K 9 Q57"8 9;8 : @ I22d 8#9V9;7G 8#EZA;78/J 7"I P I2JSA;8 P :"K I P ? P :_Ed2: U d
G U A;78 9DJ\I G K E9/IeA/EI L
A
I29
9;8\8 U : U0= X @ :_J P Gd P I ] 7"9 : K_KB> 9MA P IeA;: U d AD7"I A 8 U E GeAD78 K :_I K JS8 K_K 9V7"I W8 ? L ] I29D9;8 E^AD78 9 > P NI2J\8 GeN @ :K I A;8#9A;7"8 SJ 8 KBK I2E 78 P 8 U JS8 ADG ? :_G @ I AD8 P :_I K 9(AD7 P G > d27 P 8\G P dI U : [ I AD:BG U G2N J\L ;A G ]K I29 @ :K A > P 8 E/G U !f a4 4 9;: U AD8 P 8 E @ :_J P G9 ] 78 P 8 9;J I G K E9 IeAEI L )57: J A > P I K] P GeA;8 : U%] G K L @ 8 P : [ 8 9VA;G NcG P @ @ :K I P 9 ] P 8 I2E: U d I U E^JS8 KBK_>K I P 9CA P > J A > P 8 : U A;8\d P :BAML
8
: "
K_K : U A;8 P IJ AD:BG U 9 B: A;7 ? :_G @ IeA;8 P : d27 d8 U 8 8\R ] P 8#9;9;:_G U I U I K L 9;:"K 8#9 $ (4 9 &gI U E >U :BW8 P 9;I K"@ I P 28 P 9 !578 P 8\d >"K IeA;:_G U GeN*8 U E G2A;78 K :"U EFA;7"IeA J\8 K_K 9QJ >K A > P 8 E^G U A;78 9;J I G K E9 I U E 5 (f = 8\R ] P 8#9;9;8 EFW H,IeAQ9;: @ : K I P K 8\W28 K 9VI AQI BK K A;78 AD: @ 8 ] G : U DA 9 I29 9;7G U : U H:_d aj $ 'I & 578 d28 U 8 8SR ] P 8 9D9C:_G U G2Nf X (4 G U 9;J I G K E9 7"G 8 W28 P ] 8#I 28#E eI A EI L ZI U E B: A I29 9;:Bd U : ` J\I U A K L%7:_d27"8 P A;7I U 5 (f = H:_d j $ ? & K_K 9)d P G : U dQG U 9DJ\I G K E98SR 7: ? B: A;8#E d8 U 88\R ] P 8#9;9;:BG U NcG P @ I P 8 P 9GeN: U I @/@ IeA;:_G U X 9C8 K 8#J A;: U 2I 9 9C7G U : U H!:_d )j $J E3& Z57"8%8SR ] P 8 9D9C:_G U GeN X 9;8 K 8 J AD: U ? L J\8 _K K 9 G U f !4 4 9;J I G K E9 (I9 G ? K 8\W28 K 9 9;: @ : K I P A;G05 (f = NcG P I K_K AD78 AD: @ 8 ] G: U A 9 gI9 9;7G U : U H_: d j $J & # G (8\W8 P aAD78Fd28 U 8
8
(4
I U E (4
9C8 P W8 E IeAA;7"8
8SR ] P 8 9D9;:BG U GeN ? L/J\8 K_K 9(G U 9DJ\I G K E9 ] 8#I 8 E IeA(EI L I U E I29(9C:_d U : ` J I U A K L/7:_d278 P AD7"I U 5 (f = = J I G K E9NI ? P :_J I AD8 E
:BA;7 E : 8 P 8 U A @ :_J P G9 ] 78 P 8ZE : P NI2JS8 I U EZIE G ] AD8 EFI/9 ] P 8 IE 9;7"I ] 8 4V9!JS8 KBKe] P G K :BNc8 P I AD:BG UQ] P G2d P 8#9;9;8 EVA;7 P G > d27G > A A;78 @ IeA P : R A;78 LVNcG P @ 8#EQ8\R A;8 U 9C:_G U 9 ? 8\A 8 8 U I2ECI2JS8 U A @ : 9 9MA > E :_8 9 578 @ _: J P G9MA P > JSA > P I K] P G ] 8 P A;:_8 9QGeN(8 U d: U 8 8 P 8 E 9DJ\I G K E"9 @ I L : U"> 8 U JS8/JS8 KBK_>K I P ] P G K : Nc8 P IeA;:_G U I U E N >U J AD:BG U I U E A;7 > 9 I 8#J A A;7"8/9 > J JS8 9D9 GeN AD78%JSG U 9MA P > J A I N A;8 P : @/]K I U A I A;:_G U j T 9;: U d^f!a4 4 @ _: J P G
9 ] 78 P 8 9 aI > P 8 U JS: U K I ? G P I ADG P L 7"I29gE 8\W8 K G ] 8 E/9C: U A;8 P 8#E @ :"] 9 QU AD78 GeAD78 P 7"I U E I ;9 :_d U : ` J\I U A(: U J P 8 I9C8Q: U JS8 KBKU >@ ? 8 P I29G ? 9C8 P W8 E/NcG P I KBK AD78 9;J I G K E9 >"] ADG EI L i I N AD8 P 7:_J 7 ] P G K : Nc8 P IeA;:_G U P I A;8 ]K I A;8#I > 8#E 578 9;8 P 8#9 >K AD9(E 8 @ G U 9CA P I A;8VA;7"IeAAD78 J 7"I U d8 9g: UZ] G P 8 I P J 7: AD8 JSA > P 8 E G U 2G A8 K :_J\: AE : 8 P 8 U A8 U E G2A;78 K : U J
A;:_G U 9 I U EF7"I9 ? 8 8 U 9C7G U A;G @ 8#E :_IeA;8 JS8 KBK JS8 K_K : U AD8 P I2JSA;:_G U 9 U I2E"E : AD:BG U f X (4 @ I L ? 8 : U W2G K W28#E : U 8 U E GeAD78 K :_I K@ G2A;: K :BAML AD7 P G > d7%: A 9 N >U J A;:_G U 9I9I9;:_d U I K : U d @ G K 8 J >K 8 A;7"IeA @ 8 E:_IeA;8 9gA;7"8V: U AD\8 d P : U I2JSA;:_W IeA;:_G U = 8 W28 P I K 9CA > E :B8#9 7"I W28%E 8 @ G U 9CA P I AD8 E A;7"IeAA P 8 IeA @ 8 U A : AD7 I U A;: f X (4 I U AD: ? G E L : U 7: ? :BAD9 AD78 ?K G G E W8 9D9C8 K NcG P @ I AD:BG U : U P G E 8 U A @ G E 8 K 9E #h2i #h G P 8 9DJS8 U JS8 @ :_J P G9;J\G ] L 8 9 >K AD9 ;9 7G (8 E I 9CA P G U d K G J I K : [ 8 E f X (4 9MA Ie: U : U d%I A JS8 KBK J\8 K_K : U A;8 P NIJS8#9 9;: @ : K I P ADGVAD788SR ] P 8 9D9C:_G U ] IeACAD8 P U G ? C9 8 P W8 E : U G2A;78 P 9CA > E:B8#9 )57:U J A;:_G U G2N8 U E GeAD78 K :? 9MA P IeA;8 "NcG J\I K JSG U A I2JSAD9
> 9 > I K_K L K G J\IeA;8#E U #8 I P A;7"8 ] 8 P : ] 78 P L G2N!JS8 KBK 9 NcG P @ 9MA P G U d IE 78 9;:_G U 9 A;G AD78 9 > P NI2J\8 I U EF9C8#J > P 8 ?">U E K 8 9G2NI2JSA;: U 9 :BA;7: U A;7"8^J\8 K_K @/@ >U G > G P 8 9DJS8 U JS8F: @ I2d2: U d : U G > P 9CA > E L P 8\W28#I K 8 E A;7"IeA 8 U E G2A;78 K :K I P C9 A P > SJ A > P 8 : U AD8\d P :BAML
X U E GeAD78 K :_I K JS8 KBK ] 78 U 2G AML ] 8 \8 R ] P 8#9;9;:_G U I29 8SRI @ : U 8 E ? L @ G U B: A;G P : U d0AD78 8SR ] P 8 9D9C:_G U GeN 8 U E GeAD78 K :_I K SJ 8 KBK > U :_W28 P 9DI K@ I P 28 P 9 $cW H I U E f X (4 &VI U E I2E 7"8 9;:BG U @ G K 8 J >"K 8#9 P 8 K 8\W I U A A;GF: U I @/@ I AD:BG U $ X 9C8 K 8#J A;: U I U E
(4
& 4(AA;78 d8 U 8 K 8\W8 K A;78 8\R ] P 8#9;9;:BG U K 8\W8 K 9G2NW
H I U E X 9C8 K 8#J AD: U G U f a4 4 9DJ\I G K E9 E:_E U G2A 9;7G ;9 :Bd U : ` J\I U A E : 8 P 8 U JS8#9 : AD7&5 (f = I AI K_K AD78/A;: @ 8 ] G : U AD9 U JSG U A P I9MA af X (4 /I U E (4 /8SR ] P 8 9D9;:BG U 9 G U f a4 4 9DJ\I G K E98 8 P 8 >] P 8\d >"K IeA;8 E I A E"I L I U E (8 P 8Z9;:Bd U : ` J\I U A K L 7:_d278 P AD7"I U 5 (f = (4 :U Gd K G ?>"K : U ] P GeAD8\: U 9 A;7"IeA @ 8#E :U J AD:BG U : U A;8 d P : AML @ GeAD: K : AML I U E G P dI U : [ IeA;:_G U G2NQ: U A;8 P @ 8 E :K IeA;8QA;7"IeAA;78 E : 8 P 8 U JS8#9: U d8 U 8 8SR ] P 8 9D9;:BG U K 8 W28 K 9GeN!f X (4 I U E (4 VG U 9DJ\I G K E9(I U E 5 (f = IeA(EI L I P 8QE > 8VA;G A;78 E : 8 P 8 U JS8#9g: U J\8 K_KB>K I P ? 8\7"I W :_G P 7"8 U d P G : U dG U h O W8 P 9 > 9 O @ I A P :K I P 9;:_d U I K : U d ] I AD7 I L 9 = A > E :_8 9V7"I W28 9C7"G U AD7"I AV: U I2EE: AD:BG U ADG ? :BG J 78 @ :_J I K J\G @/] G 9C:BA;:_G U A;7"8(E : @ 8 U 9;:_G U I K :BAML E 8\NcG P @ I ? : K :BAML I U E P :_d2:K A > P 8 E0G U I JSG KBK Ied8 U d28 Kg>U E8 P E: 8 P 8 U A @ 8 J 7I U : E L
A >"@ G P J\8 K_K 9 : U I O 8 U W: P G U@ 8 U AZE:_9 ]K I L28 E @ I MG P E : 8 P 8 U JS8#9 : U 8SR ] P 8 9D9;:BG U G2N @ IeA P : R @ 8SA I K_K G ] P G2A;8 : U I9C8#9 $ fg9 &I29 J\G @/] I P 8#E ADGZh O J >"K A > P 8J\G U E: AD:BG U 9 #h "*: 28* : P NIJS8%GeN : U E :_W :_E > I K(@ : P : U d A;7"8 ` P 9CA (8\8 4V9 ] P G K :BNc8 P I AD:BG U ] P G2d P 8 9D9;8 E JS8 K_K 9Q9;8 J P 8\A;8 E^8\R A P I2JS8 KBK_>K I P @ IeA P : R I U E @ :Bd P IeA;8 E : U A;G ] G P 8#9VI U E dI ] 9 9.I29;8 E G U A;7"8 9;8 G ? ;9 8 P W I AD:BG U 9 8 ] G9CA >K I AD8%A;7I A J\8 K_K 9 >"U E 8 P (8 U A A;7 P 8\8 E: 8 P 8 U A ] 7I29;8 9I9 A;78 L% (8 P 8 d P G : U d G U A;78^9;J I G K E9 $ & ] P G K : Nc8 P IeA;: U d ] 7I29;8 $ h & P 8 @ G E8 K : U d ] 7"I9C8 I U E $ & b > :_8 9DJS8 U A ] 7"I9C8 U A;7"8
` P 9MA ] 7"I29;8 $ ] P G K :BNc8 P I A;: U d ] 7I29;8 & JS8 KBK 9E :K I P : U A;8 d P : AML G U 9;:] :_8 E&I W I2: K I ?K 8 9 > P NIJS8#9 I U E P 8 IJ 78 E SJ G U"> 8 U JSL F578 P 8\NcG P 8 : U&] 7"I29;8
A;7 P 8 8 8 G ? 9;8 P W28#EFA;78 E G U P 8\d >K IeA;:_G U G2N ] 78 U GeAML ] :"K A > P 8#EFG U 5 (f =
I U E f X ( 4 9C: @ : K I P A;G A;7"IeA
57809C: @ : K I P :BAML,: U 8\R ] P 8#9;9;:_G UK 8\W28 K 9ZGeN X 9C8 K 8#J A;: U I U E W H G U f !4 4 I U E 5 (f = 9 > d2d28#9MA 9%AD7"I A^A;7"8 L 7:"@ I U 8 U EGeA;7"8 K :_I K
J\8 K_K I A;ADIJ 7 @ 8 U A)d P G A;7&I U E ] 78 U GeAML ] J A > P I K I U E N >U J AD:BG U I K ] 78 U GeAML ] 8 9 9)V8\W28 P AD78 K 8 9D9*A;7"8 ] P G K :BNc8 P I AD:BG U I U E ] 78 U GeAML ] : E :_8 E f P :BG P ADG ? 8 J\G @ : U / d J\G U> 8 U A J\8 K_K 9G U f !4 4 9;J I G K E9(8SR ] P 8 9D9C8#E f X (4 I U E (4 /I A 9;:_d U : ` J\I U A K LF7":Bd78 P K 8 W28 K 9QI29 JSG @/] I P 8#E^A;GF5 (f = 578 A P I U 9;:_8 U A E : 8 P 8 U J\8 9Q: U >] P 8\d >"K IeA;:_G U GeNA;7"8 9;8 d8 U 8#9; 8 P 8 IeACA P : ?> A;8#EZA;G%JS8 KBK d P G AD7 ? \8 7"I W :_G P G U h O W 8 P 9 > 9 O d28 G @ 8SA P : A > P 8 9MA > E :_8 9!9C7G >K EVNcG J > 9*G U AD78gE 8 W28 K G ]@ 8 U *A GeN U G W28 K 8SR ] 8 P : @ 8 U A I K 9;L 9MAD8 @ 9 A;GV8 K_> JS:K I P @ I A P :BR $ 9 > J 7 I29/JSG KBK Ied8 U G > 9 d K L JSG ] P G2A;8 : U 9 I2E 7"8 9;:BW8Qd K L JSG ] P GeA;8 : U 9 I U EFJ\LA;G : U 8 9 &: U h O W8 P 9 > 9 O 8 U W : P G U"@ 8 U AD9
(a)
(b)
(c)
(d)
(e)
(f)
9 &H (07/ 31*33"%$) 5 42(*R$) 5/!$'&H6 U7-27(0-%6 1*& g(0 / !")U 31*(*&H1j 10167$) 510([,GR$'&H")(0 5 &H"o7&g P &H c P 5 -%(0#")3$) 42(03$) !-%6 U R$)J-%& 9 !1 - E ;>&QB S& g P78 +&!/! ( &H")(0 5 c H? ^;eB Z&g P78 +&H/5 ( &H")(0 5 =!? L;B S& g P78 +&!/! ( &H")(0 5 fP5=5? ;>B Z&gJc3P78 +&!/! ( & ")(0 5 ; B S& g+c3P78 +&!/! ( & ")(0 5 f=!?5? ;G,'B Z&gmc P78 +&!/! ( &H")(0 5 2 ?!?5? jE
2
212-450 µm 500-600 µm 710-850 µm TCPS
j
* * *
Absorbance at 492 (nm)
1.5
* 1
* 0.5
0
Day1
Day3
Day7
Day10 Day14 Day21
9 ] 10167$) !10(0,3$'&H")(0 ! ! T 8.&! -%(0#")3$) 42(03$) 5-%67U 3$)2-% & 9 51*-k,&He7$)(0& ") h(0")U 42(03$) !-%6 U73$) 7(*&H423")3$&QB +&!/! ( &H")(0 5 c ? ;eB +&!/! ( & ")(0 5 Ic jE
(a)
(b)
9 fgD") !-%aQ 103"'&!1]&!3")(0 (*- "%$)(0e77")(0 5 &H !$)/Q&H (& ")(* ! !, 7 !")U7 10(*&!1]3 101*- 710")$) , !$Fc PV7&g- 5 %- (0#")3$)V42(*R$) 5-%6 U73$) -%& 9 !1 - EkMO 7 !")U7 10(*&!1. 1010-S- "'&!(0 Vh([")UV$)U D &H42(0 6 U &!1010 5(*7(0 ;G$) B`&! VD7 10 (K I P : U E > J AD:BG U : U AD:_9D9 > 88 U d: U 8\8 P 8 E^9DJ\IeN NcG K E9ZNI2J\8 AD7 P 8 8 @ I MG P J 7"I K_K 8 U d28#9 : U J K_> E : U d $c: &Z9C8 U 9C:BA;:_W : AMLG2Nd P G A;7NIJ ADG P 9 ADG A;7"8 P @ I K ] P G J\8 9D9C: U d I U E 8SR ] G9 > P 8 A;G J 7"8 @ :_J I K 9CG K W8 U AD93$:B: & 9;7G P Ag7I K N K :BNc8VG2N*d P G A;7 NI2JSA;G P 9 : U W :BWG h I U E $ :B:_: & K : @ :BA;8 E JSG U A P G K G W28 P
A;7"8E :_9CA P : ?> A;:_G U G2N!d P G A;7ZNI2JSA;G P 9A;7 P G > 2d 7G > AA;789DJ\I G K E"9 4 U I K AD8 P U I AD:BW8 9CA P I AD8\d2L _: 9: U W :BA P G/d28 U 8 A;78 P I ] L 7: 9;8 9A P I U 9MNc8#J AD8 E J\8 K_K 9ADG P 8 K 8 I9C8VI d P G A;7 NI2J ADG P U A;7":_9I ]"] P GI2J 7 JS8 KBK 9 @ > 9CA ? 8 :_9;G K I AD8 E 8\R ] I U E 8#E : U
:BA;7 AD78 E8 9;: P 8 E^d8 U 8 I U E P 8 : @/]K I U A;8#E 7 : K 8 A;8#J 7 U : 9;: U d JS8 KBK_>K I P @ 8#J 7"I U : 9MA Ie: U 8 E ] 8 P :BG E eI A ] 7 L 9C:_G K G2d:_J EG9;8 9 U IEE :BA;:_G U AD78(E:_9CA P : ?"> A;:_G U G2Nd P G A;7 NIJ A;G P 9a: U ] G P G > 9a9DJ\I G K E"9aJ\I U? 8gA >U 8 E ? L @ G E >K I AD: U dVA;78E : AD:BG U W : A P GZI U EFA P I U 9MNc8#J AD8 E
GeNA P I U 9MNc8#J A;8#EZJ\8 K_K 9: U A;789DJ\I G K E"9 57:K I P d P G A;7%: U 9C: U A;8 P 8#E @ :@ @ >K AD: ]"K : 9C: U d IE 8 U G W : P G > 9 : AD7 J O V) 4 8 U JSG E : U d
0
W I29DJ >K I P : U d P G A;7&: U f !4 4 9DJ\I G K E9 JSG U A Ie: U : U d 4VE 0 X H A P I U 9CNc8 JSA;8 E 4 O = ( 9 8 U E G2A;8 K : IeA;8#E : U W:_W2G
6
> ?
4 " W ] G K L @ 8 P ;9 G K_> A;:_G U I29 ] P 8 ] I P 8 E ? LZE :_9D9;G K W: U % d f !4 4 $ K IJ AD:_E 8 DA G%d K L J\G K :_E8 P I AD:BG # h2i O I &4$4 K 8 P @ 8#9 : KB@ : U deADG U # & : U&@ 8SA;7 L K 8 U 8 J 7 K G P AD:BG U 57"8 f a4 4 f 04,8 @ >K 9;:_G U (I9
i
9CA;: P;P 8 E I Ah i P ]"@ cN G P h Z7 5 78 @ _: J P G9 ] 78 P 8 9 8 P 8 :_9;G K I AD8 E ? L W I2J >>@ ` K A P IeA;:_G U I29;78 E7 : AD7 E 8 :_G U : [ 8 E I A;8 P I U E0I2: P E P :_8 E G W28 P AD78 U :_d27A I U E AD78 U0K L2G ] 7: K : [ 8 E NcG P I U 2I EE: AD:BG U I K h F7 ADG 8 U 9 > P 8/J\G @/]K 8SAD8 9CG K W8 U A
P 8 @ G W I K : C9 : U d I @ :_J P G U 9;:B8 W28 /f)G P G > 9 O E :@ : U & cN G P i @ : U IeA j O >K_? 8#J\J\G 9 @ G E : ` 8 E X Ied K 8 *9 @ 8 E : >@ $ O X 7&g9 >]]"K 8 @ 8 U A;8 E ? L i Nc8\ADI K"? G W: U 8 9C8 P >@ I29 > 9; 8 E%A;G U 8 > A P I K : [ 8 AD78V8 U [ L @ 8QIJ A;:_W : AML 57"8 9CA P G @ I K JS8 KBK 98 (8 P 8ZJ\8 U A P :BN > d28#E I A NcG P i @ : U I U E0AD78^JS8 K_K] 8 KBK 8SA I29 P 8#9 > 9 ] 8 U E 8#E : U @ 8 E: >@ $ X h 0 . >K_K 8 :BA &$ (I @ ? P 8SR G P ] G P I AD:BG U I K 28 P 9;W: K_K 8 O & H"G K_K G : U d h %7 : U J >? IeA;:_G U I A j :BA;7
J\8 K_K 9 GeN/5
(8
.
9 >"]]K 8 @ 8 U A;8#E
:BA;7
P 8 I29;78#E :BA;7 f . = ;A G P 8 @ G W28 P 8#9C: I K P #8 E "? K G G EZJ\8 K_K 9
/
= J I G K E9" 8 P 8 M9 AD8 P : K : [ 8 E ? L : @ @ 8 P 9;:BG U : U jei 8\A;7"I U G K NcG P #i @ : U P : U 9C8#E :BA;7 O ! (IeA;8 P I U E \8 R ] G9;8 E A;G T 0 K :Bd7AQNcG P 7"I K NgI U "7 G > P G U 8 IJ 7 9C:K A > P 8 ]"K IeA;8 9QI U E C9 8 8 E 8#E : AD7 JS8 KBK 9 $ 4 O = (9(G P 4 O = (9 X ;& - 8 K_K 9 (8 P 8VI K_K G 8#E A;G eI ACA I2J 7/A;G 9;J I G K E9gNcG P Q7 ? 8SNcG P 8QI U I2E"E : AD:BG U I K h @/K GeN I 7 > @ :_E : ` 8#E : U J > ? IeA;G P @ 8 E : >@ $ X h 0 . >K_K 8SA :BA & (I9 I2E"E 8 E^: U A;G 8#I2J 7 (8 _K K 8 KBK 9/ (8 P 8 @ Ie: U ADI2: U 8#E^: U % I A j :BA;7
4 O =
/ 6
>
@ G P ] 7G K G2dL I29 I9;9;8 9D9C8#E I A ] P 8 E 8\A;8 P @ : U 8 E A;: @ 4 O = (9 G U 9DJ\I G K E"9; 8 P 8 ` R 8 EFI A P G G @ A;8 @/] 8 P IeA > P 8 : U A;:_W28 K L 578V9DJ\I G K E 9 8 P 8 AD78 U E 8\7 L E P I A;8#E%9C8#b > 8 U A;: 9;: U dF9DJ\I UU : U dZ8 K 8#J A P G U @ :_J P G9;J\G ] L $ = X 7& I U E d KB> A;8 P I K E 8 7L E 8QNcG P 7 I U EFh 7 P 8#9 ] 8 J > ;9 : U d 8SAD7"I U G K ;9 8 P :_8 9/$ i j i
2i
2i I U E
i
ii V & NcG P #i @ : U 8 I2J 7 = J\I G K E9 (8 P 8%I K_K G (8 E A;G E P L G W8 P U :_d27A*J\GI AD8 E% : AD70d2G K E ] I K_K IE : >@ a I U E W :_8* (8 E
>U E8 P = X
$Y
X
j ii'&
578 P 8 J\G @ ? : U I U AIE 8 U G W : P > 9! :BA;7 7 >@ I U 0 X H J O )Q4 I29 SJ G U 9CA P > J AD8 E ? L VO P 8 8 U 7"I P E # 8 P K L U 9 K I ? G P I A;G P L $ : A;8 f 7: K IE 8 K_] 7: J AQIE 8 U G W: P > 9 (578 4QE 0 X H I29 > 9;8 EFADG%A P I U 9MNc8#J AQJ\G U"> 8 U AQ4 O = ( 9QI @ >"K AD: ]K : J\8 K_K NcG P h %7 : U I/AD:_9D9 > 8 J >K A > P 8 I29 ") 8\RA AD78 A P I U 9MNc8#J A;8#E^4 O = (9/ (8 P 8 A P L ] 9;: U : [ 8#E I U EJ\8 U A P : N > d28 E,NcG P i @ : U IeN A;8 P 7 : 9 ] 8 U E8 E : U @ 8#E : >"@ 4 O = (9 (8
I A IFE 8 U 9;:BAML GeN #i2i i i2i J\8 K_K ]K IeA;8 8 P 8 J >K A > P 8#E IeAQAD78/: U 9;8 P A K I L8 P GeN(IFJSG J >K A > P 8 ]K I AD8%JSG U A Ie: U : U d X (9 IeA E 8 U 9C:BAMLG2N i i i2i2iVJS8 K_K ]K I AD8(IeAAD78 ? G2ACADG @ K I L28 P a4(A ] P 8#E 8SAD8 P @ : U 8#E A;: @ 8 ] G: U AD9 AD78: U 9;8 P A K I L8 P (I9 P 8 @ G W8 E
I U E AD78 ] P G K : Nc8 P IeA;:_G U GeN X (9; I29 I9;9;8 9D9C8#E > C9 : U d I $ E : @ 8SA;7 L K :_I [ G K h L K & $ J I P ? G R L @ 8SAD7G R L ] 78 U L K & h $ 9 >K NcG ] 7"8 U L K & h # AD8SA P I [ G K : >@ $ 5 = & JSG K G P : @ 8SA P :] 9 (8 P 8Q8\RI @ : U 8 E $c: & X (9I K G U 8 $c:_: & X (9 U G U A P I U 9MNc8#J AD8 E 4 O = (9 I U E $c:_:B: & X (9 A P I U 9MNc8#J A;8#E
4 O = ( 9
i , " 5 P I U 9MNc8#J AD8 E 4 O = (9d P G : U d G U 9;J I G K E9 (8 P 8 P : U 9;8 E :BA;7^f . = ` R 8#E: :BA;7 ] I P IeNcG P @ I K E 8\7 L E 8 NcG P @ : U I A P G G @ A;8 @/] 8 P I A > P 8 4 N A;8 P ( I29;74 : AD7 f . = 2 J\8 K_K 9 8 P 8 ] 8 P @ 8 I ? : K : [ 8 E :BA;7 i 5 P :BA;G U #i2iQNcG P #i @ : U
8 K_K 9 (8 P 88 I29;78 E :BA;7 f . = I U E . = 4 $ = :_d @ I 4 K E P :_J 7 = A aG > : A;:_G U 4 N AD8 P (I9C7 :BA;7Ff . = ' 0 X H&I U A;: ? G E L $ h2i2i E : K_> A;:_G U & $ O = L 9CA;8 @ 9 ) TQ= 4 &; I29 I2E"E 8 E^I U EZ: U J >? I AD8 EFG W28 P U :Bd7A I A 5789;J I G K E9; (8 P 8QAD78 U I29;78#E :BA;7 f!. = I U E/AD78Q9;8 J\G U EI P L I U A;: ? G EL $ 2ii 2 I U AD: @ G > 9;8V4 K 8\R I H K_> G P '& $ G K 8 J >K I P f P G ? 8#9 X > d8 U 8 TQ= 4 &6 I29 IEE 8 E/I U E : U J >? IeA;8 E NcG P 7/IeA P G G @ A;8 @/] 8 P IeA > P 8 )4 N AD8 P ( (I9C7 : AD7 f . = e 9DJ\I G K E96 (8 P 8 ]K I2JS8#E : U I U A;:BNI2E 8 P 8 Ied8 U A $ G K 8#J >K I P f P G ? 8#9 X > d28 U 8 & I U E 8SRI @ : U 8#E ? L J\G U NcG J\I K K I9C8 P 9;J I UU : U d @ :_J P G9;J\G ] 8 $ " = 7 & g57 P 8\8 E : @ 8 U 9;:BG U I K : @ Ied28#94 8 P 8^J P 8 IeA;8#E ? L I U I9;9;8 @ ?K L GeN h O 9C8#J AD:BG U 9/GeN A;78 9DJ\I G K E"9 @ G W : U d A;7 P G > d27F: A 9A;7":_J U 8#9;9 IeA E8 ] AD7F: U J P 8 @ 8 U AD9 G2N @ I U E^I NcG J > 9 E 8 ] A;7 GeN h2h @ : 6
57: EL I29 ] 8 P NcG P @ 8 E ] 8 P NcG P @ #8 E : AD7 I ]] P G W I K I U E/I2J JSG P E : U d A;G AD78 TVU B: W8 P 9C:BAML 2G N 0V: P d: U : P I U 8
] P 8 ]] 8 E I U EE P I ] 8 E 4 N A;8 P I U : U J\:_9;:_G U G U DA 78 ? I2J E : 8 P 8 U AFd P G >] 9%GeN9DJ\I G K E9%: U J KB> E: U d $I & ?K I U 9DJ\I G K E $ U \8 dI A;:_W28 JSG U A P G K & $ ? &;9 J I G K E 0 X ( H $ h d e9;J I G K E& $J &(9;J I G K E X (9 $ #i2i ii2i JS8 KBK 9 9DJ\I G K E& $3 E & 9;J I G K E 0 X H X (9 $8 & 9DJ\I G K E U G U A P I U 9MNc8#J AD8 E^4 O = (98$ ii i2i2i JS8 KBK 9 9DJ\I G K E9 & $cN & 9DJ\I G K E
A P I U 9MNc8#J A;8#EZ4 O = (98$ #i2i i i2i J\8 K_K 9 9DJ\I G K E"9 & $d &9DJ\I G K E U G U A P I U 9CNc8 JSA;8 EF4 O = (9 X (9I U E%$73& 9DJ\I G K E A P I U 9CNc8 J AD8 E^4 O = (9 X (9; (8 P 8 : @/]K I U A;8#E: :BA;7^G U 8 : @/]K I U A ] 8 P I U : @ I K 4(AVEI L 9Vj I U EFh AD78 @ :_J\8 (8 P 8 9;IJ P : ` J\8 E/I U E 9DJ\I G K E"9 8 P 8 P 8SA P :_8\W8 E ` R 8 E/: U NcG P @ I K : U ] I P I = U 8 @ ? 8#EE 8#EI U E%9;8 J AD:BG U 8 E NcG P 7:K A > P 8 EFG U f!a4 469DJ\I G K E9; (8 P 8 ADI 28 U I AVE"I L^j9$H:_d I ? &(I U E $H:_d J E& (4 A ;A 7"8 8 I P K :B8 P A;: @ 8 ] G: U A (8 G ? 9;8 P W28 E 4 O = I2E78 P 8 U J\8 A;G^A;7"8 9 > P NI2J\8%GeN @ :_J P G9 ] 7"8 P 8 9 7: K 8 9;G @ 8%GeN(A;7"8 JS8 KBK 9 NcG P @ 8 E JSLA;G ]K I9 @ : P NI2J\8 eG N @ :_J P G9 ] 78 P 8 9 5 78 9;8 P 8 9 >K AD9 JSG U ` P @ 8 E A;"7 IeA f !4 4 C9 : U A;8 P 8#E @ :]] G P A A;7 8 d P G A;7 eG N 4 O = (9 =X
X = 4 : U h O A;: 8J >K A > P 8 ] G K L 9CAML P 8 U 8$ 5 (f = &(: U SJ G @ ? : U I AD:BG U B: A;7 : @/@ > U G "> G P 8#9;J\8 U AI U I K L C9 : C9 8#E ADG 8SRI @ : U 8A;7"8/0 X H P 8 K 8 I29;8 ? LA P I U M9 Nc8#J A;8#E/4 O = (9 H :_d h 9;7G 9A;7"8VI @ G >"U A 2G N 0 X H 9 $ i P 8 K 8 I29;8 E ? L%A P I U 9MNc8#J A;8#E^4 O = (9VI9 I N >U J AD:BG U GeN (IeAVEI L j "I U E i ) G U A P I U 9MNc8#J AD8 EF4 O = (8
] N > eJS8 KBK & ( I9QJ\G U 9;:_E8 P 8 E I9 IZJSG U A P G K 57"8 I @ G >U A G2N 0 X H P 8 K 8#I29;8 E ? L U G U A P I U 9CNc8 JSA;8 E 4 O = (9 (I9 i U 6d @/K i h U d @ K I AEI L i 7": K 8VAD78 K 8 W28 K GeN9C8#J P 8SA;:_G U%? L%4 O = (9(A P I U 9MNc8#J AD8 E IeA #i2i ] N > JS8 KBK P 8 I2J 7"8 E j U d @ K i U d @/K 8QG ? 9;8 P W28#E A;7"IeAI U : U J P 8 I29;8 : U P 8 9 >K AD9: U I7:_d278 P K 8\W8 K GeN 0 X H 8SR ] P 8 9D9C:_G U AQ9;7G >"K E ? 8 U GeAD:_J\8 EFAD7"I A NcG P I K_K M9 A;78 I @ G >U A Ge6N 0 X H P 8 K 8 I9C8#E ? LF4 O = (9VE :U J AD:BG U GeN(A;: @ 8 F 57:_9G P :Bd: U IeA;8#9 N P G @ ;A 7"8/NI2J A A;7"IeA A;78 d 8 U 8\A;:"@ ? 8 P GeN A P I U 9CNc8 J AD8 E,JS8 K_K 9 NcG P I KBK AD78 AD: @ 8 ] G2: U A 9 :_9 A;7"8 9DI @ 8 ] P G W: IeA;8 E > 9C: U dF: @/@ >U G > G P 8 9DJS8 U JS8 @ :U E I ?>U EI U A I @ G > U A GeN 0 X H P 8 K 8#I29;8 E ? L A P I U 9CNc8 J AD8 E%4 O = (9G U 9DJ\I G K E"9gI299C7"G U : U d P 8 8 U G U 9C: I U A;: ` J\IeA;:_G U 9CA > E :_8 9 $H:_d h &
U G U A P I U 9MNc8#J AD8 E
4 O = ( 9QI K 9CG 9;8 J P 8\A;8 E 0
X H,G U AD78 9DJ\I G K E9 # G (8\W28 P AD78 J\G @/] I P : 9 A;G 8SRI @ : U 8 A;7"8 ? :_GIJ AD:BW :BAML Ge N 0 X H P 8 K 8 I29;8 E ? L 4 O = (9 (8 8 W I K_> I AD8 E :BAD9 8* #8 J AD9 G U A;7"8 ] P G K :BNc8 P I AD:BG U GeN X (9 H:_d
9;7G 9 A;78 ] P G K : Nc8 P IeA;:_G U eG N X (9/I A EI L i j I U E i : U A;7 P 8\8 9;L 9MAD8 @ 9 $c: & X (9/I K G U 8 $c:_: & X (9 U G U A P I U 9MNc8#J A;8#E%4 O = $c:_:B: & X (9 A P I U 9CNc8 JSA;8#E%4 O = (9 8#9 >"K A 9g9;7G 8#E A;7"IeA X (9 ] P G K : Nc8 P IeA;8 E/IeA A;78Q7:_d278#9MA P I AD8 78 U J\G J >K A > P 8# E :BA;7 A P I U 9CNc8 JSA;8#E 4 O = (9 U I2E E :BA;:_G U 8G ? 9C8 P W8 E IQ7":Bd78 P X ] P G K : Nc8 P IeA;:_G U 78 U J >"K A > P 8#E :BA;7 U G U A P I U 9MNc8#J AD8 EF4 O = (9 I29 J\G @/] I P 8#E%A;G X (9 I K G U 8 8IeACA P : ?> A;8 AD78E : 8 P 8 U JS8 : U^] P G K :BNc8 P I AD:BG U G2N X (9 A;G AD78 E : 8 P 8 U JS8 : U A;7"8 I @ G >U AGeN10 X H&: U ;A 78 J >"K A > P 8 @ 8 E: >@ 4Q9 9C7G U : U 0 X H b A P I U 9MNc8#J A;8#E%4 O = (9 P 8 K 8#I29;8I ]] P G R : @ I AD8 K L AD: @ 8 9 @ G P 8 0 X H AD7"I U%U G U A P I U 9CNc8 JSA;8 E%4 O P 8 9 >K AD8 E^: U A;: @ 8 9 7":Bd78 P ] P G K :BNc8 P I AD:BG U G2N X (/9 7"8 U JSG J >K A > P 8 E :BA;7 A P I U 9MNc8#J AD8 E^4 O
> I U AD: ` J\I AD:BG U P 8 9 >K AD9 = (9 57:"@ ? 8 P 2G N ?K G G E W8 9D9C8 K 9 : U 9CDA I2: U 8 E09C8#J AD:BG U 9 G ? A Ie: U 8 E N P G @ 9DJ\I G K E9 NcG P \8 :_d27A d P G >] 9 I29 @ 8 U AD:BG U 8 E : U A;7"8 I A;8 P : P d2GI K (I9VADG^8\W I K_> I AD8 A (G^JSG @ ? : U 8 E M9 A P IeA;8 d2:_8 9QGeN $c: &(E
P > d E 8 K :BW8 P L JS8 KBK A P I U 9 ]K I U A I A;:_G U I U E%$c:_: &d28 U 8QA;78 P I ] L JS8 KBK A P I U 9 ]K I U ADIeA;:_G U NcG P I U d:BGd28 U 8 9;:_9g: U E > J AD:BG U : U ;9 : U A;8 P 8#E @ :"@ ? 8 P G2N(W8 9D9C8 K 9 9DJ\I G K E3&VI9
I%N >"U J AD:BG U GeNgA;: @ 8
i
8 G ? 9;8 P W28#EFA;7"IeAQAD78/E 8 U 9;:BAMLFG2N ?K G G E W28 9D9;8 K 9V: U 9DJ\I G K E9VNcG P I K_K d P G > ] 9Q: U J P 8 I29;8 9 : AD7 A;: @ 8 578 E P > d E8 K :BW8 P L JS8 KBK A P I U 9 ]K I U ADIeA;:_G U 9CA P I A;8 d2LZ: U J KB> E 8 E^AD7 P 8\8 d P G >] 9 G2N $c: &/0 X H 6$c:_: & X I U E $:B:_: & X H X JSG U ADIe: U 8#E 0
8 G ? 9;8 P W28#E I^9;:Bd U : ` J\I U A K L 7:_d278 P E 8 U 9;:BAML GeN ?K G G E W8 9D9C8 K 9 NcG P I K_K A;: @ 8 ] G2: U A 9 7 8 U 9DJ\I G K E"9 X H X (9gG P ? G2A;7ZI9JSG @/] I P 8#E/A;7I A ?K I U 9DJ\I G K E9 $J\G U A P G K & ) 8 2W 8 P AD78 K 8 9D9 A;7"8 J\G @ ? : U I A;:_G U GeN
0
I U E 0 X H E :K AD9 E 8 @ G U 9CA P I A;8#E I 9;:_d U : ` J\I U A K L 7:Bd78 P W28 9D9;8 K E 8 U 9C:BAML : U 9;J I G K E9 : AD7 X
A P I U 9MNc8#J A;8#E&4 O = (9 H!:_d U J\G U A P I29CA : AD70A;78FE P > d E 8 K :_W28 P L M9 A P IeA;8\dL !A;78 ] P 8#9C8 U JS8 GeN X (9 : U E > JS8#E&I 9;L U 8 P d2:"@ ? 8 P GeN ?K G G E W28#9;9;8 K 9 U A;8 P 8#9MAD: U d K L 9DJ\I G K E9gJSG U A Ie: U : U d U G U A P I U 9CNc8 JSA;8#E 4 O = (99;7G (8 E I 7 :_d278 P W28#9;9;8 K E 8 U 9;: AML/I AgEI L I U E h I9 JSG @/] I P 8 E/ADG ?K I U 9DJ\I G K E9 8 I A;A P : ?> A;8 A;7:K A 9 : U I%7:_d278 P : U E > J AD:BG U GeN I U d2:_G2d8 U 8#9C: A;8 AD7:_9
E : 8 P 8 U JS8 ADG A;7 P 8\8 @ IMG P P 8#I29;G U 9 U AD78 E : P 8 J A
X H : U SJ G P ] G P I AD:BG U 9CA P I A;8 d2L @ G9MAG2NA;78 0 X H J K 8 I P 9 G > AGeNA;7"8 9;J I G K E9 P I ] : d E 8 K :_W28 P L^9MA P IeA;8 d2L 5 P I U 9 ]K I U A;8 E X (9VJ\I U d P I N A ADG AD78 7G9MA X (9 P 8 9 >K A;: U d : U I NI9MAD8 P NcG P @ I AD:BG U I U E^E 8\8 ] 8 P ] 8 U 8SA P IeA;:_G U GeN U *8 @ :_J P G W8 9D9C8 K 9
i
> \8 A I K h 4 O = (9 J\G U ADI2: U @ 8 9;8 J 7 L @ I K 9MAD8 @ \J 8 K_K 9 57"8 ] P 8 9;8 U JS8G2N 0 X H @ I L : U E > JS8 E : 8 P 8 U AD:_IeA;:_G U G2NA;78#9C8 9MAD8 @ J\8 K_K 9gA;G I P E X K : U Ied28 5 7:_9(J\I U P 8 9 >K A: U I7 :_d27"8 P E 8\d P 8 8VGeN ?"K G G E W28 9D9;8 K d P G A;7Z: U 9DJ\I G K E9
4V9 P 8 ] G P AD8 E ? L
$
8 P 8 ] G P AD8 E I U G W8 K I ]] P GI2J 7 A;7"IeAZJSG @ ? : U 8#9 0 X H : U JSG P ] G P I AD:BG U,? L > A;: K : [ : U d 4 O = (9%A P I U 9MNc8#J A;8#E : AD7 J O )V4 8 U JSG E : U d 0 X H I U E X A P I U 9 ]K I U A I A;:_G U A;G^8 U 7I U J\8 W I9;J >K I P d P G A;7 : U A;: 8/8 U d: U 8\8 P 8 E 9;J I G K E9 4 O = ( 9 (8 P 8 9 > J\JS8#9;9CN >K_K L A P I U 9MNc8#J AD8 E( :BA;7 J O )Q4 8 U JSG E : U d 0 X H 578 ] P G K :BNc8 P I AD:BG U GeN8 U E GeAD78 K :_I K J\8 K_K 9
I29
9;:Bd U : ` J\I U A K L 8 U 7"I U JS8#E: 78 U JSG J >"K A > P 8#E: :BA;7^A P I U 9CNc8 J AD8 EF4 O = (9VJ\G U ` P @ : U d A;78 ? :_GIJ AD:BW :BAML GeN 9C8#J P 8SAD8 E 0 X H U W :_W2G^: @ ]"K I U A I AD:BG U G2N(
f !4 4 9C: U A;8 P 8#E @ :K I P : U d P G AD7 )578 9;8 P 8 9 >K AD9gJ K 8#I P K L : U E :"K AD: ]K 8JS8 KBK 9 I U E d P G AD7 NIJ A;G P 9 P G K 8 : U A;: 8 8 U d2: U 8\8 P : U d%I U E P 8\d8 U 8 P IeA;:_G U
(a)
(c)
#i
(b)
(d)
D&!7 (0 / 10 3"%$) 5 42(03$) 5/H$'&!6 U7- 67$) !10(0,3$'&H")(0 ! &H" & g F&! c Pm 5 -%(0#")3$) 42(03$) !-%6 U73$) -%& 9 51*7- EI;>&QB S& g D8 +&H/5 ( &H")(0 5 9;eB S& g #8 +&!/57( & ")(* ! c H? ; B S & g+c P8 +&!/57( & ")(* ! ;> B S& g c P8 +&H/5 ( &H")(0 5 =!? jE
8
VEGF (ng/ml)
6
MOI=0 MOI=5 MOI=10 MOI=20 MOI=50 MOI=100
*
*
* **
4
**
2
**
***
***
0 Day3
Day7
Day10
TU7maD(0 3")(0 -2 H, ZM $) 10&H-%+e#g ]-^ 1[")$) 5 Jh31*1I6 1*& ") - E Z&H"'&Jh3$)m$)367$) -% #"'& ")(*C5m !,S= (0 6 #"3n63$)(042 #")-j&HF&!101Y &H"'& 6 5(0#")-]hR$)S6 10 !"%")F&!-42&H ; i 5BRE 7 7 !") -& -%(0/5 ( &!#")1[g ;6 ?DE ?5B U (0/!U 3$ `M $) 10&!-% &H- 5426 &H$)^") k/!$) 576 -j H")2e#g QE H") --%(0/57( &!#")1[gV;6 ?E ?5B]U (0/!U 3$ `M $) 10&!-% &!-k 5426 &H$) ") J/!$) 576 -L7 7 !") e#g QE -%71[")-k-%U7 h ")U& " ]- "%$'&!7- ,G R") &H" i c?!?J67,G H 31*1]-% 3$)3") ")U7 4o&Hn(04L74 10 C5 1Y H, ZM &!- 5426 &H$)o") ^ !")U73$I-% 10 3") - E
(a)
h
(b)
424L 7 !l !$)3-% #"- "'&!(0 (0 /I !, ZM ! ;>&5B9"%$'&H - ,G33")) ]- &! 2;eB 5 >"%$'&! - , 3")) ]- 1[")7$) ,G H$Zc? & g- ! -%(0#")3$)242(03$) 5-%67U 3$)-%& 9 !1 - E ]-]- "'&!(07^h(0")U &!#")(0e Dg27([$) 3")F&!/5&!(0 - " ZM ;/!$) 3B &! D 31*3(f ! #")3$)- "'&H(*7 h([")U ;e 10 BRE 4o&!/! - &H$)2 !426 5-% !,j-%33")(0 5 - !,]")U ^-%& 9 51*7- 42 CD(*7/F")U$) 57/5U ([")")U (0'aD -%-& "` 67")U (0 3$) 423D")-j H,"%$'&! - , 3") ]- 8 &! M ]-"%$'&! - , 3") ]- E S&H"'&JhR$)m$) 67$)3-% #"'&H")(0CQm H,Z= (0736 #"L3n63$)(042 #")-L&! &H1*1I7&H"'& 6 !(0D")-kh3$) 6 10 !"+ ")V&!-`42&! ; i 5BRE 27 7 !") -`&F-%(0/! ( &H#")10g ;6 ?E ? !B`U (0/5U73$ M 67$) !1*([,3$'&H")(0 5 (0 &oM ]-` 5V"%$'&!7- ,G R") ]-I 710")$)k- g- ") 4 &H-` !426&H$) m") M &H10 5 !E F H") -Z&^-%(0/57( &HD")1[g ;6 ?E ? !BIU7(*/!U 3$ZM 67$) !1*([,3$'&H")(0 5 (0 &^M ]-"%$'&!7- ,G 3") ]-j 710")$)S- g- ") 4 &!- !426&H$) F") 2M ]-` !m"%$'&!7- ,G 3") ]- E
(a)
(b)
(c)
(d)
oI 67$)3-% #"'&H")(0CQ2_`(0- ") !1* !/5(0&H13$) 5-%-k-% 3")(0 57-k H,j")(0-%-% o(0426 1*&!#")Vh(0")U -%(*#")3$) 42(03$) 5-%67U 3$)2-%& 9 51*7- 8 2 c & g- &H, ")3$ (0426 1*&!#"'&H")(0 ! -% e37"'&!7 57-%1[g (0 42(0 !EoTU -%2(04o&H/5 -ShR$)^"'&!aQ V,$) !4 - "'&!(0 -% 3")(0 57-k H,j-%& 9 51*7 !D"'&H(0 (0 /J;>&5BT$'&! - , 3") ]- 8;eB `M ZM 8 ; B` ! "%$'&H - ,G33") ]- 8&H ;> BTY$'&!7- ,G R") ]-ZM ]- E ]10 # D+CQ -%-%31*-hR$)S( #")( FeDgo6$) -% 7 S !,.10 42(0 &!19- "%$) 3")$)Z !D"'&H(0 (0 /^$)Fe 10 # D+ 1010- E
100
Blood vessel denisty (#/scaffold)
80
* **
Blank VEGF EC EC + VEGF Non T ADSC Non T ADSC + EC T ADSC T ADSC + EC
* **
60
** *
** 40
** 20
*
*
0 Day7
Day14
Day21
9 S(0 R")(*3-L !,I-%& 9 51* C5&H-% 1*&H$)(& ")(0 5 &H,")R$2(0426 1*&!#"'&H")(0 ! -% e "'&! 3 5 -%1[g (* 42(0 5E !$L&!'U ")(042 6 5(0#"8")U D 4ke3$I !,Oe 10 # DVCQ -%-% 10-`h&!-Z ! #")J(0V_SM - "'&H(*7V-%1*(* -`,G H$S&HRUV/!$) ! 6ESMO&!'U /H$) 576 3 5 -%(0- ")V !, C5 &!7(04o&!10- E I101f7&H"'&F6 5(0#")-`h3$)L6 10 !"%") &!-S42&H LE o7 7 !") -S&F-%(0/5 ( &!#")1[g ;6 ?DE ? 5BZU7(*/!U 3$ D74Le3$ !,]e 10 # D CQ -%-%31*-.&H- !426&H$) ") Ie 1*&!7aZ-%& 9 51*7- E ` H") -K I AD8 EZW I29DJ >K I P d P G A;7Z: U ADG A;7"8 h O ] G P G > 9E G @ Ie: U : U A;78 @ G E 8 K : U d 9MA > E :_8 9 I U E O ] G P G > 9 9MA P > J A > P 8 : U 8\R ] 8 P : @ 8 U ADI K 9MA > E :_8 9
> /
6
6
5 P I U 9 ] G P A GeN U > A P :_8 U AD9I U E&J 78 @ GI A;A P I2J A I U AD9 :BA;7: U ] G P G > 9 9DJ\I G K E"9 :_9 ] P : @ I P : K L IFN >"U J AD:BG U GeN E : > 9;:_W:BAML I U E ] G P 8 9CA P > JSA > P 8:$ ] G P 8 9;: [ 8 ] G P G9C:BAML I U E^: U A;8 P J\G UU 8#J AD:BW :BAML& Q> P @ G E 8 K J\G U 9;:_E8 P 8 E^IZh O ] G P G > 9 EG @ Ie: U A;7I A P 8 ] P 8 9;8 U A;8#EZI%9 >? 9CA P I AD8 : AD7 9CG K :K I P 9C7I ] 8 9 7: A P I U E G @/K L : U AD78%E G @ 2I : U U JSG U A P I9MA : AD7 DA 78 @ G E8 K : U d^9CA > E :_8 9*: U A;78/8SR ] 8 P : @ 8 U A I K 9CA > E :_8 9A P I U 9 ] G P A eG N J 78 @ G I A;A P I2J A I U AgADG G ] K I2J\8Q: U A;78 O W2G2 JSA > P 8 GeNaAD78 9C: U A;8 P 8#E 9 ] 78 P 8 ] G P G > 9 9;J I G K E9 )57":_9 E : 8 P 8 U J\8
: U E: @ 8 U 9C:_G U I K :BAML P 8 9 >K A;8#E : U I E : E8 I U E E : P 8 J AD:BG U GeNJSG U JS8 U A P IeA;:_G U d P I2E:B8 U A 9g: U h O W8 P 9 > 9 O ] G P G > 9 9DJ\I G K E"9 *I U E AD7 > 9 !IFE: 8 P 8 U A A;: @ 8/N P I @ 8 cN G P I^J 78 @ GI A;A P I2JSADI U AQA;G E : > 9;8/G > AI U E 9;:_d U I K 7"G9CA JS8 KBK 9 578 @ 8\A;7G E G2NaJ 78 @ GI ACA P IJ A I U A : U JSG P ] G P I A;:_G U : U A;G ] G P G > 99;J I G K E9gI U E/AD78 N I9C7:_G U A;78 L/I P 8 P 8 K 8 I9C8#E%I P 8 I K 9;G J P :BA;: E :_8 9 8 J\G U 9;:_E8 P 8 E
A;7 P 8 8 P 8 K 8#I29;8 ] IeACAD8 P U 9GeN I/d28 U 8 P :_J J 78 @ GI A;A P I2JSADI U A : U J K_> E : U d /$: & K G J\I K : [ 8#E $c:_: & E :_9CA P : ?> A;8#E"I U E $c:_:B: & P 8 K 8#I29;8 N P G @ G > A 9C: d9V: U A;: 8 8 U d: U 8 8 P 8 E 9;J I G K E9 O : AD8 E P 8 K 8#I29;8 @ : @ :K A > P 8 EG U A;7"8(9DJ\I G K E9!I U E P 8 K 8#I29;8 E 0 X HI A A;78/9 > P NIJS8 GeN @ : d27G > AVAD78 O ] G P G > 9Q9CA P > JSA > P 8 578 P 8 K 8 I29;8G2N 0 X H (I9 @ 8 I9 > P 8 E ] P :_G P ADG A P I U 9 ]"K I U A I AD:BG A P I U 9MNc8#J A;8#E 4 O = (9 P 8 K 8 I9C8 IZ9;: @ I2E"9CG P ] AD:BG U I ]] P GI2J 7 @ G9CAGeN10 X
U G U A;78 9;J I G K E9 : U h O J >"K A > P 8 A;: 8 J >K A > P 8 I 9 9 A I29QI29D9 >@ 8#EFA;7"IeA : K I P I @ G >"U A Ge!N 0 X HA;7 P G > d7G > AQAD78 9DJ\I G K E"9 eI N A;8 P : @/]K I U ADIeA;:_G U U A;7"8 H I29(I2E"9CG P ? 8 E%G U G U 8Q9;:_E8QG2N*A;78 9DJ\I G K E9 8 @ 8 I29 > P 8 E AD78 I @ G >U A(GeN
X H IE9CG P ? 8 E G U A;7"89;J I G K E ] P :_G P A;G/: U W :_W2G/: @ ]"K I U A I AD:BG U 0
/ 1
578 d8\G @ 8\A P L GeN ] G P G > 9 E G @ eI : U 9 ;9 :Bd U : ` J\I U A K L: U"> 8 U \J 8 9 AD78 @ GeAD: K :BAML GeN 8 U E GeAD78 K :_I K JS8 KBK 9gI U E W28#9;9;8 K : U d P G A;7 Q> P @ G E 8 K J I ] A > P 8 E AD78NcG P @ I AD:BG U eG N ? K GG E W28#9;9;8 K 9!: U I h O E G @ Ie: U U I29)9C7"G U A;7I A 8 U E GeAD78 K :_I K JS8 K_K 9 J P I K G U I h O 9 > P NI2JS8 I U E A;7"8 G ? 9CADIJ K 8 9E:BW8 P A A;78 E: P 8 JSA;:_G U GeN ?K G G E0W28 9D9;8 K d P G A;7 8 @ 8 I9 > P 8 E AD78 U >@ ? 8 P GeN ?K GG E W28#9;9;8 K 9QA;7"IeAd P *8 : U ;A GFA;78 ] G P G > 9 EG @ Ie: U AD78/A;G2ADI K K 8 U deA;7 GeN ?K GG E W28#9;9;8 K 9 !I U E A;78/8\RAD8 U 9;:_G U GeN W I29DJ >K I P ] 8 U 8\A P I A;:_G U )4(A EI L # i A;7"8QADGeA I K U >@ ? 8 P I U E K 8 U d2A;7ZGeN ?"K G G E W8 9D9C8 K 9gNcG P A (G 9CA P I AD8\d2:_8 9GeN K G J I K : [ 8 E I U E E : AD8 E P 8 K 8 I9C8 8 8 P 8 h h i # i h I U E @/@ @ @ P 8 9 ] 8 J AD:BW8 K L U A;7"8
8SR ] 8 P : @ 8 U A I K ] I P AGeNA;7":_9; (G P 28 U E GeAD78 K :_I K JS8 K_K 9(9CADI P AD8 E/ADG J P I K G U ;A 78 9 > P NIJS8VG2N @ _: J P G9 ] 78 P 8 9I U E ? P :@ ? 8 P GeN ?"K G G E W 8 9D9C8 K 9 : U E :U A;8#E G U AD78 h O 9C8#J AD:BG U G ? ADI2: U 8 EZN P G @ AD78 @ :_E"E K 8 GeN O 9DJ\I G K E"9 g4(A EI L - (8 G ? 9;8 P W28#E AD7"I A AD78 ADGeADI K*U >@ ? 8 P
GeN)W28#9;9;8 K 9NcG P ?K I U I U EFd8 U 8 A;7"8 P I ] L 8 U E 2G A;78 K :K IeA;:_G U 9MA > E :_8 9 G P :Bd: U 9 N P G @ AD78 @ 8\A;7G E GeNJ\G >U AD: U d
U
? P :_8SN (8 :Bd U G P 8 E^AD78 ] P G J\8 9D9VG2N A;7"8 ?"K G G E
W28#9;9;8 K P 8 @ G E 8 K : U d I U E \J G >U A;8#E/8 IJ 7 U 8* ? K G G E W28 9D9;8 K AD7"I A ? P I U J 78#E/GeN A;78QGeAD78 P ?K G G E%W8 9D9C8 K 9 1)V8\W28 P AD78 K 8 9D9 :BA 7"I29 9;7G U A;7"IeA 9;G @ / 8 GeNA;78 U 8* K L NcG P @ 8 E ?K G G E W8 9D9C8 K 9 P 8\d P 8#9;9 %57:_98 8 J A J\I U0? 8 @ : AD:BdI A;8#E : U N > A > P 8 9CA > E :_8 9 ? LF9;8SA;A;: U d >"] I K 8 U d2A;7 AD7 P 8#9C7"G K E I ? G W28 7: d27^AD78 ?"K G G E W28#9;9;8 K 9 I U E A;7"8\: P 7"I W28 P 8 I2J 7"8 E%AD78 @ I A > P IeA;:_G U 9MA Ied8
1
/
578 E : @ 8 U 9C:_G U I K E: 8 P 8 U J\8 : U A;7"8 AD78\G P 8\A;: E :B8#9 K 8 E ADG E : 8 P 8 U A @ 8 J 7I U :K I P d P G A;7&: U 9DJ\I G K E9 I29 E :_9DJ > 9;;9 8 E I ? G W8 4 K AD7G > d27 AD78 P 8 8\R :_9CAD9 I
E : AD8 W I KB> 8#9: U A;7"8 P 8#9 >K AD9(G2N!AD78h O @ G E 8 K : U d%I U E O 8\R ] 8 P : @ 8 U ADI K 9CA > E B: 8#9 AD78JSG @ E G P ] P 8 9;8 U A;8#E%: U A;7: d7G > AAD789;J I G K E9I29 J\G @/] I P 8 E A;G K G J\I K : [ 8 E P 8 K 8 I29;8 9MA P IeA;8\d:B8#9
#
578 ] G P 89CA P > JSA > P 8 ] P G ] 8 P AD:B8#9aG2N9;J I G K E9"$c8 d ] G P 89;: [ 8 e I U E ] G P G9;: AML-&*J P :BA;:"K I P : U d P G AD7
578 P 8 :@ AD7 P 8 9;7G K E0NcG P A;7"8F9DJ\I G K E 9 ] G P G9;:BAML ? 8 K G 7: 9 A;78 W I29DJ >"K I P : U d P G AD79 : KBKa? 8 K : @ :BA;8#E
57: J 7 I29 E : > 9C:_G U
] P G @ G2A;8#9%I E :_9DJ > D9 9;:BG U I ? G > A/A;78 @ #8 J 7"I U :_9 @ 9 ;A 7"IeA 8 U AD9gI K G U 8 4Q9 I U 8SRI / @ ]K 8 8 P 8\Nc8 P A;G AD78V: U"> 8 U J\8
*E8\d P I2E"I A;:_G U
I U E >"] ADI 2 8 G U AD78 8\R A;8 U A GeN W I29DJ >"K I P : U d P G A;7 : U A;G AD:_9D9 > 88 U d : U 8 8 P 8 E 9;J I G K E9 U I2EE: AD:BG U @ I AD78 @ I AD:_J I K @ G E 8 K : U dI K_K G (8 E b > I U A;:BNcL : U d ] P G ] 8 P AD:B8#9 A;7I AgI P 8 JSG @ ]"K : P 88\R ] 8 P : @ 8 U ADI K_K L 2I U E I KBK G (8 E 9CL 9CA;8 @ : [ IeA;:_G U GeNG > P U G K 8 E d8(G U AD78\: P : @/] I2JSA
G U W I29DJ >"K I P : U d P G AD7 ! 4Q9 9 > J 7 ] P G ] 8 P AD:B8#9 ' 8 P 8SNc8 P A;G AD78 A;G2ADI K W28#9;9;8 K K 8 U d2A;7%I U E W8 9D9C8 K @ G P ] 7G K G2dL: U ] G P G > 9 E G @ I2: U 9
U
N > A > P 8 C9 A > E :B8#9 G > P 9C: @ >K I AD:BG U @ G E 8 K J\I U ? 8 \8 R ] I U E8 E 9 > J 7 DA 7"I A :BA J\G PDP 8 K IeA;8#9VJ K G9;8 P :BA;7 AD78 : U W :BWG S8 R ] 8 P : @ 8 U A 9 ? L : U J K_> E : U d7$: &A;78 J\8 K_KB>"K I P d P G A;7^: U ADG O C9 A P > J A > P I K*] P G ] 8 P A;:_8 9G2N 9;J I G K E9 $:B:_: &A P I U 9 ] G P A GeN
J 78 @ GI A;A P I2J A I U AV: U O E : @ 8 U 9;:_G U I K 9DJ\I G K E6$c:_:_: & @ >K A;: JS8 K_K_>K I P J\G / @ ] G U 8 U A 9 I U E $c:_W-& ?"K G G E G 6: U W28#9;9;8 K 9 U^] I P A;:"K I P "9 > J 7 @ G E8 K 9;7G >K E^J\G U 9;:_E8 P ;A 7"8I2E 78 P 8 U JS8I U E^J P I K : U d GeN 8 U E GeAD78 K :_I K JS8 KBK 9 G U AD78 9 > P NIJS8#9GeN @ _: J P G9 ] 78 P 8 9 ? P : 9C: U d%9DJ\I U"U : U d I U EF7: 8#9 A;78 @ G P ] 7"G K G2d2L%G2NW8 9D9C8 KU 8SA (G P : U O 9;J I G K E9VJ I U ? 8G ? ADIe: U 8#E I U E J\G @/] I P 8#E ADG%N > A > P 8 @ G E8 K : U d P 8#9 >K AD9 H: U I KBK L A;7"8 : U DA 8\d P IeA;:_G U GeN J >"K A > P 8#E
8 U E GeAD78 K :_I K JS8 KBK 9 B: A;7^7G9CA 8 U EGeA;7"8 K :_I K JS8 K_K 9 J\I UZ? 8E S8 AD8 P @ : U 8#E > 9C: U d/: @ @ >U G9MA Ie: U : U d AD8 J 7 U :_b > 8#9
#h2i
+ G9C7:U : P ] 7 L I U E O Y G G U 8\L 3.:_G2: U 9 ] : P 8#Ed P G A;7 GeNJ P L 9MA I K_K : U 8J\I P ? G U IeA;8I ] IeA;:BA;8 G U ? :_G E 8\d P IEI ?K 8 ] G K L @ 8 P 9 >? 9CA P I ADI %$ - h i j 2heiih D Y 5!I ? GI29 O 8 EEG f # '5 P 8 ? 9 ? IJ 7 eI U E = Y # G KBK : 9C: U dI U G W8 K 9;: U AD8 P 8 E ] G K L @ 8 P : P d = f)G P A;8 P )I U E Y )H 5 8 KBK I @ .:_G @ IeA;8 P : 8 8 U d2: U 8\8 P : U d
* +- * h h j h heii2i Y 4 Y IE K G :_8 J #4 . 8 K : K eI U E Y # G KBK : U d28 P .(G U 8 A;: 88 U d: U 8 8 P : U d P 8 JS8 U A!I2E W I U JS8#9aI U E ] P G @ :_9;: U d AD78 P I ] 8 > A;: 7"IE : P I U E O Y G G U 8\L ^f P G @ G2A;: U d I U d:BGd28 U 8 9;:_9 : U 8 U d: U 8\8 P 8 E AD:_9D9 > 8 9 . * -
j i hei2i h = = O > dd2: P I K I Y . G E d8 P 9 I U E^f f O 8 > J\I 578 8\W I K_> IeA;:_G U GeN K LG ] 7: K : [ 8 E ] G K L @ 8 P @ IeA P :_J\8 9NcG P IE @ : U :_9CA;8 P : U d P 8#JSG @ ? : U I U AQ7 >@ I U ? G U 8 @ G P ] 7Gd28 U 8SA;: J I # 0 I29DJSG U 8 [ I U Ef f O 8 > J\I X U 7"I U J\8 @ 8 U A GeN ? G U 8 d P G AD7F9 > 9CADIe: U 8#EZE 8 K :_W28 P L GeN P 8#JSG @ ? : U I U A 7 >@ I UF? G U 8 @ G P ] 7G2d8 U 8\A;: 8 8 U d: U 8\8 P : U d * * * " - * * * -
- P G EI # 5 G U E G #4 T @ 8 [ I (I 5 7 L I 5 7 LI @ I I U E = 5 I9 > dIe: X U 7"I U JS8 @ 8 U A GeN G9CA;8 G2d8 U 8#9C: P NI2JS8J\GIeA;8 E :BA;7 9CL U A;78\A;:K : U K : 8 d P G A;7 NIJ A;G P $ H &*9CA;: @ >"K IeA;8 9a7 >@ I U G9MAD8\G ?"K I9MAaIJ A;:_W : AML " +* * j i h j hhei
h :_9DI > 8 J 7"I U :"K I P 8 U E G2A;78 K : A;G J P : U 8gI2JSA;:_W : AD:B8#9*GeN ? I9C: d P 8 K 8#I29;8 9;L 9MAD8 @ 9 $ - -* - j h h heiih 4 g4 = 7"I P I L ". 5 K :BA [ @ I U g4 (5 P > 9 28 L I U E 8\:?K I 1 *5!G P @ I U Y Y G9;8 ] 7 > P ] 7 L 5I A >@ *I U E 4 aG @ I U X W I KB> I A;:_G U GeN ] G P G > 9 U 8\A G P 9gGeN ] G K L $ h 7 L E P G R L8SA;7 L K @ 8SAD7"I2J P L K I A;8 & I9: U A;8 P NIJS: d E 8 K :_W28 P L%E 8\W :"?>K I P AD:_9D9 > 8 9 $ - * * +* hei h i
h "H P 8 9;7 U 8 L
>K A > P 8 GeN)I U : @ I K J\8 K_K 9 4 @ I U > I K G2N ? I9C: J 7 H = 7G9;7"I U L ) 8 > Nc8 K E2I U E = ' G278 U X U 7I U J\: U dQA;7"8(W I9;J >K I P : [ I AD:BG U GeNA;7 P 8\8 E : @ 8 U 9;:_G U I K] G P G > 9 I K d2: U I AD8 9;J I G K E9 ? L : U JSG P ] G P I AD: U d/JSG U A P G K_K 8#E P 8 K 8 I9C8 ? I9C: 9 = 7G > = J 78 : U G :BA [ X # G E d8 ;0 57: P >@ > P AD: 4 ) "5 : A 9C:_G > Y g4 = A;: ? 8 P 4 O *G ? G = # >U 9 ? 8 P d8 P X > 8\ACA I = X X ] 9CA;8 : U I U E X H TVU d28 P G @/] 8 P I A;:_W28 8 8 J A 9 GeN ? I9C:"K I P 8 U E G2A;78 K : 6.I G > P I U E 65 G P U G 9 : 57"8 P I ] 8 > AD:_JZ: U AD8 P W28 U AD:BG U 9 NcG P 8 U 7"I U JS: U d^JSG K_K I A;8 P I K E 8 W28 K G ]@ 8 U A ? L IE @ : U :"K A 9 I U E ] G2A;8 U AD:_I K 7"I [ I P E9 $ * * ! - h h heii 5 + 1a8\8 6 !f)8SAD8 P 9 !I U E O Y G G U 8 L G @/] I P :"K I P 8 U E G2A;78 K :U G @ :_LI 1aI U d28 P )I U E Y f 0 I G2N ? I29;:_J `"? P G ?K I9MA d P G AD7 NIJ ADG P : U J P 8 I9C8#9 ? G2A;7 I U d2:_G2d8 U 8#9C:? 8 P L Y I ? : U G :BA [ Y = I @ >K 9 : 5 ")VI I @ > P I ;5 = G ? I K_K 8 Y 5 8\8SNc8 . (H !.(G L JS8 I U E X = J 7 I PD[ 8 @ G E 8 K : U d GeNJSG P A;: 8 P 8\d8 U 8 P IeA;:_G U - * # i hj h h2i2i 0 = >? P I @ I U :_I U 78 ? P 8 I U E = I @ I P : 9 @ 8 E : ADI U A 8 U E G9MA I AD: U 9 >"]] P 8 9D9C8#9G W I P : : K E : U d I ? 8\ACAD8 P W8 JSA;G P 57"8 @ I U : ]>K I AD:BG U G2N 4V/4 0 W : P :BG U 9
hj 2i 2i heii2i 5 LdG > P I : I U AD: ` J\I AD:BG U I U E P 8 d >K I AD:BG U GeN JS8 KBK@ :_d P I AD:BG U 8 U ?> P d8 P O 8 JSG U 9CA P > J AD: U d $ I U E P 8 J\G U 9CA P > JSA;: U d &(JS8 KBK!@ :Bd P IeA;:_G U
i
# a8\8 4 6 > 9;:_J J I U A;: ;*G J\I K E 8 K :_W28 P L
- - = # :_d @ G U E4 ? : K :BAML GeN ] G K L @ G P ] 7G U > J K 8 I P K 8 > G J\LA;8 9ADG G P :_8 U A: U d P I2E:B8 U A 9gG2NJ 78 @ GeADIJ AD:_JVNI2JSA;G P 9 $ - * j i j2j 4 G K E 8 U = # I U 9;G U 5 5 : P @ I U f 4 = J 7 U 8\: 8 U JS8 E ? L d P IeN A ] G P G9;:BAML * ! . i 2i 5 5 :"K I P @ IeA P : R @ G E: ` 8#E ] G P G > 9: @/]K I U AD9 - * +- - j2j heiih Y X = I U E 8 P 9 = I K JSG K_@ = O ;.I K 8 + ) I U d I U E = ;!I @ G U A f P 8 W I9;J >K I P : [ I A;:_G U G2N I ? :BG @ IeA;8 P : 9;: U d%I J 7"G P :BGI K_K G U ADG2: A;G @ IeADI +- - jei + 1a8\8 = 5 G > W P G > 2 Gd K G > 0 J U AD: P 8 ) I U E 5 LdG > P I :K I P I > A;G @ IeA;G U @ G E8 K NcG P A;7"8 ] P G K :BNc8 P I AD:BG U GeN @ :Bd P IeA;: U d/JSG U A I2J A : U 7: ? :BA;8#EFJ\8 K_K 9
% h h
X Y W I U :_8 9;G U = (f)8 : P JS8 I U E 5 / = I K I >K AD:_J\8 K_KB>"K I P 9;: @ >K I A;:_G U ] P 8#E :>"@ I U I K L 9;:@ E:_9DJSG:_E 8 >@ -
j X f I K 9D9CG U I U E # A;7 @ 8 P V4 @ G E 8 K NcG P : U E :_W :_E > I K I U E J\G K_K 8#J A;:_W28 JS8 K_K@ G W8 @ 8 U A : U O :_JSAML2G9CA;8 K : >@ E:_9DJSG:_E 8 >@ % * * ! j i #i 2h2i2i2i j 1. O :_J : U 9;G U I U E !5 !5 P I U b > : KBK G F5 P I U 9 ] G P A8 b > IeA;:_G U 9I U E : U E :_J\8 9NcG PP I U EG @ I U E ? :@ G > P : U E > J\8 E I U d:BGd28 U 8 9;:_9I29)I P 8 : U NcG P JS8 E P I U E G @ I K G E 8 KBK : U d J I ] : K_K I P L U 8SA (G P %NcG P @ I A;:_G U :BA;7G > AV8 U E GeAD78 K : I U ) >@ 8 P :K I A;:_G U G2NgI U d:BGd28 U 8 9;:_9: U AD78 J\G P U 8 I * - hj h2i2i h I P > 9 O . G27 @ I U E = J 7 @ :_J = : @ >"K IeA;:_G U G2N)W8 9D9C8 Ka@ G P ] 7Gd28 U 8 9;:_9 > 9C: U dFJS8 K_K_>K I P I > A;G @ IeADI * h2 i
0 > A;7 > I P >]] I U - -5 >"? Ie: I U E "4 > 8 P ? IJ 7 5 >@ G P : U E > JS8#E U 8 G W I29DJ >K I P : [ I AD:BG U : U AD78 @ G > 9;8 8 L28 * $ * -
jei h D O )4 1!I > 8 U ?> P d8 P I U E Y Y 1a: U E 8 P @ I U - - U d O : P 8 JSAW :_9 > I K : [ IeA;:_G U GeN9C8#J P 8SA;:_G U N P G @ 9;: U d K 8 ? G W: U 8 I2E P 8 U I K J 7 P G @ I = U J\8 K_K 9 ? L K I29;8 P : U E > JS8#E U IeA;:_W28 "> G P 8#9;J\8 U J\8Q: @ Ied: U d @ :K I P J\I K J\: >@ (I W8 9: U d K :K I P J\G @/@ >"U :_J I AD:BG U E :_9CADI U JS8#9VI P 8 E8SA;8 P @ : U 8 E ? LFA;7"8 P 8 K I AD:BW8 A;: @ 8 J\G U 9CADI U A 9 NcG P JSLAD G J 7"8 @ G : U 8 9;8 J P 8SAD:BG U I U E E: > 9;:BG U ! * ! * h2h h2 h
j H + G9;7:U J I A;:_G U E:_9CADI U JS8 : U AD78 : U A;8 P J\8 K_KB>K I P 9C:_d U I K : U d ? L J\LADG eJ 78 @ G : U 8 G P I > A I2J\G2: AD:BG U ? L I/Nc8 ] 8 P J\8 U A 578 JSG U 9MA I U A "> R JSG U E :BA;:_G L $ $ & U 3 $ > " 8& :"U :E I AD8 P G * . h h heii2i aI ] :_E > 9FI U E H f : U E 8 P ) >@ 8 P :_J I K 9CG KB> A;:_G U G2N ] I P AD:_I K E : 8 P 8 U A;: IeA;:_G U 9Z: U 9DJS:_8 U J\8 I U E 8 U d2: U 8 8 P : U d h i2i = 8 P : U : O 24 @ ? P G9;: X : P I > E G 24 I @ ? I 2f P 8 [ :BG9C: eI U E/H . > 9D9CG K : U G G E 8 K : U d A;78 8#I P K L9CADI2d28#9 G2NW I9;J >K I P U 8SA (G P I29D9C8 @ ?K L % h2h jj jj hei i i I AD9 >@ GeADG I U E 5 )V:_9;7: @ > P I 8 P 9;8 UU 8 A : : A;8#E >U : NcG P @ ] 9C8 > E G P I U E G @ U >@ ? 8 P d8 U 8 P IeA;G P $ * * - " * . ,- . * $ & 2i
X
ih = "5aG U d ] P :_W IeA;8 JSG @/@ >U :K I P I U E ? :_G K G2d:_J I K I29 ] 8#J A 9 $ . . h j 2i
-
#h
7I U d G > Y I U d Y > + O I U d . a: 7"IeG Q:_I U Q: = >] P 8 9D9;:BG U GeN A >@ G P d P G AD7 ? L G U JSG K LA;: 9 @ 8 E :BADI28 E E8 K :BW8 P L%GeN I U A;:?"K 8 H K A - . - * h h2i2i i 5 O OV[ : >?"K I I2J P G ] G P G > 9(7 L E P Gd28 K 9I29 W I9;J >K I P : [ I ?K 8 9;GeN A AD:_9D9 > 8 : @/]K I U A : U AD8 P NI2J\8 9 I A;8 P : IeA;:_G U GeN J 7: ADG9DI U ] G K L $ K IJ A;:K I P IE 78#9C:_G UF@ G K 8 J >"K 8 $ (4 & P 8\d >K I A;8#98 U EGeA;7"8 K : K I K J\8 K_K*@ GeAD: K : AML A;7 P G > d27 I U :BA P : EL G2N @ G P ] 7"G K Gd2L0GeN ] P Gd28 9CA;8 P G U 8 K GI2E8 E @ :U G Y # > I U d H > A P 8 K_K 4 Y 5 I A [ f '.8 U 7"I2: @ # f '*G P 8 U [ I U E # # 8 E P :"K AD: K : U 8 Ied8 J\8 K_K 9VN P G @ 7 >@ I U I2E : ] G9C8 A;: 8 @/]K : P 8 U JS: U )VG W28 K ] G K L @ 8 P 9;L U AD78 [ :B8#E J\8 P I @ :_J/J\G @/] G9C:BA;8 ? I29;8 E 9;L 9MAD8 @ NcG P ? G U 8 P 8 ] I2: P 4 U : U W :BA P G 8 W I K_> I AD:BG U - * ,- - 4 jeh j j heii h + 7I U d I U E&f I .(:BG @ : @ 8SAD:_J ] G K L @ 8 P I ] I AD: AD8 JSG @/] G9;: AD8 9DJ\I G K E9 NcG P @ : U 8 P I K : [ 8 E AD:_9D9 > 8 8 U d2: U 8 8 P : U d * i2i heii 5 25 G >? G H :BLI M: # 25 : @ I U E 5 )QI I @ > P I = ] G U ADI U 8\G > 9 NcG P @ I AD:BG U GeN ? G U 8 K : 28QI ] IeA;:BA;8 K I L28 P G U J 7"8 @ :_J I K_K L A P 8 I AD8 EZA;:BADI U : >@ @ 8SA I K 9 $ - * j #hj # h
D + H 7G > Y O O >UU I U E . > U W : A P G P 8 9 ] G U 9;8 GeN % 5 X ] P GG9MAD8\G ?K I9MA 9 : AD7: U AD7 P 8\8 E : @ 8 U 9;:BG U I K I ] I AD: AD8 JSGI A;8#E !f 4 - * +- - j . i h2i2i Y :_E" I 5 + G9;7: I I 5 MJ 7": M: @ I I U E + 5I I > P I 9MAD8\G2d8 U : P 8 E ? G U 8 eJS8 P I @ : JSA !4 J\G @/] I P : E :_8 9 G U A;78 ? :_G JSG @/] IeA;: ? : K :BAML GeN @ I AD8 P :_I K 9 FH: ? P G ?K I29CA P 8\G P d U : [ I AD:BG U G2N9 >? 9CA P I A >@ ? G >"U E `"? P G U 8#J AD: U G U 9 > P NI2J\8 9 W I P L : U d : U (8SACA I ? : K :BL - * ,- - i 4 O 3)V:_9 ? 8\A # = I >U E P L 4 Y G: P 4 HG2A;78 P d: K_K I U E Y X HGeAD78 P d2: K_K (578JSG @ ]"K 8\A;8 I @ : U G IJS: 8 U J\8 G2N!78 U G W I KB?">@ : U . - i 5 f K I 8 L : K :K I P 8 U E GeAD78 K :K I AD:BG U ? L J\8 K_K E : 8 P 8 U A;: P ] 7 L - f)8SAD8 P 9 O # 25 G27 U I U E O Y G G U 8 L = > 9MA Ie: U 8 E P 8 K 8 I9C8VGeN*W I29DJ >K I P 8 U E G2A;78 K :U A;: U d NcG P A;78Z9C: [ 8 G2N @ G K 8#J >K 8 9: U E8SA;8 P @ : U I AD:BG U GeN IE9;G P ] A;:_G U :_9;GeAD78 P @ 9 ? L f = 8\R 8 @/]K : ` 8#E ? L I2E"9CG P ] AD:BG U G2NJ 7":_J 8 U 8\dd^I KB?">@ : U G U AD: A I U : >@ . +- * - * j hj hei2i D = = G > 9D I f G P EI9 H8 P;P 8\: P I . = I P I @ I2d2G 0 8 K G I U E 4 .I P ? G9;I # >"@ I U 9C8 P >"@ I K_?>@ : U IE9;G P ] A;:_G U G U 5: N P G @ 9;: U d K 8 ] P GeA;8 : U 9;G K_> A;:_G U 9 I U E N P G @ ]K I29 @ I * . h2i j j 2h2i2i . P G U 8 0 >? I P 9 L O I W :_E9;G U I U E # . P I2E K 8 L f P G2A;8\: U I2E9;G P ] AD:BG U G U ADG ] G K L 9MAML P 8 U 8 9 > P NI2JS8#99MA > E :_8 E ? L Qf = I U EF4VH . ! j hei2i . O I A U 8 P "4 = # G @ I U H Y = J 7G 8 U I U E Y 3*8 @ G U 9 ".(:BG @ IeA;8 P : J AD:BG U ADG @ I A;8 P : P 8#E : : K_K 7G2Nc8 P Y . P 8 J\8\W :"@ G P 9MAD8\8 K - % * +- - j h h j h2i2i Y IeG )V: K I29;G U I U E 6aI U d28 P = > P NI2J\8 7 L E P G K L 9;:_9 GeN ] G K L $d K L JSG K : 8#9G P P I U d8 9(GeN: @/] G P ADI U A @ G E 8 K] I P I @ 8SAD8 P 9 # F $ 2 c (*,/,021/ 5: @ 89CA;8 ] NcG P @ 8 9;7 >] E"I A;8 (* /,+ .(: 8 U JSL G2N P I U E G @ I K >] EI AD8 9 1 IeR : @ >@ JS8 KBK 9 ] 8\8#E 9 ( ; 8 I U 9CA;8 ]^K 8 U d2A;7 : 9;9;:_I U 9CA;8 ]ZK 8 U deA;7 E :K I AD:BG U 9 1 = : @ >K IeA;:_G U A;8 P @ : U I AD:BG U AD: @ 8 TV] ADI 28 P IeA;8 JS8 KBK O 8 d P I2EIeA;:_G U P IeA;8 8 K 8 I9C8 E > P IeA;:_G U #+ e I R : : @ > @ U ]">K 9;8 ] P G E > J AD:BG U P I AD8 ] 8 P JS8 K_K 021 11 - : U : @ >@ @ I R : @ >@ ]>K 9C8 AD: @ 8 9 0 : U : @ >@ @ IeR : @ >"@ b > :B8#9;J\8 U A A;: @ 8 9 0 X H J\G U J\8 U A P I AD:BG U AD7 P 8#9C7"G K E
G U JS8 U A P IeA;:_G U A;7 P 8 9;7G K E N >U J AD:BG U 9MA P 8 U deAD7 I R : @ >@ 9 ] P G > ANcG P @ I AD:BG UZ] P G ? I ? : K :BAML
8 K_K E 8 U 9C:BAM7 L $J\8 K_K eJ\I ] : K_K I P L K 8 U deAD37 & 4 2 I C 9 ; A G G 9C: AD:BG U (8 : U W8 9CA;:_dI AD8A;78V8 8 J AGeN*9 > P NIJS8 96 7":_J 7 J\G U 9 >@ 8 J 78 @ GI ACA P IJ A I U A G U A;7"8VJ 78 @ G2ADI2JSA;: 9*h O E G @ Ie: U 9 !578gdGI K :U E8 P 9MA I U E 7G ? GeA;7A;78 d8\G @ 8\A P LQI U E P 8 I2JSA;:_W : AML GeNa9 > P NI2JS8#9 : U I9CA P > JSA > P 8 E EG @ Ie: U @ G E >K I A;8 JSG U JS8 U A P IeA;:_G U/` 8 K E"9gG2Na9MAD: @ >K I U AD9$ J 78 @ GI ACA P IJ A I U AD9 & I U E 7G A;78#9C8 @ G E >K I AD:BG U 9 J\I UZ? 8 8 U d2: U 8\8 P 8#E ADG JSG U A P G K J\8 K_K*K G J\G @ GeAD:BG U
5 78%8#9;9;8 U A;: P JSG @ ]"> ADIeA;:_G U I K @ G E 8 K : AD:BG U 8/NcG J > 9 G U A;7"8%: U> 8 U J\8 GeN JSG U 9 >@/] A;:_G U GeN J 78 @ GI A;A P I2J A I U A ? L A;7"8 ? G >U EI P :_8 9 G2NG ? 9CADI2J K 8#9 : AD7 : P;P 8\d >K I P 9;7"I ] 8 9 7: P J\8 G2N(J 78 @ GI A;A P I2JSADI U A 578/A P I U 9 ] G P A GeN J 78 @ GI A;A P I2J A I U A: U A;78 h O ] G P G > 9E GI @ : U : I AD:BG U 9(A;7"IeA >] EI AD8 JS8 KBKa] G9C:BA;:_G U I P 8 G > A K : U 8 EZ: U 7I ] AD8 P = 8 J h h
a - Z. *$ 1!$# - ^"')$\ # 2 $
8 ` P 9CA!JSG U 9C: P J\8gI A!A;78JS8 U A;8 P ] G: U A ] P G E > JS8#9aJ 78 @ GI A A P I2JSADI U AIeA I^J\G U 9CADI U A P I AD8 $ ] d 73& 9 8 KBK 9 I P 8 K I >U J 78#E N P G @ I^E : 9(A;G AD789CG > P JS8 P 8SNc8 P;P 8 E A;G I9gAD78 @MAD: @ 8 ADG JSG U A I2J A B* "I29I N >U J A;:_G U G2NI U d >K I P ] G9;: AD:BG U
F1!(. " *$% 1! $# - F')$\ # 2 $ 8 U 8\RA%JSG U 9;:_E 8 P AD78Z9DJS8 U I P :BG : U 7":_J 7&A (G J\8 K_K 9 I P 8 ]K I2J\8 E&: U :BA;: 9 J\I9C8 :_9Q8 @/]K G L28#E 578A (GZJ\8 K_K 9 ] P G E > J\8 J 78 @ GI A;A P I2J A I U AV: U ]>"K 9;8 9 E 8 `U 8 E ? L IZE > AML J\L J K 8 9C8#J P 8SAD:BG U I A I P I A;8 GeN NcG P I P I U E G @ @;G U B A;: @ 8 0 1 !9C8 K 8#J A;8#E >"U : NcG P @/K L : U AD78 P I U d28 i @ : U 021 i @ : U *NcG KBK G (8 E ? L U G%9;8 J P 8SAD:BG U NcG P I P I U E G @ @;G B A;: @ 8 ,0 9C8 K 8#J A;8#E >U :BNcG P @ K L : U A;78 P I U d8 i @ : U ,0 i @ : U /$ 8 E 8 @ G U 9CA P I A;8#E ] P 8\W :BG > 9 K LZA;7"IeAVAD7:_9 P I U E G @ @ ]>K 9C8#E B 9;8 J P 8SAD:BG U GeNgJ 78 @ GI A;A P I2JSADI U A d > I P I U A;8 8 9(AD7"I AQA G J\8 K_K 9 J\I U 9 > J\J\8 9D9MN >K_K L09;:_d U I K G U 8ZI U GeA;7"8 P : U I 7G @ Gd28 U 8\G > 9E G @ I2: U : U 7I ] AD8 P & ii 9CADI AD:_9CA;: :_W I K 8 U A : U E :_W: I K E > I K J\8 K_K 9C: @ >"K IeA;:_G U 9 I P 8 ] 8 P NcG P @ 8 EZNcG P W I P :_G > 9W I KB> 8#9 GeN &I U E 578 ] P : @ I P L G ? 9C8 P W I ?"K 8 : 9C8 E : > 9;: U d J\LA;G : U 8 9gA;G/9;:Bd U I K G U 8 I U G2A;78 P I U E%A;7"8 9;8 9;:Bd U I K 9 I P 8I%J P > JS: 8d P G A;7 I U E $ ? &: U ] G P G > 9 @ 8 E : P 8G2N!AD78 9 > P NIJS8#9 J\I U ? 8%8 U d2: U 8\8 P 8#E 8%7"I W8 NcG >U E A;7"IeA A;78 ] P 8 9;8 U JS8/GeN(G ? 9CADIJ K 8 9 :BA;7 P 8#I2JSA;:_W28/9 > P NI2J\8 9 d P 8 IeA K L : U-"> 8 U JS8 9
A;7"8 J 78 @ G2ADI2JSA;: P NIJS8#9 P 8 ] 8 K @ :Bd P IeA;G P L J\8 K_K 9 7":_J 7 (G >K E U G P @ I K_K L P 8 9 ] G U E ? L @ G W: U d&: U A;78 E : P 8#J A;:_G U G2N : U J P 8#I29;: U d&J\G U J\8 U A P I AD:BG U 8 7"I W8 9C8 8 U A;7I A @ G E 8 P I AD8 9 > P NIJS8 P 8#I2JSA;:_W:BA;:_8 9 I P 8 9 > = J\:B8 U A ADG ] P 8 W28 U A 9 > J\JS8#9;9CN >K A P I U 9 @ : J 7 :@ P 8#b > : P 8 ENcG P J\8 K_K A P I U 9;: A 57"8 9;8 P 8 9 >K AD9 7: K 8 I ]]K :_J I ?K 8G UK L: U I d8 U 8 P : P NI2J\8 9GeN!I ] G P G > 99;J I G K E%A;G 8 U 7I U J\8 A;7"8 K : 28 K :_7G G E G2N)9 > J\J\8 9D9MN >"K A;: 8 : U d P G A;7
y
(a)
(b)
y
(c)
y
r
obstacles θ
point source obstacle
obstacle x
x
x
launching positions launching positions
launch positions
global boundary c=0
global boundary c=0
global boundary c=0
o DRU7 4o&H")(0`-%(04k 1*&H")(0 5m7 !4o&!(0 -, !$j")U ,G 5$j" g6 -j H, 'U 42 H"'&Hn(0-j-%(*4k 1*&H")(0 ! -j ! -%(*73$) U R$)5E;>&QB D(*7/510 hj&H10aQ3$)-&H$) 57F-%(*7/510 5e7- "'&! 105EI;eB `&!19hj&H10aQ3$)-&H$) 57F-%(*7/510 5e7- "'&! 10 - E; B Z &!19hj&!10aQR$)-& $) 57+&!1 5e7- "'&! 10 - E
2
6
Contact time (10 s)
(a) 1.5
k = 0 (10-3 cm/s) = 0.01 = 0.1 =1 = 10 = 100
1
0.5
0 0
0.5
1 1.5 θ (π radian)
2
12
150
(c)
(b)
Launching point
130
9 y (0.01 mm)
Mean contact time over θ (106 s)
6
3
k=100 k=0
110 90
k=0.1
70
point source
k=1000
0 -3 10
10
-2
-1
0
1
10 10 10 k (10-3 cm/s)
2
10
50 20
40
60 80 100 x (0.01 mm)
120
o 2;>&5B Z(0- "%$)(0e 7")(0 ! -Z(0J")(042>") 5#"'&H3"Z CQ3$ 89,G H$S-%(0 /!1*khj&!10aQR$)-Z(0 )" U7L 54o&!(0Jh([")U ")U7k-%(07/510L !e - "'&!31*!8 ,G H$IC5& $)(* ! - 5e7- "'&! 10 e 577&H$%go$)&!R")(*CD([")(0 -
7 7(0")-j H, (0m")U7/!7$)S& $)^c? 4 H - E;eB m&!m !,.&HRUm7(0- "%$)(0e 7")(0 !+(0 ;>&QBREI; BM 9 E G @ I2: U 9 )57:K 8 AD7"I A d2G W8 P U 9 A;7"8J 78 @ GIeACA P IJ ADI U A J\G U J\8 U A P I AD:BG U I U E $ '&I ? :K 8 A;7"IeAVJSG >"]K 8#9A;7"8E : P 8 JSA;:_G U GeN JS8 KBK @ GeAD:BG U ADG/A;789;: @ >K ADI U 8\G > 9 K L%8\WG K W: U d%JSG U JS8 U A P I A;:_G U ` 8 K EFGeN)J 78 @ GIeACA P IJ ADI U A(: U A;78 ] G P G > 9E G @ Ie: U
! " #$! "&%' ( ! (&)(&*% ( ! (&)(&*% ;
+ ,.-/&0 % (213, %54 %&( 6$798:
=1@?A1B>1CD1B*1C4C * P PEF V4 &*P (A1C4#*P (1C4'#&#,*P (E1C4&1W4"( >1_" 1B#*"%1BL*"#>19M*#>1R 6 &* *#1IL *6E1IM *6A1C4"L,*"#1W4&"M *#1B6,* SF P 6,*& &(& >1@ *6,*& " ( >1R 6& *< F * *#>1RH * *#F P V*,* P&P&a `E1W*,* " a&`SF P T % & E19* % E1BF 4 F 4 EF 4 ZXF 4 EF 4 &bEF 4 EF 4 EF ) 4O&7_8&aE-IP & 4 :W ,G-@ M4 &
PJ-' 4&:&:GF
PJ-' : :DF
,Ha.-K 4&4&:C &,D-@ L,4&& P % -'a `EFK " LFK : ; ,H>7I"8&aE-'' 4 :C & D-B M,4&&
PJ-' 4&:&:GF
PJ-' : :DF
&PE-IP& : :DF
X+a.-K 4&4&:C &,D-@ L,4&& P % -'a `EFK " LFK : ; XS7I"8&aE-'' 4 :C & D-B M,4&&
PE-C&4&: :DF
PE-C&: :GF
P (Ta -'&4&4 :C & ,G-@ L4 P % -'a `EFK " LFK : ; P ($7_"8&aS-' 4&:C & D-9 M4
*P (a -' 4 4 :C ,D-@&L4 P % -'a `EFK " LFK : ; *P ($7_8&aE-'&4 :W D-B&M4
&PE-K&4 ::DF
&PE-K&:&:XF
,*P (a -' 4 4 :C ,D-@&L4 P % -'a `EFK " LFK : ; ,*P ($7_8&aE-'&4 :W D-B&M4
&PE-K&4 ::DF
&PE-K&:&:XF
% a -'&4&4 :C & ,G-@ L4 P % -'a `EFK " LFK : ; %E7_"8&aS-' 4&:C & D-9 M4
* +a.-' 4 4 :C ,D-@ L4 & P % -'a `EFK " LFK : ; * S7_"8&aE-K 4 :W ,G-@ M4 &
PE-C&4&: :DF
PE-C&: :GF
&PE-'K 4 : :GF
&PE-'K :&:GF
L,*%Oa.-IP & 4 :C && ,D-9*"< % ,4 &PE-RP :&:GF M,*%Oa.-IP & 4 :C && ,D-9*"< % ,4 &PE-RP :&:GF L,* +a.-IP & 4 :C && ,D-W&% *& X4&& PJ-IP ::DF M,* +a.-IP & 4 :C && ,D-W&% *& X4&& PJ-IP ::DF ) 4 M , 2 &M
&, ' ( ,
^, &Y %+ %&% + O ,& ( = P= , %5 ]< ,"4)
%&L,* &aE-RP & 4 :C &&,X-@ ^ Y4 &PE-RP :&:GF %&M,* &aE-RP & 4 :C &&,X-@ ^ Y4 &PE-RP :&:GF %&L aS-IP & 4 :C && G-@ ^, Y4 PE-@P & :&:XF %&M aS-IP & 4 :C && G-@ ^, Y4 PE-@P & :&:XF %,* "aE-IP 4 :C & D-B&^ Y4&& & PJ-IP ::DF L,* , ,aE-RP & 4 :C &&,X-@ ^ Y4 &PE-RP :&:GF C * aS-IP & 4 :W D-B ^, &Y,4& PS-RP & : :GF C * P&P aE-IP 4&:W &&,G-B&^ "Y4& &PS-IP& : :DF & ,",*C aS-IP 4 :_ & D-9&^, Y4&& PS-IP & :&:GF %" aE-IP & 4 :W ,G-@^, &Y4 &PE-RP :&:GF
,&* "L&aE-IP 4 4&:C G-@ ^, Y4 PE-@P & 4 ::DF P % -RY&a `EF@Y, "&^, YAF@Y : ; ,&* "L 7!Y 8&aE-RP 4&:C ,G-K4& PS-RP & : :GF
&* "M&aE-IP 4 4&:C G-@ ^, Y4 PE-@P & 4 ::DF , P % -RY&a `EF@Y, "&^, YAF@Y : ; ,&* "M 7!Y 8&aE-RP 4&:C ,G-K4& PS-RP & : :GF
P %E-RY a `EFBY, &^, &YFBY : ; %" 7!Y 8&aZXF %,* S7!Y 8&a `SF C * U7Y 8&a `EF C * P&P>7!Y 8&a `SF "$7Y 8&a `EF &*& 7!Y 8&a `SF *P ($7!Y&8&aXZ`&` `&`EF #*P ($7!Y&8&aXZ`&` `&`EF #&#*P ($7Y 8&a `EF * % 7!Y 8&a & * GF "L,*"#U7!Y 8&a&`EF "M,*"#U7!Y 8&a&`EF ( $7!Y 8&a `SF L,* , ,E7!Y&8&a `EF
P %E-RY a `EFBY, &^, &YFBY : ; P %E-R( a `EFB(, " F@( : ; L,*^ Y,*< U7!Y&8 7!(&8 a `SF M,*^ Y,*< U7!Y&8 7!(&8 a `SF *L * &A7!Y 8 7!(&8&a `SF *M * &A7!Y 8 7!(&8&a `SF
P %E-RY a `EFBY, &^, &YFBY : ; P % -R(&a `EF@(, 2F@( : ; ,&* "L 7!Y 8 7!(&8&a `SF ,&* "M 7!Y 8 7!(&8&a `SF
O #, ,&(Q4)
) 4
P % -'a `EFK " LFK : ; P % -_Ha `EFIH " MFIH : ; *P ($7_8 7BH 8&a&`EF "P -' Z`&` &`&`,: ;
P ($7_"8 79H 8&a ZF
; P ($7_"8 79H 8&a `EF
P % -'a `EFK " LFK : ; P % -_Ha `EFIH " MFIH : ; ,*P ($7_8 7BH 8&a&`EF XS7I"8 7BH 8 a `EF ,H>7I"8 7BH 8 a `EF %E7_"8 79H 8&a `EF * S7_"8 7BH8&a `EF
Y a `SF 7IXZ8 79H 8&a H M,*% 7Y 8 E-BM&) M:,H>7RZ8>79H 8SF
; ,H>7IXZ8 79H 8&a H M,*% 7Y 8 H>7IXZ'8 7!H 8AF
>7_XZ8 7BH8&a? % A-@ H7_XZK8 79H84,HA7_Z8>7BH8 S7IZ'8 7!H 84J7_ XZ8>79H8:DF
"P -IP ($7_"8 79H 8&a&a Z ,*P ($7_8 7BH XZ'8&aXZF
%E7_"8>7BH 8&a&aY
O,*P ($7_8
7BH XZ'8 9aZ
TP ($7_"8
79H XZ8 !a Z
: ;
79H Z8 !a Z
: ;
) 4],% +6 ," %04) L aS-' L,*%$7!Y 8:GF "P -WL,2-RL )J- ,4 L: :&: ; XS7I"8 7BH Z8&a L,*% 7Y 8 J-BL&) L:XS7R"8>7BHZ8SF
VP.-WL, J-RL )J- ,4" L: : : ; XS7I"8 7BH Z8&a L,*% 7Y 8 E-BL&) L:XS7R"8>7BHZ8SF
; XS7I"8 7BH Z8&a L,*% 7Y 8 S7I8 79H Z8AF
M aS-_H XZ M,*%$7!Y&8:DF "P -WM,2-RM )J- ,4 M: :&: ; ,H>7I"8 7BH Z8&a H Z M *%$7Y 8 J-@M ) M: H>7I"8>79H Z8EF
VP.-WM, J-RM )J- ,4" M: : : ; ,H>7I"8 7BH Z8&a H Z M *%$7Y 8E-@M ) M: H>7I"8>79H Z8EF
; ,H>7I"8 7BH Z8&a H Z M *%$7Y 8 H7_8 7!H XZK8AF
>7_8 7BH XZ'8&a? % A-@ H7_8 7!H Z'84,HA7_"87BHXZ'8 S7I"8>79H Z84J7_8 7BHZ'8:DF
"P -T-K Z:` -_H Z:a `Q: ; "P -IP ($7_"8 79H 8&a&a Z %E7_"8>7BH 8&a&aY P ($7_"8 79H Z8&aZXF
,*P ($7_8 7BH Z'8&aXZF
O,*P ($7_8
) 4],% +6 ," %04) L aS-' L,*%$7!Y 8:GF "P -WL,2-RL )J- ,4 L: :&: ; XS7I"8 7BH Z8&a L,*% 7Y 8 J-BL&) L:XS7R"8>7BH Z8SF
VP.-WL, J-RL )J- ,4" L: : : ; XS7I"8 7BH Z8&a L,*% 7Y 8 E-BL&) L:XS7R"8>7BH Z8SF
7BH Z'8 9aZ
TP ($7_"8
P ($7_8 7BH XZ'8&aXZXF
; XS7I"8 7BH Z8&a L,*% 7Y 8 S7I8 79H ,Z8AF
M aS-_H Z M,*%$7!Y&8:DF "P -WM,2-RM )J- ,4 M: :&: ; ,H>7I"8 7BH Z8&a H Z M *%$7Y 8 J-@M ) M: H>7I"8>79H ,Z8EF
VP.-WM, J-RM )J- ,4" M: : : ; ,H>7I"8 7BH Z8&a H Z M *%$7Y 8E-@M ) M: H>7I"8>79H ,Z8EF
; ,H>7I"8 7BH Z8&a H Z M *%$7Y 8 H7_8 7!H ZK8AF
>7_8 7BH Z'8&a? % A-@ H7_8 7!H Z'84,HA7_"87BH Z'8 S7I"8>79H ,Z84J7_8 7BH Z'8:DF
"P -IP ($7_"8 97 H 8&a&a Z ,*P ($7_ Z8 B7 H8&aXZF
%E7_"8>7BH 8&a&aY
O,*P ($7_ Z8
7BH8 9aZ
TP ($7_ Z'8
) 4],% +6 ," %04) L aS-' Z L,*%$7!Y&8:DF "P -WL,2-RL )J- ,4 L: :&: ; XS7I Z8 79H 8&a Z L *%$7Y 8 J-@L ) L:S7I Z'8 7!H 8EF
VP.-WL, J-RL )J- ,4" L: : : ; XS7I Z8 79H 8&a Z L *%$7Y 8E-@L ) L:S7I Z'8 7!H 8EF
; XS7I Z8 79H 8&a Z L *%$7Y 8J7_ ZK8 7BH8AF
M aS-_H M,*%$7!Y 8:GF "P -WM,2-RM )J- ,4 M: :&: ; ,H>7I Z8 79H 8&a H M,*% 7Y 8 J-BM&) M:,H>7R Z8>79H 8SF
VP.-WM, J-RM )J- ,4" M: : : ; ,H>7I Z8 79H 8&a H M,*% 7Y 8 E-BM&) M:,H>7R Z8>79H 8SF
; ,H>7I Z8 79H 8&a H M,*% 7Y 8 H>7I Z'8 7!H 8AF
>7_ Z8 7BH8&a? % A-@ H7_ ZK8 79H84,HA7_ ,Z8>7BH8 S7I Z'8 7!H 84J7_ Z8>79H8:DF
) 4& & X' (4) P % -_HaXZXFIH 2-@ M% Z:DFIH ,: ;
7BH 8 !a Z: ;
P ($7_ Z8 7BH 8 aXZXF
P % -'aXZ`ZXFC &`&`SFK : ; "P -IP ($7_XZ'8 7BH 8 !a ` OP ($7I Z8 79H 8 9a ` P ($7_"8 79H 8&a ZF
TP (
7_"8 7BHXZ8 9a&`
QP ($7_"8>7BH Z8
"aXZ`&`EF P % -_Ha `EFIH " MFIH : ; "P -IP ($7_XZ'8 7BH 8&a a `,: ; P ($7_"8 79H 8&aXZXF XS7I"8 7BH 8 a ZXF >7_8 7BH 8&aZXF ,H>7I"8 7BH 8 a `EF
P ($7_8 7BH 8&a ZXF
"a `&`EF P % -_Ha `EFIH " MFIH : ; "P -IP ($7_ Z'8 7BH 8&a a `,: ; P ($7_"8 79H 8&aXZXF XS7I"8 7BH 8 aXZXF ,H>7I"8 7BH 8 a `EF >7_8 7BH 8&aZXF
P ($7_8 7BH 8&a ZXF
) 4 &% & & T4) P % -_Ha `EFIH " MFIH : ; P % -'aXZ`&`EFC &`ZFK : ; "P -T-KXZ: " L&M .-_H Z: L MQ: ; "P -IP ($7_"8 79H 8&a&a Z [-IP ($7_XZ8 7BH8 9aXZ % a % & L4" MF
"P -IP ($7_"8 79H 8&a&aXZ OP ($7_XZ'8 7BH 8 !a ` % a % E-I L4 M:GF
P ($7_"8>7BH XZ8 9aXZ:/: ;
P ($7I"8 7BH Z8 9a `,: ;
79H 8 *: :&:GF #&% a `SF #*%&aE-I # : (&*% (,*&"P % -R%:DF "P -@#*%
# %: ; %&L$7 &^, Y&8&aDF %&M$7 &^, Y&8&aE-'&:G- -B M Z: 4G-R &# : ( *% (,*"&X"P % -R%:&:DF ( $7&^, Y 8&aXZXF L,*^ Y,*< U7 ^, Y&8 79` 8a % L 7 ^, Y 8SF M,*^ Y,*< U7 ^, Y&8 79` 8a % M 7 ^, Y 8SF ( a$7&^, &Y 8AF &^, &Y a&^ YXZF
) 4& % /< % "4) ) 4=,, Q % ,4) % a&`@b,4`A@`&`&`&` ` `A@`b,4`A@` `&``&` SF ) 4 ,#, & +< V&% ,&4) % * a,4`A@`&`&`&` ` 4D-Z`E@`&)Z`A@` :DF "P -IP W `&`&`:3% * a `EF ) 4]< % " # MQ#" , ]^ & &4) % * a % * a `@` `Z4`Bb,4`AB`&` `&`` ,4 ` `A@` ),*^ &&2F ) 4"% < % "4) )&)0"P -IP C * * X: ; )&) % aXZ4`@`&` `&`&` ,4G-I #, ,: ( *% (,*"&X"P % -@%:DF )&) )&) 0"P -&-RP C & *,*X: [-RP C & *,* P&P:: ; )&) % a `SF )&) )&) 0"P -IPC *,* P&P: ; )&)Q*,* aXZ `,4D-I &#, : (&*% (,*&"P % -R%:GF )&)Q*,* a*,* &`SF )&)Q*,* P&P&aXZ &`&`,4D-R &# ,:3( *% (,*"&X"P % -R%:DF )&)Q*,* P&P&a `&` *,* PPAF
h
)&)Q*,* a*,* P C EF )&)Q*,* P&P&a*,* P P P C SF )&) ) 4& &]< % ""4) P % -@< a `EFB7_"8>7BH 84 L
O H>7_"8 79H 84 &:DF
=XS7_8 7BH 84"
"PE-BXS7_"8>7BH 8
a&` ,H>7I"8 7BH 8 a `: ; E7_8 7BH 8&a &4D- XS7_8 7BH 84 E7_XZK8 7BH8 ",H7I"87BH84 S7_8 7BHZ'8:")J- Y,* &4 7_"8 7BH84 L$ S7_"8 79H 84
"PE-BXS7_"8>7BH 8
a&` ,H>7I"8 7BH 8 `: ; E7_8 7BH 8&a &4D- XS7_8 7BH 84 E7_XZK8 7BH8 ,H7I"87BH84 S7_8 7 H8:)D- Y,* &4 >7_8 7BH 84" L
=XS7I"8 7BH 8,4
,H>7_8 7BH 84" :DF
H>7_"8 79H 84 &:DF =,H>7I"8 7BH 8,4 :DF
VP.-IP ($7_8 7BH 8&a aXZ&Z: ; E7_8 7BH 8&a 4D-K* >7IZ87BH8 * 7 X8 79H8 * >7_8 7BHZ'8 * & >7_"87 H8:E-'Z 4 : 4* >7_8 7BH8 % 4" EF
"aEF
"P -' a&a `: aXZXF Va `EF H a HXZXF
) 4
% 7!(&8:XF M"aS-_H ,*M,* 7< 8>7!(&8:XF X+a $ 5ZXF "P -@X `:]&aE-@&L% Z:DF ,HaQH 5ZXF "P -@,HO `:] H &aE-@&M% Z:DF Y,* aXZ`&`B` ) &` `@`SF "P -&-'&H X: a&a `: "P -&-'&H Z: a&a&`: "P -&-K H % Z: a&a `: "P -&-'&H ,: a&a&`:
"P "P "P "P
E7_"8>7BH 8&aS7_"8 7BH8 Y,*"4&J7_"8>79H84X-Z L : 4D-'Z M&:4 F E7X8 7BH 8&a,E7X"8>7BH8 Y *4&E7 8 7!H 84L4D-Z M : 4" EF E7_"8>7,H 8&a,E7_"8 7 ,H8 Y *4&E7I8>7 H 84G-Z L: 4M 4" EF E7X8 7,H 8 aE7X8 7 ,H8 Y *4 S7 X8 7 H8,4"L4"M4 F
-KE7_8 7BH 8
`:+E7I"8 7BH 8 a `EF -KE7_ Z8 7BH8
`:/E7X8 7BH 8&a&`EF -KE7_8 7BH Z'8
`:/E7_"8>7,H 8&a&`EF -KE7_ Z8 7BH Z8
`,:/S7X"8 7 ,H 8&a `SF
) 4 ,7I"8 7BH 8 `: ; 7_8 7BH 8&a &4D- XS7_"8>7BH 84&S7X"8 7!H 8 ,H7_8>7BH84 E7I8 7 ,H 8:)2- Y,* &4 >7_"8 79H 84 L E
=XS7_"8>7BH 84 ,
"PE-BXS7_"8>7BH 8 ` ,H>7_8 7BH 8
a `: ; E7_8 7BH 8&a &4D- XS7_"8>7BH 84&S7X"8 7!H 8 ,H7_8>7BH84 E7I8 7!H XZ'8:)J- Y,* 4 >7_"8>7BH 84 L
O H>7_"8 79H 84 &:DF
=XS7_8 7BH 84"
"PE-BXS7_"8>7BH 8
a&` ,H>7I"8 7BH 8 a `: ; E7_8 7BH 8&a &4D- XS7_8 7BH 84 E7_XZK8 7BH8 ",H7I"87BH84 S7_8 7BHZ'8:")J- Y,* &4 7_"8 7BH84 L$ S7_"8 79H 84
"PE-BXS7_"8>7BH 8
a&` ,H>7I"8 7BH 8 `: ; E7_8 7BH 8&a &4D- XS7_8 7BH 84 E7_XZK8 7BH8 ,H7I"87BH84 S7_8 7 H8:)D- Y,* &4 >7_8 7BH 84" L
=XS7I"8 7BH 8,4
VP.-IP ($7_8 7BH 8&a aXZ&Z: ; E7_8 7BH 8&aS-W 4D-KS7_Z'8 79H 8S7 X8 7!H 8 E7I"8>79H Z8 S7I"87,H8:J7_"8>79H8 %& ,4" :)J-'Z 4 :DF
"aEF
"P -' a&a `: aXZXF Va `EF H a HXZXF
,H>7_8 7BH 84" :DF
H>7_"8 79H 84 &:DF =,H>7I"8 7BH 8,4 :DF
"P -IP W `: ; P % -@< a `EFB7!(&8:XF M"aS-_H ,*M,* 7< 8>7!(&8:XF X+a $ 5ZXF "P -@X `:]&aE-@&L% Z:DF ,HaQH 5ZXF "P -@,HO `:] H &aE-@&M% Z:DF Y,* aXZ`&`B` ) &` `@`SF "P -&-'&H X: 9a `: S7_"8 B7 H8&aE7_8 7BH 8 Y *4&S7_8>7BH84D-Z L: 4D-Z M&:4 )J-Z 4 :DF "P -&-'&H Z: 9a&`: 7"8 7BH 8 aE7X8 79H 8 Y,*4&S7 "87BH 8,4L 4D-'Z M&:4 ,)2-Z 4,:DF E "P -&-'&H Z: 9a&`: 7_8 7,H 8 aE7_"8>7 H 8 Y,*4&S7I8 7 ,H 8,4G-Z L&:4M4 ,)2-Z 4,:DF E "P -&-'&H ,: 9a&`: 7"8 7,H8&aE7"8>7 H8 "Y,*4 S7"8 7 H84"L 4M 4" )J-Z 4 :DF E
"P "P "P "P
-KE7_8 7BH 8
`: -KE7_ Z8 7BH8
`: -KE7_8 7BH Z'8
`: -KE7_ Z8 7BH Z8
`,:
E7_"8 79H 8&a `EF E7X"8>7BH 8&a `SF E7_"8 7 ,H 8&a `SF E7X"8>7,H 8&a&`EF
) 4 % 79H ,Z8:4G-@M,*^, Y *"7BH 8 S7 8>7BH8:)D-I L:GF VP.-IP ($7 8 7BH8&a&a&`,: ,"LGZ&ZaS-KE7CZ8>7BH 8 S7I"87BH 8:)2-I L:DF ,"LGZ&ZaS-KE7CZ8>7BH 8 J7 8>7BH8:)D- 4 L:DF "P -IP ($7CZ8 7 ,H 8&a&a&`: "LXZ` aE-KS7_"8 7 H 8 J7 8>7 H 8:)2-R L:DF VP.-IP ($7 8 7 H 8&a a&`:3 "LGZ&Z'aE-KE7CZ'8 7,H 8 E7R"8 7 H8:")J-I L:GF ,"LGZ` aS-KE7CZ8>7,H 8 &E7 8 7 ,H 8,:)2- 4" L:DF
; "P -IP ($7!("8>7BH 8&a&a&`:3 "LGZ&Z'aE-KE7_8 7BH 8 S7"8>7BH8:)D-I L:GF VPE-KE7"8 7BH 8 a&a `:3 "LXZ&ZaE-KS7!("8 79H 8 J7_8 79H8:")J-I L:GF ,"LGZ&ZaS-KE7!(8 7BH 8 &E7 "8>7BH8:)D- 4 L:DF "P -IP ($7!("8>7,H 8&a a `,:3 "LXZ` aE-KS7_"8 7 H 8 J7"8>7 ,H8:)2-R L:XF VPE-KE7"8 7,H8&a&a `:3 LGZ&ZaE-CE7!("8>7,H 8 S7_8>7 H 8:)2-R L:DF ,"LGZ` aS-KE7!(8 7,H 8 S7 X8 7 ,H 8,:)2- 4" L:DF
"P -_H a&aS-@ M% Z:&: ; "P -IP ($7_"8 7WZ8&a&a `,:\ "MGZ&Z'aE-KE7_8 7BH 8 S7_8 7 8:")J-I M:GF VPE-IP ($7_"8 7 8&aa `,:\ ,"MGZ&ZaS-KE7_"8>7CZ8 S7I"87BH 8:)2-I M:DF ,"MGZ&ZaS-KE7_"8>7CZ8 J7_8>7 8:)D- 4 M:DF "P -IP ($7X"8>7CZ8&a&a&`: "MXZ` aE-KS7X"8 79H 8 J7"8>7 8:)2-R M:DF VP.-IP ($7"8 7 8&a a&`:3 "MGZ`aE-KE7"8 7CZ8 E7 X"8>79H8:")J-I M:GF
,"MGZ` aS-KE7X8 7CZ8 &E7 "8>7 8,:)2- 4" M:DF
; "P -IP ($7_"8 7( H 8&a&a&`: MGZ&ZaE-CE7_"8 79H 8 J7_8 7 H 8,:)J-R L:DF VP.-IP ($7_8 7,H 8 a&a `,: "MGZ&Z'aE-KE7_8 7!( H 8 E7R"8 79H8:)D-I L:GF ,"MGZ&ZaS-KE7_"8>7!( H 8 &E7I8 7 ,H8:)D- 4 L:DF "P -IP ($7X"8>7!( H 8&a a `,: "M `Z'aE-KE7"8 7BH 8 S78 7 ,H 8:)2-I M:DF "P -IP ($7X"8>7,H 8&a a `,: "M `Z'aE-KE7"8 7!( H8 E7 "87BH 8:)2-I M:DF ,"M `ZaS-KE7X8 7!( H 8 S7 X8 7 ,H 8,:)2- 4" M:DF
"P -IP ($7X Z8 7BH 8 a&a&`: "L `Z'aE-KE7_8 7BH 8 E7 X8>7BH8:)2-R L:XF ; "L `ZaE-KS7_"8 7BH8 S7 X ZK8 97 H8:)J- ,4 L:GF
"P -IP ($7_"8 7 ,H Z8 a&a&`: "MGZ`aE-KE7_8 7BH 8 E7I"8>7 ,H8:)2-R M:XF ; "MXZ` aE-KS7_"8 7BH8 S7I"8>7 H Z'8:)J- ,4 M:GF
"P -IP ($7X Z8 7,H8&a a ` : "L `&` aE-KS7_"8 7 H 8 S7 X8 7 H8:)D-I L:GF ; "L `&` aE-KS7_"8 7 H 8 S7 ,Z8>7 , H 8:")J- 4 L:GF
"P -IP ($7X"8>7,H Z'8&a a ` :3 "M `&`aE-KE7"8 7BH 8 S78 7 ,H 8:)2-I M:DF ; "M `&` aE-KS7X"8 79H 8 S7"87 H Z'8:")J- 4 M:GF
L"aS-' %&L 7< 8:DF M"aS-_H %&M 7< 8:DF "L&aE-Z L&: 4D-Z M :4 ,"LZ&Z L4D-'Z M&:4 ,L `Z S-Z L: 4"M4" LGZ`L 4"M 4" ,"L `&`JF "M&aE-Z L&: 4D-Z M :4 ,"MZ&Z L4D-'Z M&:4 ,M `Z S-Z L: 4"M4" MGZ`L 4"M 4" ,"M `&`JF 6 &* aE-Z L&: 4G-Z M&:4&J7!(8 7( H8 L 4G-Z M: 4 E7I8 7 ( H 8 S-Z "L&:4M 4&J7!(8 79H 8 L4"M 4E7_8 79H 8SF "P -@a, : ; P % -'a `EFK ZXFK : ; ,&* "L 7< 8 7_8&a ,* "L 7 < 8>7_ XZ8SF ,&* "M 7< 8 7_8&a ,* "M 7 < 8>7_ XZ8SF
,&* "L 7 < 8 I7 Z8 a LF ,&* "M 7 < 8 I7 Z8 a MF
; ,&* "L 7 < 8 7 8&a& ,LF ,&* "M 7 < 8 7 8&a& ,MF
,&* "L a&`EF ,&* "M a&`EF P % -'a `EFK 2FK : ; ,&* "L a& ,&* ,"L& &* L 7 < 8 R7 "8AF ,&* "M a& ,&* ,"M& &* M 7 < 8 R7 "8AF
i
"L * 6 a& ,&* ,"L,) DF "M * 6 a& ,&* ,"M,) DF "L M a? % A-I "L * 6 4 ,"L * 6 M,* 6 4 ,M,* 6 :GF "L a&`EF "M a&`EF < L a&`EF < M a&`EF
) 4 & (/7< 8:"aS-B M ) :&: ; 7 < 8: 4X-R%&L>7< 8 % L,* 7 < 8::E- -@% M$7 < 8 L&) L % M * & 7< 8: 4G-R%M$77< 8 % L,* 7 < 8::E- -@% M$7 < 8 L&) L % M * & 7< 8: 4G-R%M$77< 8 % L,* 7 < 8::E- -@% M$7 < 8 % M * 7 < 8:4D-B%&M 7 < 8 %M,* >77 < 8EF
) 4&, ,"Y' (= ," , + 4) P %E-'"a `EFC &^, &YFC : ; "P -_ *P ($7_8 9a7BH8 M *^ "Y,*< U7I8 7!` 8:aS-@ M,) ,: : ; 6,*& (& a? %&E-+-RL *^, Y *79` 8,: 4D-@L *"^, "Y,*"< U7R"8>79H 8 L,*^ Y,*< U7_8 7B` 8,: E-RM,*^ Y,*< U7_8 79H 8 LM% M,*^, Y,*7B` 8: :GF
; 6,*& (& a? %&E-+-RL *^, Y *79` 8,: 4D-@L *"^, "Y,*"< U7R"8>79H 8 L,*^ Y,*< U7_8 7B` 8,: E-RM,*^ Y,*< U7_8 79H 8 M * ^, Y *7BH8 L *# & "X:
"P
A-RL *^, Y *79H 8 L,*^ Y,*< U7_8 7B` 8,: E-RM,*^ Y,*< U7_8 79H 8 LM% M,*^, Y,*7B` 8: :GF
VP.-&-@M,*^, Y,*7B`8 "M,*^ Y,*"< U7I"8>79H 8,:aS-B&M,):&: ; 6,*& (& a? %&E-+-RL *^, Y *79` 8,: 4D-@L *"^, "Y,*"< U7R"8>79H 8 L,*^ Y,*< U7_8 7B` 8,: E-RM,*^ Y,*< U7_8 79H 8 LM% M,*^, Y,* 8#9 h U I U G2A;78 P I ]] P GI2J 7 I ? :_G @ : @ 8SA;: 8ZA;G E 8 ] G9;: A/7 L E P G R LI ] IeA;:BA;8%G U A;78^9 > P NIJS8 G2N ? :_G @ I AD8 P :_I K 9 &57: 8 > 9;8 9 I 9 >] 8 P 9DI A > P I A;8#E 9;G K_> A;:_G U U G U I29/9C: @ >"K IeA;8 E ? G E L > :_E $ = .H& A;7"IeA/J\G U ADI2: U 9 : U G P dI U : : P NIJS8/GeN ? :_G @ I AD8 P :_I K 9 J\I U NcG P @ 7"8 U A;7"8\L I P 8 : U J >? I AD8 E : U A;7: 9 IZJSG U A P G KBK 8 E 9 > P NI2J\8 @ G E: ` J I AD:BG U A;7"IeA P 8 E > JS8#9 7 L P E P G ] 7G ? : AVJSG @ ] P G @ :"U J AD:BG U I K 9;: @ : K I P :BA;:_8 9(ADG AD78 @ : U 8 P I K JSG @ ] G U 8 U A GeN ? G U 8 AD7: E L 8\R ]"K G P 8#9 A;78gNc8 I29;: ? : K :BAMLQG2N @ : U 8 P I K NcG P @ I A;:_G U G U A;78#9C8g9DJ\I G K E"9 U IEE :BA;:_G U (8 : U W8 9CA;:_dIeA;8)A;7"8 8 8 JSAG2N @ : U 8 P I K : [ IeA;:_G U G U A;78 K 8 W28 K GeN ] P GeAD8\: U I2E"9CG P ] AD:BG U G U AD78Q9 > P NI2JS8VGeNA;7"8Q f !4 4 9;: U AD8 P 8 E @ : ? f !4 4 $ K IJ A;: P 8 JSG @/]K 8\A;8 9CG K W8 U A P 8 @ G W I K T 9;: U d @ : P ] 7L 8SA I K . P :B8 L (f !4 4 9DJ\I G K E9 8 P 8 9 > P NIJS8 7 L E P G K L [ 8 E ? L^: @/@ 8 P 9;: U d AD78 @ : U i )QI # NcG P 7 I A P G G @ AD8 @/] 8 P IeA > P 8 )V8SR A A;7"8V7 L E P G K L [ 8 E%9DJ\I G K E9 8 P 8 : U J >? I AD8 E : U I @/K 9;G K_> AD:BG U GeN @ G E : ` 8 E 9;: @ >K I AD8 E ? G E L "> :?K 8 JSG U JS8 U A P I A;:_G U 9 G2N (I K I U E 5 # hef J\G @/] I P 8#E ADG = .H6& NcG P $c: & EI L 9(I U E $c:_: & E"I L 9 I A j g57"8 9;G K_> A;:_G U "9 (8 P 8 P 8 ]"K IJS8 EZEIe: K L I U E ] P 8 ] I P 8#E ? L E : 9CA;8 EZADG
?
578 @ G P ] 7"G K G2d2L GeN f a4 4 I U EF7 L E P G R LI ] IeA;:BA;8 JSGI A;8#E^f a4 469DJ\I G K E"9 8 P 8 W : I K : [ 8 E ? LF9DJ\I UU : U d%8 K 8 J A P G U@ :? 9ZI U E9 ]> A;A;8 P JSGI A;8#E : AD7 d2G K 8E ] I KBK I2E : >@ )5789;I @/]K 8#9; 8 P 8 W :_8* (8 E >U E 8 P = X I A I U IJ\JS8 K 8 P IeA;: U d W2G K ADI2d28 GeN 20 578 8 K 8 @ 8 U ADI K JSG @/] G9;: AD:BG U GeN 9;J I G K E9; I29 : U W28 9CA;:_dIeA;8#E > 9;: U d P I L 8 U 8 P dL E :"@ $ XgO & $f P : U J\8SA;G U I @/@ I 5!8 J 7 P I L%9 ] 8 JSA P G @ 8SAD8 P I ACA I2J 78#E%ADG = X Y X i4 & 4 U I2J JS8 K 8 P I AD: U dW2G K A Ied28QGeNh2i 20 (I9 > 9C8#EZNcG P I K_K XgO I2J\b > : P NIJS8 GeNf a4 4 ] P GeA;8 : U K GI2E8 E I U E >UK GI2E8 E @ : U 8 P I K : [ 8#E f !4 4 9;J I G K E9 (I9 I U I K L [ 8#E ? LQf = $ X = (4 = 4 " f 7 L 9C: 9;:_G U : U ADG O @ I A P : E :_8 9 > 9C: U d/d P G A;7 NI2JSA;G P 9 i T 9;: U d I U : U :BA;: A;8 E4 :BA;7Zf . = $ :BA;7G > A(J I K JS: >@ I U E @ Ied U 8 9;: >"@ &QADG d2:_W28%I `"U I K JSG U JS8 U A P I A;:_G U GeN ii @ d6 @/K = J\I G K E9 8 P 8 A P I U 9MNc8 P;P 8 E A;G I^d K I9;9 W :_I K I U E i K GeN A;7"8 ] P GeAD8\: U 9;G K_> A;:_G U @MAD78 : U :BA;:U B I29VIEE 8#E E P G ] :_9;8 A;GF9;IeA > P I AD8 A;7"8 8 U AD: P 8 9DJ\I G K E ) 8\R A )9;J I G K E 9 8 P 8 N P G [ 8 U > 9C: U d K :_b > : P 9 5!G E 8\A;8 P @ : U 8 04 P 8 K 8#I29;8 : U 8\A;:? IeA;8#E&: U I U I2d2:BADI AD: U d $ i P ]@ & : U J >? I A;G P IeA j 9 ] 8 JS: ` J A;: @ 8 : U AD8 P W I K 9 A;78 9 >] 8 P U I ADI U A (I9 P 8 @ G W8 E NcG P ] P GeA;8 : U b > I U A;: ` J\IeA;:_G U I U E%N P 8 9;7 f . = I29(I2EE8 E !A I29(I29D9 >@ 8 E A;7I A(A;78 ] P GeA;8 : U I2E9;G P ? 8 E/G U ADG AD78 9DJ\I G K E" 9 I29g8\:BA;78 P ? G >"U E G U A;7"8 9 > P NI2JS8QGeN*AD78 @ : A;:_G U I29 IEE 8 E ADG A;78 ] G P G > 9 9DJ\I G K E 9 (8 P 8 @ 8 I9 > P 8 E 2I U E AD78 9;8VI @ G >U AD9 (8 P 8 9 >? A P I2JSA;8#E N P G @ A;7"8 : U : AD:_I K"K GI2E8 E ] P GeAD8\: U I @ G >U A > I U A;: ` J\IeA;:_G U GeN AD78 ] P GeAD8\: U P 8 K 8#I29;8 : U 9 >] 8 P U IeADI U A I29 ] 8 P NcG P @ 8 E > 9C: U d J\G K G P : @ 8SA P :K I AD8 E ? G E L E 578 @ I29D9VG2N9DJ\I G K E9V: U J P 8#I29;8 E^ADG #i I N AD8 P ZEI L 9Q: U J >? IeA;:_G U I U E^AD78 U K 8 W28 K 8#E G 4(A E"I L ZA;7"8 "> :? IeA;:_G U I U E K G U d28 P AD: @ 8 ] G2: U AD9 57: AD8 E0ADG @ : U 8 P I K E 8 ] G9;: AD:BG U G U @ :_J P G9 ] 78 P 8 9 > P NI2J\8 = : @ : K I P 9MA > E :_8 9 > 9;: U d^!f a4 4 7"I W8 9;7G U AD7"I A AD78 @ I29D9 K G9D9 E > 8 ADGZAD78 ] G K L @ 8 P E 8 d P I2EIeA;:_G U E > P : U d /EI L 9: U J >? IeA;:_G U : U = .H :_9 @ : U : @ I K h 578 XO I U I K L 9C:@ I U E ] 7G9 ] 7"G P > 9 G U AD78Q9 > P NI2J\8 GeN @ : U 8 P I K : [ 8#E%f !4 4 9DJ\I G K E9 EI L 9 I U E E"I L 8 9 7: K 8 A;78#9C8Z8 K 8 @ 8 U AD9 (8 P 8 U GeA/E 8SAD8 JSA;8 E : U f a4 4 9;J I G K E9 O 57"8 (I f d I29 j NcG P EI L @ : U 8 P I K : [ 8 E !f a4 4 9;J I G K E9 I U E : U J P 8#I29;8 E ADG %NcG P E"I L P I A;:_G G2N(I ] I AD: AD8 J\GI AD: U : @ : U 8 P I K : [ 8 E%9DJ\I G K E9 57"8V9MADG2:K I P J\G @/] G9C:BA;:_G U (I f # 578 P 8\NcG P 8 AD78 XO P 8 9 >K AD9V9;7G (8 EZA;7I AVAD78 I ] I AD: AD8 JSGI AD8 E A;78 9 > P NI2JS8^G2N @ : E L A;78 ] P GeAD8\: U 9 > P NI2J\8 : U AD8 P I2JSA;:_G U 9F ,57"8 @ I2d U :BA > E8ZG2NVA;7"8 U :BA P G2d8 UF] 8#I ZJ I U^? 8 > 9;8 E^I29 I ADG G K : U^@ 8#I29 > P : U d AD78 I @ G >U A GeN ] P G2A;8 : U I2E"9CG P ] AD:BG U ; G U 9C:@ 8 E AD7"I A A;78:) ] 8#I :_9 : U E :_J I AD:BW8 GeN ] P GeAD8\: U&] P 8#9C8 U JS8 H:Bd O 9C7G 9 A;78 Q f = 9 > P W28 L 9 ] 8#J A P >@ NcG P f!a4 4 *H!:_d O 3 $I'& EI L @ : U 8 P I K : [ 8 E f !4 4 H:Bd O 3 $ ? &CI U E ] P GeAD8\: U : U J\G P ] G P IeA;8 E EI L @ : U 8 P I K : [ 8 E f !4 4 H:_d O $ J& 7: K 8 (8 G ? 9C8 P W8 EZA;7"8 8\R ] 8 JSA;8#E I U E ] 8#I 9VNcG P f a4 4 9;J I G K E9 EI L @ : U 8 P I K : [ 8 E f a4 4 9;J I G K E9 8\R 7": ? :BA;8#E (I I U E f ] 8 I 99 > dd28 9CA;: U d%AD7"I AQA;78 ] P 8 JS: ] :BADIeA;8 E 9 > P NI2J\8 K I L28 P :_9QI ] IeA;:BA;8 H:Bd O $ ? & 80G ? 9;8 P W28#E() ] 8 I : U A;78 f = 9 > P W28 L 9 ] 8 J A P >"@ GeN ] P GeAD8\: U K GIE 8 E @ : U 8 P I K : [ 8 E 9;J I G K E9 H:Bd O $J & 1 7: K 8/A;7":_9 ] 8 I I29 I ? 9;8 U A : U AD78 >UK GIE 8 E @ : U 8 P I K : [ 8 E 9;J I G K E9;H:_d O $ ? & A I29 I K 9;G U GeA;8#E A;7I A : U A;7"8 ] P GeAD8\: U K GIE 8 E 9;J I G K E9QA;78 Q f = 9 ] 8#J A P >@ (IZI U E f ] 8#I : U A;8 U 9C:BAML I ]"] 8#I P A;G ? 8%9;:Bd U : ` J\I U A K L 9 @ I KBK 8 P 57: 9;8 A;78 I2E"9CG P ? 8 E ] P G2A;8 : U JSG W8 P 9 AD78 @ : U 8 P I K : [ 8#EZ9 > P NI2JS8 GeN!A;789DJ\I G K E"9(I U E Q f = 9DJ\I U 9 G U"K L%ADG/A;78E8 ] AD7FG2N # i2i/4 .
H:Bd O 3 $I )& 9C7"G 9)A;78QI @ G >U A G2N ] P G2A;8\: U I2E9;G P ? 8 E G U A;G AD78V9DJ\I G K E9 NcG P E : 8 P 8 U A d P G >] 9 I N AD8 P j EI L 9 57"8
j
I2E"9CG P ? 8 E ] P G2A;8\: U @ I2: U"K LJ\G PDP 8#9 ] G U E8 E ADGVAD7"I A 8\:BA;7"8 P ? G >U E G U A;78 @ : P NI2J\8 9aA;7 P G > d7 8 K 8#J A P G9CADIeA;: JSA > P 8GeN AD78 9DJ\I G K E9 A I29VG ? 9;8 P W28#E AD7"I Aj i GeN A;7"8 A;G2ADI K I @ G >"U A G2N K GIE 8 E ] P GeA;8 : U IE9CG P ? 8 E G U ADGQAD78 U G U A P 8#I AD8 E f a4 49DJ\I G K E"96 78 P 8 I96 : AD7 AD78 7 L E P G K L [ 8 E 9DJ\I G K E9A;7"8 @ 8#I UF] P G2A;8 : U I2E9;G P ] AD:BG U : U J P 8 I29;8 E A;G i j 57"8 E"I L @ : U 8 P I K : [ 8#E 9DJ\I G K E9E :"U A G2N ] P GeAD8\: U IE9;G P ] A;:_G U I ]] P G R : @ I AD8 K L h H:Bd O 3$ ? J &%E :@ : U N P G @ A;78 f !4 4 g7 L E P G K L [ 8 E I U E @ : U 8 P I K : [ 8 E f !4 4 9;J I G K E9 578 P 8 K 8 I29;8 : U 8\A;:] 9 E : P A;7"8 P @ 8#I29 > P I ?K 8 P 8 K 8 I9C8 NcG P A;78 %NcG KBK G : U dZEI L 9 H"G P 7L E P G K L [ 8# E EI L @ : U 8 P I K : [ 8 E I U E E"I L @ : U 8 P I K : [ 8 EF f a4 4 9DJ\I G K E9 A;78 : U :BA;: P 9CA P 8 K 8#I29;8QE 8#J P 8 I29;8 E A;G i h I U E h $cG W I K_?>@ : U^K GI2E : U d/8 = JS:_8 U JSL gj & P 8 9 ] 8#J AD:BW8 K L
U 8 : 8 U AG2Na7 >@ I U 98 K 8SADG U I U E ] P G W : 8 U JS8 G U ] P GeAD8\: U I2E9;G P ] AD:BG U J\I ] I2J\: AML 7: K 8VAD78 9DJSG ] 8 GeNAD7: I AD:BG U G2N ? G U 8I U EZW I9;J >K I P : U d P G A;7F: U d P G A;7 NI2JSA;G P : U J\G P ] G P IeA;8 E
j
EFN >U JSA;:_G U 9QGeNgJ\8 K_K 9Vd P G : U d G U ? 8 8 U 9C7G U A;G ] P 8 W28 U A `"? P G > 9 K G2d:_J I K N > A > P 8 9CA;8 ] (G >K E ? 8 : U @ : U 8 P I K : [ 8#EZ9DJ\I G K E"9
$
f !4 4 @ : 9C: U d^IZ9;: @ >K I A;8#E ? G E L "> :_E$ = .H& !4 J\G U A;: U > G > 9QI ] I AD: AD8 @ : U 8 P I K : U AD78 9;7"I ] 8 GeN ]K I A;8 K : 28 U I U G J P L 9CADI K 9" I29NcG P @ 8 EFG U AD789 > P NIJS8 9G2N @ : A > P 8 9MA > E :_8 9V: U J KB> E 8 A;7"8 I2E9;G P ] AD:BG U G2NG9MAD8\G2d8 U :
