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MeV Scale Physics in MicroBooNE

by

Avinay Bhat B.Sc (Physics Honours)., University of Delhi, 2012

M.Tech (Nuclear Science and Technology)., University of Delhi, 2015

Dissertation

Submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Physics.

Syracuse University July 2021

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h?2M i?2 ~�pQ` 2B;2Mbi�i2b %⌫↵i �M/ %⌫�i +�M #2 2tT`2bb2/ �b � 7mM+iBQM Q7 TQbBiBQM �M/ iBK2�b

|⌫↵(t,!x )i = +Qb ✓e�ip1t|⌫1i+ bBM ✓e�ip2t⌫2i URXeV

|⌫�(t,!x )i = � bBM ✓e�ip1t|⌫1i+ +Qb ✓e�ip2t⌫2i URXdV

AM i?2 mHi`�@`2H�iBpBbiB+ HBKBi- i ⇠G i?2 /Bbi�M+2 i`�p2HH2/ #v i?2 M2mi`BMQ �M/ 1i@Tz,i ⇡m2

i2Ei

X h?2M i?2 T`Q#�#BHBiv 7Q` %⌫↵i iQ Qb+BHH�i2 iQ %⌫�i Bb ;Bp2M #v-

P↵!�(L) = |h⌫�|⌫↵(t, z = L)i|2 = bBM2 2✓ bBM2⇣1.27�m2 L

E⌫

⌘URX3V

AM i?Bb 2[m�iBQM 1 Bb i?2 M2mi`BMQ 2M2`;v- G Bb i?2 /Bbi�M+2 7`QK i?2 bQm`+2- �M/ �m2 4|m2

2 �m21| Bb i?2 K�;MBim/2 /Bz2`2M+2 #2ir22M i?2 %⌫1i �M/ %⌫2i K�bb 2B;2Mbi�i2bX

AM +�b2 Q7 i?`22 M2mi`BMQ ~�pQ` KBtBM;- i?2 i?`22 `Qi�iBQM �M;H2b �`2 ✓23- ✓13 �M/ ✓12

Uy ✓ij ⇡/2V �M/ i?2 i?`22 *S pBQH�iBM; T?�b2b �`2 �-�2 �M/ �3X h?2 i?`22 M2mi`BMQ

9

KBtBM; K�i`Bt +�M #2 r`Bii2M �b,

U =

0

B@1 0 0

0 c23 s23

0 �s23 c23

1

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0

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0 1 0

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CA URXNV

r?2`2 +jk /2MQi2b +Qb✓jk �M/ bjk /2MQi2b bBM✓jkX h?2 �M;H2 ✓23 Bb `2H2p�Mi 7Q` Qb+BHH�iBQMbQ7 �iKQbT?2`B+ M2mi`BMQb- i?2 �M;H2 ✓12 /2b+`B#2b bQH�` M2mi`BMQ Qb+BHH�iBQMb- �M/ i?2 �M;H2 ✓13Bb K2�bm`2/ #v `2�+iQ` M2mi`BMQ 2tT2`BK2Mib �i b?Qì #�b2HBM2bX h?2 irQ J�DQ`�M� T?�b2b�2 �M/ �3 /Q MQi �z2+i i?2 Qb+BHH�iBQM T`Q#�#BHBiB2bX �M �K#B;mBiv BM K�bb Q`/2`BM; Q7 i?2M2mi`BMQ K�bb 2B;2Mbi�i2b �`Bb2b 7`QK i?2 mMFMQrM bB;M Q7 �K2

23X

6B;m`2 RXj, _2T`2b2Mi�iBQM Q7 i?2 MQ`K�H �M/ BMp2ì2/ K�bb ?B2`�`+?v 7Q` M2mi`BMQbX h?2H2TiQM +QMi2Mi Q7 2�+? K�bb 2B;2Mbi�i2 Bb /2MQi2/ BM +QHQ` �M/ `2T`2b2Mib i?2 H2p2H Q7 KBtBM;rBi? 2�+? r2�F 2B;2Mbi�i2X

A7 ⌫1 ?�TT2Mb iQ #2 i?2 HB;?i2bi M2mi`BMQ 2B;2Mbi�i2- i?2 Q`/2`BM; Bb +�HH2/ ǳMQ`K�HǴUKR I Kk I KjV- Qi?2`rBb2 Bi Bb H�#2HH2/ �b ǳBMp2ì2/Ǵ UKj I KR I KkV- �b b?QrM BM6B; RXjX L2mi`BMQ 2tT2`BK2Mib �`2 /2bB;M2/ iQ b2�`+? 7Q` M2mi`BMQ Qb+BHH�iBQMb pB� M2mi`BMQ�TT2�`�M+2 Q` /Bb�TT2�`�M+2X AM �TT2�`�M+2 2tT2`BK2Mib i?2 M2mi`BMQb Q7 FMQrM ~�pQ`↵ �`2 T`Q/m+2/ �M/ K2�bm`2/ � /Bbi�M+2 �r�v 7`QK i?2 bQm`+2 �b �MQi?2` ~�pQ` �X AM

8

/Bb�TT2�`�M+2 b2�`+?2b M2mi`BMQb Q7 � ;Bp2M ~�pQ` �`2 T`Q/m+2/ �M/ i?2 b�K2 M2mi`BMQ ~�pQ`Bb K2�bm`2/X � ;Bp2M 2tT2`BK2Mi QTiBKBx2b i?2 /Bbi�M+2 #2ir22M i?2 bQm`+2 �M/ /2i2+iQ`- G-rBi? i?2 ;Bp2M M2mi`BMQ 2M2`;v- 1- 7Q` K�tBK�H b2MbBiBpBiv iQ � ;Bp2M ivT2 Q7 Qb+BHH�iBQMX �i�#H2 Q7 i?2 +m``2Mi Qb+BHH�iBQM T�`�K2i2`b (R) Bb ;Bp2M BM h�#H2 jXR 7Q` i?2 MQ`K�H ?B2`�`+?vX

S�`�K2i2` o�Hm2 ULQ`K�H P`/2`BM;V�m2

21 [10�5 2o2] UdX8j ±yXR3V�m2

31 [10�3 2o2] UkX8R ±yXy8VbBM2 ✓12 yXjyd ±yXyR9bBM2 ✓23 yX9Rd ±yXyk3bBM2 ✓13 UkXRk ±yXy3V Ɠ RyƐk

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e

6B;m`2 RX9, 62vMK�M /B�;`�Kb 7Q` +?�`;2/@+m``2Mi [m�bB@2H�biB+ b+�ii2`BM; Uǳ**Z1Ǵ- H27iV�M/ M2mi`�H@+m``2Mi [m�bB@2H�biB+ b+�ii2`BM; UǳL*Z1Ǵ- `B;?iVX

TQbbB#Hv Qi?2` Mm+H2QMbX � bim/v Q7 i?2b2 /2@2t+Bi�iBQM T?QiQMb rBHH #2 /Bb+mbb2/ H�i2`X

6B;m`2 RX8, 62vMK�M /B�;`�Kb 7Q` +?�`;2/@+m``2Mi `2bQM�Mi TBQM T`Q/m+iBQM Uǳ**_1aǴVX

_2bQM�Mi TBQM T`Q/m+iBQM- �b b?QrM rBi? i?2 ?2HT Q7 62vMK�M /B�;`�K BM 6B; RX8 Bb i?2/QKBM�Mi KQ/2 Q7 M2mi`BMQ@Mm+H2mb BMi2`�+iBQM 7Q` M2mi`BMQ 2M2`;v `�M;BM; 7`QK R@8 :2oX�Hi?Qm;? biBHH ?�pBM; BMbm{+B2Mi 2M2`;v iQ /Bb`mTi i?2 Mm+H2mb- i?2 M2mi`BMQ /Q2b BKT�ì

d

2MQm;? 2M2`;v iQ `�Bb2 i?2 Mm+H2mb BMiQ �M 2t+Bi2/ bi�i2- r?B+? bm#b2[m2MiHv /2+�vbX h?2/2+�v T`Q/m+ib i?2M 2Bi?2` 2b+�T2 Q` �`2 �#bQ`#2/ #v i?2 Mm+H2mb BM i?2 b�K2 K�MM2` �b i?2+QMp2ì2/ Q` b+�ii2`2/ Mm+H2mb BM [m�bB@2H�biB+ b+�ii2`BM;X

6B;m`2 RXe, 62vMK�M /B�;`�K 7Q` /22T BM2H�biB+ b+�ii2`BM; Uǳ.AaǴVX

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3

6B;m`2 RXd, SHQi b?QrBM; i?2 iQi�H M2mi`BMQ T2` Mm+H2mb +`Qbb@b2+iBQM /BpB/2/ #v M2mi`BMQ2M2`;v- mbBM; /�i� 7`QK KmHiBTH2 2tT2`BK2Mib U};m`2 i�F2M 7`QK (k)VX S`2/B+iBQMb 7Q` i?2/Bz2`2Mi BMi2`�+iBQM KQ/2b �`2 /`�rM 7`QK i?2 Ll�L*1 bBKmH�iBQM T�+F�;2X

N

*?�Ti2` k

JB+`Q "QQbi2` L2mi`BMQ 1tT2`BK2MiUJB+`Q"QQL1V

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Ry

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Rk

T`Q/m+2/- r?B+? �`2 7Q+mb2/ mbBM; � K�;M2iB+ ?Q`M �M/ � /2+�v TBT2X h?2 b2+QM/�`v ?�/`QMb/2+�v BM@~B;?i BMiQ M2mi`BMQb- r?B+? 7Q`Kb i?2 KQbiHv KmQM M2mi`BMQ #2�KX

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Rj

6B;m`2 kXj, AHHmbi`�iBQM Q7 i?2 T`Q/m+iBQM Q7 i?2 M2mi`BMQ #2�K mb2/ BM i?Bb �M�HvbBbX h?23 :2o T`QiQMb BKT�+i � #2`vHHBmK i�`;2i T`Q/m+BM; +?�`;2/ K2bQMbX h?2 K�;M2iB+ ?Q`M7Q+mb2b i?2 TQbBiBp2 K2bQMb /QrM � /2+�v TBT2 vB2H/BM; � M2mi`BMQ #2�KX U};m`2 i�F2M 7`QK(d)V

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R9

6B;m`2 kX9, h?2 �#bQHmi2 M2mi`BMQ ~mt T`2/B+iBQM i?`Qm;? i?2 JB+`Q"QQL1 /2i2+iQ` �b+�H+mH�i2/ #v i?2 #2�K bBKmH�iBQM U};m`2 i�F2M 7`QK (N)V

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R8

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Qion = Qcoll 2tT (t

⌧), UkXRV

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#2ir22M KmHiBTH2 k. +Hmbi2`b �M/ HQQF iQ ;`Qr i?2 +Hmbi2`b iQ BKT`Qp2 +QKTH2i2M2bb- rBi?Qmi+QKT`QKBbBM; Tm`BivX h?2 ivTB+�H �TT`Q�+? mb2/ #v +Hmbi2`@K2`;BM; �H;Q`Bi?Kb Bb iQ B/2MiB7vT�B`b Q7 +Hmbi2`b i?�i �`2 2Bi?2` BM +HQb2 T`QtBKBiv- Q` r?B+? TQBMi iQr�`/b 2�+? Qi?2`X AMi?2 �M�HvbBb /2b+`B#2/ BM i?Bb i?2bBb- r2 miBHBx2/ i?2 T`QtBKBiv #�b2/ +Hmbi2`BM; �H;Q`Bi?K-r?B+? ;`QmT2/ ?Bib iQ;2i?2` BMiQ +Hmbi2`b #�b2/ QM i?2B` T`QtBKBiv BM /`B7i iBK2X h?2 M2tibi2T Bb j. i`�+F `2+QMbi`m+iBQM r?B+? �BKb iQ +QHH2+i i?2 k. +Hmbi2`b 7`QK i?2 i?`22 `2�/QmiTH�M2b i?�i `2T`2b2Mi BM/BpB/m�H- i`�+F@HBF2 T�ìB+H2bX h?2 +?�HH2M;2 7Q` i?2 �H;Q`Bi?Kb Bb iQB/2MiB7v +QMbBbi2Mi ;`QmTBM;b Q7 +Hmbi2`b 7`QK i?2 /Bz2`2Mi pB2rbX h?2 j. i`�+F `2+QMbi`m+iBQMBb T`BK�`BHv T2`7Q`K2/ #v i?2 ǵh?`22.h`�Mbp2`b2h`�+FbǶ �H;Q`Bi?K (je)X h?Bb �H;Q`Bi?K+QMbB/2`b i?2 bmBi�#BHBiv Q7 �HH +QK#BM�iBQMb Q7 +Hmbi2`b 7`QK i?2 i?`22 `2�/Qmi TH�M2b �M/biQ`2b i?2 `2bmHib BM � i?`22@/BK2MbBQM�H �``�v- HQQb2Hv `272``2/ iQ �b � `�MF@i?`22 i2MbQ`X am+?� i`�+F `2+QMbi`m+iBQM Bb b?QrM BM 6B;m`2 9Xj- r?2`2 i?2 i`�+Fb B/2MiB}2/ �M/ `2+QMbi`m+i2/#v S�M/Q`� �`2 ?B;?HB;?i2/ BM `2/X

o2ì2t B/2MiB}+�iBQM Bb i?2 M2ti bi2T �7i2` i`�+F `2+QMbi`m+iBQMX _2+QMbi`m+iBQM Q7 i?2M2mi`BMQ BMi2`�+iBQM p2ì2t #2;BMb rBi? +`2�iBQM Q7 � HBbi Q7 TQbbB#H2 p2ì2t TQbBiBQMbX h?2ǵ*�M/B/�i2o2ì2t*`2�iBQMǶ �H;Q`Bi?K +QKT�`2b i?2 2M/ TQBMib Q7 T�B`b Q7 k. +Hmbi2`b- 2M@bm`BM; i?�i i?2 irQ +Hmbi2`b �`2 7`QK /Bz2`2Mi `2�/Qmi TH�M2b �M/ ?�p2 bQK2 Qp2`H�T BM i?2+QKKQM t +QQ`/BM�i2 (je)X 6Q` BMbi�M+2- i?2 HQr@t 2M/TQBMi Q7 QM2 +Hmbi2` +�M #2 B/2MiB}2/Xh?2 b�K2 t +QQ`/BM�i2 rBHH MQi M2+2bb�`BHv +Q``2bTQM/ iQ �M 2M/TQBMi Q7 i?2 b2+QM/ +Hmbi2`-#mi i?2 TQbBiBQM Q7 i?2 b2+QM/ +Hmbi2` �i i?Bb t +QQ`/BM�i2 +�M #2 2p�Hm�i2/- mbBM; � bHB/BM;HBM2�` }i �M/ �HHQrBM; bQK2 2ti`�TQH�iBQM Q7 +Hmbi2` TQbBiBQMbX h?2 irQ +Hmbi2` TQbBiBQMb-7`QK irQ pB2rb- �`2 bm{+B2Mi iQ T`QpB/2 � +�M/B/�i2 j. TQbBiBQMX lbBM; �HH Q7 i?2 +Hmbi2`2M/TQBMib �HHQrb 7Qm` +�M/B/�i2 p2ìB+2b iQ #2 +`2�i2/ 7Q` 2�+? +Hmbi2` T�B`BM;X 1�+? +�M/B@/�i2 Bb `2[mB`2/ iQ T�bb � bBKTH2 [m�HBiv +mi #27Q`2 #2BM; b2H2+i2/ �b i?2 KQbi HBF2Hv M2mi`BMQBMi2`�+iBQM p2ì2tX am+? � `2+QMbi`m+i2/ M2mi`BMQ BMi2`�+iBQM p2ì2t Bb b?QrM �b � Tm`TH2

9R

6B;m`2 9Xj, h`�+Fb Ub?QrM BM `2/V B/2MiB}2/ #v i?2 S�M/Q`� �miQK�i2/ i`�+F `2+QMbi`m+iBQMBM � JB+`Q"QQL1 +QHH2+iBQM TH�M2 Pp2`H�v M2mi`BMQ 2p2MiX

+B`+H2 BM 6B;m`2 jX9X

9Xk GQr2`BM; 1M2`;v h?`2b?QH/ BM JB+`Q"QQL16Q` �M J2o@b+�H2 `2+QMbi`m+iBQM- Bi Bb M2+2bb�`v iQ HQr2` ?Bi }M/BM; i?`2b?QH/b 7`QK i?2/27�mHi p�Hm2b iQ #2 �#H2 iQ `2+Qp2` �b Km+? 2M2`;v �b TQbbB#H2X h?`2b?QH/b �`2 T`BK�`BHvb2i �i i?2 bB;M�H T`Q+2bbBM; bi�;2 Q7 /�i� �M�HvbBbX h?2 K�BM Q#D2+iBp2 #2?BM/ �HH i?`2b?QH/HQr2`BM; 2t2`+Bb2b Bb iQ B/2MiB7v i?2 MQBb2 ~QQ` �M/ iQ p�`v i?`2b?QH/ T�`�K2i2`b bQ i?�i �Mv2M2`;v /2TQbBiBQM �#Qp2 i?�i ~QQ` +�M #2 `2+QMbi`m+i2/X h?2`2 �`2 7Qm` K�BM T�`�K2i2`br?B+? 2M�#H2 i?`2b?QH/ HQr2`BM; BM /�i� , L� 7Q`K�iBQM QM +QHH2+iBQM TH�M2- L� 7Q`K�iBQMQM i?2 BM/m+iBQM TH�M2b Ur?2`2 L� `272`b iQ i?2 MmK#2` Q7 bi�M/�`/ /2pB�iBQMb �#Qp2 7`QKi?2 `QQi K2�M b[m�`2/ U_JaV MQBb2 i?`2b?QH/b QM 2�+? rB`2 TH�M2V- _2;BQM Q7 AMi2`2bi U_PAV�KTHBim/2 BM i?2 MmK#2` Q7 2H2+i`QMb UT2�F p�Hm2 7Q` � bBM;H2 ?BiV �M/ _PA �p2`�;2 BM i?2MmK#2` Q7 2H2+i`QMb UK2�M p�Hm2 7Q` � bBM;H2 ?BiVX AM i?2 /27�mHi i?`2b?QH/ /�i� b2i- i?2`2bT2+iBp2 p�Hm2b 7Q` L� 7Q`K�iBQM QM +QHH2+iBQM �M/ BM/m+iBQM TH�M2- _PA �KTHBim/2 BMi?2 MmK#2` Q7 2H2+i`QMb �M/ _PA �p2`�;2 BM i?2 MmK#2` Q7 2H2+i`QMb �`2 j-8-Ryyy �M/ 8yy-r?2`2�b i?�i BM HQr i?`2b?QH/ /�i� b2i �`2 k-j-jyy �M/ Ryy `2bT2+iBp2HvX

AM 6B;m`2 9X9- r2 b22 i?2 +QKT�`BbQM Q7 i?2 2M2`;v bT2+i`� #2ir22M i?2 /�i� b�KTH2 rBi?

9k

6B;m`2 9X9, _2+QMbi`m+i2/ 2M2`;v bT2+i`� Q7 HQr �M/ ?B;? i?`2b?QH/ /�i� b�KTH2b

/27�mHi i?`2b?QH/b �M/ i?2 QM2 rBi? HQr2`2/ i?`2b?QH/bX AM i?2 /27�mHi i?`2b?QH/ /�i�b2i- r2�`2 �#H2 iQ `2+QMbi`m+i �+iBpBiv �b HQr �b yXk8 J2o BM 2M2`;v- r?2`2�b BM i?2 HQr i?`2b?QH//�i�b2i- i?2 2M2`;v `2+QMbi`m+iBQM +�M #2 �b HQr �b yXR J2oX �//BiBQM�HHv- BM i?2 HQr i?`2b?@QH/ /�i�b2i r2 b22 BM/B+�iBQMb Q7 +QMi`B#miBQMb 7`QK MQBb2 �M/ 39�` �+iBpBiv BM i?2 y@yX8 J2o2M2`;v `�M;2X

9Xj *QbKQ;2MB+ "�+F;`QmM/ _2KQp�HJB+`Q"QQL1Ƕb bm`7�+2 HQ+�iBQM 2tTQb2b i?2 /2i2+iQ` iQ bB;MB}+�Mi +QbKB+ `�v �+iBpBiv i?�i+�M TQi2MiB�HHv Q#b+m`2 #2�K@`2H�i2/ BMi2`�+iBQMbX h?2 K�BM +?�HH2M;2 7Q` i?2 J2o@b+�H2`2+QMbi`m+iBQM Bb i?2 HQr@2M2`;v �+iBpBiv �bbQ+B�i2/ rBi? +QbKB+ KmQM i`�+Fb- bm+? �b �@`�vb �M/ #`2Kbbi`�?HmM; T?QiQMb- i?�i Bb T`2b2Mi BM i?2 pB+BMBiv Q7 i?2 +QbKB+ KmQM i`�+FbXh?Bb �+iBpBiv Bb T`2b2Mi K�BMHv BM i?2 7Q`K Q7 bBM;H2 ?Bib QM rB`2bX � bBM;H2 ?Bi Bb MQi�#H2 iQ T`Q/m+2 2MQm;? HB;?i iQ #2 �#H2 iQ #2 `2+Q`/2/ #v i?2 JB+`Q"QQL1 SJhb- K�FBM;Bi BKTQbbB#H2 iQ #2 �#H2 iQ Q#i�BM iBKBM; BM7Q`K�iBQM 7Q` i?2b2 2M2`;v /2TQbBib �M/ i?mb`2+QMbi`m+i i?2B` i`m2 t@+QQ`/BM�i2X >2M+2 r2 K�F2 �M �bbmKTiBQM i?�i i?2 /`B7i +QQ`/BM�i2UtV Q#i�BM2/ 7Q` i?2 ?Bi Bb BM iBK2 rBi? i?2 #2�K �M/ Bb /2i2`KBM2/ #v Bib /`B7i iBK2X h?2#2�K /B`2+iBQM +QQ`/BM�i2 UxV- QM i?2 Qi?2` ?�M/- Bb /2i2`KBM2/ #v i?2 rB`2 MmK#2` QM i?2

9j

6B;m`2 9X8, *QbKQ;2MB+ i`�+Fb �`2 2M+HQb2/ rBi?BM +vHBM/`B+�H 2t+HmbBQM xQM2b Q7 `�/Bmb R8+K

+QHH2+iBQM TH�M2X h?Bb �M�HvbBb QMHv +QMbB/2`b HQr@2M2`;v 2H2+i`QK�;M2iB+ �+iBpBiv i?�i 7�HHbQmibB/2 Q7 � R8 +K k@. +vHBM/2` �`QmM/ 2�+? +QbKB+ i`�+F B/2MiB}2/ #v i?2 S�M/Q`� KmHiB�H;Q`Bi?K �miQK�i2/ T�ii2`M `2+Q;MBiBQM (je)- �b b22M BM 6B;m`2 9X8X h?Bb 2Mbm`2b i?�i QMHvi?2 2H2+i`QK�;M2iB+ �+iBpBiv i?�i Bb mM+Q``2H�i2/ iQ i?2 +QbKB+ i`�+Fb bm`pBp2b iQ i?2 M2ti�M�HvbBb bi�;2X JB+`Q"QQL1 b22b �M �p2`�;2 Q7 k9 i`�+Fb �M/ b?Qr2`b BM/m+2/ #v +QbKB+KmQMb BM Bib /�i� �+[mBbBiBQM U.�ZV rBM/Qr Q7 9X3 Kb T2` 2p2Mi (jd)X 6Q` � jXk Kb 2p2MirBM/Qr +QMbB/2`2/ 7Q` i?Bb �M�HvbBb- i?2`2 �`2 �#Qmi Re +QbKQHQ;B+�H i`�+Fb T2` 2p2Mi- 2�+?Q7 bBx2 yXkK⇥kK BM irQ /BK2MbBQMb- r?B+? rQmH/ BKTHv � HQbb Q7 �#Qmi eX9 K2 U⇠k9WV Q7 i?2bm`7�+2 �`2� /m2 iQ i?2 `2+i�M;mH�` +mibX � /Bbi�M+2 Q7 R8 +K �b i?2 `�/Bmb r�b +?Qb2M �7i2`bim/B2b QM Pz@"2�K /�i� K2�bm`BM; i?2 /Bbi�M+2 #2ir22M +QbKQHQ;B+�H i`�+Fb �M/ +Hmbi2`bUHQr@2M2`;v �+iBpBivVX

9X9 SH�M2 J�i+?BM;h?2 HQr@2M2`;v �+iBpBiv rBi?BM i?2 /2i2+iQ` pQHmK2 �7i2` +QbKB+ i`�+F `2KQp�H +QMbBbib T`B@K�`BHv Q7 bBM;H2 ?Bib- �b b?QrM BM i?2 /Bbi`B#miBQM Q7 +Hmbi2` bBx2 BM 6B;m`2 9XeX q2 �+?B2p2j@. `2+QMbi`m+iBQM #v K�i+?BM; i?2 /`B7i iBK2b Q7 +Hmbi2`b U;`QmT Q7 ?BibV �+`Qbb i?2 i?`22rB`2 TH�M2b- �b b?QrM BM i?2 b+?2K�iB+ BM 6B;m`2 9XdX q2 #2;BM #v b2�`+?BM; 7Q` i?2 /`B7i

99

6B;m`2 9Xe, aBx2 Q7 i?2 +Hmbi2`b BM i2`Kb Q7 MmK#2` Q7 ?Bib

6B;m`2 9Xd, SH�M2 J�i+?BM; Q7 � +Hmbi2` Bb 2bi�#HBb?2/ #v +?2+FBM; i?2 /`B7i iBK2 �M/ rB`2Qp2`H�T #2ir22M i?2 +QHH2+iBQM �M/ i?2 irQ BM/m+iBQM TH�M2bX

iBK2 Qp2`H�T BM i?2 irQ BM/m+iBQM TH�M2b 7Q` HQr@2M2`;v �+iBpBiv HvBM; QM i?2 +QHH2+iBQM TH�M2Xh?Bb Bb /2TB+i2/ BM i?2 7Q`K Q7 � b+?2K�iB+ BM 6B;m`2 9X3X PM+2 r2 }M/ � TH�M2 K�i+?

98

6B;m`2 9X3, a+?2K�iB+ /2TB+iBM; ?Qr i?2 K2i`B+ AQl UAMi2`b2+iBQM Qp2` lMBQMV Bb +�H+mH�i2/7Q` � TH�M2 K�i+? 7Q` i?2 +QHH2+iBQM TH�M2 +Hmbi2` �M/ i?2 BM/m+iBQM TH�M2 +Hmbi2`

6B;m`2 9XN, .Bbi`B#miBQM Q7 AQl p�Hm2b 7Q` TH�M2 K�i+?2/ �+iBpBiv 7Q` i?2 irQ BM/m+iBQMTH�M2bX

BM /`B7i iBK2 7Q` � +QHH2+iBQM TH�M2 +Hmbi2` �M/ �M BM/m+iBQM TH�M2 +Hmbi2`- r2 /2i2`KBM2 i?2p�Hm2 Q7 � K2i`B+ +�HH2/ ǵAMi2`b2+iBQM Qp2` lMBQMǶ UAQlV r?B+? Bb i?2 p�Hm2 Q7 i?2 BMi2`b2+iBQMBM /`B7i iBK2b /BpB/2/ #v i?2 mMBQM Q7 /`B7i iBK2bX h?2 /Bbi`B#miBQM Q7 AQl p�Hm2b 7Q` TH�M2

9e

K�i+?2/ +�M/B/�i2b Bb /2TB+i2/ BM 6B;m`2 9XNX h?2 /Bbi`B#miBQM 7Q` AQl p�Hm2b 7Q` #Qi? i?2l@SH�M2 �M/ i?2 o@SH�M2 T2�Fb �`QmM/ yXNX 6Q` �M B/2�H TH�M2 K�i+?- i?2 p�Hm2 AQl Bb RXh?Bb K2i`B+ Bb �HbQ miBHBx2/ H�i2` BM /2i2`KBMBM; #2bi K�i+? BM +�b2b Q7 KmHiBTH2 TH�M2 K�i+?+�M/B/�i2bX AM ;2M2`�H- TH�M2 K�i+?BM; 2Mbm`2b i?�i `�M/QK MQBb2 ?Bib �`2 `2KQp2/ �b i?2v�`2 mMHBF2Hv iQ }M/ � K�i+? �+`Qbb KmHiBTH2 TH�M2bX

6B;m`2 9XRy, J�i+? KmHiBTHB+Biv 7Q` � u SH�M2 *Hmbi2` �+`Qbb i?2 o �M/ l@SH�M2b

PM+2 TH�M2 K�i+?BM; Bb /QM2 �+`Qbb i?2 i?`22 TH�M2b- i?2`2 �`2 b2p2`�H 7�+iQ`b i?�i M22/iQ #2 i�F2M BMiQ +QMbB/2`�iBQM #27Q`2 � }M�H K�i+? 7Q` � +Hmbi2` QM i?2 u SH�M2 Bb 7QmM/ QMi?2 o@SH�M2 �M/fQ` i?2 l@SH�M2X P7i2M- r?BH2 TH�M2 K�i+?BM;- 7Q` � +Hmbi2` QM i?2 u SH�M2-i?2`2 K�v #2 +�b2b r?2`2 � p�`vBM; MmK#2` Q7 K�i+?2b �`2 7QmM/ QM #Qi? i?2 BM/m+iBQMTH�M2bX h?Bb Bb b?QrM BM 6B;m`2 9XRy- rBi? i?2 ?2HT Q7 � k@. ?BbiQ;`�K- r?2`2 i?2 MmK#2` Q7K�i+?2b 7Q` � bBM;H2 u TH�M2 +Hmbi2` QM i?2 o@SH�M2 �`2 b?QrM �HQM; i?2 v@�tBb �M/ QM i?2

9d

l@SH�M2 �`2 b?QrM �HQM; i?2 t@�tBbX h?2 +`Bi2`B� 7Q` 2bi�#HBb?BM; � bBM;H2 K�i+? 7`QK i?2�p�BH�#H2 K�i+?2b Bb H�B/ /QrM BM i?2 7QHHQrBM; bm#b2+iBQMbX

9X9XR LQ K�i+? QM #Qi? o@SH�M2 �M/ l@SH�M2AM i?Bb +�b2- i?2`2 Bb MQ K�i+? 7QmM/ QM i?2 BM/m+iBQM TH�M2b 7Q` i?2 7Q` i?2 +Hmbi2` QM i?2u TH�M2X h?Bb +�b2 Bb b?QrM �b i?2 BMi2`b2+iBQM Q7 i?2 o4y �M/ l4y #BMb BM 6B;m`2 9XRyX

9X9Xk 1t�+iHv QMHv QM2 K�i+? QM QM2 TH�M2 �M/ MQ K�i+? QM i?2Qi?2` TH�M2

AM i?Bb +�b2 i?2 K�i+? Q#i�BM2/ 7Q` i?2 +QHH2+iBQM TH�M2 +Hmbi2` QM 2Bi?2` QM2 Q7 i?2 BM/m+iBQMTH�M2b Bb i�F2M iQ #2 i?2 }M�H K�i+?X h?Bb +�b2 Bb b?QrM �b i?2 BMi2`b2+iBQM Q7 i?2 o4y-l4R�M/ �HbQ i?2 o4R-l4y #BMb BM 6B;m`2 9XRyX

9X9Xj 1t�+iHv QMHv QM2 K�i+? QM #Qi? o@SH�M2 �M/ l@SH�M2h?Bb Bb T2`?�Tb i?2 2�bB2bi Q7 i?2 +�b2b iQ +QMbB/2` bBM+2 i?2`2 Bb 2t�+iHv QM2 K�i+? 7Q`� u TH�M2 +Hmbi2` QM #Qi? o@SH�M2 �M/ l@SH�M2X h?Bb Bb /2TB+i2/ BM i?2 l4R-o4R #BMBMi2`b2+iBQM BM 6B;m`2 9XRyX PM+2 i?2 p�Hm2 Q7 i?2 v@+QQ`/BM�i2b Bb �``Bp2/ �i #v miBHBxBM;rB`2 BMi2`b2+iBQM 7Q` i?2 TH�M2 K�i+?2b- r2 `2[mB`2 i?�i i?2 irQ v +QQ`/BM�i2 p�Hm2b �;`22rBi? 2�+? Qi?2` rBi?BM � iQH2`�M+2 Q7 R +K- �b /2b+`B#2/ BM am#b2+iBQM 9X9X8X h?Bb Bb `2[mB`2/bQ i?�i �HH bTm`BQmb TH�M2 K�i+?2b- bm+? �b bi`�v 2H2+i`QMB+ MQBb2 ?Bib �`2 2HBKBM�i2/ �M/ QMHv`2�H 2H2+i`QK�;M2iB+ �+iBpBiv bm`pBp2bX

9X9X9 JmHiBTH2 K�i+?2b QM QMHv QM2 Q` #Qi? BM/m+iBQM TH�M2bh?Bb +�b2 Bb /2TB+i2/ 7Q` �HH BMi2`b2+iBQMb Q7 l �y �M/fQ` o �yX AM bm+? +�b2b- r2 +QKT�`2AQl p�Hm2b 7Q` 2p2`v K�i+? +�M/B/�i2 �M/ i?2M b2H2+i i?2 }M�H K�i+? �b i?2 QM2 rBi? i?2?B;?2bi AQl p�Hm2X

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89

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88

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dXRX8 *?�`;2 o�`B�iBQM _2H�i2/ iQ /1f/th?2`2 Bb p�`B�iBQM BM i?2 r�p27Q`K /m2 iQ HQ+�H /1f/t �i � TQBMi �HQM; i?2 T�ìB+H2Ƕb i`�D2+iQ`vr?2`2 i?2 �bbQ+B�i2/ +?�`;2 r�b /2TQbBi2/X h?Bb +�Tim`2b 2z2+ib `2H�i2/ iQ `2+QK#BM�iBQM�M/ �Mvi?BM; 2Hb2 i?�i +?�M;2b i?2 `2H�iBQMb?BT #2ir22M i?2 HQ+�H /1f/t �M/ i?2 `2bmHiBM;/Zf/tX aBM+2 r2 �`2 BMi2`2bi2/ BM K2�bm`BM; i?2 p�`B�iBQMb BM i?2 +?�`;2 i?�i /2T2M/ QMi?2 HQ+�H /1f/t �i i?2 TQBMi Q7 i?2 +Q``2bTQM/BM; 2M2`;v /2TQbBi- r2 miBHBx2 � b�KTH2 Q7 ?Bibr?2`2 i?2 HQ+�H /1f/t Bb r2HH@FMQrMX h?Bb Bb /QM2 #v mbBM; ?Bib �bbQ+B�i2/ rBi? T�ìB+H2i`�+Fb i?�i biQT BM i?2 /2i2+iQ` �M/ i?2M +QKT�`BM; iQ i?2 "2i?2@"HQ+? T`2/B+iBQM 7Q` /1f/tpbX `2bB/m�H `�M;2- /2b+`B#2/ BM 1[m�iBQM kXkX aBKBH�` iQ i?2 T`2pBQmb b2+iBQMb- r2 K2�bm`2i?2 �p2`�;2 BMi2;`�i2/ +?�`;2 �M/ rB/i? Q7 i?2 ?Bib �b � 7mM+iBQM Q7 i?2 HQ+�H /1f/tX

dXk GB;?i uB2H/ o�`B�iBQMb6QHHQrBM; �`2 i?2 Bi2Kb `2H�i2/ iQ KBbKQ/2HBM; Q7 HB;?i T`Q/m+iBQM �M/ i`�MbTQì r?B+? K�vBKT�+i /2i2+iQ` KQ/2HBM; �M/ i?mb �M�HvbBb T2`7Q`K�M+2X

dXkXR �#bQHmi2 HB;?i vB2H/ KBb@KQ/2HBM;_2;�`/H2bb Q7 �Mv iBK2@/2T2M/2M+2 Q#b2`p2/- HB;?i KBbKQ/2HBM; K�v BKT�+i T2`7Q`K�M+2�i i?2 +QbKB+@`2D2+iBQM bi�;2 Q7 i?Bb �M�HvbBbX � +QKT�`BbQM Q7 HB;?i vB2H/- K2�bm`2/ BMT?QiQ@2H2+i`QMb `2+Q`/2/ T2` +2MiBK2i2` Q7 i`�+F@H2M;i? US1f+KV- 7Q` �*Shb r�b T`Q/m+2/iQ ;mB/2 i?2 Qp2`�HH Gu b+�HBM; BM i?2 /2i2+iQ` rBi? r?B+? iQ T`Q/m+2 � /2i2+iQ` p�`B�iBQM7Q` �bb2bbBM; bvbi2K�iB+ mM+2ì�BMiB2b /m2 iQ i?Bb 2z2+iX h?2 K2�bm`2/ S1 `272`b iQ i?2BMi2;`�i2/ T`QKTi Y H�i2 HB;?i +QHH2+i2/ #v i?2 SJh �``�v 7Q` ~�b?2b BM i?2 #2�K@bTBHH

3y

rBM/QrX h?2 i`�+F H2M;i? `272`b iQ i?2 `2+QMbi`m+i2/ i`�+F@H2M;i? UpBbB#H2 rBi?BM i?2 hS*VQ7 i�;;2/ �*Sh i`�+FbX

dXkXk GB;?i `2bTQMb2 /2T2M/2M+v QM HQ+�iBQM �M/ iBK2GB;?i vB2H/ BM JB+`Q"QQL1 p�`B2b Qp2` iBK2 �M/ TQbBiBQM rBi?BM i?2 /2i2+iQ`X hBK2@/2T2M/2MiHB;?i vB2H/ 2z2+ib �`2 KQ/2H2/ �b �M Qp2`�HH [m2M+?BM; #mi �`2 K2�bm`2/ iQ #2 TQbBiBQM /2@T2M/2MiX hQ �++QmMi 7Q` i?2 Q#b2`p2/ /`QT BM HB;?i vB2H/ BM JB+`Q"QQL1- r2 mb2 � ;HQ#�H+Q``2+iBQM 7�+iQ` �TTHB2/ #Qi? �i bBKmH�iBQM bi�;2 �M/ `2+QMbi`m+iBQMX h?2 HB;?i vB2H/ /2+HBM2?Qr2p2` b?Qrb �M t@/2T2M/2Mi #2?�pBQ`- +QMbBbi2Mi rBi? #Qi? [m2M+?BM; �M/ �#bQ`TiBQM 27@72+ib- r?B+? �`2 MQi KQ/2H2/ BM i?Bb �M�HvbBbX hQ �++QmMi 7Q` i?2 /Bz2`2M+2 #2ir22M ?Qr i?Bb2z2+i Bb KQ/2H2/f+Q``2+i2/ �M/ ?Qr Bi i`mHv K�MB72bib Bib2H7 BM /�i�- r2 ?�p2 T`Q/m+2/ /2@i2+iQ` p�`B�iBQMb r?B+? 2M+�TbmH�i2 i?2 /Bz2`2M+2 #2ir22M i?2 pBbB#BHBiv K�T T`Q/m+2/ rBi?i?2 ;HQ#�H +Q``2+iBQM r2 +m``2MiHv �TTHv- �M/ i?2 pBbB#BHBiv K�T Q#i�BM2/ r?2M �TTHvBM; i?2[m2M+?BM;f�#bQ`TiBQM T�`�K2i2`bX

dXj Zm�MiB7vBM; bvbi2K�iB+ mM+2ì�BMiB2bPM+2 r2 +QKT�`2 i?2 *2Mi`�H o�Hm2 /�i� b�KTH2 Umb2/ BM i?Bb �M�HvbBbV rBi? i?2 HB;?i vB2H/UHvV �M/ rB`2 r�p27Q`K KQ/B}+�iBQM UrB`2KQ/V p�`B�iBQMb- r2 �``Bp2 �i i?2 7`�+iBQM�H mM@+2ì�BMiv �bbQ+B�i2/ rBi? 2�+? p�`B�iBQMX h?Bb Bb +�H+mH�i2/ #BM #v #BM mbBM; i?2 7QHHQrBM;7Q`KmH�,

Errorfraction =(CV � V ariation)

(CV )UdXRV

h?2 +QKT�`BbQM Q7 i?2 rB`2 r�p27Q`K KQ/B}+�iBQM UrB`2KQ/V �M/ HB;?i vB2H/ UHvV p�`B@�iBQMb iQ +�H+mH�i2 bvbi2K�iB+ mM+2ì�BMiB2b 7Q` 2p2`v #BM ?�b #22M b?QrM BM 6B;m`2 dXk-6B;m`2 dXR �M/ 6B;m`2 dXjX PM+2 i?2 mM+2ì�BMiB2b �`2 +�H+mH�i2/ 7Q` 2p2`v #BM- r2 �// i?2KBM [m�/`�im`2 iQ +�H+mH�i2 i?2 iQi�H 7`�+iBQM�H mM+2ì�BMiv �bbQ+B�i2/ rBi? �HH i?2 p�`B�iBQMbXh?2 T2`+2Mi�;2 /Bz2`2M+2 BM 2�+? #BM Bb i?2M KmHiBTHB2/ iQ i?2 #BM p�Hm2b BM 6B;m`2 eXk-6B;m`2 eXR �M/ 6B;m`2 eXj- `2bT2+iBp2Hv- iQ /2i2`KBM2 i?2 bBx2 Q7 i?2 bvbi2K�iB+ mM+2ì�BMiv2``Q` #�`bX

3R

6B;m`2 dXR, qB`2KQ/ �M/ HB;?i vB2H/ p�`B�iBQMb +QKT�`2/ rBi? i?2 *2Mi`�H o�Hm2 7Q` 2p�Hm@�iBQM Q7 bvbi2K�iB+ mM+2ì�BMiv 7Q` 6B;m`2 eXRX

3k

6B;m`2 dXk, qB`2KQ/ �M/ HB;?i vB2H/ p�`B�iBQMb +QKT�`2/ rBi? i?2 *2Mi`�H o�Hm2 7Q` 2p�Hm@�iBQM Q7 bvbi2K�iB+ mM+2ì�BMiv 7Q` 6B;m`2 eXkX

3j

6B;m`2 dXj, qB`2KQ/ �M/ HB;?i vB2H/ p�`B�iBQMb +QKT�`2/ rBi? i?2 *2Mi`�H o�Hm2 7Q` 2p�Hm@�iBQM Q7 bvbi2K�iB+ mM+2ì�BMiv 7Q` 6B;m`2 eXjX

39

*?�Ti2` 3

�TTHB+�iBQMb Q7 J2o a+�H2 S?vbB+b

h?Bb +?�Ti2` ?B;?HB;?ib bQK2 Q7 i?2 72�im`2b Q7 i?2 J2o b+�H2 `2+QMbi`m+iBQM r?2M �TTHB2/iQ bBKmH�i2/ µ.�_ �M/ amT2`MQp� 2H2+i`QM ⌫e 2p2MibX h?2b2 2p2Mib ?�p2 #22M bBKmH�i2/mbBM; i?2 J�_G1u HQr@2M2`;v M2mi`BMQ 2p2Mi ;2M2`�iQ`X

3XR JQ/2H Q7 �`;QM _2�+iBQM GQr@1M2`;v uB2H/bUJ�_G1uV

J�_G1u (9e) Bb �M 2p2Mi ;2M2`�iQ` i?�i bBKmH�i2b i2Mb@Q7@J2o M2mi`BMQ@Mm+H2mb BMi2`�+@iBQMbX 6Q` i?2 bim/B2b +QMbB/2`2/ BM i?Bb MQi2- p2`bBQM RXRXR Q7 J�_G1u r�b mb2/ iQ bBKmH�i2i?2 +?�`;2/@+m``2Mi T`Q+2bb

⌫e +40�r �! e� + 40E⇤ U3XRV

iQ;2i?2` rBi? i?2 bm#b2[m2Mi /2@2t+Bi�iBQMb Q7 i?2 `2KM�Mi 40E Mm+H2mbX a+�ii2`BM; +`Qbbb2+iBQMb r2`2 +QKTmi2/ mbBM; i?2 +QM};m`�iBQM `272``2/ iQ �b ǳ/�i�b2i �Ǵ BM `27X (9e)X h?2/27�mHi Mm+H2�` H2p2H �M/ /2@2t+Bi�iBQM �@`�v /�i�- �/�Ti2/ 7Q` mb2 BM J�_G1u 7`QK p2`bBQMRXe Q7 i?2 h�Gua Mm+H2�` +Q/2 (9d)- r2`2 �HbQ mb2/ BM i?2 bBKmH�iBQMbX h?2 Mm+H2�` /2@2t+Bi�iBQM T`Q/m+ib +QMbB/2`2/ #v J�_G1u BM+Hm/2 �@`�v T?QiQMb- Mm+H2QMb- �M/ +QKTQbBi2Mm+H2�` 7`�;K2Mib rBi? K�bb MmK#2` A 4 U2X;X- /2mi2`QMb- �HT?� T�ìB+H2bVX

hrQ b�KTH2b Q7 µ.�_ �M/ amT2`MQp� J�_G1u 2p2Mib r2`2 ;2M2`�i2/ 7Q` i?Bb MQi2mbBM; m#QQM2+Q/2- � JB+`Q"QQL1@bT2+B}+ bQ7ir�`2 T�+F�;2 i?�i BKTH2K2Mib 2ti2MbBQMb iQi?2 G�àQ7i (93) 7`�K2rQ`FX AM+B/2Mi M2mi`BMQ 2M2`;B2b r2`2 bBKmH�i2/ 7Q` i?2 }`bi b�KTH2mbBM; i?2 #mBHi@BM µ.�_ ⌫e bT2+i`mK BKTH2K2Mi2/ BM J�_G1uX h?2 b2+QM/ b�KTH2 mb2/� iBK2@BMi2;`�i2/ bmT2`MQp� ⌫e bT2+i`mK #�b2/ QM i?2 ǳ:oEJǴ +�H+mH�iBQM /2b+`B#2/ BM`27X (9N)X 6Q` bBKTHB+Biv- p2ì2t TQbBiBQMb 7Q` 2�+? M2mi`BMQ 2p2Mi r2`2 b�KTH2/ mMB7Q`KHvrBi?BM i?2 �+iBp2 pQHmK2 Q7 i?2 JB+`Q"QQL1 /2i2+iQ`X

38

3Xk _2+QMbi`m+iBQM Q7 *Q`2 *QHH�Tb2 amT2`MQp� �M/µ.�_ M2mi`BMQ 2p2Mib

6B;m`2 3XR, JB+`Q"QQL1 /2i2+iQ` +QHH2+iBQM TH�M2 2p2Mi /BbTH�vb b?QrBM; i?2 bT�iB�H �M/2M2`;v `2+QMbi`m+iBQM 7Q` i?2 }M�H bi�i2 T`Q/m+ib 7`QK µ.�_ M2mi`BMQ 2p2Mi

h?2 J2o@b+�H2 `2+QMbi`m+iBQM r�b mb2/ 7Q` #Qi? bT�iB�H �M/ 2M2`;v `2+QMbi`m+iBQM Q7 i?2HQr@2M2`;v /2@2t+Bi�iBQM �@`�vb T`Q/m+2/ BM #Qi? µ.�_ �M/ bmT2`MQp� M2mi`BMQ 2p2Mib �bb22M BM i?2 JB+`Q"QQL1 /2i2+iQ` +QHH2+iBQM TH�M2 2p2Mi /BbTH�vb BM 6B;m`2 3XR �M/ 6B;m`23XkX �b b22M BM #Qi? 2p2Mi /BbTH�vb- i?2 bmKK2/ i`m2 �M/ `2+QMbi`m+i2/ 2M2`;B2b 7Q` i?2/2@2t+Bi�iBQM �@`�vb �;`22 rBi? 2�+? Qi?2` rBi?BM � 72r ?mM/`2/ F2oX Ai Bb rQì? MQiB+BM;i?�i 2p2M i?Qm;? i?2 2M2`;v `2+QMbi`m+iBQM 7Q` 2H2+i`QM i`�+Fb Bb �HbQ T`QKBbBM;- i?2 bT�iB�H`2+QMbi`m+iBQM Q7 i?2 b?Qì 2H2+i`QM i`�+F Bb biBHH � rQ`F BM T`Q;`2bbX h?Bb Bb T`BK�`BHv #2+�mb2i?2 J2o@b+�H2 �M�HvbBb 7Q+mb2b QM `2+QMbi`m+iBQM Q7 +Hmbi2`b r?B+? �`2 ;2M2`�HHv k ?Bib BM bBx2-r?2`2�b �M 2H2+i`QM i`�+F 7Q` #Qi? µ.�_ �M/ bmT2`MQp� M2mi`BMQ 2p2Mib Bb QM i?2 Q`/2` Q7Ry ky ?Bib BM bBx2X

3e

6B;m`2 3Xk, JB+`Q"QQL1 /2i2+iQ` +QHH2+iBQM TH�M2 2p2Mi /BbTH�vb b?QrBM; i?2 bT�iB�H �M/2M2`;v `2+QMbi`m+iBQM 7Q` i?2 }M�H bi�i2 T`Q/m+ib 7`QK � amT2`MQp� M2mi`BMQ 2p2Mi

3d

*?�Ti2` N

qB`BM; Q7 a"L. �MQ/2 SH�M2�bb2K#HB2b

.m`BM; i?2 j`/ v2�` Q7 Kv S?. T`Q;`�K- A T�ìB+BT�i2/ BM i?2 rB`2 rBM/BM; 2zQì �b T�ìQ7 i?2 av`�+mb2 lMBp2`bBiv M2mi`BMQ ;`QmT �i u�H2 lMBp2`bBivX h?Bb +?�Ti2` /2b+`B#2b i?2a"L. rB`2 rBM/BM; T`Q+2/m`2 �M/ `2bmHib �i q`B;?i G�#- u�H2 lMBp2`bBivX h?2 a"L. rB`2rBM/BM; 2zQì r�b /BpB/2/ #2ir22M i?2 la �M/ lE i2�Kb- rBi? av`�+mb2 lMBp2`bBiv H2�/BM;i?2 la 2zQì #v rB`BM; irQ �MQ/2 SH�M2 �bb2K#HB2b U�S�V- i?2 Qi?2` irQ �S�b #2BM; rB`2/�i .�`2b#m`v G�#Q`�iQ`v BM i?2 lEX

6B;m`2 NXR, � KQ/2H Q7 i?2 a"L. hS*- b?QrBM; i?2 TQbBiBQMb Q7 i?2 �MQ/2 TH�M2 �M/+�i?Q/2 TH�M2 �bb2K#HB2b U�S�b �M/ *S�bVX 6B;m`2 i�F2M 7`QK (8y)X

�b /2b+`B#2/ BM a2+iBQM kXR �M/ b?QrM rBi? i?2 ?2HT Q7 � b+?2K�iB+ BM 6B;m`2 NXR- a"L.Bb � bBM;H2 T?�b2 G�`hS* rBi? �M �+iBp2 K�bb Q7 RRk iX h?2 hS*- r?B+? Bb 7mHHv BKK2`b2/ BMHB[mB/ �`;QM- +QMbBbib Q7 � +2Mi`�H 8 K⇥9 K +�i?Q/2 r�HH 7Q`K2/ Q7 irQ kX8 K⇥9 K +�i?Q/2TH�M2 �bb2K#HB2b U*S�bV BM #2ir22M irQ �MQ/2 r�HHb- 2�+? k K �r�v 7`QK i?2 +�i?Q/2X h?2�MQ/2 r�HHb �`2 �HbQ 8 K⇥9 K BM /BK2MbBQM- �M/ 2�+? +QMbBbib Q7 irQ kX8 K⇥9 K �MQ/2 TH�M2�bb2K#HB2b U�S�bVX h?2 *S�b �`2 ?2H/ �i ƐRyy Fo rBi? i?2 �S�b �i ;`QmM/X AQMBb�iBQM

33

2H2+i`QMb T`Q/m+2/ #v i?2 T�bb�;2 Q7 i?2 +?�`;2/ T�ìB+H2b i?`Qm;? HB[mB/ �`;QM /`B7i iQ i?2�S�b mM/2` i?2 BM~m2M+2 Q7 8yy of+K 2H2+i`B+ }2H/- r?2`2 i?2v �`2 `2�/ QmiX

NXR a"L. qB`2 SH�M2 aT2+B}+�iBQMbh?2 bT2+B}+�iBQM +`Bi2`B� 7Q` rBM/BM; i?2 a"L. rB`2 TH�M2b r�b T`BK�`BHv �BK2/ �i 2Mbm`BM;i?�i i?2 `2�/Qmi rB`2b �`2 mMB7Q`K BM bT�+2 iQ 2M�#H2 � mMB7Q`K /2i2+iQ` `2bTQMb2- �M/ iQQTiBKBb2 i?2 bB;M�H@iQ@MQBb2 `�iBQ �M/ bT�iB�H `2bQHmiBQMX >�pBM; � bK�HH2` rB`2 bT�+BM; 2M@�#H2b � ;`2�i2` `2bQHmiBQM �H#2Bi �i � +Qbi Q7 `2/m+2/ bB;M�H@iQ@MQBb2 `�iBQX h?Bb Bb #2+�mb2 i?2bB;M�H `2+2Bp2/ #v 2�+? rB`2b Bb T`QTQìBQM�H iQ i?2 MmK#2` Q7 BQMBx�iBQM 2H2+i`QMb T`Q/m+2/#v � T�ìB+H2 i`�p2`bBM; i?2 HB[mB/ �`;QM rBi?BM i?2 hS*X h?2 bT2+B}+�iBQM +`Bi2`B� ?�b #22M/2i�BH2/ BM h�#H2 NXRX

h2bi _2[mB`2K2Mi

qB`2 i2MbBQM �i iBK2 Q7 rB`2 H�vBM; d ±R L

1[mBHB#`BmK rB`2 i2MbBQM U�7i2` bH�+F2MBM;V 8 ±R L

qB`2 bT�+BM; j ±yX8 KK

G�v2` bT�+BM; j ±yX8 KK

1H2+i`B+�H +QMiBMmBiv I 8yy ⌦

1H2+i`B+�H BbQH�iBQM = Ry J⌦ #2ir22M �/D�+2Mi rB`2b

h�#H2 NXR, h?2 F2v bT2+B}+�iBQMb 7Q` a"L. �S� rB`BM;X

NXk �S� qB`BM;1p2M i?Qm;? i?2`2 r2`2 K�Mv bBKBH�`BiB2b BM i?2 rB`2 rBM/BM; T`Q+2/m`2 �M/ [m�HBiv +QMi`QHi2biBM; #2ir22M i?2 irQ rB`2 rBM/BM; bBi2b Uq`B;?i G�#- u�H2 �M/ .�`b2#m`v G�#- lEV- i?2�TT�`�imb mb2/ �i i?2 irQ HQ+�iBQMb r�b /Bz2`2MiX h?2 /2i�BHb Q7 i?2 i2+?MB[m2b miBHBx2/7Q` rB`2 rBM/BM; �M/ [m�HBiv +QMi`QH �i q`B;?i G�# BM i?2 la �`2 H�B/ Qmi BM i?2 7QHHQrBM;bm#@b2+iBQMbX

3N

NXkXR J�Mm�H qB`2 qBM/BM; �TT�`�imbh?2 K�Mm�H rB`2 rBM/BM; �TT�`�imb mb2/ �i u�H2 q`B;?i G�# +QMbBbi2/ Q7 TBM #HQ+Fb KQmMi2/QM � bHB/BM; b?miiH2 �b b?QrM BM 6B;m`2 NXkX liBHBxBM; � TBM #HQ+F �HHQr2/ mb iQ #`BM; KmHiBTH2rB`2b iQ i?2 `2[mB`2/ i2MbBQM QM i?2 b?miiH2- r?B+? r�b i?2M bHB/ Qp2` QM iQT Q7 i?2 �S� �M/i?2 rB`2b r2`2 i?2M bQH/2`2/ BM TH�+2 QM i?2 rB`2 +�``B2` #Q�`/bX

6B;m`2 NXk, � KQ/2H Q7 i?2 K�Mm�H rBM/BM; �TT�`�imbX h?2 TBM #HQ+Fb �M/ +�``B�;2 �`2 MQib?QrM BM i?Bb KQ/2Hc i?2v +�M KQmMi �i p�`vBM; TQbBiBQMb �`QmM/ i?2 b?miiH2X 6B;m`2 i�F2M7`QK (8y)X

h?2 �HmKBMBmK TBM #HQ+Fb #2ir22M r?B+? i?2 rB`2b r2`2 rQmM/ �`2 b?QrM BM 6B;m`2NXj UiQTVX h?2 rB`2b �`2 rQmM/ QM i?2 #HQ+F �`QmM/ i?2 �``�v Q7 `Qi�iBM; TBMb #v �MQT2`�iQ` r�HFBM; #�+F �M/ 7Qì? #2ir22M i?2 #HQ+FbX PM2 TBM #HQ+F r�b }ii2/ rBi? � i?`2�/r?B+? +QmH/ #2 /`�rM #�+F iQ �TTHv i?2 `2[mB`2/ i2MbBQM iQ i?2 rB`2bX h?2 i2MbBQM �HbQ #2/Bbi`B#mi2/ 2p2MHv #2ir22M i?2 rB`2b #v `Qi�iBM; i?2 TBMbX h?2 b�K2 T�B` Q7 #HQ+Fb +QmH/ #2KQmMi2/ BM p�`vBM; TQbBiBQMb QM i?2 b?miiH2 iQ b2i i?2 +Q``2+i �M;H2 7Q` 2�+? Q7 i?2 i?`22 rB`2TH�M2b U�+?B2p2/ #v H�vBM; i2bi rB`2b �M/ Q#b2`pBM; r?2M i?2v �HB;M2/ QM i?2 �TT`QT`B�i2bQH/2` T�/bVX

hQ bmTTQì i?2 �S� �M/ iQ �HHQr 7Q` +QMi`QH QM i?2 ?2B;?i �M/ iBHi Q7 i?2 �S�- � b2i Q7i?`22 D�+Fb Ub?QrM BM 6B;m`2 NXj- #QiiQK H27iV r2`2 miBHBx2/X h?2b2 D�+Fb �HHQr2/ i?2 �S�

Ny

iQ #2 HQr2`2/ bQ i?�i i?2 b?miiH2 +QmH/ T�bb Qp2` Bi r?2M #2BM; /`�rM #�+F iQ `2+2Bp2 � M2r#�i+? Q7 rB`2b BM i?2 rQ`FBM; �`2�- i?2M `�Bb2/ �M/ H2p2HH2/ iQ i?2 TH�M2 Q7 i?2 rB`2b QM i?2#HQ+Fb #27Q`2 i`�Mb72`X AM Q`/2` iQ rB`2 i?2 l �M/ o@SH�M2b- i?2 �TT�`�imb r�b �HbQ }ii2/rBi? � ǳ+�``B�;2Ǵ, � K�Mm�HHv QT2`�i2/ K2+?�MB+�H KQmMiBM; �HHQrBM; QM2 TBM #HQ+F iQ #27QH/2/ /QrM Qp2` i?2 r`�T 2/;2 r?2M rBM/BM; i?2 BM/m+iBQM TH�M2b Ub?QrM BM 6B;m`2 NXj-#QiiQK `B;?iVX

6B;m`2 NXj, S?QiQ;`�T?b Q7 i?2 K�Mm�H rBM/BM; �TT�`�imbX hQT H27i, � +HQb2@mT Q7 i?2 MQM@i2MbBQMBM; TBM #HQ+F- b?QrBM; i?2 `Qi�iBM; TBMb �`QmM/ r?B+? i?2 rB`2b �`2 rQmM/X hQT`B;?i, i?2 i2MbBQMBM; #HQ+F BM Bib 7Q`r�`/ TQbBiBQM- b?QrBM; i?2 /Qp2i�BH `�BH QM r?B+? Bibi?`2�/ TmHHb Bi #�+F iQ �TTHv i2MbBQM iQ i?2 rB`2bX "QiiQK H27i, � rB`2/ �S� `2biBM; QM i?2i?`22 D�+Fb mb2/ iQ H2p2H i?2 �S� iQ i?2 TH�M2 Q7 i?2 rB`2b #2BM; i`�Mb72``2/X "QiiQK `B;?i,i?2 +�``B�;2 #2BM; mb2/ iQ 7QH/ rB`2b Qp2` i?2 r`�T #Q�`/bX 6B;m`2 i�F2M 7`QK (8y)X

NXkXk J�Mm�H qBM/BM; S`Q+2/m`2h?2 K�Mm�H rB`2 rBM/BM; T`Q+2/m`2 BMpQHp2/ miBHBxBM; i?2 �TT�`�imb �++Q`/BM; iQ i?2 7QH@HQrBM; T`Q+2/m`2,

NR

RX � #�i+? Q7 rB`2b Bb rQmM/ #v ?�M/ #2ir22M i?2 irQ TBM #HQ+Fb rBi? i?2 b?miiH2 bHB/�r�v 7`QK i?2 �S�X

kX q?BH2 i?2 �S� Bb HQr2`2/- i?2 b?miiH2 Bb bHB/ Qp2` i?2 �S�X h?2M i?2 �S� Bb `�Bb2/mMiBH i?2 rB`2b �`2 BM +QMi�+i rBi? i?2 #Q�`/b iQ r?B+? i?2v rBHH #2 bQH/2`2/X

jX liBHBxBM; i?2 i?`2�/ QM i?2 i2MbBQMBM; TBM #HQ+F- i?2 rB`2b �`2 #`Qm;?i �TT`QtBK�i2HviQ i?2 `2[mB`2/ i2MbBQM Q7 d LX

9X 6Q` i?2 l �M/ o H�v2`b- i?2 rB`2b �`2 7QH/2/ Qp2` i?2 r`�T 2/;2 mbBM; i?2 +�``B�;2X

8X h?2 i2MbBQM Q7 �TT`QtBK�i2Hv kyW Q7 i?2 rB`2b BM i?2 #�i+? Bb b�KTH2/ rBi? i?2 H�b2`�TT�`�imb /2b+`B#2/ BM b2+iBQM 8XRX A7 �Mv rB`2b �`2 Q#b2`p2/ rBi? i2MbBQM QmibB/2 i?2d±R L `�M;2- i?2 i2MbBQM Q7 i?2 #�i+? Bb �/Dmbi2/ UmbBM; i?2 i?`2�/V �M/ `2@K2�bm`2/mMiBH i?2 rB`2b b�KTH2/ �`2 RyyW +QKTHB�Mi rBi? i?2 bT2+B}+�iBQMbX

eX PM+2 i?2 rB`2b �`2 bQH/2`2/ iQ i?2 #Q�`/- i?2 H2M;i?b #2?BM/ 2�+? bQH/2` DQBMi �`2 +miX

dX h?2 i2MbBQM Q7 2p2`v rB`2 BM i?2 #�i+? Bb K2�bm`2/ �;�BMX �Mv rB`2b Q#b2`p2/ iQ #2QmibB/2 i?2 bT2+B}+�iBQMb �`2 +mi �M/ `2@H�B/X

3X h?2 b?miiH2 Bb KQp2/ #�+F iQ Bib Q`B;BM�H TQbBiBQM �M/ i?2 T`Q+2bb Bb `2T2�i2/X

NXj Zm�HBiv *QMi`QH h2biBM;hQ K�F2 bm`2 i?�i i?2 rB`2 rBM/BM; Bb +QMbBbi2Mi rBi? i?2 bT2+B}+�iBQMb HBbi2/ BM h�#H2 NXR- r2T2`7Q`K2/ [m�HBiv +QMi`QH K2�bm`2K2Mib i?`Qm;?Qmi i?2 +QMbi`m+iBQM T`Q+2bbX h?Bb b2+iBQMT`2b2Mib �M Qp2`pB2r Q7 i?2 [m�HBiv +QMi`QH K2�bm`2K2Mib +�``B2/ Qmi �i u�H2 q`B;?i G�#-laX

NXjXR h2MbBQM h2biBM; J2i?Q/hQ K2�bm`2 i?2 i2MbBQM Q7 2�+? rB`2- r2 mb2 � H�b2` T?QiQ/BQ/2 b2imT T`QpB/2/ #v i?2lMBp2`bBiv Q7 qBb+QMbBM@J�/BbQM S?vbB+�H a+B2M+2b G�#Q`�iQ`vX h?Bb T`Q+2bb Bb BHHmbi`�i2/BM 6B;m`2 NX9 �M/ b?QrM BM �+iBQM BM 6B;m`2 NX8X

hQ K2�bm`2 i?2 i2MbBQM 7Q` � T�ìB+mH�` rB`2- r2 7Q+mb � H�b2` QM i?2 rB`2 �i i?2 `2[mB`2/?2B;?i �#Qp2 i?2 rB`2X h?2 `2~2+i2/ HB;?i Qz i?2 rB`2 Bb K2�bm`2/ mbBM; � T?QiQ/BQ/2X h?2rB`2 Bb �;Bi�i2/ iQ T`Q/m+2 Qb+BHH�iBQMb �M/ i?2 bB;M�H 7`QK i?2 `2~2+i2/ H�b2` HB;?i K2�bm`2/#v i?2 T?QiQ/BQ/2 mM/2`;Q2b � 7�bi 6Qm`B2` i`�Mb7Q`K iQ 2ti`�+i i?2 7mM/�K2Mi�H 7`2[m2M+vQ7 i?2 Qb+BHH�iBQMX 6`QK i?Bb r2 2ti`�+i i?2 i2MbBQM h �++Q`/BM; iQ 1[m�iBQM NXR-

Nk

6B;m`2 NX9, � +�ìQQM b?QrBM; i?2 QT2`�iBQM Q7 i?2 H�b2` T?QiQ/BQ/2 i2MbBQM K2�bm`2K2Mi�TT�`�imbX 6B;m`2 i�F2M 7`QK (8y)X

T = 4⇢(fl)2, UNXRV

r?2`2 7 Bb i?2 Q#b2`p2/ 7mM/�K2Mi�H 7`2[m2M+v Q7 i?2 Qb+BHH�iBM; rB`2- H i?2 H2M;i? 7`22 iQQb+BHH�i2 Ur?2i?2` #2ir22M bQH/2` T�/b Q` #2ir22M +QK#bV- �M/ ⇢ Bib HBM2�` /2MbBivX

h?2 �++m`�+v Q7 i?2 rB`2 i2MbBQM K2�bm`2K2Mi Bb /2T2M/2Mi T`BK�`BHv QM i?2 mM+2ì�BMiB2bQM #Qi? i?2 Qb+BHH�iBQM 7`2[m2M+v �M/ i?2 H2M;i? Q7 i?2 rB`2 i?�i Bb 7`22 iQ Qb+BHH�i2X h?2K�BM mM+2ì�BMiv QM i?2 K2�bm`2K2Mi Q7 i?2 rB`2 H2M;i? +QK2b 7`QK i?2 2``Q` K�`;BM QMi?2 b+�H2 Q7 i?2 K2�bm`BM; i�T2 �M/ i?2 mb2` 2``Q` BM BMi2`T`2iBM; Bi- rBi? �M 2biBK�i2/p�Hm2 Q7 yXR8 +KX h?2 mM+2ì�BMiv QM i?2 Qb+BHH�iBQM 7`2[m2M+v /2`Bp2b 7`QK i?2 7Q+mb Q7i?2 H�b2`- i?2 #BMMBM; Q7 i?2 6Qm`B2` i`�Mb7Q`K bQ7ir�`2- �M/ i?2 �++m`�+v rBi? r?B+? i?2T2�Fb �`2 B/2MiB}2/- rBi? �M 2biBK�i2/ p�Hm2 Q7 yX8 >x 7Q` i?2 HQM;2bi rB`2b �M/ k8 >x7Q` i?2 b?Qì2biX PM 7mHH@H2M;i? rB`2b- i?2b2 H2M;i? �M/ 7`2[m2M+v mM+2ì�BMiB2b T`Q/m+2 �ivTB+�H i2MbBQM mM+2ì�BMiv Q7 �TT`QtBK�i2Hv yXR8 L 7Q` i?2 l �M/ o@SH�M2b- �M/ yXk8 L7Q` i?2 u TH�M2X 6Q` i?2 p2`v b?Qì2bi rB`2b BM i?2 +Q`M2`b Q7 i?2 l �M/ o@SH�M2b- i?2b2mM+2ì�BMiB2b ;`Qr �b i?2 T`QTQìBQM�H mM+2ì�BMiv QM i?2 H2M;i? #2+QK2b KQ`2 bB;MB}+�Mi-T`Q/m+BM; mM+2ì�BMiB2b mT iQ R8 iBK2b H�`;2` i?�M i?2 MQKBM�H p�Hm2b 7Q` HQM;2` rB`2bX h?2

Nj

6B;m`2 NX8, S?QiQ;`�T?b Q7 i?2 i2MbBQM K2�bm`2K2Mi H�b2` BM mb2 �i q`B;?i G�#- 7Q+mb2/ QM� i2MbBQM2/ rB`2 BM � #�i+? `2�/v 7Q` i`�Mb72`X PM i?2 `B;?i- i?2 b?�/Qr QM i?2 QT2`�iQ`Ƕb?�M/ b?Qrb i?2 +?�`�+i2`BbiB+ bBH?Qm2ii2 Q7 i?2 rB`2 r?2M i?2 H�b2` Bb 7Q+mb2/X aBM+2 i?2rB`2b HB2 BM � TH�M2- QM+2 i?2 H�b2` Bb 7Q+mb2/ QM QM2 rB`2 Bi rBHH #2 7Q+mb2/ 7Q` i?2 Qi?2`bX6B;m`2 i�F2M 7`QK (8y)X

mM+2ì�BMiv QM i?2 b?Qì rB`2b Q++m`b 7Q` `Qm;?Hv ky rB`2b T2` H�v2`X h?2 i2MbBQM Q7 i?2b2rB`2b +QmH/ �HbQ #2 K2�bm`2/ #27Q`2 H�vBM; Ur?2M i?2v r2`2 biBHH Q7 � H2M;i? iQ bT�M i?2bHB/BM; +�``B�;2V- �M/ r�b Q#b2`p2/ iQ #2 +QMbBbi2Mi rBi? i?2 i2MbBQM Q7 i?2 Qi?2` rB`2bX

NXjXk h2MbBQM h2biBM; _2bmHibh?2 rB`BM; i2+?MB[m2 mb2/ iQ H�v rB`2b �i q`B;?i G�# T`Q/m2/ i2MbBQM /Bbi`B#miBQMb +QM}M2/rBi?BM � `�M;2 Q7 k L- �b T2` i?2 bT2+B}+�iBQMbX h?2b2 /Bbi`B#miBQMb �`2 b?QrM BM 6B;m`2 NXe�M/ 6B;m`2 NXd- �M/ i?2B` bi�iBbiB+�H KQK2Mib �`2 bmKK�`Bb2/ BM h�#H2 NXkX 6Q` 2p2`v TH�M2QM 2p2`v �S�- i?2 K2�M Q7 i?2 i2MbBQM /Bbi`B#miBQM HB2b rBi?BM i?2 MQKBM�H `�M;2 Q7 d ±RLX � p2`v bK�HH MmK#2` Q7 rB`2b rBi? i2MbBQMb 2t+22/BM; i?2 bT2+B}+�iBQM r2`2 K2�bm`2/ BMi?2 +Q`M2`b- #mi r2`2 �HHQr2/ iQ `2K�BM /m2 iQ i?2B` b?Qì H2M;i?X

N9

6`�K2 G�v2` J2�M h2MbBQMULV

_Ja ULV

la G27i�S�

u dXyd yX8Ro dXRj yX9kl dXyR yX99

la _B;?i�S�

u eXN3 yX98o dXyR yX93l eX3N yX8k

h�#H2 NXk, J�Mm�H rB`BM; i2MbBQMBM; `2bmHib

NXjXj 1H2+i`B+�H h2biBM; J2i?Q/bhQ i2bi i?2 2H2+i`B+�H +QMiBMmBiv �+`Qbb 2�+? rB`2 �M/ 2H2+i`B+�H BbQH�iBQM #2ir22M 2�+? T�B`Q7 M2B;?#Qm`BM; rB`2b- r2 mb2 � bQm`+2K2i2` +QMM2+i2/ iQ � /2bFiQT G�#oB2r T`Q;`�KX �T`Q#2 Bb TH�+2/ K�Mm�HHv �i 2Bi?2` 2M/ Q7 i?2 i2bi +?�MM2H- �M/ � TQi2MiB�H Q7 yXyR o Bb�TTHB2/ #2ir22M i?2 T`Q#2b iQ K2�bm`2 +QMiBMmBivX 6Bp2 +QMb2+miBp2 K2�bm`2K2Mib Q7 i?2+m``2Mi mM/2` i?Bb pQHi�;2 �`2 �p2`�;2/ iQ T`Q/m+2 � }M�H K2�bm`2K2Mi Q7 i?2 +m``2Mi U�M/i?mb i?2 `2bBbi�M+2 �+`Qbb i?2 +?�MM2HVX hQ K2�bm`2 rB`2@iQ@rB`2 BbQH�iBQM- � TQi2MiB�H Q79yyo Bb bQm`+2/ �+`Qbb T`Q#2b TH�+2/ QM irQ �/D�+2Mi rB`2bX PM+2 �;�BM- }p2 +QMb2+miBp2K2�bm`2K2Mib Q7 i?2 +m``2Mi �`2 �p2`�;2/- �M/ i?2 W `2bBbi�M+2 #2ir22M i?2 irQ +?�MM2Hb/2/m+2/ 7`QK i?2 K2�M +m``2MiX

.m2 iQ i?2 2ti`2K2Hv HQr K�;MBim/2 Q7 i?2 +m``2Mib i?�i ~Qr #2ir22M T`QT2`Hv BbQH�i2/+?�MM2Hb- i?2 �#bQHmi2 p�Hm2 Q7 i?2 `2bBbi�M+2 K2�bm`2/ BM i?2 BbQH�iBQM i2bib r�b Q#b2`p2/iQ ~m+im�i2 [mBi2 bi`QM;Hv rBi? 2MpB`QMK2Mi�H +QM/BiBQMb U2X;X HQ+�H ?mKB/BivVX q?2M i?2#Q�`/b r2`2 i2bi2/ bm#K2`;2/ BM HB[mB/ MBi`Q;2M- i?2b2 bm`7�+2 +m``2Mib r2`2 Q#b2`p2/ iQbm#bB/2 iQ � mMB7Q`K H2p2H Q7 �TT`QtBK�i2Hv 8 M� U`Qm;?Hv i?2 b2MbBiBpBiv Q7 i?2 bQm`+2K2i2`VXaBM+2 2p2M i?2 H�`;2bi ~m+im�iBQMb �i `QQK i2KT2`�im`2 H27i i?2 K2�bm`2/ `2bBbi�M+2 p�Hm2br2HH �#Qp2 i?2 bT2+B}2/ KBMBKmK- i?2b2 ~m+im�iBQMb r2`2 MQi Dm/;2/ iQ #2 � +�mb2 7Q`+QM+2`MX

NXjX9 1H2+i`B+�H h2biBM; _2bmHibaBKBH�` `2bmHib r2`2 Q#i�BM2/ 7Q` �HH K2�bm`2K2Mib Q7 2H2+i`B+�H +QMiBMmBiv �M/ BbQH�iBQM i2bi@BM; �+`Qbb i?2 irQ �S�bX �HH +?�MM2Hb r2`2 7QmM/ iQ #2 2H2+i`B+�HHv +QMiBMmQmb �M/ BbQH�i2/7`QK i?2B` M2B;?#Qm`b- b?QrBM; � `2bBbi�M+2 �+`Qbb 2�+? rB`2 Ry Ryy iBK2b HQr2` i?�M i?2bT2+B}2/ K�tBKmK 7Q` i?2 +QMiBMmBiv i2bib- �M/ � `2bBbi�M+2 #2ir22M 2�+? T�B` Q7 M2B;?@#Qm`BM; rB`2b Qp2` R-yyy iBK2b ?B;?2` i?�M i?2 bT2+B}2/ KBMBKmK 7Q` BbQH�iBQMX h?2 7mHH/Bbi`B#miBQMb Q7 i?2b2 `2bBbi�M+2b �`2 b?QrM BM 6B;m`2 NX3 �M/ 6B;m`2 NXN 7Q` i?2 �S�b rQmM/

N8

mbBM; i?2 K�Mm�H rB`BM; K2i?Q/Xq2 Q#i�BM 2tT2+i2/ /Bbi`B#miBQMb Q7 `2bBbi�M+2 b+�HBM; HBM2�`Hv rBi? rB`2 H2M;i?- ;BpBM;

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