Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen
We report the observation of high resolution (0.008 cm⁻¹) infrared absorption spectra of CO₂ molecules isolated in solid parahydrogen(pH₂) matrices at T=2.4 to 4.8 K. Several extremely sharp (0.01 to 0.04 cm⁻¹ full-width-at-half-maximum) absorption features appear in the 2343.5 to 2345 cm⁻¹ region....
Gespeichert in:
| Veröffentlicht in: | Физика низких температур |
|---|---|
| Datum: | 2000 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2000
|
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/129213 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen / Simon Tam, Mario E. Fajardo // Физика низких температур. — 2000. — Т. 26, № 9-10. — С. 889-898. — Бібліогр.: 86 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859807169318223872 |
|---|---|
| author | Tam, Simon Fajardo, Mario E. |
| author_facet | Tam, Simon Fajardo, Mario E. |
| citation_txt | Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen / Simon Tam, Mario E. Fajardo // Физика низких температур. — 2000. — Т. 26, № 9-10. — С. 889-898. — Бібліогр.: 86 назв. — англ. |
| collection | DSpace DC |
| container_title | Физика низких температур |
| description | We report the observation of high resolution (0.008 cm⁻¹) infrared absorption spectra of CO₂ molecules isolated in solid parahydrogen(pH₂) matrices at T=2.4 to 4.8 K. Several extremely sharp (0.01 to 0.04 cm⁻¹ full-width-at-half-maximum) absorption features appear in the 2343.5 to 2345 cm⁻¹ region. We assign the three strongest peaks to the v3 mode of isolated CO₂ molecules. The spectra are consistent with trapping of the CO₂ molecules in three distinct double-substitutional sites in hcp and fcc regions of the pH₂ solid. We offer several hypotheses as to the origins of the numerous weaker absorption features.
|
| first_indexed | 2025-12-07T15:16:57Z |
| format | Article |
| fulltext |
��� �������
�� ��������
����������������������� "!"!�!#��$"%� "&#�' )(�*�%,+�-�.'!#�,�/%10�0"+�2"0�+�0 3 4 5 6 7 5 8 9 4 9 : ; 4 < 4 = : 8 > 4 = 7 8 ? @ A B C = D 4 E 7 8 9 8 F E G C G 7 H G = C B 8 I J E 7 8 9 7 9 F = 4 = C : 4 A B 8 = K E 7 8 9 B K C L E = J 5 8 F M @ N 5 8 I C L J I C B 7 B 8 I 4 E C : 79 B 8 I7 : K 4 = 4 G O : = 8 H C 9
PRQTSVUXWZY\[T]�^`_bac_edf]'geUhgi^kjlgmW�U
Sn_loqpr]�^`_Xas^tand�WZ[uW�U
vs[wQTSn_uW'xn]�^`_Xa
Syx�UTz{]�W�p
| _yd~}�P���|�_wo�U�z�pTo�U�S�^`Sr_bo�[y]�UTv�^�a�Sr_Xo�^kv
xT[uWZ[Xg\�\vuWZ_wjfUla
�r���~�#�X�������������X�)�t� �������������������
�"�`�� Z¡,¢ £¥¤¦��§#¨�¤��ª©t«¬���`®¯¬�©�°/±�²�³'²1´�¤¦��µ���`«�©�¶/©k£�©t®·�ª«t¸�¹�®Zº��`®,¬¦�q��»�´�µ�¶�¹½¼'��¶�³��"°¾¿¢ À¯Á²�ÃÄ·ÅÇÆ�°ÇÈ"À�É"®Z�ªÀ,£�´"µ�¾�°�Ê,´TË·Ì·ÅÍ·Ä·Î�ÏtÐ÷ÑÒ�Ó�Ô/ÕÖ�×`Ø,Ô/ÕtÙkÖ�Ú�ۯܦÕÞÝ�ÕÙ`ß�Ú�àâá,×�ã�ä ÕÜ�ä Ô�Ö�×
å�ã�æ�ãtÖèç·ã�ß�éÇã�êZÙ`ë�ÕtÙ�ìrí¥î¯ïZð�ñ�ñ1ñZï¯Ù`ãtçZÖ òªã�ß�ó�Õ�ì�ô,ï,ð·ñ·ññ
õ�ã\Ù�ã�á,Ú·Ù�ö÷ö�ø,ãyÚ·ê,ò�ã�Ù�ç�Õö¥ÖèÚZùwÚZÜ�ø,Ö¦ú·øXÙkãtòkÚZ×ûë�ö¥ÖèÚZùuütñ,ä�ñZñýiætÔ�þ�ÿ��VÖèù�ÜûÙkÕ�Ù�ã�ßXÕê,ò�Ú·Ù�á�ö�Ö�Ú�ùXò�á,ã�ætökÙ�ÕfÚ�Ü������
Ô�ÚZצãtæë,×ûãtò)Ö�òkÚ,×�ÕökãtßTÖèù\ò�Ú,×ûÖ�ß\á,ÕÙ�Õ1ø·ì,ß,Ù�Ú1úZã�ù�ü� � � �)Ô�Õ·öªÙtÖ�ætã�ò)Õö�
=
ð�ä ôrökÚ{ô�ä ý
��ä��,ã�çZã�Ù�Õ�×�ã��,ö`Ù�ãtÔ#ã�×èì òkø,ÕÙ�á
ü¥ñÇä�ñ,í�ö�Ú{ñ,ä�ñ1ô�æÔ�þ·ÿ/ÜûëÂת×�Ó���Ö�ß,ökø�Ó Õ1ö`Óûø,ÕqתÜûÓûÔ�Õ���Ö�Ô�ë,Ô���Õê,òkÚ·Ù�á�ö¥ÖèÚZùrÜ�ãtÕ·ö`ë,Ùkãò/Õ·áZá,ã�Õ·Ù Öèù{ö�ø,ã�ð��·ô��Çä ��ökÚ�ð��Zô�� æÔ�þ1ÿ
Ù�ã�úÂÖèÚ·ù�ä�õ�ã)Õ·òkò�Ö�ú�ù{ö�ø,ã)ökø,Ùkãtã)òkö�ÙkÚZù�ú�ãtòkö�á,ãtÕ��,ò�ökÚ�ö�ø,ã
ν� Ô�Ú·ß,ã)ÚZÜ/Öèò�ÚZצշöªã�ß���� � Ô�ÚZצãtæë,×ûãtòä ��ø,ã)òká,ãtæ�ö�ÙkÕ�ÕÙ�ã
ætÚ·ù,ò�Ö�òkökãtù,ö!� Ö¦ö`ø ö�ÙkÕá,á�Ö�ù,ú�ÚZÜ�ö�ø,ã"��� � Ô�ÚÂצã�ætë�צãò�Ö�ù�öªø,Ù�ãã/ß�Ö�òkö¥Öèù,ætö�ß,Ú·ë,ê�צãtÓûòkë,ê,ò�ö�Ö�ökëZö�Ö�Ú�ù�ÕZ×�ò�Ö�ökãtò�Ö�ù)ø,æ�á�Õù,ß�Üûææ
Ù�ã�úÂÖèÚ·ù,ò�ÚÂÜ�ökø�ã � � ò�ÚZ×ûÖèß�ä,õ�ã�ÚZÜ`Ü�ã�Ù�òkãtç�ã�ÙkÕ·×�ø1ìÂá,Ú·ökø,ãtòkãtò�Õ·ò�ö�Ú#ö�ø,ã�Ú·ÙtÖ�ú,Ö�ù,ò�ÚZÜ�ökø,ã�ù,ë,Ô�ã�Ù�Ú�ë�ò���ã�Õ��,ãtÙ"Õê,ò�Ú1Ù�á,ö�Ö�Ú·ù
ÜûãtÕökë,Ù�ã�ò�ä
#%$��&��Ø�ñ·îÇä ðZñÇä ó÷æZï '¯íZä�îð�ä õ(�)ï*),+,-/.�01-32&41ï +�.5-76�0 -82 9�ïÇý'í1ä íñ,ä;:!��ï�ý�í�ä �Zñ�ä;�/Ü
< =?> @;A�@ B�CED7F�B�G�H @;A%IJ>�K L*M�C�INF�BNC�FJA�@;A3OJPJC?@;I�Q?B�=!D/IJR S C?D
T UWV�X Y�Z�[%\^]!_5Y�`3[%X
a�b c3dfe
g5hji^d�k,l�c3m%noc8dpgqd?n�g�n?i^d"lJr5m%s lJnfsth�s*i&luk�s%h n�c3h%i^v
c3h%wxr5yJy�szl�npn�s
s%{^d|r,l�}%r~g5h^��g5h g%���%��r�}!c/{�l?g�n�c�s h g*��d?mjr�k�n�l�g
sty�e~sj��r�k�i��3g5l��%s m g5hjn�d�c3d�s �3g�n?r5��c3h�k,l��%s*w r,h c�k�d?sj��c8�
m^g5l�g b%� �!lJs*w r,h��J��� ð5� b%s d|n�d1�p��d��%r�n�g*c8��r5��{ r ��s%���us%i^l
c3h }%r5d�n�c�w&g�n�c�szh�s y�n�btr�e�c�k,l�s%d?k�szmjc�k(d�n�l|i^k�n?i!lJr5d
g5h!���%� v
h^g5e�c�k5d�i^h^�tr,l����tc8h*w�e�g5h � szy¡n�bjr,d|r¢d?mjr�k�n�l?g£c3d�g�n�g
m^l|r �3c3e�c�h!g5l��¤d�n�g�wtrj�o¥~r5d?mjc�n?r�n�b!c3d����~rx{!r �3c7r�}jrxn�bjrxr�¦^v
m r5l?c3e�r5h%n�g*��s {�dJr5l�} g�n�c�s h d�n�bjr,e�d?r*��}zr5d�e~r5l�c/n�{ r5c3h*w§l|r,v
m s%l?n�r,��g�n�n�b c3d¨n�c3e�r ��© rxb s%m r�n�b^g�n�n�b%r5d�r(h%r��ªb!c7w^b v
l?r5dJs!��i n�c�szh��jg�n�g��
c����od�n�c3eqi«�3g�n?rxc3hjn?r5lJr5d�n¨c8h�n�b%r¬l?c7w s l?v
szi!dn?r5dJn�c3h*w®szy�n�bjr�szl�r�n�c7k,gt�§eqs �%r*��d¯szy�}^c7{&l�g�n�c�s h g*�
d�mtr�k�n�l�szd�k�szm%�¬s y"c3e
mti^l�c/n�c�r5d�c3h¬k�szh!�%r5h^d|r,�¡m^b g5d�r5d��
a�b%r°d|i^c�n�g�{&c8�3c�n?��szy�dJs!��c8�°�u� ð g5d�g�b%s dJnxy�szl�b!c7w^b v
l?r5dJs!��i n�c�szh±�
∆ν² ν ³¡´�µ*¶ ' � }^c7{�l?g�n�c�sthjg*��d�m%r�k�n�lJs dJk�s m%�
�
g5d�� c3d|k�s%}%r,l�r5��{ ��·
¸!g¹g5h �ºk�s v8�~szl�¸%r5l?d�» ´�¼�½ ¾ �ug5h!�y�i&l|n�bjr,lc�hj}zr5d�n�c7w^g�n�r,�¿{ �ÁÀ b c3� g&�¡Âºsze�s dJrÃg h �¿k�szv
�~s l?¸%r5l�d�»JÄ ¼f´�µj¾ �Wg5h^�¡{!�¹©�c3h!h%r���c3d?d�r5lÅg*h ��k�szv8�~s l?¸ v
r,l�d�» ´%´�¼f´�Æ�¾ �pa�b r¹yJg�}%s l?g5{E��r¹m l|stmtr,l�n�c7r5d�szy~d|s!��c3�¡��� ðk�s h%n�l�c�{ i n�c8h*wªn�sÃn�bjc3d�m bjr,htste¨r,hjszh�b!g�}%r�{ r�r,h��jc3d?v
k�i�d?d�r5��c3h�� r�n�g5c��q»?Ç!�;È«��É ¾ ���~r,l|r¬�~r¹h%s%n?r(d�c3e�m�����n�b g�n
d?sj��c8�
�u� ð c3d"}%r5l?�¹Ê%y�s l�w^c�}^c�htw�Ë
s ypb!c�w&b!���(h%s h v8r5Ì%i&c8�3c�{^v
l�c�i^e®d�g5e
m&��r°mjl?r5m g5l�g�n�c�szh�n�r�k5b^hjc3Ì%i r5dxd�i k5b�g5dx�jc3lJr�k�n
w&g5d?v8n?s v�dJs!��c8��k�s h �jr,hjd�g�n�c�szhu�&À*n�l�i k�n?i!l�g*���%r5y�r�k�n�d"c3h�d�i k5b
d�g5e�m!��r,de�g��Í{jrÎ��r5d�d£hji^e~r5lJs%i^d1�°g5h!��Ïqs lb g�} rÃg
d�e�g*����r5l¢c8h^y���i r5h%k�rÐs hÍ�jszmjg h%n£} c�{^l�g�n�c�s%h^g*��d�m r�k�n�l?gj�
n�b!g5hÃc�hÐs n�b r5l�}^g5m%s l��jr,m%s%d�c�n?r5� k,l|� s5w r5h^c�k�}^g5hÐ�jr,l
©�g g*�3d�d�sj��c3�!d�n�l?g*� c�n�c�szh!g*�N���Ðr,e�m!��s � r5�Ãg5d�bjszd�n�d�y�s l
e�g�n�l�c7¦°c3d�s �3g�n�c�s h¹d�m%r�k�n�l?s%d�k�s%m �¡��Â�Ñ�À � �·~i�l"�~s l?¸¬s%h¹dJs!�3c3����� ð c�d�d�i^mjm s%l?n�r,��{!�xn�b r�Ò¬�3ÀE�
��c3l�Ó�szl�k�r Ô/d��
c7w^b�Õph%r5lJw ��¥qr5h^d�c�n?�°Â�g1n?n�r,l����xÕp¥
 �m l�s5w�l?g5e¿» ´Ö½!¾�× s%i^lqm l|s*Ø?r�k�n5Ô/d�i«��n�c�e
g�n�r
s%{%Ø?r�k�n�c�}%rÙc8d�n�s
�jr,eqs h d�n�l?g5n�r§m l�g5k�n�c7k5g%�
r5h%r5l|wt�d�n?s%l�g�w r�c3h£k,l��%s*w r,h c�k
d�s �3c3� d�y�szl�i�dJr°g5d�g5�j} g h%k�r,��k5b r5e~c�k5g*�Ål|szk5¸%r�nxm lJs m%r*�3v
�3g5h n�d���aWbti^d1�os%i^lxg�n�n?r5h n�c�szh�c8dxy�s k�i�dJr5��s h�n�b%r�m l|sz{!v
��r,e�dps%yf��g � n�l�g5m m^c�htw(�3g lÚw rÅk�szhjk�r,h%n�l�g�n�c�s%h^d�s y�c�d�s �3g5n?r5�
r5h r5l�w r�n�c�k�� s%m^g5htn�d1�W��{ � d?k5g*�3c3h*w^v3i�m¹d�g5e�m!��r�Ì%i^g*h%n�c�n�c�r5d
{ r�� szh!��n�bjr~n�bjc3h¹yJc8��e�d�n�� m c�k5g*�N���xr5h k�s i�h%n�r,l�r5�(c8h(ÂÛÑ�À
d�n?i^�jc�r,d1����k � l�c�w^s%l�s i^d����§k5b g5l�g�k�n?r5l�c7��c8h*w�n�bjr¹k,btr,e�c�k5g*�
c3�%r5hjn�c�n�c/r5d1��k�s h%k�r,hjn�l�g�n�c�s h d1��g5h ��n�l?g*m m c3h*wd?c�n�r¤d|n�l�i k5v
n?i!l?r5d�szy"n�b r�c3h%k�s l?mjszl�g�n?r5�¹r5h%r5l|wtr�n�c�kÙd�m r�k,c7r5d1�Eg5h!����� �r�}^g*��i!g�n�c3htw�n�bjr°n�b r5l?e�g*�
g5h^��k5b%r,e�c�k5g*�¨d�n�g�{^c��3c�n�c�r5d�szy
n�bjr5dJrm^l|szn�s n��tm!c7k,gt�¤Ê*k5lJ� s%d?sj��c8��ËÃm lJs m%r*����g5hjn�d,��a�bjr,d|r
�3g5d?n�n��~sxn�g5d�¸ d�eqs%n�c�} g�n?r�s i^l�c3h%n?r5l�r,d|nÅc�h¬n�b r
d�m r�k�n�lJs d�v
k�stmt�(s%y��%s m g5hjn�d�c�h¹d�sj��c3����� ð �
·~i�lh%r�� Ê%l�g5mjc3�¿}^g5m%s l¢�jr5m%s d?c�n�c�szh«ËÜn?r�k,b h!c3Ì%ijr
m l�sz�ji k�r,d�r5g5d?c����¹� s%m%r5����e~c�����c8e~r�n?r5l?d�v8n�b c�k5¸���� ð d�s �3c3�!ds y�l�r,e�g5l?¸!g�{���r�szmjn�c7k,gt�Wk*�3g l?c�n?��» ´ ÄE� ´�Ý^¾ �Wa�b%r�k�sze�m g�n�c8v
{^c��3c�n���szy�n�bjc3d�e~r�n�btst���~c�n�b§e�szd�n�Â�Ñ�À��%s m g5hjn
n�l�g5mjv
m c3htw�d|k,bjr5eqr,dÞr,hjg�{���r,d"n�b%r
c3d|s!��g�n�c�szh¹c�h¹d|s!��c������ ð s yog�
c3�trß}!g5l�c7r�n?�¿szy£m lJr�}^c�s*i^d����Íc3h!g�k�k�r5d?d�c�{���rÐk,btr,e�c�k5g*�
d�m%r�k,c�r5d���aWbtr¹r�¦!k�r ����r5h%n�n�l�g5h!d?mjg lJr5hjk���szy�l�g5mjc3��}^g5m%s l
�jr,m%s%d�c�n?r5��d�g5e�m!��r5d�c3d¡i&hti^d�i^g*�(y�szl¬�u� ð dJs!�3c3� d�m l�s%v
�ji k�r5��{ ��}^g5m%s l¬�jr,m%s%d�c�n�c7s h�s h%n�s�g�dJi!{^d|n�l�g�n?r5vNc8h v3}!g5v
à á â ãpä å�æ�ç5ã¬ç,å�è�épç�ê3â ä�ë%ì�í�ç�î;ç,ê�è5ä ï�ð5ñ�ñ5ñ
k�i!i^e » ´ � ¾ �Ùg5h!� r,h g�{«��r,d�n�b%r,c8l�k,b g*l?g�k�n?r5l�c���g5n�c7s h { �
stmtn�c�k5g*�ue¨r�n�b s%�^d,�
·~i^lºr,g5lÖ���Ð�~s%l�¸�s hÐ�jszmjr,� k5l?�%s*w r,hjc�k¢bj�t�!lJs*w r5h
d?sj��c8�^d"r5e
m&��s*� r,�¬eqr5�!c�i^e�vNl|r,d�s ��i n�c�s hxiE��n�l?g5} c�sj��r�n�Ï�} c3d?v
c�{���r�g5h^�£c3h yJl�g5l�r,�¯�5Ñ�� � �^c8g�wjhjszd�n�c/k5d�» ´ É ¼ Ç ´ ¾ �~�~sz�~vr�} r5l����~r(l|r�k�r5h n�����g5� �jr,��g¬b c7w^b!vNl|r,d�sj��i!n�c7s h�Ñ���k5g5m g5v
{&c8�3c�n?��g hj���~r5l?r�l?r5m g5c3�Û{^��n�btr°s*{&d|r,l�} g�n�c�s h�s%y�} r5lJ�
d�bjg l?m � ∼ µ � µE´ k5e ¶ í y�i����3v3�
c��jn�b v�g5n�vNbjg*��yJv�e
g�¦�c3eqi�e��
Ó&©��
 � }^c7{&l�g�n�c�s h g*� g�{^d�szl�m%n�c�szh y�r,g1n?i^l|r,d y�stl
� s%m^g5h%n�d�c3h�l�g5m c8��} g5mjszl��%r5m%s d?c�n?r5�ßd�g5e
m&��r5d1���s l|r,v
sz}%r5l1�jb!c7w^b v�l�r,d|s^��i n�c�szh¡Ñ��Ûd�m%r�k�n�l?g�s ypd�r�}%r5l�g*�W��mjl?r5dJi�e~v
g5{���� � d�c3e�m���rÅe�s ��r�k�i«��g5l"�%s m g5hjn�d"c3hxd|s^�3c��~��� ð r�¦!b^c7{�c/ng e~g1�Öc8h%w���� l�c7k,b dJn�l?ijk�n�i^l�r ����s*n¹s h!���g l|r�n�b%r�}^c7{�l?g5v
n�c�s h g*�~n�l?g hjd�c7n�c�s h�r5h%r5lJw^c�r5d�szy�n�r,h£e~s%l�r¤m!lJr�k,c8dJr*���¢�tr,v
yJc3h r5��n�b g*h¢y�s%lxn�b r�d�g5e~r��jszm g*h%n�d¬c3h£l?g*lJr�w^g5d¬d?sj��c8�
��� �
À � b s%d?n�d��%{ i nod|i k,b�d�m%r�k�n�l�g�gt��d|s~n?� m!c/k5g%�����
c3hjk ��i^�%r
g¹�3g5l|w r,l~hti^e~{jr,lqs y�� c3d�n�c�hjk�n1���~r ���olJr5d�s ��} r5�°y�r5g�n?i�lJr5d1�
aWbjr�c3h%k5l�r,g5d|r,��mjl?r�k5c�d�c�s%h�g5h �Ük�sze�m!��r�¦�c�n?�Ãs%y�n�b r5dJr
d�mtr�k�n�l�g*�°eqr5g d|i^l�r,e�r,htn�d�e
g��Ül?r5Ì%i^c8l?r£r�¦^n�l?g5s%l�� c3h g*lJ�
r,yJy�s lJn�d¹y�s l�n�bjr,c3l�k�s e
m!��r�n?r�g5d�d?c7w^h!e~r5h%n1��{^i n¬n�b r�l|r,v
�
g5l��Îd�b%s%i��3�Ü{ r�g��jr�r,m%r5l�g h �Üe�stl|r�Ì%i^g*h%n�c�n�g�n�c�}%r
i&h �jr5l?d�n�g5h �!c3h*wÜsty��%s m g5hjn§n�l?g*m m c3h*wÍd?c�n?r�dJn�l�i k�n�i^l�r,d
g h ��}^c7{�l?g�n�c�s h g*�&�%�!h g5e
c�k,dpc8h�dJs!��c��q��� ð n�b g h�bjg d�{ r�r5h
g5k5b c�r�}zr5�¬n�s(�!g�n?r�{ �¹Â�ÑÖÀ¬c3h
����À¬b%s dJn�d1�
©r¹g5l�r¹c3h�n�b%r¹m!lJs%k�r5d?d�s%y~d�i^lJ}jr�� c3h*w�b c7w^b!vNl|r,d�s ��i^v
n�c�s h�Ñ��Ðg�{^d�szl�m%n�c�szh�d�m%r�k�n�l�g¬y�s%l~g�}^g5l?c�r�n?��szyq�%s m g5hjn�d
c3hxd|s^�3c��~��� ð �%��dJi!{^dJn�g h%n�c3g*�&�!g�n�g�{^g*dJr�sty�d|i k,b�d?mjr�k�n�l�g
d�btsziE����bjr �3m�n?s�jr�n�r,l�e
c8h%r�
b!c/k5b�m bj� d�c7k5g%�¹r5yJy�r�k�n�d
� s%e
c3hjg5n?r�n�btr°}^c7{�l?g�n�c�s h g*�¨d�m%r�k�n�l�szd�k�szm%��s%y��^c�yJy�r5l�r,h%n
k �3g d�d?r5d�s y��%s m g5hjn�d�c3h�d|s!��c3�Ð�u� ð ��Ó&s%l�r�¦^g5e�m!��r �
d�mtr�k�n�l�g�s%y
��� ô Ï���� ð d|s^�3c3� d�»JÄE� Ý �/ÉE� ´�µ �/Ç%Ç ¾ ��g�k5g5d�rÙc8h
�
b^c7k5bÐn�btr¢d�m b%r5l�c�k,g*�3v3n�szmÐ�jszm!g5h%n�yJc�n�d�r5g5d�c����ßc�h n�s�g
d�c8h*w���r5vNd�i {!d?n�c�n?ijn�c�s%h^g*� n�l�g m m c8h*w d?c�n?rj� g�k�k�s l��^c�htw&���
d�btsz� �3c�h r¬d?m!g�k,c8h*w^d
g5h!��c3h%n�r,h!d?c�n��¤mjl?s1w&lJr5d�d?c�s%h^d¨k�s e~v
e~r5h^d|i^l�g�n?r��
c7n�b�dÖ��c�wjbjn����°b!c3h �jr,l|r,��l�s*n?s l?d�»JÄE�/ÇzÇ ¼ Ç Ý ¾ �À%n�lJi!k�n?i^l�g%�����«�zn�b rqd?mjr�k�n�l�g~�%r5e~s%h^d|n�l�g�n?r�n�b!g�noc3h�g5d�v�m l|r,v
m^g5l|r,��l?g*m c3�¬}^g5mtstl�� r5m%s%d�c�n?r5� � � ð d|s^�3c��^d�d�sze�r
s%y"n�b%r
��� ô e~sj��r�k�iE��r5d�g5lJr�c8h c�n�c8g*�N���Ãn�l�g5m mtr,��c�h�yJg�k�r,v8k�r5h v
n?r5l?r5� v8k�i!{^c�k ��y�k�k � l�r�w^c�s%h^d,��g*h �Ãn�b g�n�n�b r5dJrl�r�w^c�s%h^d
k�s h%} r5lJn c3l�l?r�}%r,l�d�c�{���� n?s bjr�¦!g�w szh!g*��v8k*��s dJr5v�m g5k5¸%r5�
��b k5m � i^m%s hÃg5h!h%r5g%�3c�h%wÍ»JÇ%Ç ¾ �xa�b%r mts^�3g5l�c7��g�n�c�s hÃ�tr,v
m r5h �jr,h%k�r5dps y«n�bjr���� ô Ï���� ð n�l�g5h!d?c�n�c�szh!d"y�i^lJn�b r5loc8h �^c�vk,g1n?rxn�b^g�n�g5h!h%r,g*�3c3htw§g*��d|s�lJr5d�i���n�d
c8h�c3e�m lJs%}%r5�§g*�3c7w^h v
e~r5h n�s y«n�b%rqb%k5m�k,l�� d�n�g*����c�n�r,d,Ô���vNg�¦�c�dps%l�c�r,htn�g�n�c�sthjd��
c�n�b
n�bjr��%r,mjszd�c7n�c�sth£d�i {^d�n�l�g�n?r�d�i^l�yJg�k�r�h%s l?e�g*�x»ÚÇ%Ç ¾ �~¥Å� vh^g5e�c�k5g*�N���«��g*�N��n�b r
��� ô Ï���� ð d�m%r�k�n�l�g¬k,g*h�{!r¹l?c7w s l?v
szi!d����Îg5d�d�c�wjhtr,��{^�Ðk�s h d�c3�%r5l�c�htwÎn�btr�lJs%n�g�n�c�szh!g*��v8} c�{^v
l�g�n�c�szh!g*�x�%�^h g5e�c�k5d¹s y���� ô g�n°n�b%r�k�r5h%n�r,l�s%y¹dJn�g5n�c7k
r�¦!n?r5l?h!g*�(yJc�r*���!d�b!g�}tc8h%w�� � ¸ »JÄ ¾ g5h!��� ¸ »ÚÇ%Ç ¾ d|�^e~v
e~r�n�l�c7r,d1�~aWbti^d1�¨g�d?g�n�c3d�yJg�k�n�szl��¢r�¦^mE��g5hjg5n�c7s h£s y�n�b r5dJr
n�l�g5h^d�c�n�c�szh r,hjr,lÚw^c�r,d �js r5d h s*n l�r,Ìti^c3l�r k�szh!d?c8� r5l?g5v
n�c�s hÁszy k�szh!dJn�l�g5c8h%r,� l�s*n�g�n�c�sthjg*��v8n�l�g5h!d��3g�n�c�s h g*�3v3k�s%i^m v
��c3htw����oa�� � c8h�g¹l�c7w^c3�ºn�l�g5m m c3htw§d?c�n?r�»JÇ�� ¼ È ´1¾ �ps l~s%ye~s lJr�w r5h r5l?g*����a�� c8h%n?r5l�g�k�n�c�szh!d¹��c/n�b^c8h�g�� � h!g5e
c7k
n�l�g5m mjc3h%w d�c�n?r d�n�l|i k�n�i&l|r »�È Ç ¼ È Ý!¾ �ßaWbjr5dJr ��r5d?d�szh!d
��r,g5l�h%r5��yJl�sze±n�bjr���� ô Ï���� ð dJn�i^�!c�r,d�m^l|sz} c3�tr�g5hºr�¦!v
k�r ����r5hjnÛd�n�g5lJn�c8h%wªmjszc8h%n¢y�szlÛn�bjr�g5d�d�c7w^h^e¨r,hjn�styºs i�l
l�r�k�r5h%n����¹s {!d?r5lJ}jr,��b c7w^bE���¹d�n�l|i k�n�i&l|r,����·xÏ��u� ð d�m%r�k5vn�l�g�»�È�� ¾ �jg*h%s%n�b%r5l"k5g5d?r~c3h��
b!c/k5b�n�bjr~�%s m g5h n�eqs!��r�k�i���r
d�b%s%i��3� yJc7n®lJr5g5�^cÚ��� c3h%n�s g d?c8h*w���r d|i {&d|n�c�n�i n�c�szh!g*�
}^g�k5g5h k��«�
Ñ?h�dJn�g5l�¸ºk�s h%n�l�g5d?n1�p�~r¹yJc3h ��n�b g�n�d�m%r�k�n�l�g�szy~e�g5h �
�3g5lJw r5l�d?m%r�k5c�r,d1�odJijk,b�g5d���s �~r5l
d�� e�eqr�n�l���m%s!��� g�n?s e~c�k
e�s ��r�k�i���r5d���g5h^�¹bt�^� l�s5w r5h^vfszlÞ}^g5h¹�jr,lÞ©�g5g*��d�v8{ s h � r5�
k*��i^d�n�r,l�d~s yqd�e
g*����r5l��%s m g5h n�e~s!��r�k�i���r,d,�fd�b s*� h%s�r�}tc8v
�jr,h%k�rxs%y�sz}%r5l�g*�N��lJs%n�g�n�c�szhu��©rx{ r*�3c�r�}%r�r,h �!v8s } r5l?v8r,h!�
l�s n�g�n�c�s h�c3d�c3h b!c7{&c7n�r,��{j�§dJn�l�szhtwÛg5h!c�d�s*n�l�szm!c7k°c3h%n�r,l�g�k5v
n�c�szh!d��
c�n�b c3hÜn�bjrÃ��s ��r,l�d�� e�eqr�n�l��ªe�i���n�c3v�dJi {�dJn�c�n?i!v
n�c�szh!g*�pn�l�g5m m c3htw¤d�c�n?r5d~lJr5Ì%i�c�l?r5�¡n?s°g�k�k�s%e
e�sz�!g�n?rxd|i^k5b
�3g5lJw r�d�m%r�k5c�r5d���a�b i^d1��n�b%r5d�rx�3g5l�w!r,l�d�mtr�k5c�r5dq�3c3¸%r*���¬r�¦&c3d|n
c3h�n�b%r�Êj��c�{!l?g5n�c7sthjg%�JË��3c3e
c7n1�ts%d�k,c8����g1n�c�h%wxg l|s%i^h ��k�r5l?n�g5c3h
r5Ì%i&c8�3c�{^l�c�i^e s%l�c/r5hjn�g�n�c�szh!d§c8h^d|n?r5g5�Üszy�l|s%n�g�n�c8h*wªg d�g
i^h!c�nx»JÇ*È ¾ ���qr�n1�u�%r5d�m c�n�r(dJijk,b�dJn�l�s%h%w��%s m g5hjn�v�b%s dJn
c3hjv
n?r5l�g�k�n�c�szh!d��¹e
g5hj�Üszy�n�b%r5d�rÃ�3g5l�w^r5l��%s m g5hjn¢d|�td�n�r,e�d
r�¦&b c�{^c�n�r�}%r5hßd�b^g5l�m%r5l¡}^c�{^l�g5n�c7s h gt��g�{!d?s%l�m%n�c�s%h^d¡n�bjg h
n�bjszd�r¿sz{!d?r5lJ}jr,� y�szlÜd�e�g%����r5lÎ�tstmjg5h n�dÃn�l?g5m!m%r,� c3h
b!c;w�b!����d�� e
eqr�n�l�c�k5g*�¤d�c3h*w���r�d�i {^d�n�c�n?i n�c�szh!g*�°d�c�n?r5d��x�
d�g�n�c3d�yJg�k�n�s lJ�¢g5h gt��� d�c3d�szy�n�bjr�d?m%r�k�n�l�g�sty�n�b%r5d?r��3g5l�w^r5l
�3c�{^l�g�n�c3hzw dJ� d�n?r5e
d�e�i^d�n¢�jr,g*���
c�n�bÜn�bjrßg5�!� c�n�c�szh!g*�
k�ste�m��3c7k,g1n�c7s hxs%yod�c3e�i���n�g5h r�s i�d����xk�szh!d?c8� r5l?c3hzw({ s%n�b¬c3hjv
bjr,l|r,hjn�g5h^��n�l?g*m m c3hzw&vNd�c�n?r5v�c3h �ji k�r5�¹d�m r�k�n�l?g*�py�r,g�n�i^l�r,d,�
pr5y�s lJr~g5n�n?r5e~m n�c�h%w(d�i k5b¬g5h^g*��� d?r5d�� �~rqn�i&l�h(yJc8l?d�non�s
g¹d�c3e
m&��r5l
e¨st�tr ��dJ� d�n?r5e�s%y~g¡��c8h%r,g*lqn�l�c3g�n�sze�c�k(e�s ��r5v
k�i���r¬d�i k,b�g5d!��· ð c�h�d�s �3c3�¬��� ð �o·~i^l�Ñ"�ßd?mtr�k�n�l�g�szy
��· ð Ï���� ð d?g e�m���r,d�d?bjs � k�ste�m��3c7k,g1n?r5�ßm!g�n?n�r,l�h^dºszy
d�b g5l�m£�3c3h%r5dx��b c�k5b�� s�h s*n(g5m!m%r5g5l�n?s�e~g1n?k5b�g�lJs%n�g5v
n�c�szh!g*�&�j�th!g5e�c/k5d��#�$&%�'
$)(+*-,�. � �^g5h!�xd|sÙe�g���{ r�k�s e
mjg5v
l�g�{���rÅc3h�n�b c3dpl�r5d?m%r�k�nfn?s~n�b%r~�3g5l|wtr5lp�%s m g5hjn�d,�^�~s*�~r�}jr,l,�
n�bjr�w&g5d?v�m^bjg5d?r} c�{!l�g�n�c�szh!g*�¹n�l�g5h^d�c�n�c�szh!d�s y/��· ð g l|r
} r5lJ�Ã�qr*�N�°¸jh%s%�
h × n�bji^d��xg h%�Ãmjr�k�i��3c3g5l�y�r5g5n�i^lJr5d�c3h
d�m%r�k�n�l?g�s y0��· ð Ï � � ð g5l|r¤c8e
eqr5�!c3g�n?r*����g�n�n�l?c�{ i^n�g�{���r
n?s�r,c�n�b%r5lx�%s m g5hjn�v��%s m g5hjnxc3h%n�r,l�g�k�n�c�s%h^d�szl�n�s�c3h%n�r,l�g�k5v
n�c�szh!d��
c7n�b�n�bjr���� ð b%s d|n5�p©�r¬n�bjc3h^¸ºn�bjr
��· ð Ï���� ðd�� dJn?r5e �~c��N��m l|s%}zrÐn�sÎ{ rÃg5h±r�¦ k�r*�N��r,hjn¢g*lJr5h^gÐy�s l
r�}^g*��i!g�n�c3htw¹n�b%r�}^g5l�c7szi!d�r*��r,eqr5hjn�d�s y"n�b%r1��a�� e�sz�jr �3d
c3h¬n�b%r���c3e�c�n�s%y�dJn�l�s%h%w�����bjc3h �jr,l|r,�¹l�s*n�g5n�c7sthW�
Ñ?h��
b g�nxy�sj�N��s%�
d��qr°�%r5d?k5l?c�{ r¹{^l�c�r,y�����s*i^l�r�¦&m%r5l?c8v
e�r,h%n�g%��e�r�n�b%s � d�g h ��m l�r5dJr5h n�s i�l�m^l|r �3c3e�c�h!g5l���b^c�w&bjv
l�r,d|s!��i n�c�szh±Ñ�� g5{^d|s l?mjn�c7s hÃ�^g�n�gy�s l�n�bjr���· ð Ï � � ðd�� dJn?r5e��^©r~�~c����Wd?bjs �Ðn�bjg5n"n�bjr
dJn�l?s%h%w r5dJn�g�{�dJs l?mtn�c�s h
y�r5g�n?i�lJr5d�g lJr��%i^rqn�sxc3d�s �3g�n?r5����· ð e�s!��r�k�iE��r5d��&g5h!�¬h s*n
n?s ����· ð �·§ k ��i^d�n?r5l?d1�¹©�rÜ� c3dJk�i�d?dn�b%r5d?rÜeqs h%s e~r5l
d�m%r�k�n�l?g�c�hn�r,l�e
d¡szy�k5g5h^�jc3� g5n�r�n�l�g5m m!c�h%w�d?c�n�r§d|n�l�i k5v
n?i!l?r5d��(g5hj�Ãn�b r£k�s%l�lJr5d�mtsthj�^c�htw�l�s*n�g�n�c�sthjg*�(}^dÛ��c�{^l�g5v
n�c�szh!g*���%� h!g5e
c�k5dqs%y�n�b%rxn�l?g5m!m%r5��e~sj��r�k�iE��r5d1��©rx�~c����
w^c�} r¬g¹�3c�d�n~szyqb%�^mts n�bjr5dJr5d
g�{ s%i n�n�b%r¬m%s d?d�c7{���r�s l?c7w^c3h!d
s y¹n�b%r¢hji^e�r,l|szi!d��~r,g5¸tr,l�g�{^d�szl�m%n�c�szhÐy�r,g1n?i^l|r,d1�
{ji n
g�n?n�r,e�m%n
hts°Ì%i^g*h%n�c�n�g�n�c�}%rxg*m m!�3c�k,g�n�c�szh�s%y�k5l��td�n�g*�oyJc�r �3�
2
3�4,ñ í�â 5�â 6�ç87^â 596�â 6�:«æ<;5ã>=-;5ê�ç�?A@�êJï?ð�ñ�ñ�ñ%ïCB�ì?ðED ï�7%ä�F�ì&4�G�H?ñ
stl ��a���e~s �%r*��dfg5n�n�b!c�d�n�c3e�rj� ©r�r5h ��n�b!c3dpe~g*h%i^d�k5l?c3m%n
�
c�n�bg�d|i^e
e�g5l��«�Åg h � �3c3dJn�dJs e~r�s y�szi!l¹c�e
e�r,�jc3g�n?r
m��3g5h d�y�szl~y�i!n?i^l|rxr�¦&mtr,l�c3e~r5h%n�g%�og hj��n�bjr�s%l?r�n�c�k,g*�p�~s l�¸
n?sxn�r,d�n�n�b r
m!lJs m%s%d�r,�¹bt�^m%s n�b r5dJr5d1�
��U��������5Z�`
��5X Y
���
·~i^l"r�¦�m%r,l�c3e�r,h%n�g%��g mjm g5l�g�n?i^d�g*h �¬d�g5e�m!��r~m^l|r,m g*l?g5v
n�c�s h£n?r�k5b^h c8Ì%i r5d°b g�}jr�{ r�r,h�jr5dJk5l�c7{!r,�c8h�%r�n�g c8�
{jr,v
y�stl|r°» ´ ÄE� ´�Ý �/Ç ´ ¾ �p¥~s%m%r5�¬��� ð d|s^�3c��^d�g5l�r(m l�r5m g5l�r,�º{ �
l�g5mjc3�}^g5mtstl��%r5m%s d?c�n�c�szh¯s y(m!lJr�k�szsj��r5� � � ð wjg5d�g5h!�
l?s*s e®n�r,e�m%r5l?g5n�i^lJr ��· ð wjg5d�s%h n�s§g pg%Ó ð d�i {^d�n�l�g�n?r
k�s%s ��r5�n?s��
≈
Ç�� c3h£g��3c3Ì%i^c8�¢bjr �3c7i&e ���3��r � {&g�n�b
k,l��%s dJn�g�n1� ©�rqszmjr,l�g�n?rqn�bjrqszl�n�bts&Ï~mjg l?g�b � �!lJs*w r,h�k�s h v
} r,l|n?r5lxg�n ´�½ ���o� c�r*�3�^c�htwÛg�y���s%�Ís y�m lJr5v8k�s%s ��r5����� ðk�s h%n�g c�h^c8h*w
≈ µ � µE´�� l�rzd�c�� i!g%�^s!l?n�b s!b �^�!lJstw&r%h¬���%� ð �cNe�m%i^l�c�n�c�r%dx» ´�Ý^¾ �Wa�bjr
��� ð y��/s � c3e�m cNhzw&r%d�i^mjs^h�n�b%r
d�i {!d�n�l�g1n?r�g1nxg Æt½ °
g5htw���r × �ji^l�c3h%w�g��%r5m s%d�c7n�c�s h£n�b%r
m^l|r,d�dJi!l?r£s y�i&htk�s h �jr,hjd?r5� � � ð w^g5d�l?r5e�g5c3h d�{ r*��s%�
∼ ´�µ*¶ ô a�s%l�l��ua�bjr���· ð � s%m g h%n�c3d�e~r�n?r5l�r,��c3h%n�s�n�b%r
� r5m%s d?c�n�c�szh�k,l|� szd�n�g�n�yJl�s%e g¢d�r5m g5l�g�n?r�w^g*d�b^g5h �E�3c3h*w
e�g5h^c�y�s!��� × n�b%r��%s m g5h n�c3hE��r�n�c3d�d?c�n�i^g5n�r,�¬g�n�g h�g h*w���r~szy
Æ ½ °
yJl?s%eÐn�btr
d�i {^d�n�l�g5n?r�dJi^l�yJg�k�r
h%s l?e�g*�?��g�n�É µ °
n�sxn�btr
��� ð dJs%i^l|k�rj�~ÑÚh!� c�}^c��ji^g*�
d�g5e
m&��r�m l|r,m!g5l?g1n�c7s h¢�jr�n�g5c��3d
g5l�rqw&c7} r5h¬{ r*��s%�Ãc3h¬n�b%r�yJc;w!i^lJr�k,g5mtn�c�s h d1�
© r l|r�k�s l?� Ñ�� g�{!d?s%l�m%n�c�s%h d?mjr�k�n�l�g s y s i�l
��· ð Ï���� ð d?g5e�m!��r,d�g�k5l�szd�d�n�b%r�� µzµ n�s Ý � µzµ k5e ¶ íl�g5h*w^r°g�nxg�lJr5d�s ��i n�c�sth�s%y µ � µ µ ��k5e ¶ í × n�b%r�e~g*c�hÛstmjv
n�c�k,g*��g�¦�c3dÎc8dÎm!g5l?gt�N��r �n�s n�b r®dJij{&d|n�l�g�n?r®h%s l?e�g*���
a�b r±Ó&s*i&l�c�r5ln�l�g5h^d�y�s l?e Ñ�� d?mjr�k�n�lJs eqr�n?r5lÐ�� olJi!¸ r5l
Ñ�ÓpÀ ´ Ç µ �0� � c3d�r,Ì%i!c3m mjr,����c�n�b£g¡w���s%�~{^g5l¬d|szi!l?k�rj�Þg
�� pl£{ r5g e~d�m!�3c�n?n�r,l,�¤g5h � g±��c�Ìji^c3�Íh!c�n�lJs*w r,h¿k�s s!��r5�
�qw �o�!a«r
� r�n?r�k�n?szl1�&a«sxg1k�k�sze�e~s%�^g�n�r~n�bjr�Ñ"�¢� c3g�w&h%s d�v
n�c�k ��n�b%r£r5h n�c3lJr£s m%n�c�k5g*�¹m g�n�bÜc3d�r5hjk ��szd�r5�Ð�
c7n�b!c3hÃg
µ � ½ e � m%s ��� k5g5lJ{!szh!g�n?r�{^s*¦ m%i�l�w r5����c�n�b�gºk�s%h^d|n�g*h%n
y���sz�Ðs%y�� l��1� ð w^g5d5�
�^U�������]��8Y��
Ó�c7w i�lJr ´ d�b s*�
d�n�b r ν� í�ð � í?' · ð l�r�w^c�szh¡szy�g�{^d�s%l�mjv
n�c�szh�d�m%r�k�n�l�g°yJl�sze n�bjl?r�r°� c8yJy�r,l�r5h%nxg d�vN�jr,mtszd�c�n?r5����� ðd�s �3c3� d�k�s%h n�g5c3h c3hzw ��· ð k�s h%k�r5hjn�l?g1n�c7s h d�l?g5htwjc8h*wºyJl�s%e
∼ µ � µE´ m mje�i^m�n�s ´ ��ǹmjm e¬�Wa�bjr�k�s h%k�r5h n�l?g5n�c7sthjd~g l|r
µ¿¤èÁ²�Æ ä� `åyÕtê�ò`ÚÙ`á�ö�Ö Úù)ò`á�ã�ætöûÙ�Õ/ÚZܽö`øZÙªã�ã�Õ�ò`Ó�ß�ã�á�Ú�òkÖ ö`ã�ß � � ò`Ú�×�Ö ß�ò�Õö
=
ð�ä ô���æ�ÚùZöªÕ�Ö ù,Ö ùZúfß,Ö�Üûܦã�Ù�ã�ù�ö{æ�ÚùZæ�ã�ù�ö`Ù`Õ�ö�Ö Ú·ù·ò÷ÚZÜ ù·Õö ë�Ù`Õ·×�Ö òªÚ Ó
ö`ÚáÂÖ æ{Õê·ë�ù�ßZÕ�ùZæ�ã��!� � ä���Ù`Õ�ætãnü�íkÕ�� Ö ò�ܦÚ�Ù)ÕyíJ�rá�á·Ô ���"! � �
ò`ÕÔ�á�×�ã æ�ÚùZö`ÕÖ ùÂÖ ù�ú ∼ ñ�ä ñ¯í�á�á·Ô���� � Õtò�Õtù\ë�ù,Ö ùZöûãtù1ö�Ö Ú·ù·Õ·×/Ö Ô/áZë Ó
Ù¥Ö öûì$#"òªÕtÔ/áÂ×èã�ö ø,Ö æ?�1ùZã�ò`ò�Ö ò�ð�ä î�Ô/ÔâäE��Ù`Õæ�ã{üí�ê5��Ö�ò)ܦÚÙ Õùnýrá�á·Ô�"��×
! � � òªÕ�Ô/áZצã\æ�Ú·ù1ö`Õ�ÖèùZÖ�ù·ú
≈
ñ�ä ñqô{áZá�Ô£��� � Õò{Õ�ùlë�ùÂÖ ù�öûãtù Ó
ö�Ö Ú·ù·Õ·×�ÖèÔ�á1ëZÙ�Öèö¦ì�#�òªÕtÔ/áÂ×èã�ö`øZÖèæJ�Zù1ãtò`ò�Ö ò«�Âä ñ�Ô/Ôâä*��ÙkÕtæ�ã�ü�íkæ�� Ö ò�ܦڷÙ"Õ
í·ä ð áZá�Ô���� � ! � � òªÕtÔ/áÂ×èã�öûø�Õtö Öèò�íä ô{Ô/Ô ö`ø,Ö æJ�'äj�'ø�ã�Ö ù�ç·ã�Ù�öûã�ß
ö`Ù�Ö�Õ�ùZú·×¦ã�ò/Õtö�ö`øZã�ö`Úá�ÚZÜ�ö`ø�ã ÜûÖ�úë�Ù`ãâÖ ù�ß,Ö æ�Õ�öûã�ö`ø�ã�áZÚò�Öèö`Ö�ÚùZò�Ú·Ü"ò`ã�ç·ã Ó
Ù�Õ× ú·Õ�ò á·ø�Õtòªã Ù�ÚÓ¦çZÖ êZÙªÕtö�Ö Ú·ù1Õq×�× Ö ù�ã�ò ܦڷÙ�ö`ø�ã
ν � Ô/Ú·ß·ã Ú·Ü
ÿ � � ÿ&% � � ' ôZñ)(�ä ��ÙªÕ�æ�ã�ütíÞÕ���ø�Õtò�ê�ã�ã�ù{Ùkã�ò`æ�Õ�צã�ß{ê1ì{Õ)Ô�ë,×�ökÖ áÂצÖ�æ�ÕtökÖ ç·ã
Ü�Õæ�ö`ÚÙ"Ú·Ü�ô$#,Õ�צ×�ö`ø�ã/ö`Ù`Õtæ�ã�ò�ø�Õtç1ã�ê�ã�ãtù)ß,Ö ò`á,×�Õ�ætã�ß)ç·ã�Ù`ö�Ö æ�Õ�×û× ì�ܦڷÙ"ã�Õ�ò`ã
ÚZÜ�á�Ù`ã�ò`ãtù1ö`Õtö�Ö Ú1ù�ä
µ¿¤èÁ² Í ä�$�ù1ùZã�Õ·×�Ö ù�únêZã�ø�ÕtçZÖèÚÙ)ÚqÜ ö`øZã\íä ðná�áZÔ��� � ! � � ò`ÕtÔ/á,×�ã
ß�ã�ò`æ�Ù¥Ö ê�ã�ßrÖèùré�Ö ú�ä�íä �ÇÙ�Õ�æ�ã�ü�ðÕ��)Ö ò/Õ�ù÷ãJ�Zá�Õtù�ß·ãtß÷çZÖ ãJ�~Ú·Ü�öûøZã)Õ�ò`Ó
ß�ã�áZÚò�Ö ö`ã�ß�ò`á�ã�æ�ö`Ù`ë�ÔXá·Ùkã�ò`ã�ù�ö`ã�ß�Õ�êZÚç·ã Ö ù�öûÙkÕtæ�ã)üí�æ��ä �ÇøZã#ö ã�Ô/á·ãtÙ`Õ Ó
ö`ë�Ù`ã ò`ã+*1ëZã�ù�æ�ã Ö òtØ ükð·Õ��
=
ð,ä ô¢�#ïTükðê �
=
ô,ä ý���ï ü�ðæ��
=
ð�ä ô~��ï"ükð·ß5�
=
ô�ä ý���ï�Õù·ß�ü`ð1ã��
=
ð�ä ô
��äj��ø·ã ×èÕ�ê1ã�×�ò
α′Õtù�ß
α′′ ßZã�ù�Úö`ã�ö3��Ú ù�ãJ�fܦãtÕtöªë·Ù�ã�ò�ö`ø�Õtö�ú·Ù`Ú��fÖ ù ß·ëZÙkÖ�ù·ú)Õ�ùZù·ã�Õ�×¦Ö ùZú�ä
* � * ð � � , -
íÖâ 5?â 6?ç�7tâ 5�6�â 69:«æ�;,ã>=�;5ê/ç ? @�êNï�ð�ñ5ñ�ñ ï B,ì?ðEDzï 7 ä<F5ì&4EG<H?ñ 3�4 H
r,d�n�c8e~g5n�r,��g5d��%r,d�k5l?c�{jr,��m^l|r�}^c7s%i^d����¹»ÚÇ ´5¾ i&d�c3h*w(gq}^g*��i r
sty ½%½%µ ¸jexÏ~e�s!��y�s l~n�b%r
ν� ��· ð c3hjn?r�w^l?g5n�r,��g�{&d|s l?m v
n�c�s h¡k�s*r,yJyJc�k5c�r5h%n�»�ÈtÉ ¾ ��aWbtrxm%r,g5¸!dq�3g5{jr ��r,�
α
�
β
�Wg5h �
γ� s%e
c3hjg5n?r�g*�N��n�b l�r�r
d�m%r�k�n�l�gj�!{ i^n�d�b s*�Ãe
c3htstl�d?g5e�m!��r,v
n?s vNd�g e~mE��r�}^g5l?c3g�n�c�s h dÃc3h l|r �3g5n�c7} rÍc3hjn?r5h d�c/n�c�r5d5� ��s n
d�btsz��h�g5l?r�n�b r
ν� íJ� � í?' · ð g5h � ν� íJ' · íkð � í�ý ·�l�r�w^c�s%h^d
sty�n�b%r§d�m%r�k�n�l�i^e �%r5m c�k�n?r5��c�h¯n�l?g1k�r�� ´ k � �¨c3h£��b c�k5b
d�c8e~c��3g5l¹y�r,g1n?i^l|r,d1�Ågt��d|s¢e
g�n�l�c/¦�v�d?b!c3y�n?r5��{!�
≈ ¼�½ k,e ¶ íyJl?s%en�b rÞwjg*d?v�m b!g5d?r�} c�{^l�g�n�c�s%h^g*�!{&g5hj��s l?c7w^c3hjd�» Æ µ � ÆE´1¾ �g m m%r5g5lqy�s l�r5g5k5b¹h^g�n�i^l�g*�ug1{ i^h!� g5hjk�r�c3dJs%n�szm%s e�r,l,�Ea�b%r
sz{!d?r5lJ}jr,��m%r5g5¸°m%s d�c�n�c�s%h^dqg5h �º�3c3h r��~c3�jn�b dqg5l�rÙd|i&e�e
g5v
l�c���r5�¹c3h�n�bjr
a�g�{���r �
�c�w^i^l|r��d�b s*�
d�n�bjrxr5yJy�r�k�n�d�s%y~lJr5m%r5g5n?r5��n�r,e�m r5l?g5v
n?i�lJr~k��%k �3c3h*w¬szh�n�bjr
ν � íkð � íJ' · ð {^g h ��szyfn�b%r ´ �/Ç�m m!e
��· ð Ï � � ð d�g5e�m!��rÙ�jr5m c�k�n?r5�°c3h¡n�l�g�k�r¬� ´ k � ��a�b%rxeqs dJn
m^l|sthtszi!h%k�r5� k,b!g5htwtr s%{^d�r5lJ} r5� �%i^l�c3h*w n�b%r®c3h!c7n�c3g*�
�
g5l�e
c�htwÛyJl�sze �
=
ÇE� Æ n�s Æ � � ��c3d�n�b%r�dJn�l�s%h%w�c�l�l|r,v
} r,l�d�c�{���r¤�%r�k5l?r5g5dJr�c3h�n�b%r�c�hjn?r5h d�c�n���s y~n�b r
γ
mtr,g5¸�g�n
Ç*È Æ Æ ��Ä Æ k,e ¶ í × n�b%r§d�g5e~r�{!r5b g�}^c�s%l¹c3d�s%{^d�r,l|} r,�£y�s l
n�bjr¬s n�b r5l0��· ð c3d|s%n?szmjsze�r5l?d1�og5d��~r �����u©r¹g*�3d�s¤hjs n�r
n�bjr d�c3eqi«��n�g5h%r�s%i^dÁw&l|s%�Ån�b s%yÁn�b%r
α′
mjr5g5¸ g�n
Ç*È Æ È«��É ´ k,e ¶ í �^n�bjrq�~r,g5¸jr5h c3h*w¹g h �¬d�b g5l�m%r5h^c�htw(szyfn�btr
α
�3c3h%rj�on�bjr¹d?n�lJr5h%w n�b r5h c3h*w�g h ��{�lJs g5�%r5h^c8h*w§s yqn�b r
βm%r5g ¸«�xg5h ��n�b%rg5m m%r5g l�g5h k�r�s y�g
≈ µ � ½ k5e ¶ í {^l�s%g �
g�{�dJs l?m%n�c�s hÁ��i^e
m hjr,g5l Ç5È Æ%Æ � Ä�k5e ¶ í � a�l?g5k�r ��Ç1k �d�b%s%�~dqn�b!g�nqi^m%s h°l�r5v3k�s s!�3c3h*w°n�s �
=
Ç�� Æ ��n�btr
α
g5h!�
α′
m r5g5¸ d¿�~r5g5¸ r5h«�ßg h%r��
α′′
��c8h r g m mtr,g5l�d g�n
Ç*È Æ È«��É ��k,e ¶ í n?s1w^r�n�b%r5l��
c�n�b�s n�b r5l��qr,g*¸%r,l¬y�r5g�n?i^l�r5d
c3hºn�b%r¬Ç È Æ È��/Ä¡n?s°Ç*È Æ È��/ɹk5e ¶ í l|r�w�c/s h«�pn�b%r β
y�r,g�n�i&l|r
d�n�l|r,htw n�b%r5h^d g h � {^l|stg5�jr5h d y�i^lJn�b r5l�� g h � n�btr
Ç*È Æ Æ ��Ä�k,e ¶ í ��i^e�m�{^l�s%g5� r5h d�g5h!��Ïqs lo�!c3e~c3h!c�d�b%r,d1� �or5v
m%r5g5n�c�htw�n�bjr�n?r5e�m%r,l�g5n�i^lJr�k�� k*��r �%n�l?g�k�r5d���Ç*� � g5h ����Ç5r � �d�b%s%�~d n�b%r ��g5l|w r ��� lJr�} r5l?d�c7{���r h!g�n?i^l�r s y n�bjr,d|r
k5b^g5h*w!r,d,�u��d�l|r,mtstl|n?r5��c3h�n�b%r¹a�g�{���rj�un�b%r¬{^l�szg*�%r,h!c�h%w
s y�n�btr
ν � í�ð � í?' · ð β
y�r5g5n?i!lJrÐi&mtszh g5h^htr,g*�3c3htw c3d
�3g5lJw r*�����ji rxn�s¹n�b%r¬g5m^mtr,g5l�g5h%k�rxs y�g¬d�b%s%i��3� r5lqs%h�n�btr
a�g�{���r
#�ãkÕJ�/á·Útò`Ö ö`Ö Ú�ù·ò�ü`ækÔ þÿ ��Õ�ù·ß���Ö ß�öûø·ò�ü�é,õx�/ónïtÙªÚtë·ùß·ãkß/ö Ú�ùã�Õ�Ù ãkòûö'ñ�ä ñtñ���æ�Ô þtÿ ��ïÕ�ù·ß/Õ�òûò`Ö úù·Ô�ã�ù·öûò�Ü�ÚtÙ�ö¦ø·ã�Ô�ÕtÖ ù" ûå�Õ�ê�òûÚÙûá·ö Ö Ú�ù·ò'Ö ù"�^� � ! � � ä �ÇøZã
×�Õ�êZãt×èò
α
ï
β
ï,Õtù�ß
γ
Ù`ã�ܦã�Ù"öûÚ�ö`øZã�ö`ø�Ù`ã�ã�×�ÕÙ`ú·ã�ò`ö�á�ã�Õ?��ò"Ú�ê�ò`ã�Ù`ç1ã�ß Ö ù)ÕtòªÓ�ß�ã�áZÚò�Öèö ã�ß)ò`ÕtÔ/á,×�ã�ò+#¯ö`øZã/צÕtê�ãt×�ò
α′
Õtù�ß
α′′ Ù`ãtܦãtÙ�ö`Ú ö8��Ú�Õß·ß,Ö ö�Ö Ú·ù·Õ·×Çò`ö`ÙªÚ·ù·úÜ�ã�Õtö`ë1Ù�ã�ò�ö ø�Õtö�Õtá�áZã�Õ�Ù�ê�ã�ö3��ã�ã�ù
α
Õtù�ß
β
ëZá�Úù�ö`ã�Ô/á�ã�Ù�Õ�ö`ë·Ùkã�ækìZæt×�Ö ù�ú�ä*��ø�ã � Õtò`Ó¦ßZã�á�Úò�Ö ö`ã�ß��âòªáZã�æ�ö`ÙªÕ Õ�Ù�ã�öûÕ��·ã�ù�Õtö
=
ð,ä ô��#ï�ö`ø1ã � Õ�ùZù�ã�Õ�צÖ�ù·ú��
ò`áZã�æ�öûÙ�Õ{Õ�ö
=
ô�ä ýÙ�#ï"Õtù�ß\ö`ø·ã � Õtù�ùZã�Õ×�ã�ß��{ò`á�ã�æ�ö`Ù`Õ{ë�á�Ú�ù\Ùªã�Ó�ætÚÚ·×�Öèù·únö`Ú
=
ðÂä ôÙ�#ä!�'ø1ã ú1Õtò`Ó¦áZø·Õò`ã çZÖ ê�Ù`Õö�ÖèÚùZÕ×�ê�Õtù�ß\ÚÙ¥Ö ú�Ö ùZòtï
ν � ï"ÕÙ`ããtò`ö`Ö�Ô/Õ�ö`ã�ß�ܦÙ`Ú·Ôfß�Õtö`Õ�Ö ù�å�ãtÜ�ä¯ôqñ
�,Õê·ã�×
#Çã�Õ��)áZÚò�Ö ö�Ö Úù�ò/ü3��Öèß·ö`ø�òJ�
$�òªò�Ö ú·ù�Ô�ã�ù�öÕtò`Ó¦ßZã�á�Úò�Ö ö`ã�ß Õtù�ùZã�Õ×ûÖ ùZú Õtù�ù�ã�Õ�צã�ß
α
ð·ð·îý,ä ð���')ü�ñZä ñô·ñ�� ððZî�ý�ä �·ñ·ñ�ü¥ñ�ä ñ,í��5� ððZî�ý�ä ð ��� ü�ñ,ä ñ�ítñ��
ν � ÿ � � ÿ&% � �
α′
ù�ä Ú�ä
ν � =
ðð·ý���ä ôý
α′′
ð�ð�îtýÇä ô��·ô��Xü�ñ,ä ñtð����
β
ð·ð·îý,ä ý�'�í�ü�ñZä ñ��·ñ�� ððZî�ý�ä ý·îð ü¥ñ�ä ñ��·ñ�� ððZî�ý�ä ý�'·î�ü�ñ,ä ñ�ð����
γ
ð·ð·î �,ä ñ � ��ü�ñZä ñ,í��5�
α
ð��ð�'�ä ý�����ü�ñZä ñ����5� ð��·ð�',ä ýô·ð ü¥ñ�ä ñ,í��5� ð��·ð�',ä ýô·ð ü�ñ,ä ñ�íJ���
ν � ÿ&% � ÿ
� � ÿ�
�
α′
ù�ä Ú�ä
ν � =
ð����ð�ä�íí
α′′
ù�ä Ú,ä
β
ð��·ð·î,ä ô,íJ� ð��·ð·î,ä ô�ð�� ð��·ð·î,ä � ��� ü�ñ,ä ñ�ítñ��ð��·ð·î,ä ôð·ð ü�ñ,ä ñ�ítñ��
γ
ð��ðZî�ä '���')ü�ñZä ñð·ñ��
α
ð��ô��,ä ý�í���ü�ñZä ñô·ñ�� ð��ô��,ä ý�íký ü¥ñ�ä ñð·ñ�� ð��·ô���ä ý,í�ô ü�ñ,ä ñ�íJ���
ν � ÿ
� � ÿ&% � �
α′
ð��·ô���ä �,í�ð ü¥ñ�ä ñ,í��5�
ν � =
ð��·ô ��ä�íkô
α′′
ð��·ô���ä �·î � ü�ñ,ä ñ�ðZñ��
β
ð��ô·ô,ä ������ü�ñZä ñð��5� ð��·ôô�ä ô·ñô ü¥ñ�ä ñ��·ñ�� ð���ô1ôÂä ���·î)ü�ñ�ä ñô·ñ�� �
γ
ð��ô·ô,ä '�� ��ü�ñZä ñð·ñ��
��
���ãtÕ?��ï�ò�Ö�úù�Õ�× !�ù�Ú·Ö ò`ã ∼ í�#�ù'ä ÚÂä�
~ù�Ú�ö"Úê�ò`ã�Ù`ç·ã�ß�ï,ò�Ö ú1ùZÕ×
!�ù�Ú·Ö�ò`ã � � #���
~òªøZÚë,×�ß�ã�Ù"Õtö"ð��·ôô�ä �·îð�æ�Ô þÿ ä
2
3�4,ð í�â 5�â 6�ç87^â 596�â 6�:«æ<;5ã>=-;5ê�ç�?A@�êJï?ð�ñ�ñ�ñ%ïCB�ì?ðED ï�7%ä�F�ì&4�G�H?ñ
l?r5�Ãd�c�� r£szy�n�b%re
g5c3h�m%r,g5¸ × n�b%r
ν � í?' · í�ð � í�ý ·
βy�r,g1n?i^l|r§g�k�n?i^g*�����d?m&��c�n�d¬k�sze�m!��r�n?r*���¢c3hjn?s�n?�~s�d�b g*l?m«�
�~r ���3vNl�r5dJs!��}%r5�¹m%r5g ¸ d�dJr5m^g5l�g5n�r,�¬{j�
≈ µ � µ Ç�k5e ¶ í �Ó�c�w^i^l|r�Ȱd�b%s%�¨d¨n�b%rxÇ*È Æ ½ n�s°Ç*È ½%µ k5e ¶ í l?r�w^c�szh�s%y
n�bjrÅd�g5e~rqd?mjr�k�n�l�gqg dp�jr,mjc�k�n�r,��c8h�ÓEc�wW� ÇE�&À*r�} r5l?g*��d�b g l�m
h r��®m%r,g5¸!d�g mjm%r,g5l�i^m%s h�n?r5e
mtr,l�g�n?i!l?r¡k��%k*��c3hzwp��eqs dJn
h s*n�g5{E����n�b%s dJr¹h%r5g5l
Ç*È Æ ½ �/Ç ½ �pÇ È Æ%½ �;È Ý �oÇ5È Æ ÄE� Ä Ý �ug5h!�Ç È Æ Ý �/Ç ½ k5e ¶ í �
�!U���` ��_5]�� �5`3[%X
�������
��)��� .
� $ �+( � *���· ð�� � �A'���� �A'��
©r�g5d�d?c�wjh£n�b%r
α
�
β
�Åg5h �
γ
y�r,g1n?i^l|r,d¬n�s�c3dJs!�3g�n?r5�
��· ð e�s ��r�k�i«��r5d�g5d�szm!m%s%d?r5��n?s�����· ð �·§ k ��i�dJn?r5l�d��%i r
n?s��^� ´ � n�b r�r�¦!n�l|r,e�rÅ�!c8��i!n�c7s h dfs y�n�b%rÅd�g5e�m!��r,d1�^��Ç � n�b%r��g1k,¸¯szy¹g5hj��dJ� d�n?r5e
g�n�c�k�k�s h%k�r,hjn�l�g5n�c7s h��jr5m%r,hj� r5h%k�r �
g h �Ü��È � n�b%r¢g�{^d�r5h%k�r��y�szl�g5d?v�� r5m%s d?c�n�r,� ��· ð Ï���� ðd?sj��c8�^d � szy�g h%��szn�b%r5l¹g�{^d�szl�m%n�c�szhy�r5g�n?i^l�r5d�s i!n�d?c8�%r�g
h^g5l�lJs%�
≈ ´ k5e ¶ í ��c3h �js �¬����d�d?r5d?d�c�htw°n�b%r�}!g*��c3�jc�n?�¹s%y
n�b!c3d��3g5dJn
m%s c�hjn¨l�r5Ì%i^c3l�r5dqgx{!l�c7r5yqlJr�}^c7r��Üs y�n�bjr¬�3c�n?r5l?g5v
n?i�lJr�szh�����· ð,�·§ k ��i^dJn�r,l�d,�a�b%r�w&g5d?v�m!b g5d�r¢} c�{^l�g�n�c�szh!g*�({!g h ��szl�c�w&c�hÎy�s%l�n�b%r
��s%k5g*��c���r,��g5d|�^e~e�r�n�l�c/k�dJn�l�r�n�k,b�e�sz�jr¹s y�Êzd��3c�m!m%r5��m g5v
l�g*����r �JË0��· ð � c3e�r5l?d�c3dfs%{^dJr5l�}zr5��» Æ Ç ¾ n�s
{ r~d�b^c3y�n�r,��{ �
+ ´ ��Ä1È(k5e ¶ í l|r �3g�n�c�}jrn?sÃn�b r�e�szhjsze�r,l
ν� í�ð � íJ' · ð{&g5h �Ûszl�c7w^c3h�g�nxÇ*È Æ É&� ´�Æ k5e ¶ í × n�b%r�stl|r�n�c�k5g*�~k,g*��k�iE��g5vn�c�s h d�» Æ È ¼!Æ ½ ¾ m l�r,� c�k�nÃd�b c3y�n�d�s y¯{ r�n��~r�r,h µ g5h!�
+
Ç�k5e ¶ í �Å�%r5m r5h �!c�h%w¢s h�n�bjr�� c3e�r,l�w r�ste�r�n�lJ�«�Åa�b%r
k�� k*�3c/k�� �·¸ dJ�!e~e~r�n�l�� ��· ð n�l?c3e�r5l�{�g5h �Üs%l�c�wjc8hÎc3d
d�bjc3y�n?r5��{ �
+
ÇE� ½ ��k5e ¶ í » Æ Ä ¾ �og5h!��n�bjr¹h s%h^v8k��zk*�3c�k�� ðd?� e�e~r�n�l|����· ð n�l�c3eqr5l"d�btsz��dpn��Ås�{^g*h �^du�
c�n�b�szl�c�w&c�h^d
d�b c3y�n�r,��{ � ¼�½ � � ½ k,e ¶ í g*h �
+
È�� ½ ��k,e ¶ í » Æ%Ý^¾ �
g*���d�b c3y�n�d°g�w^g5c3h lJr5y�r,l�r5h%k�r5�n�s¢n�b%r�w^g*d?v�m b^g5d�r�eqs h%s e~r5l
ν � {^g*h �Ászl�c�w&c�h�����g5l|w r,l¯w&g5d�vNm!b g5d�r ����· ð �§ k*��i&d�v
n?r5l�d¹» Æ � ¾ g5h ��i���n�l�g5vNyJc3htr�m g5l�n�c7k ��r5d°» Æ É ¾ d?bjs �®{^l�s%g �
g�{�dJs l?m%n�c�s h d"g�k,l�szd�d�n�b rqÇ*È Æ µ n�s
Ç*È�� µ k,e ¶ í l?g5htw r � aWbtrg�{�dJs l?m%n�c�s h�e�g�¦^c3e�i^e c�hßmti^l�r �qk,l�� dJn�g%����c�hjr �~h^g�n�i^l�g*�
c3d|szn�szm!c7k¨g�{!i^h �!g5hjk�rqd?sj��c8����· ð s k�k�i l?dfg�noÇ1È Æ*Æ � �qk�e ¶ í �{ i!nodJs!�3c3��d�g5e
m&��r5domjl?r5m g5l�r5��{^���^c�yJy�r5l�r,h%n�eqr�n�bjsz�!d�k5g h
d�b%s%� g�{&d|stl�m%n�c�sthjdÍg ht�z��b r5lJrÁ{ r�n?�~r�r,h Ç È%È µ g5h!�
Ç*È�� µ k,e ¶ í » ½zµ*¼�½ È ¾ �Â�g�n�l�c�¦Îc3d�sj��g�n�c�s hÃd�n?i^�!c7r,d�c3h%}js ��}^c3h*wÃw r5h%r5l�g*��� ¼��· ð k�sze�m!��r�¦!r,d¹g5l�r�yJg5l¬n�s%s¢h%i�eqr,l�s*i&d¬n�s�3c�d�n¹bjr,l|r
r�¦&b g�i�dJn�c�}%r ���¢» ½*Æ ¼�½ Ä ¾ �oa�b%r�Ñ���g�{^d�s%l�mtn�c�s%h§d�m r�k�n�lJi!e
s yqg ´ m m!e ��· ð Ï�� ð d�s �3c3��k5g l|r,y�iE�N����m^l|r,mjg lJr5��yJl�s%e
n�bjrxe�r ��n~d�btsz��d~gxd�c�h%w���rxd�b g l�m���c�hjr��
c�n�b�g��
c�� n�b�szy
≈ µ � µ%µ Ý k5e ¶ í g�n��
= ´z´ �����
b c�k,bÜc�d§g5d�d�c7w^h r5�Ãn�s
�3c�{^l�g�n�c3hzw ��· ð e¨s^��r�k�i���r5d�c�d�sj��g1n?r5��c3h d?c3htw���r5vNd|i^{!dJn�c8v
n?ijn�c�s h g*�(d�c7n?r5d�» ½%Ý ¾ �¨�q���xs*n�bjr,l�m l�r�} c�s i�d����ßl|r,mjszl�n?r5�
ν � l?r�w^c�szhÜd�m%r�k�n�l?gs%y�d�s ��r ��� ��· ð �tstmtr,�¿l�g5l|r wjg*d
» ½ � ¼ Ä%Ç ¾ �E�jr�i n?r5l?c�i!eÍ»?Ä1È«��Ä Æ�¾ �Eg5h!�x�u� ð »�Ä ½!¾ e
g�n�l�c�k�r5dd�b%s%� eqi«��n�c�m���r¹g�{^d�szl�m%n�c�szh�y�r5g�n?i�lJr5d�d?m!g5h h^c8h*wÛg ½ n�s
´�µ k5e ¶ í l�g5htwtrj�&a�bjr,d|rÙy�r5g�n?i�lJr5d�g*lJr�m l�r,m g5l�g�n�c�szhu�^k�sthjv
k�r,hjn�l�g�n�c�s h«�
g5h!��g5h!h%r,gt��c�htw�%r5m r5h �jr,h%n1�
g5h^� g5l?r�g d�v
d�c�w&h%r5�¬n?s���· ð e�s!��r�k�i���r5d�c�h¹e�i���n�c3m&��r~n�l�g5m m^c�htw�d�c�n�r,d,�
g5h!��Ï~s%l�n?sÎg�wjwjl|r�w�g�n?r5�¿�<��· ð ��§ d�m r�k5c/r5d1�(Â�s%d?n�� c8v
l�r�k�n�����lJr*��r�}^g5h%n~n�s¹n�bjc3d~�!c�d�k�i^d�d?c�s%h�g l|rxn�btr(d?mtr�k�n�l�g�szy
����· ð5�·§ k*��i^d�n?r5l?d�c8h¹d�s �3c3����� ð �
b!c7k,b¹d�b%s%�Ãg�k�sze�m!��c8v
k5g�n?r5�®m g�n?n�r,l�h¿s y¢mtr,g5¸ d¯n�b l�s*i%w&b%s%i nn�b%rÎÇ*È Æ ½ n�s
Ç*È ½ µ k,e ¶ í lJr�w^c�s h�»JÄ ½j¾ �Ó�c3h!g*�N���«�xn�bjr�g�{&d|r,hjk�rszy�g*� �!c/n�c�s h g*�°y�r5g5n?i!lJr5d�c3h
n�l�g�k�r,d�� ´ g � g*h �¡� ´ { � �&y�szl"��b^c7k5b¬n�b%r!��· ð c8d�g�k�n�i&g*�����g5h�i!h^c�hjn?r5h%n�c�s h g*��c3e�m%i^l�c�n?��c3h�d�g5e�m!��r5d�k�s h%n�g5c3h!c�h%w
∼ ´�µ m!m e szy¬s%n�b%r,l��tstmjg5h n�d��
y�i^l�n�b%r5l�dJi�m m%s l|n�d�n�btr
g5l|w i^e~r5hjn(y�s l¬h%r�w��3c7w^c�{���r��%s m g5hjn(g�w%w^l�r�w^g�n�c�szh�i&hj� r5l
n�bjr mjl?r5dJr5hjnÎd?g*e~m���r mjlJr5m^g5l�g5n�c7s hÁk�sthj�^c�n�c7sthjd5�/��s*n
d�b%s%�~h¹g5l�r
d�m%r�k�n�l�g�yJlJs eÐs*n�bjr,lÞr�¦^mtr,l�c3eqr5hjn�d�g5n�bjc7w^b r5l
� ���"k�s%h k�r5h%n�l�g�n�c�szh!dq�
b c�k5b %�� d�b s*�ªg1{^dJs l?mjn�c7s h�y�r5g5v
n?i!l?r5d�c�hºn�bjr(Ç*È Æ Ä¡n?s�Ç*È Æ É¹k5e ¶ í l?r�w^c�szh�g�n�n�l?c�{ i^n�g�{���r
nJs¬��� ��� ��� ����· ð5��§ k�s e�m!�/r�¦ r�dq»ÚÄ*Ä ¾ �ja«b%r�d|r¨Ç�nJs ½ k�e ¶ í{���i^r�d�b c3y�n�d(yJl�s%eÁn�b%r�e�g�n�l�c7¦�c�d?sj��g1n?r5�¢e¨sthtste�r5l(g�{!v
d�szl�m%n�c�szh!dog5l�rqc3h¬�3c3hjr��
c�n�b�n�b r
+
Ç�k5e ¶ í d�b c8y�n�l|r,mjszl�n?r5�c3hÐm!lJr�}^c7szi!d�� ���JÏ ��· ð Ïq��l¹d|n?i^�!c�r5d�»ÚÄ Ý �/Ä � ¾ �ÅaWbti&d,�k*��i^d�n�r,l�c3h%w(�ji^l�c�h%w¹�%r5m%s d?c�n�c�szh�n?sxy�s l�eÃ����· ð5�·§ d�b s*i��3�{ r�r�}%r,hº��r5d�dqc3e~mjszl�n�g5h%n~y�s%l�n�b r�e�stl|rx� c���i n?r ´ ��Ǭm mje
��· ð d�g e~mE��r�� r5m c�k�n?r5�¹c�h¬n�l�g�k�rx� ´ k � �© r~n�b%i!d�k�szhjk ��i^�jr~�~c�n�b¬k�szh!yJc�� r5h%k�r~n�b!g�n�n�btr
α
�
β
�
g5h!�
γ
y�r5g�n?i^l�r5dxg5l|r¤�%ijr°n�s�c3d�s �3g�n?r5� ��· ð e~s!��r�k�i���r,d,�
a�b rqg5m mjr,g5l�g h%k�r�s y . � ���%r�n�r�k�n�g1{���rÅg5{!dJs l?mjn�c7s hxy�r5g�n?i^l�r5d
c3h£g5d?v�� r5m%s d?c�n?r5�¢d�g5e
m!��r5dx��c�n�b c8h¢g�h!g5l?l�s �
≈ ´ k5e ¶ íl�r�w^c�s%h���r,d�m%r�k5c3g*����� n�l?g�k�r,d�� ´ k � g5h!� ��Ètg � �°y�i�lJn�b r5l
d�i%w%w r,d�n�d�n�b^g�n�r�} r5h�n�bjr,d|r¹�~r5g5¸%r,l�y�r,g�n�i^l�r,d�e�g��§g*�3d�s
{ r�� ijr°n�s§c3d|s^�3g�n?r5� ��· ð e�s ��r�k�i���r5d5��aWbjr°hjr�� �~r5g5¸
y�r5g�n?i�lJr5d¬�~b^c�k5b£g5m^m%r5g5l¬s%h�����i^m%s h£g h hjr5g*��c3hzwW��r5d�m%r5v
k5c3g*�N���£n�b%s dJr��~c�n�bd�c7w^h^c3yJc7k5g h%n¹d�b c3y�n�d¹yJlJs eÁn�b%r�{^g5h!�
µ¿¤èÁ²ÇÌZ² ��ÚùZö`Öèù·ëZÕ�ö�Ö Ú·ù)Ú·Ü�ö ø�ã/ò`á�ã�æ�ö`Ù`Õ�á�Ù`ã�ò`ã�ù�ö`ã�ß�Ö�ù�é�Ö ú�ä�ð�ä
* � * ð � � , -
íÖâ 5?â 6?ç�7tâ 5�6�â 69:«æ�;,ã>=�;5ê/ç ? @�êNï�ð�ñ5ñ�ñ ï B,ì?ðEDzï 7 ä<F5ì&4EG<H?ñ 3�4��
k�r5h n�r,l,�
e
g��{ r��ji r�n?s �<��· ð �§ k*��i^d�n�r,l�d5�q©r��
c8�N�
�^c3d|k�i!d�d�n�b%r,d�r�m%s d?d�c�{^cÚ��c7n�c�r,d¬y�i^l�n�btr,l¬c3h�n�b r�y�s!�N��s ��c3h*w
d?r�k�n�c�s%h^d,�
�
���
� � � ð � � � '<��� � ' �&,�.5� � $C(�- �<$ �&'������
©r¹g�n?n�l�c�{ i n�r(n�b r¹g5m!m%r5g5l�g5htk�r¹s%y���g�n¬��r,g5d|n � n�b^l|r�r
d?r5m g5l�g�n?r£g�{^d�szl�m%n�c�szhÐm%r5g ¸ d�y�s%l�e~s%h s%e~r5l?c�k ��· ð n?s
n�l�g5m m!c�htwÎs y ��· ð e�s ��r�k�i���r,d�c8hÎe�i���n�c3m!��rn�l�g5m^mjc3h*w
d�c�n?r5d��oÕ�g5k5b��^c�d�n�c3htk�n~n�l�g5m m c3htwºd�c�n?r�{ ��� r5yJc3h c�n�c�szh�k�s l?v
l?r5d?mjszh!� d�n?s£g��^c3yJy�r5lJr5hjnxn�c8e~r5vNg�}%r5l�g�wtr5�£d?n�lJi!k�n�i^lJr�s%y
� s%m^g5h%nqg5h �¹bjszd�n�e�s ��r�k�i���r,d�g5h^�¹d|s«�&c3h¬m^l�c3h%k5c3m!��r ��k5g5h
w^r,htr,l�g�n?r�g�� c3dJn�c3hjk�n�m g�n�n?r5l�hxs yuw^g5d�v8n?s%vNe�g�n�l�c7¦°d�m r�k�n�l?g*�
d�bjc3y�n�d�y�szl�n�b r£�%s m g5h n�}!c/{�l?g�n�c�s h g*�¬n�l?g5h!d?c�n�c�s%h^d,�xÓ�stl
m i^l�m s%d�r,d£s%y�n�b!c3d£�^c3d|k�i!d�d�c�s h«�¹�~rÐk,g*hÍg*dJk5l�c7{!rÐn�b%r
y�stl�e
g�n�c�s h¿szy£eqi���n�c�mE��rÐn�l�g5mjm c3htw d�c�n?r5d�%i^l�c3h*w n�b%r
b^c7w^b!���xh%s h v8r,Ìji^c��3c7{&l�c�i^e d�g5e�m!��rÅ�jr,mtszd�c�n�c7s hxmjlJs%k�r5d?dfn?s
� ´ � c�e
m%r5l�y�r�k�n�c�szh!d§c8hÃn�b ri^h!�%r5l���� c3h*w�b s%d?n�k5lJ�^d|n�g*�
d?n�lJi!k�n�i^lJrj�Wg5h!��Ïqs l~��Ç � e~c8d�e�g5n?k5b%r5dqc3h¹n�b%r¹Ê%d?c���r5d�ˬs%y
b s%d?n�g*h ��w i!r,d|nÅeqs!��r�k�i���r,d1�
��d�e~r5h n�c7sthtr,�Üc3h�n�bjr�Ñ?h%n�l?s%� ijk�n�c�szhu�Ùn�b re�c/k5l�szv
d?k�szm!c7k¤d|n�l�i k�n?i^l�r¹s y�s%i^lxl�g5m c3�Û}tg*m%szl�� r5m%s d?c�n?r5����� ðd?sj��c8�^d�c3d�yJg5l°yJl�sze n�b g5n¹s y¬n�b%r�m%r5l�y�r�k�n5�¨d�c�htw&��r�b%k5m
k,l�� d�n�g*�3d¹n�b^g�n�k,g5h¯{^r�m^l|s �%i k�r,� { ��dÖ��s%������yJlJr�r���c3h*w
��c3Ìti&c������ ð »?Ä*É ¾ ��aWbtr°b%k5m��%�8�N� ��� ��� �
���3��� � g h ��y�k�k
�%�N��� �
�����������
�����N�3� � dJn�l�i k�n�i^l�r,d�g5l�r~s h!���¬n��~sxs%y"n�b%r
c3h^yJc�h!c�n?r�hji^e~{jr,l�s yx�%r5h!dJr5d?n�k ��s dJr5vNmjg5k5¸%r,�£dJn�l�i k�n�i^l�r,d
n�b!g�n(k5g5h�{^r�m^l|s �%i k�r,�£{ �£dJn�g1k,¸jc3h*w¢s y�k*��s dJr5v�m g5k5¸%r5�
� Ê {^g*d?g*�JË � m&��g5hjr,d,����g�n?n?r5l�h d���c�n�b���szhtw r,l�lJr5m r5g�n�i�h c�n�d
��m%s!���%n?� m!c�d�e � �fhtsthjvNmjr,l�c�sz�!c�k¬d?n�lJi k�n?i�lJr5d�dJi!k,b�g*dqn?�
c8h
g h �¬dJn�g5k5¸ c3h*w¹yJg�i���n�d1�^g5h ��r�}%r5h(l�g h �jszeÐd|n�g5k5¸%r5��k*��s d|r,v
m^g�k5¸%r5�¹d�n�lJijk�n�i&l|r,d�g5l?r�g%�3dJs(mtstd�d�c�{���rx» Ý µ!¾ �Ó�szl�n�i^h g5n�r ���«�pn�bjr(k�s e~{!c3h g�n�c�sth�s%y�Ñ"��g*h � ��g5e�g5h
d�mtr�k�n�l�szd�k�szm c�r,d"s ypm%i�lJr�dJs!��c������ ð lJr�} r5g*��d"n�b r~d�� e
e¨r,vn�l�c�r5dÃs yÐn�b%r®d�c7n�r,dÜs*k�k�i&mjc�r,� { � n�bjr���� ð e�s ��r,v
k�i«��r5d¬» ÝE´�¼�Ý*Æ�¾ �o©r°b g1}%r°h s*nx� r�n?r�k�n?r5�§g5hj��} g�k5g h%k��
� r5y�r�k�n�d�c3hÜg5d�vN�tr,mjszd�c7n?r5�Üi^h �jszmjr,� ��� ð d|s!��c3�jd5�xg5h!�
b^g�} rÃy�i�lJn�b r5ld?bjs �
h¿n�b^g�nn�b%r,d�rÃd�g5e
m&��r5dg5l�r�hjs n
g eqs l?m!b%s%i^d × l�g�n�btr,l1��n�b%r��¹g5m^m%r5g5l�n�sx{ r��%r5h^d|r,d�n�k*��s d|r,v
m^g�k5¸%r5��d?sj��c8�^d�e�g5�%r i^mÜs y§d|r,mjg l?g�n�rßbjk,m�g5hj��y�k�k
l?r�w^c�szh!d®» ´ Ä!�/Ç%ÇE� Ý*Æ^¾ � a�b%r c3h%n�l�sz�ji k�n�c�szh szy�i&m n?s
∼ ´�µ%µ µ m!m ek�szhjk�r5h%n�l�g�n�c�szh!dfszy�� s%m^g5htn�dÞ��c3¸tr���� ô g5h!�
��·¬�~�
b c�k5bÐg5lJr�hjr,g5l����n�b%r�d�g5e~r£Êzd�c���r%Ëg5d�g���� ðe~s!��r�k�i���rßc�h�n�b%r�} g h��tr,l�©�g5g*��d�d?r5h d�rj�(� s*r,d�hjs n
d�c�wjhjc3yJc�k5g5h n�����g5yJy�r�k�n�n�bjr(��� ð d�n�l|i^k�n?i!lJrj�Þa�bji^d���n�l�g5m v
m^c�htw(s yod�i k5b¹�%s m g5hjn�d�c8h(d�c3hzw&��r5vNd�i {^d�n�c�n?i n�c�szh!g*��} g5k5g5h v
k,c�r5d~l|r,d�i���n�d~c8h¹n�b rxy�s l?e�g�n�c�szh�s y�n��~s¹�^c3d|n�c3htk�n~k*�3g5d?d�r,d
sty�n�l�g5mjm^c�htw§d?c�n�r,d �Ws y � � ¸ d|�te�e�r�n�lJ��c3h�bjk,m�l�r�w^c�szh!d��
g h � � ¸ dJ� e
e�r�n�lJ��c3h�y�k�k(l�r�wjc�szh!d��ua�b%r�r�¦!m r5l?c3e�r5h%n�g*�
��� ô Ï���� ð g5h � ��·xÏ���� ð d�m%r�k�n�l?g¡g5l?r¬g%���ok�s h d�c�d�n�r,h%n
�
c�n�b�n�b c3d�l�r �3g�n�c�}%r*���¹d�c3e
m&��r�m c�k�n?i^l|r(»JÇ%ÇE� È � ¾ ��~s*�~r�}jr,l,��c3y�s%i^l£d?mjr�k�n�l|std|k�s m c�kß� c3g�w�h%s dJn�c�k,d£g5lJr
sth&���°d|r,h!d?c�n�c�}%r�n?s¬c3h%n�r,l�g�k�n�c�s%h^dÞ�
c�n�b¡h r5g5l�r,d|nÅhjr,c�w&b%{jstl
��� ð e~s!��r�k�i���r,d,�~n�b%r5h�~r��qsziE��� h%r�k�r5d�d�g5l�c�����%r�n?r�k�n
� ( � , �������u� ð r5h%}^c�l�szh!e�r,h%n�d�y�s l�.�(�,¡g5l|{&c7n�l�g5l��xd�n�g�k5¸ v
c3h*w�m^g�n�n?r5l?h�szyÞ{^g5d�g*�om!�3g5h r5d��Wc��;rj� �Wd?c�n�r,dqc3hº�3g��zr5l�d����
__ �r5e~{ r5�!�%r,� c3h lJr�w^c�s h d s%y ��s*k,g*� b%k5m dJn�g�k,¸!c�h%w
���
���
__
� �¹� Êzb%k5m v|��c8¸%rzË � �®szl ��s k5g*� y�k�k dJn�g�k,¸!c�h%w
���
���
__
� �¹��Êzy�k�k,v|�3c3¸%r%Ë � ��¥~szm!g5h%n�dÐd�i {^d�n�c/n�i^n�r,� c3h n�s
bjk,m v|�3c3¸%r§d�c�n�r,d¡�qs%i����¯r�¦�m%r5l?c�r5hjk�r�r�¦!n?r5l?h!g*�ÙyJc�r*�3�^d¡szy
} r5lJ�h r5g5l���� � �Z¸ d|�te�e�r�n�lJ����n�b s%d?r�c�h�y�k�k,v|��c�¸jr�d�c�n?r5d
�~s*i��3�¬r�¦^c3dJnqc�h¹h r5g5l����¬s k�n�g*b%r,�!l?g*��r5h%}^c�l�szh!e~r5h%n�d1��¥qr5v
m%r5h^�jc3h%w¬s hxn�b r�m g l|n�c�k�i��3g5l�d"s yfn�b%r�� s%m^g5h%n�v/�u� ð c8h n�r,l�vg�k�n�c�s h d1�zn�b%r~� c3d|n�c3hjk�n�c7sth�{ r�n?�~r�r,hW�ty�s lpr�¦^g5e�m!��r ��Êzbjk,mjv
�3c3¸%r%ËÃg5h �ÍÊ*n�l�i r�btk,m�ËÃe�g��Ã{ r£i�h � r�n?r�k�n�g�{���r c8hÎg
w^c�} r5h¹d?mtr�k�n�l�szd�k�szm!c7k
r�¦^mjr,l�c3e~r5h%n1�
Ñ?h�n�b rqk5g5dJrqs y���· ð g5dfn�bjr~�%s m g5hjn5� n�b%r~d�c�n�i^g�n�c�s%h¬c3d
y�i^l�n�btr,lqk�s e~mE��c7k5g5n?r5�¡{^�¹n�b r¬�3g5l|w r,l~d�c���r�s%y
��· ð l?r*�3g5vn�c�}zr n?sÜn�b%r£��� ð bjszd�n5�¹Ó�c7w i^l�r Æ d�btsz�~d�n�b c8d�d�c/��r
�!c�d�k5lJr5m^g5htk��xc3h�g~d�r,e�c3vNÌti&g5h%n�c�n�g�n�c�} rqe
g5h!h%r5l5�%�
c�n�b�n�btr
��· ð eqs!��r�k�i���rÃ�jr,mjc�k�n�r,�¿c3hÍd�c3hzw&��r5v��°�js i!{���r5vÖ�¡g5h!�
n�l�c�mE��r5vNd|i {�dJn�c�n?i n�c�szh!g*�°}^g�k5g5hjk,c�r5d�c3h±{^g5d�g*�¤m!�3g htr,d�szy
d�m b%r5l�c�k,g*���u� ð e�s!��r�k�iE��r5d���·~} r5l��3g m { r�n?�~r�r5h e~s%v
��r�k�i��3g l�s i n���c3hjr5dÃc3h!� c�k5g�n?r5dÎl|r,mji��3d?c�} r c3h%n�r,l�g�k�n�c�s%h^d,�
�
b%r5l�r,g5d"c3hjn?r5lJ} r5h c3hzw(d�mjg�k�r~c3h �!c7k,g1n?r5dog�n�n�l�g5k�n�c7} rÅc8h n�r,l�v
g�k�n�c�s h d1�
a�bjr§��� ð eqs!��r�k�iE��r5d�g*lJr� l�g��
hÃg5d�k,c�l�k*��r5d��
c�n�b
�!c�g*eqr�n?r5l�d�l�r,mjlJr5d?r5h%n�c3h%w�n�b%r�ȫ� ��� ��hjr5g5lJr5d?n�vNhtr,c7w^bj{ s l
d�r,mjg5l�g�n�c�szh£c3h£d�s �3c3���u� ð g�n �3�~r¬n?r5e�m%r,l�g5n�i^lJr5dx»�Ä É ¾ �©rxi!d?r�n�b%r¬h%r5g lJr5d�n~h r5c7w^b%{!szl~d�r5m g5l�g�n�c�s%h��pc�h!dJn�r,g*��szy
n�bjr¹e
c8h c3e�i^e®dJr5m g*l?g�n�c�sth�y�s%l�n�btrx��� ð ¼ ��� ð c3h%n�r,l�g�k5v
n�c�szhÐm%s n�r,hjn�c8g*�?�~n?sc3h%k*��i^� r�n�b%r�r,yJy�r�k�n�d¹s%y¹Ì%i^g*h%n?i!e
��r5lJsÐm%s c3h%n�e�s n�c�sth s h n�bjr¢dJn�l�i k�n�i^l�r�szy�d�s �3c3�£��� ð�
b c�k,b¬�qs%i��3�¬{ r
g�{!d?r5h%n�c3h¡g
d�c3e
m&��r
mts n?r5hjn�c3g*��r5h%r5l|wt�
e�c3h c3e�c7��g�n�c�s h«��©�r��~r5lJr�i^h!g�{���r�n?s¹yJc�h^��g5h�g5h*w���r,v��%r5v
m%r5h^�tr,hjn ��· ð ¼ ��� ð c�hjn?r5l?g1k�n�c7sth�m%s%n?r5h%n�c3g*�oc�h¹n�b r���c�n?r5v
l�g�n?i^l�rj�¤dJs¿�~rÎl�r5dJs lJn�r,� n�sÍg�lJr�k�r5hjn����Ík5g*��k�i��3g5n?r5�
��· ð ¼ �~r°m s*n?r5h n�c�g%�Åc3hjd?n�r,g5�¯» Ý%½!¾ �ÅÀ c3h%k�r�n�b%r°e�c3h c8e
g
s y"n�b%r���d?m!b%r5l�c/k5g%������g�}jr,l�g�w^r,� � �~r ¼ ��r ��� ð ¼ � ð �Eg5h!�
�~r ¼ � ð m%s n�r,hjn�c3g*�3d s*k�k�i^l g�n d|r,mjg l?g�n�c�s h d s%y��
ÇE��É Æ � � » Ý Ä ¾ �¨ÈE� Æ � � »JÄ%É ¾ �xg5h!�ÐÈ«� Æ � � » Ý Ý!¾ ��l|r,d�m%r�k5vn�c�}zr*�������~r�r�¦^mjr�k�n¬s h!���e�c3h%s l¹�!c�yJy�r5l�r,htk�r5d¹{jr�n��~r�r5h
n�bjr��r,htw n�bÃd�k5g*��r5d�s%y�n�b%r���· ð ¼ ��� ð g5h � ��· ð ¼ �~rm%s%n?r5h%n�c3g*��d1��À%i { n�l�g�k�n�c3h*w(n�b r ´ �/É�����r,yJy�r�k�n�c�}%r
l�g5� c�i^dÞszy
n�bjr
�u� ð e�s ��r�k�i«��r5d~yJlJs eÜn�b r¬g5h*w���rx� r5m%r5h^�%r5hjn¨e�c3h c8v
e�i^eÐszyfn�btr ��· ð ¼ �~r�m%s%n?r5h%n�c3g*��m l�sz�ji k�r5d�n�b%r~s%i n���c3htrs y¬n�bjr���· ð eqs!��r�k�i���r �
a�b rÊ%�^c8m�Ëc3h n?s%�~g l?�!d�n�btr
k�r,hjn�l�g*� �ßg�n�szeÍc8h �^c7k5g5n�r,dqn�b%r(mjlJr5d?r5h%k�rxs%yÅg5h�g�n�n�l�g�k5v
µ¿¤èÁ² ÄZ² ��ì·á�Úö`øZã�ökÖ æ�Õq× ö`Ù`Õ�áZá,Ö ùZú�ò�Ö öªã�ò ܦÚ�ÙÞ��� � Ô/Ú·×�ãtæ�ë,×�ã�ò�Ö ùrò`Ú·×¦Ö ß
� � ê�Õtò`ã�ß\Úùnò�Ö ùZú�×�ã�Ó�ï�ß�ÚëZê,×�ã�Ókï�Õ�ùZßnö`Ù�Ö á,×�ã�Ó�ò`ë1êZò`ökÖ ö`ëZö`ÖèÚ�ù�Õ�×�ç·Õ�æ�Õtù Ó
ætÖ�ã�ò"Ö�ù)æt×èÚ·ò`ã�Ó¦áZÕ�æJ�Zã�ß)á,×�Õù·ã�ò�Ú·Ü � � Ô/Ú·×�ã�ætë�×�ã�ò�ä
2
3�4�� í�â 5�â 6�ç87^â 596�â 6�:«æ<;5ã>=-;5ê�ç�?A@�êJï?ð�ñ�ñ�ñ%ïCB�ì?ðED ï�7%ä�F�ì&4�G�H?ñ
n�c�} r���r ���?�Wg5h!��k�szl�lJr�k�n�����lJr5y���r�k�n�dqn�b%rxr�¦^m%r5l�c3eqr5h n�g*�N���
� r�n?r5l?e�c3h%r5��a�v�d?b!g5m%r,�¡w���s%{^g*��e�c�h^c3e¨i&e ��· ð ¼ ��r�w r,vste�r�n�lJ��» Ý � ¾ �
� i^�tw^c3h*w(yJl|ste¯n�b%r~� l�g��
c�htw^doc�h¬Ó�c7w�� Æ �z��r�k�sthjd�c��jr,lc�n�i^hE�3c�¸jr*���«��{ i nÅhtsznqc�e
m%s d�d�c�{���rj��y�szl�g0��· ð e~sj��r�k�iE��rn?s�s%k�k�i^mt� g�d?c8h%w���r,v�dJi!{^dJn�c�n?ijn�c�s h g*��}tg�k5g htk��c�hd?sj��c8�
��� ð �o��l�r �3g�¦ r5��n�l�g5m m!c�h%w¢d?c�n?r°d�n�l|i^k�n?i!lJr��Ås%i��3��l|r,v
Ì i^c8lJrÐk�s h d�c3�tr,l�g�{���rÃ�^c3d|n?s lJn�c�szh¿s y�n�b%rÃd?i!l�l|s%i^h �!c3h*w
��� ð e�s ��r�k�i���r,d�g���g��xyJlJs en�b r5c3lfszl�c7w^c3h g*���3g�n?n�c�k�rqm s%d�c�v
n�c�s h d1����r5g5� c3htw�n?s�hji^e~r5lJs%i^d�d�e~g%����r,l�lJr5m iE��d�c�} r
�u� ð ¼��� ð c3hjn?r5l?g�k�n�c�s h d1�q·
h�n�bjr�szn�b%r5l(bjg5h^�«��n�bjr��%s%i {���r,v
d?ij{^d�n�c�n�i n�c�s%h^g*��d�c�n?rÎl�r5g5� c���� g�k�k�ste�e~s � g�n�r,d g ��· ðe~s!��r�k�i���r �pg5h^�ºn�b%r�n�l�c�m���r,v�dJij{&d|n�c�n�i n�c�s%h^g*��d�c/n�r(g*m m%r5g5l�d
m r5l?b!g5m d�s%}%r5l����(d�m g�k5c�s%i^d,�
©r�k,g*h¢e¨std|n¬r,g5d�c8����r�¦�m!�3g5c3h�s*i&l�s%{^d�r,l|}^g�n�c�s%h�s%y
n�b!lJr�rße�g5c3hÍm%r5g5¸ d£c3hÜn�bjrßd�m%r�k�n�l�g s y�g5d?v�� r5m%s d?c�n?r5�
��· ð Ï���� ð dJs!�3c��!d�{^��n�l?g5m!m c3h*w�s y ��· ð e�s!��r�k�iE��r5d
c8hn�b!lJr�r��jc3dJn�c3h k�n¢�%s%i {E��r5vNd�i {!d?n�c�n?ijn�c�s%h^g*��}tg1k,g5htk,c�r5d1�¹Ñ?h
r,g1k,b k5g5d?r n�b%r ��· ð eqs!��r�k�iE��r5dÍd�b s*i���� r�¦^c8d?nÍg5d
d?n�lJs h*w����b c3h!�%r,l�r5� ��c�{^l�g�n?szl�d¹g5h!�hjs n°g5d¹l�s*n?s l?d1�� p�
k�s e�m g5l�c�d�s%h �
c7n�b n�btr l?r�k�r,h%n ��· ð Ï�� ð r�¦�m%r5l�c�v
e~r5h n�d�» ½%Ý!¾ ���qr��~s i«���¡r�¦^m r�k�nÅgxd�c3hzw&��rxd�b g5l�m��3c3h%rxg5d
n�bjr(e�g5c3h�d�c�w&h g�n�i&l|r�y�s%l~r5g�k5b�n�l�g5m m!c�h%w§d�c�n?rj�ua�b%r5l�r(c3d
sth&����sthtr~n?� mjrÅs y"�%s%i {���r,v�d�i {^d�n�c7n�i^n�c/s h gt��d�c�n?r~c3h¬g5h¬y�k�k
d?sj��c8�����
b c���r�n�btr,l�r�g5l?r�n?��s��jc3yJy�r,l�r5h%n���g��^d�s y�l�r,e¨sz} v
c3h%wn?�qsg5�*Ø�g5k�r5h%n°b%s dJn�eqs!��r�k�iE��r5d¹c3hg5hbjk,m£d�s �3c3�u�
aWbjr5dJr�g5l�r¤�jr5d?c7w^h!g�n?r5��Ê%c3h v�m!�3g h%r%Ë£�Öc8m � c3y�{!s n�b£b%s dJn
e~s!��r�k�i���r,d�g5l�r¹l�r,eqs%}%r5�§yJl�s%eÍn�b r¹d�g5e�r({!g5d�g*��mE��g5htr �
g h ��Ê*s%i n�v8szyJv�mE��g5h%r%Ë¡��s s m � szn�b%r5l?�~c3d�rx» Ý É ¾ � pg d|r,�¯sth¯n�bjr,c�l�g5h hjr5g*��c3hzw�{ r,b!g�}^c7s l?d1�Å��rÛg5d�d�c7w^h
n�bjrxn�b!lJr�r¹e
g�Ø?s%l��3c3hjr,d�n?s���· ð e�s ��r�k�i���r,d�n�l�g5m m%r5��c8h
� s*i^{���r5vNd|i^{^d|n�c�n�i n�c�sthjg*�od�c�n?r5dÅg5d�y�s ����s%�
d ��n�b%r
α
�3c3h%r�n?s
n�bjrxs%szm v�bjk,m�d�c�n�r ��n�b%r
β
�3c�hjrxn�s°n�b%r¹c�m^v�b%k5m�d?c�n?rj�ug5h!�
n�bjr
γ
�3c3h%r�n�s¬n�b%rxy�k�kÙd�c7n?rj�Wa�b%r�} c3lJn�i&g*�p�!c3d?g5m!m%r5g5l�g5htk�r
sty¨n�bjr
γ
��c8h%r¬i&m%s%h�g5h^h%r5g%�3c�h%w§e�g�n?k5bjr,d�s*i^l�m l�r�} c�s%i^d
r�¦�m%r5l�c7r5h k�r��
c�n�b�c3l�l?r�}%r,l�d�c�{���r¬��s%d�d�s%y�y�k�kÙl|r�w&c7s h dq�ji^l?v
c3h%w¹g5h hjr,g*�3c3h*wp� ©r
g�n�n�l�c�{ ijn?r~n�b%r����3c3h r��%r�k5l�r,g5d|r
g5h!�
β
��c�hjr�c3h k5lJr5g5d�ri&mtszh�g hjh r5g*��c8h*wªn�sÃn�btrßc�e
mjl?s*} r5�
g%�3c;w�h e~r5h%n�s y¡n�b%r¢bjk5m�k5l�� dJn�gt�N�3c7n?r ��v�g5¦^c3d��!c3l|r�k�n�c�s%h^d
�
c�n�b�n�bjr¢d�i {^d�n�l�g5n?r£d?i!l�yJg�k�r¢hjszl�e�g*�?�(À c�hjk�r�szi!l�Ñ��
{^r5g5e mjl?s%m^g�w^g�n�r,d�m!g5l?g%����r �¬n?sÐn�b!c�d�d�g5e�r� c3l�r�k�n�c7s h«�
��· ð e~sj��r�k�i«��r,d¬s%l�c/r5hjn?r5�m%r,l�m r5h �!c7k�i«��g5l�n?s�n�bjr�d�i^l?v
yJg5k�r°h s%l�e
g*�q�~c��N�qr�¦^b^c7{�c7nx{ r�n?n�r,l�g*��c7w^h!e~r5h%n�szy�n�btr,c3l
ν � e�sz�jr
n�l?g5h!d?c�n�c�szh�� c3mts^��r5d��
c7n�b�n�bjr~r ��r�k�n�l�c�k
yJc�r*���¬s%y
n�bjr����{ r,g*e��
©rqr�¦^k*��i!� rqn�l�g5m mjc3h%wxs y>��· ð e�s!��r�k�iE��r5d�c3h�n�l�c3m!��r,v
d?ij{^d�n�c�n�i n�c�s%h^g*�~d�c�n?r5d�{ r�k,g�i^d�r�d�i k,b£e�s ��r�k�i���r,d¬d�b%s%i��3�
r�¦�c3dJn�g*d�d���c�w&b%n����Ðb^c8h � r5lJr5�Ãl|szn�szl�d��¬Àzc3hjk�r�n�b%r£l?s*n�g5v
n�c�s h g*�pk�s h d�n�g5hjnÅs%y
��· ð c3dqs%h���� ≈ µ � Æ k,e ¶ í �WdJr�} r5l?g*�l?s*n�g1n�c7s h g%����r�} r*��d¡�qsziE���¯{ r�m%s m%i��3g�n?r5��g5n¡n�b%r�n?r5e~v
m r5l?g�n�i&l|r,dfr,e�m!��s%�zr5�xc�h�n�bjr,d|r�r�¦&m%r5l�c�e~r5h n�d��%©r¨d|r�rqh s
r�}^c8�%r,hjk�r�c3h�n�b r�d�m%r�k�n�l?g�y�s%l¬n�b%r�r�} r5h!���¢d�m g�k�r5�g�{^v
d?s%l�m%n�c�s%h¿��c8h r5d�r�¦^m%r�k�n�r,��y�s l�l|szn�g�n�c�s%h^g*��n�l�g5h^d�c�n�c�s%h^d
yJl?s%e®dJijk,b���r�} r*�3d��o©r¹hjs n?r¡n�b g1n
s%i^l�l|r,d�i���n�d��js¤hjs n
g�{�dJs!��ijn?r*���Ðr�¦^k*��i!� r£n�b%r�mtszd�d?c�{!c���c�n?�Ðs y�n�l?g*m m c3hzwÎszy
��· ð e~sj��r�k�iE��r5dÐc3h d�c3h*w���r5vNd|i {&d|n�c�n�i n�c�szh!g*�Ûd�c�n�r,d,�§Ñ?h
g5h!g*��s*w �¢n�s�n�bjr�g5lJw i^e�r5h n¹e�g5�%r§m l|r�}!c�s i^d����¢y�s l¬n�btr
�js i {«��r5v�dJi {�dJn�c�n?i n�c�szh!g*�Wd�c�n�r,d,�^s h%r~k5g h�k�s h%k�r5c�}%r~s ypn��~s
n?� mjr,d�sty¬l�r*��g�¦ r5��d�c�htw&��r5vNd�i {^d�n�c/n�i^n�c7sthjg%�Ùd�c�n?r5d�c3hb k5m
��� ð �
b!c7k,b��^c8yJy�r,l�c�h�n�bjrxs l�c�r,hjn�g�n�c�szhºszyqn�b%rxn�l�g5m m r5�
��· ð e�s ��r�k�i���r
��c/n�b¹l�r,d�m r�k�n�n?sxn�b r�b k5m���v�g5¦^c8d��
·
hjr(yJc3h!g*��mjszc8h%n
s%yqk�sze�m g l�c3dJs h�c8dqn�bjr(g�{�dJs l?mtn�c�s h
�3c3h%r��
c3�%n�b^d�r�¦�m%r�k�n?r5�xy�s%lpn�b%rÅd�c3htw&��r5v3} d1�z� s*i^{E��r5vNd|i^{!dJn�c8v
n?ijn�c�s h g*�"n�l�g5m m c3htw�d?c�n�r,d,�oÑÚh�n�b rxyJc8l�d|n~k5g5dJrj�W{ s%n�b�r5h �!d
s y«n�b%r ��· ð e�s ��r�k�i���rÅ�qs%i��3��r�¦^mjr,l�c�r,htk�r~dJn�l�szhtw�l�r5m%i��3v
d�c7} rªc�hjn?r5l?g1k�n�c/s h d �~c�n�b n�bjrªhtr,g5l�r5dJn�v�hjr,c7w^b%{!szl���� ðe�s ��r�k�i���r5d��ud|i w%w r5d?n�c�h%w�n�b%r¡��c8¸%r �3c3b%s%s%��szyqd|n�l�szhtw°k�szi!v
m!�3c3htw¤{!r�n��qr�r5h�n�b r���· ð ν � g5dJ�^e�e~r�n�l�c7k,gt��d�n�l|r�n�k,b!c�h%w
e�sz�jr¤g5h ��n�btr(��� ð d�s �3c3�u��Ó�s l�n�btr¤�js i {«��r,v�dJi {�dJn�c�n?i!v
n�c�szh!g*�¨d�c7n?rj��r5d�m%r�k,c3g*�����Ûc8y�n�bjr°k�r,htn?r5l�s y�e~g d�d�s y�n�btr
��· ð e�s ��r�k�i���r¹c3d�dJn�l�s%h%w�������s*k,g*�3c���r5��h%r5g l¨n�bjrxk�r,hjn?r5l
s y�n�b r�n�l?g5m!m c3hzwºd�c7n?rj�Wn�b%rxr5h �!dqszy�n�btr���· ð eqs!��r�k�i���rd�b%s%i��3��r�¦!m r5l?c�r5h%k�r¤e�i k5b��qr,g*¸%r5lxg�n?n�l?g1k�n�c/}jr°c3h%n�r,l�g�k5v
n�c�szh!d��
c�n�b�n�bjszd�ro��� ð hjr,g5l�r5dJn�v�hjr,c�w&b%{jstl�dog*�3c7w^hjr,���
c�n�bn�bjr°e�s ��r�k�i��3g l�g1¦^c3d���Ñ|h�n�b^c�d�k5g5d�r �"�År¡�~s%i�����r�¦&mtr�k�n
} r5lJ���~r5g5¸�k�szi!m!��c8h*w�sty�n�b%r
ν� eqs �%r��
c7n�bÛn�bjrx��� ðd�s �3c3�«��g5h^��k�s%l�l|r,d�m%s%h^�jc3h%w����¹h g5l�lJs%�Ãg�{&d|stl�m%n�c�sth¤��c�hjr,d,�
�
��� ��� '�.��1.
� ��,J� � $ ��(0*9'�.
� � ,-'��
© r¹n?i^l�h�yJc3h g*������n?s�n�b%r¡szl�c7w^c3h d�s y�n�b%r°hti&eqr5l�s i�d
�~r5g5¸%r5l�g5{^d|stl�m n�c7sth�y�r5g�n?i^l�r5d�c3h�n�b%r���· ð Ï � � ð d�m%r�k5v
n�l�gj��Ò���n�c3e~g1n?r*���«�^dJi!k�k�r5d?d�y�i���Ì%i^g*h%n�c�n�g�n�c�}zr~e�s �%r �3c3h*w¬szy
n�bjr5dJr~y�r,g�n�i^l�r,d"d�b%s%i��3��� c�r*����n�b%rq{ r5d�noc3h d�c7w^b%n�doc3hjn?s�n�btr
��· ð n�l�g5m m c3htw(d?c�n�r~dJn�l�i k�n?i!l?r5d"g5h^����c7{�l?g�n�c�sthjg*�E�t�^h g5e�v
c�k5d��^g5df�~r ���&g*dpn�b%r~eqs lJr�w r,htr,l�g*����r5d�d|s h dp��rÅbjszm%rq�~c����
bjr �3m�i^d~c3htn?r5l�mjlJr�n~n�b%r¬d?mjr�k�n�l�g�szy���g5l|w r5l~h%s h v�l?s*n�g1n�c�h%w
�jszm g*h%nÙd|�^dJn�r,e�d��p�"nÙmjl?r5dJr5hjn5�ubjs ��r�}%r5l5���~r¬k,g5hºszhE���
s yJy�r,l�s%i^l�Ìji^g*�3c�n�g�n�c�}%r°d�m%r�k�i��3g5n�c7sthjdxc3h�n�btr°y�s l?e s%y
g
�3c3dJn�szy�b%�^mts n�bjr5dJr5d�n?s�{^r�r�¦�g5e
c�hjr,�¡c3h¬n�btrÙy�i n�i^l�r �
a�bjr°d�g5e~r°e�i���n�c3m&��r�n�l�g5m^m c8h*w¢d?c�n�r°g5l|wti!e~r5h n�i!d?r5�
g�{!s } r£n?sÃr�¦^m!�3g c�hÜn�b%r
α
�
β
�(g5h �
γ
m%r5g5¸^d�k5g5hÃ{jr
r�¦^n�r,h �jr5��n�s¢c3h%k*��i��%r�d�sze�r�s l¹g*���~sty�n�b%r�mtr,g*¸ d�sz{!v
d�r,l|} r5��c3h�n�b%r(Ç*È Æ È«� ½ n�s°Ç*È Æ%½ k5e ¶ í l?r�w^c�szh�c3h�g5d�v��%r5v
m%s d?c�n?r5� ��· ð Ï���� ð d�g5e
m!��r5d5��ÑÚh�m!�3g5k�r
s%y��%s%i {E��r5vNd�i {!v
d�n�c7n?i!n�c7s h gt�&d�c�n?r5d"c3hxb%k5mxg*h �xy�k�k~lJr�w&c7s h dp��r¨d|i {�dJn�c�n?i n�r
n�bjrxk�szhjk�r,m%n�d~s%y~b%k5m v|��c3¸tr(g hj��y�k�k,v|��c�¸jrxn�l?g5m!m c3h*w�d�c�n?r5d
�!c�d�k�i^d�dJr5�°g�{jsz}%rj�WÑJh¹k�szhjn�l�g5d�n�n?s�n�b%r0��� ô Ï � � ð k,g*dJrj�y�s l¿�¨b!c�k5b �qr y�s*i&h � hjs d|i k5b �!c�d?n�c3h%k�n�c�s%h���y�s l
��· ð Ï���� ð d|i^{ n���r¹�!c3yJy�r5lJr5h k�r,d�c�h�yJc3h!g*��l?r*�3g�¦ r,��n�l�g5mjv
m c3htw d�c�n?rÃd�n�l|i k�n?i�lJr5d�%i^rÐn�sÍh%s h vNhjr5g5lJr5d?n�vNhtr,c7w^bj{ s l
c3h%n�r,l�g�k�n�c�s%h^d�e�c7w^b%nÙc8h � ijk�r�n�bjr ∼ ´�µ�� �jc3yJy�r,l|r,hjk�r,d�c3h
w^g d�v3n�stv�e~g1n�l?c�¦ßd?b!c3y�n�d°l|r,Ì%i�c�l�r,�¯n?sg�k�k�s%i^h%n�y�szl¡n�bjr,d|r
e�c3h%s lÐm r5g5¸ d1�§a�b%rÍc3l?l�r�}%r,l�d?c�{���r�k5b!g5h%w r5d�s%{^d�r5lJ} r5�
i^mjszh¬g5h!h%r,g*�3c3htwx�~s iE����n�bti&dfk�s l�l?r5d?mtsthj�xn�s
n�b r~� c8d�g5mjv
m%r5g l�g5h k�r¬szy~d�sze�r¬szyqn�b%r5d?r¹eqr�n�g*dJn�g�{���rxn�l�g5mjm^c�htw§d?c�n�r
d�n�l|i k�n�i&l|r,d1�~aWbjr£��s1w^c�k,g*��r�¦^n�lJr5e~r�s%y¬n�b c8d°e�s �%r ���
c3h
�
b c�k,b�r,g�k5b£g h ��r�}jr,l|���c8h%r�k�s%l�lJr5d�mtszh!� d�n?s�n�b%r�g�{!v
d�szl�m%n�c�szh�s y
��· ð e�s ��r�k�i«��r5d~c�h�g¬m g l|n�c�k�i��3g5lqn�l�g5m m!c�h%w
* � * ð � � , -
íÖâ 5?â 6?ç�7tâ 5�6�â 69:«æ�;,ã>=�;5ê/ç ? @�êNï�ð�ñ5ñ�ñ ï B,ì?ðEDzï 7 ä<F5ì&4EG<H?ñ 3�4��
d�c�n?rj�tl�g5c3dJr5dfn�bjrÅc3h%n�r,l�r5dJn�c3h%wxhjs n�c�sth�s y�c3h bjsze�s*w r,h%r5c�n�c�r,d
g d~�!c�d?k5lJr�n?rj�Wk�s%i^hjn�g�{���rxr5h n�c7n�c�r5d × k5b g*�N��r5h%w^c3h*w�n�bjrxn�l?g5v
�^c�n�c7sthjg%��Ê k�szhjn�c3hti s%i^d�˧�%r5m!c/k�n�c�sthÛsty�c8h b s%e~s1w^r5h%r�s%i^d
{&l|stg5�tr,h!c3h*w��
a�b%rÜr�¦jn�l�r,e�rÎ�!c���i n�c�s%h s y£s i^lÐd�g5e
m!��r5d��qr5c7w^b^d
g�w^g5c3h d�n~g�n?n�l�c�{ i n�c8h*w¤n�b%r��~r5g5¸�y�r,g�n�i^l�r,dqc3h¡n�bjrxÇ*È Æ È«� ½n?s°Ç*È Æ ½ k,e ¶ í l|r�w�c/s h�n?s���szhtw^vNl�g h*w r°c�hjn?r5l?g1k�n�c/s h d�{jr,v
n?�~r�r,h ��· ð e�s!��r�k�i���r5d����~c/{�l?g�n�c�s h g*�¤d�b^c8y�n�d��%ijr�n?s
l?r5dJs h g*h%n�c3h%n�r,l�g�k�n�c�s%h^d�{jr�n��~r�r5h ��· ð eqs!��r�k�iE��r5d��^c7r
styJy���c�n�bÜc3h%k5l�r,g5d�c3h%wÎd�r5m g5l�g�n�c�s%hÎg5d�� −
� » Æ Ä ¾�× n�btr,c3lg5{^d|s^��i n�r¨e�g�w^h c�n�i^� r5d"yJg*�N��{ r*��s*� ∼ µ � ´ k5e ¶ í y�szl"d?r5m g5vl�g�n�c�szh!d�w^l�r,g�n�r,l�n�b^g5h
≈
Ç µ � � �p��nxg¬k�sthtk�r5h n�l?g1n�c7s h�s%y
´ mjm e®c3h�d|s!��c3� � � ð ��n�b%r�h i!e~{ r5l¹�%r5h!d?c�n���szy ��· ðe~s!��r�k�i���r,d~c8dqszhE����Ç��/Ä
⋅ ´�µ í?' k,e ¶ � × y�szl�gxl�g5h^�tste��jc3d?v
n�l�c�{ i n�c�szh�n�b%rxe�r,g5h�d�r,m g5l�g�n�c�szh�{ r�n?��r�r5h¹k*��szd�r,d|n ��· ðe~s!��r�k�i���r,d�c�d
≈
Ç µ%µ � � �¬Ó�i^l�n�b%r5l�eqs lJrj�(�%r5h s*n�c3h*wÜn�b%r
�^c3d|n�l�c7{^ijn�c�s%h szy£dJr5m^g5l�g5n�c/s h d¯{ r�n?�~r�r,h¿k*��s%d�r,d|n ��· ðe~s!��r�k�i���r,d�g5d�*
(
�
)
%��(�!n�b%r5h¬yJl?s%e n�bjr¨mjr5g5¸x} g*��i^r~hjr,g5l
�
=
Ç µ%µ � � ���
(
�
)
n�r,h!� d�n?s%�
g5l��^d���r5lJs�g5d�� ð y�s l(�tr,v
k,l�r5g5d�c�htw�d|r,m g*l?g�n�c�s h d1��a�b%i�d���}zr5l���y�r�� s%y¬n�bjr ��· ðe~s!��r�k�i���r,d��
c8����{ r¹k*��szd�r¬r,hjs i%w�b�n?s�k�s e~e�i^h^c�k,g�n�r�c8h
n�b!c3d�e
g5h!h%r5l5����h�c�h n�l?c7w i�c�h%wªe�r�k,b g*h c3d�e c3hÃ��b c�k5b
� s%m^g5h%n�dqc�hjn?r5l?g1k�n�}!c3g�n�b%r�dJn�l�g5c3h¹yJc�r*���jd�n�bjr���c�h!�%i!k�r
c8h
n�bjr¤d|i&l�l?s*i^h!� c3htw�btstd|n¹�3g5n�n�c7k�r�b!g5dx{jr�r5h�m l�szmjszd�r5��n?s
r�¦�m!�3g5c3h�d�b g5l�m�y�r5g�n?i^l�r5dxc�h£Ñ��Îg�{^d�szl�m%n�c�szh�d�m%r�k�n�l?g�s%y
À!Ó ' Ï���l�e
g�n�l�c7k�r,d�»&� µ!¾ ��ÑJh¹yJg�k�n1�^n�bjr
d�m%r�k�n�l�g�l�r,m%s%l�n?r5�
c3hÐn�bjg5n�dJn�i&�t�ß{jr,g5l�g¢m g5d�d�c3h%wÃlJr5d�r,e�{��3g5h k�r�n?ss%i^l
��· ð Ï���� ð d�m%r�k�n�l?g&���~s �~r�} r5l��^��r
yJc3h!�(c�n��^c3yJyJc7k�i���n�n?s
g5k�k�r5m%n¬n�b!g�n°dJijk,bg�e�r�k5b g hjc3d?e k�s*i����£s m%r5l?g1n?r�s*} r,l
n�bjr ∼ ´�µ%µ e�g�n�l�c�¦�b s%d?n��^c�g*eqr�n�r,l�d�c�h n�r,l|} r5h c3htw�{jr,v
n?�~r�r,h ��· ð �%s m g5hjn�d�c8h¬s i^l ´ m m eÃd�g5e�m!��r5d1�
a�b%r~e�sz�jr �3domjlJs m%s dJr5�xd�s�yJg5loc3h�n�b c8dod|r�k�n�c�s h�k,g5h hjs n
r�¦�m!�3g5c3h n�btrÃs%{^dJr5l�}zr5� ,�'+#�'�, � $ �A'�n?r5e~mjr,l�g�n?i�lJrÎ�tr,v
m r5h �jr,h%nk5b g*h*w r,d¯n?s�n�btrÎd?mjr�k�n�l�gj�§À*r�} r5l?g*��szy�n�b%r
�~r,g5¸jr5lÅy�r5g5n�i^lJr5d~g5m mjr5g5l�n�s¹szl�c7w^c3hjg�n?rxyJl�szeÜn�b r5l?e�g*�N���
m s%m%i��3g�n?r5��c3h c�n�c3g*�odJn�g5n?r5d��p·
h¡n�btr�szn�b%r5lÅb!g5h!�«��n�b%r
α′′��c3hjr�g5m!m%r,g5l�d¬n�s�szl�c�w&c�h!g�n?r§yJl|s e g�}%r5l���r,g*d?c�����n�b r5l?v
e
g*����� � r5vNmtstmti���g�n�r,�c�h!c�n�c�gt�¨d�n�g�n�r × �qr�r5dJn�c3e
g�n�r�n�b g�n
n�bjrxb r5c7w^b%n~s%y�n�b%r
α′′
mjr,g5¸��jr�k5lJr5g d|r,d
≈ ½%µ vNy�sj����i!m%s h
�
g5l�e
c�htw yJl�sze �
=
Ç�� Æ n�s Æ � � ���ÅÀ c�hjk�r�n�btr���s �~r5dJn
���^c�htw(}^c7{�l?g�n�c�s h g*�Wd�n�g�n�r~s yog¨w^g5d�v�m b!g5dJr ��· ð e~sj��r�k�iE��rc3dpn�b%r � ð { r5h!� c3h*w(e�s �%r~g�noÄ%Ä Ý k5e ¶ í �%n�b%r5d�r�n�b r5l?e�g*�N���m s%m%i��3g�n?r5�¹d�n�g�n�r,d�e~i!d?nqc�h }%s!��}%r�c3h%n�r,l�g�k�n�c�s%h^dÞ�
c�n�b�n�b%r
��� ð d?sj��c8���&g*��n�bjs itw&b��~r~k5g5h¹g5d"� r�n�szyJy�r5l�h%s¬d?m%r�k,c8yJc�k,d
g d�n�sxn�b%rx�3c7{&l�g�n�c�s h v8n�l�g5h d��3g�n�c�s%h¹�j�th!g5e�c/k5d�c8h }%s!��}%r5���
��h s*n�bjr,l�m%s d�d�c�{^c��3c/n��Îc3d�n�bjr�g�w%w^l?r�w^g�n�c�s h�szy �%� ðc3e
mti^l�c�n�c7r5d¢g5l�s i!h^�Ün�b r ��· ð eqs!��r�k�iE��r5d1�x��d?d�i^e�c3h*w
k�s e�m!��r�n?r r,Ì%i!c���c�{^l?g1n�c7s h c8h s%i^lÜs l|n�bjs^Ï~m!g5l?g k�s h v
} r,l|n?r5lq» ´�Ýj¾ g5n � = ´�½ ���zn�bjrÅl�r5d?c3�ji^g*� �*� ð k�sthtk�r5h n�l?g5vn�c�s h�c8d
≈ ´�µ%µ m m e��W��k�n?i^gt�N���«�ug d�d�i^e
c�htw§h g�n?i�l?g*��c�d�szv
n?s m c�k~g�{ i�h �!g5h%k�rj� n�bjr���� ð d|s^�3c��^d"d�b%s%i��3�(g*�3dJs�k�szhjn�g5c8h
≈
È µ%µ m m!e ��¥ e¨s^��r�k�i���r5d5��{ji n���¥ e¨s^��r�k�i���r5d¹g5lJr
c3e
e�s {!c���c���r,��c3h�n�bjr�dJs!��c8��g�n � �~r°n�r,e�m%r5l�g�n?i^l�r5d��q·
h
n�bjr�s n�bjr5l(bjg h �u��n�b r�
= ´ Ê s l|n�bjs^Ë�r�¦^k5c7n�g5n�c7sthjd¹g5lJr
e�s {�c3��rq{^�xg�m l�s k�r,d�d"¸^h%s%�~h¬g5d�Ê%Ìji^g5h n�i^e��!c3yJy�i^d�c�s h�ËE�
c��;r � �&n�b r�k�s%h }%r5l�d?c�s%h¹s%y�g �*Ø�g�k�r,hjn �t� ð ¼ ��� ð m!g5c3l?d�c3h n�s��� ð ¼ �t� ð mjg5c3l?d�»JÄ%É!� Ý È«� � ´ � �%Ç ¾ ����hj��
= ´ r�¦ k5c�n�g�n�c�s hn�b!g�n�� c3yJy�i!d?r5d�c3h%n�s�n�b%r�} c�k5c3h c�n���s y¹g�n�l�g5m mjr,� ��· ðe�s ��r�k�i���rx��sziE���Û��s%k5g*��c���r¬n?s�y�s l?e g5h � � ð ¼ ��· ð m!g5c3l{ s%i^h!�¹n�s*wtr�n�btr,lq} c3g�n�bjr
r*��r�k�n�l�c�k�Ì i!g5�^l|i^m sj��r5v�Ì%i&g5�jl?i!v
m%s!��r¹�5Õ�
�
� c3hjn?r5l?g�k�n�c�s h«�> og5d�r,��s h�mjlJr�}^c�s i!d�����m i {!v
�3c3d?bjr,� ��¥xÏ��t� ð Ï���� ð g5h!� ¥ ð Ï �*� ð Ï���� ð d�m%r�k5v
n�l�g�» Æ � ½!¾ �xn�b^c�d�d�g eqrÐÕ�
�
c8h%n?r5l�g�k�n�c�szh�d�b s*i����Ü{jr
k5g5m^g�{���r®s yÃm!lJs �%i k5c3htw k�sze�m!��r�¦ y�r5g5n?i!lJr5d�s }jr,l�g
∼ ´ k5e ¶ í l�r�w^c�szh�szy¨n�b%r
��· ð d�m%r�k�n�lJi�e���ÑÚh�n�b c3d�m c�k5v
n?i!l?rj��n�btrxl?r�}%r,l�d�c�{���r�n?r5e
m%r5l�g�n?i^l�rx�%r5m%r5h^�tr,hjn~d?m%r�k�n�l�g*�
k5b^g5h*w!r,d¬k�s%i��3�£{^r�g�n?n�l�c�{ i!n?r5�£n?sg�{^d�szl�m%n�c�szh!d¹c3h%}js �3v
}^c�htw±�!c3yJy�r5lJr5h n�Ê*szl�c�r5h%n�g�n�c�s h g*�JË�dJn�g�n�r,d�s y�n�b%r �*� ðe�s ��r�k�i���r5d��Wl�g�n�bjr,l�n�b^g5h�n�b%r¬��c�{^l�g�n�c�s%h^v8n�l�g5h^dÖ��g1n�c7s h°�j� v
h!g5e
c7k5d�s ypn�b r!��· ð e~sj��r�k�i���r,d,�
�~c7} r,h�n�btr m!lJr5d�r,h%n��^g�n�gj�Ù��r¢k5g5hÃs%h����Ãh%s%n?rc3h
m g*d?d�c�h%w n�b!g�nn�bjrÃ�~r5g5¸®y�r,g�n�i^l�r,dc8h n�b%r�Ç5È Æ ½ n�s
Ç*È Æ ��k,e ¶ í l|r�w^c�s h£d?bjs �
h£c3h¯ÓEc�wp��È��
b c�k5bÛwjl|s%� c3h
i^mjszh£g5h^htr,gt��c�htw d?bjs �®{E��i!r,v�d?b!c�y�n�d¬l�r �3g�n�c�}zr�n?s�n�b r �
g5h!���§mtr,g*¸ d�k�s%h^d�c3d�n?r5h%n¬�¨c�n�b�k ��i^d�n?r5l?c3htw�s y�g�d?e�g*���
yJl�g�k�n�c�szh�s yÞn�bjr���· ð eqs!��r�k�iE��r5dqn?s�y�szl�e ��· ð �!c�e~r5l�dg5h!�¬n�l�c3e~r5l?d1�
� U���[%X^_ ��]��1`�[jX�� �*X^\��|] Y?]jZ ��\«`/Z�� _1Y�`3[%X��
© rÙl�r5m%s lJn~b c7w^b�l?r5dJs!��i n�c�szhºÑ9�g�{&d|s l?m%n�c�s h°d�m%r�k�n�l�g
s y���· ð e�s ��r�k�i���r5dÅc8d?sj��g�n�r,��c3h�l�g5m c3�¡}tg*m%szlq�jr,mtszd�c�n?r5�
��� ð d�s �3c3� d1�paWbtr�g�{!d?r5h%k�rxs yqg¬l?r�w i��3g l�����d�mjg�k�r5��m l�s%v
w^l�r,d�d�c�szh�s yq�3c3h%r5d~c3dqn�g5¸ r5h�g5dqr�} c3� r5h%k�rxn�b g�n~n�btr���· ðe�s ��r�k�i���r5dÍk5g5h hjs n®lJs%n�g�n?rj�ßg5h � c8h^d|n?r5g5� r�¦&c8dJn g*d
d�n�l|sthzw&���°b c8h � r5lJr5�º��c�{!l?g5n�szl�d���a�b%r�n�b!lJr�rÙe�g5c3h¹g�{^d�s%l�mjv
n�c�szh¬y�r,g�n�i^l�r,d"g l|r~g5d�d�c7w^h r5��n�s���· ð e�s!��r�k�iE��r5dpn�l�g5m m r5�c3h¬�js i!{���r5v�dJi!{^dJn�c�n?i n�c�s h g*�Wd�c�n�r,d�c3h¬bjk,m¬g5h!�¬y�k�k
l�r�w^c�szh!d
s y~n�b r�g5d?v��jr,m%s d�c�n?r5��d�s �3c3� d1�8��i&e¨r,l�s i�d���r,g5¸%r5lxd�m%r�k5v
n�l�g*��y�r,g�n�i^l�r,d¹l�r5e
g5c8h£i^h r�¦^mE��g5c8h%r,�u���or�} r5l?d�c7{���r�n?r5e�v
m%r5l�g�n?i^l�r �jr5m%r,h!�%r5h nÜc3h%n?r5h!d?c�n�c�r,dÜ�%r5e~s%h^d|n�l�g�n?r¿n�b!g�n
d�sze�r�s y�n�bjr,d|rÐ�År5g ¸tr,l�n�l�g5h^d�c�n�c�s%h^d�szl�c�w&c�h!g�n?rßyJl�s%e
��sz�~v|���!c�htwxn�btr,l�e�g*�N���xm%s m%i��3g�n?r5�¬dJn�g�n�r,d1��À%sze�rÅs%y�n�bjrÅÇ
n?s ½ k5e ¶ í {���i r5vNd�b c8y�n?r5�¬�qr,g*¸(y�r5g�n?i�lJr5d�s*{&d|r,l�}%r5�¬i^m%s h
g5h!h%r,gt��c�htwÍs y�n�bjrÃd?g e�m���r,d£e�g��Í{ rÃ�ji rÐn?sÍd?e�g*���
����· ð �·§ k*��i^dJn�r,l�d��© r¢g l|r m l�r5m g5l�c�h%wÃn?sÐm%r5l�y�s%l�e gh r�� dJr5l�c�r,dºszy
r�¦&m%r5l?c8e~r5h%n�d¡s h���· ð Ï��u� ð d?g e�m���r,d,�¨c3htk ��i&�jc3h*w�n�btr
i^d�r®s yÜc3dJs%n?s%m c�k5g*�N��� dJi!{^dJn�c�n?ijn?r5� ��· ð e~s!��r�k�i���r,d,�
olJr5g ¸jc3h*w°n�b%rxc3h%} r5l?d�c7s h°d|�^e~e�r�n�l��(s y"n�b r0��· ð e�s ��r5vk�i���r£{ � n�l�g5m m!c�htwßn�b r íÚ' · í�ð � í�ý · c3d�s*n?s m%sze�r5l��~c����
g*��n?r5l¬n�bjr�h g5n�i^lJr�s y�n�b%r�gt�N��s �~r5�¯��c�{!l�g�n�c�szh!g*�
d�n�g�n�r,d,�
a�l�g5m m c3htw w^l�g �%i^gt�N��� c�hjk5lJr5g d?c8h*w k�s h%k�r,hjn�l�g5n�c7s h d�szy
��· ð e~s!��r�k�i���r,d�d�b%s%i��3��m r5l?e�c�n�n�bjr°c�� r5h%n�c3yJc�k5g�n�c�s%h�szy
d�m%r�k�n�l?g%��y�r,g�n�i^l�r,d��%i^r�n�s¤�jc3e~r5l?d�g h ���3g lÚwtr5l�k ��i^dJn�r,l�d,�
Â�g5h!c�m iE��g�n�c3h*wÍn�btrßl�r,d�c3�ji^g*� �t� ð k�s%h k�r,htn�l�g�n�c�s%h�{ �
}^g5l|�^c�h%w n�b%r s%l�n�b%s�Ï~m g5l�g k�s%h }%r5l?n�r,lÁn�r,e�m r5l?g�n�i&l|r
d�b%s%i��3��k �3g5l�c�y��§n�b r�c3e
mtszl�n�g5hjk�r¡sty �%� ð ¼ ��· ð k*��i&d|n?r5vl�c�h%w��
2
3�4<D í�â 5�â 6�ç87^â 596�â 6�:«æ<;5ã>=-;5ê�ç�?A@�êJï?ð�ñ�ñ�ñ%ïCB�ì?ðED ï�7%ä�F�ì&4�G�H?ñ
©r¹r�¦�m%r�k�nxn�b g�n(Ìti^g5h n�i^e®d�c�e~iE��g1n�c7s h�n?r�k,bjh^c�Ìji r,d
�
c����
{ r�}zr5l��¢} g*��i&g�{E��r�c3h£r ��i k5c3� g1n�c�h%wn�btr�n�l�g5m^mjc3h*w
d�c�n?rÍd�n�l|i k�n�i&l|r,d�g5h^� ��c�{^l�g�n�c�s%h^g*�¢�j� h^g5e�c7k,dÐs y¯n�b%r
��· ð Ï���� ð dJ�^d|n?r5e¬��g5d¬�%r,e�s h d�n�l�g�n?r5�¢m l�r�} c�s i�d�����y�stl
· ð �jszmjr5�¹b%� �^l|s*wtr5h¹d�s �3c3� d�»��5È ¼ �%Ä ¾ �
�Å_�� X�[���� �1\���� �1X Y��
©r�n�bjg5h^¸¯n�b%r�g�i!n�b%s l?d¡s y
�pr5yJd5� ½%Ý g5h ��Ä ½ y�stl
g �%}^g5htk�r�k�s%m^c7r5dqs y�n�bjr5c3lqe
g5hji^d�k,l�c3m%n�d5��©r�n�b^g5hj¸�n�b%r
l?r5y�r5lJr�rxy�szlqm%s c�h n�c3h*w°s*i n~g�d?r5l?c�s i�d�r5l�l|s l�c3h¬s%i^l�s%l�c�w&c�v
h^g*�W�jc3d�k�i^d�d�c�szh�s y�n�bjrqn?r5e
mtr,l�g�n?i!l?r~�jr,mtr,h �jr5h%k�r�szyfn�b%r
α′′
mtr,g5¸«�
íä�ó\äE���·ë�Ô�ë�Ù`Õ�ï�ó\äE��ä!��øZÕ�ù'ï�Õtù�ß~�"ä!���ZÕ�ï �¿¸q»·£¥²¿¶�©��·² ¹�©¬`¬ ä)
,ï5�1ð�ütí �ý����ä
ð,ä5��ä%�«�ZÕ�ï ´�§·§·¡�²Ç¶�©��·²'�¿¸�»�£¥²�Ê�¸©�� ä��
�Âï¯ð�� ��üí � ���1��ä�,äo��ä�����ÕZï#µ¿¤ ��²��⤠���·²q
¯©��� �ä�
,ï�í|��ôbü�í ����'�� ' ¹��·É�
ǩ �� ²
��¸�»·£ ä� � Çï ��')üí � �Ö',�+(�ä
ô,ä��)ä #�ä�õyãt×�Ö��ì'ï^�#ä�Ò"ä^� ã�Ù`Ùtïj�¿ä��,ä^:Çì�ã�Ù�òtï���ä��Çø·Õù·úÇï ��ä�ó Ú�Ó
Ô/Ú·ò`ã·ï¯Õtù�ß���ä%����ÕZï
� ²�Ê�¸©���²,��¸�»·£ ä��J0
�,ï,ô·ô�',í#ütí � ��'���ä�,ä���ä��¯øZÕ�ùZú�ï«��ä���äW:½ì·ãtÙ`ò�ï�ó\äf��äf�'ø�Õtù�ï��"ä/ó�ÚÔ/Ú�òªã·ïp��ä/Ò�ä� ãtÙ`Ùtï��)äp#�ä�õyãt×�Ö;�qì'ï�Õ�ùZß¹�"ä"����ÕZï �¿¸�»�£¥²#¶�© � ä�!"��.,ï�ð,í�ý
üí � �·ý���ä'�ä5��ä�ó Ú�Ô/Úò`ã·ï � ²�Ê�¸© ��²'�¿¸�»�£�ä��?0�+,ï�î�' ����üí ���·î���ä
î�ä���ä�ó�ÚÔ/Úò`ã·ï/ó\ä�ó{Ö �,Öûï��"ä"õyÕ?��Õtê�Õ�ìZÕ�ò`ø,Öûï��"ä���øZÖèß·Õ,ï�ó\äf�¿ä��ø�Õtù�ï���ä��Çä �Çã�ã·ï�Õ�ùZß��"ä��«�ZÕ�ï � ²�Ê�¸©���²��"¸�»Z£ä��J0�+�ï�î·îñ·î
üí � �Zî���ä
ý,ä^�"ä�ó�ÚÔ�Ú1ò`ã·ï��)ä��"Õtöªò`ë��,Öûï&��ä&� Ú�òªøÂÖ ù�ÕZï$#�ä���Úú·Úò`ø,Öûï^��ä�õTÕtÓ��Õtê�Õ�ìZÕ�ò`ø,Öûï,Õtù�ß��"ä,��ø,Ö ß�ÕZï
� ²�Ê�¸©���²¯��¸�»·£ ä��J0�+�ï�î1îZí�î)ütí � �Zî��ä
�,äp�"ä ó�ÚÔ/Úò`ã\Õtù�ß���äo�1ø,Ö ßZÕ�ï�¾�¡Â¢¦¢�²�Ê�¸©���²)³,�«t² � §,ä"+
��ï�í
üí � �·ý���ä
ítñ�äz�)ä%�/Úò`ø,Ö ùZÕ�ï �"ä,õyÕ��·Õê·Õ�ìqÕò`ø�Ö`ï*��ä�ó�Ú1Ô�Úò`ã·ïÇÕtù�ß��"ä ��ø�Ö�ß·Õ,ï
� ²
Ê�¸1© ��²Ç�"¸�»Z£ä%�
�Ú0Çï���îtð1ý�üí � � �1�tä
í·íä'å/ä%��öûã�Ö ù�ø·ÚZÜûÜkïz�#ä%&�ä%��ä'å�ä*$�á�áZÕ�Ù`ÕtÚÇï'��äÇõlä�é�ã�Ùªú·ëZòªÚ�ù�ï%��ä(#�ä
å�Õ�Ú�ï :�ä!#�ä�õ
Ö�ù1ùZãJ�/Ö�ò`ò`ã�Ù�ï�Õtù�ßró\ä�õ�Ö�ù·ù�ãJ��Öèò`ò`ã�Ùtﯴ� Z ¢¦²*)" �¬�ä6
,ï 'Ö�qî1î)ütí � �����ä
í�ð,ä'å/ä%��öûã�Ö ù�ø·ÚZÜûÜkïz�#ä%&�ä%��ä'å�ä*$�á�áZÕ�Ù`ÕtÚÇï'��äÇõlä�é�ã�Ùªú·ëZòªÚ�ù�ï%��ä(#�ä
å�Õ�Ú�ï�:"ä�#�ä�õ�Ö ùZù�ãJ��Ö ò`òªãtÙtï�Õtù�ßXó\ä�õ
Ö ù�ùZãJ�/Ö ò`ò`ã�Ùï�Ê�®·§�² � ²
��¸�»·£ ä*+ Çï�íí�ðð�üí � ��ô1��ä
íJ�,ä ó\ä�ó�ã�ù�ú·ãt×`ïq:�äÅ#�ä õ
Ö�ù1ùZãJ�/Ö�ò`ò`ã�Ù�ï�Õù·ß ó\ä)õ�Ö�ù·ù�ãJ��Öèò`ò`ã�Ùtï
��¸�»·£¥²'¶�©�� ä�!"�
�,ï�í�ñôðZñ�ü�í ���·î��tä
í�ô,ä�ónä/ó�ã�ù·ú·ãt×kï�:�ä�#�ä�õ�Ö ùZù1ã?��Ö òªò`ã�Ùtï�Õtù�ß
ónä"õ
Öèù·ù�ãJ��Ö�òªò`ã�Ùtï � ²
+T�¢�²Ç³, Z©�«¬ � ä%��.�.Çï,ðð�í�ütí � �1ý��ä
íJ�,ä,�¿�ª�«�©�©tÀ�¤û§�Á�£��-,�¬ ¸©/.⤠Á�¸�È¿§1©t��ÁZ» ¨ ©�§�£�¤`¬è»0+\®,¬`¬�©t�*12.�È�¨�+43
Ê��·§�¬ �ª®·«¬���û£65{Ê��§-,�©t�ª©�§«�©�¸·©t¢èÀ�Æ�ÏtÎ�ÍÂÑ7+\®» ÆûË·Ë·Ãl¤û§7+T��§68
¬�©�`©k» ï�� $/ï�ó\ä å/ä�:�ãtÙªÔ�Õ�ùfükã�ß'ä��tï:9)ä ��äE$¿Ö Ù�é,Ú·Ù`æ�ã���ÜûÜûÖ�æ�ã�Ú·Ü��ætÖ ã�ù·ö�Ö�ÜûÖ�æ/å�ã�ò`ãtÕ�Ù`æ�ø'ï1$�Ù�×¦Ö ùZú1ö`Úù'ï(&�$�üí ��� �5�tä
í?'�äâónä)Ò�ä)é,Õ�Ý`ÕtÙ`ß�Ú�Õ�ù1ߤ��äf��ÕÔ)ï;� ² Ê�¸©���²��¿¸�»�£ ä��Ú0�.Âï#ô·ð��Zî
üí � �·ý���ä
ítî�äW�Çä���ÕtÔ Õù·ß
ó\ä�Ò"ä�éÇÕ�Ý`ÕÙ`ß�ÚÂï ¶�© ��²/³�«t¤¦²�<�§�£�¬ �`¡ � ä«+?0Çï�í �ð�'
üí � ������ä
í�ý,ä�#�äq�¿ä��·Ú·ë1ãtÙ`òtï .�»ZÀ'�ª��Á,©t§i�¿�ª�� Z©��Þ¬ ¤�©Þ£=,k���nµ�¡£¥¤¦��§iÈ¿§1©t��ÁZ» ï
9#ùZÖ�çÇäZÚ·ÜE��Õ�צÖ�Ü�Ú1Ù`ùÂÖ Õ"#�Ùªã�ò`òtï :�ã�Ù3��ãt×�ãkì�ü�í �·ý�'��ä
í �,ä�ó\ä,Ò"ä,éÇÕ�Ý`ÕÙ`ßZÚ,ï
� ²�Ê�¸q©���²¯��¸�»·£ ä�>�.Çï�íítñ)ütí � �����ä
ðZñ�ä ó\ä Ò"ä�éÇÕ�Ý`ÕÙ`ß�ÚÂïq�Çä��ÇÕtÔ)ï��"ä ��ä��ÇøZÚÔ/á�ò`Úù'ï Õtù�ß ónä�Ò�ä��ÚÙkß·Ú·ù·ù,Ö ãtÙtï½Ê�¸© ��²Ç�"¸�»Z£ä%��.�>Çï5����í�ütí � �1ô��ä
ð�íä���ä���ÕÔ)ï�ónä�ó�Õ�ætצã�Ùtï"Õtù�ß
ónä�Ò ä�é,Õ�Ý`ÕtÙ`ß�Ú,ï�� ²�Ê�¸q©���² ��¸�»·£ ä
�?0�)�ï¯ý ����� ü�í ���·î��ä
ð·ð,ä&��äj��ÕtÔ)ï"ó\ä"Ò�ä"éÇÕ�Ý`Õ�Ù�ß·ÚÇï&��ä^�"Õ�ö`ò`ë��ÂÖûï��)ä!�/Úò`ø,Ö ùZÕ�ï^�"ä�õTÕtÓ��Õtê�Õ�ìZÕ�ò`ø,Öûï�Õtù�ß§��ä ó Ú�Ô/Úò`ã�ï?� ²VÊ�¸©���² �¿¸�»�£ ä@�J0�.,ï ô·ð��Zî
üí � �·ý���ä
ð��,ä���ä,#ÇÕëZ×ûÖ ù�úÂïÂ�¿¸»1£¥²Ç¶�©��¯ä56�)�ï�ô��·ñ)üí ���Zñ���ä
ð·ô,ä�$/ä�é�ä���ã�ç·ÚùZò`ø�Ö�Ù`ã·ï �¿�ª�«t²#¶���»Â²�³���«t²�1t¹���§ÀÇ��§(3BA � ��6�ïp'ñ,í
ü�í ����'���ä
ð��,ä,õwä,��ä�é�×èì·ú·ÕtÙkã·ï
� ²�Ê�¸©���²¯��¸�»·£ ä566>�ï¯ð�ð�'?� ü�í ��'��5�ä
ð�'�ä��)ä/é�ä���Ö ù�ú\Õtù�ßC��ä/é�ä��/ÚÙ`ù,Ö ú�ï � ²�Ê�¸q©���²��¿¸�»�£�äD�6��ï"ô��ðZñ
ü�í ��'�'���ä
ðZî�ä�å/ä"Ò"ä�ó÷Ö�×�×�ã�Ù)Õtù�ßE��ä���ä*�/ã�ætÖ ëZò�ï � ²�Ê�¸© ��²��¿¸�»�£�ä"�
>,ï"ô·ý·î,í
ü�í �Zî��5��ä
ð·ý,ä��)ä)éÇÙ�Ö ã�ßZÔ/Õ�ùZùXÕ�ùZß���äo��Ö�Ô/ãt×`ï�� ²÷Ê�¸©���²���¸�»·£ ä?��6Âï"���ð��
ü�í ��'��5��ä
ð��,ä�ónä%��ä :�Ú���ã�Ù`òtï"F�ä �ä �"ã�Ùk×�ã�ì�ï�Õ�ùZß�õlä%�)ä�é�× ìZú·Õ�Ù`ãZï(� ² Ê�¸·© ��²
�¿¸»1£�ä��6��ï���� ��� ü�í ��'�'��tä�Zñ�ä��)ä)éÇÙ�Ö ã�ßZÔ/Õ�ùZùXÕ�ùZß���äo��Ö�Ô/ãt×`ï�� ²÷Ê�¸©���²���¸�»·£ ä?��+Zï"���ý��
ü�í ��'î���ä��íä��)ä"é,Ù�Ö ã�ßZÔ/Õ�ùZù�ï!$�ä���ø·Õ·×�ÚÔ)ï�Õ�ùZßx�Çä���Ö Ô/ãt×kï%� ²#Ê�¸©���²¿�¿¸»1£ ä
��0,ï,ðô���')üí ��' ����ä�·ð,ä #�ä��)ä�ó Õù·ù�øZãtÖ Ô)ï �¿¸q»·£¥²'¶�©�� ä�!"�,ï�îô�� ü�í �Zî�ð5��ä���,ä #�ä��)ä�ó Õù·ù�øZãtÖ Ô)ï
� ²¿Ê�¸© ��²Ç�"¸�»Z£ ä���)Âï�ítññ�')ütí �qîqð��ä�·ô,ä(�,ä�ó Õ�ù
G·ï � ²�´ ��²�Ê�¸©���²Ç³���«·ä��J0
,ï�í�ý·ñ,í#ütí �ýZñ���ä���,ä�ó\ä $"×�×èÕtç·ã�ù·Õ,ïz��ä ��ø·Õ��·ÙkÚëZùÇï�Õtù�ßH�)äÇõTø,Ö ö`ã·ï(� ²"Ê�¸q© ��²½�¿¸»1£ ä+�+�ï�í�î��·î)üí �ý·ð���ä��'�ä �)ä5� Ú�ù�Ú�Õtù�ß���ä �)ä ��Ö ù'ï
� ²�Ê�¸©���²,��¸�»·£ ä +�.�ï,ð�'·ñî)üí �·ý��5��ä�Zî�ä� �ä ��äDF"ÕtÙIG�ÚùnÕù·ßTÒ�ä&:�×�ÕÖ ò`ö`ã�ù�Ó�:�ÕtÙ`ÚqÝ�Õ�òtï�� ²/Ê�¸q©���²¿� ¸�»·£ ä!.�6�ï
ô��,í·í�ütí ��ý����ä�·ý,ä�ónä�Ò"ä,éÇÕ�Ý`Õ�Ù�ß·ÚÇï,��ä���ÕtÔ)ï,Õ�ùZß��"ä,ó�ÚÔ/Úò`ãZï�ë�ùZá�ë·ê,×�Ö�òªø·ãtß�ä���,ä�+T�¢�©�«�¡,¢�®·�y³� ©�«¬ �ª��£�«��� 1»�JK+\�À,©��k§i¶�©k£�©�®Z�ª«t¸ML"��¢è¡ �"©N<2<-<Zï��ä(#�ä,å�Õ�Ú�ükã�ß'ä��tï5$�æ�Õ�ßZã�Ô�ÖèæW#�Ù`ã�òªòtï(#�ãJ�O��Ú·Ù3��üí �·ý��5��ä
ôZñ�ä�F�ä�F"ë·ã×�Õtæ�ø�çZÖ�×ûÖÇÕtù�ßÅ�#ä(#�ä�å�ÕÚ,ï(.)®q§�º�����)�P,D<�§-,¥�ª®Z�ª©�À{³�¬�®·§1À�8
®Z�`À�£ ï5$�æ�Õ�ßZã�Ô�ÖèæW#�Ù`ã�òªòtï(#�ãJ�O��Ú·Ù3��üí �·ý��5��ä
ô�íä*F�ä;F�ëZãt×èÕæ�øZçZÖ�צÖ"ã�ö�Õ·×`ä�ï ³¯ Z©�«¬ �ª��«t¸1¤ ��¤�«�® ´"«¬�®{��®Z��¬�A �� Çï¿î�ítî
ü�í ����'���ä
ô·ð,ä)ó\ä"$�ä�õyÕ�×�òªø'ï"�"äo�)ä)Ò�ù�ú·×¦Õtù�ß�ï"�¿ä)å�äQ��ì��·ã�ï Õ�ùZß�:�ä��,ä�/Ú���ÕÙ`ß�ï�Ê�¸1© ��²'�¿¸�»�£¥²Ç¹�©·¬`¬kä%�-�� Çï,ð�'���ütí ��ý�î��ä
ô��,ä�å/ä�Ò�úú·ã�ù�êZã�Ùªú·ã�Ù�ï �Çä"F"ã�Ù`ê�ã�Ù�ï�Õ�ùZß
��ä �/ë·ê�ã�Ù�ï +\�·¢�²��¿¸»1£ ä +- �ï
ô�����üí � �ÂíÖ��ä
ô·ô,äD��ä��,×�Õ�ùÂÖ ù�ÕZï���äR�¯ä���Ö Ôâï�Õ�ùZß���ä"éÇÚ��'ï L�¤�º·�ª®,¬ ¤è�·§®Z¢"³¯ Z©t«¬û�`�Þ£S8
«��t 1»0�Âï¯ð��,í�üí � ���1��ä
ô��,ä���ä,ó\ä(#^��ë·Ô/Õ·×�Ú,ï5�"ä�$�äÇé�ÚÙ`ß�ï,Õ�ùZß�$/ä(�Âät��Ú���ï
� ²'+ �¢�²�³�¬ �`¡1«¬ ²
1Ö
Ǹ·©��«t¸© ��²T3�6�0Ö+¯ï�í�����ütí � �1ô��ä
ô�'�ä�óVä��¯ä�õTãtÖ ß�ÕZïR�¯ä�óVä^�1áZã�Ùkø·Õæ·ï�Õ�ùZß=��ä��ÂäR#�ã�ò`ê,Ö ö`ötï � ²�Ê�¸·© ��²
�¿¸»1£ ä��J0�6,ï�î�'ý���üí � ������ä
ôZî�ä�ó\ä(��ä�õyãtÖ ßZÕ�Õtù�ßH��ä��,ä�#�ã�òªêÂÖ ö`ö�ï�� ² Ê�¸© ��²��¿¸�»Z£ äR�?06��ï�í�ñð,ítñ
ü�í ����'���ä
ô·ý,ä"�,ä�$�ä«:�ÕÙ`ùZã�ò)Õ�ùZß��"ä"Ò"ä*F"ÚëZú·øÇï � ²�Ê�¸© ��²��¿¸�»�£�ä!.�),ï�'·ñ�í�ð
ü�í �·ý·î���ä
ô��,ä�F/ä�Ò"ä�Ò*��Öèù·ú\Õtù�ßU�)ä!�"ä���øZã�ù�ú,ï � ²��¿¸�»Z£¥²#Ê�¸©���ä">
,ï"ôZñ�'��
ü�í �·ýý5��ä�Zñ�ä�õlä�Ò�ä!��òªêZã�Ù`ú�Õ�ùZß@�)ä�é�ä%�/ÚÙ�ùZÖèú,ï�� ²�Ê�¸© ��²��"¸�»Z£ ä% �0,ï"íJ�ô��
ü�í ���ð5��ä��íä�:�ä/Ò"ä�õTÚÚß
Õ�ùZß4��ä�$�ä/å�Úë���ï"� ²�)" �¬ ²/³Ç��«t²¿´�� ä�+- �ï�î�ðZñ
ü�í �·ýð5��ä�·ð,ä�ónä�éÇÕ�×��'ï
� ²�Ê�¸©���²,��¸�»·£ ä5.�)�ï5��'·ñ�ütí �ýZî���ä���,ä�óVä%$�äE��ç·æ�ø,Ö ùZù,Ö �ZÚç{Õ�ùZß���ä%$�ä�õ�Ö�úøZö�ï � ²�Ê�¸©���²���¸�»·£�ä$>6>�ï���·îô�ütí � �����ä�·ô,ä L"¤ûº�`®,¬û¤��§®Z¢�³, �©t«¬ �ª��£�«��� ·»T�-,�
��ª® · ,©�À�³, Z©�«t¤�©�£ ï&��ä�Ò�ä��/Õ�×èÓ
×�ÕÔXü�ã�ß�ä;�ï�õ
Ö�×èãkì'ï��¯Ú·ù·ß�Ú�ù÷ütí �·î�����ä���,ä;�)ä õlä�:�Õ�צ×�ï*��ä��)ä«�"շܦÕ�ÜûÖûï ��ä�éÇÙ`ã�ß,Ö ù'ï�å/ä«�)ä��/Õ�ëZú·ã·ï Õ�ù1ß
�¯ä ��ä�ó�Õ�Ù`ú·Ù`Õ�ç·ãZï�´u¾¿¤¦º·¢�¤è�tÁ,�`® ,¸�» �-,�+T®�¬ �k¤WVE<�£��·¢ ®,¬ ¤¦�§{³� ,©�«28
¬ �`��£�«��Þ ·»%J"ƪËqÅ1Ä�Î ÆûËZÃÅ ï,å"Ö ætã:9 ä5#ÇÙ�ã�ò`ò�ï �/ÚëZòªö Ú1ù�ï5��Xiü�í �ý·ý���ä��'�ä��)äÇõlä!��æ�ø�ò`ù�ã�Ùtï��)ä�õwä :�Õ·×�×`ï�Õ�ùZß@��ä%�)ä �"ÕÜ�ÕÜûÖ`ï*$f¾¿¤¦º·¢�¤è��Á�8
�`® ,¸�»
�P,?+T®�¬ �k¤YVZ<t£��¢�®,¬ ¤è�·§n³� ©�«¬ �ª��£�«��� 1»�J�Æ`˷÷ÅÎ"ÆûË·Ë,Ï ïD9 ä �Çä
#�Õtç·Õ·×�å�ã�ò`ã�ÕtÙ`æ�ø��,Õê·Ú·Ù`Õ�ö`ÚÙûì'ï,õyÕtò`ø,Ö ù�ú·öûÚ·ù�ï%�"�yü�í ���ý5�ä�Zî�ä ónä/&"ã�ö`ö`ã�Ùtïf$�äp#�äp:�Ù`Ú·ßìZÕ�ùZò8�ÂÖûï#Õtù�ß°�)ä*�Âä[��Úß,×`ï;� ²#�¿¸»1£¥²
Ê�¸©��#ä A �J0
�,ï5��' �ý ü�ðZññ·ñ��ä�·ý,ä ��ä�éÇÙ`ãtß�Ö�ù�ï :�ä�#�ãt×�Õù·ß�ã�Ù�ïÇÕtù�ßEF ä�å"Ö ê�ê·ãtúÕÙ`ß�ï � ²R+\�q¢¦²�³� ,©�«¬ ��ä
��6,ï,ô,ítñ)üí �Zî�ô5�tä
* � * ð � � , -
íÖâ 5?â 6?ç�7tâ 5�6�â 69:«æ�;,ã>=�;5ê/ç ? @�êNï�ð�ñ5ñ�ñ ï B,ì?ðEDzï 7 ä<F5ì&4EG<H?ñ 3�4(\
���,ä�å/ä*F¿ë1Õ�òªö�Öªï"& ä���æ�øZã�öªö�Öèù·Ú�ï�Õù·ßZ#/ä&:�Ù�Ö ú·Úötï Ê�¸©���²"�"¸�»Z£ ä^6
�Âï���,í#ü�í �·îý��ä'·ñ�ä ��ä�ó\äR#^��ë·Ô/Õq×èÚ�Õtù�ß
��ä $/ä�éÇÚÙ`ß'ï�� ²"+T�¢�² ³, Z©�«¬ � ä 6
Ö+¯ï�íkô��
üí � �·ô���ä',íä���ä ��ú1Õ?��Õ�Ù�Õ�ï%$�ä :�Ù`ëZù1ãtÕtë�ïÇÕ�ù1ß~��ä ��Ö Ô�ë�Ù`Õ�ï ´ §q®Z¢�² Ê�¸©�� ä )�)Âï
ô����·ô ü�í ���ô5�tä'ð,ä�Ò"äW� ùZÚ6G�Ö�ù·ú1ã�Ù Õ�ùZß¹#"ä�:�ãtÖ ætø·ã�Ù`ötï � ²#�¿¸�»�£¥²�Ê�¸©��#ä;>6>�ï�ô��·ñ�'
üí � ������ä'��,ä�ó\ä���ä ûÙkçZÖ ùZã#Õ�ù1ßÅ$/ä��)ä'Ò äz#�ë�× ×¦Ö ù'ï ´�¡£�¬ ² � ² Ê�¸©�� ä 66��ï�í ��',í
üí �ý·ð���ä'ô,ä ó\ä[�Âä �Ù`çZÖ�ù1ã\Õ�ù1ß°$�ä��)ä�Ò"äp#�ë�× ×¦Ö ù'ï#³� ©�«¬û�`�«t¸·¤ ��¤¦«�®n´�«¬�®
��6 A ï5',íí#ü�í �ýZî���ä'��,ä�ó\ä�é¯ëZò`ø,Ö ö`Õ�ùÂÖûï��"ä���ø,Ö ßZÕ�ï���ä�ó Ú�Ô/Úò`ã�ï"Õtù�ßTó\ä�å�Õò`Õtù�ã�ù'ï � ²
��¸�»·£¥²¿Ê�¸©�� ä A �?06��ï5��'���� ü�ð·ñ·ññ��ä'�'�ä�ó\ä,Ò"ä,éÇÕ�Ý`ÕÙ`ßZÚ#Õ�ù1ßÅ�Çä5��Õ�Ôâï¯ëZù�á·ë�êÂ×¦Ö ò`øZã�ß�ä'·î�ä ��ä�$�ù�ß·ÙkãJ��òtï å/ä���ä�$�Ù�צÖ�ù·ú·ø�Õtë�òtï)Õ�ùZßMF�ä ��ä��·ÚøZù·òªÚ·ù�ï�� ²
Ê�¸1© ��²Ç�"¸�»Z£ ä,+Ö.Âï*'?����� ü�í ��ý����ä'ý,ä"#�ä"éÇÚ�ë�Ù`Õ�ö�Öûï�:"ä���Ö�צçZÖûï�Õù·ßE��ä&#�ä�#Çã�Ù`æ�ø·ÕÙ`ß�ï � ²�Ê�¸1© ��² ��¸�»·£�ä.��·ï,ô�î?��î)ütí �ý·ô��ä' �,ä$ �ä�é�ä �ZÖ¦×�ç·ã�ÙªÕÂï1¶/© �Z²�+T�tÀ�²¯�¿¸»1£�ä��6 �ï�������üí �ýZñ���ä
î·ñ�ä ��ä%��Ö ö`öûã×`ï <�§�¬ �ª��À,¡�«¬ ¤è�q§ ¬���³���¢¦¤¦À{³�¬�®�¬�©#�¿¸�»�£¥¤è«k£ Ð1¬ ¸�È"À�¤ª¬ ¤��·§ ï
õ�Ö�×�ãkì�ï(#�ãJ�N�"ÚÙN��üí �1ýÖ',�tä
î,íä��Âä�&�Õtù°� Ù`Õtù�ã�ù�ßZÚù��fÕtù�ß¹�)äp#"ä�F�ë�ò`ø�ï �¿¸�»�£¥²�¹�©1¬`¬ ä��·ï/ð·ð
üí ��'ð���ä
îð,ä���ä�&"Õtù~�"Ù`Õù·ã�ù·ß�Ú�ù���Õtù�ßEF�ä%�"ÕtÙ�×`ﯶ�© ��²R+ ��À'²½�¿¸�»�£�ä%��0�ï*����í
üí ��'ý���ä
î��,ä"��ä�&�Õtùx� Ù�Õ�ùZã�ù�ß·Ú·ù���ï"³Ç��¢�¤¦À7.�»,À��`��ÁZ©§
Jp
Ǹ·©��·��»T�2,�¬ ¸·© �¿�ª� 8
,©t��¬û¤�©k£n� ,n³,�q¢¦¤�À � � ° ���)ï#Õ�ù1ß � � ï�#�×�ã�ù�ëZÔÃ#ÇÙ�ã�òªòtï�#�ãJ�
�"ÚÙ���ü�í �·ý��5�tä
îô,ä�F/ä"õlä«��Ú·×�×ûÖ ù�òtï�õlä�F/ä 9#ùZÖèö ã�òtï"Ò"ä"å/ä"ó�Õtá�Ú·×�ãtò�ï�Õ�ùZß��"ä�#�ä:�ã�Ù`ù�Õtö�ï��¿¸�»�£¥²¯¶�© �Çä(!D��6Çï'í�ñtð ü�í � ��'��ä
î��,äQF/ä���Õù�ï ó\ä��"Õ�ùZúÇï?��ä?X�Ö ãZïD� ² Ê�¸©���²#�¿¸»1£ äQ�J0
>,ï�í�ñðý·ô
ü�í ���ý5��ä
î�'�ä"�,ä�:"ä�$�ù·ß�ã�Ù�ò`Úù�ï«��ä^$/ä!��Ù`Õ�ìZù�ÚÙtï"Õ�ùZßx:"ä�órä«:�Ú·úøZÚò�ÖèÕtù�ï�� ²
Ê�¸©���²,��¸�»·£ä�>6>�ï5�ô�� ütí � ������ä
î·î�ä�õlä�å/ä�å�Úß���ãt×û×/Õù·ß F ä«��æ�Úq×èãtòtï � ²���¸�»·£¥²�Ê�¸© ��ä«.�)�ï�ítñ����
ü�í �·ýð5��ä
îý,ä�ó\ä*��ä/õTãtÖèß·Õ,ï*��ä�ó\äp�·á�ã�Ùkø·Õæ·ï��)ä*��ä*#�ã�ò`ê,Ö ö`ötï/Õtù�ßN�,ä�ó\ä�/ëZöªò`Úù'ï6� ²�Ê�¸q©���²¯�¿¸q»·£ äR�Ú0��qï¯ý����Âí#ü�í � �1ô��ä
î �,ä!$�ä�:�ä!�/ÕtÙkÙ�Ö òtï!$/ä���ä^:�ã�Ù�×ûÖ ù�ò3�ì'ï�Õtù�ßnõlä$#�ä^� ÕtÙkßì'ï�Ê�®Z§·² � ²
�¿¸»1£ ä��6��ï�í·íkýZñ�ü�í �Zîî��tä
ýZñ�ä �)ä��/Õ·×�×èÕtÔ/Õò`ãJ��ï Ò�äq:�Õ�ê��·Õ,ï)Õù·ß Ò�äq�"ù�Ú�G�Ö ù�ú·ã�Ùtï � ² +\��¢¦²
³�¬ �ª¡·«¬ ä���0�. � ��0
>Âï�í�ð���üí � �qî,�tä
ý�íä ��ä� Þä%$�Ô/ò`ö`ë�öIG�ï��,ä�å�ä%�ÇøZÚÔ/á�ò`Úù'ïÇÕù·ß~�)ä�ó ã�ì·ãtÙtï ��¸�»·£¥²�¶�©6�·²
¹�©·¬`¬ ä� ��qï�í·í�î���ütí �Ö'qý��ä
ý·ð,ä�å�ä�� ìZÕtÙIGkë�ù{Õù·ß ��ä�&"Õù
�"Ù`Õ�ùZã�ù�ß�Ú�ù���ï �¿¸�»�£¥²�¶�© ��²�¹�©·¬ª¬ ä� �)�ï'ô�')üí ��îZíÖ��ä
ý��,ä*$�ä�&�ä%�/Õ�ùÂÖ�×èì·ætø·ã�ç�ï�&�ä'Ò�ä%:�Úù�ßìZê�ãkì'ï%&�ä1$�ä*$�á��ZÕ�Ù�Ö�Õ�ù'ï ��ä1�'Õ�Ó
ùZÕ��ZÕ�ïz�)ä%�"ÕÞÝ�Ö øZÕ�Ù�Õ�ï�Õ�ùZßq��äz� Ú�ß�ÕZï � ² Ê�¸© ��²½�¿¸q»·£�ä$�J0�6,ï�ô·ð �·ð
ü�í �����5��ä
ý·ô,ä�ó\ä���ö`ã�Ù�צÖ�ù·ú�ï���ä ��Öûï/Õ�ù1ßO&�ä $/ä�$�á��ZÕ�Ù�Ö�Õ�ù'ï"� ² Ê�¸©���² �¿¸»1£ ä
�?0�6�ï���'î ��üí �����5�tä
ý��,ä���ä ��Öûï�&�ä $/ä*$�á��·ÕÙ�Ö Õtù�ï�Õtù�ß ��ä :"ä � ÕtÙ`ß,Ö ùZúÇï � ² Ê�¸1© ��²½�¿¸»1£�ä
�?0�)�ï �·ôð�üí � �Zî���ä
ý�'�ä0��ä ��Ö�Õ�ùZß &�ä"$�ä�$�á���ÕtÙ�Ö Õtù�ï�� ²÷Ê�¸©���²�� ¸�»·£ ä �J0�+�ï{íJ�ô·ô
ü�í ���·î���ä
2
3�4 3 í�â 5�â 6�ç87^â 596�â 6�:«æ<;5ã>=-;5ê�ç�?A@�êJï?ð�ñ�ñ�ñ%ïCB�ì?ðED ï�7%ä�F�ì&4�G�H?ñ
|
| id | nasplib_isofts_kiev_ua-123456789-129213 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T15:16:57Z |
| publishDate | 2000 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Tam, Simon Fajardo, Mario E. 2018-01-16T20:01:13Z 2018-01-16T20:01:13Z 2000 Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen / Simon Tam, Mario E. Fajardo // Физика низких температур. — 2000. — Т. 26, № 9-10. — С. 889-898. — Бібліогр.: 86 назв. — англ. 0132-6414 PACS: 07.20.Mc, 61.72.Ww, 67.80.-s, 78.30.-j, 81.10.Bk, 81.30.Kf https://nasplib.isofts.kiev.ua/handle/123456789/129213 We report the observation of high resolution (0.008 cm⁻¹) infrared absorption spectra of CO₂ molecules isolated in solid parahydrogen(pH₂) matrices at T=2.4 to 4.8 K. Several extremely sharp (0.01 to 0.04 cm⁻¹ full-width-at-half-maximum) absorption features appear in the 2343.5 to 2345 cm⁻¹ region. We assign the three strongest peaks to the v3 mode of isolated CO₂ molecules. The spectra are consistent with trapping of the CO₂ molecules in three distinct double-substitutional sites in hcp and fcc regions of the pH₂ solid. We offer several hypotheses as to the origins of the numerous weaker absorption features. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Low-Temperature Physics and Chemistry in Cryomatrice Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen Article published earlier |
| spellingShingle | Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen Tam, Simon Fajardo, Mario E. Low-Temperature Physics and Chemistry in Cryomatrice |
| title | Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen |
| title_full | Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen |
| title_fullStr | Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen |
| title_full_unstemmed | Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen |
| title_short | Observation of the high resolution infrared absorption spectrum of CO₂ molecules isolated in solid parahydrogen |
| title_sort | observation of the high resolution infrared absorption spectrum of co₂ molecules isolated in solid parahydrogen |
| topic | Low-Temperature Physics and Chemistry in Cryomatrice |
| topic_facet | Low-Temperature Physics and Chemistry in Cryomatrice |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/129213 |
| work_keys_str_mv | AT tamsimon observationofthehighresolutioninfraredabsorptionspectrumofco2moleculesisolatedinsolidparahydrogen AT fajardomarioe observationofthehighresolutioninfraredabsorptionspectrumofco2moleculesisolatedinsolidparahydrogen |