l?i|@h) l* u) ? @ 6 ?@?u @* h t t hi* 4 ?@hc) l44i?|t i*`ul4ilchrist/... · i l4mih .c 2fff...
TRANSCRIPT
�L?i|@h) �L*�U) �? @ 6�?@?U�@* �h�t�t�
�hi*�4�?@h)c �L44i?|t i*UL4i
w@�hi?Ui a� ��h�t|�@?L| ��h�t|LT�ih B�t|} aLh}i +L*_Lt{
�L�i4Mih .c 2fff�
Devwudfw
Zh prgho d �qdqfldo fulvlv dv d wlph zkhq froodwhudo frqvwudlqwv duh elqglqj1 Zh
dvn zkhwkhu d fxw lq wkh grphvwlf lqwhuhvw udwh zloo/ xqghu vxfk flufxpvwdqfhv/ fdxvh
dq h{sdqvlrq ru d uhfhvvlrq1 Zh ghvfuleh prgho hfrqrplhv wkdw fdq udwlrqdol}h hlwkhu
ylhz1 Wkh gl�huhqfh ehwzhhq wkhp kdv wr gr zlwk �h{lelolw| lq surgxfwlrq1 Li wkhuh
duh vxevwdqwldo vxevwlwxwlrq srvvlelolwlhv dprqj idfwruv ri surgxfwlrq/ dqg glplqlvklqj
uhwxuqv wr vfdoh duh qrw wrr juhdw/ wkhq dq lqwhuhvw udwh fxw zloo surgxfh dq h{sdqvlrq1
Li wkhuh duh vxevwdqwldo lq�h{lelolwlhv lq wkh hfrqrp|/ wkhq dq lqwhuhvw udwh fxw zloo
surgxfh d uhfhvvlrq1
�Zh duh judwhixo iru dgylfh dqg frpphqwv iurp Shwhu Fodun dqg Dqg| Qhxph|hu1 Wkh �uvw dxwkrudfnqrzohgjhv vxssruw iurp d judqw wr wkh Qdwlrqdo Exuhdx ri Hfrqrplf Uhvhdufk iurp wkh Qdwlrqdo VflhqfhIrxqgdwlrq1 Wkh dxwkruv duh judwhixo iru wkh vxssruw ri wkh Lqwhuqdwlrqdo Prqhwdu| Ixqg lq wkh suhsdudwlrqri wklv pdqxvfulsw1 Krzhyhu/ wkh rslqlrqv vwdwhg khuh duh wkrvh ri wkh dxwkruv/ dqg gr qrw uh�hfw wkh ylhzvri wkh Lqwhuqdwlrqdo Prqhwdu| Ixqg/ ru wkh Ihghudo Uhvhuyh Erdug ri Jryhuqruv1
|Qruwkzhvwhuq Xqlyhuvlw|}Ihghudo Uhvhuyh Erdug ri Jryhuqruv1{Lqwhuqdwlrqdo Prqhwdu| Ixqg1
�� W?|hL_�U|�L?
W? hiUi?| )i@ht |�ihi �@t Mii? UL?t�_ih@M*i UL?|hL�iht) L�ih |�i @TThLTh�@|i 4L?i|@h) TL*�U)
�? |�i @u|ih4@|� Lu @ �?@?U�@* Uh�t�t� 5L4i @h}�i |�@| |�i Ui?|h@* M@?! t�L�*_ h@�ti _L4it|�U
�?|ihit| h@|it |L _iui?_ |�i U�hhi?U) @?_ �@*| |�i ��}�| Lu U@T�|@*� �|�iht @h}�i |�@| �?|ihit|
h@|i hi_�U|�L?t @hi U@**i_ uLh� A�i) ?L|i |�@| @ UL�?|h) |�@| �@t ��t| i Tih�i?Ui_ @ �?@?U�@*
Uh�t�t �t |)T�U@**) t*�_�?} �?|L @ t|iiT hiUitt�L?� A�i) @TTi@* |L |�i ��_itThi@_ ��i� |�@|
�? _i�i*LTi_ iUL?L4�it *�!i |�i N5c Ui?|h@* M@?!t |)T�U@**) hitTL?_ |L t�|�@|�L?t *�!i |��t
M) hi_�U�?} �?|ihit| h@|it� A�iti @�|�Lht �h}i |�i t@4i 4i_�U�?i uLh i4ih}�?} 4@h!i|
iUL?L4�it �? |�i �@!i Lu @ �?@?U�@* Uh�t�t� A�i) @h}�i |�@| |L h@�ti �?|ihit| h@|it @| t�U� @
|�4i �t @ 4�t|@!ic @?_ �t *�!i*) |L 4@!i @ M@_ t�|�@|�L? i�i? �Lhti� �?i i TLt�|Lh Lu |��t
��i�c �@�* kh�}4@? E�bbbc TT��f���fD�c T�|t �| |��t �@)G
R��| ��i? �?@?U�@* _�t@t|ih t|h�U! �t�@c |�i TL*�U�it |�Lti UL�?|h�it uL**L�i_ �? hitTL?ti
�ihi @*4Lt| i @U|*) |�i hi�ihti Lu ��@| |�i N?�|i_ 5|@|it _Lit �? |�i u@Ui Lu @ t*�4T�
6�tU@* @�t|ih�|) �@t |�i Lh_ih Lu |�i _@)( �?|ihit| h@|it �ihi �?Uhi@ti_c Lu|i? |L T�?�|��i
*i�i*t����`�) _�_ |�iti i |hi4i*) U*i�ih 4i? @_�LU@|i TL*�U�it uLh i4ih}�?} 4@h!i|
iUL?L4�it |�@| �L�*_ �@�i Mii? hi}@h_i_ @t UL4T*i|i*) Tih�ihti �u @TT*�i_ @| �L4iq�
i _itUh�Mi @ uh@4i�Lh! |�@| @**L�t �t |L @h|�U�*@|i |�i |�L ��i�t ��t| _itUh�Mi_� A�i
uh@4i�Lh! �@t |�L u�?_@4i?|@* M��*_�?} M*LU!t� 6�ht|c �i @tt�4i |�@| |L U@hh) L�| ThL_�U�
|�L?c �h4t hi^��hi _L4it|�U �Lh!�?} U@T�|@* |L ��hi *@MLh @?_ �?|ih?@|�L?@* �Lh!�?} U@T�|@*
|L T�hU�@ti @? �4TLh|i_ �?|ih4i_�@|i �?T�|� 5iUL?_c �i @_LT| |�i @tti| 4@h!i| uh�U|�L?t
uLh4@*�3i_ �? |�i *�4�|i_ T@h|�U�T@|�L? 4L_i* @t @?@*)3i_ �? w�U@t E�bbf�c 6�iht| E�bb2�
@?_ ��h�t|�@?L @?_ ,�U�i?M@�4 E�bb2c �bbD�� A�i *�4�|i_ T@h|�U�T@|�L? @tt�4T|�L? �@t
|�i UL?ti^�i?Ui |�@| @? i T@?t�L?@h) 4L?i|@h) @U|�L? 4@!it |�i _L4it|�U M@?!�?} t)t|i4
hi*@|��i*) *�^��_ @?_ �?_�Uit �h4t |L ��hi 4Lhi *@MLh� AL |�i i |i?| |�@| |�i �4TLh|i_ �?�
|ih4i_�@|i �?T�| UL4T*i4i?|t *@MLhc |�i �?|ihit| h@|i _hLT *i@_t |L |�i �?Uhi@ti_ �ti Lu |��t
u@U|Lh |LL� A��t �t �? |�i tT�h�| Lu |�i |h@_�|�L?@* *�^��_�|) U�@??i* i4T�@t�3i_ �? |�i U*Lti_
iUL?L4) *�|ih@|�hic ���U� t|hittit |�i TLt�|��i igiU|t Lu @? �?|ihit| h@|i U�| L? L�|T�|�
W? L�h LTi? iUL?L4)c @? �?|ihit| h@|i U�| 4@) @*tL *i@_ |L @ hi@* i U�@?}i h@|i _iThiU�@�
|�L?� N?_ih ?Lh4@* UL?_�|�L?tc |��t _Lit ?L| 4�|�}@|i |�i TLt�|��i L�|T�| igiU|t @ttLU�@|i_
��|� |�i |h@_�|�L?@* *�^��_�|) U�@??i*� OL�i�ihc _�h�?} @ Uh�t�t |�i hi@* i U�@?}i h@|i _i�
ThiU�@|�L? 4@) *i@_ |L �ih) _�gihi?| igiU|t �? L�h 4L_i*�
i 4L_i* @ Uh�t�t @t @ |�4i ��i? �?|ih?@|�L?@* *L@?t 4�t| Mi UL**@|ih@*�3i_ M) T�)t�U@*
@tti|t t�U� @t *@?_ @?_ U@T�|@*c @?_ |�@| |��t hit|h�U|�L? �t M�?_�?}� i t�TTLti |�@| �?_ih
?Lh4@* UL?_�|�L?tc UL**@|ih@* UL?t|h@�?|t i�|�ih _L ?L| i �t| Lh @hi ?L| M�?_�?}� A��t U@?
LUU�hc uLh i @4T*ic MiU@�ti L�|T�| �? @__�|�L? |L *@?_ @?_ U@T�|@* �t @UUiT|@M*i @t UL**@|ih@*
2
�? t�U� |�4it� �*|ih?@|��i*)c @ Uh�t�t 4@) Mi @ |�4i ��i? |�i uh@U|�L? Lu _L4it|�U @tti|t
@UUiT|i_ @t UL**@|ih@* M) uLhi�}?iht _iU*�?it� W? @?) U@tic u@U|Lht |�@| U@�ti |�i UL**@|ih@*
UL?t|h@�?| |L MiUL4i M�?_�?} @hi |hi@|i_ @t i L}i?L�t �? L�h @?@*)t�t�
W? |�i 4L_i* uh@4i�Lh! �i @_LT|c |�i 4L?i|@h) |h@?t4�tt�L? 4iU�@?�t4 U@? Mi �ih)
_�gihi?| _�h�?} @ Uh�t�tc @?_ |�i uL**L��?} tUi?@h�L �t TLtt�M*i� `�i? |�i Ui?|h@* M@?!
i?}�?iiht @ u@** �? |�i _L4it|�U h@|i Lu �?|ihit|c |�i hit�*|�?} hi@* _iThiU�@|�L? *i@_t |L @
hi_�U|�L? �? |�i �@*�i Ei Thitti_ �? �?�|t Lu |h@_i@M*i }LL_t� Lu _L4it|�U UL**@|ih@*�3@M*i
@tti|t� `�i? UL**@|ih@* UL?t|h@�?|t @hi @*hi@_) M�?_�?}c |��t ThL_�Uit @ u�h|�ih hi_�U|�L?
�? |�i t�TT*) Lu �?|ih?@|�L?@* Uhi_�| ?ii_i_ |L t�t|@�? �4TLh|t Lu |�i �?|ih4i_�@|i }LL_�
B��i? @ t��U�i?| *@U! Lu t�Mt|�|�|@M�*�|) Mi|�ii? |�i �4TLh|i_ }LL_ @?_ _L4it|�U u@U|Lht Lu
ThL_�U|�L?c |�i u@** �? �4TLh|t U@? i @UihM@|i |�i u@** �? L�|T�| @ttLU�@|i_ ��|� |�i �?@?U�@*
Uh�t�t� i _�tT*@) @ 4L_i* ���U� @h|�U�*@|it |��t hiUitt�L? ��i� @ML�| @? �?|ihit| h@|i U�|�
�*|�L�}� |�i tUi?@h�L ��t| _itUh�Mi_ �t @ TLtt�M�*�|)c |�i LTTLt�|i U@? LUU�h |LL� W?
T@h|�U�*@hc @? �?|ihit| h@|i U�| 4@) *i@_ |L @? i T@?t�L? �? L�|T�| @?_ �? �4TLh|t Lu |�i
�?|ih4i_�@|i }LL_t� A��t U@? �@TTi? �u |�i �?|ihit| h@|i U�| ThL_�Uit @ hi*@ @|�L? Lu UL**@|�
ih@* UL?t|h@�?|t M) h@�t�?} @tti| �@*�it� A�ihi �t @ �@h�i|) Lu U�@??i*t |�hL�}� ���U� |��t U@?
LUU�h �? |�i 4L_i*� �tti| �@*�it 4@) h�ti MiU@�ti |�i 4@h}�?@* T�)t�U@* ThL_�U| Lu U@T�|@*
�?Uhi@tit ��|� �?Uhi@ti_ �|�*�3@|�L? Lu �@h�@M*i u@U|Lht Lu ThL_�U|�L?� A�i) 4@) h�ti �u |�i
hi@* �?|ihit| h@|i �ti_ |L _�tUL�?| u�|�hi �?UL4i �L�t uhL4 @tti|t u@**t ��|� |�i _L4it|�U h@|i
Lu �?|ihit|� 6�?@**)c @tti| �@*�it 4@) @*tL h�ti �u |�i t�@_L� �@*�i Lu U@T�|@* �? hi*@ �?} |�i
UL**@|ih@* UL?t|h@�?| �?Uhi@tit� i _�tT*@) @ tiUL?_ 4L_i* ���U� @h|�U�*@|it |��t i T@?t�L?
��i� @ML�| @? �?|ihit| h@|i U�|�
i �ti |�i |�L 4L_i*t ��t| _itUh�Mi_ |L �i*T �t �_i?|�u) |�i ui@|�hit Lu |�i i?��hL?4i?|
|�@| @hi !i) |L _i|ih4�?�?} ��i|�ih @? �?|ihit| h@|i U�| ��** Mi i T@?t�L?@h) Lh UL?|h@U�
|�L?@h) �? |�i @u|ih4@|� Lu @ �?@?U�@* Uh�t�t Lh Uhi_�| Uh�?U��
A�i Lh}@?�3@|�L? Lu |�i T@Tih �t @t uL**L�t� A�i �ht| tiU|�L? Thiti?|t @? i4T�h�U@*
_�tU�tt�L? Lu UL**@|ih@* UL?t|h@�?|t� A�i tiUL?_ tiU|�L? Thiti?|t L�h }i?ih@* 4L_i*� A�i |��h_
tiU|�L? Thiti?|t @ �iht�L? Lu |�i 4L_i* t�4T*��i_ M) |�i @tt�4T|�L? |�@| |�i U�hhi?| @UUL�?|
�t �i*_ �_i?|�U@**) i^�@* |L 3ihL� V@h�L�t �iht�L?t Lu |��t 4L_i* U@? Mi t|�_�i_ @?@*)|�U@**)c
@?_ �i i T*L�| |��t |L }@�? �?t�}�|t �?|L |�i ?@|�hi Lu |�i 4L?i|@h) |h@?t4�tt�L? 4iU�@?�t4
�? |�i Thiti?Ui Lu @ M�?_�?} UL**@|ih@* UL?t|h@�?|� A�i uL�h|� tiU|�L? i |i?_t |�i @?@*)t�t M)
@**L��?} |�i U�hhi?| @UUL�?| |L Mi i?_L}i?L�t� A�i �?@* tiU|�L? UL?U*�_it�
�
2� �L**@|ih@* �L?t|h@�?|t @?_ +i*@|i_ w�|ih@|�hi
A�i @tt�4T|�L? |�@| |�i *@?_ @?_ U@T�|@* Lu |�i �h4 �t UL**@|ih@* uLh �?|ih?@|�L?@* *L@?t
T*@)t @? �4TLh|@?| hL*i �? L�h @?@*)t�t� A��t tiU|�L? Thiti?|t @ Mh�iu _�tU�tt�L? Lu �L�
�i �?|ihThi| |��t @tt�4T|�L?� i hiUL}?�3i |�i i?uLhUi4i?| ThLM*i4t @?_ L|�ih �?@?U�@*
4@h!i| �4TihuiU|�L?t |�@| @hi Tih�@t��i �? i4ih}�?} 4@h!i|t �i?Ui _L ?L| hit|h�U| L�hti*�it
|L @ ?@hhL� E*i}@* Lh UL?|h@U|�@*� ��i� Lu UL**@|ih@*� +@|�ihc �i tii UL**@|ih@* UL?t|h@�?|t @t
U@T|�h�?} |�i |�}�|i?�?} Lu Uhi_�| UL?_�|�L?t @?_ @ttLU�@|i_ M@*@?Ui t�ii| ThLM*i4t tii? �?
|�i @u|ih4@|� Lu @ �?@?U�@* Uh�t�t� A�i) _L ?L| ��t| hi�iU| |�i �?t�t|i?Ui M) Uhi_�|Lht |�@|
UL**@|ih@* Mi �h�||i? i T*�U�|*) �?|L *L@? UL?|h@U|tc M�| @*tL |�i TLtt�M�*�|) |�@| hi}�*@|Lht
�?_�Ui M@?!t |L �?�it| L?*) �? �tiU�hi< *L@?tc *L@?t |L UL4T@?�it |�@| �@�i @4T*i @tti|t �?
|�i i�i?| |�@| |��?}t }L �hL?}� i ?L� Mh�i�) ThL��_i tL4i i4T�h�U@* i��_i?Ui L? |�i �ti
Lu UL**@|ih@* �? *L@? 4@h!i|t�
A�i �ti Lu UL**@|ih@* �? *L@? 4@h!i|t �t ��_itThi@_� �ih}ih @?_ N_i** E�bbf� _LU�4i?|
|�@| @hL�?_ .f TihUi?| Lu UL44ihU�@* @?_ �?_�t|h�@* *L@?t �? |�i N5 @hi tiU�hi_ @?_ �*@U!c
#i �i3@ @?_ aighi)t hiTLh| t�4�*@h i��_i?Ui uLh |�i Nk� W? i4ih}�?} 4@h!i|tc Bi*Lt @?_
ih?ih E�bbb� hiTLh| |�@| @hL�?_ Sf TihUi?| Lu *L@?t @hi UL**@|ih@*�3i_ �? �i �ULc ���*i
t�h�i) i��_i?Ui uhL4 |�i �@?! Lu A�@�*@?_ T�| |�i �}�hi @| 4Lhi |�@? Hf TihUi?| uLh |�@|
UL�?|h)� � hi��i� Lu �?@?U�@* UL?_�|�L?t Lu |�i �t�@? Uh�tit UL�?|h�it EW�6 �bbb� ?L|it |�@|
*i?_�?} @}@�?t| UL**@|ih@* �@t @ ��_itThi@_ Th@U|�Ui @*tL �? |�iti UL�?|h�it�
A�ihi �t @*tL @4T*i i��_i?Ui |�@| UL**@|ih@* Th@U|�Uit @hi ThLU)U*�U@*� �ti@ @?_ �*L4Mih}
E�bbH� ThL��_i i��_i?Ui |�@| M@?! *i?_�?} t|@?_@h_t �@h) L�ih |�i N5 M�t�?itt U)U*iG �? @?
@�ih@}i UL?|h@U|�L?c |�i _i}hii Lu *L@? UL**@|ih@*�3@|�L? @?_ tThi@_t U�@h}i_ L�ih Ahi@t�h�it
�?Uhi@ti L�ih |�i )i@h MiuLhi |�i |hL�}�� W? @? �?|ihit|�?} T@Tih L? |�i hiUi?| i4ih}�?}
4@h!i| Uh�titc ,_�tL?c w�@?}@h@4 @?_ ��**ih E2fff� hiTLh| |�@| A�@� M@?!t |�@| �ti_ |L
*i?_ �T |L .f�Hf TihUi?| Lu |�i �@*�i Lu T*i_}i_ UL**@|ih@* MiuLhi |�i Uh�t�tc 4L�i_ |L *i?_
�T |L ��t| Df�Sf TihUi?| @u|ih |�i Uh�t�t� �Lhi �4TLh|@?| uLh L�h T@Tihc |�i uh@U|�L? Lu
t)?_�U@|i_ *L@?t �? �?|ih?@|�L?@* 4@h!i|t |�@| �t UL**@|ih@*�3i_ hi@U�i_ @ Ti@! E@| e2 TihUi?|
Lu |�i |L|@*( tii A@M*i �� �? |�i )i@h Lu |�i �t�@? Uh�tit� A��t �t hi�?uLhUi_ M) |�i u@U|
|�@| |�i *i�i* Lu t)?_�U@|i_ *L@?t @*tL Ti@!i_ �? �bb.c �? *�?i ��|� |�i �?_�?} �? ��@_�@
@?_ 6L*!ih|t�w@?_@� E2fff� |�@| t�}}it|t |�@| UL44ihU�@* M@?!t @TTi@h |L Mi *i?_iht Lu
RtiUL?_�|L�*@t| hitLh|��i|t
e
A@M*i �G 5)?_�U@|i_ wL@?t |L ,4ih}�?} �@h!
E�? M�**�L?t Lu N�5� _L**@ht�
vi@h AL|@* 5iU�hi_ 5iU�hi_ @t I Lu AL|@*
�bb� e.�D .�b �S�D
�bbe Se�b ���D �.�.
�bbD b��f �S�� �.��
�bbS �fe�� 22�f 2���
�bb. �e��. S��e e2�.
�bbH ..�� 2D�b ���D
�bbb .��� 2S�� �D�b
5L�hUiG �@T�|@* #@|@c wL@?�@hi
A�ihi �tc �L�i�ihc t�Mt|@?|�@* _iM@|i L? ��@| UL?t|�|�|it �?|ih?@|�L?@* UL**@|ih@*� W? @
hiUi?| T@Tihc �@M@**ihL @?_ kh�t�?@4�h|�) E�bbb� @tt�4i E?L| ��|�L�| U@�i@|t� |�@| L?*)
@ uh@U|�L? Lu |�i @tti|t �ti_ �? |�i |h@_@M*i tiU|Lh �L�*_ Mi @UUiT|i_ @t UL**@|ih@* M) uLhi�}?
Uhi_�|Lhtc ��ihi@t |�i |L|@*�|) Lu _L4it|�U @tti|t �L�*_ Mi @UUiT|i_ @t _L4it|�U UL**@|ih@*�
W?@_i^�@|i @4L�?|t Lu �?|ih?@|�L?@* UL**@|ih@* @?_ �4TihuiU| @}}hi}@|�L? Lu _L4it|�U UL**@|�
ih@* @hi t�L�? |L *i@_ |L �hi t@*it Lu _L4it|�U @tti|t @?_ �?@?U�@* Uh�tit�
W? hiUL}?�|�L? Lu |�i _��U�*|�it _i�?�?} ��@| UL?t|�|�|it �?|ih?@|�L?@* UL**@|ih@* @?_
|�i _�gihi?| �?t|�|�|�L?@* @hh@?}i4i?|t |�@| U�@h@U|ih�3i i4ih}�?} �?@?U�@* 4@h!i|tc �i
UL?t�_ih |�L @TThL@U�it |L 4L_i*�?} UL**@|ih@* UL?t|h@�?|t�
W? |�i �ht|c UL**@|ih@* �t |�i T�)t�U@* @tti|t Lu |�i MLhhL�ih� A��t �t |�i UL**@|ih@* |�@|
�L�*_ Mi �h�||i? i T*�U�|*) �?|L _iM| UL?|h@U|tc �u UL**@|ih@* �ihi �?U*�_i_ @| @**� W| �t
@*tL ��@| �L�*_ UL4uLh| hi}�*@|Lht UL?Uih?i_ @ML�| |�i h�t!�?itt Lu M@?! *L@? TLh|uL*�Lt�
N?_ih |��t tTiU��U@|�L? Lu |�i UL**@|ih@* UL?t|h@�?|c MLhhL��?} U@??L| i Uii_ |�i �@*�i Lu
|�i �?_���_�@* �h4<t @tti|t�
N?_ih @? @*|ih?@|��i 4L_i* Lu |�i UL**@|ih@* UL?t|h@�?|c �?_���_�@* �h4t �L�*_ u@Ui ?L
UL**@|ih@* UL?t|h@�?| @| @**� W?t|i@_c 4@h!i| �?|ihit| h@|it �L�*_ @_��t| �?|�* |�i @4L�?| Lu
MLhhL��?} M) �h4t 4@|U�it |�i �@*�i Lu |�i @}}hi}@|i UL**@|ih@* Lu |�i iUL?L4)� A��t �@)
Lu 4L_i*�?} |�i UL**@|ih@* UL?t|h@�?| �@t TL|i?|�@**) _�gihi?| �4T*�U@|�L?t uLh |�i igiU|t Lu
�?|ihit| h@|i U�|t� N?_ih |�i �?_���_�@* UL**@|ih@* UL?t|h@�?|c @ }i?ih@* t�Lh|@}i Lu UL**@|ih@*
D
�@t @ |i?_i?U) |L h@�ti @tti| Th�Uit i?_L}i?L�t*)� A��t �@TTi?t MiU@�ti �? M�__�?} uLh
U@T�|@*c �?_���_�@* �h4t hiUL}?�3i |�i �@*�i Lu U@T�|@* @t UL**@|ih@*� N?_ih |�i @}}hi}@|i
UL**@|ih@* UL?t|h@�?|c |��t 4iU�@?�t4 �L�*_ Mi @Mti?|� �t @ hit�*|c t�Lh|@}it Lu UL**@|ih@*
�L�*_ ?L| �@�i |�i t@4i |i?_i?U) |L }i?ih@|i @? �?Uhi@ti �? UL**@|ih@* i?_L}i?L�t*)�
�?i �?|ihThi|@|�L? Lu |�i @}}hi}@|i UL**@|ih@* 4L_i* �t |�@| i?uLhUi4i?| ThLM*i4t Thi�i?|
|�i �?U*�t�L? Lu t|@?_@h_ UL**@|ih@* �? UL?|h@U|t� W?t|i@_c �| �t @ t)t|i4 Lu }L�ih?4i?|
}�@h@?|iit |�@| M@U! �T *L@?t� �t @ hit�*|c �| �t |�i }L�ih?4i?|<t UL**@|ih@* |�@| �*|�4@|i*)
4@||iht� N?_ih |��t 4L_i* Lu UL**@|ih@*c |�i }L�ih?4i?|<t UL**@|ih@* �t hi*@|i_ |L |�i iUL?L4)�
��_i �@*�i Lu @tti|t� A��t 4L_i* tii4t UL?t�t|i?| ��|� |�i *�|ih@|�hi L? i |ih?@* _iM|
Ei}c ,@|L?c BihtL��|3 @?_ 5|�}*�|3c �bHS�c ��ihi |�i _iU�t�L? |L _iu@�*| @?_%Lh hi?i}L|�@|i
i |ih?@* _iM| �t 4L_i*i_ @t @ UL�?|h)���_i T�i?L4i?L?c _iTi?_i?| L? @}}hi}@|i �@h�@M*it�
A��t 4L_i* @*tL tii4t UL?t�t|i?| ��|� |�i Mi�@��Lh Lu uLhi�}? Uhi_�|Lhtc ��L �t�@**) ti|
RUL�?|h) i TLt�hi *�4�|t� @?_ tThi@_t |�@| @hi hi*@|i_ |L @}}hi}@|i �@h�@M*it�
A�i �4TLt�|�L? Lu ML|� |)Tit Lu UL**@|ih@* UL?t|h@�?|t �t @*tL UL?t�t|i?| ��|� hiUi?| 4L_i*t
Lu �?@?U�@* Uh�tit |�@| uLU�t L? |�i hL*i Lu }�@h@?|iit @?_ 4Lh@* �@3@h_ @t U@�tit Lu i4ih}�?}
4@h!i|t Uh�tit Et�U� @t kh�}4@?c �bbbc �Lhti||�c �itti?|� @?_ +L�M�?�c �bbHc #LL*i)c �bbHc
@?_ ��h?t�_ic ,�U�i?M@�4 @?_ +iMi*Lc 2fff�� W? u@U|c �i t�L�*_ t|hitt |�@| L�h 4L_i* _Lit
?L| @||i4T| |L 4L_i* |�i U@�tit Lu |�i �?@?U�@* Uh�tit M�| �|t igiU|t L? Uhi_�| UL?_�|�L?t�
�L� @u|ih @ Uh�t�t �@TTi?tc ��i� @u|ih |�i }�@h@?|iit @hi i ihU�ti_c |�i L?*) �@) �? ���U�
uLhi�}?iht �L�*_ i |i?_ u�h|�ih Uhi_�| |L @ UL�?|h) �L�*_ Mi �?_ih u�h|�ih }�@h@?|iit Lh
@__�|�L?@* UL**@|ih@*� A��t @__�|�L?@* UL**@|ih@* �@t Mii? tii? �? i T*�U�| Th��@|i Et)?_�U@|i_
*L@?� UL?|h@U|tc �? |�i |�}�|i?�?} Lu M@?! hi}�*@|�L?t |�@| �4TLti _�hiU|*) Lh �?_�hiU|*)
UL**@|ih@* hi^��hi4i?|tc @?_ �? }L�ih?4i?|t< �?|ih�i?|�L? @?_ t@*it Lu _�t|hitti_ @tti|t�
�| |��t TL�?|c |��t T@Tih L?*) �?U*�_it L�h �Lh! @?@*)3�?} |�i hL*i Lu �?_���_�@* UL**@|ih@*
UL?t|h@�?|tc |�i �ht| �@) Lu 4L_i*�?} UL**@|ih@* _�tU�tti_ @ML�i� i �@�i Mi}�? |L t|�_) |�i
igiU|t Lu �?ULhTLh@|�?} |�i @}}hi}@|i UL**@|ih@* 4L_i*� OL�i�ihc |�i �?�|�@* hit�*|t t�}}it|
|�@| |�ihi �t *�||*i _�gihi?Ui Mi|�ii? |�i |�L 4L_i*t uhL4 |�i t|@?_TL�?| Lu L�h u�?_@4i?|@*
�?|ihit| �? |��t T@TihG �?_iht|@?_�?} |�i iUL?L4�U igiU|t Lu �?|ihit| h@|i U�@?}it �? |�4it
Lu Uh�t�t� W? *@|ih _h@u|t �i T*@? |L �?U*�_i L�h @?@*)t�t Lu |��t @*|ih?@|��i �@) Lu 4L_i*�?}
UL**@|ih@* |L _LU�4i?| ��i|�ih �| _Lit Lh _Lit ?L| 4@!i @ _�gihi?Ui�
A�i UL**@|ih@* UL?t|h@�?| �? |��t T@Tih ThL��_it @ �?@?U�@* uh�U|�L? |�@| U@T|�hit �? @
?@|�h@* �@) |�i RM@*@?Ui t�ii|� igiU|t uhi^�i?|*) 4i?|�L?i_ �? |�i _�tU�tt�L? Lu hiUi?|
Uh�tit� � ?�4Mih Lu hiUi?| T@Tiht Ekh�}4@? E�bbb�c �}��L?c �@UU�i||@ @?_ �@?ih�ii E2fff�c
�itTi_itc ��@?} @?_ Vi*@tUL E2fff�c Bih|*ihc B�*U�h�t| @?_ �@|@*�UU� E2fff�c �i?_L3@
E2fff�� �?|hL_�Ui Uhi_�| UL?t|h@�?|t |�@| U@T|�hi tL4i @tTiU|t Lu |�i M@*@?Ui t�ii| U�@??i*�
OL�i�ihc ���*i |�iti T@Tiht �?ULhTLh@|i |�i @_�ihti igiU|t _ih��i_ uhL4 |�i i �t|i?Ui Lu
uLhi�}? U�hhi?U) _i?L4�?@|i_ _iM|tc |�i Uhi_�| uh�U|�L?t �? |�Lti T@Tiht UL?t|h@�? MLhhL��?}
S
|L Mi @ uh@U|�L? Lu U�hhi?| �?UL4i�h@|�ih |�@? |�i U�hhi?| �@*�i Lu T�)t�U@* @tti|t�� A�i
4�t4@|U� Mi|�ii? @tti|t @?_ *�@M�*�|�it |�@| �?_ihtULhi_ |�i �?@?U�@* ��*?ih@M�*�|) Lu |�i
Uh�tit UL�?|h�it �t U@T|�hi_ �? L�h 4L_i* M) |�i u@U| |�@| @ *@h}i uh@U|�L? Lu _L4it|�U @tti|t
@hi �? |�i ?L?|h@_i_ tiU|Lh ���*i @ hi*@|��i*) *@h}i uh@U|�L? Lu *�@M�*�|�it @hi _i?L4�?@|i_ �?
|ih4t Lu |�i |h@_i_ }LL_� Oi?Uic @ *@h}i @?_ Tiht�t|i?| u@** �? |�i hi*@|��i Th�Ui Lu ?L?|h@_i_
}LL_t E�i� @ hi@* i U�@?}i h@|i _iThiU�@|�L?� hit�*|t �? @ u@** �? |�i �@*�i Lu @tti|t hi*@|��i |L
*�@M�*�|�it |�@| i?_L}i?L�t*) 4@}?��it |�i |�}�|i?�?} Lu Uhi_�| UL?_�|�L?t _ih��i_ uhL4 |�i
�?�|�@* �4TLt�|�L? Lu UL**@|ih@* UL?t|h@�?|t �? |�i @u|ih4@|� Lu |�i Uh�t�t� W? L|�ih �Lh_tc L�h
iUL?L4) �t U@T@M*i Lu _�tT*@)�?} @ Rt�__i? t|LT� �? U@T�|@* �?�L�t E�@*�Lc �bbH� |�@| �t
@ttLU�@|i_ ��|� *@h}i @?_ Tiht�t|i?| u@**t �? L�|T�| @?_ i |ih?@* _iM|�
�� A�i �L_i*
i @_LT| @ t|@?_@h_ |h@_i_ }LL_�?L? |h@_i_ }LL_ t4@** LTi? iUL?L4) 4L_i*� A�i 4L_i*
�@t �L�ti�L*_tc �h4tc @ �?@?U�@* �?|ih4i_�@h)c @?_ @ _L4it|�U 4L?i|@h) @�|�Lh�|)�
���� OL�ti�L*_t
A�ihi �t @ hiThiti?|@|��i �L�ti�L*_c ���U� _ih��it �|�*�|) uhL4 UL?t�4T|�L?c S|c @?_ *i�t�hi
@t uL**L�tG"[|'f
q|�ES|c u|�c E����
��ihi u| _i?L|it *@MLh� i @_LT| |�i uL**L��?} tTiU��U@|�L? Lu �|�*�|)G
�EScu� '
kS� �f
�n�u�n�
l�3j�� j
� E��2�
A�i �L�ti�L*_ Mi}�?t |�i Tih�L_ ��|� @ t|LU! Lu *�^��_ @tti|tc ��|� �u |��tc �| _iTLt�|t
(| ��|� |�i �?@?U�@* �?|ih4i_�@h)c @?_ |�i hit|c ��| � (|c �t @**LU@|i_ |L UL?t�4T|�L?
i Ti?_�|�hit� A�i U@t� UL?t|h@�?| |�@| |�i �L�ti�L*_ u@Uit L? �|t UL?t�4T|�L? i Ti?_�|�hit
�tG
�|S| � `|u| n ��| �(|c E����
4D qrwdeoh h{fhswlrq lv Jhuwohu/ Jlofkulvw dqg Qdwdoxffl +5333,/ exw wkh qdwxuh ri wkh fuhglw frqvwudlqwlv gl�huhqw iurp wkh rqh lq wklv sdshu1 Pruhryhu/ wkh fxuuhqw dffrxqw lv dozd|v }hur lq wkdw sdshu/ khqfhplvvlqj wkh frqqhfwlrq ehwzhhq fdslwdo �rzv dqg dvvhw sulfhv revhuyhg lq wkh fulvhv hslvrghv1
.
��ihi `| _i?L|it |�i 4L?i) �@}i h@|i @?_ �| _i?L|it |�i Th�Ui *i�i*�
A�i �L�ti�L*_ @*tL u@Uit @ �L� M�_}i| UL?t|h@�?| }L�ih?�?} |�i i�L*�|�L? Lu �|t @tti|tG
��|n� ' -|E(| nf|� n � A| Z| n
k`|u| n ��| �(| � �|S|
l� E��e�
Oihic -| _i?L|it |�i }hLtt _L4it|�U h@|i Lu �?|ihit|c Z| �t ThL�|t ���U� _ih��i uhL4 �L�ti�
�L*_<t L�?iht��T Lu �h4tc @?_ f| �t @ *�^��_�|) �?�iU|�L? uhL4 |�i 4L?i|@h) @�|�Lh�|)� Oihic
Z| �t 4i@t�hi_ �? �?�|t Lu |h@_i_ }LL_tc @?_ � A| �t |�i _L4it|�U U�hhi?U) Th�Ui Lu |h@_i_
}LL_t� A�i |ih4 L? |�i h�}�| Lu |�i i^�@*�|) hi�iU|t |�i �L�ti�L*_<t tL�hUit Lu *�^��_ @tti|t
@| |�i Mi}�??�?} Lu Tih�L_ |n� G �?|ihit| i@h?�?}t L? _iTLt�|t @?_ L? |�i *�^��_�|) �?�iU|�L?c
ThL�|t @?_ @?) U@t� |�@| 4@) Mi *iu| �?tTi?| �? |�i Tih�L_ | }LL_t 4@h!i|�
A�i �L�ti�L*_ 4@ �4�3it E���� t�M�iU| |L E�����E��e�c @?_ |�i uL**L��?} |�4�?} UL?t|h@�?|�
� }��i? Tih�L_<t _iTLt�| _iU�t�L? �t 4@_i MiuLhi |�@| Tih�L_<t *�^��_�|) �?�iU|�L? �t hi@*�3i_c
���*i @** L|�ih _iU�t�L?t @hi 4@_i @u|ih�@h_� A�i �L�ti�L*_<t ,�*ih i^�@|�L? uLh *@MLh �tG
�fu�| '
`|
�|
c E��D�
���U� �t |�i *@MLh t�TT*) i^�@|�L?� A�i �?|ih|i4TLh@* ,�*ih �tG
�Sc| ' q-|�Sc|n��|
�|n�� E��S�
��2� 6�h4t
A�ihi @hi |�L |)Tit Lu hiThiti?|@|��ic UL4Ti|�|��ic �h4t� A�i �ht| ThL_�Uit |�i �?@* UL?�
t�4T|�L? }LL_c Sc T�hU�@ti_ M) �L�ti�L*_t� 6�?@* }LL_t ThL_�U|�L? hi^��hit �?|ih4i_�@|i
}LL_t ���U� @hi ThL_�Ui_ M) |�i tiUL?_ |)Ti Lu hiThiti?|@|��i �h4� i ?L� _�tU�tt |�iti
|�L |)Tit Lu �h4t�
��2��� 6�?@* BLL_ 6�h4t
A�i ThL_�U|�L? u�?U|�L? Lu |�i �?@* }LL_ �h4t �tG
S '
+kE� � �� SA
l #3�# n
k�S�
l #3�#
, #
#3�
c � � # � fc f � �c
H
��ihi SA @?_ S� _i?L|i ^�@?|�|�it Lu |h@_i@M*i @?_ ?L?�|h@_i@M*i �?|ih4i_�@|i �?T�|tc hi�
tTiU|��i*)� W? igiU|c |�iti �h4t @hi hi|@�*iht |�@| T@U!@}i |h@_i_ @?_ ?L?|h@_i_ �?|ih4i_�@|i
}LL_t �?|L @ �?@* UL?t�4T|�L? }LL_� Oihic # _i?L|it |�i i*@t|�U�|) Lu t�Mt|�|�|�L? �? ThL�
_�U|�L? Mi|�ii? |�i |�L �?|ih4i_�@|i �?T�|t� �t # $ fc
S ' 4�?qE�� �� SA c �S�
r� E��.�
i i U*�_i # � � uhL4 UL?t�_ih@|�L? L? i4T�h�U@* }hL�?_t� �t ?L|i_ @ML�ic |�i Th�Ui Lu
S �t _i?L|i_ M) �c ���*i � A @?_ �� _i?L|i |�i 4L?i) Th�Uit Lu |�i |h@_i_ @?_ ?L?|h@_i_
�?T�|tc hitTiU|��i*)� A�i �h4 |@!it |�iti Th�Uit T@h@4i|h�U@**)�
~ihL ThL�|t @?_ i�U�i?U) �4T*) |�i uL**L��?} hi*@|�L? Mi|�ii? Th�UitG
R '
57# �
� � �
$�3#
n
#R�
�
$�3#68
�
�3#
c R '�
� A� E��H�
6Lh # 9' �c i�U�i?U) @*tL _�U|@|itG
R� '�
�� �
#E� � �� SA
�S�
$ �
#
c R� '��
� A� E��b�
`�i? # ' fc |��t i Thitt�L? �t hiT*@Ui_ M) E�� �� SA ' �S� c @t �4T*�i_ M) E��.�� A�i LM�iU|c
�c �? |�i 4L_i* ULhhitTL?_t |L |�i 4L_i*<t �UL?t�4ih Th�Ui �?_i <c _i?L4�?@|i_ �? �?�|t Lu
|�i _L4it|�U U�hhi?U)� A�i LM�iU|c Rc �t |�i UL?t�4ih Th�Ui �?_i _i?L4�?@|i_ �? �?�|t Lu
|�i |h@_i_ }LL_�
��2�2� W?|ih4i_�@|i W?T�|t
� t�?}*i hiThiti?|@|��i �h4 ThL_�Uit |�i |h@_i_ @?_ ?L?�|h@_i_ �?|ih4i_�@|i �?T�|t� A�@|
�h4 4@?@}it |�hii |)Tit Lu _iM|c |�L Lu ���U� @hi t�Lh|�|ih4� A�i �h4 MLhhL�t @| |�i
Mi}�??�?} Lu |�i Tih�L_ |L �?@?Ui �|t �@}i M�** @?_ |L T�hU�@ti @ uLhi�}? �?T�|c @?_ hiT@)t
|�iti *L@?t @| |�i i?_ Lu |�i Tih�L_� W? @__�|�L?c |�i �h4 �L*_t |�i L�|t|@?_�?} t|LU! Lu
i |ih?@* E?i|� �?_iM|i_?ittc �|�
b
A�i �h4<t LT|�4�3@|�L? ThLM*i4 �tG
4@ "[|'f
q|\|n�Z|c E���f�
��ihi
Z| ' R�| +�| n +A| � �|-|u| �-W5| � oW�| n E�|n� ��|�c E�����
_i?L|it _���_i?_tc _i?L4�?@|i_ �? �?�|t Lu |h@_i_ }LL_t� �*tLc �| �t |�i t|LU! Lu i |ih?@*
_iM| @| |�i Mi}�??�?} Lu Tih�L_ |c _i?L4�?@|i_ �? �?�|t Lu |�i |h@_i_ }LL_( -W �t |�i }hLtt
h@|i Lu �?|ihit| E� i_ �? �?�|t Lu |�i |h@_i_ }LL_� L? *L@?t uLh |�i T�hTLti Lu T�hU�@t�?} 5|(
@?_ oW �t |�i ?i| h@|i Lu �?|ihit| E@}@�?c � i_ �? |ih4t Lu |�i |h@_i_ }LL_� L? |�i L�|t|@?_�?}
t|LU! Lu i |ih?@* _iM|� A�i Th�Uic \|n�c �t |@!i? T@h@4i|h�U@**) M) �h4t� W? i^��*�Mh��4c �|
�t |�i 4�*|�T*�ih L? Z| �? |�i Ew@}h@?}�@? hiThiti?|@|�L? Lu |�i� �L�ti�L*_ ThLM*i4G2
\|n� '�Sc|n�R|n�
� A|
� A|n�
q E���2�
'�Sc|n�R|n�
RA|RA|n�
�
� n %|qc
��ihi
RA| '� A|
�|
�
Oihic �| �t |�i @}}hi}@|i t|LU! Lu 4L?i) @| |�i Mi}�??�?} Lu Tih�L_ |c ���U� �t @tt�4i_ |L
i�L*�i @UULh_�?} |LG�|n�
�|
' � n %|� E�����
�L|i |�@| �?_ih L�h ?L|@|�L?@* UL?�i?|�L?c @** *L�ih U@ti Th�Uit i UiT| L?ic i Thittit |�@|
Th�Ui �? �?�|t Lu |�i |h@_i_ }LL_� A�i i UiT|�L?c RA| c �t |�i _L4it|�U U�hhi?U) Th�Ui Lu |h@_i_
}LL_tc tU@*i_ M) |�i Mi}�??�?} Lu Tih�L_ t|LU! Lu 4L?i)� �*|ih?@|��i*)c RA| �t |�i �?�ihti Lu
@ 4i@t�hi Lu hi@* M@*@?Uit�
5Wkh lqwxlwlrq xqghuo|lqj +6145, lv vwudljkwiruzdug1 Wkh remhfw �w.4 lq +6145,/ lv wkh pdujlqdo xwlolw| rirqh xqlw ri glylghqgv/ ghqrplqdwhg lq wudghg jrrgv/ wudqvihuuhg e| wkh �up wr wkh krxvhkrog dw wkh hqg rishulrg w1 Wklv fruuhvsrqgv wr S W
w �w xqlwv ri grphvwlf fxuuhqf|1 Wkh krxvhkrogv fdq xvh wklv fxuuhqf| lqshulrg w . 4 wr sxufkdvh SW
w �[email protected] xqlwv ri wkh frqvxpswlrq jrrg1 Wkh ydoxh/ lq shulrg w/ ri wkhvh xqlwvri frqvxpswlrq jrrgv lv �xf>w.4S
Ww �[email protected]> ru �xf>w.4S
Ww �w@+sw.4S W
w.4,> zkhuh xf>w lv wkh pdujlqdo xwlolw| rifrqvxpswlrq1 Wklv lv wkh �uvw h{suhvvlrq lq +6145,1
�f
A�i �h4 ThL_�U|�L? u�?U|�L?t @hiG
+A '�w d>�T o
13�
1 n E� � w� d>25o13�
1
� 1
13�
c E���e�
T ' ��gA
�D �uA��3D
c
+� '�g�
�k �u�
��3kc
��ihi 1 �t |�i i*@t|�U�|) Lu t�Mt|�|�|�L? Mi|�ii? �@*�i�@__i_ �? |�i |h@_i_ }LL_ tiU|Lhc T|c
@?_ |�i �4TLh|i_ �?|ih4i_�@|i }LL_c 5|� W? |�i ThL_�U|�L? u�?U|�L?tc gA @?_ g� _i?L|i
U@T�|@* �? |�i |h@_i_ @?_ ?L?�|h@_i_ }LL_ tiU|Lhtc hitTiU|��i*)� A�i) @hi L�?i_ M) |�i
hiThiti?|@|��i �?|ih4i_�@|i �?T�| �h4� i !iiT |�i t|LU! Lu U@T�|@* � i_ |�hL�}�L�| |�i
@?@*)t�t� W| _Lit ?L| _iThiU�@|i @?_ |�ihi i �t|t ?L |iU�?L*L}) uLh 4@!�?} �| M�}}ih�
��h tTiU��U@|�L? Lu |iU�?L*L}) �t _it�}?i_ |L i?UL4T@tt @ �@h�i|) Lu U@tit� A�L @hi Lu
T@h|�U�*@h �?|ihit| MiU@�ti |�i) ULhhitTL?_ |L _�gihi?| �@)t Lu uLh4@*�3�?} |�i ?L|�L? |�@|
5 �t itti?|�@* �? |�i ThL_�U|�L? Lu |h@_i_ }LL_t� W? |�i �ht|c |�ihi �t ?L t�Mt|�|�|@M�*�|)
Mi|�ii? 5 @?_ T �? ThL_�U|�L?c ��i�c 1 ' fc tL |�@|
+A ' 4�? i>�Tc >25j � E���D�
W? |��t U@tic �u uLh tL4i hi@tL? 5 �t hi_�Ui_c |�i? @_��t|4i?|t �? T U@??L| Thi�i?| @ u@**
�? +A � Wu �? @__�|�L?c |�ihi �t ?L t�Mt|�|�|�L? Mi|�ii? +A @?_ +� �? |�i ThL_�U|�L? Lu |�i
UL?t�4T|�L? }LL_ E��i�c # ' f� |�i? @ u@** �? +A ��** @*tL Mh�?} _L�? +� � A��t �t ��@| �i
�@_ �? 4�?_ �? |�i �?|hL_�U|�L?c ��i? �i t@�_ |�@| ��|� *@U! Lu t�Mt|�|�|�L?c @ UL**@|ih@*
UL?t|h@�?|�i?uLhUi_ hi_�U|�L? �? 5 UL�*_ Mh�?} _L�? |�i ��L*i iUL?L4)� A�i tiUL?_ U@ti
��ihi 5 �t itti?|�@*c LUU�ht ��i? �| �t |�i L?*) �@h�@M*i u@U|Lh Lu ThL_�U|�L?� A��t ULhhitTL?_t
|L 1 ' >� ' >2 ' D ' �c ��i?
+A '��gA
�w5�3w� E���S�
�}@�?c �u tL4i|��?} Et@) @ |�}�|i?�?} Lu |�i UL**@|ih@* UL?t|h@�?|� �?_�Uit @ u@** �? 5c |�i?
+A 4�t| u@** @?_ +� 4�t| |�ihiuLhi u@** |LLc �u # �t t4@** i?L�}��
i �4TLti |�i uL**L��?} hit|h�U|�L? L? MLhhL��?}G
�|n�
E� n oW�|$ fc @t |$4� E���.�
i t�TTLti |�@| �?|ih?@|�L?@* �?@?U�@* 4@h!i|t �4TLti |�@| |��t *�4�| U@??L| Mi TLt�|��i�
A�@| �| U@??L| Mi ?i}@|��i �t @? �4T*�U@|�L? Lu �h4 LT|�4@*�|)�
��
A�i �h4<t ThLM*i4 @| |�4i | �t |L 4@ �4�3i E���f� M) U�L�Ui Lu �|n�n�c +�|n�c +
A|n�c 5|n�c
uA|n� @?_ u�
|n�c � ' fc�c 2c ��� @?_ |�i �?_�U@|i_ |iU�?L*L})� W? @__�|�L?c |�i �h4 |@!it @**
Th�Uit @?_ h@|it Lu hi|�h? @t }��i? @?_ Mi)L?_ �|t UL?|hL*� A�i �h4 @*tL |@!it |�i �?�|�@* t|LU!
Lu _iM|c �|c @t }��i?� A��t UL4T*i|it |�i _itUh�T|�L? Lu |�i �h4 ThLM*i4 �? |�i Thi�Uh�t�t
�iht�L? Lu |�i 4L_i*c ��i? UL**@|ih@* UL?t|h@�?|t @hi �}?Lhi_�
A�i Uh�t�t Mh�?}t L? |�i �4TLt�|�L? Lu |�i uL**L��?} UL**@|ih@* UL?t|h@�?|G
��^�| g� n � A ^A| g
A � -W5| n E� n oW��| n �|-|u|c E���H�
��ihi u| � uA| n u�
| � Oihic ^�c � ' �cA _i?L|i |�i �@*�i E�? �?�|t Lu |�i |h@_i_ }LL_� Lu
@ �?�| Lu U@T�|@* �? |�i ?L?|h@_i_ @?_ |h@_i_ }LL_ tiU|Lhtc hitTiU|��i*)� �*tLc � � _i?L|it
|�i uh@U|�L? Lu |�iti t|LU!t @UUiT|i_ @t UL**@|ih@* M) �?|ih?@|�L?@* Uhi_�|Lht� A�i *iu| t�_i Lu
E���H� �t |�i |L|@* �@*�i Lu UL**@|ih@*c @?_ |�i h�}�| t�_i �t |�i T@)L�| �@*�i Lu |�i �h4<t _iM|�
W| �t |�i |L|@* @4L�?| |�@| |�i �h4 �L�*_ �@�i |L T@)c |L UL4T*i|i*) i*�4�?@|i @** �|t _iM|
M) |�i i?_ Lu Tih�L_ |� �iuLhi |�i Uh�t�tc �h4t �}?Lhi E���H�c @?_ @tt�}? @ 3ihL ThLM@M�*�|)
|�@| �| ��** Mi �4T*i4i?|i_� `�|� |�i UL4�?} Lu |�i Uh�t�tc �h4t Mi*�i�i |�@| E���H� 4�t|
Mi t@|�t�i_ �? i�ih) Tih�L_ �i?UiuLh|�c @?_ _L ?L| i?|ih|@�? |�i TLtt�M�*�|) |�@| �| ��** Mi
hi4L�i_�
A�i i^��*�Mh��4 �@*�i Lu |�i @tti| Th�Uitc ^�|c � ' �cAc �t |�i @4L�?| |�@| @ TL|i?|�@*
�h4 �L�*_ Mi ��**�?} |L T@) �? Tih�L_ |c �? �?�|t Lu |�i |h@_i_ }LL_c |L @U^��hi @ �?�| Lu
U@T�|@* @?_ t|@h| ThL_�U|�L? �? Tih�L_ |� i *i| b| � f _i?L|i |�i 4�*|�T*�ih L? |�i UL**@|ih@*
UL?t|h@�?| E' f �? |�i Thi�Uh�t�t Tih�L_� �? �h4 ThLM*i4� A�i?c ^�| �t |�i _ih��@|��i Lu |�i
w@}h@?}�@? hiThiti?|@|�L? Lu |�i �h4<t ThLM*i4 ��|� hitTiU| |L g�| G
^�| ' T �� �&c| n b|�
�^�| nq
\|n�
"[�'�
q�3�\|n�n�
qT�� �
&c|n� n b|n���^�|n�
rE���b�
Lhc
^�| 'T�� �
&c| n q\|n2
\|n�^�|n�
�� b|� �c � ' �cA� E��2f�
Oihic T�� �&c| _i?L|it |�i Tih�L_ | �@*�i E�? |ih4t Lu |h@_i_ }LL_t� 4@h}�?@* ThL_�U| Lu
U@T�|@* �? tiU|Lh �� `�|� L�h @tt�4T|�L?t L? |iU�?L*L})c |�iti @hiG
T ���&c| ' kR�|
+�|g�
c
�2
T �� A&c| '
;AAA?AAA=
�+A|>�T|
� �
1
wD >�T|gA c 1 9' f
D >�T|gA
k� � E�nb|�-W
>2
lc 1 ' f
�
`�i? b| � fc E���b� �t ��t| |�i t|@?_@h_ @tti| Th�U�?} i^�@|�L?� W| �t |�i Thiti?| _�tUL�?|i_
�@*�i Lu |�i �@*�i Lu |�i 4@h}�?@* T�)t�U@* ThL_�U| Lu U@T�|@*� `�i? |�i UL**@|ih@* UL?t|h@�?|
�t M�?_�?}c tL |�@| b| �t TLt�|��ic |�i? ^�| �t }hi@|ih |�@? |��t� A��t hi�iU|t |�@| �? |��t U@ti
U@T�|@* �t ?L| L?*) �tiu�* �? ThL_�U|�L?c M�| @*tL uLh hi*�i��?} |�i UL**@|ih@* UL?t|h@�?|� W?
L�h 4L_i* U@T�|@* �t ?i�ih @U|�@**) |h@_i_ t�?Ui @** �h4t @hi �_i?|�U@*� OL�i�ihc �u |�ihi
�ihi |h@_ic |�i? |�i Th�Ui Lu U@T�|@* �L�*_ Mi ^�|� Wu @ �h4 �ihi |L _iu@�*| L? �|t Uhi_�|
LM*�}@|�L?tc |�i ?L|�L? �t |�@| uLhi�}? Uhi_�|Lht UL�*_ UL4Ti* |�i t@*i Lu �|t T�)t�U@* @tti|t �?
@ _L4it|�U 4@h!i| uLh U@T�|@*� A�i Th�Uic ^�|c �t �L� 4�U� |h@_i_ }LL_t @ _L4it|�U hit�_i?|
�t ��**�?} |L T@) uLh @ �?�| Lu U@T�|@*� 6Lhi�}? Uhi_�|Lht �L�*_ hiUi��i |�Lti }LL_t �? |�i
i�i?| Lu @ _iu@�*|� i @tt�4i |�@| ��|� |�iti UL?ti^�i?Uit uLh _iu@�*|c _iu@�*| ?i�ih LUU�ht
�? i^��*�Mh��4�
i ?L� _ih��i |�i ,�*ih i^�@|�L?t Lu |�i �h4� #�gihi?|�@|�?} |�i _@|i f w@}h@?}�@?
hiThiti?|@|�L? Lu |�i �h4 ThLM*i4 ��|� hitTiU| |L �|n�G
� ' q\|n2
\|n�E� n oW�E� n b|n��c | ' fc�c 2c ��� � E��2��
6L**L��?} t|@?_@h_ Th@U|�Ui �? |�i t4@** LTi? iUL?L4) *�|ih@|�hic �i @tt�4i qE� n oW� ' �c
tL |�@|�
\|n� ' \|n2E� n b|n��c | ' fc �c2c ��� � E��22�
� ��}� �@*�i uLh bc ���U� LUU�ht ��i? |�i UL**@|ih@* UL?t|h@�?| �t M�?_�?}c h@�tit |�i igiU|��i
h@|i Lu �?|ihit| L? _iM|� A�i �?|ihThi|@|�L? �t |�@| ��i? b �t *@h}ic |�i? |�i _iM| �@t @?
@__�|�L?@* ULt|c Mi)L?_ |�i _�hiU| �?|ihit| ULt|� A��t ULt| hi�iU|t |�@| ��i? |�i �h4 h@�tit
�|n� �? Tih�L_ |c �| ?L| L?*) �?U�ht @? @__�|�L?@* �?|ihit| U�@h}i �? Tih�L_ | n �c M�| �| �t
@*tL u�h|�ih |�}�|i?t �|t UL**@|ih@* UL?t|h@�?| �? |�@| Tih�L_� A��t �@t @ ULt| MiU@�tic ��@ |�i
UL**@|ih@* UL?t|h@�?|c |�i i |h@ _iM| �?��M�|t |�i �h4<t @M�*�|) |L @U^��hi �Lh!�?} U@T�|@* �?
Tih�L_ |n�� A��tc ��i? b �t ��}�c |�ihi �t @? @__�|�L?@* �?Ui?|��i uLh �h4t |L hi_�Ui Z @?_
�t@�i< M) T@)�?} _L�? |�i i |ih?@* _iM|� �*|�L�}� |�i �h4<t @U|�@* �?|ihit| h@|i L? i |ih?@*
_iM| |@!i? L? �? Tih�L_ | �t � n oWc �|<t �igiU|��i< �?|ihit| h@|i �t E� n oW� E� n b|n�� �
A�i �h4<t �ht| Lh_ih UL?_�|�L?t uLh *@MLh �? |�i ?L?|h@_i_ @?_ |h@_i_ tiU|Lhtc @?_ uLh 5
6Vhh/ iru h{dpsoh/ Revwihog dqg Urjr� +4<<:,1
��
@hic ��i? 1 9' fG
E�� k�R�|+�|u�|
' �|E� n b|�-| E��2��
#+A|>�T|
$ �
1
wE� � D�>�T|uA|
' �|E� n b|�-| E��2e�
#+A|>25|
$ �
1
E� � w�>2 ' E� n b|�-W E��2D�
A�i Thiti?Ui Lu -| L? |�i h�}�| t�_i Lu E��2���E��2e� hi�iU|t |�@| |L ��hi *@MLhc �h4t 4�t|
MLhhL� U@t� �? @_�@?Ui �? |�i _L4it|�U 4L?i) 4@h!i|c @| |�i }hLtt �?|ihit| h@|ic -|� `�i?
|�i UL**@|ih@* UL?t|h@�?| �t M�?_�?}c |�i? |�i igiU|��i �?|ihit| h@|i �t ��}�ih |�@? -|� A�i
}hLtt �?|ihit| h@|i L? t�Lh| |ih4 uLhi�}? *L@?tc -Wc @TTi@ht L? |�i h�}�| Lu E��2D� MiU@�ti
�h4t 4�t| MLhhL� uLhi�}? u�?_t �? @_�@?Ui |L @U^��hi 5|� �L|i |�@| |�i igiU|��i uLhi�}?
�?|ihit| h@|i �t ��}�ih |�@? |�i @U|�@* �?|ihit| h@|i ��i? |�i UL**@|ih@* UL?t|h@�?| �t M�?_�?}�
`�i? 1 ' fc |�i? Lu UL�hti E��2�� t|�** �L*_tc M�| E��2e� @?_ E��2D� @hi hiT*@Ui_ M)G
E�� D�>�T|uA|
%� �
E� n b|�-W
>2
&' �|E� n b|�-| E��2S�
>�T| ' >25| E��2.�
W}?Lh�?} |�i |ih4 �? t^�@hi Mh@U!i|t �? E��2S�c |��t �t ��t| |�i 4@h}�?@* ThL_�U| Lu uA �?
ThL_�U�?} >�T|� A�i |ih4 �? t^�@hi Mh@U!i|t hi�iU|t |�@| i T@?t�L?t �? +A @*tL hi^��hit @?
�?Uhi@ti �? 5�
���� 6�?@?U�@* W?|ih4i_�@h) @?_ �L?i|@h) ��|�Lh�|)
A�i �?@?U�@* �?|ih4i_�@h) |@!it _L4it|�U U�hhi?U) _iTLt�|tc (|c uhL4 |�i �L�ti�L*_ @| |�i
Mi}�??�?} Lu Tih�L_ |� W? @__�|�L?c �| hiUi��it |�i *�^��_�|) |h@?tuihc f| ' %|�|c uhL4 |�i
4L?i|@h) @�|�Lh�|)�e W| |�i? *i?_t @** �|t _L4it|�U u�?_t |L �h4t ��L �ti �| |L �?@?Ui |�i�h
i4T*L)4i?| �Lh!�?} U@T�|@* hi^��hi4i?|tc `|u|� �*i@h�?} �? |�i 4L?i) 4@h!i| hi^��hit
7Lq sudfwlfh/ lqmhfwlrqv ri oltxlglw| gr qrw rffxu lq wkh irup ri oxps vxp wudqvihuv/ dv wkh| gr khuh1 Lw lvhdv| wr vkrz wkdw rxu irupxodwlrq lv htxlydohqw wr dq dowhuqdwlyh/ lq zklfk wkh lqmhfwlrq rffxuv dv d uhvxow ridq rshq pdunhw sxufkdvh ri jryhuqphqw erqgv zklfk duh rzqhg e| wkh krxvhkrog/ exw khog e| wkh �qdqfldolqwhuphgldu|1 Zh gr qrw dgrsw wklv lqwhusuhwdwlrq lq rxu irupdo prgho lq rughu wr frqvhuyh rq qrwdwlrq1
�e
(| nf| '`|u|c Lhc @u|ih tU@*�?} M) |�i @}}hi}@|i 4L?i) t|LU!c
_| n %| ' �|RA| u|c E��2H�
��ihi _| ' (|*�|�
A�i 4L?i|@h) @�|�Lh�|) �? L�h 4L_i* t�4T*) �?�iU|t u�?_t �?|L |�i �?@?U�@* �?|ih4i_�@h)�
W|t Tih�L_ | _iU�t�L? �t |@!i? @u|ih |�i �L�ti�L*_ �@t ti*iU|i_ @ �@*�i uLh (|c @?_ MiuLhi @**
L|�ih �@h�@M*it �? |�i iUL?L4) @hi _i|ih4�?i_� A��t �t |�i t|@?_@h_ @tt�4T|�L? �? |�i
*�4�|i_ T@h|�U�T@|�L? *�|ih@|�hi� W| �t �?|ihThi|i_ @t hi�iU|�?} @ t*�}}�t�?itt �? |�i hitTL?ti
Lu �L�ti�L*_ TLh|uL*�L _iU�t�L?t |L U�@?}it �? 4@h!i| �@h�@M*it� `�|� |��t @tt�4T|�L?c @
�@*�i Lu %| |�@| _i��@|it uhL4 ��@| �L�ti�L*_t i TiU|i_ @| |�i |�4i (| �@t ti| ThL_�Uit @?
�44i_�@|i hi@U|�L? M) �h4t @?_ |�i �?@?U�@* �?|ih4i_�@h) M�| ?L|c �? |�i �ht| �?t|@?Uic M)
�L�ti�L*_t� A�i ?@4ic �*�4�|i_ T@h|�U�T@|�L?<c _ih��it uhL4 |��t ui@|�hic ?@4i*) |�@| ?L| @**
@}i?|t hi@U| �44i_�@|i*) |L ELhc �T@h|�U�T@|i �?<� @ 4L?i|@h) t�LU!� �t @ hit�*| Lu |��t |�4�?}
@tt�4T|�L?c 4@?) 4L_i*t i ��M�| |�i uL**L��?} Mi�@��Lh �? i^��*�Mh��4� �? �?i TiU|i_*)
��}� �@*�i Lu %| t�i**t |�i t�TT*) Lu u�?_t �? |�i �?@?U�@* tiU|Lh E(| L? |�i *iu| t�_i Lu E��2H�
U@??L| u@** �? hitTL?ti |L @ TLt�|��i %| t�LU!�� AL }i| �h4t |L @MtLhM |�i �?Uhi@ti �? u�?_tc
@ u@** �? |�i i^��*�Mh��4 h@|i Lu �?|ihit| �t hi^��hi_� `�i? |�@| u@** _Lit LUU�hc |�i) MLhhL�
|�i �?Uhi@ti_ u�?_t @?_ �ti |�i4 |L ��hi 4Lhi *@MLh @?_ ThL_�Ui 4Lhi L�|T�|�
i @Mt|h@U| uhL4 @** L|�ih @tTiU|t Lu }L�ih?4i?| �?@?Ui� A�i L?*) TL*�U) �@h�@M*i Lu
|�i }L�ih?4i?| �t %|�
��e� ,^��*�Mh��4
i UL?t�_ih @ TihuiU| uLhit�}�|c ti^�i?Ui�Lu�4@h!i| i^��*�Mh��4 UL?UiT|� W? T@h|�U�*@hc �| �t @
ti^�i?Ui Lu Th�Uit @?_ ^�@?|�|�it �@��?} |�i ThLTih|�itG E�� uLh i@U� _@|ic |�i ^�@?|�|�it tL*�i
|�i �L�ti�L*_ @?_ �h4 ThLM*i4tc }��i? |�i Th�Uitc @?_ E��� |�i *@MLhc }LL_t @?_ _L4it|�U
4L?i) 4@h!i|t U*i@h�
�*i@h�?} �? |�i 4L?i) 4@h!i| hi^��hit |�@| E��2H� �L*_ @?_ |�@| @U|�@* 4L?i) M@*@?Uitc
�|c i^�@* _it�hi_ 4L?i) M@*@?Uitc ��|� �L4M�?�?} |��t ��|� |�i �L�ti�L*_<t U@t� UL?t|h@�?|c
E����c �i LM|@�? |�i i^��*�Mh��4 U@t� UL?t|h@�?|G
RA| R|S| ' � n %|� E��2b�
�UULh_�?} |L |��tc |�i |L|@*c i?_ Lu Tih�L_ t|LU! Lu 4L?i) 4�t| i^�@* |�i �@*�i Lu �?@*
�D
L�|T�|c S|� �@h!i| U*i@h�?} �? |�i |h@_i_ }LL_ tiU|Lh hi^��hitG
+A| �-W5| � oW�| � SA| ' � E�|n� ��|� � E���f�
A�i *iu| t�_i Lu |��t i Thitt�L? �t |�i U�hhi?| @UUL�?| Lu |�i M@*@?Ui Lu T@)4i?|tc ��i�c |L|@*
ThL_�U|�L? Lu |h@_i_ }LL_tc ?i| Lu uLhi�}? �?|ihit| T@)4i?|tc ?i| Lu _L4it|�U UL?t�4T|�L?�
A�i h�}�| t�_i Lu E���f� �t |�i U�@?}i �? ?i| uLhi�}? @tti|t� ,^�@|�L? E���f� hi�iU|t L�h
@tt�4T|�L? |�@| i |ih?@* MLhhL��?} |L �?@?Ui |�i �?|ih4i_�@|i }LL_c 5|c �t u�**) T@�_ M@U!
@| |�i i?_ Lu |�i Tih�L_� A�@| �tc |��t MLhhL��?} hiti4M*it t�Lh|�|ih4 |h@_i Uhi_�|� �L|ic
�L�i�ihc |�@| |��t �t ?L| @ M�?_�?} UL?t|h@�?| L? |�i �h4c t�?Ui L�h ti|�T Tih4�|t |�i �h4
|L �?@?Ui |�iti hiT@)4i?|t �t�?} *L?} |ih4 _iM|� �@h!i| U*i@h�?} �? |�i ?L?|h@_i_ }LL_
tiU|Lh hi^��hitG
+�| ' S�| � E�����
W| �t �?t|h�U|��i |L t|�_) |��t 4L_i*<t �4T*�U@|�L?t uLh �?|ihit| T@h�|)� �L4M�?�?} |�i
�L�ti�L*_ @?_ �h4 �?|ih|i4TLh@* UL?_�|�L?tc E��S� @?_ E��2��c ��|� E���2�c �i LM|@�?
-|n� ' E� n oW�� A|n�
� A|
E� n b|n�� c | ' fc �c 2c ��� E���2�
�? |�i h�}�| �@?_ t�_ic Lu |��t i Thitt�L?c E�n oW�� A|n�*�
A| �t |�i h@|i Lu �?|ihit| L? i |ih?@*
_iM|c i Thitti_ �? _L4it|�U U�hhi?U) �?�|t� , Thitt�L? E���2� ��|� b ' f �t |�i �t�@*
�?|ihit| h@|i T@h�|) hi*@|�L?� `�i? b : fc |�ihi �t @ UL**@|ih@* Thi4��4 L? |�i _L4it|�U h@|i
Lu �?|ihit|� , Thitt�L? E���2� ��}�*�}�|t L�h �4T*�U�| @tt�4T|�L? |�@| uLhi�}? @?_ _L4it|�U
4@h!i|t uLh *L@?@M*i u�?_t @hi �tL*@|i_c @| *i@t| �? |�4it ��i? |�i UL**@|ih@* UL?t|h@�?| �t
M�?_�?}� `�i? b : fctL |�@| |�i _L4it|�U �?|ihit| h@|i i Uii_t |�i uLhi�}? h@|ic *i?_iht Lu
uLhi�}? U�hhi?U) �L�*_ Thiuih |L i U�@?}i |�i�h U�hhi?U) uLh _L4it|�U U�hhi?U) @?_ *i?_ �?
|�i _L4it|�U U�hhi?U) 4@h!i|� 5�4�*@h*)c �h4t MLhhL��?} _L4it|�U u�?_t uLh |�i T�hTLti Lu
T@)�?} |�i�h �@}i M�** �L�*_ Thiuih |L MLhhL� �? uLhi�}? U�hhi?U) 4@h!i| @?_ UL?�ih| |�i
ThLUii_t �?|L _L4it|�U U�hhi?U)� A�@| b : f �t TLtt�M*i �? i^��*�Mh��4 hi�iU|t |�@| �i h�*i
L�| |��t |)Ti Lu UhLtt�MLh_ih MLhhL��?} @?_ *i?_�?}�D
�t @? i4T�h�U@* ThLTLt�|�L?c �?|ihit| h@|i T@h�|) _Lit TLLh*)� W? hitTL?ti |L |��tc hi�
8Rxu pdunhw0vhjphqwdwlrq dvvxpswlrq pd| fdswxuh zkdw dfwxdoo| kdsshqv lq wkh diwhupdwk ri d �qdqfldofulvlv1 Grphvwlf uhvlghqwv pd| eh ihduixo ri eruurzlqj lq iruhljq pdunhwv ehfdxvh ri frqfhuqv derxw h{fkdqjhulvn +khgjlqj pdunhwv whqg wr ehfrph yhu| looltxlg dw wlphv olnh wklv,1 Vlploduo|/ iruhljq uhvlghqwv pd| qrwzdqw wr ohqg lq grphvwlf pdunhwv1 Zkloh rxu pdunhw0vhjphqwdwlrq dvvxpswlrq pd| eh sodxvleoh/ wkh idfwruvwkdw mxvwli| lw duh qrw suhvhqw lq rxu prgho1
�S
ti@hU�iht Lu|i? �?|hL_�Ui i L}i?L�t*) @ |ih4 *�!i L�h b �? E���2�� W? UL?�i?|�L?@* Th@U|�Uic
b �t �?|ihThi|i_ @t hi�iU|�?} @ h�t! Thi4��4� ��h ti|�T 4@) ThL��_i @? @*|ih?@|��i �?|ih�
Thi|@|�L?�
#i|@�*t @ML�| UL4T�|�?} i^��*�Mh��4 uLh |��t 4L_i* @hi hiTLh|i_ �? |�i @TTi?_� �
e� "�@*�|@|��i �?@*)t�t Lu |�i ,^��*�Mh��4
��h u�** 4L_i* �t ?L| @?@*)|�U@**) |h@U|@M*i @?_ tL |L �?_iht|@?_ �|t �4T*�U@|�L?t uLh |�i
^�it|�L?t �i @t! hi^��hit ?�4ih�U@* t�4�*@|�L?� OL�i�ihc �? tTiU�@* U@tit Lu L�h 4L_i* �|
�t TLtt�M*i |L LM|@�? @?@*)|�U hit�*|tc @| *i@t| *LU@**)� i hiTLh| |�iti hit�*|t �ihi� i
�?_ |�@| |�i �4T*�U@|�L?t Lu @ 4L_i* uLh |�i UL?ti^�i?Uit Lu @? �?|ihit| h@|i U�| _iTi?_
ti?t�|��i*) L? |�i @tt�4T|�L?t� 6Lh i @4T*ic �i _itUh�Mi @ tUi?@h�L �? ���U� |�i Thiti?Ui
Lu @ UL**@|ih@* UL?t|h@�?| �@t |�i igiU| Lu @4T*�u)�?} |�i i T@?t�L?@h) igiU|t Lu @? �?|ihit|
h@|i U�| |�@| �L�*_ LUU�h �? |�i @Mti?Ui Lu |�i UL?t|h@�?|� i @*tL t�L� �L� |�i UL**@|ih@*
UL?t|h@�?| U@? U@�ti |�i iUL?L4) |L UL?|h@U| �? hitTL?ti |L @? �?|ihit| h@|i U�|� W? |��t
U@tic |�i UL?|h@U|�L? �t 4@h!i_ M) @ hi_�U|�L? �? uLhi�}? U@T�|@* �?�L�t�
i �_i?|�u) @ ti| Lu @tt�4T|�L?t �?_ih ���U� @ U�| �? |�i _L4it|�U h@|i Lu �?|ihit| U@?
ThL_�Ui |�i *@||ih igiU|� N?_ih |�iti @tt�4T|�L?tc 5 �t |�i L?*) �@h�@M*i u@U|Lh Lu ThL_�U|�L?
�? |�i ThL_�U|�L? Lu |h@_i_ }LL_t @?_ �t t�M�iU| |L _�4�?�t��?} hi|�h?t( |h@_i_ @?_ ?L?�
|h@_i_ }LL_t @hi ?L| �ih) t�Mt|�|�|@M*i �? |�i ThL_�U|�L? Lu �?@* }LL_t( @?_ |�i t�3i Lu |�i
i |ih?@* _iM| �t t4@**� A�i @tt�4T|�L?t |�@| |�i i*@t|�U�|) Lu t�Mt|�|�|�L? Mi|�ii? |h@_i_
@?_ ?L?�|h@_i_ }LL_t �t *L� @?_ |�@| |�i _iM| �t *L� @TTi@ht Uh�U�@* |L |�i hit�*|� A�@|
�tc �| �t TLtt�M*i |L UL?t|h�U| i @4T*it ��ihi @ UL4M�?@|�L? Lu |�i L|�ih @tt�4T|�L?t _Lit
?L| �L*_ @?_ ��ihi @? �?|ihit| h@|i U�| t|�** ThL_�Uit @ hiUitt�L?� OL�i�ihc �? |�i i @4T*it
UL?t�_ihi_ Mi*L�c @ 4L_it| _i}hii Lu t�Mt|�|�|�L? Mi|�ii? |h@_i_ @?_ ?L?�|h@_i_ }LL_t
@?_ @ 4L_it| @4L�?| Lu i |ih?@* _iM| @*�@)t �@t |�i UL?ti^�i?Ui |�@| @? �?|ihit| h@|i U�|
ThL_�Uit @? i T@?t�L?� W? u�|�hi _h@u|t �i T*@? @ 4Lhi t)t|i4@|�U ti| Lu i Tih�4i?|t �? |�i
tT@Ui Lu 4L_i* iUL?L4�it UL?t�_ihi_ �? |��t T@Tih�
W? |�i �ht| t�MtiU|�L? Mi*L�c �i _itUh�Mi |�i ?@|�hi Lu |�i 4L?i|@h) i Tih�4i?|t @?@�
*)3i_ �ihi� A�i tiUL?_ t�MtiU|�L? �_i?|��it @ T@h|�U�*@h �iht�L? Lu L�h 4L_i* uLh ���U� �i
�@�i @?@*)|�U hit�*|t� A�@| tiU|�L? @*tL i T*@�?t ��) L�h t|h@|i}) Lu U�@h@U|ih�3�?} 4L?i�
|@h) TL*�U) �? |ih4t Lu |�i �?|ihit| h@|i t�4T*��it |�i |iU�?�U@* @?@*)t�t Lu |�i 4L_i*c ���*i
i?|@�*�?} ?L *Ltt Lu }i?ih@*�|)� A�i |��h_ t�MtiU|�L? �?�it|�}@|it |�i ThLTih|�it Lu |�@| 4L_i*c
@?_ Lu _i��@|�L?t uhL4 |�@| 4L_i*�
�.
e��� A�i �@|�hi Lu |�i �L*�U) , Tih�4i?|
W? L�h @?@*)t�tc �i UL4T@hi |�L i^��*�Mh�@c uLh | ' fc �c 2c ���� � W? ML|�c |�i UL**@|ih@*
UL?t|h@�?| �t M�?_�?} �? i@U� _@|i� W? i@U� U@tic �i U�@h@U|ih�3i 4L?i|@h) TL*�U) M) |�i U�L�Ui
Lu |�i ?L4�?@* �?|ihit| h@|ic -|c �? |�i _L4it|�U 4L?i) 4@h!i|� W? |�i M@ti*�?i i^��*�Mh��4c
-| �t �i*_ UL?t|@?|c -| ' -rc �? i@U� Tih�L_� ��h hit|h�U|�L? |�@| |�i U�hhi?| @UUL�?|
�t @*�@)t 3ihL }�@h@?|iit |�@| |�i hi*@|��i Th�Uit @?_ ^�@?|�|�it �? |��t i^��*�Mh��4 @hi
|�4i��?�@h�@?|� W? |�i TL*�U) �?|ih�i?|�L? i^��*�Mh��4c |�i 4L?i|@h) @�|�Lh�|) �?i TiU|i_*)
�4T*i4i?|t @ L?i�|�4i _hLT �? |�i �?|ihit| h@|i �? | ' fc ��ic -f -rc -| ' -r uLh | � ��
A��t _hLT �@t @ ?L?�?i�|h@* �4T@U| L? @**LU@|�L?t MiU@�ti Lu L�h @tt�4T|�L? � |@!i? uhL4
|�i *�|ih@|�hi L? |�i *�4�|i_ T@h|�U�T@|�L? 4L_i*t Lu 4L?i) � @ML�| |�i |�4�?} Lu @U|�L?t M)
_�gihi?| @}i?|t _�h�?} |�i Tih�L_� �| |�i Mi}�??�?} Lu |�i Tih�L_c |�i �L�ti�L*_ 4@!it @
_iTLt�| _iU�t�L?� A�i?c |�i 4L?i|@h) @�|�Lh�|) |@!it �|t @U|�L? @?_ @u|ih |�@| @** |�i L|�ih
Tih�L_ | �@h�@M*it @hi _i|ih4�?i_� i @tt�4i |�@| @| |�i Mi}�??�?} Lu Tih�L_ | ' fc ��i?
|�i �L�ti�L*_ 4@!it �|t _iTLt�| _iU�t�L?c �| i TiU|t -| ' -r uLh | � f� �| |�i Mi}�??�?} Lu
Tih�L_ | ' �c 2c ��� |�i �L�ti�L*_ i TiU|t -| ' -r _itT�|i |�i u@U| |�@| �|t i TiU|@|�L? �@t
��L*@|i_ �? Tih�L_ | ' f�
B��i? |�i @tt�4T|�L?t Lu L�h 4L_i*c |�i hi*@|��i Th�Uit @?_ ^�@?|�|�it �? |�i M@ti*�?i
@?_ TL*�U) �?|ih�i?|�L? i^��*�Mh�@ @hi �_i?|�U@* �? | � �c M�| |�i) _�gih �? | ' f� ��h
@?@*)t�t uLU�tit L? |��t _�gihi?Ui �? Tih�L_ f� W? T@h|�U�*@hc �i �?�it|�}@|i ��@| UL?_�|�L?t
}�@h@?|ii |�@| L�|T�| @?_ i4T*L)4i?| �? | ' f uLh |�i TL*�U) �?|ih�i?|�L? i^��*�Mh��4 @hi
*L�ih |�@? |�i) @hi �? |�i M@ti*�?i i^��*�Mh��4� �iU@�ti |�i) @hi |�4i �?�@h�@?|c �i hiuih
|L �@*�it Lu hi*@|��i Th�Uit @?_ ^�@?|�|�it �? | � f �? |�i M@ti*�?i i^��*�Mh��4c @?_ | : f �?
|�i TL*�U) �?|ih�i?|�L? i^��*�Mh��4 @t |�i�h t|i@_) t|@|i �@*�it� �iU@�ti Lu |�i t�4T*�U�|) Lu
|�iti i^��*�Mh�@c |�i @?@*)t�t �@t @ t|@|�U �@�Lh� W| L?*) �?�L*�it UL4T@h�?} |�i t|i@_) t|@|i
hi*@|��i Th�Uit @?_ ^�@?|�|�it ��|� |�i | ' f �@*�it Lu |�i �@h�@M*it �? |�i TL*�U) �?|ih�i?|�L?
i^��*�Mh��4�
e�2� � 5�4T*��i_ �L_i*
A�hL�}�L�| |��t tiU|�L?c �i @tt�4i �|n� � �|� W? @__�|�L?c �i @tt�4i |�@| 5 �t itti?|�@* �?
ThL_�U|�L? Lu |�i |h@_i_ }LL_c @?_ |�@| *@MLh U@??L| Mi @_��t|i_ �? |�@| tiU|Lh� i U@T|�hi
|��t ��|� |�i tTiU��U@|�L?c 1 ' D ' >� ' >2 ' �c tL |�@| |�i |h@_i_ }LL_t ThL_�U|�L?
u�?U|�L? �t }��i? M) E���S�� 6Lh t�4T*�U�|)c �i @*tL i U*�_i |�i �@}i M�** uhL4 |�i UL**@|ih@*
UL?t|h@�?|G
��^�g� n �A ^AgA � -W5 n E� n oW��� Ee���
`�|� |�iti t�4T*��U@|�L?tc �i t�L� |�@| �i U@? @?@*)3i |�i hitTL?ti Lu |�i | ' f �@*�it
�H
Lu |�i �@h�@M*it �? L�h 4L_i* |L |�i | ' f U�| �? |�i �?|ihit| h@|i @t |�i �?|ihtiU|�L? Lu |�L
U�h�itc i@U� L?i �?�L*��?} |�i i?_L}i?L�t �@h�@M*itc R� @?_ uc @?_ |�i i L}i?L�t TL*�U)
�@h�@M*ic -f E��i? |�ihi �t ?L h�t! Lu UL?u�t�L?c �i _hLT |�4i t�MtUh�T|t�� A�i �ht| U�h�i
t�44@h�3it i^��*�Mh��4 �? |�i *@MLh 4@h!i|c @?_ tL �i hiuih |L �| @t |�i w� E�w@MLh �@h!i|<�
U�h�i� A�i L|�ih U�h�ic MiU@�ti �| �?ULhTLh@|it hit|h�U|�L?t uhL4 |�i @tti| 4@h!i|c �t U@**i_
|�i �� E��tti| �@h!i|<� U�h�i� i ?L� _�tU�tt |�iti �? |�h?� A�i t�4T*�U�|) Lu |�i @?@*)t�t
hi�iU|t �? T@h| |�i u@U| |�@| �i U�@h@U|ih�3i TL*�U) �? |ih4t Lu |�i �?|ihit| h@|ic h@|�ih |�@?
|�i 4L?i) t�TT*)� A�i *@t| t�MtiU|�L? Mi*L� t�L�t |�@| |��t �?�L*�it ?L *Ltt Lu }i?ih@*�|)c
t�?Ui |�ihi �t @*�@)t @ 4L?i) }hL�|� h@|i |�@| U@? t�TTLh| @?) �?|ihit| h@|i TL*�U)c @t *L?}
@t - : ��
e�2��� w@MLh �@h!i|
,^�@|�?} |�i �L�ti�L*_ @?_ ?L?|h@_i_ }LL_ �h4 ,�*ih i^�@|�L?t uLh *@MLhc E��D� @?_ E��2��c
�i LM|@�?GS
-u�nk 'R� E�� k�
�g�
�k�fR
� Ee�2�
W? |��t i Thitt�L?c �| �t �?_iht|LL_ |�@| R �t |�i t�4T*i u�?U|�L? Lu R� }��i? �? E��H�� �t
?L|i_ @ML�ic �i |��?! Lu - @t @? i L}i?L�t �@h�@M*i� 5Lc |��t i Thitt�L? U�@h@U|ih�3it |�i
hi*@|�L?t��T Mi|�ii? u @?_ R� �4TLti_ M) i^��*�Mh��4 �? |�i *@MLh 4@h!i|� W| �t i@t) |L tii
|�@| |��t w� i^�@|�L? �t TLt�|��i*) t*LTi_ ��i? }h@T�i_ ��|� R� L? |�i �ih|�U@* @ �t @?_
u L? |�i �Lh�3L?|@*� � ��}�ih R� �t UL?t�t|i?| ��|� @ ��}�ih u MiU@�ti �| t��u|t |�i *@MLh
_i4@?_ U�h�i |L |�i h�}�|c ���*i *i@��?} |�i *LU@|�L? Lu *@MLh t�TT*) �?U�@?}i_�. W| �t @*tL
i@t) |L tii |�@| @ u@** �? - t��u|t |�i w� i^�@|�L? |L |�i h�}�|� A��t hi�iU|t |�@| @ u@** �? -
t��u|t *@MLh _i4@?_ |L |�i h�}�| @?_ |��t hit�*|t �? @? �?Uhi@ti �? i^��*�Mh��4 u uLh @ � i_
*i�i* Lu R� �
e�2�2� �tti| �@h!i|
i ?L� |�h? |L |�i �� i^�@|�L?� A��t �t UL?t|h�U|i_ M) UL4M�?�?} |�i ThL_�U|�L? u�?U�
|�L?t �? ML|� tiU|Lhtc E���e�c |�i �ht| Lh_ih UL?_�|�L? uLh |�i �?|ih4i_�@|i �?T�|c E��2D�c |�i
R� i^�@|�L?c E��b�c @?_ |�i UL**@|ih@* UL?t|h@�?|c Ee���c �?_ih |�i @tt�4T|�L? |�@| �| �t M�?_�
�?}� 5�Mt|�|�|i |�i i Thitt�L? uLh @tti| Th�Uitc E���b�c �?|L |�i UL**@|ih@* UL?t|h@�?|c Ee���c
9Wkh devhqfh ri d pxowlsolhu lq +715, uh�hfwv wkdw zh qrz gurs wkh zdjh eloo iurp wkh froodwhudo frqvwudlqw1:Iroorzlqj frqyhqwlrq/ zh wklqn ri oderu vxsso| dqg ghpdqg dv fruuhvsrqglqj wr wkh Hxohu htxdwlrqv/
+618, dqg +6156,1 Zh wklqn ri wkhvh uhodwlrqvklsv lq d gldjudp zlwk Z@S rq wkh yhuwlfdo d{lv dqg O rq wkhkrul}rqwdo1
�b
i�@*�@|i_ ��|� @? i^�@*�|) @?_ @tt�4i |�@| �� ' �A ' � |L LM|@�?G
�
�� b�dw+A n kR�+� n lRSo ' -W5 n E� n oW��c Ee���
��ihi l ' q
RrSrE^�r g
�n^Ar gA � �t @ UL?t|@?|� �Mti?Ui Lu @ |�4i t�MtUh�T| �?_�U@|it | ' fc @?_
|�i t�MtUh�T|c rc _i?L|it t|i@_) t|@|i� Oihic �i �@�i �ti_ |�i u@U|c \2*\� ' RS*RrSr� A�i �ht|
|�L |ih4t �? |�i *iu| �@?_ t�_i Lu |�i UL**@|ih@* UL?t|h@�?| @hi |�i | ' f T�� �g 4�*|�T*�i_
M) |�i hitTiU|��i U@T�|@* t|LU!t @?_ |�i |��h_ �t |�i Thiti?| _�tUL�?|i_ �@*�i Lu u�|�hi U@t�
�L�t� Nt�?} |�i 3ihL ThL�| UL?_�|�L? L? �?@* UL?t�4T|�L? }LL_ �h4tc RS ' SA n R�S� c �i
U@? �h�|i U�hhi?| tTi?_�?} �? |ih4t Lu |h@_@M*it @t
RS '
;?=� n%E�� ��R�
�
�<@> R�S� � Ee�e�
5�Mt|�|�|�?} |��t �?|L Ee���c L�h i Thitt�L? uLh |�i UL**@|ih@* UL?t|h@�?| hi_�Uit |LG
�
� � b�
;?=w+A n
57kn l
3C� n %E�� ��R�
�
�4D68 R�+�<@> Ee�D�
' -W5 n E� n oW��
,^��*�Mh��4 �? |�i }LL_t 4@h!i| )�i*_t |�i uL**L��?} i Thitt�L? uLh R� G
R� '
#�� �
�
$ �3#
##SA
S�
$ �
#
'
#�� �
�
$ �3#
#
3EC��gA
�w5�3w �-W5 � oW�
Eg� �k u�3k
4FD�
#
� Ee�S�
6�?@**)c |@!i �?|L @UUL�?| |�i �ht| Lh_ih UL?_�|�L? uLh 5G
E� � w���gA
�w53w ' E� n b�-W� Ee�.�
,^�@|�L?t Ee�D�c Ee�S�c @?_ Ee�.� hiThiti?| |�hii i^�@|�L?t �? |�i uL�h �?!?L�?tc bc 5c R�
@?_ u� A�i |��h_ _i�?it b @t @ u�?U|�L? Lu 5 @?_ |�i tiUL?_ _i�?it 5 @t @ u�?U|�L? Lu R�
E�| �t t�?}*i��@*�i_ @t *L?} @t b � f� @?_ u� 5Lc |�i |�hii i^�@|�L?t U@? Mi �ti_ |L _i�?i @
2f
hi*@|�L?t��T Mi|�ii? R� @?_ u @*L?i� A��t hi*@|�L?t��T �t ��@| �i U@** |�i �� U�h�i�
W| �t U*i@h |�@| |�i t*LTi Lu |�i �� U�h�i �t itti?|�@* �? _i|ih4�?�?} ��i|�ih @? �?|ihit|
h@|i U�| �t i T@?t�L?@h) Lh UL?|h@U|�L?@h)� 6Lh i @4T*ic �u �| �t _L�?�@h_ t*LTi_c |�i? @
t��u| h�}�| �? |�i w� U�h�i �?_�Ui_ M) @ U�| �? |�i �?|ihit| h@|i _h��it u �T @?_ R� _L�?�
A�i UL?|h@U|�L?@h) U@ti hit�*|t ��i? |�i �� U�h�i �t TLt�|��i*) t*LTi_ @?_ U�|t |�i w�
U�h�i uhL4 Mi*L�� W? }i?ih@*c �| �t ?L| TLtt�M*i |L t@) ��@| |�i t*LTi Lu |�i �� U�h�i �t� i
t�@** tii �? |�i ?i | t�MtiU|�L? |�@| uLh T@h|�U�*@h T@h@4i|ih UL?�}�h@|�L?tc �| �t TLtt�M*i |L
_i|ih4�?i |�i t*LTi�
6�?@**)c �i �?_ �| �tiu�* |L _i�?i |�i �iht�L? Lu |�i �� U�h�i |�@| �L*_t ��i? |�i
UL**@|ih@* UL?t|h@�?| �t ?L| M�?_�?}�H W? |��t U@tic �?�|i 5 hi^��hit w : f� `�i? |�i UL**@|ih@*
UL?t|h@�?| �t ?L| M�?_�?}c �i *Lti L?i i^�@|�L?c Ee�D�c @?_ L?i �@h�@M*ic bc uhL4 L�h t)t|i4�
�t @ hit�*|c |�i �� U�h�i �t _i�?i_ t�4T*) M) Ee�S� @?_ Ee�.� ��|� b ' f� W| �t |h���@* |L tii
|�@| �? |��t U@tic |�i �� U�h�i �t _i�?�|i*) _L�?�@h_ t*LTi_�
e�2��� ,^��*�Mh��4
�t |�i Thi��L�t _�tU�tt�L? �?_�U@|itc |L UL?t|h�U| |�i �� U�h�i �| �t ?iUitt@h) |L �ht|
UL4T�|i |�i �@*�it Lu |�i �@h�@M*it �? |�i M@ti*�?i i^��*�Mh��4 E��i�c |�i t|i@_) t|@|i �@*�it
Lu |�i �@h�@M*it�� A��t �t @ t|h@�}�|uLh�@h_ i ihU�tic ���U� �t _�tU�tti_ �? |�i @TTi?_� � W?
|�i ?�4ih�U@* i Tih�4i?|t hiTLh|i_ �? |��t T@Tihc �i @*�@)t uL�?_ |�@| |�i t|i@_) t|@|i Lu
|�i 4L_i* �t �?�^�i�
W? |�i hi4@�?_ih Lu |��t t�MtiU|�L? �i �ih�u) |�@| uLh @ }��i? Tih�L_ f �?|ihit| h@|ic
-c �@*�it Lu R� c u _i�?i_ M) |�i �?|ihtiU|�L? Lu |�i �� @?_ w� U�h�it ULhhitTL?_ |L
@ TL*�U) �?|ih�i?|�L? i^��*�Mh��4� �) |��t �i 4i@? |�@|c }��i? t�U� �@*�it Lu R� @?_ uc
�@*�it uLh Rc S� c SA c Sc �c bc 5c +A c +� c ^A c ^� c RA c % U@? Mi uL�?_ ���U� t@|�tu) @** |�i
i^��*�Mh��4 UL?_�|�L?t uLh | ' f� Vih�u)�?} |�@| |��t �t |h�i uLh @** M�| |�i *@t| |�L �@h�@M*it
�t t|h@�}�|uLh�@h_� 6Lh i @4T*ic R U@? Mi UL?t|h�U|i_ uhL4 R� �t�?} E��H�c S� U@? Mi
UL?t|h�U|i_ uhL4 |�i ?L?|h@_i_ }LL_ ThL_�U|�L? u�?U|�L?c @?_ tL L?�
i ?L� Mh�i�) _�tU�tt |�i UL?t|h�U|�L? Lu RA @?_ %� #���_i |�i 4L?i) 4@h!i| U*i@h�?}
UL?_�|�L?c E��2H�c M) |�i i^��*�Mh��4 U@t� UL?t|h@�?|c E��2b�c |L LM|@�?G
_n %
� n %'
�
R
u
S'
R� E�� k� S�
R-u
u
S'
� � k
-
R�S�
RS
'�� k
-�� n
�E�3��R�
�
�#3�� c
;Wkh DP fxuyh lq wklv fdvh lv d elw ri d plvqrphu/ vlqfh dvvhw sulfhv gr qrw dsshdu1
2�
@u|ih �t�?} E��2�� @?_ Ee�e�� 5�?Ui _ �t Thi_i|ih4�?i_ @| �|t t|i@_) t|@|i �@*�ic |��t i Thitt�L?
U@? Mi �ti_ |L _i_�Ui %� �M��L�t*)c |�ihi �t @*�@)t @? % |�@| t@|�t�it |��t i Thitt�L?c uLh
@?) - : ��b `�i|�ih @ U�| �? - hi^��hit |�@| |�i 4L?i|@h) @�|�Lh�|) �?Uhi@tit Lh _iUhi@tit
% _iTi?_t �TL? |�i hitTL?ti Lu R� � i U@? _i|ih4�?i RA uhL4 E��2b��
6�?@**)c �i �ti @ t|@?_@h_ @h}�4i?| |L _i_�Ui |�i ?L4�?@* i U�@?}i h@|i uhL4 RA �
i @tt�4i T�hU�@t�?} TL�ih T@h�|) �? uLhi�}? @?_ _L4it|�U |h@_i_ }LL_t� A�i?c |@!�?}
|�i �?�|�@* t|LU! Lu 4L?i) @?_ |�i uLhi�}? Th�Ui *i�i* @t Thi_i|ih4�?i_c �i U@? �?|ihThi|
�@h�@|�L?t �? RA @t hi�iU|�?} 4L�i4i?|t �? |�i ?L4�?@* i U�@?}i h@|i�
e��� ,giU|t Lu @? W?|ihit| +@|i ��|
W? |��t tiU|�L?c �i i @4�?i |�i hitTL?ti Lu i^��*�Mh��4 L�|UL4it @| | ' f |L @? �?|ihit| h@|i
U�|� �L?t�_ih �ht| |�i U@ti ��i? |�i UL**@|ih@* UL?t|h@�?| �t ?L| M�?_�?}� �t ?L|i_ @ML�ic
�? |��t U@ti |�i �� U�h�i �t _L�?�@h_ t*LT�?}� 6hL4 |��t �i UL?U*�_iG
�hLTLt�|�L? � Wu |�i UL**@|ih@* UL?t|h@�?| �t ?L| M�?_�?} @?_ � : -Wc |�i? @ U�| �? -
ThL_�Uit @ h�ti �? uc @ u@** �? R� c @?_ ?L U�@?}i �? 5�
A�i 4L?i|@h) |h@?t4�tt�L? 4iU�@?�t4 �?_ih*)�?} |��t hit�*| ULhhitTL?_t |L |�i t|@?_@h_
4iU�@?�t4 i4T�@t�3i_ �? |�i *�|ih@|�hi L? |�i *�4�|i_ T@h|�U�T@|�L? 4L_i* Lu 4L?i)� � U�|
�? - hi_�Uit |�i ULt| Lu ��h�?} *@MLhc @?_ tL hit�*|t �? @? i T@?t�L? �? i4T*L)4i?| @?_ @
h�ti �? |�i ThL_�U|�L? Lu ?L?|h@_i_ }LL_t� A�i U�| �? |�i �?|ihit| h@|i ThL_�Uit @ u@** �?
|�i 4@h}�?@* ULt| Lu ThL_�U�?} ?L?|h@_i_ }LL_tc hi*@|��i |L |�i 4@h}�?@* ULt| Lu ThL_�U�?}
|h@_i_ }LL_tc @?_ |��t hit�*|t �? |�i u@** �? R� � A�i Ui?|h@* M@?! i?}�?iiht |�i U�| �? - M)
ThL_�U�?} @ t��|@M*i 4L�i �? %�
i ?L� |�h? |L |�i U@ti ��i? |�i UL**@|ih@* UL?t|h@�?| �t M�?_�?} �? ML|� |�i M@ti*�?i
@?_ TL*�U) �?|ih�i?|�L? i^��*�Mh�@� i Mi}�? ��|� |�i U@tic w ' fc ��i? 5 �t |�i L?*) u@U|Lh Lu
ThL_�U|�L? �? |�i |h@_i_ }LL_ tiU|Lh� W? |��t U@tic @ U�| �? - �t @*�@)t i T@?t�L?@h)� `�i?
w ' fc t�Mt|�|�|�L? Lu Ee�S� @?_ Ee�.� �?|L Ee�D� hit�*|t �? |�i uL**L��?} @?@*)|�U hiThiti?|@|�L?
Lu |�i �� U�h�iG
%#b�
� � b�
$l� �
& #�� �
�
$#3�
Ee�H�
<Zh h{foxgh U � 4= Iru U ? 4 lw fdq eh yhul�hg wkdw wkhuh lv qr htxloleulxp1 Zlwk d qhjdwlyh lqwhuhvwudwh/ �upv frxog pdnh lq�qlwh sur�wv e| eruurzlqj lq�qlwh dprxqwv ri prqh|1 Iru h{dpsoh/ d �up wkdweruurzv \ xqlwv ri grphvwlf fxuuhqf| dw wkh ehjlqqlqj ri wkh shulrg uhwxuqv U\ xqlwv ri fxuuhqf| wr wkh�qdqfldo lqwhuphgldu| dw wkh hqg ri wkh shulrg dqg sd|v +4 �U,\ A 3 xqlwv ri fxuuhqf| rxw dv glylghqgv1Glylghqgv duh pdgh lq�qlwh e| pdnlqj \ lq�qlwh1 Qr htxloleulxp frxog h{lvw lq wklv fdvh/ vlqfh wkh vxsso|ri ixqgv lq wkh prqh| pdunhw dw dq| gdwh lv erxqghg deryh1 Zh dovr h{foxgh U @ 4 ehfdxvh rxu fdofxodwlrqvdvvxph wkdw wkh htxloleulxp fdvk lq dgydqfh frqvwudlqw/ +615<,/ krogv dv d vwulfw htxdolw|1
22
'
+doW n bE� n oW�o�
ER��# +��
#b�
� � b�
$Ekn l�
�R���3#,
�
W? @__�|�L?c �| �t i��_i?| uhL4 Ee�S� |�@| ��i? w ' fc 5 �t @? �?Uhi@t�?} u�?U|�L? Lu�R��#+� �
6�?@**)c @t *L?} @t � : -Wc b �t @ TLt�|��i UL?t|@?|�
�L|i �ht| |�@| ��i? � ' fc Ee�H� T�?t _L�? @ �?�^�i �@*�i uLh R� c tL |�@| |�i ��
i^�@|�L? �t �Lh�3L?|@*� W? |��t U@tic @ U�| �? - ThL_�Uit @ h�ti �? u @?_ ?L U�@?}i �? R�
Lh 5� A�i �?|��|�L? uLh |��t �t t�4T*ic @?_ U@? Mii? tii? M) �?tTiU|�?} Ee�D� @?_ Ee�S�� �L|i
|�@|c ��i? � ' w ' f |�L |��?}t �@TTi?� 6�ht|c @? i^��ThLTLh|�L?@* h�ti �? 5 @?_ +�
ThL_�Uit ?L U�@?}i �? R� � A��t �t MiU@�ti ��|� � ' w ' f |�ihi @hi ?L _�4�?�t��?} hi|�h?t
@t @? �?Uhi@ti �? 5 ThL_�Uit @? �?Uhi@ti �? SA � 5iUL?_c uLh � i_ R� c @? i^��ThLTLh|�L?@*
�?Uhi@tit �? +� @?_ 5 ThL_�Uit i^��ThLTLh|�L?@* �?Uhi@tit �? |�i *iu| @?_ h�}�| t�_i Lu |�i
UL**@|ih@* UL?t|h@�?|� N?_ih |�iti U�hU�4t|@?Uitc |�i UL**@|ih@* UL?t|h@�?| t�4T*) _Lit ?L|
}i| �? |�i �@) Lu |�i |)Ti Lu i T@?t�L? �? L�|T�| @ttLU�@|i_ ��|� @? �?|ihit| h@|i U�| ��i?
|�i UL**@|ih@* UL?t|h@�?| �t ?L?M�?_�?}� �? |�i UL?|h@h)c |�i UL**@|ih@* UL?t|h@�?| @4T*��it
|�i hitTL?ti Lu i4T*L)4i?| |L @? �?|ihit| h@|i t�LU! M) Thi�i?|�?} |�i _iU*�?i �? R� |�@|
�L�*_ LUU�h �? |�i @Mti?Ui Lu |�@| UL?t|h@�?|c @UULh_�?} |L �hLTLt�|�L? ��
`�i? � : f |�i? ML|� ThLTLh|�L?@*�|) hit�*|t U�|i_ �? |�i Thi��L�t T@h@}h@T� u@�*c @?_
|�i �� U�h�i �t ?L *L?}ih �Lh�3L?|@*� 6Lh i @4T*ic |�ihi @hi ?L� _�4�?�t��?} hi|�h?t �?
|h@?tuLh4�?} @__�|�L?@* 5 �?|L i |h@ SA � `�|� � : f |�i �� U�h�i �@t @ ?i}@|��i t*LTic
@UULh_�?} |L Ee�H���f�� wLLti*)c @ h�ti �? � ThL_�Uit @ U*LU!��ti hL|@|�L? �? |�i �� U�h�i�
�t @ hit�*|c @ U�| �? - }i?ih@|it @ h�ti �? u @?_ @ u@** �? R� ��i? � : f� ,^�@|�L? Ee�H�
@*tL t�L�t |�@|�R��#+� h�tit ��|� |�i U�| �? - uLh f � # �� A��t �4T*�it |�@| |�i U�| �?
- }i?ih@|it @ h�ti �? 5� i t�44@h�3i |�iti �?_�?}t �? @ ThLTLt�|�L?G
�hLTLt�|�L? 2 E�� `�i? w ' � ' fc � : -Wc @ U�| �? - ThL_�Uit @ h�ti �? u @?_ 5c @?_
?L U�@?}i �? R� �
E��� `�i? w ' fc � : f @?_ � : -Wc @ U�| �? - ThL_�Uit @ h�ti �? u @?_ 5c @?_ @ u@**
�? R� �
43Htxdwlrq +71;, vxjjhvwv wkh srvvlelolw| wkdw zkhq � A 4 dqg odujh hqrxjk/ wkhq wkh DP fxuyh pd| ehsrvlwlyho| vorshg zlwk E A 3/ shukdsv hyhq vwhhshu wkdq wkh OP fxuyh1 Wkh odwwhu fdvh lv wkh rqh wkdw lvuhtxluhg iru d fxw lq U wr jhqhudwh d uhfhvvlrq1 Zh kdyh qrw frqvlghuhg wklv fdvh ehfdxvh zh ylhz wkh fdvh/� A 4> dv hpslulfdoo| lpsodxvleoh1 Vwloo/ dqdo|vlv ri wklv fdvh pd| |lhog lqvljkwv lqwr wkh qdwxuh ri rxu prgho/dqg zh sodq wr gr wklv lq ixwxuh gudiwv1
44Wkh vorsh ri wkh DP fxuyh lv jlyhq e|=
gsQ
gO@ �
^� . � +4 . u�,`E
� ^� . � +4 . u�,`E@sQ . +4� �, |Q�� +�. , @+4� ��,
4� �
O=
2�
i UL?U*�_i uhL4 |��t _�tU�tt�L? |�@| ��i? w ' fc L�h t�4T*i i?��hL?4i?| U@??L|
h@|�L?@*�3i |�i ?L|�L? |�@| @? �?|ihit| h@|i U�| ThL_�Uit @ hiUitt�L?�
i ?L� |�h? |L |�i U@tic w : f� 5�TTLti �ht| |�@| # ' �� 6hL4 Ee�S�c �i tii |�@| 5 U@?
Mi i Thitti_ @t @ u�?U|�L? Lu R�+� ��2 �UULh_�?} |L Ee�.� b �t @ u�?U|�L? Lu 5c @?_c �i?Ui Lu
R�+� � 5�Mt|�|�|�?} |�iti hit�*|t �?|L Ee�D�c �i UL?U*�_i |�@| ��i? w : f @?_ # ' �c |�i ��
U�h�i T�?t _L�? R�+� � W? T@h|�U�*@hc |�i U�h�i �t _L�?�@h_�t*LT�?}� �t @ hit�*|c @ U�| �?
- ThL_�Uit @ h�ti �? u @?_ @ u@** �? R� � �iU@�ti R�+� hi4@�?t �?U�@?}i_c �| uL**L�t |�@| 5
_Lit ?L| U�@?}i� A�i �� U�h�i @?_ |�i w� U�h�it MiuLhi @?_ @u|ih |�i U�| �? |�i �?|ihit|
h@|i @hi _�tT*@)i_ �? 6�}�hi �� i t�44@h�3i |��t �?_�?} @t uL**L�tG
�hLTLt�|�L? � `�i? w : f @?_ # ' �c |�i? @ U�| �? - ThL_�Uit @ h�ti �? uc @ u@** �? R� c
@?_ ?L U�@?}i �? 5�
i �@�i ?L| Mii? @M*i |L LM|@�? @?@*)|�U hit�*|t uLh f � # �c ��i? w : f� OL�i�ihc
��i? �i *�?i@h�3i |�i �� U�h�i @ML�| t|i@_) t|@|i �i �?_c uLh # ' fG��
_R�
_u'
R�
u
qw+A � E�� b�� doW n bE� n oW�o�
rE�� k�
�bEk n l�R�+��
�L|i |�@| ��i? � ' fc |��t i Thitt�L? �t _i�?�|i*) TLt�|��i� Wuc �? @__�|�L?c |�i t*LTi �t
t|iiTih |�@? |�i t*LTi Lu |�i w� U�h�ic �i !?L� |�@| ��|� @ t4@** U�| �? |�i �?|ihit| h@|ic
|�ihi �t @ Tih�L_ f ti| Lu i^��*�Mh��4 @**LU@|�L?t �? ���U� u @?_ R� @hi ML|� *L�ih� W? |��t
U@tic 5 4�t| u@** |LL� i �@�i UL?t|h�U|i_ ?�4ih�U@* i @4T*it ��|� � ' # ' fc �? ���U�
|�i �� U�h�i �?_ii_ _Lit U�| |�i w� U�h�i uhL4 Mi*L� @?_ @ U�| �? |�i �?|ihit| h@|i _Lit
}i?ih@|i @ _hLT �? u @?_ 5� W? |�iti i @4T*itc �i �ih��i_ ?�4ih�U@**) |�@| |�ihi �t @ �?�^�i
�?|ihtiU|�L? |L |�i w� @?_ �� U�h�it� 6�}�hi 2 _�tT*@)t |�i �� @?_ w� U�h�it uLh L?i
i @4T*i ��|� # ' f��e
5L u@hc �i �@�i uL�?_ |�i uL**L��?}� i �@�i @? i @4T*i ��|� _�4�?�t��?} hi|�h?t �?
|�i ThL_�U|�L? Lu |h@_i_ }LL_tc 3ihL i*@t|�U�|) Lu t�Mt|�|�|�L? Mi|�ii? |h@_i_ @?_ ?L?|h@_i_
}LL_tc @?_ *L� i |ih?@* _iM|c �? ���U� @ U�| �? - �?_�Uit @ u@** �? L�|T�|� OL�i�ihc �i �?_
|�@| t�Mt|@?|�@* _i��@|�L? uhL4 @?) L?i Lu |�iti @tt�4T|�L?t hi�ihtit |�i hit�*|�
45Wklv uhtxluhv wkdw wkh ixqfwlrq pdsslqj } lqwr D�NW
��}4���U�}� u�E eh lqyhuwleoh1 Lw lv lqyhuwleoh/
jlyhq wkdw zh uhvwulfw } wr wkrvh ydoxhv wkdw vdwlvi| +71:, zlwk � � 3=46Vhh wkh dsshqgl{ iru d ghulydwlrq147Wkh sdudphwhu ydoxhv xqghuo|lqj wklv h{dpsoh duh= � @ 4@4=38> � @ 3=58> � @ 3=9> {v @ 3=39> # @ 4>
#3 @ 3=6> NQ @ NW @ 4> D @ 4=<> U� @ 4 . u� @ 4=38> � @ 3=34> � @ 3=8> E @ 3= Zkhq/ � @ 3> zh rewdlqwkh iroorzlqj vwhdg| vwdwh surshuwlhv iru wklv prgho= Ov @ 3=937> sQv f
Qv @f
Wv @ 4=78<> � @ 3=:<9= Zh gh�qhg
JGS dv sQv fQ .fW . u�E= Lq wklv h{dpsoh/ zh irxqg wkdw wklv txdqwlw| gursv 9 shufhqw zlwk d 7 shufhqwdjh
srlqw fxw lq U1
2e
�L?t�_ihc uLh i @4T*ic |�i T@h@4i|ihc #� i uL�?_ |�@| ��i? �| �@t �?Uhi@ti_ |L @ML�|
f�2c |�i? @? �?|ihit| h@|i U�| *i@_t |L @? i T@?t�L? �? u� OL�i�ihc 5 t|�** u@**t �? |��t U@ti�
W| u@**t i?L�}� tL |�@| C(� u@**t |LLc ��i? 4i@t�hi_ �? M@ti )i@h Th�Uit� `�i? # �@t
�?Uhi@ti_ |L f��c |�i? C(� @U|�@**) h�tit��D
�L?t�_ih |�i igiU| Lu h@�t�?} �� A�i ThiUi_�?} _�tU�tt�L? t�}}it|t |�i TLtt�M�*�|) |�@|
�?Uhi@t�?} |�i _iM| UL�*_ hL|@|i |�i �� U�h�i U*LU!��ti uhL4 @ TLt�|�L? ��|� TLt�|��i t*LTi
|L L?i ��|� @ ?i}@|��i t*LTi� W? ?�4ih�U@* i Tih�4i?|t �i �@�i uL�?_ |�@| |��t �t �?_ii_
|�i U@ti� 6�}�hi � _�tT*@)t |�i hit�*|t Lu L?i t�U� i Tih�4i?|� W| ULhhitTL?_t |L |�i 4L_i*
iUL?L4) �?_ih*)�?} 6�}�hi 2c i UiT| |�@| � �@t Mii? �?Uhi@ti_ |L f��c Lh 2. TihUi?| Lu
C(���S i �?_ �| �?|h�}��?} |�@| |�i @__�|�L? Lu t�Mt|@?|�@* @4L�?| Lu i |ih?@* _iM| U@?
UL?�ih| @ t�|�@|�L? uhL4 L?i �? ���U� @? �?|ihit| h@|i U�| hit�*|t �? @ UL?|h@U|�L?c �?|L L?i
�? ���U� �| hit�*|t �? @? i T@?t�L?� A�i iUL?L4�U �?|ihThi|@|�L? Lu |��t �?_�?} _itih�it
u�h|�ih i T*Lh@|�L?�
i �@�i @*tL i T*Lhi_ 4Lhi M@t�U Tih|�hM@|�L?t L? |�i ThL_�U|�L? u�?U|�L?c M) U�@?}�?}
>�c >2c Dc 1 uhL4 |�i�h �@*�it Lu �?�|) �? |�i @ML�i i @4T*it� �?i UL?t�t|i?| hit�*| �i uL�?_
�t |�@| hi_�U|�L?t �? Dc ���U� LTi?t �T @ hL*i uLh �@h�@M*i *@MLh �? |�i ThL_�U|�L? Lu +A c
4L�it |�i t)t|i4 �? |�i _�hiU|�L? Lu |�i hit�*| |�@| @ _hLT �? - ThL_�Uit @? i T@?t�L?
�? |�i iUL?L4)��. �) hi_�U�?} |�i ULt|t @ttLU�@|i_ ��|� _�4�?�t��?} *@MLh ThL_�U|���|) Lu
hi@**LU@|�?} *@MLh @UhLtt tiU|Lhtc _hLTT�?} D tii4t |L �i*T t�TTLh| @tti|t �@*�it @?_ Thi�i?|
@ |�}�|i?�?} Lu |�i UL**@|ih@* UL?t|h@�?| �? |�i �@!i Lu @ U�| �?-� A��t tii4t |L LTih@|i �? |�L
�@)t� 6�ht|c @ hi@**LU@|�L? Lu hitL�hUit @�@) uhL4 |�i ?L?|h@_i_ }LL_ tiU|Lh @?_ |L�@h_t |�i
|h@_i_ }LL_ tiU|Lh *�4�|t |�i u@** �? R� @u|ih @ U�| �? -� �|�ih |��?}t |�i t@4ic |��t t�TTLh|t
@tti| �@*�it �? |�@| tiU|Lh� 5iUL?_c |�i @**LU@|�L? Lu *@MLh |L�@h_t |�i |h@_i_ }LL_ tiU|Lh
T�t�it �T @tti| �@*�it |�ihi M) h@�t�?} |�i ThL_�U|���|) Lu U@T�|@* �? |�@| tiU|Lh� �*|�L�}�
�i _�_ �?_ �@*�it uLh >�c >2c Dc 1 |�@| �4T*) @ *@h}i hi_�U|�L? �? L�|T�| @?_ i4T*L)4i?|
@u|ih @? �?|ihit| h@|i U�|c |�i hi_�U|�L? �? L�|T�| @?_ i4T*L)4i?| �@t UL?�ih|i_ �?|L @?
i T@?t�L? ��|� |�i �?|hL_�U|�L? Lu @ 4L_it| @4L�?| Lu t�Mt|�|�|@M�*�|) Mi|�ii? S� @?_ SA
@?_ @ 4L_it| @4L�?| Lu i |ih?@* _iM|��H
48Zkhq wkh h{dpsoh ri wkh suhylrxv irrwqrwh zdv prgl�hg vr wkdw � @ 3=5> 3=6 wkh shufhqw fkdqjh lq edvh|hdu JGS lqgxfhg e| d 7 shufhqwdjh srlqw gurs lq U lv �3=45 dqg 3=6 uhvshfwlyho|1
49Zh glg dq h{shulphqw xvlqj wkh sdudphwhu ydoxhv iurp wkh suhylrxv irrwqrwh1 Zh vhw � @ 3 dqg E @ 3=7=Lq wkh vwhdg| vwdwh/ wklv lpsolhv d ghew wr JGS udwlr ri 3193/ ru 93 shufhqw1 Zh irxqg wkdw O dqg } ulvh 418dqg 614 shufhqw/ uhvshfwlyho|/ zlwk d 7 shufhqwdjh srlqw gurs lq U= Zlwk E @ 3> O dqg } erwk gurs e| :=<dqg 56 shufhqw/ uhvshfwlyho| zlwk wkh vdph gurs lq U=
4:Iru h{dpsoh/ � zdv uhgxfhg iurp xqlw| wr 31;8/ wkhq d irxu shufhqwdjh srlqw fxw lq U surgxfhv dq 3=37shufhqw mxps lq JGS dqg dq 31;: shufhqw mxps lq wrwdo hpsor|phqw1 Uhfdoo iurp d suhylrxv irrwqrwh wkdwzkhq � @ 4> wkhq wkhuh lv d :1<7 shufhqw gurs lq hpsor|phqw dqg d 9 shufhqw gurs lq JGS1
4;Iru h{dpsoh/ zlwk �4 @ 4> �5 @ 5=4> � @ 3=:> � @ 3=;8> E @ 3> d irxu shufhqwdjh srlqw fxw lq U surgxfhvd 48 shufhqw gurs lq wrwdo hpsor|phqw dqg d 47 shufhqw gurs lq uhdo JGS1 Zkhq E lv wkhq udlvhg wr 3=4+vr wkdw wkh ghew wr JGS udwlr lq wkh vwhdg| vwdwh lv 3=4;, dqg � lv lqfuhdvhg wr 316/ wkhq wrwdo hpsor|phqw
2D
D� "�@?|�|@|��i �?@*)t�t
W? |��t tiU|�L? �i t|�_) �iht�L?t Lu L�h 4L_i* �? ���U� |�i i |ih?@* _iM| �t i?_L}i?L�t�
i t@� �? |�i Thi��L�t tiU|�L? �L� |�i �4T*�U@|�L?t Lu @ 4L_i* uLh |�i igiU|t Lu @ _L4it|�U
�?|ihit| h@|i U�| @hi ti?t�|��i |L @tt�4T|�L?t� AL u�h|�ih U*@h�u) |�i ?@|�hi Lu |��t ti?t�|���|)c
|��t tiU|�L? @?@*)3it |�L �iht�L?t Lu L�h 4L_i*G L?i |�@| h@|�L?@*�3it |�i ��i� |�@| @? �?|ihit|
h@|i U�| hi_�Uit L�|T�| @?_ �|�*�|) @?_ @?L|�ih |�@| h@|�L?@*�3it |�i LTTLt�|i ��i��
A�i ?@|�hi Lu |�i 4L?i|@h) i Tih�4i?| �t t�4�*@h |L |�i L?i t|�_�i_ �? |�i Thi��L�t
tiU|�L?� A�ihi �t @ Mi?U�4@h! @?@*)t�tc �? ���U� 4L?i|@h) TL*�U) �t |hi@|i_ @t UL?t|@?| @?_
|�i iUL?L4) �t UL?uhL?|i_ ��|� @ M�?_�?} UL**@|ih@* UL?t|h@�?|� `�i? |�i _iM| �t i?_L}i?L�tc
|�i iUL?L4) hitTL?_t |L |��t t�|�@|�L? M) h�??�?} @ U�hhi?| @UUL�?| t�hT*�t �?|�* |�i _iM|
�t hi_�Ui_ |L |�i TL�?| ��ihi |�i UL**@|ih@* UL?t|h@�?| �t 4@h}�?@**) ?L?�M�?_�?}� �| |��t
TL�?|c |�i U�hhi?| @UUL�?| _hLTt |L 3ihL @?_ |�i iUL?L4) �t �? @ t|i@_) t|@|i� i @?@*)3i
|�i igiU|t Lu @ U�| �? |�i ?L4�?@* h@|i Lu �?|ihit|c @t |�i iUL?L4) |h@?t�|t |L |��t ?i� t|i@_)
t|@|i� �t �? |�i Thi��L�t tiU|�L?c |�i TL*�U) �?|ih�i?|�L? �@t @ ?L?�?i�|h@* �4T@U| MiU@�ti
�| U@? igiU| |�i _i}hii Lu *�^��_�|) �? _L4it|�U �?@?U�@* 4@h!i|t� A��t �? |�h? hi�iU|t L�h
tTiU��U@|�L? |�@| 4L?i|@h) @U|�L?t LUU�h @| @ TL�?| �? |�4i ��i? |�i �L�ti�L*_<t _iTLt�|
_iU�t�L? �t @ Thi_i|ih4�?i_ �@h�@M*i��b
A�i �4T@U| L? |�i |h@?t�|�L? T@|� Lu |�i �?|ihit| h@|i U�| �t �ih) _�gihi?| uLh |�i |�L
iUL?L4�it |�@| �i UL?t�_ih� A�i |�L iUL?L4�it _�gih �? |�i �@) |�i) 4L_i* ThL_�U|�L? �?
|�i |h@_i_ }LL_ tiU|Lh� W? L?ic *@MLh T*@)t ?L hL*i @?_ L�|T�| �t |�i �LMM�#L�}*@t u�?U|�L?
Lu 5 @?_ gA L?*) }��i? �? E���S�� W? |�i L|�ihc *@MLh �t �ti_ �? |�i |h@_i_ }LL_ tiU|Lh�
W? |��t U@tic |�i ThL_�U|�L? u�?U|�L? �t }��i? M) |�i wiL?|�iu tTiU��U@|�L? �? E���D�c ��|�
�@*�i�@__i_c Tc }��i? M) |�i tTiU��U@|�L? �? E���e�� W? i@U� 4L_i* iUL?L4)c |�i ThL_�U|�L?
u�?U|�L? �? |�i ?L?|h@_i_ tiU|Lh ULhhitTL?_t |L |�i tTiU��U@|�L? �? E���e�� �*tLc �? i@U�
4L_i* ThL_�U|�L? Lu |�i UL?t�4T|�L? }LL_ �?�L*�it 3ihL i*@t|�U�|) Lu t�Mt|�|�|�L? Mi|�ii?
|h@_i_ @?_ ?L?�|h@_i_ }LL_tc @t �? E��.�� 6�?@**)c Thiuihi?Uit �? |�i |�L iUL?L4�it @hi |�i
t@4i�
�L?t�t|i?| ��|� |�i @?@*)t�t Lu |�i Thi��L�t tiU|�L?c �i �?_ |�@| |�i 4L_i* ��|�L�| *@MLh
�? |�i |h@_i_ }LL_ ThL_�U|�L? u�?U|�L? �@t |�i �4T*�U@|�L? |�@| L�|T�| UL?|h@U|tc uLhi�}?
U@T�|@* �?�L�t _h) �T @?_ �i*u@hi u@**t ��|� @ U�| �? |�i _L4it|�U h@|i Lu �?|ihit|� A�i L|�ih
4L_i* �4T*�it |�@| @? iUL?L4�U i T@?t�L? uL**L�t @ U�| �? |�i �?|ihit| h@|i�
A�i uL**L��?} tiU|�L? _�tU�ttit |�i T@h@4i|ih �@*�it �ti_ uLh |�i |�L 4L_i*t� A�i tiU|�L?
@u|ih |�@| Thiti?|t @?_ _�tU�ttit |�i ?�4ih�U@* t�4�*@|�L? hit�*|t�
ulvhv 5 shufhqw dqg JGS ulvhv e| 4 shufhqw/ zlwk d irxu shufhqwdjh srlqw lqwhuhvw udwh fxw14<Zh kdvwhq wr dgg wkdw lw lv rqo| suhghwhuplqhg iru rqh shulrg1 Diwhu wkdw/ wkh ghsrvlw ghflvlrq lv iuhh
wr uhvsrqg1
2S
D��� �@h@4i|ih V@*�it @?_ 5|i@_) 5|@|i
A�i T@h@4i|ih �@*�it uLh L�h |�L 4L_i*t @hi _�tT*@)i_ �? A@M*i 2� �L?t�_ih �ht| |�i T@�
h@4i|ih �@*�it uLh |�i 4L_i* �? ���U� *@MLh i?|iht �? |�i ThL_�U|�L? Lu |h@_@M*it E|�i *iu|
t�_i Lu A@M*i 2�� A�iti �ihi U�Lti? |L hiT*�U@|i ti�ih@* t|)*�3i_ ui@|�hit Lu i4ih}�?} 4@h!i|
iUL?L4�itc �? T@h|�U�*@h |�Lti Lu tL4i Lu |�i hiUi?| Uh�tit UL�?|h�it� A�i t�@hi Lu |h@_@M*it
�? |L|@* ThL_�U|�L? uLh kLhi@c @tt�4�?} |�@| |h@_@M*it ULhhitTL?_ |L |�i ?L?�tih��Ui tiU|Lhtc
�@t @TThL �4@|i*) L?i |��h_ MiuLhi |�i Uh�t�t� �L4M�?�?} |��t @tt�4T|�L? ��|� it|�4@|it Lu
*@MLh t�@hit uhL4 �� vL�?} E�bbD�c �i it|�4@|i t�@hit Lu U@T�|@* uLh |�i |h@_@M*i @?_ ?L?�
|h@_@M*i tiU|Lh �? kLhi@ |L Mi hitTiU|��i*) f�eH @?_ f�2�� �@ti_ L? �}�hit uLh �h}i?|�?@c
Nh�Mi E�bbD� @?_ +iMi*L @?_ Vi}� E�bbD� it|�4@|i |�i t@4i t�@hit |L Mi f�D2 @?_ f��.� i
|@!i @? �?|ih4i_�@|i TL�?| Mi|�ii? |�iti it|�4@|it M) tTiU�u)�?} D ' f�Df @?_ k ' f��D�
+i�?�@h| @?_ Vi}� E�bbD� it|�4@|i |�i i*@t|�U�|) Lu �?|ih|i4TLh@* t�Mt|�|�|�L? �? UL?t�4T�
|�L? uLh �h}i?|�?@ |L Mi i^�@* |L f�2� i @_LT| @ tL4i��@| ��}�ih i*@t|�U�|) M) ti||�?}
j ' 2� i |@!i |�i uLhi�}? �?|ihit| h@|i |L Mi i^�@* |L S TihUi?| @?_ �i @tt�4i @ h@|i
Lu 4L?i) }hL�|� Lu S TihUi?| |L LM|@�? @ ?L4�?@* _L4it|�U �?|ihit| h@|i Lu �2�� TihUi?|c
hL�}�*) �? *�?i ��|� |�i i Tih�i?Ui Lu kLhi@ @?_ A�@�*@?_ �? |�i )i@ht MiuLhi |�i Uh�tit� i
ti| � ' �c �4T*)�?} @ *@MLh t�TT*) i*@t|�U�|) Lu �*�� A��t �t *L� M) UL4T@h�tL? |L |�@| �ti_
�? t|@?_@h_ M�t�?itt U)U*i 4L_i*t� ��h U�L�Ui Lu @ *L� *@MLh t�TT*) i*@t|�U�|) �t UL?tih�@|��i�
A�i hit�*| M@ti_ L? |��t 4L_i* |�@| �i t|hitt �t |�@| @ U�| �? - }i?ih@|it @?_ i T@?t�L?�
i Thit�4i |�@| @ ��}�ih *@MLh t�TT*) i*@t|�U�|) �L�*_ �@�i t�4T*) hit�*|i_ �? @ }hi@|ih
i T@?t�L?�
�t 4i?|�L?i_ @ML�ic |�i t�@hi Lu |h@_@M*i }LL_t �? ThL_�U|�L? �t hL�}�*) L?i |��h_c
tL �i U@*�Mh@|i |�i hi4@�?�?} T@h@4i|iht Lu |�i 4L_i* |L ThL_�Ui @ h@|�L Lu UL?t�4T|�L?
Lu ?L?|h@_@M*it |L |h@_@M*it Lu @TThL �4@|i*) 2� W? @__�|�L?c �i U�Lti � @?_ |�i t|LU! Lu
_iM| �? |�i �?�|�@* t|i@_) t|@|i i^��*�Mh��4 tL |�@| |�i �?�|�@* @?_ �?@* _iM| |L L�|T�| h@|�L
ULhhitTL?_ hL�}�*) |L |�i i Tih�i?Ui Lu kLhi@ @?_ A�@�*@?_� kLhi@<t EA�@�*@?_<t� i |ih?@*
_iM| t|@h|i_ @| ��I Lu B#� M) i?_��bb. ESf��I� @?_ �t uLhiU@t|i_ |L Mi @| 2S�HI Lu B#�
ED�I Lu B#�� @?_ |�i i?_ Lu |�i )i@h 2fff� �@ti_ L? |�iti LMtih�@|�L?tc �i @�4i_ |L
T@h@4i|ih�3i |�i 4L_i*t tL |�@| |�i 4L_i* iUL?L4) t|@h|t �? |�i h@?}ic �f�SfIc @?_ |�i?
_hLTTi_ �? |�i h@?}i Lu H � �f ThiUi?|@}i TL�?|t�
i U�Lti UL4T@h@M*i T@h@4i|ih �@*�it uLh |�i 4L_i* �? ���U� *@MLh _Lit ?L| @TTi@h
�? |�i |h@_i_ }LL_ ThL_�U|�L? u�?U|�L? Eh�}�| t�_i Lu A@M*i 2�� �?i _�gihi?Ui �t |�@| �i
U�Lti @ ��}�ih *@MLh t�TT*) i*@t|�U�|) uLh |��t 4L_i*� W? |�i U@ti Lu |��t 4L_i*c �i t|hitt �|t
�4T*�U@|�L? |�@| @ U�| �? - }i?ih@|it @ u@** �? L�|T�|� i Thit�4i |�@| @ *L�ih *@MLh t�TT*)
i*@t|�U�|) �L�*_ L?*) �@�i 4@_i |��t UL?|h@U|�L? �Lhti�2f
53Wklv frqmhfwxuh lv vwloo wr eh yhul�hg1
2.
A@M*i 2G �@h@4i|ih V@*�itc A�L �L_i*t Nti_ �? �?@*)t�t
w@MLh �? Ah@_i_ BLL_ 5iU|Lh �L w@MLh W? Ah@_i_ BLL_ 5iU|Lh
q f�be � f���� q f�be � f���
� ��ff - ���2 � � - ���2
-W ��fS oW f�fS -W ��fS oW f�fS
k f��S g� e�ff k f��S g� ���2D
D f�Df gA ��ff D � gA D�
>� f�bD >2 ��Hf >� � >2 �
� f��S w �� � f��� w f�S
�f f�ff�S j 2 �f f�ff�S j 2
� 2�ef 1 f� � ��2 1 �
A�i t|i@_) t|@|i ThLTih|�it Lu |�i �iht�L? Lu |�i 4L_i* 4i@?| |L U@T|�hi |�i Thi�Uh�t�t
t�|�@|�L?c |�i L?i |�@| �}?Lhit |�i UL**@|ih@* UL?t|h@�?|c �t hiTLh|i_ �? A@M*i �� A�i UL**@|ih@*
UL?t|h@�?| �t �4TLti_ �? Tih�L_ fc @?_ |�i iUL?L4) i�i?|�@**) UL?�ih}it |L |�i ?i� t|i@_)
t|@|ic L?i �? ���U� |�i UL**@|ih@* UL?t|h@�?| �t ?L| M�?_�?}� A�i ThLTih|�it Lu |�@| t|i@_)
t|@|i @hi hiTLh|i_ �? A@M*i e�
2H
A@M*i �G 5|i@_) 5|@|i uLh A�L �L_i*tc W}?Lh�?} �L**@|ih@* �L?t|h@�?|
w@MLh �? Ah@_i_ BLL_ 5iU|Lh �L w@MLh W? Ah@_i_ BLL_ 5iU|Lh
u ��D 5 f�Sf u 2S� 5 S�H
uA f�bb u� 2�D� uA f u� 2S
SA ��eH S� 2�b. SA b�. S� �b�e
� f�.e T 2��b � f�e T ��
R� S�
SA2��b +A 2�2. R� S�
SA2��2 +A �H��
R� ���f RA f�22 R� ��fS RA f�f�D
^A �e�e ^� D��D ^A �H�D ^� ���S
� 2�DD �R� S�n+A3-W5
f�De � 2f �R�S�n+A3-W5
f�SS
A@M*i eG 5|i@_) 5|@|i uLh A�L �L_i*tc +itTiU|�?} �L**@|ih@* �L?t|h@�?|
w@MLh �? Ah@_i_ BLL_ 5iU|Lh �L w@MLh W? Ah@_i_ BLL_ 5iU|Lh
u ��D 5 f�Db u 2H� 5 S�H
uA f�bS u� 2�De uA f u� 2H
SA ��eb S� 2�bb SA �f�f� S� 2f��
� f�.e T 2��b � f�ee T ��
R� S�
SA2�2� +A 2�2. R� S�
SA2�Sb +A �H��
R� ���� RA f�22 R� ���e RA f�f2b
^A �e�2 ^� D�2b ^A �H�D ^� �D�2
� ��bb �R� S�n+A3-W5
f�e� � �e�S2 �R� S�n+A3-W5
f�ef
D�2� �@ti*�?i 5Ui?@h�L
i ?L� UL?t�_ih |�i _)?@4�U igiU|t Lu |�i �4TLt�|�L? Lu |�i UL**@|ih@* UL?t|h@�?|c ��i?
4L?i|@h) TL*�U) |@!it |�i uLh4 Lu @ UL?t|@?| 4L?i) }hL�|� h@|i |�hL�}�L�| |�i |h@?t�|�L?
2b
|L |�i ?i� t|i@_) t|@|i� 6�}�hit e@�eM t�L�t |�i �@h�@M*it Lu |�i 4L_i* �? i^��*�Mh��4c
@t |�i iUL?L4) |h@?t�|t uhL4 |�i ��}� �?�|�@* _iM| |L |�i *L�ih *i�i* Lu _iM| �? |�i t|i@_)
t|@|i ��ihi |�i UL**@|ih@* UL?t|h@�?| �t 4@h}�?@**) ?L?�M�?_�?}�2� EN?*�!i �? |�i iUL?L4)
��|�L�| _iM|c |�ihi U@??L| Mi @ t|i@_) t|@|i i^��*�Mh��4 �? ���U� |�i iUL?L4) �@t @ M�?_�?}
UL**@|ih@* UL?t|h@�?|�� A�i hit�*|t �? 6�}�hit e@�eM Tih|@�? |L |�i iUL?L4) �? ���U� *@MLh �t
�ti_ �? |�i |h@_i_ }LL_ tiU|Lh� �L|i |�@| �h4t hitTL?_ |L |�i i?Lh4L�t H. TihUi?|@}i TL�?|
��4T �? |�i t�@_L� ULt| Lu uLhi�}? MLhhL��?} M) T@)�?} Lg |�i i |ih?@* _iM| Ebf ' f�H.��
A�i U�hhi?| @UUL�?| }Lit uhL4 3ihL MiuLhi |�i UL**@|ih@* UL?t|h@�?| �t �4TLti_ |L ��H TihUi?|
Lu L�|T�| �? |�i Tih�L_ |�@| �| LUU�ht� A�i U�hhi?| @UUL�?| hi4@�?t ��}�ih |�@? hL�}�*) L?i
TihUi?| Lu L�|T�| uLh @ML�| uL�h )i@ht� A�i �4TLt�|�L? Lu |�i UL**@|ih@* UL?t|h@�?| }i?ih@|it
@ U�|M@U! �? �4TLh|t Lu 5 @?_ |��t � MiU@�ti Lu *@U! Lu t�Mt|�|�|@M�*�|) @UhLtt tiU|Lht E�i �@�i
# ' f� � *i@_t |L @ }i?ih@* t*L�_L�? �? iUL?L4�U @U|���|) @UhLtt |�i i?|�hi iUL?L4)� AL|@*
i4T*L)4i?| _hLTt hL�}�*) 2f TihUi?|c M�| @*4Lt| @** Lu |��t _hLT UL4it uhL4 |�i ?L?�|h@_i_
}LL_ tiU|Lh� �hLTLh|�L?@**)c |�ihi �t 4Lhi i4T*L)4i?| �? |�i |h@_i_ }LL_ tiU|Lh @u|ih |�i
�4TLt�|�L? Lu |�i UL**@|ih@* UL?t|h@�?|� A��t hi�iU|t |�i t��u|�?} Lu hitL�hUit |L�@h_t |�@|
tiU|Lh |L �i*T ThL_�Ui |�i |h@_i_ }LL_t ti?| @MhL@_ |L T@) _L�? |�i i |ih?@* _iM|� A�i
L�ih@** t*L�_L�? �? iUL?L4�U @U|���|) UL?|h�M�|it |L @ u@** �? @tti| �@*�itc @t |�i 4@h}�?@*
T�)t�U@* ThL_�U| Lu @tti|t _iU*�?i� A�i _L4it|�U h@|i Lu �?|ihit|c -c hi4@�?t ��}� �? |�i
Tih�L_ Lu |�i t�LU!c @?_ @*tL uLh ti�ih@* )i@ht @u|ih �@h_t� 6�?@**)c |�i ?L4�?@* i U�@?}i
h@|i t�L�t @? �44i_�@|ic t�Mt|@?|�@* _iThiU�@|�L? uL**L�i_ M) @ Tih�L_ Lu @TThiU�@|�L? |L
ULhhiU| uLh |�i �?�|�@* L�iht�LL|�?}� 5�4�*@h*)c |�ihi �t @ t�@hT hi@* i U�@?}i h@|i _iThiU�@|�L?
E@ u@** �? R��c uL**L�i_ M) @ }h@_�@* @TThiU�@|�L?�
6�}�hit D@�DM _�tT*@) |�i ULhhitTL?_�?} hit�*|t uLh |�i 4L_i* �? ���U� *@MLh U@??L| Mi
�ti_ �? |�i |h@_i_ tiU|Lh� A�i igiU|t @hi @** ^�@*�|@|��i*) t�4�*@hc @*|�L�}� |�i) |i?_ |L
Mi *@h}ih MiU@�ti |�i _iM| �? |��t 4L_i* �t 4�U� ��}�ih �? |�i �?�|�@* t|i@_) t|@|i |�@? �|
�t �? |�i 4L_i* _�tU�tti_ �? |�i Thi��L�t T@h@}h@T�� A��tc |�i t�@_L� ULt| Lu MLhhL��?}
��4Tt SeH TihUi?| �? |�i Tih�L_ Lu |�i �4TLt�|�L? Lu |�i UL**@|ih@* UL?t|h@�?|� �ttLU�@|i_
��|� |��t |�ihi �t @ 4@�Lh hi_�U|�L? �? i4T*L)4i?| @?_ �4TLh|t Lu |�i �?|ih4i_�@|i }LL_�
�@T�|@* �?�L�t E|L �?@?Ui 5� _�tT*@) |�i �t�__i? t|LT< ui@|�hi i4T�@t�3i_ M) �@*�L E�bbH��
6�?@**)c @t �? |�i Thi��L�t T@h@}h@T�c |�i UL**@|ih@* UL?t|h@�?| |h�}}iht @? �44i_�@|i hi@*
54Khuh duh vrph qrwhv rq Wdeoh 81 Lq hdfk fdvh/ wkh wrs ri wkh froxpq fruuhvsrqgv wr w @ 3> dqg wkh erwwrpwr w @ 45= Wkh w @ 3 shulrg fruuhvsrqgv wr wkh gdwh lq zklfk wkh froodwhudo frqwudlqw lv lpsrvhg1 Lq wkh uhvxowvlq Wdeoh 8/ prqh| jurzwk lv nhsw frqvwdqw {w @ { wkurxjkrxw1 Wkh fruuhvsrqghqfh ehwzhhq wkh qrwdwlrq lqwkh wdeoh dqg wkh qrwdwlrq lq wkh sdshu lv dv iroorzv1 E �Ew> tq �tQw > Oq �O
Qw / Ow �O
Ww / sq �sQw > } �}w> fq �f
Qw >
fw �fWw > odp ��w> |w �|Ww > fd2+| suh0fulvlv,= fxuuhqw dffrxqw glylghg e| suh0fulvlv jurvv vwhdg| vwdwh rxwsxw/O �Ow> U �Uw> g �Gw@Pw> sw �sWw > sw2swv �s
Ww @+s
Ww lq suh0fulvlv vwhdg| vwdwh,/ jurvv rxwsxw +lq wudghg jrrg
xqlwv, �sQw fQw . |Ww > z �zw> YPSnw �YPSW
n>w> YPSnq �Y PSQn>w> Ydoxh ri wrwdo dvvhwv �� +t
Qw N
Q . tWw NW ,>
iruhljq ghew �+4. u�,Ew.zwUwOw. }wU�> eljodp+ll04,2eljodp+ll, 04 ��w�4@�w� 4> glylghqgv ��w irup +BB,/
sl+w,@S+w,2S+w04, ��w @ Sw@Sw�4> U+w,2sl+w.4, �Uw@�w.4> puv+w/w.4, �xf>w@+�xf>w.4,=
�f
@?_ ?L4�?@* _iThiU�@|�L? |�@| L�iht�LL|t�
i |@!i �| |�@| |�iti U�@h@U|ih�t|�Ut Lu L�h 4L_i*t ULhhitTL?_ hi@tL?@M*) �i**c @| *i@t|
^�@*�|@|��i*)c ��|� ��@| @U|�@**) �@TTi?i_ @u|ih |�i �bb. �?@?U�@* Uh�tit �? ti�ih@* �t�@?
UL�?|h�it Etii �LLh4@?c e|� @,� E2fff��� �? |��t M@t�tc �i uii* ��t|��i_ �? �t�?} |�iti 4L_i*t
|L t|�_) |�i igiU|t Lu @ U�| �? _L4it|�U �?|ihit| h@|it �? |�i �@!i Lu @ �?@?U�@* Uh�t�t� i
|�h? |L |��t ?L��
D��� A�i ,giU| Lu @? W?|ihit| +@|i ��|
i ?L� t�TTLti |�@| �? Tih�L_ fc @u|ih |�i UL**@|ih@* UL?t|h@�?| �@t Mii? �4TLti_c |�i
4L?i|@h) @�|�Lh�|) |i4TLh@h�*) _i��@|it uhL4 �|t UL?t|@?| 4L?i) }hL�|� T@|�� W| _Lit tL
M) _L�?} ��@|i�ih �| |@!it |L |�i 4L?i) t�TT*) |L LM|@�? @ }��i? hi_�U|�L? �? |�i Tih�L_ f
h@|i Lu �?|ihit|� A��t TL*�U) @U|�L?c ���U� �t �?@?|�U�T@|i_c �t i iU�|i_ @u|ih |�i �L�ti�L*_
�@t 4@_i �|t _iTLt�| _iU�t�L?� �}i?|t i TiU|c ULhhiU|*)c |�@| |�i 4L?i|@h) @�|�Lh�|) ��**
hi�ih| |L �|t UL?t|@?| 4L?i) }hL�|� T@|� �? | � �� A��t L?i�|�4i U�@?}i TL*�U) �@t ?L �4T@U|
L? |�i �*|�4@|i t|i@_) t|@|i |L ���U� |�i iUL?L4) �t �i@_i_� W| L?*) @giU|t |�i ?@|�hi Lu
|�i |h@?t�|�L? T@|�� i @t! ��@| �| _Lit |L |�i iUL?L4�U �@h�@M*it @*L?} |�@| T@|�c @?_
��i|�ih |��?}t @hi 4@_i Mi||ih Lh �Lhti �? @ �i*u@hi ti?ti�
A�i hit�*|t @hi hiTLh|i_ �? A@M*i D�22 A�i U�| �? |�i �?|ihit| h@|i �t b��f TihUi?|@}i
TL�?|t �? |�iti |�L iUL?L4�it� W| �t @UUL4T*�t�i_ M) @ L?i�|�4i U�@?}i �? 4L?i) }hL�|�
�? Tih�L_ fc @u|ih ���U� |�i t|i@_) t|@|i 4L?i) }hL�|� h@|i Lu S TihUi?| �t hit�4i_� W?
i T*@�?�?} ��@| �@TTi?t �? |�i |�L 4L_i*tc �| �t �tiu�* |L Ui?|ih |�i _�tU�tt�L? L? |�i
UL**@|ih@* UL?t|h@�?|c Ee���c ���U� �i hiThL_�Ui �ihiG
�^�g� n �^AgA ' -W5 n E� n oW���
Oihic �i �@�i ?L| �?U*�_i_ |�i �@}i M�**c ���U� �i @Mt|h@U| uhL4 |i4TLh@h�*)� W? ML|�
4L_i* iUL?L4�itc |�i U�| �? |�i �?|ihit| h@|i }i?ih@|it @ ?L4�?@* _iThiU�@|�L? Etii A@M*i
D��2� �|�ih |��?}t |�i t@4ic |��t 4@!it |�i *iu| t�_ic |�i @tti| t�_ic Lu |�i UL**@|ih@* UL?t|h@�?|
u@**� AL tii |��tc hiU@** |�@| |�i UL**@|ih@* UL?t|h@�?| �t 4i@t�hi_ �? �?�|t Lu |h@_i_ }LL_t� 5L
�u L?*) � A hLtic @?_ ?L L|�ih Th�Ui � ��i? 4i@t�hi_ �? _L4it|�U U�hhi?U) �?�|t � Lh ^�@?|�|)
55Zh kdyh qrw ehhq deoh wr hvwdeolvk irupdoo| wkh xqltxhqhvv surshuwlhv ri wkh edvholqh htxloleulxp dqgwkh srolf| lqwhuyhqwlrq htxloleulxp1 Zh frpsxwh wkh htxloleulxp e| vroylqj iru pxowlsolhuv wkdw vdwlvi| dsduwlfxodu kljk glphqvlrqdo htxdwlrq1 Wr exlog frq�ghqfh lq xqltxhqhvv zh vhdufk iru dowhuqdwlyh vroxwlrqvwr wklv htxdwlrq e| lqlwldwlqj wkh qxphulfdo fdofxodwlrqv iurp gl�huhqw lqlwldo frqglwlrqv1
56Wklv fruuhvsrqgv wr wkh wudglwlrqdo ylhz ri prqhwdu| srolf| lq rshq hfrqrplhv1 Vhh Pxvvd +5333, iruhylghqfh iurp hslvrghv ri hphujlqj pdunhw fulvhv wkdw vhhp wr surylgh vxssruw iru wkh wudglwlrqdo ylhz1
��
U�@?}i_c |�i @tti| t�_i �L�*_ u@**c hi^��h�?} @ u@** �? 5� A�ihi �t @?L|�ih Th�Ui igiU| |�@|
4@) �@�i @ t�4�*@h �4T@U| L? |�i UL**@|ih@* UL?t|h@�?|� W? T@h|�U�*@hc |�i U�| �? |�i _L4it|�U
h@|i Lu �?|ihit|c M) �@��?} @ hi*@|��i*) *@h}i �4T@U| L? 4@h}�?@* ULt|t �? |�i ?L?�|h@_i_ }LL_
tiU|Lhc 4@) U@�ti |�i hi*@|��i Th�Ui Lu }LL_t ThL_�Ui_ �? |�@| tiU|Lhc R� c |L u@**� A��t �@t @
u�h|�ih _iThitt��i igiU| L? |�i @tti| t�_i Lu |�i UL**@|ih@* UL?t|h@�?|c MiU@�ti R� �t �ti_ |L
�@*�i |�i ThL_�U|���|) Lu |�i @tti|t �? |�i ?L?|h@_i_ }LL_ tiU|Lh�2e Wu |��t �ihi |�i ��L*i
t|Lh)c |�i? |�i �?|ihit| h@|i U�| *i@�it �t ��|� @ 4�t4@|U� Mi|�ii? |�i @tti| @?_ *�@M�*�|)
t�_it Lu |�i UL**@|ih@* UL?t|h@�?|c ���U� UL�*_ L?*) Mi hitL*�i_ M) hi_�U�?} U@T�|@* �?�L�t
|�hL�}� @ U�| �? 5�
��|c |��t �t ?L| |�i ��L*i t|Lh)� W?tTiU|�L? Lu |�i UL**@|ih@* UL?t|h@�?| hi�i@*t @?L|�ih
LT|�L?G L?i UL�*_ �? Th�?U�T*i �?Uhi@ti 5� �u UL�htic |��t �@t |�i �hL?} igiU| L? |�i *�@M�*�|)
t�_i Lu |�i UL**@|ih@* UL?t|h@�?|� OL�i�ihc |��t ThLM*i4 �t tL4i��@| @**i��@|i_ �u |�i i |ih?@*
_iM| �t �ih) *@h}i�2D W? |��t U@tic |�i TihUi?|@}i �?Uhi@ti �? |�i *�@M�*�|) t�_i Lu |�i UL**@|ih@*
UL?t|h@�?| @ttLU�@|i_ ��|� @ }��i? h�ti �? 5 �t t4@**� `�@| @ML�| |�i �4T@U| Lu @ h�ti �? 5
L? |�i @tti| t�_i Lu |�i UL**@|ih@* UL?t|h@�?|q W? }i?ih@* � @?_ �? L�h 4L_i*t tTiU��U@**) �
L?i i TiU|t |�i �?Uhi@ti_ �ti Lu 5 |L h@�ti |�i �@*�i Lu |�i iUL?L4)<t @tti|t M) h@�t�?} |�i�h
4@h}�?@* T�)t�U@* ThL_�U|� OL�i�ihc |��t U�@??i* �t ?L| t|hL?} i?L�}� �u 5 �t t�M�iU| |L
t|hL?}*) _�4�?�t��?} hi|�h?t� W? |��t U@tic |�i h�ti �? @tti| �@*�it @ttLU�@|i_ ��|� @ h�ti �? 5
�t t4@** @?_ *�!i*) |L Mi _L4�?@|i_ M) |�i h�ti �? *�@M�*�|�it�2S
A��t �t |�i t�|�@|�L? �? |�i 4L_i* ��ihi *@MLh _Lit ?L| i?|ih |�i |h@_i_ }LL_ tiU|Lh�
W? |�@| 4L_i*c |�i i^��*�Mh��4 hitTL?ti Lu 5 �?�L*�it @ hi_�U|�L? �? 5c ?L| @? �?Uhi@ti�
A��t hi_�U|�L? �? 5 ti|t �?|L 4L|�L? @__�|�L?@* uLhUit �? L�h 4L_i* ���U� !iiT �| u@**�?}� W?
T@h|�U�*@hc |�i *@U! Lu t�Mt|�|�|@M�*�|) Mi|�ii? |h@_i_ @?_ ?L?|h@_i_ }LL_t �? |�i ThL_�U|�L?
Lu �?@* UL?t�4T|�L? }LL_t �@t |�i UL?ti^�i?Ui |�@| @ u@** �? 5 hi_�Uit _i4@?_ uLh |�i
?L?|h@_i_ }LL_c tL |�@| i4T*L)4i?| |�ihi u@**t� A��t �@t |�i igiU| Lu u�h|�ih hi_�U�?} @tti|
�@*�itc @}}h@�@|�?} |�i @tti|t @?_ *�@M�*�|) 4�t4@|U� �? |�i UL**@|ih@* UL?t|h@�?|� A�i igiU|t
L? @tti| Th�Uit U@? Mi tii? �? A@M*i Dc ���U� t�L�t |�@| ^A h�tit M) @ �ih) t4@** @4L�?|c
57Uhfdoo wkdw sQ hqwhuv lq wkh ydoxh ri wkh pdujlqdo surgxfw ri fdslwdo lq wkh qrq0wudghg jrrg vhfwru +vhh+614<,1,
58Lq wklv frqwh{w/ rxu dqdo|vlv ri wkh suhylrxv vhfwlrq lv uhohydqw1 Wkhuh zh suhvhqwhg hylghqfh wkdwvxjjhvwv= +l, li d prgho lv wr udwlrqdol}h wkh qrwlrq wkdw dq lqwhuhvw udwh fxw jhqhudwhv d uhfhvvlrq/ wkhq wkhDP fxuyh pxvw eh srvlwlyho| vorshg dqg fxw wkh OP fxuyh iurp ehorz/ dqg +ll, lqfuhdvlqj wkh h{whuqdo ghewurwdwhv wkh DP fxuyh forfnzlvh1 Frqglwlrqv +l, dqg +ll, vxjjhvw wkdw li dq hfrqrp| zlwk orz ghew surgxfhvd uhfhvvlrq zlwk dq lqwhuhvw udwh fxw/ wkhq wkh uhfhvvlrq zloo eh vpdoohu ru lw pd| hyhq wxuq lqwr d errp irud prgho lq zklfk wkh h{whuqdo ghew lv kljkhu1
59Wkhuh lv dqrwkhu fkdqqho wkdw frxog lq sulqflsoh eh rshudwlyh1 D fxw lq wkh grphvwlf lqwhuhvw udwh/ e|lqfuhdvlqj wkh vxsso| ri qrqwudghg jrrgv +uhfdoo/ wkh lqwhuhvw udwh fxw uhgxfhv wkh pdujlqdo frvw ri wkrvhjrrgv,/ udlvhv wkh ghpdqg iru wudghg jrrgv/ wr wkh h{whqw wkdw wkhvh frpsohphqw zlwk qrqwudghg jrrgv1 Livr/ wkhq wkh vkdgrz frvw ri wkh froodwhudo frqvwudlqw lv olnho| wr lqfuhdvh dqg wklv fdq kdyh wkh h�hfw ri udlvlqjdvvhw sulfhv1 Wklv h�hfw grhv qrw dsshdu wr eh vwurqj lq wkh sduwlfxodu qxphulfdo h{dpsohv glvsod|hg khuh1
�2
@?_ �t _L4�?@|i_ �? |�i UL**@|ih@* UL?t|h@�?| M) |�i u@** �? ^� � Oi?Uic |�i �@*�i Lu @tti|t @t
@ ��L*i u@**t�
A�i t�|�@|�L? �t _�gihi?| �? |�i 4L_i* ��ihi *@MLh _Lit T*@) @ hL*i �? |�i |h@_i_ }LL_
tiU|Lh� �L� |�i LT|�L? Lu hit|Lh�?} i^�@*�|) |L |�i UL**@|ih@* UL?t|h@�?| M) �?Uhi@t�?} 5 �t
@ }hi@|ih TLtt�M�*�|)� A��t �t MiU@�ti @? �?u�t�L? Lu *@MLh �?|L |�i |h@_i_ }LL_ tiU|Lh U@?
�Lh! @}@�?t| |�i _�4�?�t��?} hi|�h?t @ttLU�@|i_ ��|� @? �?Uhi@ti �? 5� �t @ hit�*|c @ h�ti �?
5 UL�*_ �? Th�?U�T*i h@�ti |�i @tti| t�_i Lu |�i UL**@|ih@* UL?t|h@�?| M) 4Lhi |�@? |�i *�@M�*�|)
t�_i� A�i |@M*it �?_�U@|i |�@| |��t �t ThiU�ti*) ��@| �@TTi?t �? |�i 4L_i* �? ���U� *@MLh
i?|iht |�i |h@_i_ }LL_ tiU|Lh�
��
A@M*i DG ,giU| Lu ��| �? - @| #@|i f E+i*@|��i |L UL?t|@?| T@|��
��@?}i �?G w@MLh �? Ah@_i_ BLL_ 5iU|Lh �L w@MLh W? Ah@_i_ BLL_ 5iU|Lh
- �f��f �f�fb
b �f�f�H f�fb
�ihUi?| ��@?}i �?G
u ��S2 �f�e�
5 2��2 �2�fe
uA e�.f ��
u� ��fH �f�e�
SA c S� ��bS �f�2.
`%� A ���b �e�D�
`%� ���S2 e���
��hhi?| �UUL�?| S�fb ���Hb
RA 2��� e�D.
+i@* , U�@?}i +@|i f�bb ��fe
R� f�bH �H��S
^A ��Df f��f
^� ��eH �f�ef
T�� A& e�DH �f�H2
T���& 2�bS �H�e�
i U@*U�*@|i_ |�i Thiti?| _�tUL�?|i_ �@*�i Lu �|�*�|) uhL4 Tih�L_ f L?c uLh L�h M@ti*�?i
tUi?@h�L @?_ uLh |�i tUi?@h�L �? ���U� |�i 4L?i|@h) @�|�Lh�|) hitTL?_t M) U�||�?} |�i h@|i
Lu �?|ihit|� i _�_ |��t uLh i@U� Lu L�h |�L 4L_i*t� �L|i |�@| �|�*�|) �? |�i t|i@_) t|@|i |L
���U� |�i iUL?L4) UL?�ih}it @u|ih |�i UL**@|ih@* UL?t|h@�?| �t �4TLti_ �t ��}�ih |�@? �|�*�|)
�e
�? |�i Thi�Uh�t�t t|i@_) t|@|i� A��t hi�iU|t |�i �i@*|� igiU|t Lu |�i hi_�Ui_ *i�i* Lu _iM| �?
|�i UL**@|ih@*�UL?t|h@�?i_ t|i@_) t|@|i� W? |�i U@ti Lu |�i 4L_i* ��|� *@MLh �? |�i |h@_i_
}LL_ tiU|Lhc |�i Thiti?| _�tUL�?|i_ �|�*�|) �? |�i i^��*�Mh��4 ��|� |�i �?|ihit| h@|i U�| �t
��}�ih |�@? ��@| �| �t ��i? |�i 4L?i|@h) @�|�Lh�|) _Lit ?L| hi@U|� N|�*�|) u@**t ��|� |�i
�?|ihit| h@|i U�| �? |�i L|�ih 4L_i*�
A�i �i*u@hi U@*U�*@|�L? �? |�i 4L_i* ��|� *@MLh �? |�i |h@_i_ }LL_ tiU|Lh �t Tih�@Tt *itt
�?|ihit|�?} |�@? �| �t uLh |�i L|�ih 4L_i*� W? ML|� 4L_i*t |�ihi @hi uLhUit |�@| 4@!i |�i
6h�i_4@? h�*ic - ' �c LT|�4@*� A�@| U�||�?} |�i �?|ihit| h@|i 4�}�| tii4 @ }LL_ �_i@ �? @
4L_i* �t |�ihiuLhi ?L| t�hTh�t�?}� `�@| �t ?L|i�Lh|�) �t L�h �?_�?} |�@| U�||�?} |�i �?|ihit|
h@|i �? |�i 4L_i* ��|�L�| *@MLh �? |�i |h@_i_ }LL_ tiU|Lh }i?ih@|it @ u@** �? �|�*�|)� A��t
t�L�t UL?Uhi|i*) �L� UL�?|ihThL_�U|��i @ TL*�U) *�!i |��t �t �? t�U� @? iUL?L4)�
A@M*i SG `i*u@hi �?@*)t�t
,^��*�Mh��4 �hiti?| #�tUL�?|i_ V@*�i Lu N|�*�|)
w@MLh �? �L w@MLh �?
Ah@_i_ BLL_ 5iU|Lh Ah@_i_ BLL_ 5iU|Lh
�hi�Uh�t�t t|i@_) t|@|i �2f�SH.Db ����b�fe
�L**@|ih@*�UL?t|h@�?i_ t|i@_) t|@|i �2f�D�.Db �����bDD
�@ti*�?i |h@?t�|�L? T@|�c | � f �2f�H��Hb ���beSD2
�@|�c | � fc ��|� �?|ihit| h@|i U�| �2f�.b2ff ���bD.�b
S� �L?U*�t�L?
i @?@*)3i_ @ t4@** LTi? iUL?L4) 4L_i* �? ���U� �h4t hi^��hi |�L |)Tit Lu �Lh!�?}
U@T�|@*G _L4it|�U U�hhi?U) |L ��hi _L4it|�U �?T�|t @?_ uLhi�}? U�hhi?U) |L �?@?Ui �4TLh|t
Lu @? �?|ih4i_�@|i �?T�|� i @_LT| @ hi_�Ui_ uLh4 4L_i* Lu @ �?@?U�@* Uh�t�tc @?_ @t! ��@|
�t |�i iUL?L4�U �4T@U| Lu @ U�| �? |�i _L4it|�U h@|i Lu �?|ihit| @| t�U� @ |�4i� i 4L_i*
@ �?@?U�@* Uh�t�t @t @ |�4i ��i? UL**@|ih@* UL?t|h@�?|t L? MLhhL��?} @hi �4TLti_ @?_ @hi
M�?_�?}� ��h ?L|�L? Lu @ ��?@?U�@* Uh�t�t< ULhhitTL?_t |L ��@| tL4i 4�}�| |��?! Lu @t @
�Uhi_�| Uh�?U�<�
W? L�h 4L_i*c @TT*�U@|�L? Lu M�?_�?} UL**@|ih@* UL?t|h@�?|t U@�tit |�i iUL?L4) |L h�? @
U�hhi?| @UUL�?| t�hT*�t @?_ Mh�?}t �|t _iM| _L�? |L |�i TL�?| ��ihi |�i UL**@|ih@* UL?t|h@�?|
�t 4@h}�?@**) ?L?�M�?_�?}� #�h�?} |�i |h@?t�|�L?c |�i UL**@|ih@* UL?t|h@�?| *�4�|t �L� 4�U�
�D
Lu |�i �?|ih4i_�@|i }LL_ U@? Mi �4TLh|i_c @?_ tL L�|T�| @?_ i4T*L)4i?| @hi *L�� W?
@__�|�L?c @tti| �@*�it u@** ��|� |�i t*L�_L�? �? @U|���|)c @?_ hi@* @?_ ?L4�?@* i U�@?}i
h@|it _iThiU�@|i @?_ L�iht�LL| ��|� |�i L?ti| Lu |�i Uh�t�t� A�iti ui@|�hit Lu |�i |h@?t�|�L?
_)?@4�Ut �? L�h 4L_i* ULhhitTL?_ � @| *i@t| ^�@*�|@|��i*) � ��|� ��@| �i LMtih�i_ �? |�i
�t�@? Uh�t�t |�@| Mi}@? �? *@|i �bb.� i �LTi |�@| |��t ��t|��it |@!�?} L�h hi_�Ui_ uLh4
4L_i* Lu @ �?@?U�@* Uh�t�t tih�L�t*)c @t @ *@MLh@|Lh) uLh t|�_)�?} |�i iUL?L4�U igiU|t Lu @
U�| �? |�i _L4it|�U �?|ihit| h@|i �? |�i @u|ih4@|� Lu @ �?@?U�@* Uh�t�t�
AL �?_iht|@?_ L�h @?@*)t�t Lu |�i igiU|t Lu |�i �?|ihit| h@|i U�|c �| �t t��U�i?| |L !iiT
�? 4�?_ �h4t< UL**@|ih@* UL?t|h@�?|G |�i hi^��hi4i?| |�@| |�i �@*�i Lu |�i�h @tti|t Mi ?L *itt
|�@? |�i �@*�i Lu |�i�h *�@M�*�|�it� i 4L_i* |�i uLh4ih @t UL?t�t|�?} Lu ThL_�U|��i @tti|t
t�U� @t *@?_ @?_ U@T�|@* �? |�i _L4it|�U iUL?L4)� �*tLc 4Lt| Lu �h4t< *�@M�*�|�it |@!i |�i
uLh4 Lu �?|ih?@|�L?@* _iM|� ��h uh@4i�Lh! U@T|�hit |�i |i?t�L?t i4T�@t�3i_ �? |�i *�|ih@|�hi
|�@| @hi Uhi@|i_ M) LTih@|�L? Lu |��t UL**@|ih@* UL?t|h@�?|�
6�ht|c @? �?|ihit| h@|i U�| �t *�!i*) |L ThL_�Ui @ ?L4�?@* i U�@?}i h@|i _iThiU�@|�L?�
�|�ih |��?}t |�i t@4ic |��t |�}�|i?t |�i UL**@|ih@* UL?t|h@�?| M) ThL_�U�?} @ u@** �? |�i �@*�i
Lu |�i _L4it|�U @tti|t Lu |�i �h4c ���*i ?L| @giU|�?} |�i �@*�i Lu �?|ih?@|�L?@* *�@M�*�|�it�
A��t igiU| @h�tit uhL4 |�i ��_i*) _�tU�tti_ 4�t4@|U� �? |�i U�hhi?U) _i?L4�?@|�L? Lu @tti|t
@?_ *�@M�*�|�it� A��t igiU| UL�*_ Mi UL4TL�?_i_ �u �? @__�|�L? |L @ ?L4�?@* _iThiU�@|�L?c
|�ihi �t @*tL @ hi@* _iThiU�@|�L?�
i @h}�i_ |�@| �?*itt |�ihi �t tL4i|��?} �? |�i i?��hL?4i?| |�@| U@? Lgti| _�4�?�t��?}
hi|�h?t |L |�i �?|ih4i_�@|i }LL_c |�i? |�i iUL?L4) �t *�!i*) |L hitTL?_ |L |�i 4�t4@|U� ��t|
_itUh�Mi_ M) U�||�?} M@U! L? |�i T�hU�@ti Lu |�i uLhi�}? �?|ih4i_�@|i }LL_� Wu |�@| }LL_ �t
?L| �ih) t�Mt|�|�|@M*i �? ThL_�U|�L? ThLUittit �? |�i iUL?L4)c |�i? |�i �4T*�U@|�L? �t |�@| @
}i?ih@* UL?|h@U|�L? 4�t| uL**L�� i _�tT*@)i_ @ 4L_i* iUL?L4) ��|� ThiU�ti*) |��t ThLTih|)�
OL�i�ihc �i @*tL _�tT*@)i_ @ 4L_i* iUL?L4) �@��?} |�i ThLTih|) |�@| @? �?|ihit| h@|i U�|
ThL_�Uit @? i T@?t�L?� W? |�@| 4L_i*c |�ihi �t @?L|�ih u@U|Lh Lu ThL_�U|�L?c *@MLhc ���U�
U@? Mi �ti_ |L hit�t| _�4�?�t��?} 4@h}�?@* ThL_�U|���|) Lu |�i �?|ih4i_�@|i }LL_� A�i !i)
|L |�i i T@?t�L? �t |�@| |�i *@MLh �t �ti_ uLh |�@| T�hTLti�
W? L�h @?@*)t�t �i �LTi |�@| �i �@�i Mii? @M*i |L �_i?|�u) |�i ui@|�hit Lu |�i i?���
hL?4i?| |�@| @hi !i) |L _i|ih4�?�?} ��i|�ih @? �?|ihit| h@|i U�| ��** Mi i T@?t�L?@h) Lh
UL?|h@U|�L?@h) �? |�i @u|ih4@|� Lu @ �?@?U�@* Uh�t�t Lh Uhi_�| Uh�?U�� � UL?|h@U|�L? �t *�!i*)
|L LUU�h �u |�i iUL?L4) �t hi*@|��i*) �?�i �M*ic �u u@U|Lh t�Mt|�|�|�L? TLtt�M�*�|�it @hi *�4�|i_
@?_ _�4�?�t��?} hi|�h?t @hi t|hL?}� Wu |�ihi @hi t�Mt|@?|�@* t�Mt|�|�|�L? TLtt�M�*�|�it @?_
_�4�?�t��?} hi|�h?t @hi ?L| t|hL?}c @? �?|ihit| h@|i U�| U@? }i?ih@|i @? i T@?t�L?c i�i? @
t|hL?} L?i� i UL?U*�_i |�@| hitL*��?} |�i _iM@|i L�ih |�i igiU|t Lu @? �?|ihit| h@|i U�|
�? |�i @u|ih4@|� Lu @ �?@?U�@* Uh�t�t hi^��hit �?_iht|@?_�?} �L� 4�U� t�Lh|�h�? �i �M�*�|)
|�ihi �t �? |�i iUL?L4)�
�S
.� �TTi?_�
W? |��t |iU�?�U@* @TTi?_� �i _�tU�tt �@h�L�t �tt�it h@�ti_ �? |�i |i |� A�i �ht| t�MtiU|�L?
_�tU�ttit |�i UL4T�|@|�L? Lu |�i t|i@_) t|@|i �? |�i �iht�L? Lu |�i 4L_i* Lu tiU|�L? e �? ���U�
|�i UL**@|ih@* UL?t|h@�?| �t M�?_�?}� A�i tiUL?_ t�MtiU|�L? _ih��it |�i *�?i@h�3@|�L? uLh4�*@t
�ti_ �? |�i *LU@* @?@*)t�t �? tiU|�L? e� A�i |��h_ t�MtiU|�L? _�tU�ttit |�i tL*�|�L? Lu |�i
�iht�L? Lu L�h 4L_i* @?@*)3i_ �? tiU|�L? Dc �? ���U� |�i U�hhi?| @UUL�?| �t ?L| UL?t|h@�?i_
|L Mi 3ihL�
.��� 5|i@_) 5|@|i �? |�i �L_i* Lu 5iU|�L? e
6Lh UL?�i?�i?Uic �i hiTi@| tL4i Lu |�i i^�@|�L?t Lu |�i 4L_i* �ihiG
-u�nk 'R� E�� k�
�g�
�k�fR
� E.���
A�i UL**@|ih@* UL?t|h@�?| �tG
��kR��g�
�ku�3k
�� b�� � qn�A w�
�gA
�w5�3w
� � b� A � q' -W5 n E� n oW��� E.�2�
A�i �ht| Lh_ih ?iUitt@h) UL?_�|�L? uLh 5 �? |�i |h@_i_ }LL_ tiU|Lh �tG
E�� w���gA
�w5�3w ' E� n b�5-W� E.���
A�i Th�Ui i^�@|�L? �tG
R� '�� �
�
3EC��gA
�w5�3w �-W5 � oW�
Eg� �k u�3k
4FD�
#
� E.�e�
`�i? # ' fc �i hiT*@Ui E.�e� ��|�
�g�
�ku�3k ' �
�gA
�w5�3w �-W5 � oW�� E.�D�
�.
A�i �?!?L�?t @hi uc R� c 5c b�
i ?L� _�tU�tt �L� |L �?_ |�i t|i@_) t|@|i ��i? w : f @?_ # ' f� d|�i U@tic # : f ��**
Mi @__i_ *@|iho� i �ti |�i i^�@|�L?tc E.����E.��� @?_ E.�D� |L _i�?i @ 4@TT�?} uhL4 5 |L
5�c ��Lti � i_ TL�?| ULhhitTL?_t |L @? i^��*�Mh��4� +i�h�|i E.�2� @t uL**L�tG
R� '
��� b�� � q
� %-W5 n E� n oW�� �
�A w�EgA �w5�3w
�3b�A3q
&��k Eg��k u�3k
c E.�S�
�L4M�?�?} E.�D� @?_ E.���c �i LM|@�? E|�i _�tU�tt�L? Mi*L� @tt�4it � ' fc ���U� ��** Mi
� i_ *@|ih�G
�g�
�ku�3k ' 5
���gA
�w53w �-W
�' 5
%� n b
�� w-W �-W
&
'bn w
� � w-W5 E.�.�
Lhc
u '
%bn w
� � w
-W5
Eg� �k
& �
�3k
� E.�H�
�L|i |�@| E.��� _i�?it @ 4@TT�?} uhL4 5 |L b� A@!�?} |��t @?_ E.�H� �?|L @UUL�?|c E.�S�
_i�?it @ 4@TT�?} uhL4 5 |L R� G
R� ' sE5�c E.�b�
��ihi
sE5� '� � b�� � q
� � b� A � q
E� � w�
Ebn w�
k��� b� A � q
�� � A E� n b�w*E�� w�
l��k
� E.��f�
Oihic �| �t �?_iht|LL_ |�@| b �t |�i u�?U|�L? Lu 5 �4T*�i_ M) E.����
5L*��?} E���� uLh u G
u '
;?=E� � k��g�
�k-�f
k�R�
n �l<@>
�
�nk
�
�H
�L4M�?�?} |��t ��|� E.�.�c �i LM|@�?G
%bn w
� � w
-W5
Eg� �k
& �
�3k
'
57E� � k��g�
�k-�f
��R�
n ��68
�
�nk
�
5L*�i |��t uLh 5 G
5 '�� w
bn w
�g�
�k-W
57E� � k��g�
�k-�f
��R�
n ��68
�3k�nk
E.����
' }ER� c b�c
t@)� i U@? �ti |��t @?_ s �? E.�b� |L _i�?i @ 4@TT�?} uhL4 5 �?|L �|ti*uG
5� ' }ER� c b� ' } EsE5�c bE5�� ' �E5�c
t@)c ��ihi bE5� t�44@h�3it E.���� W| �t i@t) |L tii |�@| � �t @? �?Uhi@t�?} u�?U|�L? Lu 5 @t
*L?} @t �� ' �A �
AL @U|�@**) �?_ |�i � i_ TL�?|c �u �| i �t|tc �| �t �tiu�* |L Mi @M*i |L hit|h�U| |�i ti| Lu
U@?_�_@|i i^��*�Mh��4 �@*�it Lu 5� i !?L� |�@| �i 4�t| �@�i b � fc�� � b�� � q
�� fc�
�� b�A � q�� fc R� � f� A�i �ht| Lu |�iti �4T*�it @? �TTih ML�?_ L? 5c @?_ |�i L|�iht
�4T*) @ *L�ih ML�?_� EA�iti UL?_�|�L?t �4T*) u � fc tL �i _L?<| *�t| |�@| tiT@h@|i*)�� 6hL4
E.�b� �i tii |�@| R� � f hi^��hitG
b ��� w
� A
%� � q � � A
w
� � w
&'
E� � w� E�� q�
�A� w
A��t T*@Uit @ *L�ih ML�?_ L? 5 G
5 �
+-W
E� � w�� EgA �w
%E�� w� E�� q�
� A� w n �
&,3�
w
�
i �@?| |��t *L�ih ML�?_ ELu UL�hti-� |L Mi *itt |�@? |�i �TTih ML�?_ L? 5 �4T*�i_ M)
�b
b � f� A��t T*@Uit @ hit|h�U|�L? L? |�i T@h@4i|ihtG
w �E�� w� E� � q�
� Ac
Lhc
� A �E�� w� E�� q�
w�
A��t �t @ Thi||) |�}�| �TTih ML�?_ L? � A �
A�i �@*�i Lu @ �?�| Lu U@T�|@* �? |�i ?L?�|h@_i_ @?_ |h@_i_ }LL_ tiU|Lht �tc hitTiU|��i*)G
^� 'kR�
�g�
�k3�u�3k
�� b�� � qc ^A '
w��gA
�w3�5�3w
�� b�A � q�
.�2� w�?i@h�3@|�L? Lu |�i �L_i* �? 5iU|�L? e
i _ih��i ThL��_i uLh4�*@t uLh *�?i@h�3�?} |�i 4L_i* Lu tiU|�L? e @ML�| �|t t|i@_) t|@|i�
#i�?i |�i TihUi?| _i��@|�L? Lu @ �@h�@M*i uhL4 �|t t|i@_) t|@|i �@*�i @t % ' _%*%�
w�?i@h�3�?} |�i u� U�h�i @hL�?_ |�i t|i@_) t|@|i �i LM|@�?G
-n E� n k�u ' R� � R�
Lh
-| n E� n k�u| '
57�� #R�
R�
$#3�68 R�| c
��ihi �i �@�i �ti_ |�i u@U| |�@|
R '
#R�
R�
$#3�
R�
6�?@**)c hi@hh@?}i |L LM|@�?
R�| '-| n E� n k�u|
� ��R�R�
�#3� c E.��2�
ef
��ihi
� �
#R�
R�
$#3�
� fc
@u|ih i�@*�@|�?} R �? |ih4t Lu R� �
AL *�?i@h�3i |�i �� U�h�ic Mi}�? ��|� |�i R� i^�@|�L?G
R� ' �� � k
#un
�
#SA
6hL4 |�i hitL�hUi UL?t|h@�?| �i LM|@�?G
_SA '�E�� w��
�gA
�w53w �-W
�_5c
tL |�@|
SA '
�E� � w��
�gA
�w53w �-W
�SA
55c
��ihi 5 ' _5*5� A�i?c
R� ' ��� k
#u n
�
#
�E�� w��
�gA
�w53w �-W
�5
SA5c
Lh
R� ' ��� k
#u n
#b-W5
#SA
$5�
i U@? ?L� LM|@�? 5 @t @ u�?U|�L? Lu R� @t uL**L�tG
5 '�3k#
un R�
b-W5#SA
'SA
b-W5
kE�� k� un #R�
l� E.����
6hL4 |�i �ht| Lh_ih UL?_�|�L? uLh *@MLh �? |�i |h@_i_ }LL_t tiU|Lhc E��w���gA
�w53w '
E� n b�-Wc �i LM|@�?
�w5 ' gE� n b� 'E� n b|� � E� n b�
E� n b�'
b| � b
� n bE.��e�
e�
' bb
� n b�
AL|@**) _�gihi?|�@|�?} |�i i Thitt�L? uLh |�i M�?_�?} UL**@|ih@* UL?t|h@�?| ��|� hitTiU| |L
uc bc 5c @?_ R� c �i LM|@�?G
�
� � b�-W5bb
n�
�
�� b�
�3Ckn l
57� n %E�� ��R�
�
�684D E�� k�R��g�
�ku�3k u
��
�
�� b�
�ikR�
�g�
�ku�3k
nR��g�
�ku�3kl
3C57� n %E�� ��R�
�
�68n E# � ��
%E�� ��R�
�
�4DjR�
'
;A?A=-W5 �E�� w� �w�
�gA
�w5�3w
� � b�
<A@A> 5
Lhc
�
� � b�-W5bb E.��D�
n�
�
� � b�
�3Ckn l
57� n %E� � ��R�
�
�684D E�� k�R��g�
�ku�3ku
n�
�
� � b�
�;?=R� �g��k
u�3k
57k n l
3C57� n #
%E�� ��R�
�
�684D68<@> R�
'
;A?A=-W5 �E� � w� �w�
�gA
�w5�3w
�� b�
<A@A> 5
wi|<t t�4T*�u) |�i i Thitt�L? L? E� � k�u� �UULh_�?} |L |�i UL**@|ih@* UL?t|h@�?|G
�
�� b�dw�
�gA
�w5�3wn
3Ckn l
;?=� n%E� � ��R�
�
�<@>4D R�
�g�
�ku�3ko ' -W5nE�noW��
e2
tL |�@|c
�b
� � b�
3Ckn l
;?=� n%E�� ��R�
�
�<@>4DR�+�
' b-W5 n bE� n oW�� ��b
�� b�w+A
' E� � w�+A �-W5 ��b
�� b�w+A n bE� n oW��
' +A � w+A�
�� b��-W5 n bE� n oW��
' SA n oW� �w+A
�� b�n bE� n oW��
' SA �w+A
�� b�n doW n bE� n oW�o�
�L� UL?t�_ih |�i |ih4 L? R� �
#SA ��b
�� b�
3Ckn l
;?=� n #
%E� � ��R�
�
�<@>4D R�+�
' SA ��b
�� b�
3Ckn l
;?=� n%E� � ��R�
�
�<@>4D R�+�
nE# � ��
3CSA � �b
� � b�l
%E�� ��R�
�
�R�+�
4D'
w+A
� � b�� doW n bE� n oW�o� n E# � ��
3CSA � �b
�� b�l
%E� � ��R�
�
�R�+�
4D �
��|c
SA ��b
�� b�l
%E� � ��R�
�
�R�+�
' +A �-W5 � oW� ��b
� � b�l
%E� � ��R�
�
�R�+�
' +A � E� n b�-W5 n b d-W5 n E� n oW��o
�b E� n oW�� � oW� ��b
�� b�l
%E�� ��R�
�
�R�+�
e�
' +A n�b
�� b�dw�
�gA
�w5�3w n
3Ckn l
;?=� n%E�� ��R�
�
�<@>4DR�+� o
��b
� � b�l
%E� � ��R�
�
�R�+� � E� n b�-W5 � doW n b E� n oW�o�
' +A � E�� w�+A n�b
�� b�dw�
�gA
�w5�3w n Ek n l� R�+� o� doW n b E� n oW�o�
' w+A n�b
�� b�dw+A n Ekn l� R�+� o� doW n b E� n oW�o�
'w+A
�� b�n
�b
� � b�Ek n l�R�+� � doW n b E� n oW�o�
5LG
�b
�� b�
3Ckn l
;?=� n #
%E�� ��R�
�
�<@>4D R�+�
' #SA �
;?= w+A
� � b�� doW n bE� n oW�o� n E# � ��
3CSA � �b
�� b�l
%E�� ��R�
�
�R�+�
4D<@>' #SA � i
w+A
� � b�� doW n bE� n oW�o� n
E# � ��
#w+A
� � b�n
�b
�� b�Ekn l�R�+� � doW n b E� n oW�o�
$j
' #SA �
+w+A
�� b�� # doW n bE� n oW�o� n E# � ��
#w+A
� � b�n
�b
�� b�Ek n l�R�+�
$,
5�Mt|�|�|�?} |�i @ML�i i Thitt�L? �?|L E.��D�G
�
�� b�-W5bb
n�
b
%SA �
w+A
�� b�n doW n bE� n oW�o�
&E�� k�u
n�
b
%#SA � #
w+A
�� b�� E# � ��
�b
� � b�Ek n l�R�+� n # doW n bE� n oW�o�
&R�
'
;A?A=-W5 �E�� w� �w�
�gA
�w5�3w
�� b�
<A@A> 5
5�Mt|�|�|�?} L�| uLh b �? |ih4t Lu 5 uhL4 E.��e� @?_ uLh 5 �? |ih4t Lu u @?_ R� uhL4 E.����c
ee
�i LM|@�?G
��
� � b�-W5w E� n b�
SA
b-W5
kE�� k� un #R�
ln�
b
%SA �
w+A
�� b�n doW n bE� n oW�o�
&E�� k� u
n�
b
%#SA � #
w+A
�� b�� E# � ��
�b
� � b�Ek n l�R�+� n # doW n bE� n oW�o�
&R�
'
;A?A=-W5 �E�� w� � A w�
�gA
�w5�3w
�� b�A
<A@A> SA
b-W5
kE�� k� u n #R�
l
�L**iU|�?} |ih4t @?_ t�4T*�u)�?} E�t�?} |�i �ht| Lh_ih ?iUitt@h) UL?_�|�L? uLh 5 @?_ |�i
UL**@|ih@* UL?t|h@�?|�G
�
b
%SA �
w+A
� � b�n doW n bE� n oW�o�
&E� � k� u
n�
b
%#SA � #
w+A
�� b�� E# � ��
�b
� � b�Ek n l�R�+� n # doW n bE� n oW�o�
&R�
'�-W5 n
�
� � b�-W5w E� n b��
��
� � b�
�dwE� n b�-W5o
��
SA
b-W5
kE�� k� un #R�
l'
SA
b
kE� � k� un #R�
l
Lh
%�
b
#SA �
w+A
� � b�
$�SA
bn
doW n bE� n oW�o�
b
&E� � k� u
n
%�
b
##SA � #
w+A
� � b�� E# � ��
�b
� � b�Ekn l�R�+�
$� #
SA
bn# doW n bE� n oW�o�
b
&R�
' f
��*|�T*) M) bc U@?Ui* |ih4tc @t @TThLTh�@|ic 4�*|�T*) M) � � b�c |L }i|G
��#w+A � E# � ���bEk n l�R�+� n E� � b� � # doW n bE� n oW�o�
�R�
eD
'qw+A � E� � b� � doW n bE� n oW�o�
rE�� k� u�
Lhc
R�
u'
qw+A � E�� b� � doW n bE� n oW�o�
rE� � k�
#w+A n E# � ���bEk n l�R�+� � E� � b� � # doW n bE� n oW�o�' r�� c E.��S�
t@)c ��ihi r�� �t |�i t*LTi Lu |�i �� U�h�i� 6hL4 |��t i Thitt�L? �i U@? tii |�@| uLh |�i
�LMM�#L�}*@t U@ti E# ' ��c |�i t*LTi �t _i�?�|i*) ?i}@|��iG
R�
u' �E�� k� f
5Lc ��|� TihuiU| t�Mt|�|�|@M�*�|)c |�i �� U�h�i t*LTit _L�?�@h_c @?_ @ U�| �? - 4�t|
ThL_�Ui @ u@** �? R� @?_ @ h�ti �? u� `�|� # ' fG
R�
u'
qw+A � E� � b� � doW n bE� n oW�o�
rE�� k�
�bEkn l�R�+��
�L|i |�@| ��i? � ' fc |��t i Thitt�L? �t _i�?�|i*) TLt�|��i� W| U@??L| Mi t�}?i_ ��i? � : f�
�) t�Mt|�|�|�?} L�| uLh R� �? E.��S� uhL4 |�i w� U�h�ic E.��2�c �i �?_G
-
���R�
�R
��3# n ru� u ' r�� uc
��ihi
ru� '� n k
���R�
�R
��3# �A�i?c
u-'
�
Er�� � ru���� �
�R�
�R
��3#��
5Lc uLh @ U�| �? -c - fc |L ThL_�Ui @? i^��*�Mh��4 _hLT �? i4T*L)4i?|c u fc �i ?ii_
r�� : ru� � 5�?Ui |�i *@||ih �t TLt�|��ic |��t hi^��hit |�@| r�� Mi 4Lhi |�@? ��t| TLt�|��i�
eS
W| 4�t| Mi M�} i?L�}�� A�i UL?_�|�L? �tG
qw+A � E�� b�� doW n bE� n oW�o�
rE�� k�
#w+A n E# � ���bEkn l�R�+� � E� � b� � # doW n bE� n oW�o�:
� n k
���R�
�R
��3# �
.��� 5L*��?} |�i �@�? �L_i*
i t|hitt |�i U@ti ��ihi |�ihi �t t�Mt|�|�|�L? Mi|�ii? S� @?_ SA c @?_ Mi|�ii? 5| @?_ T|�
A�i U@ti Lu ?L t�Mt|�|�|@M�*�|) �?�L*�it LM��L�t 4L_��U@|�L?t L? |�i _�tU�tt�L? Mi*L� @?_
tL �t ?L| �?U*�_i_� � |iU�?�U@* 4@?�tUh�T| ���U� UL�iht |��t U@ti �? _i|@�* �t @�@�*@M*i L?
hi^�it|�
i Mi}�? ��|� @ _�tU�tt�L? Lu |�i t|i@_) t|@|i �? ���U� @** hi@* �@h�@M*it @?_ hi*@|��i
Th�Uit ��|� |�4i t�MtUh�T|t @hi UL?t|@?|� i UL?t�_ih |�L t|i@_) t|@|it� A�i Thi�Uh�t�t
t|i@_) t|@|i �t L?i �? ���U� |�i �?�|�@* *i�i* Lu _iM|c t@) �fc ��L*@|it E���H�� i _i�?i |�i
TLt|�Uh�t�t t|i@_) t|@|i @t L?i �? ���U� |�i �?�|�@* *i�i* Lu _iM|c t@) �"c �@t |�i ThLTih|)
|�@| |�i UL**@|ih@* UL?t|h@�?| �t t@|�t�i_ @t @? i^�@*�|)� i |�i? _�tU�tt |�i UL4T�|@|�L? Lu
|�i _)?@4�U T@|� |@!�?} |�i iUL?L4) uhL4 �ht| t|i@_) t|@|i |L |�i tiUL?_� i _L |��t �?_ih
|�L tUi?@h�Lt� W? L�h M@ti*�?i tUi?@h�L }L�ih?4i?| TL*�U)c _i�?i_ �ihi �? |ih4t Lu 4L?i)
}hL�|�c _Lit ?L| U�@?}i� W? |�i @*|ih?@|��i tUi?@h�L |�i 4L?i) }hL�|� h@|i �t U�@?}i_ �?
|�i Tih�L_ ��i? |�i UL**@|ih@* UL?t|h@�?| �t �4TLti_�
.����� 5|i@_) 5|@|i
AL �?_iht|@?_ �L� |�iti t|i@_) t|@|it @hi UL4T�|i_c �| �t �tiu�* |L ?L|i |�@| � t�M�iU| |L
ui@t�M�*�|) � ULhhitTL?_�?} |L @?) �?�|�@* *i�i* Lu _iM| |�ihi �t @ �?�^�i t|i@_) t|@|i ��i? |�i
UL**@|ih@* UL?t|h@�?|c E���H�c �t �}?Lhi_� AL �?_ |�i TLt| Uh�t�t t|i@_) t|@|ic �i t�4T*) @*|ih
|�i �?�|�@* _iM| �?|�* |�i UL**@|ih@* UL?t|h@�?| �t t@|�t�i_ @t @? i^�@*�|)� A�i?c �f �t ti*iU|i_
@t @ ?�4Mih M�}}ih |�@? �"c |L Mi UL?t�t|i?| ��|� _@|@ @t _�tU�tti_ �? |�i |i |�
A�i uL**L��?} _�tU�tt�L? i T*@�?t �L� �i �?_ |�i t|i@_) t|@|i ULhhitTL?_�?} |L @? @hM��
|h@h) �?�|�@* �@*�i Lu |�i _iM|�
A�i t|i@_) t|@|i �?|ihit| h@|ic -c �t _i|ih4�?i_ uhL4 E��S�c E�����c @?_ |�i u@U| |�@|
R| ' �|*�| �t UL?t|@?| �? t|i@_) t|@|iG
- '� n %
q�
6hL4 �ihi L?c �i |hi@| - @t @ !?L�? ^�@?|�|)�
e.
+i�h�|�?} |�i �h4<t �ht| Lh_ih UL?_�|�L? uLh 5 G
+A ' >25
#-W
>2
$1
�
A�i hitL�hUi UL?t|h@�?| �? |�i |h@_i_ }LL_ tiU|Lh �tG
+A � SA �-W5 ' oW��
�L4M�?�?} |��t ��|� |�i Thi��L�t i Thitt�L?c
5-W
57#-W
>2
$13�
� �
68 ' SA n oW�� E.��.�
Oihi �t @? @*}Lh�|�4 uLh �?_�?} |�i t|i@_) t|@|i ���U� �?�L*�it @ ?L?*�?i@h ti@hU� �? |�i
t�?}*i �@h�@M*ic SA �
5�TTLti SA �t }��i?� A�i?c 5 U@? Mi UL4T�|i_ uhL4 E.��.�� uA 4@) |�i? Mi LM|@�?i_
uhL4G
5 '>�T
>2
;?=#-W
>2
$13�
� �
<@>31
13�
E.��H�
B��i? uA c u� 4@) Mi LM|@�?i_ M) UL4M�?�?} |�i Th�Ui i^�@|�L?G
R� '�
�� �
#E� � �� SA
�S�
$ �
#
E.��b�
@?_ i^�@*�|) Lu T��u<t @UhLtt |�i |�L tiU|LhtG
E� � k�R��g�
�k �u�
�3k
'
;?=��#-W
>2
$�31<@>
�
�31
E� � w�>���gA
�w �uA�3w�
eH
5�Mt|�|�|i |�i uLh4ih �?|L |�i *@||ihc |L LM|@�?G
E�� k��
� � �
#E�� �� SA
� Eg��k Eu���3k
$ �
# �g�
�k �u�
�3k
'
;?=� �#-W
>2
$�31<@>
�
�31
E�� w�>���gA
�w �uA�3wc
Lh �u�
�3d �# E�3k�nko ' (c E.�2f�
��ihi
( '
�� �
�-W
>2
��31� �
�31
E�� w�>���gA
�w �uA�3w
E� � k� �
�3�
�E�3��SA
�Eg� �k
� �
# Eg��k
`�|� u� c SA �? �@?_c UL4T�|i R� uhL4 |�i Th�Ui i^�@|�L?c E.��b�� 6�?@**)c @ttitt ��i|�ih
*@MLh t�TT*) i^�@*t *@MLh _i4@?_ �? |�i |h@_i_ }LL_ tiU|LhG
�
-
;?=� �#-W
>2
$�31<@>
�
�31
E�� w�>���gA
�w �uA�3w
' �f
�uA n u�
��R� E.�2��
�_��t| SA �?|�* E.�2�� �L*_t i @U|*)� A�i ��i i^�@|�L?tc E.��.��E.�2��c U@? Mi �ti_ �? |��t
�@) |L T�? _L�? |�i ��i �@h�@M*itc u� c uA c R� c SA c 5�
A�i �@h�@M*itc R @?_ Sc 4@) Mi LM|@�?i_ uhL4 E.�2e� @?_ E.�2D�� A�i?c LM|@�? RA uhL4
RRA S ' � n %�
A�i �@}i h@|i UL4it uhL4
� ' �fu�Rc u ' uA n u�
i ?L� LM|@�? |�i t|i@_) t|@|i �@*�i Lu _c |�i h@|�L Lu _iTLt�|t |L |�i Mi}�??�?} Lu Tih�L_
4L?i) t|LU!� #���_�?} E���� M) � A G
RS ' �un�
RA�
_
RAc
eb
tL |�@|
_ ' RA d�u� RSo n ��
i hi^��hi f � _ � ��
�L� �i }L uLh |�i @tti| �@*�it� 6hL4 E��2f�c
^� ' T �� �g n
^�
� n oWc
tL |�@|
^� '� n oW
oWT�� �
gc � ' �cAc
��ihi
T���g ' R�
k+�
g�c
T �� Ag '
%+A
>�T
& �1 w>�T
gA�
A�i �@*�i Lu UL**@|ih@* �tc �? �?�|t Lu |�i |h@_i_ }LL_c
^�g� n ^AgA
A��t UL4T*i|it |�i _�tU�tt�L? Lu |�i t|i@_) t|@|i�
.���2� A�i Ah@?t�|�L? �@|�
i �4@}�?i |�@| �? _@|i f |�i iUL?L4) �@t @? �?�|�@* _iM| *i�i* Lu �f� �| |��t *i�i* Lu _iM| |�i
UL**@|ih@* UL?t|h@�?| �t M�?_�?}� W? |�i M@ti*�?i i^��*�Mh��4c 4L?i) }hL�|� �t !iT| UL?t|@?|�
A�@| �tc %| ' % uLh | ' fc �c 2c ���� i UL4T�|i |�i i^��*�Mh��4 T@|� Lu |�i iUL?L4) |L |�i
?i� t|i@_) t|@|i ��ihi |�i _iM| *i�i* �t �"� W? |�i tiUL?_ i^��*�Mh��4c %f 9' %c M�| %| ' %
uLh | ' �c 2c ��� � W? |��t i^��*�Mh��4c |�i 4L?i|@h) @_��t|4i?| �t �?@?|�U�T@|i_ �? |�i ti?ti
|�@| ��i? �L�ti�L*_t 4@!i |�i�h _iTLt�| _iU�t�L? �? |�i Mi}�??�?} Lu Tih�L_ f |�i) _L tL
�?_ih |�i @tt�4T|�L? |�@| |�i) @hi �? |�i M@ti*�?i i^��*�Mh��4� �t ?L|i_ @ML�ic |�i) _L
?L| @_��t| |��t _iU�t�L? ��i? �| |�h?t L�| |�@| %f 9' %�
i �ht| UL?t�_ih |�i UL4T�|@|�L? Lu |�i M@ti*�?i i^��*�Mh��4� i |�i? _�tU�tt |�i
UL4T�|@|�L? Lu |�i i^��*�Mh��4 �? ���U� |�ihi �t @ 4L?i|@h) �?|ih�i?|�L?� A�i M@t�U t|h@|i})
Df
�t M@ti_ L? tL*��?} @ t)t|i4 Lu ?L?�*�?i@h i^�@|�L?t �? |�i w@}h@?}i 4�*|�T*�iht L? |�i
UL**@|ih@* UL?t|h@�?|� 6Lh @ }��i? ti| Lu w@}h@?}i 4�*|�T*�ihtc �i UL4T�|i @ ti^�i?Ui Lu
U@?_�_@|i @**LU@|�L?t @?_ Th�Uitc �4TLt�?} |�i uL**L��?} UL?_�|�L?tG E�� ^�@?|�|�it @?_ Th�Uit
i�i?|�@**) i?_ �T �? |�i ?i� t|i@_) t|@|i( E��� |�i �?�|�@* *i�i* Lu _iM| �t �f( @?_ E���� @**
i^��*�Mh��4 UL?_�|�L?t i UiT| |�i UL**@|ih@* UL?t|h@�?| @hi �4TLti_� i |�i? i�@*�@|i |�i
UL**@|ih@* UL?t|h@�?| @| i@U� _@|i� i @_��t| |�i w@}h@?}i 4�*|�T*�iht �?|�* �| �t t@|�t�i_� Wu
|�i 4�*|�T*�iht |�h? L�| |L ��L*@|i ?L?�?i}@|���|)c |�i? �i UL?U*�_i |�ihi �t ?L i^��*�Mh��4�
�@ti*�?i 5Ui?@h�L �| _@|i fc �f �t }��i?� i �@?| |L UL4T�|i @? i^��*�Mh��4 ti| Lu
ti^�i?Uitc
^A| c ^�| c S
A| c S
�| c u
A| c u
�| c R
�| c R
A| c -|c �|c 5|c �|n�c b|c | ' fc�c 2c �c ���c
uLh @ }��i? ti^�i?Ui Lu %|<t� A�iti �� ti^�i?Uit 4�t| t@|�tu) �� i^��*�Mh��4 UL?_�|�L?t� A�iti
@hi |�i |�L i^�@|�L?t _i�?�?} |�i ^<t E��2f�( |�i �h4<t �?|ih|i4TLh@* ,�*ih i^�@|�L? E��22�c
@?_ �|t |�hii �?|h@�|i4TLh@* ,�*ih i^�@|�L?tc E��2��c E��2e�c E��2D�( |�i 4@h}�?@* UL?_�|�L?
hi*@|�?} R� |L |�i UL?t�4T|�L? }LL_tc E��b�( |�i hitL�hUi UL?t|h@�?| �? |�i |h@_i_ @?_
?L?|h@_i_ }LL_ tiU|Lhtc E���f� @?_ E�����( |�i UL**@|ih@* UL?t|h@�?|c E���H�( |�i �L�ti�L*_<t
�?|h@� @?_ �?|ih� |i4TLh@* ,�*ih i^�@|�L?tc E��D�c E��S�( @?_ �?@**)c |�i U@t� �? @_�@?Ui
UL?t|h@�?|c E��2b��2.
i tii! @? i^��*�Mh��4 ���U� UL?�ih}it @t)4T|L|�U@**) |L |�i t|i@_) t|@|i ��ihi |�i
_iM| �t �" @?_ |�i UL**@|ih@* UL?t|h@�?| �t 4@h}�?@**) ?L?�M�?_�?}� A��t 4i@?t |�@| @** |�i
@ML�i ti^�i?Uit UL?�ih}i |L |�i�h �@*�it �? |�i t|i@_) t|@|i i^��*�Mh��4 ��Lti UL4T�|@|�L?
�t _�tU�tti_ �? |�i Thi��L�t tiU|�L?�
Oihi �t L�h t|h@|i}) uLh @UUL4T*�t��?} |��t� i @tt�4i |�@| |�i t)t|i4 @hh��it �? @
t|i@_) t|@|i �? Tih�L_ A n 2 E�? Th@U|�Uic �i uL�?_ |�@| A ' �f �Lh!t �i**�� i tTiU�u)
i L}i?L�t*) EMi*L�c �i i T*@�? �? _i|@�* �L� |��t �t _L?i�c @ ti^�i?Uic b � Ebfc b�c ���c bAn��c
��|� b| ' f uLh | � A n 2� �*tLc \An2 ' \rc ��ihi |�i t�MtUh�T|c �r<c 4i@?t t|i@_) t|@|i�
5�4�*@h*)c @** |�i L|�ih �� �@h�@M*it @hi @tt�4i_ |L Mi �? |�i ?i� t|i@_) t|@|i uLh | � A n2�
A�i �@*�i Lu A |�@| �i �ti_ �? |�i U@*U�*@|�L?t t@|�t�it |�i ThLTih|) |�@| |�i iUL?L4) �@t
uLh @** Th@U|�U@* T�hTLtit @U��i�i_ UL?�ih}i?Ui |L |�i ?i� t|i@_) t|@|i MiuLhi A n 2�
5:Htxloleulxp dovr uhtxluhv wkdw wkh olplwlqj frqglwlrq/ +614:,/ eh vdwlv�hg1 Zh fdq yhuli| wkdw wklv lvvdwlv�hg h{ srvw/ zkhq zh kdyh irxqg d vhw ri Odjudqjh pxowlsolhuv zklfk surgxfh doorfdwlrqv zkhuh wkhfroodwhudo frqvwudlqw lv vdwlv�hg lq hdfk shulrg1
D�
A�i �_i@ �t |L �@h) b �?|�* |�i UL**@|ih@* UL?t|h@�?|c
��^�| g� n � A ^A| g
A �-W5| � E� n oW��| ' f
�t t@|�t�i_ uLh | ' fc �c ���c A n �� EA��t i^�@|�L? �t t@|�t�i_ M) UL?t|h�U|�L? uLh | � A n 2��
AL _L |��tc �i ?ii_ |L UL4T�|i @ 4@TT�?} uhL4 b |L |�i ^�|<tc |�i 5|<t @?_ |�i �|<t�
6�ht|c �i ti| �T @ 4@TT�?}G
�\|n�c R
A|
�$
�S�| c S
A| c R
�| c �|c -|cu
�| c u
A| c\|c R
A|3�
�c E.�22�
t|@h|�?} ��|� | ' A n 2 @?_ i?_�?} ��|� | ' �� i |�i? �@?_*i | ' f tiT@h@|i*)�
#@|itc | : � A�i LM�iU|c \| �t LM|@�?i_ �t�?} E��22�G
\| ' \|n�E� n b|�c
���U� �t @? i^�@|�L? |�@| �t @�@�*@M*i uLh | ' �c ��� A n 2� A�i?c �i 4@!i �ti Lu E���2� |L
tL*�i uLh RA|3� G
\| '�Sc|R|
RA|3�RA|
�
� n %|3�qc E.�2��
���U� �t @�@�*@M*i uLh | ' �c ���c A n 2� AL tL*�i |��tc �i hi^��hi |�i L|�ih �@h�@M*it �ht|� i
_L |��t �t�?} L�h i^��*�Mh��4 UL?_�|�L?t @?_ |�i }��i? \|c RA| � `i �?_ |�iti �@h�@M*it M)
ti||�?} �T @ L?i�_�4i?t�L?@* ti@hU� uLh u�| � 5Lc t�TTLti |�@| �? @__�|�L? |L
�\|c b|c R
A|
�c �i
�@�i u�| � A�i?c uhL4 L�h @tt�4T|�L?t @ML�| |iU�?L*L})c S�| '
�g�
�k �u�|
��3k� B��i? u�
|
@?_ S�| c |�i uL**L��?} |�L i^�@|�L?t U@? Mi tL*�i_ uLh R�| @?_ SA| G
R�| '�
�� �
#E� � �� SA|
�S�|
$ �
#
E.�2e�
R|RA| S| ' � n %|c
D2
��ihi
R '
57# �
� � �
$�3#
n
#R�
�
$�3#68 �
�3#
E.�2D�
S '
+kE�� �� SA
l#3�# n
k�S�
l#3�#
, #
#3�
� E.�2S�
A��t U@? Mi |hi@|i_ @t @ L?i _�4i?t�L?@* ti@hU� ThLM*i4 �? SA| @*L?i�
i ?L� �@�i u� c R� c Rc S� @?_ SA �? �@?_� A�i ?i | t|iT �t |L �?_ 5 @?_ uA � �?i
i^�@|�L? |�@| �t �tiu�* uLh |��t T�hTLti �t |�i �ht| Lh_ih UL?_�|�L? uLh 5 G
#+A
>25
$ �
1
>2 ' E� n b�-W�
5�?Ui
+A
>25'
;?=%>�T
>25
& 13�1
n �
<@>1
13�
c T ' ��gA
�w �uA��3w
c
�i �@�i
>�T
>25'
;?=%E� n b�-W
>2
&13�� �
<@>1
13�
� E.�2.�
i hi^��hiE� n b�-W
>2 �c
���U� }�@h@?|iit |�@|c @t *L?} @t f � 1 � �c |�i LM�iU| �? Mh@Uit �t TLt�|��i� A��t �t
?iUitt@h)c uLh 5 @?_ T |L Mi TLt�|��i� A��t �t @ hit|h�U|�L? �i T*@Ui L? b�
,^�@|�L? E.�2.� �?�L*�it |�L �?!?L�?tc 5 @?_ uA � i ?ii_ @?L|�ih i^�@|�L? |L T�? |�iti
|�L �@h�@M*it _L�?� �iuLhi LM|@�?�?} |�itic �| �t �tiu�* |L �Lh! L? |�i i Thitt�L? uLh |�i
4@h}�?@* ThL_�U| Lu *@MLh �? |�i |h@_i_ }LL_ tiU|LhG
T �� Au '
#+A
>�T
$�
1
E�� w�>�T|uA|
c
D�
Lhc
T �� Au '
;?=� n%>25
>�T
& 13�1
<@>�
13�
E�� w�>�T
uA� E.�2H�
6hL4 E.�2.�c %>�T
>25
&313�
1
'
;?=%E� n b�-W
>2
&13�� �
<@>3�
�
5�Mt|�|�|�?} |��t �?|L E.�2H�c
T�� Au '
;?=� �#E� n b�-W
>2
$�31<@>
�
�31
E�� w�>�T
uA�
,^�@|�?} |�i T��u<t �? i@U� tiU|LhG
E�� k�R�+�
u�'
;?=��#E� n b�-W
>2
$�31<@>
�
�31
E�� w�>���gA
�w �uA�3w�
A��t U@? Mi tL*�i_ uLh uA G
uA '�u�
�kw
;AAA?AAA=���
�E�nb�-W
>2
��31� �
�31
E�� w�>���gA
�wE�� k�R� Eg��k
<AAA@AAA>
�
w
� E.�2b�
A�i?c ti||�?} T ' ��gA
�w �uA��3w
c �i LM|@�? 5 uhL4 E.�2.�G
5 '>�T
>2
;?=%E� n b�-W
>2
&13�� �
<@>31
13�
� E.��f�
�L4T�|i
�Sc| '
#S| �
�f
� n �
�uA| n u�
|
��n�$3j� E.����
�L�c �| �t TLtt�M*i |L tL*�i uLh RA|3� �t�?} E.�2��� ��|c �i @hi ?L| _L?i )i|c MiU@�ti �i
De
t|@h|i_ ��|� @ }�itt uLh u�| �
6hL4 |�i *@MLh t�TT*) i^�@|�L?c E��D�c
� ' R�f
�uA n u�
��� E.��2�
6hL4 E���2� �i LM|@�? -| G
q-| ' E� n %|3�� E� n b|� ERA| *R
A|3��c E.����
| ' �c 2c ��� � ,�@*�@|�?} |�i ThL_�U| Lu - LM|@�?i_ uhL4 �ihi @?_ � LM|@�?i_ uhL4 E.��2�c
�i U@? i�@*�@|i E��2e�G
s Eu�| ( \|c b|c R
A| � � E� � k�R�|
+�|u�|
� �|-|� E.��e�
A�i �_i@ �t |L @_��t| u�| �?|�* sEu�
| ( \|c b|c RA| � ' f�
#@|i | ' f i ?L� �@�i �? �@?_c
�S�| c S
A| c R
�| c �|c -|c u
�| c u
A| c\|c R
A|3�
�c uLh | ' �c ���c A n 2�
�i |c �i tii!�S�| c S
A| c R
�| c �|c-|c u�
| c uA|
�uLh | ' f� �L|i |�@| �i _L ?L| �@�i \fc t�?Ui E��.�
�t ?L| @�@�*@M*i uLh | ' f� A��t 4i@?t |�@| �i U@??L| �?_ u�f M) ti||�?} s ' fc �? E.��e� @t
�i _L uLh | ' �c ���c A n �� i hiT*@Ui i^�@|�L? E.���� M)
�ScfRfRAf
'q-f�Sc�
R�RA� E� n %f�� E.��D�
A�i?c �i tL*�i uLh u�f @t uL**L�t� 6� u�
f � 5L*�i uLh R�f c Rfc S�f c S
Af c Sf �t�?} |�i �|ih@|��i
@*}Lh�|�4 _itUh�Mi_ @hL�?_ E.�2e�� A�i?c UL4T�|i uAf �t�?} E.�2b�c 5f �t�?} E.��f�c �Scf
�t�?} E.����c @?_ �f �t�?} E.��2�� 5L*�i uLh �f-f �t�?}
�f-f ' E�� k�R�f
#g�
u�f
$k
c
DD
@?_ UL4T�|i -f uhL4 �f-f*�f� 6�?@**)c i�@*�@|i
}Eu�f � '
�ScfRfRAf
��Sc�R�RA�
q-f
� n %f�
�_��t| u�f �?|�* }Eu�
f � ' f� �?L|�ih �@) |L �h�|i |�i } u�?U|�L? t�Mt|�|�|it M@ti_ L?
RRA S ' � n %c
}Eu�f � '
�ScfSf� n %f
��Sc�S�� n %�
q-f
� n %fc
Lhc
}Eu�f � ' �ScfSf � �Sc�S�
q-f
� n %�c
A�i ?i | t|iT �t |L i�@*�@|i |�i ^�|<t @?_ |�i �|<t� A�i ^�|<t U@? Mi tL*�i_ hiU�ht��i*) uhL4
E��2f�� A�i �|<t U@? Mi LM|@�?i_ M) t�4�*@|�?} E���f� uLh�@h_c uLh |�i � i_ �f�
W? Th@U|�Uic �i uL�?_ |�@| |�i uL**L��?} T@h@4i|ih�3@|�L? Lu |�i b<t �Lh!t �i**� i *i|
b| uLh | ' fc �c ���c �c � A Mi uhii T@h@4i|iht @?_ �i ti| b| uLh � | A n 2 M) *�?i@h
�?|ihTL*@|�L? @?_ �4TLt�?} bAn2 ' f� i U�Lti |�i uhii b<t |L i?uLhUi i @U|*) |�i UL**@|ih@*
UL?t|h@�?|t �? Tih�L_t | ' fc �c 2c ��� � � � @?_ A� A�i @_i^�@U) Lu |��t UL4T�|@|�L?@*
t|h@|i}) U@? Mi i�@*�@|i_ i TLt| M) i�@*�@|�?} |�i UL**@|ih@* UL?t|h@�?|t uLh _@|it ��|�
| 9' A @?_ | *5 ifc�c ���c �j� i uL�?_ |�@| |��t ThLUi_�hi �Lh!t �i** uLh A ' �f @?_ � ' S�
5�hTh�ti 5Ui?@h�L i ?L� t�TTLti |�@| _f �t ti| @UULh_�?} |L |�i i^��*�Mh��4 �? |�i
Thi��L�t t�MtiU|�L?� W? hi�iU|�L? Lu |��tc �i _hLT |�i �L�ti�L*_<t _)?@4�U �ht| Lh_ih UL?�
_�|�L?c E.��D�c uhL4 UL?t�_ih@|�L? �? Tih�L_ f� A�i UL4T�|@|�L?@* t|h@|i}) uLh �?_�?} |�i
i^��*�Mh��4 �? |��t tUi?@h�L �t �_i?|�U@* |L ��@| �i _itUh�Mi_ �? |�i Thi��L�t t�MtiU|�L?c
��|� |�i i UiT|�L? Lu |��t U�@?}i uLh Tih�L_ f� i hi��i� |�i Tih�L_ f U@*U�*@|�L?t ?L�� i
t�TTLti |�@| bf @?_ RAf @hi }��i? @?_ �i tii! |L tL*�i uLh�SA| c S
�| c R
�| c �|c -|cu�
| c uA| c 5|
�uLh
| ' f� d|L Mi UL4T*i|i_o
DS
+iuihi?Uit
d�o �}��L?c ���*�TTic ���*�TTi �@UU�i||@c �M����| �@?ih�iic 2fffc R��hhi?U) �h�tit @?_
�L?i|@h) �L*�U) �? @? ,UL?L4) ��|� �hi_�| �L?t|h@�?|t�c 4�4iL�
d2o �ti@c �@|h�U! @?_ �� �*L4Mih}c �bbHc Rwi?_�?} �)U*it�c aL�h?@* Lu ,UL?L4i|h�Utc H�G
Hb��2H�
d�o ��ih?�i�4ihc wiL?@h_L @?_ +LMih|L B@hU�@�5@*|Ltc �bbbc RW?|ih?@|�L?@* #iM| @?_ |�i
�h�Ui Lu #L4it|�U �tti|t�c 4�4iL�
deo �ih}ihc �**i? @?_ Bhi}Lh) N_i**c �bbfc R�L**@|ih@*c wL@? "�@*�|) @?_ �@?! +�t!�c
aL�h?@* Lu �L?i|@h) ,UL?L4�Utc 2DG2��e2�
dDo �*@U!c a@?ic #@��_ _i �i3@ @?_ #@��_ aighi)tc �bbSc ROL�ti �h�Uitc |�i 5�TT*) Lu
�L**@|ih@* @?_ |�i ,?|ihTh�ti ,UL?L4)�c A�i ,UL?L4�U aL�h?@*c �fSG Sf�.D�
dSo �LLh4@?c a@U!c A� w@?ic ��5U��*3i�B@||@tc �� ��*�hc �� B�Lt�c a� O@4@??c �� �L�h�
4L�h@tc 5����**�Ttc 2fffc R�@?@}�?} 6�?@?U�@* �h�titG A�i , Tih�i?Ui �? ,@t| �t�@�c
uLh|�UL4�?}c �@h?i}�i �+LU�it|ih �L?uihi?Ui 5ih�it L? ��M*�U �L*�U)�
d.o ��h?t�_ic �h@�}c �@h|�? ,�U�i?M@�4 @?_ 5ih}�L +iMi*Lc �bbbc ROi_}�?} @?_ 6�?@?U�@*
6h@}�*�|) �? 6� i_ , U�@?}i +@|i 5)t|i4t�c ��,+ Lh!�?} �@Tih �L� .�e��
dHo �@M@**ihLc +�U@h_L @?_ �h��?_ kh�t�?@4�h|)c �bbbc R,4ih}�?} �@h!i|t �h�titG �?
�tti| �@h!i|t �ihtTiU|��i�c 4�4iL�
dbo �@*�Lc B��**ih4Lc �bbHc R�@T�|@* 6*L�t @?_ �@T�|@* �@h!i| �h�tit�c 4�4iLc N?��iht�|)
Lu �@h)*@?_�
d�fo �itTi_itc w��tc +LMih|L ��@?} @?_ �?_hit Vi*@tULc 2fffc R�@*@?Ui 5�ii|t @?_ , �
U�@?}i +@|i �L*�U)�c 4�4iL�
d��o ��@_�@c �@?!�4 @?_ #@��_ 6L*!ih|t�w@?_@�c �bbbcRA�i ,�L*��?} +L*i Lu �@?!t �?
W?|ih?@|�L?@* �@T�|@* 6*L�t�c �? 6i*_t|i�? i_�c W?|ih?@|�L?@* �@T�|@* 6*L�tc A�i N?��
�iht�|) Lu ���U@}L �hitt�
d�2o ��h�t|�@?Lc w@�hi?Ui a� @?_ �@h|�? ,�U�i?M@�?c Rw�^��_�|) ,giU|t @?_ A�i �L?i|@h)
Ah@?t4�tt�L? �iU�@?�t4�c �4ih�U@? ,UL?L4�U +i��i�c H2G �eS�D��
d��o ��h�t|�@?Lc w@�hi?Ui a� @?_ �@h|�? ,�U�i?M@�?c Rw�^��_�|) ,giU|tc �L?i|@h) �L*�U)
@?_ |�i ��t�?itt �)U*i�c aL�h?@* Lu �L?i)c �hi_�| @?_ �@?!�?}c 2.G ��������S�
D.
d�eo �Lhti||�c B�c �� �iti?|� @?_ �� +L�M�?�c �bbHc �`�@| �@�ti_ |�i �t�@? ��hhi?U) @?_
6�?@?U�@* �h�t�tq �@h| WG � �@UhLiUL?L4�U ��ih��i��c ��,+ Lh!�?} �@Tih �L� SH���
d�Do #LL*i)c ��U�@i*c 2fffc R� �L_i* Lu �h�tit �? ,4ih}�?} �@h!i|t�c A�i ,UL?L4�U aL�h�
?@*c ��fG 2DS�2.2�
d�So ,@|L?c aL?@|�@?c BihtL��|3 @?_ a� 5|�}*�|3c �bHSc RA�i ��hi A�iLh) Lu �L�?|h) +�t!�c
,�hLTi@? ,UL?L4�U +i��i�(
d�.o ,_�tL?c O@*�c �L?}t@! w�@?}@h@4 @?_ �@hU�t ��**ihc 2fffc R�tti| ��MM*itc wi�ih@}i
@?_ Rw�uiML@|t�G ,*i4i?|t Lu |�i ,@t| �t�@? �h�t�t�c A�i ,UL?L4�U aL�h?@*c ��fG 2eD�
2DD�
d�Ho 6�iht|c A�4L|�)c �bb2c Rw�^��_�|)c wL@?@M*i 6�?_tc @?_ +i@* �U|���|)�c aL�h?@* Lu
�L?i|@h) ,UL?L4�Utc 2bG ��2e�
d�bo Bi*Ltc B@t|L? @?_ �*i�@?_hL ih?ihc �bbbc R6�?@?U�@* w�Mih@*�3@|�L?c �hi_�| �L?�
t|h@�?|t @?_ �L**@|ih@*G W?�it|4i?| �? |�i �i �U@? �@?�u@U|�h�?} 5iU|Lh�c W�6 Lh!�
�?} �@Tih �L�bb%2D�
d2fo Bih|*ihc �@h!c 5�4L? B�*U�h�t| @?_ 6@M�L �@|@*�UU�c 2fffc R, |ih?@* �L?t|h@�?|t @?_
|�i 6�?@?U�@* �UUi*ih@|Lh�c 4�4iL�
d2�o k�)L|@!�c �LM���hLc @?_ aL�? �LLhic �bb.c R�hi_�| �)U*it� aL�h?@* Lu �L*�|�U@* ,UL?�
L4)c �fDG 2���2eH�
d22o kh�}4@?c �@�*c �bbbc R�@*@?Ui 5�ii|tc |�i Ah@?tuih �hLM*i4c @?_ 6�?@?U�@* �h�tit�c �?
��Wt@h_c �� +@3�? @?_ ��+Ltic i_t�c W?|ih?@|�L?@* 6�?@?Ui @?_ 6�?@?U�@* �h�titG ,tt@)t
�? OL?Lh Lu +LMih| �� 6*LL_c ah�c k*��ih �U@_i4�U ��M*�t�iht�
d2�o kh�}4@?c �@�*c �bbbc A�i +i|�h? Lu #iThitt�L? ,UL?L4�Utc `` �Lh|L? :�L4T@?)c
�i� vLh!�
d2eo w�U@tc +LMih| ,�c �bbfc Rw�^��_�|) @?_ W?|ihit| +@|it�c aL�h?@* Lu ,UL?L4�U A�iLh)c
DfG2.��2Se�
d2Do �i?_L3@c ,?h�^�ic 2fffc RA�i �i?i�|t Lu #L**@h�3@|�L? ��i? 5|@M�*�3@|�L? �L*�U) w@U!t
�hi_�M�*�|) @?_ 6�?@?U�@* �@h!i|t @hi W4TihuiU|�c uLh|�UL4�?}c aL�h?@* Lu �L?i)c
�hi_�| @?_ �@?!�?}�
d2So ��tt@c ��U�@i*c 2fffc RNt�?} �L?i|@h) �L*�U) |L +it�t| , U�@?}i +@|i #iThiU�@|�L?�c
4�4iLc W�6�
DH
d2.o �Mt|ui*_c �@�h�Uic @?_ ki??i|� +L}Lgc �bb.c 6L�?_@|�L?t Lu W?|ih?@|�L?@* �@UhLiUL�
?L4�Utc �WA �hitt�
d2Ho +iMi*Lc 5ih}�L @?_ �@h*Lt Vi}�c �bbDc R+i@* ,giU|t Lu , U�@?}i�h@|i�M@ti_ 5|@M�*�3@�
|�L?G �? �?@*)tt� Lu �L4Ti|�|?} A�iLh�it�c ��,+ �@UhLiUL?L4�Ut �??�@*c �2D��H.�
d2bo Nh�Mic �@h|�?c �bb.c R, U�@?}i�h@|i�M@ti_ W?�@|�L? 5|@M�*�3@|�L?G A�i W?�|�@* +i@*
,giU|t Lu �hi_�M*i �*@?t�c aL�h?@* Lu �L?i|@h) ,UL?L4�Utc �bG �b.�22��
d�fo vL�?}c �*�)?c �bbDc RA�i A)h@??) Lu ��4MihtG �L?uhL?|�?} |�i 5|@|�t|�U@* +i@*�|�it Lu
|�i ,@t| �t�@? BhL�|� , Tih�i?Ui�c "�@h|ih*) aL�h?@* Lu ,UL?L4�Utc ��fE��G Se��SHf�
Db
0.013 0.0135 0.014 0.0145 0.015 0.0155 0.016
24
24.5
25
25.5
26
26.5
27
27.5
28
28.5
29
Figure 1 The Effect of an Interest Cut with Some Elasticity of Substition and No Debt
pn
L
β=1/1.05, α=.25, θ=.6, xs=.06, ψ =1, ψ 0=.3,
KN=KT=1, A=1.9, R*=1+r*=1.05, τ=.01, B=0, η=.9
AM Curve
LM Curve (R high)
LM Curve (R low)
0.65 0.7 0.75 0.8
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Figure 2 The Effect of an Interest Cut with Low Elasticity of Substition and No Debt
pn
L
β=1/1.05, α=.25, θ=.6, xs=.06, ψ =1, ψ 0=.3,
KN=KT=1, A=1.9, R*=1+r*=1.05, τ=.01, B=0, η=0AM Curve
LM Curve (R high)
LM Curve (R low)
0.35 0.4 0.45 0.5
0.4
0.45
0.5
0.55
Figure 3 The Effect of an Interest Cut with Low Elasticity of Substition and Modest Debt
pn
L
β=1/1.05, α=.25, θ=.6, xs=.06, ψ =1, ψ 0=.3,
KN=KT=1, A=1.9, R*=1+r*=1.05, τ=.01, B=0.2, η=0
AM Curve
LM Curve (R high)
LM Curve (R low)
0 5 10 15 200
0.2
0.4
0.6
0.8
1Multiplier (λ)
0 5 10 15 20-25
-20
-15
-10
-5
0Debt (Bt)
% d
ev fr
om s
s
0 5 10 15 200
0.01
0.02
0.03
0.04Current Account
% o
f ss
outp
ut
0 5 10 15 20-4
-3
-2
-1
0
1Imports (z)
% d
ev fr
om s
s
0 5 10 15 20-25
-20
-15
-10
-5
0
5Labor (L)
% d
ev fr
om s
s
0 5 10 15 200.35
0.4
0.45
0.5
0.55LT/LN
Figure 4a: Transitional Path to Lower Debt During Crisis, No Policy Response, Labor in Traded Sector
Notes: % dev from ss - Percent Deviation from Pre-Crisis Steady State % of ss output - Percent of Pre-Crisis Gross Output
0 5 10 15 20-30
-25
-20
-15
-10
-5
0Price of Capital in Traded Sector (qT)
% d
ev fr
om s
s
0 5 10 15 20-30
-20
-10
0
10Price of Capital in Nontraded Sector (qN)
% d
ev fr
om s
s
0 5 10 15 20-40
-30
-20
-10
0
10Price of Nontraded Good (pN)
% d
ev fr
om o
utpu
t
0 5 10 15 20-20
0
20
40
60
80Price of Traded Good (PT)
% o
f ss
outp
ut
0 5 10 15 201.12
1.13
1.14
1.15
1.16
1.17Domestic Interest Rate (R)
0 5 10 15 200.9
1
1.1
1.2
1.3Inflation Rate (Pt/Pt-1)
Figure 4b: Transitional Path to Lower Debt During Crisis, No Policy Response, Labor in Traded Sector
Note: % dev from ss - Percent Deviation from Pre-Crisis Steady State
0 5 10 15 200
2
4
6
8Multiplier (λ)
0 5 10 15 20-30
-25
-20
-15
-10
-5
0Debt (Bt)
% d
ev fr
om s
s
0 5 10 15 200
0.01
0.02
0.03
0.04Current Account
% o
f ss
outp
ut
0 5 10 15 20-100
-80
-60
-40
-20
0Imports (z)
% d
ev fr
om s
s
0 5 10 15 20-100
-80
-60
-40
-20
0
20Labor (L)
% d
ev fr
om s
s
0 5 10 15 20-80
-60
-40
-20
0
20Consumption of Traded Good (cT)
% d
ev fr
om s
s
Figure 5a: Transitional Path to Lower Debt During Crisis, No Policy Response, No Labor in Traded Sector
Notes: % dev from ss - Percent Deviation from Pre-Crisis Steady State % of ss output - Percent of Pre-Crisis Gross Output
0 5 10 15 20-50
-40
-30
-20
-10
0
10Price of Capital in Traded Sector (qT)
% d
ev fr
om s
s
0 5 10 15 20-40
-20
0
20
40Price of Capital in Nontraded Sector (qN)
% d
ev fr
om s
s
0 5 10 15 20-60
-40
-20
0
20
40Price of Nontraded Good (pN)
% d
ev fr
om o
utpu
t
0 5 10 15 20-100
0
100
200
300
400
500Price of Traded Good (PT)
% o
f ss
outp
ut
0 5 10 15 201
1.2
1.4
1.6
1.8
2Domestic Interest Rate (R)
0 5 10 15 200
1
2
3
4Inflation Rate (Pt/Pt-1)
Figure 5b: Transitional Path to Lower Debt During Crisis, No Policy Response, No Labor in Traded Sector
Note: % dev from ss - Percent Deviation from Pre-Crisis Steady State