a finite element method for domain decomposition with non - hal

Post on 13-Feb-2022

3 Views

Category:

Documents

0 Downloads

Preview:

Click to see full reader

TRANSCRIPT

HAL Id: inria-00073065https://hal.inria.fr/inria-00073065

Submitted on 24 May 2006

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

A Finite Element Method for Domain Decompositionwith Non-Matching Grids

Roland Becker, Peter Hansbo

To cite this version:Roland Becker, Peter Hansbo. A Finite Element Method for Domain Decomposition with Non-Matching Grids. RR-3613, INRIA. 1999. <inria-00073065>

ISS

N 0

249-

6399

ap por t de r ech er ch e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

A finite element method for domain decompositionwith non-matching grids

Roland Becker — Peter Hansbo1

N˚ 3613

Janvier 1999

Unité de recherche INRIA Sophia Antipolis2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex (France)

Téléphone : 04 92 38 77 77 - International : +33 4 92 38 77 77 — Fax : 04 92 38 77 65 - International : +33 4 92 38 77 65

� ����������� ������������������������������������� �����"!�����#$��%����� �&�(')������*�&�,+-���.��!/���0��121����0��%

3547698-:/;=<?>A@�B->ACED/FG>IHJ>AC�K�8L:�MJNO4QP

R.SUTWVYX5Z�[ \-]^V*_Q`baAc�]edgfhXWc&dgiQc�]^V�]ej0aAc�]edgfk X*j�lLj c TWVYX�j�m�dgV�iQ`eXJn7X�j

o�p dAqrXWc?s.aA]^VtaAf

u?aAiQi�dgp�c k X,p X�m SUXWp m SUXvfw"xzy7{|x}[�~�aAf-�-]eXWp�{|�z�z��[ {���i�aA��X�j

�$�����|�I�Q������� f�c�SQ]ejOfUdgc X"�GX"iQp dgi/dzj X�aAf k aAf�aA`^l7j X�a�fUXW�=VYXWc�SUd k,� dgp�S�aAf k `^]^fQ��]^f-c XWp � agm�X�j� XWc���X�XWf�fUdgf7��VtaAc m SQ]^fQ���zp�] k j � agj X k dgf�aAf�aAiQiQp d�agm0S�j�_Q�z��X�j�c X k�� l���]^c j m0SUX¡ ^{|¢g£ � dgpc�SUX¤aAiQiQp d|nL]^VtaAc�]edgf¥d �,¦ ]^p�]em SQ`eXWc � dg_Qf k aAp�l§m�dgf k ]^c�]edgfUj|¨¡R.SUX©XJnLi/dzj�]^c�]edgfª]ej«`^]^V�]^c X k c dj0XW` � �¬a k q�dg]^f�c�XW`^`^]^iQc�]emYiQp d � `eXWVYj|­�_Uj�]^fQ�®o¯dg]ej j0dgf±°²j�X�³-_�aAc�]edgf§agj�a©VYd k XW`�¨©´µiQp�]edgp�]�aAf k ai/dzj�c XWp�]edgp�]OXWp�p dgp&X�j�c�]^VtaAc X�j&aAp X��z]^��XWf±­�aAf k �GX k ]ej mW_Uj j�c�SUX5p XW`baAc�]edgf}c d�c�SUX�VYdgp�c0aAp�¶UfQ]^c XXW`eXWVYXWf-c�VYXWc�SUd k ¨G\LdgVYX�f-_QVYXWp�]em|aA`Op X�j�_Q`^c j�aAp X5]^fUmW`^_ k X k ¨

·}¸�¹/º »�¼ �I½���� a k aAiQc�]^�L]^c�l�­ k dgVtaA]^f k X�m�dgV�i�dzj ]^c�]edgf±­Q¶UfQ]^c X5XW`eXWVYXWf-c j

¾"¿ÁÀrÂAÃ0ÄÆÅ�ÇÈÀrÉ�Å/Ê0ËÌ�Ê ÍÏÎÏÐ�Ñ?ÀrÒ�ÓAà ÉAÎÏÒÕÔrÖz×�ÓgÃ0ÍÏÇÈÀ¬Ä�Ô�Ø�ÉAÎÚÙWÀ¬Ä�ÔÆÎÚÅÜÛ�Ê ËUÝLÀrÒ�ÓIÉAÊJÍÚÊ Þ Û�Ö�ß�à0Å�ÀrázÊ Ä�Þ�Ö�Ì�â/À�Ð�ÀrÉ

� �*� ���������������������������%������0%�#t�����)�0� ���"!�����#$��%����� ��� ������&�����0���"% ����"!µ�����0� � ��1��"%��0��!�����#��.����«� �"%

� � ����� � � ¦ aAfUj,m�XWc,aAp�c�]emW`eX«fUdg_Uj?iQp���j XWf-c dgfUj,_QfUX�fUdg_Q��XW`^`eX�V��Wc�SUd k X�i�dg_Qp?`eX�c�p0aA]^c XJ�VYXWf-c k ° ]^f�c XWp � agm�X�j5XWf�c�p X k XW_7n VtaA]^`^`baA��X�j�]^fUm�dgV�i�aAc�] � `eX�j�¨*s�XWc�c X�V��Wc�SUd k X«X�j�c � agj���X«j�_Qp_QfUX�aAiQiQp d-m0SUX5iQp dgi/dzj���X�i�aAp��&]^c j m SUXt ^{|¢I£ k aAfUjÈ`eX5m|a k p X k X5`�°ÚaAiQiQp d�n7]^VtaAc�]edgf k X�j&m�dgf k ] �c�]edgfUj�aA_7n}`^]^V�]^c X�j k X�c�lLi�X ¦ ]^p�]em SQ`eXWc|¨ � mW]�­�fUdg_Uj?fUdg_Uj?p X�j�c�p XW]^�zfUdgfUj5aA_7n m|agj k °���³�_�aAc�]edgfUjXW`^`^]^iQc�]e³-_UX�jtj l-V��Wc�p�]e³-_UX�j|­�XWf iQp XWf�aAf�c$`�°���³�_�aAc�]edgf k X o¯dg]ej j0dgf¥m�dgV�VYX���³-_�aAc�]edgf VYd k XW`�¨�?dg_Uj��Wc0a � `^]ej j dgfUj k X�jÈX�j�c�]^VtaAc�]edgfUj�a�iQp�]edgp�]±XWc�a�i�dzj c XWp�]edgp�]�¨�"f}j�_Q]^c Xz­7fUdg_Uj k ]ej0mW_Qc dgfUjÈ`eX`^]eXWf a|��X�m�`ba���V��Wc�SUd k X k X�jÈVYdgp�c�]eXWp j��0¨��]^f�aA`eXWVYXWf�c|­�fUdg_UjÈiQp���j dgf-c dgfUj�³-_UXW`e³�_UX�j.p���j�_Q`^c0aAc jf-_QV��Wp�]e³�_UX�j�¨

� ¼ �|� º ��� � �}� a k aAiQc0aAc�]^�L]^c��z­ k ��m�dgV�i/dzj�]^c�]edgf k X k dgVtaA]^fUX�j�­ �W`!�WVYXWf�c j�¶UfQ]ej

������������� ����������������������������� �"!�#$���&%'%��(�*)+� x

{z¨-,/.1012�3547678�019�3:.

� fEaAf-l k dgVtaA]^f k X�m�dgV�i�dzj�]^c�]edgfEVYXWc�SUd k ­LdgfUX&S�agjGc d k XJ¶UfUX&SUd|��c�SUX&m�dgf-c�]^f�_Q]^c�l � XWc��GX�XWfc�SUX�j _ ��k dgVtaA]^fUj�]ejÈc d � X�XWf � dgp m�X k ¨ ¦ ]<;�XWp XWf�c&aAiQiQp d�agm0SUX�j�S�a|��X � X�XWf¤iQp dgi�dzj0X k1=

> � c XWp0aAc�]^��X iQp dLm�X k _Qp X�j|­,XWf � dgp mW]^fQ� c�S�aAc¤c�SUX aAiQiQp d�n7]^VtaAc X=j dg`^_Qc�]edgf�dgp¤]^c j}fUdgp�VtaA`k XWp�]^�gaAc�]^��X?dgp�m�dgV � ]^f�aAc�]edgfUj.c�SUXWp X�d � j�SUdg_Q` kt� X&m�dgf�c�]^f�_Udg_Uj�agmWp dzj0j�]^f-c XWp � agm�X�j|¨�R.SQ]ej� dgp�VYj�c�SUX � agj ]ej � dgp�c�SUX�j�c0aAf k aAp k \Lm0S��.aAp@?©aA`^c XWp�f�aAc�]^fQ�}VYXWc�SUd k agj k XJ¶UfUX k ­¯Xz¨ �U¨^­� lBA�]edgfUj* ^{z{J£�¨

> ¦ ]^p X�mWc?iQp dLm�X k _Qp X�j|­�_Uj�]^fQ�CAOaA�zp0aAfQ��X�V�_Q`^c�]^iQ`^]eXWp?c X�m0SQfQ]e³�_UX�j?c d©agm SQ]eXW��X«m�dgf�c�]^f-_Q]^c�l�¨¦ ]<;�XWp XWf�c��zaAp�]baAf�c j�S�a|��X � X�XWf§iQp dgi�dzj0X k ­�Xz¨ �U¨^­ � lDA±X$R�aA`^`eX�m}aAf k \7agj j�]& ^{FEg£�­�aAf kG�XWp�f�a k ]�­�H®a k a|l�­�aAf k oÁaAc XWp0a} Ï��£�¨

R.SUX�V�_Q`^c�]^iQ`^]eXWp�VYXWc�SUd k S�agjÁc�SUX�a k �zaAf�c0aA��XÈd �/k ]^p X�mWc�`^l�lL]eXW` k ]^fQ�5a,j dg`^_ � `eX��z`ed � aA`Uj�l7j�c XWV}¨I?d|��XW��XWp|­U]^f}c�SUX5`baAc�c XWp�VYXWc�SUd k ­QfUXW��_QfKJLfUd|�ÈfUjML9c�SUX�V*_Q`^c�]^iQ`^]eXWp j(NÈV*_Uj�c � X,]^f-c�p d k _Um�X kaAf k j0dg`^��X k�� dgp|­,aAf k V*_Uj�c}XW]^c�SUXWphj0aAc�]ej � l c�SUX ]^f � ��j _Qi�m�dgf k ]^c�]edgf±­&�ÈSQ]em0S�fUX�m�X�j j�]^c0aAc X�jj i�X�mW]baA`Om0SUdg]em�X�j,d � V�_Q`^c�]^iQ`^]eXWp?j i�agm�X�jL j�_Um0S®agj�VYdgp�c0aAp?XW`eXWVYXWf-c j|­m � ¨? Ï�I£�NJ­�dgp�_Uj0X*j�i/X�mW]baA`j c0a � ]^`^] ?�aAc�]edgf c X�m SQfQ]e³-_UX�j'L m � ¨OGÈaA]ed-m�m0SQ]�­�G�p X�?P?�]�­�aAf k H aAp�]^fQ]� Ú¢A£�NJ¨

� f©c�SQ]ej.fUdgc Xz­Q�GX,iQp dgi/dzj X�a�c�SQ]^p k i/dzj j�] � ]^`^]^c�lE]^fUj�iQ]^p X k©� l$�&]^c j m SUXz°²jÈVYXWc�SUd k  ^{|¢A£�­L�ÈSQ]em S�.agj,dgp�]^�z]^f�aA`^`^l}]^f�c�p d k _Um�X kh� dgp?c�SUX*iQ_Qp�i/dzj X�d � j dg`^�L]^fQ� ¦ ]^p�]em SQ`eXWc,iQp d � `eXWVYj,�È]^c�SUdg_Qc,XWf7�� dgp mW]^fQ� c�SUX � dg_Qf k aAp�l�m�dgf k ]^c�]edgfUjt]^f¥c�SUX k XJ¶UfQ]^c�]edgf�d � c�SUX©¶UfQ]^c XhXW`eXWVYXWf�c$j i�agm�X�j|¨¥´VYd k XWp�f j XWc�c�]^fQ� � dgp?c�SQ]ej,VYXWc�SUd k ­±aAf k ]^c j,p XW`baAc�]edgf c dEV*_Q`^c�]^iQ`^]eXWp5VYXWc�SUd k j|­�]ej?�z]^��XWf � l\-c XWf � XWp��� ^{|xA£&aAf kª� lQG�p X�?P?�]�­ �Qp0aAfUm|a7­RH aAp�]^fQ]�­�aAf k u�_Uj j dª TSA£�¨ªR.SQ]ej�VYXWc�SUd k aA`^`ed|��j� dgp�]^f k XWi/XWf k XWf�c�aAiQiQp d�n7]^VtaAc�]edgfUj,dgf}c�SUX k ]<;�XWp XWf�c,j�_ ��k dgVtaA]^fUj�¨GR.SUX5m�dgf-c�]^f�_Q]^c¬lhd � c�SUXj0dg`^_Qc�]edgfªagmWp dzj j�]^f-c XWp � agm�X�j«]ej«XWf � dgp m�X k ��X|a+J-`^l�­ � _Qc�]^fªj�_Um S a ��a|l=c�S�aAc�c�SUX$p X�j _Q`^c�]^fQ�k ]ej0mWp XWc X5j m SUXWVYX5]ej�m�dgfUj�]ej�c XWf-c��È]^c�S}c�SUX5dgp�]^�z]^f�aA`¯i�aAp�c�]baA` k ]<;/XWp XWf-c�]baA`¯X�³-_�aAc�]edgf±¨

R.SUdg_Q�zS§�GX k ]ej mW_Uj j*c�SUXtfUXW�vVYXWc�SUd k ]^f=c�SUXtm�dgf-c XJnLc«d ��k dgVtaA]^f k X�m�dgV�i/dzj�]^c�]edgf±­Á]^c�]ejaA`ej0d�j�_Q]^c X k©� dgp�dgc�SUXWp&aAiQiQ`^]em|aAc�]edgfUj|­�Xz¨ �U¨^­

> c d�S�aAf k `eX k ]<;/_Uj�]edgf}c XWp�VYjÈ]^f}c�SUX k ]ej0m�dgf�c�]^f�_Udg_UjVU�aA`eXWp@JL]^f}VYXWc�SUd k  TWI£X> c d*j�]^V�iQ`^] � l�VYX�j�St��XWfUXWp0aAc�]edgfYL k ]<;�XWp XWf�c.i�aAp�c j�m|aAf � X�VYX�j�SUX k ]^f k XWi�XWf k XWf-c�`^l � p dgV

X|agm Shdgc�SUXWp(N�X> ¶UfQ]^c X5XW`eXWVYXWf�c&VYXWc�SUd k j��È]^c�S k ]<;/XWp XWf-c�i/dg`^l-fUdgV�]baA` k XW�zp X�X�dgf a k q�agm�XWf-c&XW`eXWVYXWf-c jFX> fUXW��¶UfQ]^c X5XW`eXWVYXWf�c&VYXWc�SUd k j&j�_Um S®agjÈ`^]^fUX|aAp&aAiQiQp d�n7]^VtaAc�]edgfUj?dgf ³�_�a k p�]^`baAc XWp0aA`ej�¨

Z:Z �[K\�]F^@\

Z � �/!����������V���K���@�¢7¨��9 0� 8����Y0����������K0�� 354

¢7¨^{z¨��)¼ ½ ¸ ����� ¼ � � ¸ ��� ��dgp�j�]^V�iQ`^]emW]^c�l�­-�GX�m�dgfUj�] k XWp�dgfQ`^l«c�SUXÈo¯dg]ej0j dgftiQp d � `eXWV d � j dg`^�-�]^fQ��c�SUX5i�aAp�c�]baA` k ]<;/XWp XWf-c�]baA`�X�³-_�aAc�]edgf� "!$#&%(' ) * ]^f,+.-

' ) / dgf,01+2-Lr{ N

�ÈSQ]em0S m|aAf � X,�Èp�]^c�c XWf ]^f¤��X|a+J � dgp�V agj = ¶Uf k '4365879�: +<;Gj�_Um0S¤c�S�aAc= : ' -?>�; ) : * -?>�;?-A@B> 365 79 : +.;?-LÆ¢ N�ÈSUXWp X = : ' -?>�; )�CEDF('�GHF >JIK+2- : * -?>E; )�CED* >LIK+2-aAf k 5M79�: +<;,]ej5c�SUX$j�i�agm�Xtd � j0³�_�aAp XJ��]^f-c XW�zp0a � `eX � _QfUmWc�]edgfUj|­��È]^c�S¡j0³�_�aAp XJ��]^f-c XW�zp0a � `eXE¶Up j�ck XWp�]^�zaAc�]^��X�j|­Qc�S�aAc?aAp X ?|XWp dYdgf}c�SUX � dg_Qf k aAp�lN0B+�d � +�¨

¢7¨Ú¢7¨PO¤¸RQTSVU � U9¼1S®¼1W �HX ¸ � ¸ �HX ¼ ½L� �Udgp"X|agj X�d � iQp X�j XWf�c0aAc�]edgf±­��GX�m�dgfUj�] k XWp"dgfQ`^l�c�SUX.m|agj X�ÈSUXWp XY+ ]ej k ]^�L] k X k ]^f�c d¤c¬�Gd fUdgf7��d|��XWp�`baAiQiQ]^fQ� j�_ �/k dgVtaA]^fUjZ+ 7 aAf k +\[A¨^] XYm�dgfUj ] k XWpc�SUX,]^f-c XWp � agm�XP_ � XWc���X�XWf4+ 7 aAf k + [ c d � X5a«j�c�p0aA]^�zS-c�`^]^fUXz¨��dgp&c�SUX�m�dgfUj�]ej�c XWfUmWl}d � dg_Qp?f�_QVYXWp�]em|aA`ÁVYXWc�SUd k ��X�fUX�X k j dgVYX�a kQk ]^c�]edgf�aA`�p XW�z_Q`baAp�]^c¬lhd �c�SUX�j dg`^_Qc�]edgf®c d LÆ¢ NJ¨ Hhdgp X*iQp X�mW]ej XW`^l�­ � dgp&c�SUX�j dg`^_Qc�]edgf '`3a5M79 : +.;.aAf k > 3cbd5M7 : + 7 ;Je5 7 : + [ ;gfh> )i/ dgfj0B+.k�c�SUXWp X�V�_Uj�c�SUdg` k1=

ClD F('�GHF >mIK+ ) CnD * >LIo+8p Cnq 0 '0�r : >�s D1t # >�s D�u ;oIovR-LÆx N�ÈSQ]em0Shj0a|lLj�c�S�aAc�c�SUX�fUdgp�VtaA` k XWp�]^�zaAc�]^��X*d � c�SUX5j0dg`^_Qc�]edgf}]ej�m�dgf-c�]^f�_Udg_Uj?]^fha��GX|a+J}j0XWfUj Xz¨R.SQ]ej�]ej�c�p�_UX � dgp�XJnUaAV�iQ`eX5] � %('a34w [ : +<;0­j X�XY ^{J£�¨ �Udgp&j ]^V�iQ`^]emW]^c�l�­�GX�aA`ej0d$agj j�_QVYX5c�S�aAc' ]ej�m�dgf�c�]^f-_Udg_Uj?aAc�c�SUX�]^f�c XWp � agm�X_�¨x _Qp k ]ej mWp XWc X�VYXWc�SUd k � dgp5c�SUX$aAiQiQp d|nL]^VtaAc XEj dg`^_Qc�]edgf§d � Lr{ N�]ej�a©fUdgfUm�dgf � dgp�V�]^fQ�h¶UfQ]^c XXW`eXWVYXWf-c�VYXWc�SUd k �ÈSQ]em S ]ej�m�dgf�c�]^f-_Udg_Uj&�È]^c�SQ]^fhX|agm Sj+Jy"aAf k}k ]ej m�dgf-c�]^f�_Udg_Uj�agmWp dzj j\_G¨R¯d � dgp�V*_Q`baAc X*dg_QpÈVYXWc�SUd k ­Q��X�]^f�c�p d k _Um�X5c�SUX � dg`^`ed|�È]^fQ�Ej�i�agm�X�jz y )|{ > y fR> y s D�} 3~5 7 : + y ;?-&> y s � D1� � D�} )i/�� - � )�� -��o-aAf k aAiQiQp d�n7]^VtaAc�]^fQ�$j�i�agm�X�jzP�y )�b >�y 3 zEy�f�>�yÁ]ej�a�iQ]eX�m�XW�È]ej X�i/dg`^lLfUdgV�]baA`Od �Ák XW�zp X�X\� dgfj+Jy�kT���dgpOj�]^V�iQ`^]emW]^c�l�­A��XGagj j�_QVYXÁc�S�aAc¯c�SUX"i/dg`^l-fUdgV�]baA` k XW�zp X�X��5]ej�c�SUX�j aAVYX � dgpOaA`^`-j�_ ��k dgVtaA]^fUj�¨] XGj X�X�J5dg_Qp�aAiQiQp d|nL]^VtaAc�]^��XÈj0dg`^_Qc�]edgfY� ) :�� 7 - � [ ;]^f�c�SUX�iQp d k _UmWc�j i�agm�Xmz � ) z �7 e&z �[

���5Z����

������������� ����������������������������� �"!�#$���&%'%��(�*)+� W

aAf k®� dgp�m�dgV�i�aAp�]ej dgf ��X«]^f�c�p d k _Um�X�c�SUX«��X�mWc dgp���m�dgp�p X�j�i/dgf k ]^fQ�¤c d©c�SUX�j dg`^_Qc�]edgf d � LÆ¢ N�L]ba � ) � '�G�� :��+ 7 ;?- 'hG�� :��+ [ ;� 3 z ) z 7 ejz [ ��ÈSUXWp X � : �+ y ;*]ejtc�SUX m S�aAp0agmWc XWp�]ej c�]em � _QfUmWc�]edgf�dgf �+ y ¨ �Q_Qp�c�SUXWp�VYdgp Xz­���X}]^f-c�p d k _Um�X c�SUX� dg`^`ed|�È]^fQ�tfUdgc0aAc�]edgfUj = � -?>�� q f ) Clq � >LIlv - '�� f ) ' 7 #`' [ - bd' kf ) : ' 7 p ' [ ;�� �o-aAf k¡k XWfUdgc X � l��=c�SUXtj�] ?|XEd � c�SUX$j VtaA`^`eX�j�c�XW`eXWVYXWf-c«dgf + 7 aAf k + [ fUXW]^�zS � dgp�]^fQ� c d,_G¨R.SUX*dg_Qc���aAp k i�dg]^f-c�]^fQ�tfUdgp�VtaA`±c dY+ y ]ej k XWfUdgc X k�� y ­UaAf k �GX�`eXWc � f ) � 7 ) # � [ ¨x _Qp�VYXWc�SUd k m|aAf¤fUd�� � X k XJ¶UfUX k agj � dg`^`ed|��j = ¶Uf k � 3 z � j�_Um0S}c�S�aAc= � : �a-���; ) : : * -���; ; @�� 3 z �L9Z&N�ÈSUXWp X = � : �a-���; f ) : F � 7 - F > 7 ; D t p : F � [ - F > [ ; D u #�� � � -�� 01>01r�� � q#!� � 0 �01r"� -# > � � q p%$� � � -# "> � � q -aAf k : : * -���; ;Lf ) : * -?> 7 p > [ ;?�I?XWp Xz­ $�& / ]ej�aȶQn7X k f�_QV � XWpÁc�S�aAc�V*_Uj�c � XGm SUdzj XWf«j�_�'tmW]eXWf�c�`^l*`baAp���X�c d&XWfUj�_Qp XGj c0a � ]^`^]^c�ld � c�SUXÈVYXWc�SUd k L j0X�X&\LX�mWc�]edgf©x N"�&dgc X�c�S�aAc�c�SUX � dgp�V = � : G - G ;�]ejGj�l-V�VYXWc�p�]emz­-�ÈSQ]em S$Vta�l � X]^V�i/dgp�c0aAf�c&]^f}dgp k XWp�c d«¶Uf kE� agj�c�j dg`^_Qc�]edgf}VYXWc�SUd k j � dgpÈc�SUX�p X�j�_Q`^c�]^fQ�tVtaAc�p�] n©iQp d � `eXWV}¨

x7¨ ��219�35219)(:.*(,+ �� 9� C3.- 0��������K0�� 3:4��dgp�c�SUX,iQ_Qp�i�dzj0X5d � aAf�aA`^l7j�]ej|­7��X��È]^`^`±_Uj X,c�SUX � dg`^`ed��È]^fQ�YfUdgp�V dgfjz =s0/1��/ s [ )32 y / F�' y4/ [5 u�6 D�}87 p:999 ��; 7< [ '=� 999 [5 u�6 q>7L*W N

] X,�È]^`^`OfUX�X k c�SUX � dg`^`ed|�È]^fQ�CAOXWV�Vtagj =?�¸ � � �A@��CB1�ED #K��� ����# � ) L9Z&NV���V! ���K�(����������GFO����#BLr{ N�H ��)$���-��#K�'��� �4H �JI ���*��� LÆx NLKZ:Z É�[K\�]F^@\

y � �/!����������V���K���@��R� �F�@�LK � fUj XWp�cÈc�SUX5j dg`^_Qc�]edgf c d Lr{ N�]^f�c d = � : G - G ;.aAf k _Uj X-U?p X�XWf±°²j � dgp�V*_Q`baYc d�d � c0aA]^f

: : * -���; ; # = � : ��-���; ) 2 y : * -?> y ; # 2 y : F(' - F > y ;�p � 0 '0�r -# > � � q) 2 y : * p %�' -?> y ; )i/ -�ÈSQ]em0S j�SUd���j�m�dgfUj�]ej�c XWfUmWl©�È]^c�S Lr{ NJ¨

] X,fUdgc X5]^f}i�aAp�c�]emW_Q`baAp�c�S�aAc AOXWV�VtaYx7¨^{�]^V�iQ`^]eX�j�c�SUX-U5aA`eXWp@J-]^f dgp�c�SUdg��dgf�aA`^]^c¬l}p XW`baAc�]edgf= � : � # �&-���; )i/ @�� 3 z � �LÆy N?�¸ � � �A@������ED #K��� ����# � ) L9Z&NV��� ���"�K��� �-� � $ ���V!�# �+�P��� � ���*%$������� H�%+# K�R� �F�@�LKL] X��È]^`^`"j�SUd|��c�S�aAc = � : �j-��4;����hs0/d� / s [ � dgp�j dgVYX«m�dgfUj�c0aAf-c���­��ÈSQ]em S ]^V�iQ`^]eX�jj c0a � ]^`^]^c�l�¨�Udgp�c�SQ]ej.iQ_Qp�i/dzj Xz­���X,j�S�aA`^`_Uj0X�c�SUX � dg`^`ed|�È]^fQ�«�GXW`^` JLfUd|�Èf¤]^f���XWp j0X&iQp dgi/XWp�c�l$]^fz �y = 9999 � 7< [ 01> y01r y 9999

[5 u�6 q>7� � 9 / F >�y1/ [5 u 6 D�}C7 @B>�y 3 z �y -L���N

L j0X�Xz­QXz¨ �U¨^­UR.SUdgV���Xt ^{WZg£�NJ¨T] X,c�SUXWf S�a���X5c�S�aAc

= � : �4-��j; ) 2 y / F � y / [5 u 6 D�}C7 p � 0 � 70�r p 0 � [0�r - � [ # � 7 � q p $ 999 � ; 7< [ :�� [ # � 7 ; 999 [5 u 6 q>7 ��?d|�5­�j�]^fUm�X

� 0 � y0�r y - � [ # � 7 � q � # 9999 � 7< [ 0 � y0�r y 9999 5 u 6 q>7 999 � ; 7< [ :�� [ # � 7 ; 999 5 u 6 q>7� # � 9999 � 7< [ 0 � y0�r y 9999[5 u 6 q 7 # � 999 � ; 7< [ :�� [ # � 7 ; 999 [5 u 6 q 7 -

�ÈSUXWp X©��XE_Uj X k � dg_QfQ�U°²j«]^fUX�³�_�aA`^]^c¬l�­���X©S�a���Xz­�_Uj�]^fQ� L���N�aAf k c�SUX©c�p�]baAfQ�z`eX©]^fUX�³-_�aA`^]^c�l�­c�S�aAc = � : �4-��j;�� � �&# ��� 9�� 2 y / F � y / [5 u�6 D�}87 p�� $ # ��� / � ; 7< [ � � / [5 u�6 q>7� �Ys /d��/ s [agj�`edgfQ�$agj $�& � � & � 9 ¨

���5Z����

������������� ����������������������������� �"!�#$���&%'%��(�*)+� �

?�¸ � � �A@�� @��ED #K� ������� ��FO���&% �������� I ��� ��������� �(������������C# ���<)�� �P��� ��# � � HE��� I � !(� z � FO����#� ��� � � p ��������� ��� s0/1� # � / s � � ��� ; 7 2 y /1� /���� 6 D�}C7 - ' y 365 � : +<;?- ' y s � D )i/ �L*S N

�R� �F�@�LKÈ\-]^fUm�X�c�SUX*fUdgp�V s0/1� # � /?s�m�dgfUj�]ej�c j?d � m�dgf-c�p�] � _Qc�]edgfUj � p dgV2c�SUX*c¬�Gd k dgVtaA]^fUj2+ 7aAf k +\[A­7c�SUXVA±XWV�Vta«p X k _Um�X�j�c d�c�SUX�³�_UX�j c�]edgf}�ÈSUXWc�SUXWp������ } � �} ��/ F('Y#8F > y / [5 u�6 D�}87 p / � ; 7< [ : 'Y# > y ;*/ [5 u�6 q>7 � 7< [ � � ��� ; 7 / ' / � � 6 D�}C7� dgp ',3,5 � : + y ;0­ ' s � D )�/ ¨�R.SQ]ej�agj j XWp�c�]edgf � dg`^`ed���j � p dgV A±XWV�Vtat¢7¨Úx«]^f  ^{WZ�£�¨

G�l�_Uj XÈd � c�SUX.iQp X�m�X k ]^fQ�A±XWV�Vtagj|­���X�aAp XÈfUd|�¥a � `eX�c d�j�SUd|��c�SUX � dg`^`ed|�È]^fQ�«a�iQp�]edgp�]XWp�p dgpX�j c�]^VtaAc Xz¨� X ¸-¼ � ¸ � @��CB���� ����#P� ��# �R����� H ������� � �RL9Z&N�� ' ��# � �P��� H ���*���C� � Lr{ N��7����) � ��# � ��������K��������@� ' �����"�^z��GF �V# � �+�'��# ���s /d� # ��/?s � � � � ; 7 / ' / � � 6 D 7 - � ��� � � p � ��R� �F�@�LK �Udgp?aAf�lE� 3 z � ­7�GX�S�a|��X�c�S�aAcs0/d� # � / s � s0/d� # � /?sHp�s /1� # � / saAf k ­ � l A±XWV�Vtatx7¨Ú¢7­s /d� # � / s [ � � = � : � # ��-�� # ��; ) � = � : � # ��-�� # �V;

� �Ys /d� # � / s ! s0/1� # � /?s�p 9999 � 7< [ � 0 '0�r # 01>01r�� 9999 5 u�6 q>7#" �R.S-_Uj|­�A±XWV�Vtatx7¨Úx«l-]eXW` k j

s0/d� # � / s � � ! s /1� # � / sdp 9999 � 7< [ � 0 '01r # 0�>01r � 9999 5 u 6 q>7 " pis0/1� # � / s� � � � ; 7 / ' /$� � 6 D 7

�ÈSQ]em0S}]ejÈc�SUX5j c0aAc XWVYXWf�c&d � c�SUX�c�SUX�dgp XWV}¨�E¸ �=�Q�&% @��8B1�(' ����-��# ��� ����������� ��F ����# ��� /. � � / 5 u 6 q>7 )*) : � � ; 7< [ ; KZ:Z É�[K\�]F^@\

S � �/!����������V���K���@��E¸ �=�Q�&% @�� ����� �K����@�$) � � H&�(���&% ��# �B� ���(� s / G / s �P��� ��# � � I �(�*��������������� ��� � ���� � !/����P�����<� F ��# �'���������+�(���P��� D # �����/�� ^{WZg£ ����� ' ������!�#K��� ��� ����# � ) � ����) ���K����@�$) H&�P�'��# �V�������s0/1� / s `f ) 2 y / F(' / 5 u 6 D�}87 p 999 ��; 7< [ '=� 999 5 u 6 q 7 p 9999 � 7< [ � 0 '01r�� 9999 5 u�6 q 7�"� �K���"�����Ms /d� # ��/?s � � � � ; 7 / ' / � � 6 D�7 K�E¸ �=�Q�&% @�� @�� D # ��I �@�(�F������@) � ����# � ) �/�(�F���h��� ��� �Y� �(�(#$� )&� IK����)&����� IK������� ��Y� ����# �F) �� H � FO����#Y� ) )$�/) ! ���K�(���������!�� �������������+��� � ���&% ������������)$����� �+����� ���(�C� !��@�+� � ��#K��������������$! ��K' ���� ��# ���7��#K� �P����� H&� �����*��� ����� ��F � H$� �"�)$�@)�HK! ���4I �������������@)$��� ���(�@��� ����������� ��(�"�È]^c�S�iQp XJ�j0XWp���X k m�dgf k ]^c�]edgf f-_QV � XWp � � ) : � ; [ ;��P�����#K�M�/�(�4H � �����&% )�����!��/�������!�# ������K � H&�/� I��������<��� ����# �F)+������� !/������� ����� � ���/��� ����!/�����(���������� ����� ) �4I ���������7����� ���'����������� ��(���@� �LH&���@�)$�"%�� �$)�����&%C��# �!/����)������*��� ��H&�h�/����������#$� %+# ��� IK������������*���7�4I I�� � �����������*������!���K?  Zg£�� K

ZU¨ ��3V 0���219�35219J��212�352��� 0 9 � ( 0��� ZU¨^{z¨ � S � � ¼ �|� ¸ � Uܼ � U,¸ �I� ¼ � ¸ ��� U � �7� ¸�U�S �HX ¸ S �7� �O�A� � S¯¼ � ��� ] X«¶Up j�c�m�dgfUj ] k XWpm�dgf-c�p dg`Èd � c�SUX$XWp�p dgp�� ) � # � ]^f§c�SUXtf�aAc�_Qp0aA`�fUdgp�V s / G / s ¨®ROd � XEa � `eXtc d®m�dgf�c�p dg`c�SUX&fUdgp�VtaA` k XWp�]^�gaAc�]^��X�jÈagmWp dzj j�c�SUX&]^f�c XWp � agm�Xz­7�GX&]^f�c�p d k _Um�X,c�SUX � dg`^`ed|�È]^fQ� L �¬j0aAc�_Qp0aAc�]edgf � Nagj0j�_QV�iQc�]edgf = �Udgp�c�SUX*XWp�p dgp|­Qc�SUXWp X�SUdg` k j9999 � 7< [ � 0��01r � 9999 5 u 6 q 7 � �Ys /�� / sLÆ� N

� dgp"j dgVYX.m�dgfUj�c0aAf�c �Y¨¯R¯d,j�_QiQi�dgp�c"c�SQ]ej�agj0j�_QV�iQc�]edgf±­z�GX.p X � XWpÁc d,u�XWVtaAp@J�x7¨Ú¢7¨RL ´¥j ]^V�]^`baApagj0j�_QV�iQc�]edgft�.agjG_Uj0X k�� l(] dgSQ`^V�_Qc�S  ^{FWg£�]^ftc�SUX&m�dgf�c XJn7c�d � a5i�dzj�c XWp�]edgp�]�XWp�p dgpGX�j�c�]^VtaAc X�j� dgpÈc�SUX�VYdgp�c0aAp�XW`eXWVYXWf-c�VYXWc�SUd k ¨ N] X,S�a|��X5c�S�aAcs0/��,/ s [ ) = � : �B-��1;Bp�� � �� � -�� 0��01r � � q p �\# $� �� � -# �� � � q

) : : * -��1; ; # = � : �4-��1;Bp�� � �� � -�� 0��01r�� � q p �&# $� �� � -# �� � � q �] X,c�S-_Uj�S�a|��X5c d�X�j�c�]^VtaAc X�c¬�Gd k ]<;/XWp XWf-c�c XWp�VYj|­� 7 ) : : * -���; ; # = � : �j-��1;?-

aAf k

� [ ) � � �� � -�� 0��0�r � � q # $ # �� �� � -# �� � � q ����5Z����

������������� ����������������������������� �"!�#$���&%'%��(�*)+� �

] X?¶Up j c�fUdgc X�c�S�aAc|­ � dgp $ � � L9�ÈSQ]em S ]ej.fUX�X k X k}� dgp�j c0a � ]^`^]^c�l�­�j0X�X*\LX�mWc�]edgfhy NJ­

� [ � � � �� � -�� 0��01r�� � q� � � s � � s -����� � 0��01r � ���� � q� � 999 � ; 7< [ � � 999 5 u�6 q>7 s /��,/ s

_Qf k XWp�c�SUX*agj j�_QV�iQc�]edgf LÆ� NJ¨��&XJn7c|­7_Uj�]^fQ��c�SUX5dgp�c�SUdg��dgf�aA`^]^c¬l¤p XW`baAc�]edgfDLÆy NJ­= � : � # �&-���; )i/ @�� 3 zZ�l-�È]^c�S�� )�� � � 3 z � a«j�_Q]^c0a � `eX�]^f-c XWp�i�dg`baAf-c?d � ��­Q��X,¶Uf k c�S�aAc

� 7 ) : : * -�� #�� � ��; ; # = � : �j-�� #�� � ��;?-\LXWc�c�]^fQ��� ) � #�� � ��­7c�SUX�]^f�c XW�zp0aA`ej&dgf}c�SUX,p�]^�zS�cr��S�aAf k j�] k X,Vta�l � X,�Èp�]^c�c XWfhagj

� 7 ) 2 y 2� � C � *� y I�� # C � F � y GHF y I�� � p2�� C � � �Kq � 0 �0�r"� =� Ilvmp 2�� C � � �Kq � 0 0�r�� � � Ilv #2 � C � � �Kq $ � �� � � IovR��?j�]^fQ�CU?p X�XWf±°²j � dgp�V�_Q`ba��GX*d � c0aA]^f

C � *� y I�� # C � F � y GHF� y I�� ) C � : * p % � y ; y I�� # C � � 0 � y0�r � y Ilv�ÈSUXWp X � � k XWfUdgc X�jÁc�SUXÈdg_Qc��.aAp k _QfQ]^cÁfUdgp�VtaA`Qc d&c�SUX � dg_Qf k aAp�l 0��2d � c�SUX.XW`eXWVYXWf�c��ª¨ �����XÈfUd|��j�_QV�_Qi$aA`^`UXW`eXWVYXWf�c�m�dgf�c�p�] � _Qc�]edgfUj|­QaAf k _Uj X.c�SUX � agmWc"c�S�aAc�X|agm0S ��������������ÁXW`eXWVYXWf�cj ] k X��§]ej�j�S�aAp X k¤� l$c¬�Gd$XW`eXWVYXWf�c j|­��GX5d � c0aA]^f

� 7 ) 2 y 2 � C � : * p % � y ; y I���p 2 y 2���� q C � � 0 � y0�r ��� y k v p� � 0 �0�r � - b� k � q p � � � -�� 0 01r�� � q p%$� =� -# � � � q �

] X,c�S-_Uj&aAp�p�]^��X*aAc

Z:Z �[K\�]F^@\

{FE � �/!����������V���K���@�� X ¸-¼ � ¸ ���V�CB���� ��)&�����#K���+� � H&�JI ���*��� LÆ� N�� ��# �����(�@���M���Y��#K�M������� s / G / s !/���c� �C�(�������������/)N��� s0/��,/ s � 2� � D�� � p 2� � q�� �Lr{FE N

F #K���@��� ) � y7 � � / * p % � / 5 u�6 � 7 p � y[ � 7< [� 9999 � 0 �0�r � � 9999 5 u�6 � � 7

����)

� � ) � � ; 7< [� /. � � / 5 u 6 � 7 -F #K���@� � y7 ��� ) � y[ ���/� �������� I ��� �����*��� !/���K���"������� �/�(� H&�<����� % �(�@��� �������� IK���<� ������� � ���CF �/���/ G / 5 u�6 � 7 ��� ) s0/ G / s � ����)N�/���CF �/��� / G / 5 u�6 � � 7 ����)Ns / G /?s ���/�(� IK�@!P��� �+����� KZU¨Ú¢7¨ � � ¸oS¯¸ �A� �E� � ¼ ��� ¸ � U9¼ � Ut¸ ��� U � �7� ¸ � �Udg`^`ed|�È]^fQ�) Ú�7­�yI£,�GX®]^f�c�p d k _Um�X c�SUX k _�aA`iQp d � `eXWV d � ¶Uf k ]^fQ�� 365879 : +.;Gj�_Um S c�S�aAc: F >�- F �l; )� : >E; @B> 365 79 : +<;?�Lr{z{ N�ÈSUXWp X ]ej}a¡�z]^��XWf � _QfUmWc�]edgf�aA` L9c0aA]^`edgp X k�� dgp©c�SUX k X�j�]^p X k XWp�p dgp}m�dgf-c�p dg`�NJ­5aAf k �ÈSUXWp X��X¤agj j�_QVYXEc�S�aAc�� � _Q` ¶U`^`ej«c�SUX©m�dgf�c�]^f-_Q]^c�lªp X�³-_Q]^p XWVYXWf�c LÆx NJ¨ �?dgc XEc�S�aAc � dgp�m�dgf�c�p dg`�d �³-_�aAf�c�]^c�]eX�j�fUdgc�]^f���dg`^�L]^fQ� k XWp�]^�zaAc�]^��X�j�d � c�SUX�j dg`^_Qc�]edgf±­Q��X k d«fUdgc�fUX�X k agj j�_QV�iQc�]edgf LÆ� NJ¨] X,S�a|��X5c�S�aAc

: ��; ) : F � - F �l; # � � 0 �0�r � -# �� � � q) = � : ��-���;�p � � 0��01r�� -# � � � q # � � 0 �0�r�� -# � � � q) = � : ��-�� #�� � ��;) = � : �&-�� #�� � ��; # = � : �a-�� # � � ��;) : : * -�� #�� � �V; ; # = � : �a-�� #�� � �V;?-

j0d«c�S�aAc

: ��; � 2� � D�� ��� � p 2� � q�� � � �Lr{|¢ N

�ÈSUXWp X

�� ) � � / * p % � / 5 u 6 � 7 p �� � 7< [� 9999 � 0 �01r � 9999 5 u�6 � � 7 -

���5Z����

������������� ����������������������������� �"!�#$���&%'%��(�*)+� {z{

� � )������ �#��; 7� / � #�� � ��/ 5 u�6 � 7 -4� ; 7< [� / � #�� � ��/ 5 u�6 � � 7 � -� � ) : $ p � ;�� ; 7< [� /� � � / 5 u�6 � 7 -

aAf k� � ) � ; 7< [� / � #�� � ��/ 5 u�6 � 7 p � 7< [� 9999 0 : � # � � �l;01r 9999 5 u�6 � 7 �

�E¸ �=�Q�&%��V�8B1� � �@��� ��#K� %$��� ���@���K� I �+������(�*����� �����@��� ����������� �� � ��� � � �/�+��� �"� I��@� �+� ��# ���=F �# � �+�M��� �4I ���������:!/��� �+���*%$����! ���@����-��� ��# � w [ # � ���(� �O������!(� � FO����# ��# �M!�# ���*! � : �1;mf ) � �F � # � �+�M��� ����� � I ���*! �@�"%�H&� �������� ��# � � / ��/ � u 6 D 7 � � /�� / 5 u 6 D�7 K � � !/���K�F� � H�����! � � �(����! �s0/ � #�� � � /?s � � ��/ ��/�� u 6 D 7 � H&�(���&% ��# �-�P��� �M����% H&� �������M�+�-��� ��# � I � �F�@�� � D #K�@���/������(# ��F �V��# ��� /�� / 5 u�6 D 7 � � � � / ' / � � 6 D 7 �

W7¨� 3�����(:219� 35.� 9�0��Q0������ 3:2$0 (:2 ��+o�1����.10 ���K0�� 354AOXWc�_Uj,�z]^��Xta k ]<;/XWp XWf-c5]^f�c XWp�iQp XWc0aAc�]edgfªd � dg_Qp�VYXWc�SUd k ¨ ] X�j�c0aAp�c��È]^c�S=a©mW`bagj j�]em|aA` � dgpr�V�_Q`baAc�]edgf � dgp«]^V�i�dzj�]^fQ�=�GX|a+Jªm�dgf�c�]^f�_Q]^c¬l¥dgf�c�SUX¤]^f-c XWp � agm�X � l¡c�SUX}_Uj X©d � a AOaA�zp0aAfQ��XV�_Q`^c�]^iQ`^]eXWp = ��]^f k : ' - ��; 3 z e��&­Qj�_Um0S}c�S�aAc =��� ��! C D1tBF('hGHF >mIo+ 7 p C D�uBF('hG F >LIo+ [ p C q > � �&Ilv ) � : >E;?-

Cnq '���� Ilv ) / -Lr{|x N

� dgp�aA`^` : >�- ��; 3 z e����È]^c�ShaAiQiQp dgiQp�]baAc X�j�i�agm�X�j�zvaAf k �?¨´µ¶UfQ]^c XEXW`eXWVYXWf�c k ]ej0mWp XWc�] ?�aAc�]edgfªd � Lr{|x N � l¡m SUdLdzj�]^fQ�®j _ � j0aAi�m�X~z ��� z�aAf k � ��� �V�_Uj�c � X k X�j�]^�zfUX k m|aAp X � _Q`^`^l¡]^f¥dgp k XWp�c d � X©j�c0a � `eXz¨ � f k dgVtaA]^f k X�m�dgV�i/dzj�]^c�]edgf±­�]^c�]ejVYXWp XW`^lªc�SUX©V�_Q`^c�]^iQ`^]eXWpEj�i�agm�X©�ÈSQ]em0S¥]ejYd � ]^f�c XWp X�j c|­�j ]^fUm�X¤�GX¤��dg_Q` k `^] J�X¤c d _Uj0X©�z]^��XWfVYXWc�SUd k j�dgf}c�SUX*j�_ ��k dgVtaA]^fUj�¨R.SUXWp X aAp Xhc��Gd§i/dzj j�] � `eXhj�c�p0aAc XW�z]eX�jEc d¡d � c0aA]^f�a j c0a � `eX k ]ej mWp XWc�] ?�aAc�]edgf = XW]^c�SUXWpEm0SUd-dzj0Xj i�agm�X�j��ÈSQ]em S�j0aAc�]ej � l=c�SUX¤]^f � ��j�_Qi m�dgf k ]^c�]edgf�dgpYm0S�aAfQ��X}c�SUX k ]ej0mWp XWc X � ]^`^]^fUX|aAp � dgp�V c d]^fUmWp X|agj0X5j�c0a � ]^`^]^c�l�¨R.SUXE¶Up j c�i/dzj j�] � ]^`^]^c¬l¡]ej � dg`^`ed|��X k�� l¡c�SUX©VYdgp�c0aApYXW`eXWVYXWf�cYVYXWc�SUd k ­�j X�X  Ï��£�¨ I?XWp X©dgfUX� agj ]em|aA`^`^lEc0a+J�X�j�c�SUX5c�p0agm�X�j&d � c�SUX�¶UfQ]^c X*XW`eXWVYXWf�c � _QfUmWc�]edgfUj?dgf dgfUX5j i�X�mW] ¶�X k j�] k X5d � c�SUX]^f-c XWp � agm�Xz¨G´.cÈc�SUX�]^f�c XWp � agm�X � dg_Qf k aAp�]eX�j|­�j i�X�mW]baA`±m�dgf k ]^c�]edgfUj�S�a���X5c d � X�j0aAc�]ejr¶�X k ¨

Z:Z �[K\�]F^@\

{|¢ � �/!����������V���K���@�R.SUX�j X�m�dgf k i/dzj j�] � ]^`^]^c�l�]ej�c d5a kQk `eX|agj�c�j ³-_�aAp X�j"c XWp�VYj�]^f$dgp k XWp�c d*agm SQ]eXW��X�VYdgp X � p X�X k dgVdgf�c�SUX�m SUdg]em�X.d � � � ¨�R.SQ]ej���agj¯¶Up j�c¯iQp dgi�dzj X k�� dgpOc�SUXG]^fQSUdgVYdg��XWf�_Udg_Uj ¦ ]^p�]em0SQ`eXWc�iQp d � `eXWV� l�G.aAp � dzj0a�aAf k I�_Q�zSUX�jG ÚxI£ L j X�XGaA`ej d5 ^{|xI£�NJ­zaAf k ��agj�XJn7c XWf k X k c d k dgVtaA]^f k X�m�dgV�i�dzj�]^c�]edgfiQp d � `eXWVYj � l�GÈaA]edLm�m SQ]�­ G�p X�?P?�]�­LaAf k H®aAp�]^fQ]� Ú¢A£�¨Á´�j c�p0aA]^�zS�c � dgp���aAp k ��XWfUXWp0aA`^] ?�aAc�]edgf$`eX|a k jc dYa kQk ]^fQ�$c�SUX,c XWp�VYj =

#�� � � � p � 0 ' �0�r � - � p � 0�>01r�� � q ���dgp�a¤iQp dgi/XWp�`^l m SUdLdzj XWf¡i�aAp0aAVYXWc XWp ��� ��­Áj�c0a � ]^`^]^c�l¡d � c�SQ]ej�VYXWc�SUd k � dg`^`ed|��j � p dgV aAf]^f-��XWp j XEX�j�c�]^VtaAc Xz¨��Udgp�]^fUj�c0aAfUm�Xz­��GXEm|aAfªm SUdLdzj XYc�SUXEj�i�agm�Xtd � iQ]eX�m�XW�È]ej0X$m�dgfUj�c0aAf-c j«dgfaAf=aAp � ]^c�p0aAp�l VYX�j�S¡dgf c�SUX�]^f�c XWp � agm�Xz¨ �?j�]^fQ�¤c�SUXtaA_Q�zVYXWf�c X k X�³�_�aAc�]edgfUj�­±c�SUX�AOaA�zp0aAfQ��XV�_Q`^c�]^iQ`^]eXWp&m|aAf � X�XW`^]^V�]^f�aAc X k ­

� � )�� � � # � 0 ' �0�r � p �� ' � � � -

k XWfUdgc�]^fQ� � l � � c�SUX w [ # iQp dAq�X�mWc�]edgf dgf}c�SUX k ]ej mWp XWc X5V*_Q`^c�]^iQ`^]eXWp&j i�agm�Xz¨] XYfUd|� � dgp�VtaA`^`^l `eXWc� � c XWf k c d ��aAf k ]^fUj0XWp�c*c�SUX�p X�j�_Q`^c�]^fQ�®X�³�_�aAc�]edgf¡]^f Lr{|x NJ¨ER.SQ]ej�z]^��X�j�_Uj�dg_Qp�VYXWc�SUd k agjÈiQp X�j XWf-c X k a � d|��Xz­Uj�]^fUm�X > � - ��� q #�� � � p � 0 '0�r � -�� 0�>0�r � � q )

) # � > � - � 0 '01r�� � q p �� '=� -# > � � q # � '=� - � 01>01r�� � q �

R.SUX&fUXW��VYXWc�SUd k m|aAf$c�SUXWp X � dgp X � X�]^f�c XWp�iQp XWc X k agj.a*j�c0a � ]^`^] ?|X k V*_Q`^c�]^iQ`^]eXWpÈVYXWc�SUd k �È]^c�Sa«m�dgf-c�]^f�_Udg_Uj AOaA�zp0aAfQ��X*V*_Q`^c�]^iQ`^]eXWp&j i�agm�X�L m � ¨� ^{|x7­¢I£�NJ¨�E¸ �=�Q�&%����8B1��� ��! ��� ���� �@)������������)$����� �+���CF�� � ���(�*��������� � ��# � ���P��# �F) KR�����(��� �.F ��!/���!�# �F�+�F�M��� ���(�*)$�� �V��# �V����������P� ! �<_ � ����)��F��� � ) # ���� ��� K D #$��� � �@� )��-�"� �

� = � : �4-���; f ) : F � 7 - F > 7 ; D1t p : F � [ - F > [ ; D�u # � � � - 01> 01r � q# � 0 � 01r -# > � � q p $ � � � -# "> � � q �� �@!/����) ����# � �����JI�� ��� ���"�K����� ��� �����*��� ��� q : �2p { ������ � ; � IovC!/��H �<)~�/��H$�F�@)C�"� �K���"����� ��#K� � H&��������� �������*! �Y����� ��� �@�����P����� �� = � : �4-���; f ) : F � 7 - F > 7 ; D1t p : F � [ - F > [ ; D�u# � � 0 �0�r � -# > � � q p%$� � � -# > � � q �

���5Z����

������������� ����������������������������� �"!�#$���&%'%��(�*)+� {|x

D #K�-��� �����+��� �-� �V��# ���P� � �������������-!��<���P����� �P�����<��F �V��# ���� � %�� �+���8�/�������/��K�E¸ �=�Q�&%���� ����� ���)H&�V!/���JI ���/�'��# ��� � F � ����# �F) FO����#C��# �V�������"��� � ����# � ) ��� ��� � I��@� !�����*!/��� I ��������� � � �*� F K D # � � ) � �����"�F%$� ���C��# � �JF ��%$��� ����) � � ��# �M%�� �K�@��� !/� H�I�� ���&%Y��� ��# �����������P� ! � F #$�*!�# !/��� �(� ��� ��� ��# �7��� !F�:��# � �7��# � �������"��� ��� ��� �����:� ����# �F) H&�P�(� �'� H&�<��� I�� �"���� I � ! � � �! ����������H � H$� �4H ��!P���*���K��K D # � I�����! ���"� I � � �����'��#$������/�M��# ���$) )���������� ���:�������-�����#K������� ��� �@��� �P���(���R��� IK�������*! H �<����� ��# ����� ��� H �����*���Q� �'��# �M������"%�� ��� �M��� � ��� �F��� %B��# ������(�����)&���(� � ����� �+�'� �@� )+�-�"� � !/��H�I�� ���&% � �������� ��� � �$���'� �'��� ��� �������LK

y7¨ ��3�����610>( 019�3:. 3,- � 9 (:. 4 $��dgp?aAf�l}XW`eXWVYXWf-c&c¬l-i/Xz­Q]^c&]ej�]^V�i/dgp�c0aAf�c?c d�S�a���X«a�j�S�aAp�i®X�j�c�]^VtaAc X*d � � 9 ]^f dgp k XWp&c d � Xa � `eX�c d5j0a � XW`^l�m SUdLdzj X $ ¨V] XÈiQp dgi�dzj0XÈc d5m�dgV�iQ_Qc X � 9 ]^fYc�SUX � dg`^`ed��È]^fQ�*��a|l L9�GX�m�dgfUj ] k XWpc�SUX m|agj X d � c�p�]baAfQ�z_Q`baApEXW`eXWVYXWf-c jE]^f c���d k ]^VYXWfUj�]edgfUj�­ � _Qc$c�SUX}m�dgfUm�XWiQcE]ejYm�dgV�iQ`eXWc XW`^l��XWfUXWp0aA`�NJ¨´&f=aAp � ]^c�p0aAp�l c�p�]baAfQ�z_Q`baAp*XW`eXWVYXWf�c � ]ej�iQ_Qc�]^f=a©`edLm|aA`�m�d-dgp k ]^f�aAc XYj lLj�c XWV(j0d©c�S�aAc5dgfUXj ] k X�`^]eX�j�aA`edgfQ�hc�SUX����LaIn7]ej|­ / � � � ��­ÁaAf k c�SUXYc�SQ]^p k fUd k XtaAc�aAf¡aAp � ]^c�p0aAp�l i�dzj ]^c�]edgf:� 7 -� 7 ;�]^f}c�SUX,¶Up j�c�³-_�a k p0aAf�c|¨GR.SUXWf 0 '0�r ) # 0 '0 �aAf k �GX�`edLd�J � dgp�j dg`^_Qc�]edgfUjÈc dYc�SUX5XW]^��XWf��zaA`^_UX�iQp d � `eXWV d � j X�X�JL]^fQ� ' aAf k � 9 j0d«c�S�aAc

C �9 � 0 '0 � 01>0 � I�� # � 9 C � F('�G F >LI � I�� )i/� dgp�aA`^`n>,dgf�c�SUX�XW`eXWVYXWf�c|¨"R.SQ]ej¯iQp d � `eXWV�m|aAf � X�j0dg`^��X k aAf�aA`^lLc�]em|aA`^`^l5c d&l-]eXW` k � 9 � � �=� � 7 ­j0d«�GX�S�a|��X�c�S�aAc�]^f}c�SUX,��XWfUXWp0aA`�m|agj X

$�& � �� � -�ÈSUXWp X ��� ]ejtc�SUXhi/XWp�i�XWf k ]emW_Q`baAp k ]ej�c0aAfUm�X � p dgV c�SUX � dg_Qf k aAp�l¥j XW�zVYXWf-c©c d c�SUXhc�SQ]^p kL9]^f-c XWp�]edgp(N�fUd k Xz¨VL ´?j j�_QV�]^fQ�EX�³�_�aA`��-j�] ?|X k c�p�]baAfQ�z`eX�j|­�GX�j�]^V�iQ`^l¤iQ_Qc $ & � � ¨ N¤�&d��5­���Xm0SUd-dzj0X�c�SUX,`baAp���X�j�c�j�_Um0S � 9 m�dgV�iQ_Qc X k aA`edgfQ�Yc�SUX5]^f�c XWp�]edgp&X k ��XZ_=j d«c�S�aAc

� 9 2 � / F > y / [5 u 6 � 7 � 9999 � ; 7< [ 0�> y0�r y 9999[q �

\-]^fUm�X / F > y / [5 u�6 D�} 7 ) / F > y / [5 u�6 D��} 7 p / F > y / [5 u 6 D�}�� D��} 7 �ÈSUXWp X2+��y k XWfUdgc X�j.c�SUX,j�_ � j XWcÈd � + ym�d���XWp X k}� l$c�p�]baAfQ�z`eX�j�fUXW]^�zS � dgp�]^fQ�$c d«c�SUX � dg_Qf k aAp�l¤j d«c�S�aAc

2� / F > y / [5 u 6 � 7 ) / F > y / [5 u 6 D �} 7Z:Z �[K\�]F^@\

{WZ � �/!����������V���K���@���X5j X�X,c�S�aAc

� 9 / F >�y4/ [5 u 6 D�}87 � � 9 / F >�y1/ [5 u�6 D �} 7 � 9999 ��; 7< [ 01> y01r y 9999[q -

agj�p X�³�_Q]^p X k©� dgp�j�c0a � ]^`^]^c¬l�¨

�L¨Z�6V����219�8=(.+,��� (T�&�=+K�� �L¨^{z¨����G¸ �z� ¼1W $ �V� ¼1S ���|�Q� U � U � ¹ � R.SQ]ej�XJnUaAV�iQ`eX�j SUd|��j�c�SUX�X�;/X�mWc�d � c�SUX�m0SUdg]em�X�d � c�SUXi�aAp0aAVYXWc XWp $ dgf�c�SUXÈj�c0a � ]^`^]^c¬l«d � c�SUXÈj dg`^_Qc�]edgf±¨ÁR.SUX k dgVtaA]^f : / - � ;�e : / � � ;"S�agj�aAf�]^f�c XWp�]edgpi�aAp�c : � -��K;�e : � � �o- � � �K;5�ÈSQ]em S¡]ej5VYX�j�SUX k ]^f k XWi�XWf k XWf-c�`^l=d � c�SUX$dg_Qc XWp5i�aAp�c|¨ ] XYj X�X�Jc�SUX«j dg`^_Qc�]edgf c d #&%�'4) � dgf c�SQ]ej k dgVtaA]^f±­��È]^c�S ?|XWp d ¦ ]^p�]em SQ`eXWc � dg_Qf k aAp�lhm�dgf k ]^c�]edgfUj|¨� f ��]^�z_Qp X {z­��GX j�SUd|� aAf XW`eXW�zaAc�]edgf d � c�SUX©f-_QVYXWp�]em|aA`&j dg`^_Qc�]edgf�_Uj�]^fQ� $ ) / aAf k§� dgp$ ) � � ¨.R.SUX5]^fUj c0a � ]^`^]^c�l � dgp $ ) / ]ej&fUdgc���XWp�l©iQp dgfUdg_QfUm�X k ¨\]�SQ]^`eX*dgfUX*V�]^�zS�c,XJnLi/X�mWcc�SUX�j�l7j�c XWV2VtaAc�p�] nhc d � X�j�]^fQ�z_Q`baAp,]^fhc�SQ]ej�m|agj0X LÆaAf k ]^c?]ej&`^] J�XW`^l c�S�aAc?c�SQ]ej?�È]^`^`ÁS�aAiQi/XWf]^fEj dgVYX�j ]^c�_�aAc�]edgfUj(NJ­-dg_Qp�XJnLi/XWp�]eXWfUm�X�]ejGc�S�aAc���X�dgVYXWc�p�]em|aA`�p X�j�c�p�]emWc�]edgfUj�Vta�ltaA`^`eXW�L]baAc X&c�SQ]ejiQp d � `eXWV ]^f}VtaAf�l¤m|agj X�j|¨"´.c?aAf�lEp0aAc Xz­Qc�SUX�_Uj X�d � $ ) / ]ejÈfUdgc�c d � X,p X�m�dgV�VYXWf k X k ¨

0 0.5 1 1.5 2 2.5 3

0

1

2

30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.5 1 1.5 2 2.5 3

0

1

2

30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

�R9��5672�����u&X�j�_Q`^c j � dgp $ )i/ L9`eX � c(NÈaAf k $ ) � � L9p�]^�zS-c(NJ¨

�L¨Ú¢7¨� � � ¸ � U ��� ��� ¸ � U Q ���7� U9¼1S ¼�W �HX ¸ � �¯� U9¼ � U,¸ ��� U �=�7� ¸ �R� R¯d ��XWp�] � l c�SUX$a}iQp�]edgp�]X�j c�]^VtaAc X�j|­Q�GX*m SUdLdzj X�c�SUX,VYd k XW`±iQp d � `eXWV d � a«_QfQ]^c�j ³-_�aAp X,�È]^c�S XJnUagmWc�j dg`^_Qc�]edgf' ) � � : ��# � ; : �<# ��;m�dgp�p X�j i�dgf k ]^fQ�«c d«a5p�]^�zS-cr��S�aAf k j�] k X&d � *N) � # �

[ p � # � [ ¨"R.SUX k dgVtaA]^f©]ej k ]^�L] k X k$� la���XWp�c�]em|aA`Oj�`^]^c&aAc � )�/ ���L¨GR±��d k ]<;�XWp XWf�c&c�p�]baAfQ�z_Q`baAc�]edgfUj���XWp X5_Uj X k1= dgfUX*VtaAc m SQ]^fQ�©aAf kdgfUX5fUdgf7��VtaAc m SQ]^fQ�U­�j X�X ��]^�z_Qp X*¢7¨

���5Z����

������������� ����������������������������� �"!�#$���&%'%��(�*)+� {FW

� 9�� 6 2���� � H®aAc m0SQ]^fQ�$aAf k fUdgf7��VtaAc m0SQ]^fQ�$�zp�] k j|¨

� f ��]^�z_Qp Xhx L9`eX � cr��S�aAf k j�] k X N«��X �z]^��X c�SUX m�dgf-��XWp���XWfUm�Xh]^f¥c�SUX � p d�J�XWf XWfUXWp��zl�fUdgp�V}¨R.SUX k agj�SUX k `^]^fUX?]ej�c�SUX�fUdgf7��VtaAc m0SQ]^fQ�Y�zp�] k m�dgV�iQ_Qc0aAc�]edgf±¨�G.dgc�SEVYX�j SUX�j�j SUd|� c�SUX,j0aAVYXm�dgf-��XWp���XWfUm�X©�È]^c�S�j�`edgi�X / �����L¨ �ÈSQ]em0S�]ej�mW`edzj XEc dhc�SUXEc�SUX�dgp XWc�]em|aA`È�gaA`^_UXEd � {z¨ x f§c�SUXp�]^�zS-cr��S�aAf k j�] k X,��X�j�SUd|��c�SUX,m�dgf���XWp���XWfUm�X�d � c�SUX w [ # fUdgp�V d � c�SUX�qr_QV�iEc XWp�V L k agj SUX k`^]^fUX � dgp*c�SUX�fUdgf7��VtaAc m SQ]^fQ� �zp�] k NJ¨ I&XWp Xt�GX$d � c0aA]^f§a � XWc�c XWp*m�dgf-��XWp���XWfUm�X L j `edgi�XY�o� � ��N� dgpEc�SUX VtaAc m0SQ]^fQ���zp�] k j$c�S�aAf � dgptc�SUX®fUdgf7��VtaAc m SQ]^fQ���zp�] k j L j�`edgi/X � ��� �L­&mW`edzj Xhc d¡c�SUXc�SUX�dgp XWc�]em|aA`¯�gaA`^_UX�d � x��g¢ NJ¨

-2.8 -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4

-4.6

-4.4

-4.2

-4

-3.8

-3.6

log(h)

log(

ener

gy e

rror

)

-3.5 -3 -2.5 -2 -1.5 -1 -0.5-10.5

-10

-9.5

-9

-8.5

-8

log(h)

log(

inte

rfac

e ju

mp)

�R9��5672��� �&s�dgf-��XWp���XWfUm�X*]^f}XWfUXWp��zl}aAf k m�dgf-��XWp���XWfUm�X*d � c�SUX.qr_QV�i}c XWp�V}¨

Z:Z �[K\�]F^@\

{|y � �/!����������V���K���@��L¨Úx7¨ �«½¯�E�¯� U � ¸ � ¼ �M� �±�|�7� U9¼BS �R� ] X�iQp X�j XWf-c�p X�j _Q`^c j"d � a k aAiQc�]^��XÈm�dgV�iQ_Qc0aAc�]edgfUj�dgf�c�SUXA���j�S�aAi�X k k dgVtaA]^f + ) : / - � ;Je : / - � ;�� : � � �o- � ;Je : / - � � �K;?�R.SUX*iQp d � `eXWV ]ej � dg_Qf k aAp�l k p�]^��XWfQL *,)$/ NJ­��È]^c�S � dg_Qf k aAp�l k aAc0aYm�dgp�p X�j�i/dgf k ]^fQ�$c dYc�SUXXJnUagmWc�j dg`^_Qc�]edgf ' )��

[ <���� ��� : ��� � � ;5]^fªi/dg`baAp�m�d-dgp k ]^f�aAc X�j L9�È]^c�S�dgp�]^�z]^f¥aAc : � � �o- � � �K; NJ¨] X�`eXWc2+ 7 ) : / - � � �K;&e : / - � ;&aAf k + [ ) : � � �o- � ;�e : � � �o- � ;0­¯aAf k _Uj X«a$fUdgf7��VtaAc m SQ]^fQ�c�p�]baAfQ�z_Q`baAc�]edgf±¨�R.SUX�iQ_Qp�i/dzj X5d � c�SQ]ej�XJnUaAV�iQ`eX5]ejÈfUdgc�c dtd � c0aA]^f XJnQagmWc&XWp�p dgp�m�dgf�c�p dg`�­ � _Qcp0aAc�SUXWptc d j�SUd|� SUd|� c�SUX a k aAiQc�]^��X®aA`^��dgp�]^c�SQV � XWS�a���X�j$�È]^c�S p X�j�i/X�mWc�c d c�SUX¤XW`eXWVYXWf�c ja k q agm�XWf�c&c d�c�SUX�]^f-c XWp � agm�Xz¨ � f m�dgfUj X�³-_UXWfUm�Xz­U�ÈSQ]^`eX5��X5m�dgfUj�] k XWp,a k aAiQc�]^��X*m�dgf�c�p dg`Ád � c�SUXVtaIn7]^V*_QV�XWp�p dgp|­g��X�S�a|��XGfUdgc"aAiQiQp d�n7]^VtaAc XW`^l�j0dg`^��X k c�SUX k _�aA`-iQp d � `eXWV Lr{z{ NJ¨ � fUj c X|a k ��XS�a|��XÈj�]^V�iQ`^l5c�_QfUX k c�SUX�]^f�c XWp�i/dg`baAc�]edgfYm�dgfUj�c0aAf-c j"c d�aAiQiQp d�n7]^VtaAc XW`^l�VtaAc m0S�c�SUXGVtaIn7]^V*_QVXJnUagmWc�XWp�p dgp|¨� f ��]^�z_Qp XGZ*aAf k W&�GXÈj SUd|�¥a?j X�³-_UXWfUm�XÈd � a k aAiQc�]^��XÈVYX�j�SUX�jÁp X�j�_Q`^c�]^fQ� � p dgV�X�³�_Q]^`^] � p0aAc�]^fQ�c�SUX*XWp�p dgp k ]ej�c�p�] � _Qc�]edgfhd���XWp�c�SUX5j0XWc�d � XW`eXWVYXWf-c jL � dgp k XWc0aA]^`ej|­j X�X� Ú�7­�yI£�NJ¨G�&dgc X�c�S�aAc�c�SUX]^f-c XWp � agm�X XWf � dgp m�X�jta®j�`^]^�zS-cY]^fUmWp X|agj X k p XJ¶UfUXWVYXWf-cEagj�m�dgV�i�aAp X k �È]^c�S¥a j�]^fQ�z`eXJ� k dgVtaA]^fj0dg`^_Qc�]edgf±¨

�R9�� 6 2�� � ��]^p j�cÈVYX�j ShaAf k ¶Up j�c�a k aAiQc X k VYX�j�S±¨

�Z��-n��2���.78B�� � ^� ���� ����� ��� áAÎÚÉ�Ö�������� �"!$#&%('*)&#+�$,-� .0/21&1 # ��)&#+3540�$67,�8�'$�:9*;=<�'*1 6?>A@2� ��B�1C>D%FE&G¤ÎÚÍÚÀÕÛ�Ö$^"H�I$J*KD�� J= �×0�ML/Ã0ÎÚÊ|ÒrÒ�ÓIÎ^Ö�N��ML�Ä�À�O�OrÎ^Ö-à ÉAÐQPR�z¿S��Ñ,à Ä�ÎÚÉAÎ^ÖLÌ|Å�à áIÎÚÍÏÎTO�à Å�ÎÚÊJÉ*Ê Ë/ßÁà ÍÚÀÕÄVU|ÎÚÉ�ÇÈÀÕÅ�ÓIÊ|ÐIԯà ÉAÐ�à ÂAÂIÍÚÎ ÒÕÃ0Å�ÎÚÊJÉIÔ

Å�Ê�Ð�ÊJÇ�à ÎÚÉ�Ð�À�ÒÕÊ ÇÈÂzÊJÔÆβÅ�ÎÚÊJÉ-ÖUÎÚÉXWZYX6[)&67�V>-\�>D,�8]>D,�3�#^>D_`#&,bac�$%0��6[)^>D�ed�3�#^>D,�3:>Df(ac�g,�)&�h�$12'$,�8i������1 #^>h8j '*)lk�>D%Z'*)&#+3�_VfAÌ�Â�Ä�ÎÚÉAÞJÀ¬ÄcP-À�ҬŠ� Ä�À � Ê0Å�ÀrÔQÎÚÉÈ×�Ê ÇÈ � Å�À¬Ä�ÌIÒÕÎÚÀrÉAÒÕÀ1]*m(\�Ö � �$L�ÀrÉIÔÆÊ � ÔÆÔ�Ã0ÉÈà ÉAÐS��� �����gnÀÕÄpo � ÔE^À�Ð�Ô�� K¬ÖqEbÌ�Â�Ä�ÎÚÉAÞJÀ¬Ä�Ö$^�H*H*J*K¬Ö \gr]m"sP\�m$m7�

� \g ����I×0��L/à Ä�ázÊJÔ�Ã.Ã0ÉgÐ�Ý5�?�[� Z �7t � ÞJÓIÀrÔrÖ[L�Ê � ÉgÐIÃ0ÄÆÛePLÃ0Þ Ä�Ã0ÉAÞJÀ�Ç � ͲÅ�ÎÚÂAÍÚÎÚÀÕÄ�Ô/ÎÚÉ`ugÉIÎÚÅ�À¯ÀrÍÚÀrÇÈÀrÉ�Å/ÇÈÀ¬Å�ÓAÊ|ÐIÔ�WÀÕÄÆÄ�Ê0Ä�Ã0ÉgÃ0ÍÚÛ�ÔÆÎÚÔOÎÏÉ&Égà Š� Ä�à Í�ÉAÊ0Ä�ÇÈÔrÖ �5� ÇÈÀ¬Ä"�gÑ,à Å�Óq��v�wXxRE�^�H*H�J$KO^:s�^"m

���5Z����

������������� ����������������������������� �"!�#$���&%'%��(�*)+� {��

0

0.5

1 0

0.5

10

0.2

0.4

0.6

0.8

�R9�� 6 2���� � ��]^f�aA`±VYX�j S aAf k XW`eXW�gaAc�]edgfhd � c�SUX5j0dg`^_Qc�]edgf±¨

� r$ �����G �ML/Ã0ÄÆÄ�À¬ÅÆÅ�à ÉAÐ�×0��Ñ-����ÍÚÍÚÎÚÊ Å�ÖqN7ÎÚÉAβÅ�À�ÀrÍÚÀrÇÈÀÕÉ|Å�à ÂIÂIÄ�Ê���ÎÚÇ�Ã0Å�ÎÚÊJÉ�Ê0ËÅ�ÓIÀ�¿�ÎÚÄ�ÎÏÒ�ÓAÍÚÀÕÅ�ÂIÄ�ÊJáIÍÚÀrÇ � ÔÆÎÏÉIÞÅ�ÓAÀ�ázÊ � ÉAÐAà ÄÆÛ&ÂzÀÕÉgà ͲÅÜÛ&ÇÈÀ¬Å�ÓAÊ|Ð�Ö �0� ÇÈÀÕÄ"�AÑ,à Å�Óq����XxRE�^"H��]*K7\gr�\=sP\�](][�

� m= Z �ML�À�ÒVUWÀÕÄÁà ÉgÐQ����tÁÃ0ÉAÔÆázÊ�Ö-¿�ÎÏÔ�Ò¬ÊJÉ�Å�ÎÚÉ � Ê � Ô"ßÁà ÍÚÀÕÄVU|ÎÚÉ*ÇÈÀÕÅ�ÓAÊ|Ð�Ô¯Ë Ê0Ä�ÒÕÊ É�ÙJÀ�Ò¬Å�ÎÚÊJÉ[�9Ð�Î � � ÔÆÎÚÊJÉ5ÂIÄ�Ê áAÍÚÀrÇÈÔâ±Î²Å�Ó,à Ä�áAβÅÆÄ�Ã0ÄÆÛ ����ÒÕÍÚÀÕÅ¯É � Ç�ázÀ¬Ä�Ö|ÎÏÉ&ÂIÄ�ÀrÂAÃ0Ä�à Å�ÎÏÊ Éq�

� ]g Z �7L�À�ÒVUWÀÕıÃ0ÉgÐ Z � Z Ã0ÉAÉAÃJÒ�ÓAÀÕÄ�Ö � Ë ÀÕÀ�Ð[�bágà Ò:U.à ÂAÂ�Ä�ÊWà Ò�Ó�Å�ÊGÀ¬ÄÆÄ�Ê Ä±ÒÕÊ É�ÅÆÄ�ÊJÍzÎÚÉeuAÉAβÅ�ÀOÀrÍÚÀrÇÈÀrÉ�Å�ÇÈÀ¬Å�ÓAÊ|ÐIÔ�WágÃ0ÔÆÎÏÒ"à ÉgÃ0ͲÛIÔÆÎÚԯà ÉAÐ&À��Ià ÇÈÂIÍÚÀrÔrÖ��Ã0Ô Åh�^G�ÀrÔ Å0��� �0� ÇÈÀÕÄ"�IÑ,à Å�Óq��� E�^"H$H�]�K�J(\*I"s7J(]$r

� I= �×0�qL�ÀÕÄ�ÉAÃJÐIÎ^Ö��S�LÑ,ÃJÐIÃ�Û�ÖLà ÉAÐ � �q�QÃ0Å�ÀÕÄ�Ã|Ö � ÉIÀÕâ ÉAÊ ÉgÒÕÊ ÉIË Ê Ä�ÇÈÎÚÉAÞ?à ÂAÂ�Ä�ÊWà Ò�Ó5Å�Ê�ÐIÊ Ç�à ÎÚÉ�ÐIÀ�ÒÕÊ ÇÈÂzÊ$�ÔÆβÅ�ÎÚÊJÉqW�Å�ÓAÀ&ÇÈÊ ÄÆÅ�à Ä.ÀrÍÚÀrÇÈÀrÉ�Å�ÇÈÀÕÅ�ÓAÊ|Ð�ÖÎÚÉXW��A�$,�1 # ,M>h'$�Z@ '$�D)&#+'*1�� # �5>D�h>D,�)&#+'$1 /���6�'*)&#+�g,?_ '$,�8b\Xk?>D# �������1 #+3V'*)&#+�g,?f�t ��LÄ�À�OrÎÚÔ¯Ã0ÉgÐ �[��PR��P�ÎÏÊ ÉAÔ E^À�Ð�Ô�� K¬ÖqE+�UÎÚÅ�Ç�Ã0É-Ö ^"H�*H*KD�

� g �N�� LÄ�À�O�OrÎ^ÖAPR� ��� N�Ä�à ÉgÒÕÃ�Ö¯¿S�OÑ,Ã0Ä�ÎÚÉIÎeÖÁà ÉAÐ � � Z�� ÔÆÔÆÊ�Ö"Ì�Å�à áAÎÚÍÚÎTO�Ã0Å�ÎÚÊ É Å�À�Ò�ÓAÉIÎ�� � ÀrÔ�Ë Ê Ä,ÐIÊ Ç�à ÎÚÉ}ÐIÀ��ÒÕÊ ÇÈÂzÊJÔÆβÅ�ÎÚÊJÉ�ÇÈÀÕÅ�ÓIÊ|ÐIÔ�â±Î²Å�Ó�ÉAÊJÉ[�bÇ�Ã0Å�Ò�ÓAÎÚÉAÞ.Þ0Ä�ÎÏÐIÔrÖ ���V� �9× �:Z Z ÀrÂzÊ ÄÆÅ � �&^��(\�I|Ö � Ô Å�βŠ� Å�Ê�ÐIÎ � ÉAà ÍÚÎÚÔÆÎ�5� ÇÈÀÕÄ�ÎÏÒrà �Qà Ù|ÎÏÃ[�

� Hg �×0��� ÊJÓAÉIÔÆÊJÉ Ã ÉAÐb���2tÁÃ0ÉAÔÆázÊ�Ö � ÐAÃ0ÂIÅ�ÎÚÙWÀ uAÉAβÅ�À�ÀrÍÚÀrÇÈÀrÉ�Å&ÇÈÀÕÅ�ÓAÊ|Ð�Ô�ÎÚÉ}ÒÕÊ ÇÈ � Å�Ã0Å�ÎÚÊJÉAà Í�ÇÈÀrÒ�ÓAà ÉAÎÏÒÕÔrÖ×�ÊJÇÈ � Å"�IÑ?ÀÕÅ�ÓIÊ|ÐIÔ � ÂIÂAÍp�AÑ?À�Ò�ÓX���UÉAÞ0Ä�Þ���� ����xcE�^�H*H�J$KO^�r�\"s�^�F^*�

� ^!�g ����cP-À?Ý7à ÍÚÍÚÀ�Ò�à ÉAÐ$Ý5��Ì�à ÔÆÔÆÎ^Ö�¿ÁÊ Ç�à ÎÚÉtÐIÀ�ÒÕÊ ÇÈÂzÊJÔÆβÅ�ÎÚÊJÉtâ±ÎÚÅ�ÓtÉAÊ ÉAÇ�à Å�Ò�ÓIÎÏÉIÞ5Þ Ä�ÎÏÐIÔ�W5à � Þ ÇÈÀrÉ�Å�À�Ð PLÃg�Þ Ä�Ã0ÉAÞ Î Ã0É�à ÂIÂIÄ�ÊJÃJÒ�Ó-ÖgÑ,Ã0Å�Óq�z×�ÊJÇÈÂX��v"� xcE�^"H*H*m*K5^@\(]�I�s�^@\$H�]7�

� ^(^� ����[Pc�[P�ÎÏÊ ÉAÔrÖ$#�ÉÈÅ�ÓAÀ�ÌIÒ�Ó�â�Ã0ÄVO�à ͲÅ�ÀÕÄ�ÉAÃ0Å�ÎÚÉAÞGÇÈÀÕÅ�ÓAÊ|Ð � � � W�Ã�Ù Ã0Ä�ÎÏà É�Å/Ë Ê Ä�ÉIÊJÉIÊ0ÙJÀÕÄ�ÍÏà ÂAÂIÎÚÉAÞ�Ô � á�ÐIÊ Ç�à ÎÚÉAÔrÖÎÚÉqW \Xk7#&�h8&%:,�)^>D�:,�'*)&#+�g,�'*1�d?9g%5�[�g_:# 6[% �$,'� �$%Z'g#&,(� >h3:�g%5�[�$_V#p)&#+�g, j >�)lk��"8$_ .��$��@�'$��)&#p'*1��A# �0>D�V>D,?)&#+'*1/)��6?'$)&#+�$,?_Vf�Ý5� N��7×�ÓgÃ0É-Ö Z �Qß�ÍÚÊ�â±ÎÚÉAÔhU|Î^Ö �����7À¬Ä�Î Ã � ��ÖUÃ0ÉgÐ*#�� L0� G©Î Ð�Í � ÉgÐ E^À�ÐIÔ�� K¬Ö�EbÌ ��� Ñ�Ö�^�H+*H*K¬ÖJ��*J"s7J*J(\7�

� ^"J= ���� � βÅ�Ô�Ò�ÓIÀJÖ-,�ázÀ¬Ä�ÀrÎÚÉ nÃ0Ä�ÎÏÃ0Å�ÎÚÊ ÉAÔÆÂIÄ�ÎÚÉ�OrÎÚ O � ÄSP-àJÔ � ÉAÞ�ÙWÊ É�¿ÁβÄ�ÎÏÒ�ÓIÍÏÀ¬Åh� �QÄ�ÊJáIÍÚÀrÇÈÀrÉ�ázÀrÎ nÀÕÄÆâ�ÀrÉgÐ � ÉIÞÙWÊ É�Ý-ÀrÎÚÍÚÄ/. � ÇÈÀrÉ�Ö7Ð�ÎÚÀSUWÀrÎÚÉIÀrÉ Z à ÉAÐIázÀ�Ð�ÎÚÉAÞ � ÉAÞ ÀrÉ � É�Å�ÀÕÄÆâ/Ê0ÄÆË ÀrÉ�ÔÆÎÚÉgÐ�Ö � áAÓq�-Ñ,à Å�Óq��Ø�ÉIÎÚÙM��tÁà ÇGá � Ä�Þ0 vXxRE�^�H�I1��K H=s�^"m7�

� ^ \g Z �IÌ|Å�ÀrÉ|ázÀÕÄ�Þ�Ö�#�É�ÔÆÊJÇÈÀOÅ�À�Ò�ÓAÉAÎ�� � ÀÕÔ�Ë Ê0Ä�Ã0ÂAÂ�Ä�Ê2��ÎÚÇ�Ã0Å�ÎÚÉIÞGázÊ � ÉgÐIÃ0ÄÆÛ�ÒÕÊ ÉgÐ�ÎÚÅ�ÎÚÊ ÉAÔ�ÎÚÉ&Å�ÓIÀ0ugÉIβÅ�ÀÁÀrÍÚÀrÇÈÀrÉ�ÅÇÈÀÕÅ�ÓIÊ|Ð�Ö[���z×�ÊJÇÈ � Å"� � ÂAÂIÍp�gÑ,à Å�Óq��v 0 xRE�^�H*H�m$KO^ \*H"s�^�r+[�

� ^�r$ n��IÝ/ÓIÊJÇ3�rÀJÖ54 '*1C>D�76g#&, Y #&,�#p)^>5/21C>D%`>D,?) j >�)lk[�"8$_c.��$�5@�'$�h'*B:�$1 #+3A@��h��B�1C>D%�_�Ö�EbÌ�Â�Ä�ÎÚÉAÞJÀ¬Ä�Ö$^�H*H*I*K� ^"m= �L0� � � G�ÊJÓIÍÏÇ � Å�Ó�Ö � Ä�ÀrÔÆÎÏÐ � à ͱágÃ0ÔÆÀ�ÐYÀÕÄÆÄ�Ê Ä�ÀrÔ Å�ÎÚÇ�à Å�Ê ÄÈË Ê0Ä�ÇÈÊ ÄÆÅ�à Ä(ugÉIÎÚÅ�À&ÀrÍÚÀrÇÈÀrÉ�Å�Ð�ÎÏÔ�Ò�Ä�ÀÕÅ�ÎTO�Ã0Å�ÎÚÊJÉIÔrÖ

�QÄ�ÀrÂIÄ�ÎÚÉ�Å�ÖAÑ,Ã0Å�Óq� � ÉIÔ Å�ÎÚÅ � Å�Ö�Ø�ÉAÎÚÙWÀ¬Ä�ÔÆÎÚÅ/. Å �0� ÞJÔÆá � Ä�Þ��

Z:Z �[K\�]F^@\

Unité de recherche INRIA Sophia Antipolis2004, route des Lucioles - B.P. 93 - 06902 Sophia Antipolis Cedex (France)

Unité de recherche INRIA Lorraine : Technopôle de Nancy-Brabois - Campus scientifique615, rue du Jardin Botanique - B.P. 101 - 54602 Villers lès Nancy Cedex (France)

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France)Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38330 Montbonnot St Martin (France)

Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - B.P. 105 - 78153 Le Chesnay Cedex (France)

ÉditeurINRIA - Domaine de Voluceau - Rocquencourt, B.P. 105 - 78153 Le Chesnay Cedex (France)��������� ���� ���������� ��� ���

ISSN 0249-6399

top related