41

3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

  • Upload
    others

  • View
    0

  • Download
    0

Embed Size (px)

Citation preview

Page 1: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

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

*�+-,�.0/2143�576$398;:<+�=> 3�5?6$3-8;:@+BA4:C.D5&8FE$GHE�IKJ-LM5&EN:

OP+�8Q5 >SR9TNTNUWV�X 3-,�.0GY3�/<ZN[]\_^ R-T�TNUB`

ab3�5 > =].c59+�\ X 3-deEN8FJOgf Xih a XjhkTNU-hHl�m

nporqts�u�vYu-w0x�y{z?vYzt|�s�q?}~i�$� |��Nq?z �p� z?q?}$�Nu��ru�������o � oMvYoMuN�

nporqts�u�vHu�w0x��{u�sY�$u�sH|�xHoru��� �Nz4nporqts�u�vHu�w0x{�W|&�y{z ��� u�� �e� � ~����������

Page 2: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

����������� ������������������������� �!��#"$�%��&�� ��&��'(���*)+�)(�#,���,-/.���"����()+��#��0*��,12%#��3�����"$� %#%��435��67��8���'(�9��:����)<;1/,��(0>=>?2!��2�&�� ��(�4'(���*)�� )(�#,@���#'A���'(8B)(,�"�,���'()&�(.�"4)/���3C�#�*)(���& ��(��)�D*8@��)E!�� 'E-F,��(�G� % ��(,�H��H���%#�#'()&�#"'(���I��*)(�#"�'��I�0*�#���J�#)/'&.��#)��H�%��K-F,@�L'()+�)&��'&)(�#"$� %>�G����� �.�%9�)(�#,�M=N���O'(!�,1P!�,1P1/�O"$��I.�'&�J)(!���(�� ��&��'(�4�Q)+�)&��,��I)(,�%#�$� �(������1R0Q��,12%��43��@�2H*8C"�,@��H��#���#���O3�,@�I��#��0*��,12%#��3����S12�#)(!�'&)�� )(�#'()&��"��%3��)+��=

T UWV�XWY�Z\[^]\_LXA`�ZaV

n |�����xHz?qQ}$�No#b>cNz?v�wcu�s{�rzt|�sH�No �N�ps�z?�r�<}Nzt| � or�r�pu�� � |�xF|>d�e �pq?u���xFsH|-vYx � xF}NzIf��Nu*g��rz � ��z�zt�Nq?u � z � o �zh$�$zts�x vH��vYxHz � vicNv�c$|-�r�M� q?u � z?v)vYu��rz?�M� w s�u � |���zh$�$ztskx@d2eK� xF}Norv �$|��Bzts � g z zh | � o �Nz�|�fN�NuQg �Mz � ��zs�zt�$s�z?vYzt��xF|�xHoru�� � qt|��M�rz � |kjml�nQo prqsl�tutWo@vxw2y�z4{@|�x;}$|-xe�rz?xHv2cNv }$| � zbxF}NzJ}$z?vHx�u-wA}Bu�xF}Cg{u�s�� � v@d2~i| � z?�r� �xF}Nz�s�zt�$s�z?vYzt��xF|�xHoru���|-�r�Mu*g�vScNvbxYu �rzt|�sH���Nzg�fN�Nu*g��rz � ��z�}�� q?u � }No �No �N� zh �Bzts�x � u � |-o �IfN�NuQg �Mz � ��z|�� � vHx;|-xHorvHxHorqt|-� � |�xF|>d

~�� |t��z?vHo |�� �Nz?x+g{u�s�f�orv{|���sH|��$}NoMqt|���s�zt�$s�z?vHzt��xF|-xHoru�� u-w�c$�Nq?zts�x;|-o �5fN�Nu*g��rz � ��z�xF}$|-x � u�vHx)�$z?u���N�rzI� � � zt|-vY�'xHu�q?u��NvYxFs�cNq?x4|�� � o ��xYztsH�$s�z?x@due � | �$� orxHoru�� � x;}Nz skzt�$s�z?vHzt��xF|-xHoru�� }$|�viw0u�s � |-�b�$s�u�}��|�}Nor�rorvHxHorqpvHz � |���xHorq?v �)� |�f�o �N� orx v$cNorxF|�}N�Mz w0uNs4vYxF|-xHorvHxHorqt|-� � |��No �>cN� |-xYoMuN���x� u*g�|�s �e�J�t���>���O� zt|�s�� ��t������� d �i� ztsixF}Nz�� |�vHx � z?qt| � z � xF}Nz � |&��z?vHo |��p�Nz?x+g uNs�f�}$|-v�}$z?q?u � z | �Bu��>cN� |�s4s�zt�$skz?vHzt��x;|-xHoru��wcu�sezt�Nq?u � o �N�uc$�Nq?zts�xF|-o ��zh$�$zts�xSfN�Nu*g��rz � ��z�o ��zh$�$zts�xbvY��vHxYz � v��x� z?qrf-zts � |���z?x)|���d �M�t����� | � d]npu�s�zs�z?q?zt��xH�r� � s�z?vYzt|�s�q?}Nzts�v4}$| � z � z � z?�ru��$z �P� z?xF}Nu � viw0uNs��rzt|�sH�No �N� � |&��z?vHo |��p�Nz?x+g uNs�f�v wKs�u � | q?u � �}No �$|-xHoru��Cu-wbzh �Bzts�x�f��Nu*g��rz � ��z�|�� �'� |-x;|>d � }Nz xHz?qQ}$�No#b>cNz?v�xF}$|-x }$| � z\}Bz?zt� � z � z?�ru��$z � |�s�z��Nzg|�� � vYxHor�M� z � u�� � o �N� � }>cNx�x;}Nz?�@}$| � zu}Bz?zt� vF}Nu*g �CxHu�}Bz skz � |�s�f&|�}N�r�<z��ez?q?xHo � z o �@vHu � z � u � |-o �Nv�c�{uNu��Bzts�|�� � � zts�v$f-u � oMxYv �t��������~ �ro w0zts�orv4|�� � ��u�u��Bzts �t�����M� ��z?qf-zts � |�� z?x |-�xd �t����� } � d

� vHo �N� � |&��z?vHo |��P�Nz?x+g{u�s�f�v � xF}Nz��rzt|�sY�No �N�P�$s�uNq?z?vHv ��u�z?v |-v w0u��r�ru*g�v@d��bo s�vYx � g{z�zt�Nq?u � zCxF}NzzhNoMvYxHo �N��fN�NuQg �Mz � ��z u-w |��Czh �Bzts�x4uNsivHz?x�u-w zh$�$ztskxHv4o � | � |&��z?vHo |�� �Nz?x+g{u�s�f � |-v4orv � uN�NzGgi}Nzt�}>cNor� � o �N��| �$s�u�}$|�}NoM�rorvHxHorq zh$�$ztskx vH�NvHxHz � d � }Nzt� � g{z�cNvHzp| � |-xF|�}$|-vHz'xYu�c$� � |-xHzpxF}Norv�f��Nu*g����z � ��z � qtskzt|-xHo �N� u��Nziu�s � uNs�zj�Nzg � |&��z?vYo |����Nz?x�g{u�s4f�v@d � }Nz4s�z?v$cN�rx�o �Nq?�9c � z?v4| s�z�� �Nz � zt��x�u�wxF}Nzu�s�or��o �$|-��zh �Bzts�xSfN�NuQg �Mz � ��z |�� � vHu � z?xHo � z?v)x;}Nz o � zt��xHo���qt|-xHoru�� u-w�Nzg � orvHxHo �Nq?xHoru��Nv |�� � s�z?� |-xYoMuN���vF}No �Nv@d � }Nz�|��$�$s�u�|�qQ} orv�s�u�}>cNvHx�xYu ztsHs�u�skv�o ��xF}NzIf��Nu*g��rz � ��z u-w x;}Nz4zh$�$zts�x@dJ� � zt��g }Nzt� zh �Bzts�xfN�NuQg �Mz � ��z�orvmc$�$skz?�Mo |�}N�rz4|�� � o �Nq?u � �N�rz?xHz � g{z{qt|���u-wcxHzt�ucNvHz oMx xHu�o � �$s�u � z�x;}Nz��rzt|�sH�No �N� �$s�u�q?z?vYv@d

� zt|�sH�No �N�5cNvHo �N� � |t��z?vHo |�� �Nz?x+g{u�s�f�v)orv�vYo � oM� |�s�xHu4xF}$|�xmcNvYo �N� �Nz@c$sH|�� �Nz?x+g{u�s�f�v@d � }Nz4�$s�uNq?z?vHvz � �N�ru-��o �N� � |t��z?vHo |��'�Nz?x+g{u�s�f�v � }Nu*g{z � zts � }$|-vix+g{u�o � �Bu�s�xF|���x�| �$� |���x;|-��z?v@d � �Nz � g z�qt|���zt|-vHor�r�zt�Nq?u � z'zh$�$zts�x�f��Nu*g��rz � ��zCo �S| � |&��z?vYo |��P�Nz?x�g{u�s4f |�� � cNvYz'xF}Norv�f��Nu*g��rz � ��zCxHu o �Nqts�zt|-vHzCxF}Nzz�� q?orzt�Nq?�<|�� � |-q?q@c$sH|-q?��u-wb�rzt|�sH�No �N�Md � g{u � xF}Nz��Nu � z?v�|�� � |�s�q?v�o � �Mzt|�sH�Nz �P� |&��z?vYo |����Nz?x�g{u�s4f�vu-wcxHzt�2q?u�sHs�z?vF�Bu�� � xHups�z?q?u����No#�t|�}N�rz � orvHxYo �Nq?xYoMuN�Nv |�� � qt|�cNvF|-��s�z?� |-xHoru��NvF}No �Nv@d#�{u��NvHzb>cNzt��xH�r� � g{zqt|�� � uNs�z�zt|-vHor�r��o ��xHztsY�$s�z?xj|�� � c$� � zts�vHxF|�� � xF}Nz\fN�NuQg �Mz � ��z4zt�Nq?u � z � o ��xF}Nz�s�zt�$s�z?vHzt��xF|-xYoMuN�Ed

Page 3: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� }NoMv��$|��Bzts oMv�|�}$s�orz;wx$cNxHu�sko |���u�� � |&��z?vHo |�� �Nz?x+g{u�s�f�v)|�� � � z?xF}Nu � v wcu�sb�rzt|�sY�No �N��xF}Nz � wKs�u �� |-xF|�dGe � � z?q?xHoru��Nv � |�� ��� g{z � orvHq@cNvHv�xF}Nz � |&��z?vHo |��p�$}Nor�ru�vHu��$}��W|�� � x;}Nz skzt�$s�z?vHzt��xF|-xHoru��Edue �� z?q?xHoru��Nv � xF}$s�u�cN��}�� � g{z � z?vHqtsko }Bz � z?x;}Nu � v{wcu�s{�rzt|�sY�No �N� xF}Nz4�$s�uN}$|�}Nor�MorxHorz?v4|�� � vYxFs�cNq?x$c$s�z�u�w |� |&��z?vHo |�� �Nz?x�g{u�s4fMd2eK� � z?q?xYoMuN�Nv � |�� � �B� g{z � orvHq@cNvHv � z?x;}Nu � v{wcu�s o � zt��xYo wc�No �N���Nzg � orvHxHo �Nq?xHoru��Nv|�}Bu�cNx�xF}Nz5g{u�sk� � |�� � o ��xHz?��sH|-xYo �N�pxF}Nz?vYz � oMvYxHo �Nq?xHoru��Nv o ��xHu | � |&��z?vYo |��W�Nz?x+g{u�s�fWd'�2z s�z?vYxFs�orq?xu�c$s � orvHq@cNvHvHoru��#xYu � |&��z?vHo |��#|�� � b>c$|-vHo�� � |&��z?vHo |�� � z?x;}Nu � v wcu�s��rzt|�sH�No �N�Md ~ �2o ��xHzts�z?vYxHo �N�W|�� �u-wcxHzt��z��ez?q?xHo � z��Nu���� � |&��z?vHo |�� |��$�$s�u�|-q?}�orv)��o � zt�5}�� � zt|�s���|�� ��� zts � |�� �t���>�@� |�� ��� �No s�xYz?v z?x{|-�xd� �t������� d ~ �rvHu � g{z4�ro � orx�u�c$s � orvHq@cNvYvHoru��pxHu �$sku�}N�rz ��� u � |-o �Nv�g }Nzts�z � |�s�o |�}N�rz?v�xF|�f�z�u�� � orvHqts�z?xYzvHxF|�xHz?v@d�npu�s�z���zt�NztsY|-��xHz?q?}$�No#b cNz?v�|�s�z ��o � zt� o � � c$��xHo �Nz5� �t���*��� |�� � ��z?qf-zts � |�� z?x�|-�xd�� �t����� } � d

��� ������� ��E`��kV����\`���Z��EZ���� �

� z;w0uNs�zJg z � orvHq@cNvHv � |t��z?vHo |�� �Nz?x+g{u�s�f�v |�� � }Nu*gPxHui�rzt|�sH��xF}Nz � wKs�u � � |-xF| � oMxOg�or�r��}Nz?� � xHu�s�z � oMzgxF}Nz � |&��z?vHo |�� o ��xHztsY�$s�z?xF|-xHoru�� u-w �$s�u�}$|�}Nor�rorx���d ~ �$s�o � |�s�� z?�Mz � zt��x u-w xF}Nz{� |��N��c$|���z{u-w �$s�uN}$|�}Nor�Morx��� � |&��z?vHo |�� u�s�u�xF}Nzts+g�orvHz � orv x;}Nz�z � zt��x�d � ��z � zt��x � g{z � zt|���| vHxF|�xHz u�w vHu � z��$|�skx�u-wbu�c$sJg{u�s�� �o � vHu � z xHo � z o ��xHzts � |-�]o � xF}Nz��$|-vHx � �$s�z?vHzt��x � u�s�w(cNx$c$s�z�d ~ q?� |-vYvHorq�zh | � �N�Mz�u�w |�� z � zt��x)orv{xF}$|-x{|�$|�s�xYoMq@cN� |�s"!�o �Cu-w | q?u�o ��g oM�r�bq?u � z\c$�<}Nzt| � v@d ~ �BztsH}$|��Nv � u�s�z o ��xHztskz?vHxHo �N� z � zt��x�orv�xF}$|�x���u�� �g�or�r�q?�ru�vYz�|-x � u�skz�xF}$|���# ����� �Bzts�uNc$�Nq?z4u��%$�|���c$|�sk� ���$�����>� d

& o � zt��|�� z � zt��x�' � xF}Nz��$s�z � |-�rzt��x q?u��Nq?zt�NxHoru�� u-w orxHv)�$sku�}$|�}Nor�roMx���orv)xF}$|�xboMxborv{| � zt|-v$c$s�z{u-w]xF}NzwKs�zb cNzt�Nq?�Rg�orxF}Pgi}NoMq?}(' uNq?q@c$s�v � g }Nzt�Rg{z s�zt�$zt|�x � |����CxHo � z?v |��pzh$�$zts�o � zt��xug�orxF}2�$u�vHvYo }N�rzu�cNxHq?u � z?v�''|�� ��)'P�c�Nu�x*' � d ~ � o��ezts�zt��x �Nu�xYoMuN�#oMv xF}$|-x�xF}Nz'�$s�u�}$|�}NoM�rorx��Pu-w+'�s�zt�$skz?vHzt��xYv xF}Nz, o.-�z+o�o5y0/�1�o32�qso4/P}Nz?� � }�� |'�Bzts�vHu��@xF}$|-x4x;}Nz z � zt��x5':g�or�r�)uNq?q@c$s o �#|�vYo �N���Mz�zh$�$ztsko � zt��x@d e_w |�$ztskvHu��p|-vHvHor���Nv�| �$s�u�}$|�}Nor�rorx �Cu-w � xHu�' � x;}Nzt�'}Nzu}$z?�rorz � z?v\g oMx;}'q?ztskxF|-o ��x���xF}$|�x�'�g�or�M�buNq?q@c$sd�e_w}Nz |-vYvHor���Nv4|��$s�u�}$|�}Nor�rorx�� u-w � xYu�' � xF}Nzt� }Nzu}Bz?�Morz � z?v^g�orxF}Cq?zts�xF|-o ��x �CxF}$|-x�'Ig oM�r�{�Nu�x4}$|��$�$zt�Ede_w }Nz |�vHvHor���Nv�|��$sku�}$|�}Nor�roMx�� }Bz?x+g z?zt� � |�� ��� xHu6' � xF}Nzt� }Nz oMv xHu�vHu � z � z?��s�z?z5c$�Nv�c$s�z |�}Bu�cNxg }Nz?xF}Nzts�u�s��Nu�x�'ag�or�r�uNq?q@c$sd

� }Nz'o ��xYztsH�$s�z?xF|-xYoMuN�Su�w�|W�$s�uN}$|�}Nor�Morx�� |-v�|pwKs�zb>cNzt�Nq?�So ��| vHztskoMz?v�u�w�s�zt�$zt|-x�zh$�$ztsko � zt��xHvorv xFsH| � oMxYoMuN�$|-�r�M�Sskz;w0ztsHskz � xHu |-v�xF}NzPy7198o;:�vxq=<�o�u�s>/rz+o@?BANo@tMvxq pvbo ��xHztsY�$s�z?xF|-xHoru��Ed eK�#q?u���xFsH|�vHx � xF}Nzo ��xYztsH�$s�z?xF|-xYoMuN�Su�w�|W�$s�uN}$|�}Nor�Morx�� |-v�| � z?��skz?z<u�wG}$z?�rorz;w orv�qt|-�r�Mz � xF}Nz pCAD198o;:�vxq=<�o u�s j�l�n*opqFl�to ��xYztsH�$s�z?xF|-xYoMuN� � o � }NuN�Nu�sbu-wexF}Nziy{z � zts�zt� ��� }Nu � |�v � |&��z?v � |�vYq?oMzt��xHorvHx wKs�u � xF}Nz � o � � � � ��� vOg }Nu}Nz?� �$z � xHu �Noru��Nz?zts xF}Nz�xF}Nz?u�s��2u-w �$sku�}$|�}Nor�roMvYxHorq<o ��wczts�zt�Nq?z � � |&��z?v �t�����>� � |-qf�o �N� ���t� � ��� d ~ vg{z v;}$|-�r��vHz?z o � � z?q?xYoMuN� ��� xF}Nz wKs�zb>cNzt��xHorvHx�o ��xHztsH�$s�z?xF|�xHoru��#orv |CvF�$z?q?o |-��qt|�vHz u�w xF}Nz � |&��z?vHo |��o ��xYztsH�$s�z?xF|-xYoMuN�Ed

e �pxF}Nz � |&��z?vHo |��Co ��xHztsY�$s�z?xF|-xHoru�� � |��$s�u�}$|�}Nor�rorx�� u�sC}$z?�rorz;wkg�or�r� |���g�|&�Nv � zt�Bzt� � u��CxF}Nz vHxF|-xHzu-wifN�Nu*g��rz � ��z4u-wbxF}Nz �$ztskvHu���gi}Nu �$s�u � o � z?v xF}$|�x �$s�u�}$|�}Nor�rorx���d���u�s{zh$| � �N�rz � o wSg{z\g{zts�z�xHu ��o � zvHu � z?u��Nzj| q?u�o � � }Nz�g{u�cN� � �Mo9f-z?�r�'|-vYvHor��� | �$s�u�}$|�}Nor�rorx�� u-w �BE�� xHu xF}Nz z � zt��x xF}$|-x)x;}Nz q?u�o �:g{u�cN� �

Page 4: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

vF}Nu*g }Nzt| � v u�� xF}Nz<�NzhNx xYu�vHv@d�e0w � }Nu*g z � zts � g{z'q?u�� � o �Nq?z � xF}$|�x �$zts�vYu��PxF}$|�x xF}Nz'q?u�o � g�|-vg{z?or��}�xYz � o �2wK| � u�siu-wj}Nzt| � v � }Nz5g{u�cN� � |-vHvHor���#|p}Nor��}Nzts �$s�u�}$|�}NoM�rorx��WxYu'xF}Nz z � zt��x@d � }�cNv � g{zg s�orxHz{xF}Nzi�$s�u�}$|�}Nor�rorx ��u-w '�|-v � � '�� � �?� g }Norq?}�orv s�zt| � |�vbxF}Nz��$s�u�}$|�}Nor�rorx � u-w ' -Nq=<�o@t��Md � }Nz�vH� � }$u��� s�zt�$s�z?vHzt��xHv�x;}Nz4vHxF|�xHz u�wKfN�Nu*g��rz � ��z�u-wbxF}Nz4�$zts�vYu���g }Nu �$s�u � o � z?vixF}Nz4�$s�u�}$|�}Nor�rorx���d

~ �rvHu � o � xF}Norv{o ��xHztsH�$skz?xF|-xHoru�� � |��$zts�vYu�� qt|�� |-vYvHz?vHv�|4�$s�uN}$|�}Nor�Morx���}$|-vHz � u�� o ��w0u�s � |-xHoru�� xF}$|-x}NzIl*p$p A��Go pxHuI}$zixFs�cNz�dL��uNsbzh$| � �N�rz � u�c$sbq?u�o � xHu�vHvYztsbqt|�� |�vHvHz?vHv xF}Nzj�$sku�}$|�}Nor�roMx�� x;}$|-x)xF}Nz q?u�o �g{u�cN� � vF}Nu*g }Nzt| � v u�� x;}Nz z?�rz � zt��xF} xHu�vYv � c$� � zts{xF}Nz�|-vHv$c � �NxYoMuN� xF}$|-x)x;}Nz vF| � z q?u�o � q?u � z?v�c$�}Nzt| � v�uN� zt|-q?} u-wxF}NzB� s�vHx{xHzt� xHu�vHvYz?v@d�� z�gis�orxHz � �4'��� '� ��� � xYu � zt�Nu�xHz�x;}Nzj�$s�uN}$|�}Nor�Morx�� u-wz � zt��x' � -Nq=<�o@t�xF}$|�x�z � zt��x�' orvixFs�cNz4|�� � ��o � zt� }$|-qf���sku�c$� � f��Nu*g��rz � ��z��Md

n |���� s�z?vHzt|�skqQ}Nzts�v�}$| � zCg s�orxHxHzt� � u*g � � o �ezts�zt��x{vHz?xHv{u-w �$sku��$zts�xYoMz?v xF}$|-x)v;}Nu�cN� � }$zivF|-xYoMv ��z �}�� � z?��s�z?z?v{u-w/}$z?�rorz;wk�_z�d �Wd � �{u*h �t�*���>�7& uNu � �t�����>� � | � |���z �t�����M� ��z�bo �Nz?xHxHo �t� � ��� � sku � zt|-q?}�u-wxF}Nz �MorvHxYvu-w��$s�u��Bzts�xHorz?v � xF}Nz?vYz s�z?vHzt|�s�qQ}Nztskv}$| � z � zts�o � z � xF}NzbvF| � z s�cN�rz?v��SxF}Nz{s�cN�rz?vbu-w��$s�u�}$|�}Nor�rorx ��d� g{uu}$|-vHorq�s4cN�Mz?v � wKs�u � g }Norq?}�u�xF}Nzts s�cN�rz?v � |&��}$z � zts�o � z �e� |�s�z x;}Nzup A�� z@A72�o � g }Norq?}�vF|&�Nv�xF}$|-xwcu�s�|���� z � zt��x�'�|�� � orxHv�q?u � �N�Mz � zt��x )' �

� �4'�� � ��� � � )'�� � ��� �

|�� � xF}Nz��Az+y , A7:@vJz@A 2#o � gi}NoMq?}�v;|t�Nv�xF}$|�x)wcu�s�|���� x+g u�z � zt��xHv�' |�� � ' � �

� �4'� �;'��� � ��� � �4' ��� '� ��� � � �4'� � � �

g }Nzts�z � �4'� �@' ��� � �)� zt�Nu�xHz?v x;}Nz4�$s�u�}$|�}Nor�rorx �CxF}$|-x '� |�� � ' ��|�s�z�x;s�cNz���o � zt���Md� x;}Nztsbq?u � � u��N�r� cNvYz � s�cN�rz?v�|�s�z u-w0xYzt��zh �$skz?vHvHz � o � xHzts � v)u-w � |�s�o |�}N�rz?v sY|-xF}Nztsbx;}$|���z � zt��xHv@d

~ <�l�z�qFl 1 2#ox;|�f-z?v�u�� � |-�9cNz?vbwKs�u � | q?u��r�Mz?q?xYoMuN��u-w � cNx$c$|��M�r� zh�q?�9cNvHo � z |�� � q?u��M�rz?q?xHo � z?�r� zh$}$|�cNvHxYo � zvHxF|�xHz?v � g }Nzts�z�zt|-q?}'vYxF|-xHz q?u�sHs�z?vF�Bu�� � v4xYu vHu � z�z � zt��x�d ~ � |�sko |�}N�Mz � |&��}$z , q9p :@z+o�vxo � }$| � o �N�'|� �NorxHz�u�s q?u�c$��xF|�}N�rz���c � }$zts u-w�vHxF|-xHz?v � uNs4orx � |&�P}$z :�y�tMvxqst ANy�A�prd ��uNs4zh$| � �N�rz � |Cx+g{u*�KvHxF|�xHzu�s�1 qFtWl�z�n � |�sko |�}N�Mz qt|���}BzGcNvHz � xHu skzt�$s�z?vHzt��x xF}Nz��$u�vYvHo9}N�Mz u�cNxHq?u � z?v u-w | q?u�o ��!�o � � g }Nzts�zt|-v�|q?u���xHo ��cNuNcNv � |�s�o |�}N�rz�qt|�� }$zucNvHz � xHu�s�zt�$s�z?vHzt��x x;}NzGg{z?or��}�x u�w xF}Nz�q?u�o �EdCeK�CxF}Norv4�$|��$zts � g zIcNvHz�ru*g zts��Kqt|-vHz��rz?xHxHzts�v��xcNv$c$|-�r�r�W�Nzt|�sixF}Nz zt� � u-w x;}Nz |-� �$}$|�}$z?x � xHu's�zt�$skz?vHzt��x vHo �N���rz � |�s�o |�}N�rz?v |�� �c$�$�$zts��Kqt|-vHz��rz?xHxHzts�v xHu<skzt�$s�z?vHzt��x4vHz?xHv u-w � |�sko |�}N�Mz?v�d'� z^g s�orxHz�� ��� xHu � zt�Nu�xYz xF}$|�x � |�s�o |�}N�rz�porv�o �pvHxF|�xHz � d � }Nzt��g{z�u�}NvHzts � z�xF}Nz�vHxF|-xHz w0uNs�z � ztsk� � |�s�o |�}N�rz o �CvHz?x�� � g{z�qt|-�r�bxF}Norv4vYz?x u-wu�}NvHzts � |-xHoru��Nv�| vHxF|-xYz�u�w � � |�� � g skoMxYz!� �"� d � u � z?xHo � z?v � g{z��rzt| � z xF}Nz vYxF|-xHz�u-w�| � |�s�o |�}N�rzu�s vHz?x�u-w � |�s�o |�}N�rz?v4o � �N�rorq?orx@d � }Nz��Az+y 14l 1q92#qFvxn , q prvxz�q 1 A�vxqsy�tPy <@o@z�l�po@vOy0/�<@l�z�qFl71 2#op#� �$� zt�Nu�xYz �� �$�%� � �?� orv xF}Nz�vYz?x�u-w)�$s�u�}$|�}Nor�rorxHorz?v � �$� �&� � � � w0u�s |-�r�evHxF|-xYz?v u�w'��d

(*)!+�,.-0/21�34- 5*6879-�:;34- <>=?1�38- 5$79-A@�38@�:�B868C*7>64D <>,�:�E�F�GH/!I JLKM7>:;:*3ONP,Q5$7>NP,�:R1�64<9<>,QST6�U�C.38D�68D�79<97V5$=0S ,W-�:$7>5X=OYZ)!+�,.-�/1�38- 5*6479-:[D\3O5$+]S^7>:*1WC.,Q5*,_64-SP1�38- 5$79-A@�38@�:RB864C*7>68D�<>,Q:�EOF�GH/!I JAK�7>:[:*3`NP,�5$7>NP,Q:[1�68<9<>,�S?6;aO,W-,WC.68<97>b�,�S�U C.34D64D 79<97>5$=cS�,.-�:$7>5X=OY)0,�S�3d-3O5;NP64eL,�5$+�,Q:*,�S^7>:*5$79-1�5$7>34-�:f79-g5$+�7>:RU�68U\,WC8Y

Page 5: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� �Nz q?u � � uN� s�cN�rz u-w �$sku�}$|�}Nor�roMx��CoMvajml�nQo p � v��No$y�z+o����� � � � � ��� � � � ����� � ��� �

� ��� � � � � �$�%� � � wcu�s � ��� � � ���g�

� zts�z � � � � � � � orv4xF}Nz �$s�uN}$|�}Nor�Morx�� � orvHxFsko }>cNxYoMuN� u-wP� }Bz;w0uNs�zug{zuf��Nu*g�� � |�� � � � � � � ��� � oMv xF}Nz�$s�u�}$|�}NoM�rorx�� � orvHxFs�o9}>cNxHoru��#u�w]� |&wcxHzts�g{z5fN�Nu*g�:d � }Nz?vHz � orvHxFs�o9}>cNxHoru��Nv |�s�z vHu � z?xHo � z?v4qt|��M�rz �xF}NzT�Az�qFy�z�p4|�� � �>y*pvxo@z�qFy�z4p u�w � � skz?vF�$z?q?xHo � z?�r��d�eK� � |����Cqt|-vHz?v � u��N�r�<x;}Nz skz?� |�xHo � z �$u�vHxHzts�oru�siu-w� orviu-wbo ��xHzts�z?vYx@dSeK� xF}Norv�qt|-vHz �W� |&��z?v��x;}Nz?u�s�z � orvCg s�orxHxHzt�

� �$�%� �P��� �R� � � ��� � � ��� � � �$�%� � �g }Nzts�z � orv�| �Nu�s � |-�ro��t|�xHoru���q?u��NvYxF|���x@d ~ �Nu�x;}Nzts�s�cN�rz4orvixF}Nz�:���l�qFt z@A 2#o��

� �*� ���������`����� � �������� � �*� � �9� ���������`� ��� ��� �

� z v;}$|-�r� vYz?z xF}$|-x xF}Norv�s�cN�rz oMv�o � �Bu�s�xF|���x4o �2xF}Nz � z�� �NorxHoru��#u-w � |&��z?vHo |�� �Nz?x+g{u�s�f�v@d ~ �rvHu � g{z}$| � z�xF}Nz -No@tMo�z+l�2#q��o , pCA�� z@A 2#o��

��� � �$� ��� � � ��� � �$�%� � �g }Nzts�z�� �

orv�| ��zt�NztsH|-�ro#�?z � v$c � x;}$|-x{o �Nq?�9c � z?v o ��xHz?��sY|-�rv�g }Nzt��vYu � z�u�s{|-�r��u-wxF}Nz � |�s�o |�}N�rz?vio ���|�s�z�q?u���xHo �NcNu�cNv@d2�bo �$|-�r�r� � g{z4}$| � z�xF}Nzuo �8�>l�t>pqFy�t�z@A72�o��

� �$�%� � �_� ��� � �$�%� �P��� � � ��� � � �� }Nz � |&��z?vHo |��p�$}Nor�ru�vHu��$}��pzh�xYzt� � v�xHu � z?q?orvHoru�� � |�f�o �N��c$� � zts\c$�Nq?zts�x;|-o ��x��'o � | � orvHq?o �N�roD�Nz

fN�NuQgi�W|-v , o@:@q prqsy�t�v���o�y�z�nQdPe �#��zt�NztsH|-� � | � z?q?orvHoru��S}$|-v�xF}$skz?z q?u � �$u��Nzt��xHv��^g }$|-x�| � z?q?orvHoru��� |�f�ztsbqt|�� � u��c}Norvkl 2�vxo�z$tWl�vxq9<@op �?� g }$|-x }Nz�fN�NuQg vk�c}Norv514oB2#qso4/�p �?� |�� � g }$|-x�}NzCg�|���xHv�� }NoMv]�Az+o4/o@z"!o@t :$o p � d�eK� � z?q?orvHoru�� xF}Nz?u�s�� � g{z�cNvHz | , o@:@q prqsy�t%<@l�z�qsl 1 2#obxHu4skzt�$s�z?vHzt��x)|ivHz?xbu-w � cNx$c$|-�r�r��zh�q?�9cNvHo � z|�� � zh$}$|�cNvHxHo � z |-�rxHztsH�$|�xHo � z?v �E� |&��z?vYo |��<�$sku�}$|�}Nor�roMxYoMz?v�xHu�s�zt�$s�z?vYzt��x�| � z?q?orvHoru�� � |�f�zts� v�}Bz?�Morz;wcv �|�� � ANvxq=2#qsvxqFo p4xHuWskzt�$s�z?vHzt��x | � z?q?oMvYoMuN� � |�f-zts� v��$s�z;wczts�zt�Nq?z?v@dP��z?q?orvHoru�� xF}Nz?u�s��P}$|-v�z?vHvHzt��xHo |-�r�r�u��Nz�s�cN�rz#���Il$�Qq$�Iq��o�o �8� o@:@vxo , A�vxq92#qFvxn �_nP�S� � d � }Norv s�cN�rz?v vF|&�Nv4xF}$|-x � ��o � zt�#|CvHz?x4u-w � cNx$c$|-�r�r�zhNq?� cNvYo � z |�� � zh$}$|�cNvHxHo � z�|-�rxHztsH�$|-xHo � z?v � | � z?q?orvHoru�� � |�f-zts{v;}Nu�cN� � � �@� |-vHvHor���C|ucNxHor�roMx��CxHu z � zts���$u�vHvHo9}N�rz u�cNxHq?u � z4u-wbz � zts��'�Bu�vHvHo9}N�rz |-�rxHztsH�$|�xHo � z � � ��� |-vHvYoM�N� � � |&��z?vYo |�� � �$s�u�}$|�}Nor�rorxHorz?v�xHu z � zts���$u�vHvHo9}N�rz4u�cNxHq?u � z ��o � zt� z � ztsk� �$u�vYvHo9}N�Mz�|-�rxHztsH�$|-xYo � z � |�� � � ��� q?}NuNu�vHzixF}Nzj|��MxYztsH�$|-xHo � z�xF}$|�x � |*h��o � o#�?z?v4}Norv�zh �Bz?q?xHz � cNxHor�rorx ��d � z � ztsH|-�bs�z?vHzt|�s�qQ}Nztskvj}$| � z�vF}Nu*g � xF}$|-x�x;}NoMv4s4cN�Mz wcu��r�ruQg v�wKs�u � vYz?xHvu-wbq?u � �Bz?�M�ro �N�'|*hNoru � vG�_z�d �Md �N� u���~ z@c � |��$�C|�� � npu�s���zt�NvHxYztsH� �&�*� � �D� | � |-��z ���t���*�N� d

e �4�$sH|�q?xHorq?z �-� z?q?oMvYoMuN� � |�f�o �N��c$� � zts/c$�Nq?ztskxF|-o ��x���qt|���}Bz�| � o�� q@cN�rxbxF|-v$fWd�eK� wK|-q?x � s�z?vYzt|�s�q?}Nzts�v}$| � z�vF}Nu*g �CxF}$|-x4�Bz?u��N�rz u-wcxHzt� � oru�� |-xHz xF}Nz nP�S� s�cN�rz�� �{� ztskv$f��'|�� �&% |�}$�Nz � |�� �t� � ��� d � }Nz

Page 6: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� z � o |�xHoru��Nvj|�s�z4vHu vHor���No���qt|���x�|�� � �$s�z � orq?xF|�}N�rz�xF}$|-x�vHu � z4s�z?vHzt|�skqQ}Nzts�vi}$| � z�q?u � z4xYu skz�� z?q?xixF}Nzs�cN�rz � % |�}$�Nz � |�� z?x |-�xd �C�t������� dWn |���� u�x;}Nzts s�z?vHzt|�skqQ}Nzts�v � }Nu*g{z � zts � |�s���cNz�xF}$|-x xF}Nz'|*hNoMu � vcNvHz � xHu � ztsko � z xF}Nz4nP�O� s�cN�rz |�s�z4xHuNu q?u � �$z?�r�ro �N�'xHu�s�z���z?q?x � |�� � |�sk��cNz�w(c$s�xF}Nzts xF}$|-x��$z?u��N�rz# v� z � o |�xHoru��Nv{wKs�u � x;}Nz s�cN�rz � |�f-z xF}NzkcNvYz u-w � z?q?orvHoru����KxF}Nz?uNs�z?xHorq4q?u��Nq?zt�NxYv�|�� � s�zt�$skz?vHzt��x;|-xHoru��Nv�|-�r�xF}Nz � uNs�z�o � �$u�skxF|���xG�x� uQg�|�s ���t������� dLe_wbxF}Nzts�z# v |���� � u�c>}Nx � x;}NoMv�|�cNxF}NuNs }$|�v�xF}Nz4� |-xYxHzts � orzg\d� ��� �� �A` �CV�� 2X�� ZBY����

~ �Az+y 1 2#o � , y\�Il�qst��_u�s>A�tWq=<�o@z4pro � orv� cNvHx�| vHz?x{u-w � |�s�o |�}N�rz?v@d ~�� |&��z?vHo |�� �Nz?x+g uNs�f oMv�| � u � z?��u-wxF}Nz��xcNv$c$|-�r�r��c$�Nq?zts�xF|-o � � s�z?� |-xHoru��NvF}No �Nv4| � u��N� � |�s�o |�}N�rz?v�o �C| � u � |�o �Ed npu�s�z4�$s�z?q?orvHz?�r� � ��o � zt�C|� u � |�o � u-w � |�s�o |�}N�rz?v� � � � L�������8�`����� � xF}Nz 8ry�qstMvM�Az+y 1�l71q92�qsvxn , q9pvxz�q 1 A�vxqsy�t>/ry�z� orv)|��$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru�� u � zts�|-�r�$xF}Nz{vHxF|-xHz?v�u-wGd ~ � |&��z?vHo |����Nz?x+g{u�s�f wcu�s��s�zt�$s�z?vHzt��xHv)|���u�o ��x)�$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru�� w0u�s�Gd � }Nz@skzt�$s�z?vHzt��xF|-xHoru�� q?u��NvHorvHxHv u-w�|2vHz?x u�w4�MuNqt|-�iq?u�� � orxHoru��$|-�4�$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru��Nv � q?u � }No �Nz � g oMx;}�|4vYz?x�u-w |-vYvHzts�xHoru��Nv{u-wbq?u�� � orxHoru��$|-�eo � � zt�Bzt� � zt�Nq?z xF}$|-x�|-�r�ru*g u��NzxHu q?uN�NvHxFs�cNq?x{xF}Nz ���ru�}$|-����u�o ��x � oMvYxFs�o9}>cNxHoru�� wKs�u � xF}Nz��ru�qt|-� � orvHxFs�o9}>cNxHoru��Nv�d

� u�or�r� cNvYxFsH|-xHzixF}Nz�s�zt�$s�z?vYzt��xF|�xHoru�� � �rz?xicNv q?u��NvHo � zts xF}Nz � u � |-o ��u�w x;s�u�c>}N�rz?vF}NuNu�xHo �N��|iqt|�s xF}$|-xg{u�� x�vYxF|�s�x@d � }Nz�� s�vHx�vHxYzt��o �pq?u��NvHx;s�cNq?xHo �N�'| � |&��z?vHo |��p�Nz?x+g{u�s�f orv�xHu � z?q?o � z:g }$|-x � |�sko |�}N�Mz?v|�� � vYxF|-xHz?v�xHu � u � z?�xd � �Nz �Bu�vHvHo9}N�rz qQ}Nu�orq?z u-w � |�s�o |�}N�rz?v w0uNs�xF}Norv � u � |-o �porv:jml�vxvxo@z�n���� � g�orxF}vHxF|�xHz?v{��u�u � |�� � }$| �e��� ANoB2A��� � g�orxF} vYxF|-xHz?v��Nu�x�z � �Nx � |�� � z � �Nx�� ��� l�A3-�oI��� � g�orxF} vHxF|�xHz?v��Nu�xz � �Nx���|�� � z � �Nx�� ��� ANz�t � <@o�z\�"! � g�orxF}�vHx;|-xHz?v{��z?v |�� � �Nu � |�� �$# vxl�z�vS��% � g�orxF}�vYxF|-xHz?v���z?v |�� ��NuMd � weq?u�c$s�vHz � g{z{q?u�cN� � o �Nq?�9c � z � |���� � u�s�z � |�s�o |�}N�rz?va� |-v/g{z�g{u�cN� � o � |�skzt|-���(g uNs�� � zh | � �N�rz � d~ �MvYu � g{z q?u�cN� �@� u � z?��xF}Nz4vYxF|-xHz?viu-wbu��Nz�u�s � u�skz4u-w)xF}Nz?vYz � |�s�o |�}N�rz?v4|-xj| � �Nzts �Mz � z?�bu-w � z?x;|-or��d��uNs�zh$| � �N�rz � g{z�q?u�cN� � �rz?x � l AB-No\}$z | q?u���xYo �NcNu�cNv � |�s�o |�}N�rzIg�orxF}CvHxF|-xHz?visH|��N��o �N� w s�u � �'& xHu�t���(& d

� }Nz�vYz?q?u�� � vYxHzt�Co �2q?u��NvHx;s�cNq?xHo �N�<| � |&��z?vHo |�� �Nz?x+g{u�s�f orv4xHu�q?u��NvYxFs�cNq?x4| � o s�z?q?xYz � |-q?�Nq?�Morq��sH|��$}�xF}$|-x�zt�Nq?u � z?v)|-vHvHzts�xYoMuN�Nvu-w�q?uN� � oMxYoMuN�$|-��o � � zt�$zt� � zt�Nq?z�d{�2z)qt|-�r�$xF}Norvb��sH|��$}�xF}NzBjml�nQo prqsl�t�!tMo�vxw2y�z4{�prvxz@A :�v4A�z+o*) & o � zt�#| � u � |�o �+ �,� � �������8�O� � � � g{z qt|�� g s�orxHz xF}Nz-��u�o ��x �$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru��Cu-w. cNvYo �N� xF}Nz�q?}$|-o �'s�cN�rz u-w �$sku�}$|�}Nor�roMx��'|-v�w0u��r�ru*g�v��

� �*�ZA�������8�O� ��� � ������ � � � � � �9�ZA�������8�O� ��� L��� � � � �@�

~ uQg � w0u�s z � zts�� � � � xF}Nzts�zJg�or�r�A}Bz�vHu � z{v$c>}NvYz?x�/ ��0 � � �������8�`� � � v�cNqQ}�x;}$|-x'� � |�� �1� � �������8�O� � �|�s�z�q?uN� � oMxYoMuN�$|-�r�M�Co � � zt�$zt� � zt��x4��o � zt�2/ � d � }$|-x{orv �

� �*� � �9�Z �������Q�O� ��� ��� �_� � �*� � �3/ � ��� � � ���

� }Nz?vHz�q?uN� � oMxYoMuN�$|-�o � � zt�Bzt� � zt�Nq?o z?v � z�� �Nz xF}Nz � |t��z?vHo |���� �Nz?x+g uNs�f vYxFs�cNq?x$c$s�z�d � }Nz4�Nu � z?vio � xF}Nz

Page 7: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

Battery Fuel

Gauge

Turn OverStart

p(b=bad | ξ) = 0.02

p(f=empty | ξ) = 0.05

p(g=empty | b=good, f=not empty,ξ) = 0.04p(g=empty | b=good, f=empty,ξ) = 0.97p(g=empty | b=bad, f=not empty,ξ) = 0.10p(g=empty | b=bad, f=empty,ξ) = 0.99

p(t=no | b=good,ξ) = 0.03p(t=no | b=bad,ξ) = 0.98 p(s=no | t=yes, f=not empty,ξ) = 0.01

p(s=no | t=yes, f=empty ,ξ) = 0.92p(s=no | t=no, f=not empty ,ξ) = 1.0p(s=no | t=no, f=empty ,ξ) = 1.0

�bor��c$s�z � � ~ � |&��z?vHo |���� �Nz?x+g{u�s�f wcu�s�x;s�u�c>}N�rz?vF}NuNu�xHo �N�<| qt|�sixF}$|-xCg{u�� x�vYxF|�s�x@d ~ s�q?v4|�s�z � sH|�g �wKs�u � qt|�cNvHz�xHu z�� z?q?x�d � }Nz �ruNqt|-� �$s�uN}$|�}Nor�Morx�� � oMvYxFs�o9}>cNxHoru����_v � |-vYvHu�q?o |-xYz � g�orxF} |4�Nu � zj|�skz�vF}Nu*g �| � �H|-q?zt��x�xHu�xF}Nz��Nu � z�d

vHxFs4cNq?x$c$s�z�q?u�sHs�z?v;�$u�� � xYu � |�s�o |�}N�rz?v�o �pxF}Nz � u � |-o �Ed � }Nz �$|�s�zt��xHv�u-w#� � q?u�sHs�z?v;�$u�� � xYu�xF}Nz�vHz?x/ � d

e �Cu�c$sizh | � �N�rz � cNvHo �N�'x;}Nz�uNs � zts�o �N� � � � � � � ! � |�� � % � g{z }$| � z�xF}Nz�q?u�� � orxHoru��$|��)o � � zt�$zt���� zt�Nq?orz?v

� ���'� ����� �;� � ���'� � � � �"!L� ��� �[���R��� �Z� � �"!A�3����� � � ��%��3��� �[���R��!`��� �Z� � ��%��3�[� !O��� � � ���

�{u��NvYzb cNzt��xH�r� � g{z�u�}Nx;|-o � xF}Nz�vHxFs�cNq?x�c$s�z�vF}Nu*g � o ���bor��c$s�z � d� }Nzu� �$|-� vHxHzt�2o � q?u��NvHxFs4cNq?xHo �N�W| � |&��z?vYo |��W�Nz?x+g{u�s�fporv xYu@|�vHvHz?vHv�xF}Nz��ruNqt|-� � oMvYxFs�o9}>cNxHoru��Nv

� �*� � � / � ��� � �Su��Nz � orvHxFs�o9}>cNxHoru��Cwcu�s z � zts��CvHxF|-xHz u-w / � d � }Nz?vHz � oMvYxFs�o9}>cNxHoru��Nv w0uNs�u�c$si|�cNxHu � u�}Nor�rzzh$| � �N�rz<|�skz vF}Nu*g �#o � �boM�Nc$s�z � dP�{u � }No �No �N� �Kb c$|-xYoMuN�Nv � |�� � �$� g z�vYz?z�xF}$|-x | � |&��z?vHo |���Nz?x+g{u�s�f wcu�s |-�#g�|&�Nv{zt�Nq?u � z?vixF}Nz���u�o ��x �$s�u�}$|�}Nor�rorx�� � oMvYxFs�o9}>cNxHoru�� w0uNs Gd

~ � sH|�g�}$|-qf�u-w � |&��z?vHo |�� �Nz?x+g uNs�f�v�|-v � z�� �Nz � oMv{xF}$|�x��Nz?x+g{u�s�f vHxFs�cNq?x$c$skz � zt�Bzt� � v u�� � |�s�o��|�}N�rz'uNs � ztsd e0wjx;}Nz�u�s � zts orv qQ}Nu�vHzt�#qt|�s�z?�rz?vHvH�r� � xF}Nz'skz?v$cN�rxHo �N� �Nz?x+g{u�s�fpvYxFs�cNq?x$c$s�z � |&�pwK|-or��xHus�z � zt|�� � |�����q?u�� � orxHoru��$|-�)o � � zt�Bzt� � zt�Nq?o z?v o � x;}Nz � u � |-o �Ed ~ v�|��'zhNzts�q?orvHz � xF}Nz s�zt| � ztsiv;}Nu�cN� �q?u��NvHx;s�cNq?x�| � |&��z?vHo |�� �Nz?x+g{u�s�f wcu�sbx;}Nz4|�cNxHu � uN}NoM�rz�xFsku�c>}N�rz?vF}Nu�u�xHzts � u � |-o ��cNvHo �N� xF}Nz�uNs � zts�o �N���% � !`� � � � � � � dM��u�s�x$c$�$|-xYz?�M� � o � �$sH|-q?xHorq?z � g{z{qt|���u-wcxHzt��s�zt| � or�r� |-vHvYzts�xbqt|�cNvF|-��skz?� |�xHoru��NvF}No �Nv�| � u��N�� |�s�o |�}N�rz?v�o �C| � u � |�o � � |�� � qt|���cNvYz�xF}Nz?vHz�|�vHvHzts�xHoru��Nv xHu q?u��NvHx;s�cNq?x | � |&��z?vHo |���� �Nz?x+g{u�s�f�vYxFs�cNq��x$c$s�zJg�orxF}NuNcNx)�$s�z?u�s � zts�o �N� xF}Nz � |�s�o |�}N�rz?v@dS~i| � z?�r� � xHu�q?uN�NvHxFs�cNq?xb| � |t��z?vHo |�� �Nz?x+g{u�s�f wcu�sb|���o � zt�vHz?x{u-w � |�sko |�}N�Mz?v � g{z � sH|�g |�s�q?v w s�u � qt|�cNvHz � |�sko |�}N�Mz?v xHu�xF}Nz?o s�o � � z � o |-xYz�z�� z?q?xYv@dSeK��|�� � u�vHx�|-�r�

Page 8: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

qt|-vHz?v �$� u�o �N� vYu s�z?v�cN�MxYv o �'| � |&��z?vYo |��'�Nz?x+g{u�s�f^g }Nu�vHz�q?u�� � orxHoru��$|�� �Ko � � zt��zt� � z9�Nq?z o � �N�rorqt|-xHoru��Nv|�s�z |-q?q@c$sH|-xHz�d^��u�sizh$| � �N�rz � x;}Nz �Nz?x+g uNs�f�o �R�boM�Nc$s�z � g�|-v�q?uN�NvHxFs�cNq?xHz � cNvHo �N�<x;}Nz |-vHvHztskxHoru��NvxF}$|-x � l AB-No4orv4x;}Nz � o s�z?q?x4qt|�cNv;|-�bz��ez?q?x�u-w�jml�vxvxo@z�n |�� � � A�o32 � � ANz$t � <@o�z�orv�xF}Nz � o s�z?q?x�qt|�cNvF|-�z��ez?q?x�u-wJj�l�vxvxo@z�n � |�� � # vxl�z$v oMv xF}Nz � o s�z?q?xiqt|�cNvF|-�]z��ez?q?x�u-w � ANz$t$� <@o@z{|�� �$� ANoB2#d

� z?qt|�cNvYz4| � |t��z?vHo |����Nz?x+g uNs�f wcu�s{|���� � u � |�o � � z?xYzts � o �Nz?vj| � u�o ��x �$s�u�}$|�}NoM�rorx�� � orvHxFs�o9}>cNxHoru��wcu�sbxF}$|�x � u � |�o � � g{ziqt|�� �So ���$s�o �Nq?o �N�rzO� cNvHz | � |&��z?vHo |�� �Nz?x�g{u�s4f4xYu4q?u � �>cNxYzj|���� �$s�uN}$|�}Nor�Morx��u-w)o ��xHzts�z?vHx@dJ��u�s{zh$| � �N�rz � v$c$�$�Bu�vHzIg{z\g�|���x�xHu q?u � �>cNxHz4xF}Nz��$s�u�}$|�}Nor�rorx�� � orvHx;s�o9}>cNxHoru��Cu-w � A�o32��o � zt� xF}$|-x{xF}Nz�qt|�s � uNz?vF� x vHxF|�s�x�d/�]s�u � x;}Nz4s�cN�rz?v u-w)�$s�u�}$|�}NoM�rorx���g{z4}$| � z

� ���'� % � �Nu ��� ��� � ���[� % � �NuZ� � �� ��% � �Nu�� � � � � ��� ��� � � ����� � � � � !`� % � �Nu�� � �

� ��� ��� ��� � � ����� �[���R� !O� % � �NuZ� � � � ���

eK�#|�s�zt|-���(g{u�s�� � �$s�u�}N�rz � g�orxF}� � |�s�o |�}N�rz?v � xF}Norv |��$�$s�uN|-qQ}@oMv��Nu�x�wczt|-vHo9}N�rz � }Bz?qt|�cNvHz oMx zt��x;|-or�Mvv$c � � o �N� u � zts � � u�s � u�s�z{xHzts � v@d���u�s�x$c$�$|�xHz?�r� � g z{qt|�� zh �N�ru�orx)x;}Nz q?uN� � oMxYoMuN�$|-��o � � zt�$zt� � zt�Nq?o z?vzt�Nq?u � z � o ��| � |&��z?vHo |�� �Nz?x+g uNs�f xHu � |�f-z x;}NoMv q?u � �>cNxF|-xYoMuN� � uNs�z�z�� q?orzt��x@dSeK� x;}NoMv qt|-vHz � ��o � zt�xF}Nz�q?u�� � orxHoru��$|��o � � zt�$zt� � zt�Nq?o z?v4o ���Kb c$|-xYoMuN� �$� �2b>c$|-xHoru�� � }$z?q?u � z?v

� �����3% � �Nu ��� ��� � ���'� � � � � � ���\� � � � � � ��% � �Nu � !O� �[��� � � �"!A�3����� � � � � ���;�3��� �[��� �� � � ����� � � � � � ���\� � � � � � ��% � �Nu�� !O� �[��� � � � !L�3����� � � � � ���;�3��� �[��� �� ���

� }$|-x{orv � q?uN� � oMxYoMuN�$|-�o � � zt�Bzt� � zt�Nq?z �$s�u � cNq?z?v | � z?q?u � �Bu�vHorxHoru�� u-wxF}Nz.��u�o ��xi�$s�u�}$|�}Nor�rorx � � orvHx;s�o��}>cNxHoru�� xF}$|-xeqt|���}$z�cNvHz � o � q?u�� ��c$�Nq?xHoru���g�orxF}�xF}Nz � orvHxFs�o9}>cNxHo � z{� |�gWxHuis�z � cNq?z)xF}Nz � o � zt�NvHoru��$|-�rorx��u-wbxF}Nz�q?u � �>cNx;|-xHoru��Nv@d

� }Nz ��zt�NztsY|-���$s�u�}N�rz � u-w q?u � �>cNxYo �N�#�$s�u�}$|�}Nor�rorxHorz?v u-wio ��xHzts�z?vYx4wKs�u � | �c�$u�vYvHo9}N�M�Po � �N�rorq?orx ���u�o ��x{�$s�u�}$|�}Nor�rorx � � orvHxFs�o9}>cNxHoru�� orv qt|��M�rz � �Az+y 14l 1 q=2#q prvxq9:�qFt /ro�z+o@t :�o@d ~ �r�]zh |-q?x{|-�r��u�s�orxF} � v)wcu�s �$s�u�}��|�}Nor�rorvHxHorq o ��wczts�zt�Nq?z�o � � |&��z?vHo |�� �Nz?x�g{u�s4f�v�zh �N�ru�orxbq?u�� � orxHoru��$|���o � � zt�$zt� � zt�Nq?z4s�uNcN��}N�r��|-vLg{z }$| � z� z?vHqts�o9}Bz �e� |-�rxF}Nu�cN��}�g�orxF} � o �ezts�zt��x)x+g�orvHxYv@d���u�s�zh | � �N�rz � � uQg�|�s � |�� � n |-x;}Nz?vHu���� �t�����@�?�-� � � �vHxHz � � �t�������{� |�� �6� }$|-q?}�xYztsk� �t��������� z � z?�MuN�$z � |�� |-�r��uNs�orxF} � xF}$|-x skz � zts�vHz?v�|�s�q?v{o � xF}Nz��Nz?x+g uNs�fvHxFs4cNq?x$c$s�z5c$��xHor�{xF}Nz |��Nv�g{zts�xHuCxF}Nz ��o � zt�#�$s�u�}$|�}Nor�rorvHxHorq�b>cNzts�� qt|��P}$z's�zt| � � o s�z?q?xH�r� wKs�u � xF}Nz��sH|��$}Ed7e ��xF}Norv�|-�r��u�s�orxF} � � zt|-qQ} |�s�q s�z � zts�vF|-�$q?u�sYs�z?vF�$uN� � v)xHu4|�� |��$�N�roMqt|�xHoru�� u�w � |&��z?v�-x;}Nz?u�s�z � d� zt|�s���� �t���\��� � z � z?�ru��$z � | � z?vHvF|���z�� �$|-vHvHo �N��vHq?}Nz � z�x;}$|-xSc$� � |-xYz?vbxF}Nz �$s�u�}$|�}NoM�rorx�� � oMvYxFs�o9}>cNxHoru��Nvwcu�s�zt|�qQ}p�Nu � z�o � | � |&��z?vHo |��p�Nz?x+g uNs�f o � skz?vF�$u��NvYz�xYu u�}NvYzts � |-xYoMuN�Nv�u-w)u��Nz�u�s � u�s�z � |�s�o |�}N�rz?v@d�e|�c$skoMx4�?zt�'|�� ��� �Norz?��z?� }$|-�rxHztsu� �t������� qts�zt|�xHz � |���|-�r��u�s�orxF} � xF}$|-xO� s�vYx x;sH|��Nv�wcu�s � v xF}Nz � |&��z?vHo |���Nz?x+g{u�s�fpo ��xHuW|pxFskz?z�g }Nzts�z�zt|-q?}S�Nu � z�o �PxF}NzCxFs�z?z�q?u�sHskz?vF�$u�� � v xHuW|pv$c>}NvYz?x u-w � |�s�o |�}N�rz?v o �xF}Nz � u � |-o �Ed � }Nz�|-�r��u�s�orxF} � xF}Nzt�#zh �N�ru�orxHv�vHz � ztsH|-� � |-xF}Nz � |-xYoMqt|�� �$s�u��Bzts�xHorz?v u-w�xF}Norv�xFs�z?z xHu�$zts w0u�s � �$s�u�}$|�}Nor�rorvHxHorq o ��wczts�zt�Nq?z�d�npu�vHx�s�z?q?zt��xH�r� � � ~�� }$s�u�vHoruP� �t���>���{� z � z?�ru��$z � |��Co ��wczts�zt�Nq?z|-�r��u�skoMx;} � x;}$|-x�vHo � �N�ro ��z?v�v�c � v |�� � �$s�u � cNq?xHv�vH� � }Bu��roMqt|��M�r� � |-v�o �#x;}Nz�xFsH|��Nv�wcu�s � |-xHoru��CwKs�u ��2b>c$|-xHoru�� � xHu5�2b>c$|-xHoru�� � d

~ �rxF}Nu�cN��}ag{zbqt|��izh �N�ru�orx)|-vYvHzts�xHoru��Nveu�w q?u�� � orxHoru��$|���o � � zt�$zt� � zt�Nq&z�o �4| � |t��z?vHo |����Nz?x+g uNs�f{wcu�s�$s�u�}$|�}NoM�rorvHxHorq{o ��w0ztskzt�Nq?z � zh$|-q?xeo ��w0ztskzt�Nq?z o � |���|�s�}NorxFsH|�s�� � |&��z?vHo |��4�Nz?x+g{u�s�f�oMvL~ � � }$|�s � � �{u�uN�$zts �

Page 9: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

Battery Fuel

Startbefore d

d

Startafter d

u

�bor��c$s�z � � ~ o � !AcNzt�Nq?z � o |-�NsH| � �_vHxFs�cNq?x�c$s�z � wcu�s�| � z?q?oMvYoMuN�pu-w2g }Nz?xF}Nzts xHu q?}$|��N��z xF}NzG}$|�xHxHzts�� ���z?x{w(cNz?� � uNs � u �Nu�xF}No �N�Md � }Nz v�b c$|�s�z4�Nu � z � skzt�$s�z?vHzt��xHv�u�c$s�|��MxYztsH�$|-xHo � z?v@d � }Nz � o | � uN� � �Nu � z� s�zt�$s�z?vHzt��xHviu�c$sCcNxHor�MorxHorz?v u-w |-�r�x;}Nz��$u�vHvHo9}N�rz u�cNxHq?u � z?v@d � }Nz � u�c>}N�rz��K�ro �Nz�|�s�q w sku � # vxl�z�vexHu �

s�zt�$s�z?vYzt��xHv{xF}Nz�|-vHvYzts�xHoru�� xF}$|-xSg{z�fN�Nu*g�g }Nz?xF}Nzts u�s)�Nu�x x;}Nz qt|�s vHxF|�skxHvSg }Nzt�^g{z � |�f-z � z?q?orvHoru��� d

�t������� dJ� � zt�C|��$�$s�u*h�o � |�xHz4o ��wczts�zt�Nq?z�� w0uNs�zh$| � �N�rz � cNvHo �N��n<uN��xHz�� � |�s��ru � z?xF}Nu � v � orv\~ � � }$|�s ��_�4|-�Nc � |�� � ��c>}�� �/�&���*��� dK��u�s � |�����|��$�N�rorqt|-xHoru��Nv � }Nu*g{z � zts � xF}Nz��Nz?x+g uNs�f�v�|�skz�v � |-�r��zt�Nu�cN��}�_u�s qt|�� }$z�vHo � �N�ro���z � v$c�� q?orzt��xY�M� � vHu xF}$|-xixF}Nz?vHz�q?u � �N�rzhNorx �ps�z?v$cN�rxHv4|�skz��Nu�x w |�xF|-�xd���u�s�x;}Nu�vHz|��$�N�rorqt|-xHoru��Nv�g }Nztskz�xF}NzGcNv$c$|��eo ��w0zts�zt�Nq?z � z?x;}Nu � v |�s�z�o � �$sH|-q?xHorqt|-� � s�z?vHzt|�skqQ}Nzts�vi|�s�z � z � z?�ru��No �N�xHz?q?}$�No#b cNz?vpxF}$|-x�|�s�zpq@cNvHxYu � xF|-or�ru�s�z � xYuS�$|�s�xHorq@cN� |�s'�Nz?x+g{u�s�f#xYu��$u��ru���oMz?v��x� z?qrf-zts � |�� �&�����>�� cNzts � uN� � x�|�� � ��u�u��Bzts �S�&���>�@�?� u�s��$|�skxHorq@cN� |�s�o ��w0ztskzt�Nq?z5b>cNzts�orz?v��cy�| � | � c$skxF}No |�� � ~ ��u���o �Nu�t�����>�D� }$|-qQ}�xHzts{z?xi|-�xd �t������� $�zt�NvHzt�'|�� ��~ � � zts�vHzt� �t������� d

� }Nz�qst�� A�o�t :�o , qFl -�z+l\�goMv)|���zhNxHzt�NvHoru�� u-w�xF}Nz � |&��z?vYo |���� �Nz?x�g{u�s4f s�zt�$skz?vHzt��x;|-xHoru�� xHu � z?q?orvHoru���$s�u�}N�rz � v�dS�]o9f-z�xF}Nz � |&��z?vYo |�� �Nz?x+g uNs�f � |���o � !AcNzt�Nq?z � o |���sH| � q?u���x;|-o �Nv)�Nu � z?v�s�zt�$s�z?vYzt��xHo �N�Ic$���q?zts�xF|�o � � |�s�o |�}N�rz?v�|�� � |�s�q?v�s�zt�$s�z?vHzt��xHo �N�<�$sku�}$|�}Nor�roMvYxHorq � zt�$zt� � zt�Nq?z�dIeK� |���o � !AcNzt�Nq?z � o |-�NsH| ���xF}Nz?vHziq?u��NvHx;s�cNq?xHv |�s�z�qt|-�r�rz � :���l�t :�o\tMy , opb|�� � z�o32#oB<@l�t :�o�l�z0: p � s�z?vF�$z?q?xYo � z?�M��d�e � | �$� oMxYoMuN� � o � !Ac��zt�Nq?z � o |-�NsH| � v � |&� q?u���xF|-o � , o@:@q pqFy�t tMy , op � g }Norq?}'s�zt�$skz?vHzt��x � z?q?oMvYoMuN� � |�s�o |�}N�rz?v � |�� � |-x � u�vHxu��Nz%A�vxq92#qFvxn:tMy , o|Eg }NorqQ}ps�zt�$skz?vHzt��xYvj| � z?q?orvHoru�� � |�f-zts� v �$skz;w0zts�zt�Nq?z?v�d ~ �MvYu � o � !AcNzt�Nq?z � o |-��sH| � v� |&�4q?uN��xF|�o � qFt /ry�zO�Il�vxqsy�t�l�z0:p�|>g }NorqQ} o � � oMqt|�xHz�gi}$|-xborvmfN�Nu*g ��|-x)x;}Nz�xHo � z | � z?q?orvHoru�� orv � | � z�d

��u�s�zh$| � �N�rz � o �#u�c$s xFs�u�c>}N�rz?vF}NuNu�xHo �N� � u � |-o � � v�c$�$�$u�vHz�g{z�}$| � z x;}Nz u��NxYoMuN�Nv�xYu@skzt�N� |�q?zxF}Nz5}$|�xHxHzts�� � ��z?x w<cNz?� w0uNsixF}Nz qt|�s � uNs � u<�Nu�xF}No �N�Md ~ �po � !AcNzt�Nq?z � o |-��sH| � wcu�s xF}Norv � z?q?orvHoru��2oMvvF}Nu*g �Co � �bor��c$s�z � d � }Nz�v�b>c$|�s�z �Nu � z � orv4| � z?q?orvHoru��W�Nu � z |�� � s�zt�$skz?vHzt��xYv�u�c$s�|-�rxHztsH�$|-xYo � z?v@d� }Nz � o | � u�� � �Nu � z � orv x;}NzGcNxHor�rorx � �Nu � z�d � }Nz�|�s�q?v��$u�o ��xHo �N��xHu xF}Nz qQ}$|��Nq?z �0u � |-� � �Nu � z?v�|�s�zs�z?�rz � |��Nq?z'|�s�q?v@d � }Nz |�skq wKs�u ��# vxl�z�v)xYu � orv |�� o ��wcu�s � |-xYoMuN�W|�skq�d�ecxHv��$s�z?vHzt�Nq?z'|-vYvHzts�xHv xF}$|-x �|-x x;}Nz<xYo � z�g{z � |�f-z'xF}Nz � z?q?orvHoru�� � g z f��Nu*g gi}Nz?xF}Nzts uNs �Nu�x xF}NzCqt|�s vYxF|�s�xHv�d e �S��zt�NztsH|-� �

Page 10: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

“tails”“heads”

0 0.2 0.4 0.6 0.8 1

p(θ|ξ)

θ

(a) (b)

�bor��c$s�z � �I�c| ��� }Nz�u�cNxHq?u � z?v u�w�| xF}Nc � }NxF|-qf�!�o �Ed��x} �i~ �$s�u�}$|�}Nor�rorx � � orvHxFsko }>cNxYoMuN�pwcu�s ��� xF}Nz�$}���vHorqt|-���$s�u�}$|�}Nor�rorx �Cu-w)}Nzt| � v@d

o ��w0uNs � |-xHoru��C|�s�q?v �Bu�o ��xiu��N�r��xHu � z?q?orvHoru��p�Nu � z?v � g }Nzts�zt|-v�s�z?�rz � |��Nq?z |�skq?v �$u�o ��x uN�N�M��xYu qQ}$|��Nq?z�Nu � z?v@d

� �� �JYLV\�V�� ��Y�Z��5���G ��+XA ��� ��� � V� ��� �mY� ��� �� ����>�

� z?qt|�cNvHz � |&��z?vHo |�� �Nz?x+g uNs�f�v{}$| � zj|��$s�uN}$|�}Nor�MorvHxYoMq o ��xHztsY�$s�z?xF|-xHoru�� � g{ziqt|��5cNvYz�xFsH| � orxHoru��$|-�]xHz?q?}���No#b cNz?v�wKs�u � � |&��z?vHo |���vYxF|-xHorvHxHorq?v�xHui�Mzt|�sH��xF}Nz?vYz � u � z?�rv�wKs�u ��� |-x;|>de� z � orvHq@cNvHvbxF}Nz?vHz{xHz?q?}$�No#b cNz?vo �CxF}Nz�s�z � |-o � � ztsiu-w)xF}Nz��$|��$ztsd � z � ztsH|-��u-wbxF}Nz�xHz?qQ}$�No#b>cNz?v�xF}$|-xCg{z4�Nz?z � qt|���}Bz � orvHq@cNvHvYz � o �xF}Nz q?u���xYzh�x�u�w �rzt|�sH�No �N��xF}Nz��$s�u�}$|�}Nor�rorx�� � orvHxFs�o9}>cNxHoru��@u-w | vHo �N���rz � |�sko |�}N�Mz�dCeK� xF}Norv vHz?q?xYoMuN� � g{zzh$| � o �Nz4xF}Norviqt|-vHz�d

��u��NvHo � zts{|4q?u � � u�� xF}Nc � }Nx;|-qrf��Su��Nz�g oMx;}�|4s�u�c$� �e� ! |-x�}Nzt| � xF}$|-x{qt|��:}$ziwcu�c$� � o � � u�vHxv$c$�Bzts � |�s�f�z?xHv@d�e_w\g{z�xF}$s�u*g xF}Nz�xF}Nc � }NxF|-qfPc$�Po � xF}Nz'|-o s |�� � �Mz?x o � � |�� � u��P|2}$|�s �e� ! |-xv$c$s wK|-q?z � oMx�g oM�r�{q?u � z�xHu'skz?vHx�z?orxF}Nzts�u��@oMxYv4�$u�o ��x � ��o$l , p � u�siu��@oMxYv4}Nzt| � �+vxl�q92�p �7� |-v�vF}Nu*g �Co ��bor��c$s�z � |�d � � c$�$�Bu�vHz�g{z���o � z�xF}NzixF}Nc � }NxF|-qf�xHu�vHu � z?uN�Nz � gi}Nu xF}Nzt�*!�o �Nviorx � |���� xHo � z?v � |�� �� zt|-v�c$s�z?v)xF}Nz wKsH|-q?xHoru���u�w xYo � z?v x;}Nz�xF}Nc � }Nx;|-qrf q?u � z?v�c$� }Nzt| � v@d ~ w s�zb>cNzt��xHorvHxJg uNcN� � vF|&��xF}Norv�ru��N�*� s�c$� wKsH|-q?xHoru�� orv�| �$s�u�}$|�}Nor�rorx�� � |�� � g uNcN� � u�}NvHzts � z !�o �Nv�u-wexF}NzixF}Nc � }Nx;|-qrf xHu4z?vYxHo � |-xHzixF}Norv�$s�u�}$|�}NoM�rorx���die ��q?u���xFsH|�vHx � wKs�u � xF}Nz � |&��z?vHo |����Bzts�vF�Bz?q?xHo � z � g{z4s�z?q?u����No#�?z4xF}Nz4�Bu�vHvHo9}N�rz � |-�9cNz?v u-wxF}Norv w sY|-q?xHoru�� |-v�| � |�s�o |�}N�rzO�Sqt|-�r��orx � ��g }Nu�vHz xFs�cNz � |�� cNz orvuc$�Nq?zts�xF|-o �EdC� z qt|��pzh �$skz?vHv�u�c$sc$�Nq?zts�xF|�o ��x��'|�}$uNcNx � g oMx;}'| �$s�u�}$|�}Nor�rorx � � orvHxFs�o9}>cNxHoru�� � � � � � �?� |�� � c$� � |-xHz�xF}Norv � orvHx;s�o9}>cNxHoru��p|-vg{z�u�}NvHzts � z�!�o �Nviu-wbxF}Nz�xF}Nc � }NxF|-qfMd

�2z �Nu�xHz�xF}$|-x � |-�rxF}Nu�cN��} � � u�z?v4�Nu�x4skzt�$s�z?vHzt��x4| � z?��s�z?z�u-wm}Bz?�roMz;w � q?u��r�rz?q?xHoru��Nv u-w �ru��N�*� s4c$�wKsH|-q?xHoru��Nv �Mo9f-z � vF|-xYoMvkw0��xF}Nz s4cN�Mz?v u-w�$s�u�}$|�}Nor�rorx���dSeK� xF}Norv �$|��Bzts � g{z v;}$|-�r� s�z;wcztsbxHu � |�v |?� ��n�prq9:$l 2

���Z+ 7>:_,��A6`NdU <>,f7>:;5*64eA,.-�� C.3`N��_3��Z64C.S0G���� �"!AKWY

Page 11: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

xm

θ

x2x1 . . .

�bor��c$s�z � � ~�� |&��z?vYo |���� �Nz?x�g{u�s4fivHxFs�cNq?x$c$skz � zt�Norq?xHo �N� xF}Nz{q?u�� � orxHoru��$|-�$o � � zt�$zt� � zt�Nq?o z?vi|-vHvHuNq?o |-xHz �g�orxF}C|G}No �Nu � o |��vF| � �N�rz�d

�Az+y 14l 1q92#qFvxnI�c|&wcxHzts & u�u �e�E�t������� xHu � orvHxHo �N��cNorvF} oMx�w s�u � | � z?��skz?z u-w2}$z?�rorz;w d � �bor��c$s�z � vF}Nu*g�v{u��Nz�$u�vHvHo9}N�rz �$sku�}$|�}Nor�roMx�� � orvHxFsko }>cNxYoMuN��wcu�s � d

~ u*g v$c$�$�Bu�vHzIg{z�u�}NvHzts � z�� � � �ZA�������8�O���-� � xF}Nz4u�cNxYq?u � z?v�u-w�� !�o �Nv�u-w x;}Nz4xF}Nc � }NxF|-qfMd� z�vYu � z?xHo � z?v{s�z;w0zts xHu�xF}Norv)vYz?x)u-w]u�}NvHzts � |-xHoru��Nv |�v | , l�vxl71�l*po )Oe_w�g{z�fN�NzgSxF}Nz � |-�9cNziu-w �N� xF}Nzt�u�c$s��$s�uN}$|�}Nor�Morx��Cw0uNs }Nzt| � v�uN�<|���� !�o ��g uNcN� � }Bz zb c$|��xHu �N� �Nu � |�xHxHztsi}NuQg � |�����u�cNxHq?u � z?vg{z�u�}NvHzts � z�d � }$|-x{orv �

� �*��� � '�� � %��9� �������8�`� � � ��� ��� �R� � � ���

g }Nzts�z0� � orv�x;}Nz4u�cNxHq?u � z u�w xF}Nz��_x;}�!�o � u-wbxF}Nz�xF}Nc � }Nx;|-qrfWd � o � or� |�s��r� � g z4}$| � z� �*� � � !�������%��9�ZA�������8�O� � � A��� ��� �_� ��� � �4� �

eK�C�$|�s�xHorq@cN� |�s � xF}Nz4u�cNxYq?u � z?v |�skz � cNx$c$|-�r�r��o � � zt�$zt� � zt��x � ��o � zt� � d � z�qt|��Cs�zt�$s�z?vHzt��x�xF}Norviq?u����� orxHoru��$|-��o � � zt�$zt� � zt�Nq?z |-vYvHzts�xHoru���cNvHo �N��| � |&��z?vHo |���� �Nz?x+g{u�s�f�vHx;s�cNq?x$c$s�z � |�v�vF}Nu*g � o ���bor��c$s�z � d

e ��s�zt|-�rorx�� � g{z�|�s�z�c$�Nq?zts�xF|-o �C|�}$u�cNx{xF}Nz � |-�9cNz�u-w � dSe � xF}Norv�qt|-vHz � g{z qt|���cNvHz�xF}Nzizh �$|��NvYoMuN�s�cN�rz4xYu � z?xHzts � o �Nz u�c$s��$s�u�}$|�}NoM�rorx���xF}$|-x�x;}Nz4�Nzh�x�xYu�vHv�u-w�xF}Nz4xF}Nc � }NxF|-qfIg�or�r�q?u � z\c$�'}Nzt| � v��

� �*� �� '�� � %�� � �d��� � �*� �� '�� � %�� � ��� � � � � � � � � ����� � � � � � � � � ����� � � � � �g }Nzts�z � � � � � ��� zt�Nu�xHz?v)xF}Nz zh �Bz?q?xF|-xHoru�� u-w � ��o � zt�T�Md � }$|-x oMv � u�c$s �$s�u�}$|�}Nor�rorx � w0u�s }Nzt| � v)uN��xF}Nz�NzhNx)xHu�vYvboMv � cNvYx)xF}Nz{zh$�$z?q?xF|-xYoMuN� u-w � d2�Ac$s�x;}Nzts � u�s�z � v�c$�$�$u�vHzCg{z !�o � xF}Nz�x;}�c � }NxF|-qf�uN�Nq?z |�� �u�}NvHzts � z4}Nzt| � v@dS� vHo �N� � |&��z?v��x;}Nz?u�s�z ��� x;}Nz4�$u�vHxYzts�oru�s��$s�u�}$|�}NoM�rorx�� � orvHxFsko }>cNxYoMuN��wcu�s � }Bz?q?u � z?v

� � � �9� �� '�� � % ��� ��� � � � � �� '�� � %�� � ��� � � � � � � ��� � � � � � � � �

g }Nzts�z � orv�vHu � z �Nu�s � |-�ro��t|�xHoru��pq?u��NvHx;|���x�d � }$|-x�orv � g z�u�}Nx;|-o �pxF}Nz �$u�vYxHzts�oru�s � orvHx;s�o9}>cNxHoru��pwcu�s� }�� � cN�MxYo �N�r�No �N� orxHv��$s�oru�s � orvHxFsko }>cNxYoMuN��}��pxF}Nz�w(c$�Nq?xHoru�� �2� �*��� � |�� � s�zt�Nu�s � |��Mo#�?o �N�Md � }NoMv���Z+,�B864C*7>64D <>, �d7>:;64<>:*3PC., �H,.C*C.,�S?5*3P6`:R6 � C.,"!O@,W-1�=OE�38D�#*,�1�5$7>B`,fU C.34D64D 79<97 5X=OE�64-S�5$C*@�,_U C.34D64D 79<97 5X=OY

�t�

Page 12: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

0 0.2 0.4 0.6 0.8 10 0.2 0.4 0.6 0.8 1

x →

p(θ|ξ)

θ

p(θ|heads,ξ)

θ0 0.2 0.4 0.6 0.8 1

θ

�bor��c$s�z � � ~ �NsH|��$}Norqt|-� � zt�Norq?xHoru���u�wjxF}Nz cNvHz'u�w � |&��z?v�bxF}Nz?u�s�z � xHu q?u � �>cNxYz'xF}Nzp�$u�vHxYzts�oru�s�$s�u�}$|�}NoM�rorx�� � orvHxFs�o9}>cNxHoru��Cu-wbxF}Nz4�$}���vHorqt|-�b�$s�u�}$|�}NoM�rorx�� � d

�$s�uNq?z � c$s�z orv � zt�Norq?xHz � ��sY|��$}Norqt|-�r�M�po � �bor��c$s�z � d ~ v�zh �Bz?q?xHz �e� x;}Nz��$u�vHxHzts�oru�siorv�vF}No wcxHz � xHu xF}Nzs�or��}�x |�� � orvivH�roM�N}�xH�r�'�$|�sYs�u*g zts d � o � or� |�s��r� � o wSg{z�u�}NvHzts � z4|4vYo �N���Mz�xF|�oM�rv � g z�uN}NxF|-o �

� � � �9� � !�������%\��� ��� � � ��� �*� � � � � � �

eK� ��zt�NztsH|-� � o wSg{z�u�}NvHzts � z }Nzt| � v�|�� � !{xF|-or�rv�o ��x;}Nz � |-xF|�}$|-vHz�� � x;}Nzt�:g z4}$| � z� � � � ! '�� � % � !"� � ��%\��� �_� � � � � � � �Q� � � � � � � �

� }$|-x orv � u��Nq?z�g{z }$| � z�|-vHvHz?vYvHz � |p�$s�oru�s � orvHxFsko }>cNxYoMuN�#wcu�s �N� g{z qt|�� � z?xYzts � o �Nz�orxHv �$u�vHxYzts�oru�s� orvHxFs�o9}>cNxHoru�� ��o � zt�S|����S�$u�vHvHo9}N�rz � |-xF|�}$|�vHz�d ~�u�xHz'xF}$|�x xF}Nz'uNs � zts o � g }Norq?}�g{zCu�}NvHzts � zCxF}Nzu�cNxHq?u � z?v orv o sHskz?�Mz � |���x�xHu xF}Nzp�$u�vHxYzts�oru�sW� |-�r�ixF}$|-x orv�s�z?�rz � |���x�orv xF}Nzp��c � }Bzts u-w4}Nzt| � v�|�� �xF}Nz �Nc � }Bzts�u-w)x;|-or�Mv o �pxF}Nz � |-xF|�}$|�vHz�d�� z v;|t��x;}$|-x |�� � !�|�s�z�| p A�� :@qso@tMvmprvxl�vxq pvxq=: wcu�sixF}Nz� |-xF|�}$|-vHz�d

e �gxF}Norv vHo � �N�rz zh$| � �N�rz � u�c$s u�cNxHq?u � z � |�s�o |�}N�rz@}$|�v u��N�r�gx�g{u vYxF|-xHz?vP� ��o�l , p |�� � vxl�q92 p � d~ uQg � o � |-��o �Nz g z }$| � zp| � orvHqts�z?xYz<uNcNxHq?u � z � |�s�o |�}N�rz � g�orxF}���� � vYxF|-xHz?v@d ��u�s zh | � �N�Mz �xF}Norv � |�s�o |�}N�rz<q?uNcN� � s�zt�$s�z?vHzt��x x;}Nz'u�cNxHq?u � z'u-w�|#s�u��r�iu-w�|2�MuN| � z ��� oMz���� � ��� d ~ v o �gxF}NzxF}Nc � }NxF|-qfpzh | � �N�rz � g{z�qt|�� � z�� �Nz�xF}Nz'�$}��NvHorqt|-� �$s�u�}$|�}NoM�rorxHorz?v�u-w�zt|-q?} u�cNxYq?u � z � g }NorqQ} g{z� zt�Nu�xHz� � ��� � �������4� � ��� ��d�� z |-vYv$c � z{xF}$|-xbzt|-q?}�vHx;|-xHz{orv��Bu�vHvHo9}N�rzivHu4xF}$|�xbzt|-qQ} � �� �S� deK� | �$� orxHoru�� � g{z }$| � z � � � � �� � � d ~ �rvHu � o w/g{zkfN�Nu*gSxF}Nz?vHz��$}���vHorqt|-�e�$s�uN}$|�}Nor�MorxHorz?v � xF}Nzt� xF}Nzu�cNxHq?u � z�u-wbzt|-qQ}��YxHu�vHv���u-w���g oM�r�/}Bz4q?u�� � orxHoru��$|��M�r�po � � zt�$zt� � zt��x�u-wbxF}Nz�u�xF}Nzts{xYu�vHvHz?v � |�� �

� �*� � �&� �9�ZA�������8�O� � � A��� ��� �_� � �� � ���

~ ��� � |-x;|�}$|-vHz�u-wbu�cNxHq?u � z?v � � ���������`��� �4xF}$|-x�v;|-xHorv+��z?vixF}Nz?vHz4q?uN� � oMxYoMuN�Nv�oMviqt|-�r�rz � |�� ��� ���@� !, q$�Io@t>pqsy�tMl�2Z� A72�vxqstMy �Gqsl�2 prl �#� 2�oIw2qsv�� � ��n�pq=:�l�2��Az+y 14l 1 q=2#qsvxqFo p���� & uNu �e�A�&�\����� d�� }Nzt��� � �$�|-v�o �pxF}Nz�xF}Nc � }NxF|-qf�zh$| � �N�rz � x;}Nz�vYzb cNzt�Nq?z orv�vF|-o � xHu�}Bz | 1qstMy\�Iqsl�2 prl\��� 2#o�d � }Nz�q?u��Nq?zt�Nx

���

Page 13: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

u-w)| � cN�rxHo �Nu � o |-��vF| � �N�rz5�c|�� � orxHv���zt�NztsH|��Mo#�t|-xYoMuN� � xF}Nz�sH|�� � u � vF| � �N�rz � g�or�r�2}$z4q?zt��xFsH|�� xYu xF}Nzs�z � |�o �No �N� � orvHq@cNvHvHoru��Nv�o ��x;}NoMv��$|��Bztsd

~ �$|-�ru���uNcNv�xHu�xF}Nz4x;}�c � }NxF|-qf�zh$| � �N�rz � g z�}$| � z

� �*� �&� � � ����� � �� � ��� � � � � � ��� � � �� � � � � ���

g }Nzts�z � � � � � � � � orv�u�c$s��$sku�}$|�}Nor�roMx���xF}$|-x�� � � o �gxF}Nz �Nzh�x�qt|-vYz�d ~ u�xHzpxF}$|�x � }$z?qt|�cNvYz� � � � �� � ��� xF}Nz � orvHxFs�o9}>cNxHoru�� wcu�s �PoMvCxHz?q?}$�NoMqt|��M�r� | � orvHxFs�o9}>cNxHoru�� u � zts x;}Nz � |�sko |�}N�Mz?v� � � � �� �4wcu�s{vHu � z � �_xF}Nz�vH� � }$u�� � � zt�Nu�xHz?v�vYz?x � o�� ztskzt�Nq?z � d ~ �rvHu � ��o � zt�C|���� � |�xF|�}$|-vHz��u-wbu�cNxHq?u � z?v � g z4}$| � z

� ��� � � ��� �_� ����� � ����� �� � ��� � � � � �t���

g }Nzts�z�� oMvixF}Nz4�Nc � }$zts{u-wbxHo � z?vc� �&� o � � � |�� � � orv | �Nu�s � |-�ro#�t|-xHoru���q?uN�NvHxF|���x@d2~�u�xHz�xF}$|-xxF}Nz�q?u�c$��xHv� A�������8�� � |�s�z4|�v$c�� q?oMzt��xivHxF|-xHorvHxYoMqiwcu�s{x;}Nz � cN�rxHo �Nu � o |��vF| � �N�rz�d

& o � zt� | � cN�rxHo �Nu � o |-�]vF| � �N�Mz � |\cNvHzts{orv wKs�z?z xYu |�vHvHz?vHv{|���� �$s�u�}$|�}Nor�rorx � � orvHxFs�o9}>cNxHoru�� w0uNs � deK���$sY|-q?xHorq?z � }Nu*g{z � zts � u��Nz�u-wcxHzt�:cNvHz?v�xF}Nz���o s�orq?}N�Mz?x � orvHxFs�o9}>cNxHoru�� }Bz?qt|�cNvHz�orx }$|-v�vYz � ztsH|-�]q?u�� � z���Norzt��x��$s�u��Bzts�xHorz?v@d � }Nz � |�s�o |�}N�rz?v � |�s�z�v;|-o � xHu }$| � z�|���qFz�q=: � 2#o@v , q prvxz�q41 ANvxqFy�tRw2qFv���o �8� y�tMo@tWvsp�� �������8���� � g }Nzt� xF}Nz4�$s�u�}$|�}NoM�rorx�� � orvHxFs�o9}>cNxHoru��Cu-w ��oMvi��o � zt� }��

� ��� � � ����� ��� � � � �� � � � ��� �

�� � �

���� � �� ��� �S� � ���@�

g }Nzts�z � � � � orv�xF}Nz � l\� �Il w<c$�Nq?xHoru�� � gi}NoMq?}pvF|�xHorv+��z?v � �*� � �@�#� � � �*� � |�� � � � �@�P� � di� }Nzt�xF}Nz � |�s�o |�}N�rz?v � }$| � z | ��o s�orq?}N�Mz?x � orvHxFsko }>cNxYoMuN� � g{z |-�rvHu�vF|&�CxF}$|-x � ��� � � � q9p���qFz�q9:�� 2#o@v ) � }Nzzh$�$u��Nzt��xHv�� � cNvHxJ}$z���s�zt|�xHzts�xF}$|�� � xHu ��c$|�sH|���xHz?z xF}$|-xbxF}Nz � orvHxFs�o9}>cNxHoru�� qt|��:}$z��Nu�s � |-�ro��?z � d~ u�xHz{xF}$|-x xF}Nz{zh �Bu��Nzt��xYv�� |�s�z | w(c$�Nq?xHoru�� u�w xF}Nz�cNvYzts� v)vYxF|-xHz{u-w]o ��wcu�s � |-xHoru��T�Md�� }Nzt� � � �$�xF}Nz���o s�orq?}N�Mz?x � orvHx;s�o9}>cNxHoru��CoMvi|-�rvHu5fN�NuQgi��|-v |614o@vxl , q prvxz�q 1 A�vxqsy�tWd � }Nz4�$s�u�}$|�}NoM�rorx�� � orvHxFs�o9}>cNxHoru��u�� xF}Nz��rz;w0x+� }$|�� � �KvHo � z u-w\�bor��c$s�z � orv | }$z?xF| � oMvYxFs�o9}>cNxHoru���g�orxF} zh �Bu��Nzt��xHv�� ������� � � � |�� ��� �!�"� � � � � d � }Nz#�$s�u�}$|�}Nor�rorx � � orvHxFsko }>cNxYoMuN��u��gxF}Nz s�or��}�x+� }$|�� � �KvHo � z#u-w�xF}Nz ����c$skz<orv'|�}Bz?xF|� orvHxFs�o9}>cNxHoru�� g�orxF} zh$�$uN�Nzt��xHv"� ���#�� � � � |�� � � �!�"� � � � � d

�]s�u � �Kb c$|�xHoru�� �t�$� g{z�vHz?zCxF}$|-x o w4xF}Nzp�$s�oru�s � orvHx;s�o9}>cNxHoru��gu-w �2oMv���o s�orq?}N�rz?x � xF}Nzt� xF}Nz�$u�vHxHzts�oru�s � orvHx;s�o9}>cNxHoru��Cu-w ����o � zt� � |-xF|�}$|�vHz�� � � �ZA�������8�`� �-�4orv |-�rvHu ��o s�orqQ}N�rz?x��

� ��� � � ��� �_� � �� � �

�����$ � � � �� � �t���

� z vF|&�pxF}$|-x4x;}Nz ��o s�orq?}N�Mz?x � oMvYxFs�o9}>cNxHoru��#orv�q?�Mu�vHz � c$� � zts � cN�rxHo �Nu � o |���vF| � �N�ro �N� � uNs�xF}$|-x xF}Nz��o s�orqQ}N�rz?x � orvHxFs�o9}>cNxHoru�� oMvi| :�y�t 8CA3-�l�vxo /l\�Iq=2#nIy0/ , q pvxz$q41 ANvxqFy�t>pbwcu�s � cN�MxYo �Nu � o |-�evF| � �N�Mo �N�Md ~ �MvYu �g }Nzt� � }$|-v)|i��o s�orq?}N�Mz?x � orvHxFsko }>cNxYoMuN� � x;}Nz zh$�$z?q?x;|-xHoru���u-w � �� �Szb c$|��$xHu�xF}Nz��$s�u�}$|�}Nor�rorx�� xF}$|-x

�t�

Page 14: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� �&� o ��xF}NzC� s�vYx�u�}NvHzts � |-xHoru�� � }$|-v�|�vHo � �N�rz zh �$s�z?vYvHoru�� �� � � �� � � ��� � �*� � � � � ��� �

� � �B���

g }Nzts�z�� � � � � � d ~ v�g z�vF}$|��M� vHz?z � xF}Nz?vHz �$s�u��$ztskxHorz?v � |�f�z�x;}Nz���o s�orq?}N�rz?x |�cNvYz;w<cN�{�$s�oru�swcu�s{�rzt|�sH�No �N�Md

~ v$c$s � z?��u-w � z?xF}Nu � v)wcu�s |-vHvHz?vHvYo �N��|I}$z?xF| � oMvYxFs�o9}>cNxHoru�� orv{��o � zt�5}�����o �>f��rzts\� �t� � � � d � }Nz?vHz� z?xF}Nu � v�o �Nq?� c � zpxF}Nz � o s�z?q?x |-vHvHz?vYv � zt��x�u�w�x;}Nz'�$s�u�}$|�}Nor�rorx � � orvHxFs�o9}>cNxHoru���cNvYo �N�Rb cNz?vHxYoMuN�Nv s�z����|�s � o �N� s�z?� |-xYo � z'|�s�zt|-v � |-vYvHz?vHv � zt��x�u-w xF}Nz q@c � cN� |-xHo � z � orvHxFs�o9}>cNxHoru�� w<c$�Nq?xYoMuN��cNvHo �N�pw sY|-q?xHor�rz?v �|-vHvYz?vHvHo �N�'xF}Nz �$u�vHxYzts�oru�s � zt|��Nv�u-w�xF}Nz � orvHxFs�o9}>cNxHoru��2��o � zt� }��$�$u�xF}Nz?xYoMqt|��)z � o � zt�Nq?z � |�� � |-vHvYz?vHv+�� zt��x o �#xF}Nz�wcu�s � u-w�|��#zb cNo � |-�rzt��x�vF| � �N�rz�vHo#�?z�d � }Nz?vYz � z?xF}Nu � v qt|���}$zC��zt�NztsH|-�ro#�?z � g�orxF}� |�s���o �N� � o�� q@cN�rx ��xYu xF}Nz4�Nu�����}No �$|�s���qt|�vHz�d

� }Nz�zb>cNo � |-�rzt��x+�KvF| � �N�Mz��KvYo��?z � z?xF}Nu � ��zt�NztsY|-�ro��?z?v��$|�s�xHorq@cN� |�s��r� g{z?�r��d � }Nz � z?xF}Nu � orvI}$|-vHz �u����Kb c$|-xYoMuN� �B�$� g }NorqQ} vF|&��v x;}$|-xIg z�qt|��S|-vHvYz?vHv |p��o s�orq?}N�Mz?x � orvHxFs�o9}>cNxHoru���}�� |�vHvHz?vHvHo �N�#xF}Nz�$s�u�}$|�}NoM�rorx�� � oMvYxFs�o9}>cNxHoru�� � �*�;� � � wcu�s xF}Nz �Nzh�x�uN}NvHzts � |�xHoru�� � |�� � � d e ��vHu � u�o �N� � g{z � |&�s�zg skoMxYz\�2b>c$|-xHoru�� ��� |�v

� ��� � � ��� � ��� � � � � ��� �� �� ����� �� � ����

g }Nzts�z � orv | �NuNs � |-�ro#�t|-xHoru�� q?u��NvHxF|���x@d ~ vHvHz?vHvHo �N� � �*�_� � � orvivHxFsH|�oM�N}�x�wcu�s+g�|�s � d��Ac$skxF}Nzts � u�skz � xF}Nzwcu��r�Mu*g�o �N� x+g u�u�}NvYzts � |-xYoMuN�Nv�v$cN����z?vYx |�vHo � �N�rz � z?xF}Nu � w0uNs |�vHvHz?vHvHo �N� � d

� }Nz � |�s�o |��Nq?zCu-w4| � orvHxFs�o9}>cNxHoru�� wcu�s �porv |��#o � � orqt|-xHoru��gu-w4}Nu*g � cNqQ}#x;}Nz � zt|��#u�w �orv zh$�$z?q?xHz � xHuCqQ}$|��N��z � ��o � zt�P�Nzg u�}NvHzts � |-xHoru��Nv�d � }Nz }Nor��}Nzts xF}Nz � |�s�o |��Nq?z � xF}Nz ��s�zt|-xHzts xF}Nzzh$�$z?q?xHz � qQ}$|��N��z�dSecx�orvivHu � z?xYo � z?v�vF|-o � x;}$|-x{xF}Nz � |�s�o |��Nq?z4orv | � zt|-v$c$s�z�u�w |ucNvYzts� v�:�y�t� , o@t :$oo ��xF}Nz � zt|�� wcu�s � d � }Nz � |�s�o |��Nq?z u-w x;}Nz���o skoMq?}N�rz?x � orvHx;s�o9}>cNxHoru��CoMvi��o � zt� }��

�� �>� � �� � � ��� � �*� �&� � � � � � � � �*� �&� � � ���� ��� � �t���

� }NcNv � � orv�| s�z@!�z?q?xHoru�� u-wbxF}Nz\cNvHzts� v q?u���� � zt�Nq?z�de � | �$� oMxYoMuN� � v�c$�$�$u�vHzCg{z�g{zts�z�o �NorxHo |-�r�r��q?u � �N�rz?xHz?�r� or���NuNsH|���x |�}Bu�cNx | � u � |-o � �SxF}$|-x orv � u�c$s

� orvHxFs�o9}>cNxHoru�� � ��� � � � g�|-v���o � zt� }��P�Kb c$|-xYoMuN� ��� g�orxF}Czt|-qQ}Czh$�$u��Nzt��x �� � � d�� � c$�$�Bu�vHzug{zxF}Nzt�2vF|�g � qt|-vHz?vIg�orxF}2v$c�� q?orzt��x�vHxF|-xHorvHxYoMq?v � �������8��� � d � }Nzt� � }�� �2b>c$|-xHoru�� �t�$� u�c$s��$s�oru�sg{u�cN� � }Bz�xF}Nz4��o s�orq?}N�Mz?x � orvHxFs�o9}>cNxHoru��C��o � zt� }����2b>c$|-xHoru�� ��� d

� }�cNv � g{z qt|��P|-vHvHz?vYv � |-v�|���o@?BANq=<�l�2#o@tMvBpl\��� 2#o:prq �ro���xF}Nz���c � }$zts u-w u�}NvHzts � |-xHoru��NvIg{zg{u�cN� � }$| � z }$| � xHu'}$| � z�vHz?zt�pvHx;|�s�xHo �N� w s�u � q?u � �N�rz?xHz or���Nu�sY|��Nq?z o �pu�s � ztsixYu'}$| � z�x;}Nz�v;| � zq?u���� � zt�Nq?zpo ��� xF}$|-xug{zp|-q?x$c$|-�r�r�S}$| � z�d���u�s zh | � �N�Mz � g{z g uNcN� � u�}NxF|-o � xF}Nz<�$s�uN}$|�}Nor�Morx��

�Z+ 7>:_U�C*7>38CPSA7>:*5$C*79D @�5$7>38-�1�68-�-3O5_D\, -�38C.NP64<97>b�,QS E 64-ST7>:�:*3`NP,�5$7>NP,�:�1Q64<9<>,�S!64-���������������������������� 3PD\,PNP38C.,U C.,�1W7>:*,OE �Z,;:$+�38@�<>S0:*68=?5$+6O5R,�6`1 +g,��OU\34-,W- 5R7>:_,"!O@64<M5*3P:*3ONP,�-A@NfD\,.C_1.<>3O:*, 5*3Pb�,WC.3 Y

�B�

Page 15: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� orvHxFs�o9}>cNxHoru�� w0uNs � o �:�boM�Nc$s�z � o w/g{z�|-vHvHz?vHvYz � � � '�� � %�� � � xHuG}Bz ��E�� |�� � x;}Nz�zb cNo � |��Mzt��x�vF| � �N�rzvHo#�?z4xYu5}$za� � z�d

� u#wK|�s � g{z }$| � zpu��N�r� q?u��NvHo � zts�z � | � |�sko |�}N�Mz g�orxF} � orvHqtskz?xHz u�cNxHq?u � z?v@d eK� ��zt�NztsH|�� � g{zqt|��go � |-��o �NzP|P�$}��NvHorqt|-�4�$s�uN}$|�}Nor�Morx�� � orvHxFsko }>cNxYoMuN� u � zts�| � |�s�o |�}N�rz � � orvHqts�z?xYz u�s q?u���xHo ��cNuNcNv �wKs�u � g }NorqQ} � |-xF|�}$|�vHz qt|�vHz?v |�s�z � sY|@gi�W|-x sH|�� � u � d � }Norv �$}��NvHorqt|-� �$s�u�}$|�}NoM�rorx�� � orvHxFs�o9}>cNxHoru��x�� �Norqt|-�r�r��qt|���}BzpqQ}$|�sY|-q?xHzts�o#�?z � }��S|�� �NorxHzpvHz?x u-w�� l�z+l\�Io�vxo@z4prd e_w�x;}Nz'u�cNxHq?u � z � |�s�o |�}N�rzpoMv� orvHqts�z?xHz � x;}Nzt�'x;}Nz��$}���vHorqt|-�)�$sku�}$|�}Nor�roMx�� � oMvYxFs�o9}>cNxHoru�� }$|-v�| �$|�sH| � z?xYzts�q?u�sYs�z?vF�$uN� � o �N��xYu zt|-q?}�$}���vHorqt|-�)�$sku�}$|�}Nor�roMx�� o �CxF}Nz � orvHxFs�o9}>cNxHoru����c|�� �e� }Nztskz?o � � g{z�vYu � z?xHo � z?v4s�z;wcztsixHu xF}Nz?vHz �$}��NvHorqt|-��$s�u�}$|�}NoM�rorxHorz?v�|-v �$|�sY| � z?xHzts�v � d/e0w x;}Nz u�cNxYq?u � z � |�s�o |�}N�rz orv{q?u���xHo ��cNuNcNv � xF}Nz �$}���vHorqt|-�e�$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru�� � |&�P}$zP�_z�d �Md � |'�Nu�s � |-� � orvHxFsko }>cNxYoMuN�Ed eK�2xF}Norv qt|-vYz � x;}Nz �$|�sY| � z?xHzts�v�g{u�cN� � }BzxF}Nz � zt|��S|�� �S� |�s�o |��Nq?zpu-wjx;}Nz � orvHxFs�o9}>cNxHoru��Ed ~ � |-x;|�}$|-vHz�u-w4qt|�vHz?v � sH|�g � w s�u � |W�$}��NvHorqt|-��$s�u�}$|�}NoM�rorx�� � orvHxFs�o9}>cNxHoru��Corv u�w0xHzt� qt|��M�rz � |�z+l�t , y\� pl\��� 2#o )

& o � zt� v�cNqQ}#|'�$}���vYoMqt|�� �$s�u�}$|�}Nor�rorx�� � orvHxFsko }>cNxYoMuN� g�orxF} c$�>fN�Nu*g �#�$|�sH| � z?xYzts�v � g{z qt|�� c$���� |-xHz u�c$sS}Bz?�Morz;wcv |�}Bu�cNx)xF}Nz?vYzj�$|�sY| � z?xHzts�vb��o � zt� | sH|�� � u � vF| � �N�rz�wKs�u � xF}Norv � orvHxFs�o9}>cNxHoru���cNvYo �N�xHz?q?}$�No#b cNz?vCvHo � or� |�s xHuWx;}Nu�vHz�g{zp}$| � z � orvHq@cNvHvHz � d ��u�s sY|�� � u � vF| � �N�rz?v wKs�u � � |����S�$| � z �� orvHxFs�o9}>cNxHoru��Nv��So �Nq?�sc � oD�N���NuNs � |-� � & | � � | � |�� � c$�No wcu�s � � oMvYxFs�o9}>cNxHoru��Nv��SxF}NztskzSzhNoMvYx<q?uNsHs�z��vF�Bu�� � o �N� q?u�� ��cN��|-xYzj�$s�oru�skv�xF}$|-x u*�ezts)q?uN� � zt�Norzt��x �$s�u��Bzts�xHorz?v{wcu�s �rzt|�sH�No �N� �$sku�}$|�}Nor�roMxYoMz?v�vYo � oM� |�sxHu xF}Nu�vHz��$s�u��Bzts�xHorz?v4u-w)x;}Nz���o s�orq?}N�rz?x@d � }Nz?vHz �$s�oru�skv4|�s�z4vYu � z?xHo � z?v4s�z;wcztsHs�z � xHu q?u��r�Mz?q?xYo � z?�M�#|-vxF}Nz�o��4� y�tWo@tWvxqFl�2 /rl\�Iq92#nQd � }Nz s�zt| � ztsio ��xHzts�z?vYxHz � o �@�Mzt|�sH�No �N�'|�}$u�cNx�x;}Nz?vHz � oMvYxFs�o9}>cNxHoru��Nv4v;}Nu�cN� �s�zt| � ��z & s�uNu�x\� �t� � �B� ��}$|��NxYzts ��� d

� �� �JYLV\`�V�� ��Y�Z��5���G` ��`+XA` ����� V\Z�� V��CXMYL]\_LX�]�Y

� }Nz��Nu�xHoru�� u-w |�sH|�� � u � vF| � �N�rz{��zt�NztsH|��Mo#�?z?v{xHu � u � |-o �Nvbq?u���x;|-o �No �N� � u�s�z{xF}$|��4uN�Nz � |�sko |�}N�Mzi|-vg{z?�r��d & o � zt��| � u � |-o � � � �ZA�������8�O� ��� � g{z qt|�� o � |-��o �Nz4| � cN�rxHo � |�s�o |-xYz4�$}��NvHorqt|-��$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru�� w0uNs Gd e_w �q?u���x;|-o �Nv�uN�N�M� � oMvYqts�z?xHz � |�s�o |�}N�rz?v � x;}NoMv � orvHxFsko }>cNxYoMuN�#oMv � cNvHx�| � �NoMxYzq?u��r�rz?q?xHoru�� u-w � orvHqts�z?xHz �$}��NvHorqt|-���$s�u�}$|�}Nor�rorxHorz?v@dJe_w�Pq?u���x;|-o �Nvbu��N�r��q?uN��xHo �NcNu�cNv � |�s�o |�}N�rz?v � xF}Norv � oMv �xFs�o9}>cNxHoru�� q?uNcN� � }$z5�0z�d �Md � | � cN�rxHo � |�s�o |-xHz�� �Nu�s � |-� � oMvYxFs�o9}>cNxHoru�� q?}$|�sH|-q?xHztsko��?z � }�� | � zt|�� � z?q?xHu�s|�� � q?u � |�s�o |��Nq?z � |�xFs�o#hAd & o � zt� |4sH|�� � u � vF| � �N�rz w sku � |��$}��NvHorqt|-�e�$s�u�}$|�}NoM�rorx�� � orvHxFs�o9}>cNxHoru�� � g{zqt|��:c$� � |-xYz u�c$s{�$s�oru�skv�|�}$u�cNx xF}Nzj�$|�sH| � z?xHztskv)u-wexF}Nz � orvHxFs�o9}>cNxHoru��Ed � }Norv�c$� � |-xHo �N� orv{z?vF�Bz?q?o |��M�r�vHo � �N�rzIg }Nzt� q?u�� ��cN��|-xHz4�$skoMuNs�v{wcu�s{xF}Nz4�$|�sY| � z?xHzts�vi|�s�z4| � |-or� |�}N�rz �0vHz?z4��z & s�u�u�x �&� � ��� d

~ u*g � }Nu*g{z � zts � �rz?xGcNv�q?u��NvYo � zts xF}Nz wcu��r�ruQg o �N� g sko �>f��rz�d � c$�$�Bu�vHzug{z5fN�Nu*g xF}$|-xixF}Norv � cN���xHo � |�s�o |-xHzW�$}���vYoMqt|�� �$sku�}$|�}Nor�roMx�� � orvHx;s�o9}>cNxHoru�� qt|�� }$z#zt�Nq?u � z � o � vYu � z �$|�s�xHorq@cN� |�s � |&��z?vHo |�����Nz?x+g{u�s�fivHxFs4cNq?x$c$s�z�����d � z � |&�4}$| � z)��u�xHxHzt��x;}NoMvbo ��wcu�s � |�xHoru�� �Pw0uNs�zh | � �N�MzO�PwKs�u � uNc$s�qt|�cNvF|-�fN�NuQg �Mz � ��z |�}$u�cNxixF}Nz � u � |-o �Ed�eK��x;}NoMv�vYz?q?xHoru�� � g{z4q?u��NvHo � ztsixF}Nz xF|-v$f u�w)�Mzt|�sH�No �N��xF}Nz��$|�sY| � �z?xHzts�viu-w� � d{� z � orvHq@cNvYv u��N�r�CxF}Nz4vF�Bz?q?o |-�qt|�vHz\g }Nztskz�|-�r��xF}Nz � |�s�o |�}N�rz?v�o � |�skz � oMvYqts�z?xHz |�� �

��

Page 16: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

g }Nzts�z xF}Nz sY|�� � u � v;| � �N�rz��0o�d z�d ��� |-xF|�}$|-vYz � � �,��� �������8� � � � q?u���xF|-o �Nv��Nu � oMvYvHo �N� � |�xF|��xF}$|-x oMv � zt|-q?}�qt|�vHz � � q?u��NvHorvHxHviu-w)xF}Nz u�}NvHzts � |-xHoru���u�wml�292$xF}Nz � |�sko |�}N�Mz?v�o � ��g z�v;|t��x;}$|-x � oMv:�y\��� 2#o@vxo � dke � � z?q?xHoru�� �$� g{z4q?u��NvHo � zts xF}Nz � uNs�z � o � q@cN�Mx��$s�u�}N�rz � g }Nzts�z � q?u���xF|-o �Nv � orvHvYo �N�� |-xF|�d � c$��xHo �Nz�� �t���*�N� |�� � � z?qrf�zts � |��P|�� ��& z?or��zts�� �t���*��� � orvHq@cNvHv�xF}Nz�qt|-vYz�g }Nzts�z � |&�q?u���xF|-o � q?u���xHo ��cNuNcNv � |�s�o |�}N�rz?v@d

� }Nzt� | � |�xF|�}$|-vHz � orv |�sH|�� � u � vF| � �N�rz�wKs�u � | � cN�rxHo � |�s�o |-xHz��$}��NvHorqt|-�{�$s�u�}$|�}Nor�rorx � � oMv �xFs�o9}>cNxHoru��CxF}$|�x qt|�� }Bz�zt�Nq?u � z � o � � � � g{z�vHo � �N�r�'v;|t��x;}$|-x � orv4|�sH|�� � u � v;| � �N�rz w s�u � ���Ed~ v |��2zh | � �N�Mz � q?uN�NvHo � zts xF}Nz � u � |-o � �q?u��NvHorvHxHo �N�#u-w�x�g{u }No �$|�s�� � |�s�o |�}N�rz?v��S|�� ��� d��]z?x� �� � � ��� � � ��� � |�� � � ��� � zt�Nu�xHz xF}Nz��$|�sH| � z?xHztskvG�_oxd z�d � �$}���vHorqt|-�b�$s�u�}$|�}NoM�rorxHorz?v � w0u�s�xF}Nz.� u�o ��xivF�$|-q?zu-w� � g }Nzts�z � �� orv x;}Nz �$}��NvHorqt|-�e�$s�u�}$|�}NoM�rorx�� u-wexF}Nziz � zt��xSg }Nzts�z?� oMv xFs�cNz�|�� ��� orv w |-�rvHz � |�� � vHuu��Ed��<~�u�xYz xF}$|�x � o ��cNvYo �N� xF}Nz�u � zts�}$|�s � g{z4|�s�z � zt�$|�s�xYo �N� wKs�u � u�c$s vHxF|�� � |�s � �Nu�xF|-xYoMuN�Ed ��� }Nzt� �vF|&�No �N��x;}$|-x�� oMv�|�sH|�� � u � v;| � �N�rz�wKs�u � xF}Nz �Nz?x+g{u�s�f�vYxFs�cNq?x$c$s�z�q?u���xF|-o �No �N�<�Nu'|�s�q5}$z?x+g{z?zt��#|�� ����� orv4xF}Nz�|-vHvHztskxHoru��pxF}$|-x xF}Nz �$|�sY| � z?xHzts�v u-w�xF}Nz-��u�o ��x vF�$|-q?z vF|-xHorv�wc�pxF}Nz o � � zt�Bzt� � zt�Nq?zq?u��NvHx;sH|-o ��xYv � �� � � � ��� � �� � � � ����e|�� � vHu�u�� � g }NztskzO�Pw0u�s zh | � �N�rzO� � � � �� � � �� oMv xF}Nz�$}���vHorqt|-���$sku�}$|�}Nor�roMx�� |-vHvYu�q?o |-xHz � g�orxF} xF}Nz{z � zt��xLg }Nzts�z#��orvbxFs4cNz�d7e xborv)�Nu�x � o�� q@cN�rx)xHuivF}Nu*gPxF}$|-xxF}Norv�|�vHvHzts�xHoru��@oMv�zb>cNo � |-�rzt��x�xYu'xF}Nz |�vHvHzts�xHoru��@xF}$|-x�xF}Nz � |�xF|�}$|-vHz � qt|��P}Bz � z?q?u � �$u�vYz � o ��xHux+g{u � cN�MxYo �Nu � o |-�bvF| � �N�rz?v�� xF}Nz�u�}NvHzts � |-xHoru��Nv�u-w �p|�skz�| � cN�rxHo �Nu � o |-�bvF| � �N�MzIg�orxF}p�$|�sY| � z?xHzts� � |�� � xF}Nz4u�}NvYzts � |-xYoMuN�Nv�u-w � |�skz4| � cN�MxYo �Nu � o |-�v;| � �N�rz�g�orxF}'�$|�sH| � z?xHzts � � d

~ v�|��Nu�xF}Nzts{zh$| � �N�rz � v$c$�$�Bu�vHzIg{z�|-vYvHzts�x�xF}$|�x | � |�xF|�}$|-vHz w0uNs{u�c$s x�g{u � |�s�o |�}N�rz � u � |-o � oMv| sH|�� � u � vF| � �N�Mz w sku � xF}Nz4�Nz?x+g{u�s�f�vYxFs�cNq?x$c$s�z0�� � dS� zts�z � x;}Nzts�z4|�s�z4�Nu q?u��NvHxFsY|-o ��xHv u�� xF}Nz�$|�sH| � z?xHzts�v�u-w x;}Nz ��u�o ��xbvF�$|-q?z�dL�Ac$s�x;}Nzts � u�s�z � x;}NoMv)|�vHvHzts�xHoru�� o � �N�rorz?v{xF}$|-xbxF}Nz � |-xF|�}$|-vHz)orv � | � zc$� u-w |-x � u�vHx xF}$s�z?z�}No �Nu � o |-�evF| � �N�Mz?v���� �@� xF}Nz uN}NvHzts � |�xHoru��Nv{u-w;��|�s�z�|G}No �Nu � o |�� v;| � �N�rz�g�orxF}�$|�sH| � z?xHzts � � � ��� x;}Nz�u�}NvHzts � |-xHoru��Nv u-w � o � x;}Nu�vHz�qt|-vYz?vk�_o w|���� � g }Nztskzg� orv)xFs�cNzi|�s�z |�}No �Nu � o |-�vF| � �N�Mz^g�orxF}p�$|�sH| � z?xYzts � � � � |�� � � ��� x;}Nz�uN}NvHzts � |�xHoru��Nv�u-w � o �pxF}Nu�vHz�qt|-vYz?v5�_o w�|���� � gi}Nzts�z!�orv�wK|-�rvHz |�s�z |:}No �Nu � o |-�)vF| � �N�rzug�orxF}p�$|�sH| � z?xHzts � � � � d4��u��NvHzb>cNzt��xH�r� � xF}Nz uNq?q@c$sHs�zt�Nq?z?v4u�w �po �� |�s�z�q?u�� � orxHoru��$|-�r�r�#o � � zt�Bzt� � zt��x ��o � zt� � � |�� ��� o � qt|-vYz � |�s�z q?u�� � orxHoru��$|-�r�r�Wo � � zt�$zt� � zt��xu-w�xF}Nz u�xF}Nzts�uNq?q@c$sHs�zt�Nq?z?v u�w � o � � ��o � zt� � � � � � � � � � |�� � �2o � qt|�vHz � d � z qt|��p�NsH|��$}Norqt|-�r�r�s�zt�$s�z?vYzt��x xF}Nz�q?u�� � orxHoru��$|-���Ko � � z9�Bzt� � zt�Nq?zP|-vHvHztskxHoru��Nv |�vHvHuNq?o |�xHz � g�orxF}Px;}Nz?vHz<sH|�� � u � vF| � �N�Mz?vcNvHo �N��| � |t��z?vHo |���� �Nz?x+g uNs�f�vHxFs4cNq?x$c$s�z4|-v�v;}NuQgi� o � �bor��c$s�z � |>d

& o � zt� xF}Nziq?u��r�Mz?q?xYoMuN��u-w sY|�� � u � vF| � �N�rz?v�vF}Nu*g � o �:�bor��c$skz � | � orx orv�xYz � �NxHo �N� xHu |��$�N�r� u�c$su��Nz�� � |�s�o |�}N�rz�xHz?q?}$�No�b>cNz?v�xHu��rzt|�sH�2zt|-q?} �$|�sH| � z?xHztsivHzt�$|�sH|�xHz?�r��d �i��wcu�s�x$c$�$|-xYz?�M� � xF}Norv�|��$�$s�u�|-q?}orvj�Nu�x q?u�sYs�z?q?x�g }Nzt�CxF}Nz��$|�sH| � z?xYzts�v |�s�z � zt�Bzt� � zt��x�|-v�vF}Nu*g � o ��xF}Nza����c$s�z�d���u�s{zh$| � �N�rz � |-vg{z vYz?z uNq?q@c$sHs�zt�Nq?z?v u�wg�P|�� � c$� � |-xHz�uNc$sG}Bz?�roMz;wcv�|�}$u�cNx � � u�c$s\}Bz?�Morz;wcv |�}$u�cNx � � � |�� � � � � �g�or�r�)|-�rvHu�q?}$|��N��z�d � c$�$�Bu�vHz � }Nu*g{z � zts � xF}$|-x�|-�r�bu-w)xF}Nz �$|�sY| � z?xHzts�v�|�s�z�o � � zt�$zt� � zt��x � |-vivF}Nu*g �o ���bor��c$s�z � }Ed � }Nzt� � �$s�u � o � z � xF}Nz � |�xF|�}$|-vHz orv q?u � �N�rz?xHz � g{z�qt|���c$� � |-xHz�zt|-q?}S�$|�sY| � z?xHztsvHzt�$|�sY|-xHz?�r��d

�t�

Page 17: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

case 1

case 2

M

x y

x y

θy x| θy x|θx

(a) (b)

case 1

case 2

M

x y

x y

θy x| θy x|θx

�bor��c$s�z � �J�c| �]~�� |&��z?vYo |���� �Nz?x�g{u�s4fivHxFs�cNq?x$c$skzbwcu�sb|�x+g{u*��}No �$|�s���� � |�s�o |�}N�rz � u � |-o � � � � � �)vF}Nu*g�o �N�q?u�� � orxHoru��$|-��o � � zt�Bzt� � zt�Nq?oMz&v<|-vYvHu�q?o |-xYz � g oMx;}PxF}Nzp|-vHvHzts�xYoMuN�PxF}$|-x xF}Nz � |-x;|�}$|-vHz�orv'| sH|�� � u �vF| � �N�Mz wKs�u � xF}Nz vHxFs4cNq?x$c$s�z � � d �x} � ~ �Nu�xF}Nzts � |t��z?vHo |���� �Nz?x+g uNs�fpvHxFs4cNq?x$c$s�z vF}Nu*g�o �N� xF}Nz| �$� z � |-vHv$c � �NxYoMuN� u-w �$|�sH| � z?xHzts o � � zt�$zt� � zt�Nq&z�d

e �CxF}Nz�s�z � |-o � � ztsiu-w)xF}Norv�vHz?q?xHoru�� � g{z4v;}$|-�r�)|-vHv$c � z xF}$|-x�|-�r� �$|�sH| � z?xHztskvj|�skz4o � � zt�$zt� � zt��x@d� zpqt|-�r��xF}Norv<|�vHv$c � �NxHoru�� �So ��xFs�u � cNq?z � }�� � �Norz?��z?� }$|-�rxHztsp|�� � �e|�c$s�orx��?zt� � �t������� � � l�z+l\�Io@vxo�zqst , o�� o@t , o@t :$o�d/e � � z?q?xHoru�� �$� g z � orvHq@cNvYv � z?xF}Nu � v{w0uNs�}$|�� � �ro �N� � zt�Bzt� � zt��x4�$|�sY| � z?xHzts�v�d

� u'q?u � �N�rz?xHz x;}Nz � orvHq@cNvHvYoMuN� � g{z �Nz?z � vHu � z �Nu�xF|-xHoru��Ed �]z?x � �� � zt�Nu�xHz xF}Nz |-vYvHzts�xHoru����_u�s}�� �Bu�xF}Nz?vHorv � xF}$|�x'| � |-x;|�}$|-vHz � orv<|#sH|�� � u � v;| � �N�rzpwKs�u � | � |&��z?vHo |����Nz?x+g{u�s�f#vHxFs4cNq?x$c$s�z����d & o � zt�2xF}Norv �Nz?x+g{u�s�fCvHxFs4cNq?x$c$s�z � �rz?x � � }Bz�xF}Nz���c � }$zts u-w vHxF|�xHz?v4u-w � |�s�o |�}N�rz � � � |�� � �Mz?x� � ��� �������� � � }$z xF}Nz �Nc � }$zts u-w�vHxF|�xHz?v�u-w / � d5� z?x � � � zt�Nu�xHz xF}Nz �$}��NvHorqt|-� �$s�uN}$|�}Nor�Morx�� u-w� � �&� ��o � zt� / � ��� dSe ��| �$� orxHoru�� � �rz?x

� � �� � � � ��� � ������ �� �� � �� � � � �

~ u�xHzixF}$|-x{xF}Nz4�$|�sH| � z?xHzts�v � ��� o � q?u�� ��c$�Nq?xHoru���g�orxF} ��� � z?xHzts � o �Nz�|-�r�]xF}Nz4�$}��NvHorqt|-��$sku�}$|�}Nor���orxHorz?v u�w xF}Nz.��u�o ��x�vF�$|-q?z�d

� z?x�cNv |-vHv�c � z�xF}$|-x�zt|�qQ} � |�s�o |�}N�rz�vHz?x�� � }$|-v�| ��o skoMq?}N�rz?x � orvHxFs�o9}>cNxHoru�� �� � � �� � � �� ��� ��� ��� �

� ���� � � � �� � � ���

g }Nzts�z � orv | �Nu�s � |-�ro#�t|-xHoru�� q?u��NvHxF|���x@d � }Nzt� � o w � � orvixF}Nz4�Nc � }Bzts{u-wbqt|-vHz?v�o � � |-xF|�}$|-vYz � o �g }Norq?} � � �&� |�� � / � ���]� g{z�u�}NxF|-o �

� � � �� � � � � �� ��� ��� � � �

� ���� � ��$ � � � � � �� � � � �

� �

Page 18: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

g }Nzts�z � orv vHu � z�u�xF}Nzts��NuNs � |-�ro#�t|-xHoru��Cq?u��NvHx;|���x�d2�Ac$s�x;}Nzts � u�s�z � |��$�N�r�No �N���2b>c$|-xHoru�� �3� xHu zt|-q?}� cN�rxHo �Nu � o |-�evF| � �N�rz � g{ziqt|�� q?u � �>cNxHzixF}Nz��$s�u�}$|�}Nor�rorx � xF}$|-x{zt|-q?}�� � � � |�� � / � � � o � � � $ �xF}Nz4�NzhNx qt|�vHz�xHuu}$z vHz?zt�'|&wcxHzts xF}Nz � |-xF|�}$|-vYz � �

� � � � $ � � � � �� ��� �;������

� ����

� � � � � � � � � � � �t���

g }Nzts�z�� � � � � � � � ��� |�� � � � � � � � � � � d� �� �JYLV\`�V�� �CXMYL]\_LX�]�Y

eK� xF}Nz �$skz � oru�cNv{vHz?q?xHoru�� � g{z�q?u��NvHo � zts�z � xF}Nz vHorx$c$|-xHoru��^g }Nzts�z�g{z |�s�z�c$�Nq?zts�xF|-o ��|�}Bu�cNxbxF}Nz��$}��Nv+�orqt|-��$s�uN}$|�}Nor�MorxHorz?v � }>cNx{q?zts�xF|-o ��|�}Bu�cNx�xF}Nz��Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z x;}$|-x{zt�Nq?u � z?v�x;}Nz?vHz4�$s�u�}$|�}Nor�rorxHorz?v@d~ uQg � v$c$�$�$u�vHzug{z�|�skz4�Nu�x uN�N�M� c$�Nq?zts�xF|-o �p|�}Bu�cNx x;}Nz �$sku�}$|�}Nor�roMxYoMz?v � }>cNx4|-�rvHu�c$�Nq?zts�xF|-o �p|�}Bu�cNxxF}Nz�vYxFs�cNq?x$c$s�z xF}$|-x)zt�Nq?u � z?v{xF}Nz � d ~ vig oMx;} |�����vYz?x)u-wez � zt��xHv � g z qt|�� zh$�$s�z?vHv xF}Norv�c$�Nq?zts�xF|-o ��x �}��'|-vHvHor���No �N�<| �$s�oru�s��$s�uN}$|�}Nor�Morx�� � � � �� � � � xYu zt|-q?}<�Bu�vHvHo9}N�rz }�� �Bu�xF}Nz?vHorv � �� d��Ac$skxF}Nzts � u�skz � g{zqt|���c$� � |-xHz�xF}Nz?vHz��$s�u�}$|�}NoM�rorxHorz?v4|-vJg{z�vHz?ziqt|-vHz?v@dSe � vHu � u�o �N� � g{zi�Mzt|�sH��|�}$uNcNx�xF}NzivHxFs�cNq?x$c$skz u-wxF}Nz � u � |-o �Ed

~ v�o � x;}NzW�$s�z � oMuNcNv<vYz?q?xHoru�� � �rz?x � �� � zt�Nu�xHz xF}Nz � �NuQg c$�Nq?ztskxF|-o � � }��$�$u�x;}Nz?vHorv<x;}$|-x�xF}Nz� |-xF|�}$|-vHz � orv�|<sY|�� � u � vF| � �N�rz w s�u � x;}Nz � |&��z?vYo |��P�Nz?x�g{u�s4fpvHxFs�cNq?x�c$s�z � � d � s�u � � |&��z?v�xF}Nz?u�skz ��� g{zj}$| � z

� � � �� � � ��� �;� � � � � �� � � � � � � � � �� ��� � � �t���g }Nzts�z � orv�| �Nu�s � |-�ro��t|�xHoru���q?u��NvYxF|���x@d ~ �rvHu � w s�u � x;}Nz��$s�u � cNq?x s�cN�rz � g z4}$| � z

� � � � � �� ��� �_���� � � � � � � � L��������� � � � A� �

�� ��� � � �����

� z�qt|���z � |-�9c$|-xYz�zt|-q?}�xHzts � u�� xF}Nz�s�or��}�x � }$|�� � �KvHo � z u�w x;}NoMv zb c$|�xHoru��ucNvHo �N�G�Kb c$|�xHoru�� �t�$� c$� � ztsxF}Nz�|-vHv$c � �NxHoru�� x;}$|-x)xF}Nz � |-xF|�}$|-vHz � orv{q?u � �N�rz?xHz�d � }�cNv � g{z�uN}NxF|-o � x;}Nzj�Bu�vHxHzts�oru�s{�$s�uN}$|�}Nor�Morx��u-w� �� ��o � zt� � �

� � � �� � � ��� � � ��� � � � �� � � � ������

� �� �

��� � � �� �� � � � � �

�� � ��� ����� � �� � � �� � ��� � � � � ����� �

� �� � �� � � � � � � � � ���

� � � � � � � ����� �� � � � � � � ���� � � � � � � � � � ��� ������ � � � �

� � � � � � � � � �� � �� � � � ���

� �� � � � � � � � ��� ��� ����� �� � � � � � � � � ���

� � � � � � ����� ��� � � � �� � � � �

�����

� �� �

� ���� � �� ���� �� � � � � �

� �� �

� ��� � � � � �� ���� � � � �>�@�

� �

Page 19: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� vHo �N�'x;}Nz?vHz �$u�vHxHzts�oru�s �$s�u�}$|�}Nor�rorxHorz?v |�� � �Kb c$|-xYoMuN� �t�$� g z � |&�'q?u � �>cNxYz xF}Nz �$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru�� wcu�s xF}Nz<�NzhNx qt|-vHzCxHu }Bz<uN}NvHzts � z � |&w0xYztsIg{z'}$| � z'vHz?zt�g| � |-x;|�}$|-vHz�d � s�u � xF}Nzzh$�$|��NvHoru��'s4cN�Mz � g{z�u�}NxF|-o �

� � � � $ ^� � ��� �_� �� ��� � � � $ � � � � �� ��� � � � � �� � � ��� � � �����

� }Nzts�z |�s�z xF}$s�z?z o � �$uNs�xF|���x��Bu�o ��xHv�xHu }$z � | � z |�}Bu�cNx4x;}NoMv |��$�$sku�|-q?}Ed � �Nz � orx�qt|��#}$|�����$zt� xF}$|-x�x+g{u � |&��z?vHo |���� �Nz?x+g{u�s�fpvHx;s�cNq?x$c$s�z?v s�zt�$s�z?vYzt��x zh$|-q?xH�r�#xF}Nz�vF| � z vHz?xYv�u�w �$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru��Nv�d�� z vF|&� xF}$|�x�xF}Nz4x+g{u�vHxFs�cNq?x�c$s�z?vj|�s�zuo;?3A�q9<@l 2�o�tMvS� � zts � | |�� � � zt|�s�� �/�&������� dK��u�szh$| � �N�rz � w0u�s xF}NzixF}$s�z?z � |�s�o |�}N�rz � u � |-o � � �R� � ����� � zt|-q?}�u-w�xF}Nz �Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z?v �� � �� ���� � �� � |�� � ��� � ����s�zt�$s�z?vHzt��xHv�xF}Nz � orvHx;s�o9}>cNxHoru��Nv\g }Nztskz � |�� � �'|�s�z�q?u�� � orxHoru��$|-�r�r�o � � zt�$zt� � zt��x u-w � d �{u��NvHzb>cNzt��xY�M� � xF}Nz?vHz �Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z?v4|�s�z zb>cNo � |-�rzt��x@d ~ v4|��Nu�xF}Nzts�zh��| � �N�rz � |6:�y\��� 2#o@vxo:tMo�vxw2y�z�{:pvxz;A7:@v4ANz+o�orv4u��Nz�xF}$|-x�}$|-v4�Nu � orvHvYo �N�Cz � ��z?v��SxF}$|�x�oMv � orx�zt�Nq?u � z?v�Nu |-vHvHztskxHoru��Nv4u-w�q?u�� � orxHoru��$|�� o � � zt�Bzt� � zt�Nqtz�d ~ � u � |-o �2q?u���x;|-o �No �N�� � |�s�o |�}N�rz?v }$|�v � q?u � ��N�rz?xHz��Nz?x+g{u�s�f vHx;s�cNq?x$c$s�z?v�� u��Nz4�Nz?x+g uNs�f vHxFs�cNq?x$c$skziw0u�s zt|-q?}��$u�vHvHo9}N�rz�uNs � zts�o �N� u-wx;}Nz � |�s�o |�}N�rz?v@d~ �M� q?u � �N�rz?xHz��Nz?x�g{u�s4fpvHxFs�cNq?x�c$s�z?v�wcu�s�|C��o � zt� � u � |-o �#s�zt�$s�z?vHzt��x�xF}Nz�vF| � z ��u�o ��x �$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru��Nv�� �$| � z?�r� � |-�r��Bu�vHvHo9}N�rz � orvHxFs�o9}>cNxHoru��Nv�� |�� � |�s�z�xF}Nzts�z;wcu�s�z�zb>cNo � |-�rzt��x@d

e �P��zt�NztsY|-� � x+g{uW�Nz?x+g uNs�f vYxFs�cNq?x$c$s�z?v�|�s�z�zb>cNo � |-�rzt��x'o w |�� � u��N�r�So w4xF}Nz?�S}$| � zCxF}Nz'v;| � zvHxFs4cNq?x$c$s�z�or���Nu�s�o �N��|�s�q � o s�z?q?xHoru��Nv4|�� � xF}Nz�vF| � z � �KvYxFs�cNq?x$c$s�z?vu� � zts � | |�� ��� zt|�s�� ���&������� d ~ < !pvxz;A7:@v4ANz+o�orv |�� u�s � zts�z � x�c$�N�Mz5� �R� � ��� � v$cNqQ} x;}$|-x{xF}Nzts�zioMvi|���|�s�q w sku � � xHu � |�� � w s�u � � xHu ���}>cNx��Nu |�skq\}$z?x+g{z?zt� �p|�� � � d�� vHo �N� xF}Norv q?}$|�sH|-q?xYzts�o#�t|-xHoru���u�w �Nz?x�g{u�s4f*�KvHx;s�cNq?x$c$s�z�zb>cNo � |-�rzt�Nq?z ���}Norqf-zts�o �N� � �t������� }$|-v qts�zt|�xHz � |��2z�� q?orzt��x�|-�r��u�s�orxF} � w0u�s o � zt��xHo w0�No �N�S|-�r� � |t��z?vHo |���� �Nz?x+g uNs�fvHxFs4cNq?x$c$s�z?v�xF}$|�x�|�s�z�zb cNo � |-�rzt��x�xHu |���o � zt���Nz?x+g{u�s�f�vHx;s�cNq?x$c$s�z�d

& o � zt�pxF}$|-x � �� orv4x;}Nz |�vHvHzts�xHoru��@xF}$|-x�xF}Nz �$}���vHorqt|-�{�$s�u�}$|�}Nor�rorxHorz?v�wcu�sixF}Nz-��u�o ��x�v;�$|-q?z u-w qt|��:}$z�zt�Nq?u � z � o � xF}Nzj�Nz?x+g{u�s�f vHx;s�cNq?x$c$s�z � � � oMx wcu��r�ruQg v x;}$|-x{xF}Nzj}��$�$u�xF}Nz?vYz?v�|�vHvHuNq?o |�xHz � g�orxF}x+g{u�zb cNo � |��Mzt��x��Nz?x�g{u�s4f�vHxFs4cNq?x$c$s�z?v � cNvHxi}Bz o � zt��xHorqt|-�xd��{u��NvHzb>cNzt��xY�M� � x+g{u4zb>cNo � |-�rzt��x �Nz?x+g uNs�fvHxFs4cNq?x$c$s�z?v � cNvHx4}$| � z4x;}Nz vF| � z��c�$skoMuNs�|�� � �$u�vHxYzts�oru�s � �$s�u�}$|�}NoM�rorx���dI��u�sizh$| � �N�rz � o �@xF}Nz�x�g{u� |�s�o |�}N�rz � u � |-o � � �R� � � � xF}Nz �Nz?x+g uNs�f vHxFs�cNq?x�c$s�z?v0� � |�� � � � |�s�z�zb>cNo � |-�rzt��x � |�� � g�or�M�}$| � z{xF}Nz{vF| � z��$s�uN}$|�}Nor�Morx���dSe ����zt�NztsH|-� � xF}Norv)�$s�u��$ztskx � orv)qt|-�r�rz � �Nn8�>y�v���o prq p�o;?3A�q9<@l�2#o�t :�o )LeK� �ror��}�xu-wexF}Norv �$sku��$zts�x�� � g z vF}Nu�cN� � |�vHvHuNq?o |�xHz�zt|-q?} }��$�$u�xF}Nz?vYoMvJg�orxF} |���zb>cNo � |-�rzt�Nq?z4q?� |-vHv{u-w]vHxFs�cNq?x�c$s�z?vsH|-x;}Nzts�xF}$|��P|pvYo �N���Mz �Nz?x+g{u�s�fpvYxFs�cNq?x$c$s�z � |�� � u�c$s � z?xF}Nu � v wcu�s �rzt|�sH�No �N�S�Nz?x+g uNs�fpvHxFs4cNq?x$c$s�zvF}Nu�cN� � |-q?x�c$|-�r�M�:}$zio ��xHztsH�$skz?xHz � |�v � z?xF}Nu � v w0uNsb�rzt|�sH�No �N� zb>cNo � |-�rzt�Nq?z4q?� |-vYvHz?v{u-w�Nz?x�g{u�s4f4vYxFs�cNq��x$c$s�z?vI�c|-�rxF}Nu�cN��} � w0u�s xF}Nz vF|�f-ziu-wS}$s�z � oMx�� � g{z�u-wcxHzt��}N�9c$s xF}Norv � orvHxHo �Nq?xHoru�� � d �� �;=OU\3O5$+,�:$7>: ,"!O@ 7>B468<>,W-1�,�+34<>S :fU C.38BO7>S�,QS ��,f79- 5*,WC*U C.,�5��Z68=`,�:$7>64-��H-�,�5 �Z34C*e :*5$C*@�1�5$@ C.,�:�:$7>NdU <>=06O:_C.,WU C.,�:*,W- 5*6��

5$7>34-:�3"� 1�34-S^7>5$7>38-�68<Z79-S�,WU�,W-�S ,W-1�,AY��;34-,�5$+�,.<>,�:*:�E :*5$C.34-aO,.CPS ,�� -�7>5$7>38-�:P3�����64=`,�:$7>64- -�,�5 �Z34C*e :�, �O7>:*5� +,WC.,P68C.1�:+64B`,d6#1�68@�:*68<�79- 5*,WC*U C.,�5*6`5$7>34-�GH,OY a�Y>E�� ,Q64C*< 68-�S�� ,WC.NP6�E ��� � �8KWY �_,�1*eA,.C.NP64-0,�5;64<HY�G�� � ����D\KR64C.a8@�, 5$+�6`5�E\64<>5$+34@a4+7>5[7>:[@ - C.,�6O:*38-�68D�<>, 5*3d6`:*:$@�N , + =OU\3`5$+�,�:$7>:;,"!O@ 7>B468<>,W-1�, �Z+,W- �Z34C*eA79-a �Z7>5$+c1�64@:*64<��Z68=O,�:$7>68-�-�,�5 �Z34C*e :�EA7>5[7>:�3"�H5*,W-

�t�

Page 20: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� }Nz vHz?q?uN� � o � �$u�s�x;|���x��$u�o ��x |�}Bu�cNx�xF}Norv |��$�$s�u�|�qQ}porv x;}$|-x � o � g s�orxHo �N� �2b>c$|-xHoru�� ���$� g{z}$| � z�|-vHv$c � z � x;}$|-x�xF}Nz'}��$�$u�xF}Nz?vHorv zb>cNo � |-�rzt�Nq?zpq?� |-vHvHz?v |�s�z � cNx$c$|-�r�r�WzhNq?�9cNvHo � z�d�e �Ss�zt|-�rorx�� �xF}Nz?vHzp}��$�$u�xF}Nz?vHz?v�|�s�z'�Nu�x � cNx$c$|-�r�r�Pzh�q?�9cNvHo � z�d ��u�s�zh$| � �N�rz � o �gu�c$s x�g{u*� � |�s�o |�}N�rz � u � |-o � �}$u�xF} �Nz?x+g{u�s�fCvHxFs�cNq?x�c$s�z?v0�� � |�� � xF}Nz z � �Nx��@�Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z qt|��2zt�Nq?u � z��$|�sH| � z?xHzts�vvF|-xYoMvkw0�No �N�WxF}NzCzb c$|��Morx�� � � � � � � d � }Nzts�z;wcu�s�z � xF}Nzp}��$�$u�xF}Nz?vHz?v�|-vHvHuNq?o |-xHz � g oMx;}PxF}Nz?vHzp�Nu����zb>cNo � |-�rzt��x �Nz?x+g{u�s�f vHx;s�cNq?x$c$s�z?viu � zts�� |��EdI~�u��Nz?x;}Nz?�Mz?vYv � o �pxF}Norv4|��$�$sku�|-q?} � g z |-vYv$c � z�xF}$|-xixF}Nz�$s�oru�s�v�u��2�$|�sH| � z?xYzts�v�wcu�s4|���� ��o � zt�W�Nz?x+g{u�s�f vHxFs�cNq?x$c$skz }$| � z5}Bu�c$� � z �P� zt�NvHorxHorz?v � |�� � }Nzt�Nq?zxF}Nz�u � zts�� |�� u�w }�� �Bu�xF}Nz?vHz?vCg�or�r�/}$z u-w � zt|-v$c$s�z��?ztskuMd

�bo �$|-�r�r� � o ��g skoMxYo �N���2b>c$|-xHoru�� ���$� g{z�}$| � z��ro � orxHz � u�c$s�vHz?� � z?vixHu }��$�$u�xF}Nz?vYz?v q?u�sYs�z?vF�$uN� � o �N�xHu'|-vYvHzts�xHoru��Nv xF}$|-x4x;}Nz �$}��NvHorqt|-�{�$s�u�}$|�}Nor�rorx � � orvHxFs�o9}>cNxHoru��2u-w�xF}Nz-��u�o ��x4vF�$|-q?z q?u � z?v�wKs�u � u��Nz�$|�s�xYoMq@cN� |�s �Nz?x�g{u�s4f'vYxFs�cNq?x$c$s�z�dp�2z�qt|��Wskz?� |�hWxF}Norv |�vHv$c � �NxHoru�� � |-vHv$c � o �N� x;}$|-x4xF}Nz'�$}��NvHorqt|-��$s�u�}$|�}NoM�rorx�� � orvHxFs�o9}>cNxHoru�� qt|�� }Bz zt�Nq?u � z � o � | pro�v�u-w �Nz?x+g{u�s�f#vYxFs�cNq?x$c$s�z?v�d eK� xF}Norv<�$|��Bzts �}Nu*g{z � zts � g{z � u �Nu�x �>c$s�v�cNz4xF}Norv���zt�NztsY|-�ro��t|�xHoru��Ed

e �'�$s�o �Nq?o �N�rz � xF}Nz�|��$�$s�u�|�qQ}:g{z4}$| � z � orvHq@cNvYvHz � o � xF}Norv�vHz?q?xHoru�� oMviz?vHvHzt��xHo |-�r�r�<|-�r��xF}Nzts�z�orv�xHu�rzt|�sH�No �N�'�Nz?x+g{u�s�f�vHx;s�cNq?x$c$s�z�dJeK�p�$sH|-q?xYoMq?z � g }Nzt� xF}Nz\cNvHztsC}$z?�rorz � z?v4xF}$|�x�u��N�r�'| wczg�|-�rxHztsY�$|-xHo � z�Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z?v�|�s�z �$u�vHvYo }N�rz � }Nz qt|�� � o skz?q?xH�r�W|-vHvHz?vYv�xF}Nz �$s�oru�s�viwcu�sixF}Nz �$u�vHvYo }N�rz��Nz?x+g uNs�fvHxFs4cNq?x$c$s�z?v4|�� � x;}Nz?o s��$|�sY| � z?xHzts�v � |�� � v$c>}NvHzb>cNzt��xH�r� cNvHz5�Kb c$|-xYoMuN�Nv �>� |�� �#��� u�sixF}Nz?o s ��zt���ztsH|-�ro#�t|-xHoru��Nv w0u�s q?u���xHo ��cNu�cNv � |�s�o |�}N�rz?v |�� � � orvHvYo �N� � |-xF|>d ��u�s zh | � �N�rz �i� c$��xHo �Nz � �t���*�N� }$|-v� z?vHor���Nz � | vHu-wcx+g�|�s�z�vH�NvHxHz � g }Nzts�z@}��<|:cNvHzts vF�$z?q?o���z?v }Norv4�$s�oru�s�viwcu�s�| vHz?xiu-w �$u�vHvHo9}N�rz � u � z?�MvcNvHo �N� � |&��z?vHo |��'�Nz?x+g{u�s�f�vio �p| � |��$�Nzts vHo � or� |�sixHu xF}$|-xivF}Nu*g ��o � �bor��c$s�z � d � }Nz�vH�NvHxHz � xF}Nzt�q?u � �Nor�rz?v�xF}Norv�vF�Bz?q?o���qt|-xHoru��Co ��xHu |�q?u � �>cNxHztsi�$s�u��NsH| � xF}$|-x{�rzt|�sH�Nv w sku � | � |-xF|�}$|�vHz�d

~ u��Nz?xF}Nz?�rz?vHv � x;}Nz ��c � }Bzts�u-w �Nz?x+g{u�s�f�vYxFs�cNq?x$c$s�z?v w0uNs�| � u � |�o �@q?u���x;|-o �No �N�� � |�s�o |�}N�rz?v�oMv� u�skz x;}$|�� zh �Bu��Nzt��xYo |���o � �Ldb�{u��NvYzb cNzt��xH�r� � g }Nzt� xF}Nz�cNvHzts qt|��$�Nu�xbzhNq?� c � z�|-� � u�vYx)|-�r��u-w]xF}Nz?vHz�Nz?x+g{u�s�f�vHx;s�cNq?x$c$s�z?v � xF}Nztskzj|�skz�vHz � ztsH|-��orvHv$cNz?vixF}$|-x � cNvHx�}$z�q?u��NvHo � zts�z � dJeK�C�$|�s�xHorq@cN� |�s � q?u � �>c��xF|-xYoMuN�$|-�eq?u��NvHx;sH|-o ��xYv qt|��p�$s�z � zt��x�cNv�wKs�u � v$c � � o �N��u � zts |-�r�xF}Nz }�� �Bu�xF}Nz?vHz?vio � �2b>c$|-xHoru�� ��� d��|��Rg{z |��$�$s�u*hNo � |-xHz � � � � $ ^� � ��� � |-q?q@c$sH|-xHz?�r� }��Ws�z?x;|-o �No �N�2u��N�r�W|Cv � |-�r�bwKsH|-q?xYoMuN� u-wixF}Nz?vHz}�� �Bu�xF}Nz?vHz?v o � xF}Nz�v$c ��� e_wevHu � gi}NoMq?} }��$�$u�x;}Nz?vHz?v)vF}NuNcN� � g{z{o �Nq?�9c � z � e � | �$� orxHoru�� � }Nu*gPqt|��Ig{zz�� q?orzt��xH�r�<|-vHvYoM�N�'�$s�oru�si�$s�u�}$|�}Nor�rorxHorz?v4xHu xF}Nz � |����'�Nz?x+g{u�s�f�vYxFs�cNq?x$c$s�z?v�|�� � xF}Nz?o s �$|�sY| � z?xHzts�v �eK� xF}Nz�v$c>}NvHz?q?xYoMuN�Nv xF}$|�x{w0u��M�ru*g � g{z�q?u��NvYo � zts zt|-q?} u-wbxF}Nz?vHz�orvHv$cNz?v@d

����� ������ ������������� ���

� }Nz � u�vHx�o � �$uNs�xF|���x4orvHv$cNz orv\g }Nz?x;}Nzts\g{z�qt|��#|��$�$s�u*hNo � |-xHz � � � � $ ^� � ��� � g{z?�r�icNvHo �N�1��cNvHx4|v � |��M�b�Nc � }Bzts�u�w �Nz?x�g{u�s4f*�KvHx;s�cNq?x$c$s�z4}�� �Bu�xF}Nz?vHz?v�d � }NorvCb cNz?vHxYoMuN�'orv � o�� q@cN�rx4xHu |��Nv�g{zts�o �CxF}Nz��u�s���dJ~ u��Nz?xF}Nz?�rz?vHv � vHz � ztsH|��s�z?vHzt|�skqQ}Nzts�vi}$| � z�vF}Nu*g � zh �Bzts�o � zt��xF|-�r�r�<x;}$|-x�z � zt�C|�vHo �N���rz �H��uNu � �C.,�6`:*34-64D <>,�5*3T6`S�38U�5P6 ��,�64eL,WCP6`:*:$@�N U�5$7>38- 3"��� ������ ��� ���! ��"$#��&%$'(� �$)+* ��, � + 7>1*+�:*68=A:P5$+6O5 5$+�,#34D:*,WC.B86O5$7>38-�:#79- 6S 6O5*64D6O:*, 1�68-�-�3`5 +,W<9U05*3PSA7>:*1WC*7>Nd79-6O5*,#5 �Z3d,�!O@�7>B864<>,.- 5f-,�5 ��34C*ec:*5$C*@�1Q5$@�C.,�:�Y

�t�

Page 21: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

�Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z�u-wcxHzt� �$sku � o � z?v |�� zhNq?z?�r�Mzt��x�|��$�$s�u*h�o � |�xHoru���� �{u�uN�$zts�|�� � � zts�v$f-u � oMxYv �&�����>�~ �Mo wczts�orv |�� � �{uNu��Bzts �t�����M� � z?qrf-zts � |��pz?x |-�xd �J�t����� } � d�� z ��o � zt�#|��2zh | � �N�Mz o � � z?q?xHoru�� �>d� }Nz?vHzps�z?v$cN�rxHv�|�s�z�vHu � zg }$|-x�v$c$sH�$skoMvYo �N� � |�� � |�s�z�� |�s���z?�r�Ss�z?v;�$u��NvHo9}N�rzCw0uNs�xF}Nz'�Ns�zt|-x � zt|-��u-ws�z?q?zt��x�o ��xYzts�z?vHx�o �C�rzt|�sH�No �N� � |&��z?vHo |����Nz?x+g{u�s�f�v@d

& o � zt� xF}Norv uN}NvHzts � |�xHoru�� � |��Nu�x;}Nzts)o � �Bu�s�xF|���x�q?uN�NvHo � ztsH|-xHoru�� oMv�}Nu*g�xHu o � zt��xYo wc� �H��uNu � � �Nz?x+�g{u�s�f2vHxFs�cNq?x�c$s�z?v@d � }Nzp|��$�$s�u�|�qQ}#xF}$|�x }$|-v�}$z?zt��| � u��NxHz � }�� � |����Ps�z?vHzt|�s�q?}Nzts�v orv xHu cNvHzp|p :$y�z�qst�- �Io@vxz�q=: o �gq?u � }No �$|�xHoru�� g�orxF}S|2vHzt|�s�q?}S|��M��u�s�orxF} � d � }Nz'vHq?uNs�o �N� � z?xFs�orq'x;|�f-z?v��$s�oru�sfN�NuQg �Mz � ��z � | � |-xF|�}$|�vHz � |�� � |�vHz?x u-w�Nz?x�g{u�s4f�vHxFs4cNq?x$c$s�z?v � |�� � q?u � �>cNxYz?v x;}Nz���uNu � �Nz?vHv u-wE��x)u-wxF}Nu�vYz�vHxFs�cNq?x$c$skz?v xHu xF}Nz4�$s�oru�sCf��Nu*g��rz � ��z�|�� �'� |-x;|>d � }Nz4vHzt|�skqQ}�|-�r��uNs�orxF} � o � zt��xHo���z?v4�Nz?x+g uNs�fvHxFs4cNq?x$c$s�z?v xHu }$z'vYq?u�s�z � d�eK�Px;}NoMv vHz?q?xHoru�� � g{z � oMvYq@cNvHv vYq?u�s�o �N� � z?xFs�orq?v@d�eK� � z?q?xYoMuN� � d ��� g{z� orvHq@cNvHvivHzt|�s�q?}�|-�r��u�skoMx;} � v@d

~ � u�} � oru�cNv vHq?u�s�o �N� � z?x;s�orq�wcu�s{|�vHo �N���rz��Nz?x+g{u�s�f��KvHxFs�cNq?x�c$s�z �0zb cNo � |��Mzt�Nq?z q?� |�vHv � orv�xF}Nz4skz?� |Q�xHo � z{�$u�vHxYzts�oru�s�$sku�}$|�}Nor�roMx�� u-w x;}$|-xevHxFs4cNq?x$c$s�z)��o � zt��xF}Nz � |-xF|�}$|-vYz�d���uNs]zh | � �N�rz � g z qt|���q?u � �>cNxHz� � � � � �� � � �_� � � � �� � � � � � � � � �� ��� � uNs�q?u � �>cNxHz�|�j�l�n*op /l�:�vxy�z � � � � �� � � ��� ��E � � � �� � � � ��� � g }Nzts�z� ��

�orv)vHu � z�s�z;w0ztskzt�Nq?zj�Nz?x+g{u�s�fivHx;s�cNq?x$c$s�z{v$cNq?} |-vbxF}Nz z � �Nx����Nz?x+g{u�s�f�vYxFs�cNq?x$c$s�z�d � }Nzt�Ig{z�cNvHz

�2b>c$|-xHoru�� ��� xYu�q?u � �>cNxHz�xF}Norv s�z?� |-xYo � z��$u�vHxHzts�oru�s��$sku�}$|�}Nor�roMx�� � xF}NzivHq?u�s�o �N� � z?x;s�orq4orv�vHu � z?xHo � z?vqt|-�r�rz � xF}NzIj�l�n*opqFl�t���qFz�q9:�� 2#o@vS� � � � � z?xFs�orq�d ~ �Nz?x+g uNs�f�vHxFs4cNq?x$c$s�z�g�orxF} xF}Nz4}Nor��}Nz?vHx��$u�vHxYzts�oru�s�$s�u�}$|�}NoM�rorx��'orviu-w0xYzt� qt|-�r�Mz � |��Il$�*qX� A�� lT� y*pvxo@z�qsy�z$q2�_n ~��S� vHx;s�cNq?x$c$s�z�d � u vHq?uNs�z�|�vYz?x�u-w � oMv �xHo �Nq?x �Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z?v�� g{z�qt|��5cNvYz�� ��� � � � � � � � �� � � � d2~ u�xHzixF}$|-x��$sH|-q?xYoMxYoMuN�Nzts�v�x�� �Norqt|-�r�r�q?u � �>cNxYz��Mu���|�s�orxF} � v u-w x;}Nz��$s�u�}$|�}NoM�rorxHorz?v�xHu | � u�o � �Nc � zts�orqt|-�Lc$� � zts.!�u*g\d

n | � or��|��P|�� � y�|9w0zts�x�� � �t������� v$cN����z?vHx |��S|-�rxHztsY�$|-xHo � z'vYq?u�s�o �N� � z?xFskoMqpxF}$|�x cNvYz?v s�z?� |-xYo � z�$u�vHxHzts�oru�s��$s�u�}$|�}Nor�rorx���o � q?u�� ��c$�Nq?xHoru���g�orxF}�}Nz@c$s�orvHxHorq?vS}$|-vHz � u�� xF}Nz �$sko �Nq?o �N�rz�u-w � q?qt| � vby�|*�?uNsd

� x;}Nzts�vHq?u�sko �N� � z?x;s�orq?v |��$�$s�u*h�o � |-xYz xF}Nz��$u�vHxYzts�oru�s&� �$s�u�}$|�}NoM�rorx�� � z?xFs�orq�d�e � � z?q?xYoMuN� �$� g{z� orvHq@cNvHv�|-�r��u�s�orxF} � v xF}$|-x�qt|���� � � |C�ru�qt|�� � |*hNo � c � o � xF}Nz��$s�u�}$|�}Nor�rorx � � � � � � �� � � � � ��� � |-v| w(c$�Nq?xHoru��pu�w � � � �_xF}Nz �$}��NvHorqt|-� �$sku�}$|�}Nor�roMxYoMz?v |-vHvHuNq?o |-xHz � g�orxF}#�Nz?x+g{u�s�f�vYxFs�cNq?x$c$s�z ��� � d � zqt|��$�Nu�x�cNvHz v$cNqQ}p|��ruNqt|-� � |*hNo � c � |-v�| vHq?uNs�z�wcu�s ��� � }$z?qt|�cNvYz�orxCg�or�r�)|-�#g�|&�Nv{wK| � u�s{xF}Nz � u�vHxq?u � �N�rzh'�Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z?v � g }Norq?}p�N� |�q?z��Nu q?u��NvHxFsH|�o ��xHv�uN� xF}Nz��$|�sY| � z?xHzts�v�����>dJ~�u��Nz?x;}Nz���rz?vHv � g{z4qt|���cNvHz | �MuNqt|-� � |�h�o � c � u�w � � � � � �� � � � ����� � |-v�| vHq?u�s�z wcu�s ���'o wJg z�|-�rvHu'�$zt�$|��Mo#�?zvHxFs4cNq?x$c$s�z?v�}$|-vYz � u���xF}Nz?o s{q?u � �N�rzh�orx���d ~ ft|�o f�z � �t� � ��� v$cN����z?vYxHv{xF}Nz�vHq?u�s�o �N� � z?xFs�orq

�ru�� � � � ��� ���� � �M��� �Z� ��o � ��� �g }Nzts�z�� orv�| � u � z?� � �� � � � zt�Nu�xHz?v xF}Nz � |�� cNz?v u-w � � �'xF}$|�x � |*hNo � o��?z�x;}Nz �$s�u�}$|�}Nor�rorx�� � |�� ���o � ��� � orv�x;}Nz �Nc � }$zts u-w��Mu���orqt|-�r�M�2o � � zt�Bzt� � zt��x �$|�sH| � z?xYzts�v�o �� d � }Norv4vHq?uNs�o �N� � z?xFskoMq oMvvHu � z?xHo � z?v{qt|-�r�Mz � x;}Nz ~ o ��wcu�s � |�xHoru�� qtskoMxYzts�oru���� ~ e � � d���u�s)| � |&��z?vHo |�� �Nz?x+g uNs�f � x;}Nzj�Bzt�$|-�rx � oMv��o � zt� }��

��o � � � � ��������

� �� � � � ��� � ���@�

���

Page 22: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� q?}�g�|�s+� � �t� � ��� v$cN����z?vYxHv | vHo � or� |�s vHq?uNs�o �N� � z?x;s�orq g�orxF} | �Bzt�$|-�rx�� xHzts � ��o � zt� }��� �BE���� ��o � ��� � �ru��M� � �?� gi}Nzts�z � orv�xF}Nz �Nc � }$zts u-w4qt|-vYz?v�o � xF}Nz � |-xF|�}$|-vYz�d � }NoMv � z?xFs�orqpoMvvHu � z?xHo � z?v�qt|-�r�rz � xF}Nz � |t��z?vHo |���o ��wcu�s � |-xYoMuN� qts�orxHzts�oru�� � � e � � d

~ �Nu�xF}Nzts � z?xFs�orqixF}$|-x)|��$�$skuQhNo � |-xHz?v xF}Nz��$u�vHxYzts�oru�s&� �$s�u�}$|�}NoM�rorx�� � z?xFskoMqiorv � o �No � c � � z?vYqts�o ���xHoru��2�rzt�N��xF}��_np�\� � �cy�oMvYvF|��Nzt� �t��� � � d � }Nz np�\�Su�w |C�Nz?x+g uNs�f�vHx;s�cNq?x$c$s�z orv�x;}Nz v$c � u-w�xF}Nz�Nc � }Bzts�u�wi}NoMxYv4s�zb cNo s�z � xHu zt�Nq?u � z�xF}Nz � u � z?�m��g }NorqQ} o �Nqtskzt|-vHz?v�g�orxF}Co �Nqts�zt|-vHo �N� � u � z?��q?u � ��N�rzh�orx�� � |�� � xF}Nz���c � }$zts u-w�}NorxHv s�zb cNo s�z � xHuCzt�Nq?u � z xF}Nz � |-x;|�}$|-vHz ��o � zt� xF}Nz � u � z?���sg }Norq?}� z?qts�zt|-vYz?v2g�orxF}�o �Nqts�zt|-vYo �N� � u � z?��q?u � �N�MzhNorx�� � s�z?� |-xYo � z)xHu�| �$|�s�xHorq@cN� |�s�q?u � o �N��vHq?}Nz � z�d�� z{�Nu�xHzxF}$|-x � o � xF}Nz4�ro � orx � |-v�xF}Nz4�Nc � }$zts u-w qt|�vHz?v�o ��xF}Nz � |-xF|�}$|�vHz4|��$�$s�u�|�qQ} o ��� �NoMx�� � xF}Nz � � � z?xFs�orqg�orxF} c$�No wcu�s � �$skoMuNs�v uN��vHxFs4cNq?x$c$s�z?v �M� e � � |�� � np�\� ��o � z4xF}Nz vF| � z�s�z?� |-xHo � z4vYq?u�s�z?vu� % |-vHv�|�� �y�|&wczts�x�� �E�t������� d2� ��wcu�s�x$c$�$|�xHz?�r� � o �'�$sH|-q?xYoMq?z � xF}Norv |-vY� � �NxYu�xHorq�zb cNo � |-�rzt�Nq?z orvjsH|�s�z?�r� |-q?}Norz � z � d

�bo �$|-�r�r� � g{z)qt|���vYq?u�s�z{vHxFs�cNq?x�c$s�z?v7}$|�vHz � u���| � z?q?orvHoru�� � u � z?�Nwcu�s�xF}Nz � u � |-o �Ed2eK� v$cNqQ} qt|-vYz?v �g{z)qt|�� vHq?uNs�z�| �Nz?x+g{u�s�fivHx;s�cNq?x$c$s�z�}���zh�xHzt� � o �N� xF}$|-x�vHxFs�cNq?x$c$skz xYuj|�� o � !AcNzt�Nq?z � o |-��sY| ��� g }Norq?}o �Nq?�9c � z?v4| � z?q?orvHoru�� � u � z?� w0u�s�xF}Nz � u � |-o �Ed

��u�s zh | � �N�rz � v$c$�$�$u�vHz�g{z�g�orvF} xYu�q?u � �>cNxHz4| vHq?u�s�ziwcu�s xF}Nz � |t��z?vHo |����Nz?x+g uNs�f wcu�s � z � orqt|-�� o |-���Nu�vYoMv�v;}NuQgi��o � �boM�Nc$s�z���| � ��o � zt�p| q?u � �N�rz?xHz � |-xF|�}$|-vHz4u�w � oMvYzt|-vHz |�� � vH� � �NxHu � v�d � u � uvHu � g{z zh�xHzt� � xF}Norv)�Nz?x+g{u�s�fixHu�|�� o � !AcNzt�Nq?z � o |-�NsH| ��� v$cNq?}�|�vbxF}Nz)u��Nz{vF}Nu*g � o ���bor��c$s�z ��}Ed � }Nz� z?q?orvHoru�� � u � z?�{s�zt�$s�z?vHzt��xHz � }��pxF}Norv4o � !AcNzt�Nq?z � o |���sH| � o �Nq?�9c � z?v | vYo �N���Mz xFs�zt|�x � zt��x � z?q?orvHoru��|�� � xF}Nz |-vHvHzts�xYoMuN� xF}$|-xixF}Nz��$|-xYoMzt��x� v�cNxHor�rorx � � zt�$zt� � v u��N�r��u��CxF}Nz � orvHzt|-vYz |�� � xF}Nz xFs�zt|-x � zt��x� z?q?orvHoru��Ed � z{q?u � �>cNxHz |ivYq?u�s�z{wcu�s�xF}Nz � |&��z?vHo |�� �Nz?x+g{u�s�f�}�� �$s�u�q?z?vYvHo �N�4xF}Nz�qt|�vHz?vbvHzb>cNzt��xHo |-�r�r��d~i| � z?�r� � wcu�s�zt|-q?}2qt|-vHz � � o �2xF}Nz � |�xF|�}$|-vHz � g{z5cNvHz��2b>c$|-xHoru�� �t� xHu<�$s�z � orq?x x;}Nz �$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru��2u � zts � orvHzt|-vHz?v o �pxF}$|-x�qt|-vYz � ��o � zt�pxF}Nz�vH� � �NxHu � v�o �@xF}$|-x�qt|-vHz |�� � xF}Nz �$s�z � oru�cNvqt|-vHz?v � L�������4� � � � d � }Nzt� � g{z�cNvHz{xF}Nz{o � !AcNzt�Nq?z � o |-��sH| � xYu � z?xHzts � o �Nz xF}Nz{u��NxYo � |-�$xFs�zt|-x � zt��x�d~ zh�x � wKs�u � x;}Nz5cNxHor�roMxYoMz?v�zt�Nq?u � z � o �px;}Nz o � !AcNzt�Nq?z � o |-��sY| ��� g{z � z?xHzts � o �Nz xF}NzucNxHor�Morx�� u-w{xF}Nzu�cNxHq?u � zIg }Nzts�z�xF}Nz �$|-xHorzt��x�oMv���o � zt�'x;}Nz�q?}Nu�vHzt�@xFs�zt|-x � zt��x � }>cNx4}$|-v�xF}Nz � orvHzt|-vHz skz?q?u�s � z � o �xF}Nz � |-x;|�}$|-vHz wcu�s qt|-vHz � � dP� z�q?u � �>cNxYz�xF}Nz�vHq?u�s�z wcu�s�x;}Nz � |&��z?vYo |��P�Nz?x�g{u�s4fpvHxFs�cNq?x�c$s�z�}��v$c � � o �N�#xF}Nz?vHz�cNxYoM�rorxHorz?v�u � zts |-�r��qt|�vHz?v@d � }Norv � z?xFs�orq'qt|���}Bz'��zt�NztsY|-�ro��?z � xHupvHq?uNs�z � cN�MxYo �N�rz�Nz?x+g{u�s�f vHxFs�cNq?x$c$skz?v@d � }Nz�| �$� |���xF|���z4u-w)x;}NoMv � z?q?orvHoru����Kx;}Nz?u�s�z?xHorq |��$�$sku�|-q?}�orv�xF}$|-x�orx�u��NxYo � o��?z?vg }$|-x�g{z o � � z?z � g�|���x4xHuCu��NxHo � o#�?z#� zh$�$z?q?xHz � cNxYoM�rorx���d � }Nz � orvF| �$� |���x;|-��z oMv�xF}$|�x4orx s�zb cNo s�z?vxF}$|-xJg{z�q?u��NvHx;s�cNq?x |�� o � !AcNzt�Nq?z � o |-��sY| � �_oxd z�d �N� z?q?orvHoru�� � u � z?� � wcu�s{xF}Nz � u � |-o �Ed

����� ��� ����� � � ������� ��� ��� �

� }Nz��$u�vYxHzts�oru�s&� �$s�uN}$|�}Nor�Morx��'|�� � � z?q?orvHoru����KxF}Nz?u�s�z?xYoMq � z?x;s�orq?v�skzb cNo s�z�xF}$|�xSg{zj|�vHvHor��� �$s�oru�s�v�xHu�|-�r��$u�vHvHo9}N�rz<�Nz?x+g{u�s�fCvHxFs�cNq?x�c$s�z?v@d eK�#xF}Norv vHz?q?xYoMuN� � g{z �$s�z?vYzt��x |��2z�� q?orzt��x � z?xF}Nu � wcu�s � u�o �N�pvHu� z?vHqts�o9}Bz � }�����z?qf-zts � |�� z?x |-�xd�� �t����� } � d

� }Nz |��$�$s�uN|-qQ}�s�zb>cNo s�z?vbxF}$|-x�xF}NzJcNvHzts�q?u��NvHxFs4cNq?xHv |]�Az�qFy�z�!+tMo@vxw2y�z�{�pvxz;A7:@v4ANz+o�wcu�sex;}Nz � u � |-o �Ed�>�

Page 23: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

Symptom 1

Disease

Treatment

u

Symptom 2

Symptom n. . .Symptom 1

Disease

Symptom 2

Symptom n. . .

(a) (b)

�bor��c$s�z6� � �c| � ~ � |&��z?vHo |��g�Nz?x+g uNs�fCwcu�s � z � orqt|-� � o |-�N�Nu�vHorv@d �x} � ~ q?u�sHs�z?vF�Bu�� � o �N�Wo � !AcNzt�Nq?z� o |-��sH| � w0uNs � z � oMqt|��xFskzt|-x � zt��x@d

� }Nz � z?xF}Nu � |-vYv$c � z?v�xF}$|-xixF}Norv4vYxFs�cNq?x$c$s�z�orv�|�cNvYzts� v �$}Bz?vHx���cNz?vHv���u�w xF}Nz �Nz?x+g{u�s�f vHxFs4cNq?x$c$s�zxF}$|-x{zt�Nq?u � z?v�xF}Nz4�$}���vHorqt|-���$s�u�}$|�}Nor�rorxHorz?v@d

& o � zt�'| �$s�oru�s��Nz?x+g{u�s�f vHxFs�cNq?x$c$skz�� � g z q?u � �>cNxHz xF}Nz �$s�oru�si�$s�u�}$|�}Nor�rorx �pu-w���<|�v�wcu��r�ruQg v@d��uNsbz � zts�� � |�s�o |�}N�rz0� � o �2 � �rz?x�� � � zt�Nu�xHzixF}Nzj�Nc � }$zts{u�w �Nu � z?v�o � xF}Nz vY� � � z?xFs�orq � o��ezts�zt�Nq?z�u-w/ � � ��� � |�� � / � ��� � �SxF}$|-x{orv � ��/ � � ��� � / � ��� ��� � ��/ � � ��� ��� / � ��� ��� d � }Nzt� � � ��|�� � x;}Nz4�$s�oru�s�Nz?x+g{u�s�f � o��ezts�}���� � � ���� � � |�skq?v@d)�2z�q?u � �>cNxHz xF}Nz��$s�oru�s �$s�u�}$|�}Nor�rorx � }����$zt�$|��Mo#�?o �$� � � }��|�q?u��NvYxF|���x)wK|-q?xHuNs ���� � w0u�s�zt|-qQ} v�cNqQ}C|�s�q�d � }$|-x�orv � g z�vYz?x

� � � �� � � ��� ����� � �����

g }Nzts�z � orv�| �Nu�s � |-�ro��t|�xHoru���q?u��NvYxF|���x � g }Norq?}�g{z�qt|�� or���Nu�s�z�dJ~ u�xHz�xF}$|-x{xF}Norv�|��$�$s�u�|�qQ}�|-vYvHor���Nvzb>c$|-� �$skoMuNs�vxYu zb>cNo � |-�rzt��x �Nz?x+g{u�s�f vHxFs�cNq?x$c$skz?vu��N�r��g }Nzt� xF}Nz{�$s�oru�sb�Nz?x+g{u�s�f vHxFs�cNq?x$c$skz)orvz � �Nx ��_vHz?z\� z?qf-zts � |�� z?xi|-�xd�� �t����� }��]w0u�s{| � orvHq@cNvYvHoru��Cu-w x;}NoMv��$u�o ��x � d

� }NoMviwcu�s � cN� | orv�vHo � �N�rz � |-v orx4s�zb>cNo s�z?v4uN�N�M�pxF}Nz |-vYvHz?vHv � zt��xiu-w�| �$s�oru�s��Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z|�� � | vHo �N���rz q?uN�NvHxF|���x � du~ u��Nz?xF}Nz?�rz?vHv � o w�xF}Nz:cNvHzts�orv\g oM�r�ro �N� � }Nz qt|�� �$s�u � o � z � u�s�z � z?xF|�oM�rz �fN�NuQg �Mz � ��z�}�� |-vYvHz?vHvHo �N� � o��ezts�zt��x �$zt�$|-�rxHorz?v wcu�s � o��ezts�zt��x �Nu � z?v�� � |�� � wcu�s � o��ezts�zt��x �$|�s�zt��xq?u�������c$sY|-xHoru��Nv�u-w{zt|-qQ}p�Nu � z�� � c$��xHo �Nz �O�t���>�@� d ~ �Nu�xF}Nzts � |�s�o |���x u�w xF}Norv4|��$�$s�uN|-qQ}Corv�xHu'|-�r�ru*gxF}Nz5cNvYztsixHu�qt|-xHz?��uNs�orqt|-�r�M�#|-vHvHzts�x�x;}$|-x�vHu � z |�skq?v�o �@xF}Nz �$s�oru�s �Nz?x�g{u�s4f � cNvYx\}$z��$s�z?vHzt��x@d�� zqt|���|-�N|-o �5cNvHz\�Kb c$|�xHoru�� � �$� zh�q?zt�Nx�x;}$|-xJg zivHz?x{xHuI�?zts�u�xF}Nz4�$s�oru�skv u�w �Nz?x+g uNs�f�vHxFs4cNq?x$c$s�z?v{xF}$|-x� u �Nu�x q?u���w0uNs � xHu�xF}Nz?vHz q?u��NvHxFsY|-o ��xHv�d

����� ��� ����� ��� ����� ���� ��� ���� ��� � ���

� }Nz �$u�vHxHzts�oru�s&� �$sku�}$|�}Nor�roMx�� |�� �p� z?q?orvHoru����KxF}Nz?u�skz?xHorq � z?x;s�orq?v4|-�rvHu's�zb>cNo skz�x;}$|-x�g{z |-vHvYoM�N�<�$skoMuNs�vxHu��Nz?x�g{u�s4f4�$|�sH| � z?xHzts�v w0u�sb|��M�e�Bu�vHvHo9}N�rz4�Nz?x+g uNs�f�vHx;s�cNq?x$c$s�z?v@d�� z qt|�� |��MvYuGcNvHzixF}Norv{o ��wcu�s � |-xHoru��

���

Page 24: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

xHuCq?u � �>cNxHz xF}Nz ~ e ��|�� ��� e � � z?xFs�orq?v � u�s�z z�� q?orzt��xH�r� �_vYz?z � z?q?xHoru�� � d ��� d � z � ztsH|���|�cNxF}Nu�s�v}$| � z � orvHq@cNvHvYz � vHo � or� |�s��$sY|-q?xHorqt|-��|��$�$s�uN|-qQ}Nz?v w0uNs)|-vHvYoM�N�No �N��xF}Nz?vYz �$s�oru�s�vOg }Nzt� � |���� vHxFs�cNq?x�c$s�z?v|�s�z��$u�vYvHo9}N�Mz��c��u�u��Bzts |�� � � zts�v$f-u � oMxYv ���t���������t�����>�>� c$��xHo �Nz �2�t������� � �Norz?��z?� }$|-�rxHzts�z?x�|-�xd ���&�����>�� z?qrf-zts � |�� z?x |-�xd � �t����� } � d/eK� xF}Norv vYz?q?xHoru�� � g{z � z?vHqts�o9}$z�xF}Nz4|��$�$s�u�|-q?} u-wS��z?qf-zts � |�� z?x |-�xd

� }Nz?o s |��$�$s�u�|-q?}#orv5}$|-vHz � u��P|ps�z?v$cN�rx w s�u � & z?or��zts |�� � ��z?qf-zts � |�� � �&������� d ~ | � z?�r� � o w|-�r� |��M�ru*g{z � � |�� cNz?v�u-w{xF}Nz �$}���vYoMqt|�� �$s�u�}$|�}NoM�rorxHorz?v |�skz �Bu�vHvHo9}N�rz � xF}Nzt�2�$|�sH| � z?xYztsio � � zt�Bzt� � zt�Nq?z|�� � }�� �Bu�xF}Nz?vHorv'zb>cNo � |-�rzt�Nq?z � o � �N�r��xF}$|-x�xF}Nz �$}���vYoMqt|��4�$s�u�}$|�}Nor�rorxHorz?vpw0uNs q?u � �N�Mz?xYzW�Nz?x+g uNs�fvHxFs4cNq?x$c$s�z?v � cNvHx }$| � zi��o s�orqQ}N�rz?x � oMvYxFs�o9}>cNxHoru��Nv |-v{vF�Bz?q?o���z � o ���2b>c$|-xHoru�� � � g�orxF} xF}Nz q?uN�NvHxFsH|-o ��x

� � � � � �*� � �&� � / � ��� � � ������ � � �*���

g }Nzts�z �� orv�xF}Nz�cNvHzts� v zb cNo � |-�rzt��x v;| � �N�rz�vHo#�?z wcu�s xF}Nz � u � |�o � � � ���orv�xF}Nz�}��$�$u�xF}Nz?vHorv�q?u�s&�

s�z?vF�Bu�� � o �N�pxHu'|����'q?u � �N�rz?xHz��Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z � |�� � � �*� � ��� � / � � � � � ������ � oMv xF}Nz5cNvHzts v

�$s�u�}$|�}NoM�rorx���xF}$|-xc� � �&� |�� � / � � � o �CxF}NzC� s�vHx�qt|�vHz�xHuu}$z vHz?zt��o ��x;}Nz � |-xF|�}$|-vYz�d�i� � zts xF}Nz?vHz�q?u�� � orxHoru��Nv � xF}Nz'�$s�oru�s�v�u��#�$|�sH| � z?xHzts�v w0u�s |-�r�{q?u � �N�rz?xHz'�Nz?x+g{u�s�fCvHxFs�cNq?x�c$s�z?v

� |&��}$z � z?xHzts � o �Nz � }�� � �@� q?u��NvHx;s�cNq?xHo �N�'| �$skoMuNs �Nz?x+g{u�s�f wcu�s{xF}Nz�� s�vYx qt|-vYz4xHu�}$z�vHz?zt��� wKs�u �g }Norq?}�xF}Nz��$s�u�}$|�}Nor�rorxHorz?v�o � �Kb c$|-xYoMuN� �*� � |&��}$z4q?u � �>cNxHz �M� |�� � � ��� |-vHvYz?vHvHo �N� x;}Nz�zb cNo � |��Mzt��xvF| � �N�Mz�vHo#�?z��0o�d z�d � q?uN��� � zt�Nq?z � o �CxF}$|-x��$s�oru�s��Nz?x+g uNs�fMd�e � � z?q?xHoru�� � � g{z4��o � z |��Czh$| � �N�rz�u-w |�$s�oru�s��Nz?x+g{u�s�fWd

� u � z?xHzts � o �Nz �$s�oru�s�v�w0u�s �$|�sH| � z?xYzts�v{u-w o �Nq?u � �N�Mz?xYz��Nz?x+g{u�s�f vHxFs�cNq?x$c$skz?v � ��z?qf-zts � |�� z?x |-�xd� �t����� } � cNvHz xF}Nz�|-vHv$c � �NxYoMuN� u-wP�>l�z+l\�Io@vxo@z��Iy , A72#l�z�qFvxn�|�g }Norq?} vF|&�Nv4xF}$|�x4��o � zt�#x+g{u'�Nz?x+g uNs�fvHxFs4cNq?x$c$s�z?v � �� |�� � � �\� � o w � � }$|�v�xF}Nz�vF| � z4�$|�s�zt��xHv�o � � �� |�� � � �\� � xF}Nzt�

� ��� � � � ��� ��� �_� � ��� � � � ��\� ��� �wcu�s � � � �������8� � � d � }Nz?�pqt|-�r�)xF}Norv �$s�u��Bzts�x��<�$|�sH| � z?xHzts � u � cN� |�s�orx�� � }$z?qt|�cNvYz orx4v;|t�Nv4x;}$|-x�xF}Nz� orvHxFs�o9}>cNxHoru��Nv w0uNs �$|�sY| � z?xHzts�v� �� � zt�Bzt� � u��N�r�'uN��xF}Nz vHxFs�cNq?x$c$skz4u-w)xF}Nz��Nz?x+g uNs�f x;}$|-x orv��ruNqt|-�xHu � |�s�o |�}N�rz � � � �$| � z?�r� � � � u��N�r� � zt�$zt� � v�u�� � � |�� � orxHv �$|�s�zt��xHv@d ��u�s�zh$| � �N�rz � q?u��NvYo � ztsxF}Nz��Nz?x+g uNs�fCvHxFs�cNq?x$c$skz � � |�� � xF}Nz�z � �Nx �pvHx;s�cNq?x$c$s�z w0uNs4uNc$s4x+g{u*� � |�s�o |�}N�rz � u � |-o � g�orxF}q?u�sHskz?vF�$u�� � o �N� }��$�$u�xF}Nz?vYz?v � ��� � |�� � � ��� dSeK�:}$u�xF} vYxFs�cNq?x$c$s�z?v � ��}$|-v{xF}NzivF| � z vHz?x{u-w�$|�s�zt��xHv�_xF}Nz�z � �Nx � vHz?x � d ��u��NvHzb>cNzt��xH�r� � }����$|�sH| � z?xHzts � u � cN� |�s�orx � � � � � � � ��� � ��� �_� � � � � � ��� ��� � d

& o � zt��xF}Nz |�vHv$c � �NxHoru��Nvbu�w �$|�sH| � z?xHzts � u � cN� |�s�orx�� |�� � o � � zt�$zt� � zt�Nq?z � orx)orv | vHo � �N�rz � |-xHxHztsxHu q?u��NvHxFs�cNq?x��$s�oru�skv)wcu�s xF}Nzj�$|�sH| � z?xHztskv)u-w|�� |�s�}NorxFsH|�s�� �Nz?x�g{u�s4f4vYxFs�cNq?x$c$s�zi��o � zt� xF}Nz��$s�oru�s�v{u��q?u � �N�rz?xHz'�Nz?x+g{u�s�fCvHx;s�cNq?x$c$s�z?v@d eK�P�$|�s�xYoMq@cN� |�s � ��o � zt�P�$|�sH| � z?xHzts�o � � zt�Bzt� � zt�Nq?z � g{z q?u��NvHx;s�cNq?xxF}Nz��$s�oru�s�v{wcu�s{xF}Nz��$|�sH| � z?xHzts�v{u-w)zt|-q?}��Nu � z vHzt�$|�sH|�xHz?�r��dJ�Ac$s�xF}Nzts � u�s�z � o w �Nu � z � � }$|-vi�$|�s�zt��xHv/ � o �pxF}Nz���o � zt�p�Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z � g z�o � zt��xHo w0� | q?u � �N�rz?xHz �Nz?x+g{u�s�f vHx;s�cNq?x$c$s�z�g }Nzts�z!� � }$|-vxF}Nz?vHz��$|�s�zt��xHv � |�� � cNvHz �$|�sH| � z?xHzts � u � cN� |�s�orx �2xHu � z?xHzts � o �Nz�xF}Nz �$skoMuNs�v w0u�s xF}Norv �Nu � z�d � }Nz

���;1�5$@64<9<>=OE��_,W7>a`,WC�68-�S �;,�1*eA,WC.NP68- G�� � ���`K U C.38BO,�S�5$+ 7>: C.,�:$@ <>5 @:$79-a�38-�<>=#<979eA,W<979+�3A3AS ,"!O@ 7>B468<>,W-1�,OY���

Page 25: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

s�z?v$cN�rx�orv�| vF�Bz?q?o |��)qt|-vHz�u-w)x;}Nz � � � z?xFskoMq � qt|-�r�rz � xF}Nz � ��z � z?xFs�orq � xF}$|-x4|-vYvHor���Nv�zb c$|��vHq?uNs�z?vxHu zb>cNo � |-�rzt��xj�Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z?v@d2eK� � z?q?xHoru��6� � g{z or�r�9cNvHxFsH|-xYz�x;}Nz\cNvHz4u-w�xF}Norv � z?x;s�orq�d

����� ����� ����� ������������

eK�#x;}NoMv vHz?q?xHoru�� � g z zh$| � o �Nz�vHzt|�s�q?} � z?xF}Nu � v w0uNs4o � zt��xHo w0�No �N�S�Nz?x+g uNs�fCvHxFs�cNq?x$c$skz?vGg oMx;}P}NoM�N}vHq?u�skz?v@d/� vHvHzt��xHo |-�r�M��|-�r��v�cNqQ} vHzt|�s�q?} � z?xF}Nu � v � |�f-zScNvHz u-wB|i�$s�u��Bzts�x�� u�w xF}Nz vHq?u�s�o �N� � z?xFs�orq?v�xF}$|-xg{z{qt|-�r� � z?q?u � �Bu�vF|�}Nor�rorx���d & o � zt� |��Nz?x+g uNs�fivHxFs�cNq?x�c$s�z w0u�s � u � |-o �1 � g{z v;|t� xF}$|-xb| � zt|�v$c$s�z{u��xF}$|-x vHxFs�cNq?x$c$skz�oMv , o;:�y\��� y�prl 1 2#o�o w)orx�qt|���}Bz�g s�orxHxHzt�C|-v | �$sku � cNq?x�u�w � zt|�v$c$s�z?v � zt|�qQ} u-w2g }Norq?}orv | w<c$�Nq?xYoMuN��u��N�r� u-wu��Nz4�Nu � z4|�� � orxHv �$|�skzt��xHv�d/��u�s zh | � �N�rz � w sku � �2b>c$|-xHoru�� �>��� g{z�vHz?z�xF}$|-xxF}Nz �$s�u�}$|�}NoM�rorx�� � � � � � �� ��� � ��o � zt�P}��'xF}Nz � � � z?xFskoMq�orv � z?q?u � �$u�v;|�}N�rz�d �{u��NvYzb cNzt��xH�r� � o w�xF}Nz�$s�oru�s��$s�u�}$|�}NoM�rorxHorz?v�u-wj�Nz?x+g{u�s�fCvHx;s�cNq?x$c$s�z?v |�s�z � z?q?u � �Bu�vF|�}N�rz �c|�v�x;}Nz?�W|�s�z o ���2b>c$|-xHoru�� �����?�xF}Nzt� vHu�oMvixF}Nz � � � z?xFskoMq�d � }NcNv � g{z�qt|���g skoMxYz

� � � � � �� � � �������� %��*� � � / � � � �����

g }Nzts�z1%��*� � �3/ � � oMv u��N�r�W| w(c$�Nq?xHoru��pu-wc� � |�� � orxHv��$|�s�zt��xHv@d�npu�vHx � |&��z?vHo |�� |�� � �NuN��� � |&��z?vYo |��� z?xFskoMq?v |�s�z � z?q?u � �Bu�vF|�}N�rz�d & o � zt�g| � z?q?u � �$u�vF|�}N�rz � z?x;s�orq � g{z�qt|��#q?u � �$|�s�z xF}Nz�vHq?u�s�z wcu�sx+g{u<�Nz?x+g{u�s�fpvHx;s�cNq?x$c$s�z?v�xF}$|-x � o��eztsu}��WxF}Nz�| �$� orxHoru�� u�s � z?�Mz?xYoMuN�Pu-w4|�s�q?v �$u�o ��xHo �N�#xHu � � � }��q?u � �>cNxYo �N� u��N�r� xF}Nz4xHzts � %N�*� � � / � � w0u�sB}$u�xF} vYxFs�cNq?x$c$s�z?v�d

�bo s�vYx � �rz?xkcNviq?u��NvHo � ztsixF}Nz vF�$z?q?o |-�bqt|�vHz�u-w2� � � o �N��xF}Nz��Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z�g�orxF} xF}Nz�}Nor��}Nz?vHxvHq?u�skz | � uN�N�j|-�r�$vHx;s�cNq?x$c$s�z?v�o �\gi}NoMq?}�z � ztsk�4�Nu � z�}$|-v)|-x � u�vYxeu��Nz��$|�s�zt��x@d���u�s zt|-qQ}�|�skq � � ��_o �Nq?�9c � o �N��qt|�vHz?v2g }Nzts�z#� orv{��cN�r� �?� g{z�|-vHvYu�q?o |-xHz{|Cg{z?oM�N}�x��I�*� � �`� � � �ru�� %N�*� � �9� � � �ru���%�� � � �� � d� sku � �2b>c$|-xHoru�� ���$� g z4}$| � z

�ru�� � � � � � �� � ������ �Mu���%N�*� � � � � � �\���

������ �G�*� � �� � � �

����� �ru�� %N�*� � �� �

g }Nzts�z� � orv{xF}Nzu�c�$u�vYvHo9}N�M� � ��cN�r�e�$|�s�zt��x)u�w � � d � }Nzi� |-vHx{xHzts � o �5�Kb c$|-xYoMuN� �\� orv{xF}NzivF| � z�w0u�s |-�r��Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z?v@d � }�cNv � | � u��N� xF}Nz �Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z?v�o � g }Norq?}pzt|-q?}<�Nu � z }$|-v4|�x � u�vHxu��Nz��$|�s�zt��x � sY|��>f�o �N� �Nz?x+g{u�s�f�vYxFs�cNq?x$c$s�z?vI}��2v$c � u-w�g{z?or��}�xHv�� ���� �G�*� � � � � u�s�}�� vHq?u�s�z }$|-vxF}Nz�vF| � z4s�z?v$cN�rx@d

�bo � � o �N� xF}Nzj�Nz?x+g{u�s�f vHxFs�cNq?x$c$skz�g�orxF} xF}Nz4}Nor��}Nz?vHx�g{z?or��}�x{oMv�| vF�$z?q?o |-��qt|-vHziu-w)|�g z?�r����fN�NuQgi��$s�u�}N�rz � u-w�� � � o �N�&�Il$�Qq$� A�� 1z+l�t :���qst�-�p � z?vHqts�o9}Bz � �Pw0u�s zh$| � �N�rzO�So � � � |��Nv |�� � npo �Norz@ft|� �t���>�@� d � }Nz<�$sku�}N�rz � oMv � z�� �Nz � |-v wcu��r�Mu*g�v�d ~ vxz�o�o�!02#q9{*o�tWo@vxw2y�z4{�orv'| q?u��$�Nz?q?xYz � � o s�z?q?xYz �|-q?�Nq?�roMq��NsH|��$}�o �^g }NorqQ} �Nu4x+g{u�z � ��z?v |�s�z � o s�z?q?xHz � o ��xHu4xF}Nz vF| � z �Nu � z�d � }Nz�s�uNu�xbu-w|�x;s�z?z��K�ro f�z�Nz?x+g{u�s�f�orv�|\c$�No#b>cNz4�Nu � zixF}$|-x)}$|�v �Nu4z � ��z?v � o s�z?q?xYz � o ��xHu�oMx�d ~ 1 z�l�t :��NqFt - orv | � o s�z?q?xHz � wcu�s�z?vHx

�*�

Page 26: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

xF}$|-x�q?u��NvYoMvYxHv u-w � orv�� u�o ��x xFskz?z��K�Mo9f-zp�Nz?x+g uNs�f�v�d ~ p.�>l�tMtWqFt -�1z+l�t : ��qst�-�orv |���� }$sY|��NqQ}No �N�#xF}$|-xo �Nq?�9c � z?v |-�r� �Nu � z?v�o �@xF}Nz �NsH|��$}Ed ~ �Il$�Qq$� A�� 1z+l�t :���qst�- oMv |����'v;�$|��$�No �N��}$sY|��NqQ}No �N� g }Norq?}� |*hNo � o#�?z?v x;}Nz v$c � u-wj|�s�q:g{z?or��}�xYv �0o �#uNc$s�qt|-vHz � � ���� �I�*� � �� � ��� d ~ �#z�� q?orzt��x �$u��M�$�Nu � o |-�|-�r��u�skoMx;} � w0u�sm� � � o �N�<| � |�h�o � c � }$sY|��NqQ}No �N� g�|�v�� s�vYx � z?vHqtsko }Bz � }���� ��� u�� � v5� �&�\� � �?� � |�xHztszh$�N�MuNs�z � }�� % |�sY�u� �t� � ���?� |�� ��� | � z � u�s�zbz�� q?orzt��xS}�� � |�s"�H|��u� �t� ��� � |�� �5& |�}$u*g z?x�|-�xdm� �t���*��� d

� }Nz?vHz |-�r��u�skoMx;} � v4qt|�� }$z�cNvHz � xHu:� � � xF}Nz }$sY|��NqQ}No �N� g�orxF}px;}Nz }Nor��}Nz?vHx�vHq?uNs�z s�z?��|�s � �rz?vHvu-w x;}Nz � z?x;s�orq5g{z�cNvHz � |-v��ru��N�W|-v u��Nz�qt|��#|-vHvHuNq?o |-xHz�| g z?or��}�xIg�orxF}2z � zts�� z � ��z�d � }Nzts�z;w0uNs�z �xF}Norv�|-�r��u�s�orxF} � orv�|��$�$s�u��$s�o |-xHz wcu�s)|���� � z?q?u � �Bu�vF|�}N�rz � z?xFskoMq�d�� }Nzt�:cNvHo �N� � z?xFs�orq?v{xF}$|-x |�vHvHor���zb>c$|-�evHq?u�skz?v�xHu�zb cNo � |-�rzt��x4�Nz?x+g{u�s�f�vYxFs�cNq?x$c$s�z?v � }Nu*g z � zts � g z4}$| � z

%��*� � � � � %N�*� �� �_� %��*� � � � � %N�*� � �� �� }NcNv � wcu�sb|�����x+g uiz � ��z?vP� � � |�� � � � � � � xF}Nz�g{z?or��}�xYv �I�*� � �O� � |�� � �I�*� �O� � � |�s�z�zb>c$|-�xd�{u��NvYzb cNzt��xH�r� � xF}Nz � o s�z?q?xHoru��$|-�rorx��'u-wexF}Nz4|�skq?v��N� |&�Nv��Nu s�u��rz�wcu�s v$cNq?} � z?xFs�orq?v � |�� � x;}Nzj�$s�uN}N�Mz �s�z � cNq?z?v xHuu� � � o �N�CxF}NzGc$� � o s�z?q?xHz � wcu�s�z?vHx w0uNs�g }Norq?} � �I�*� � �`� � orv4| � |�h�o � c � d � }Norv�vHzt|�s�q?}qt|���}Bz � u��NzIcNvHo �N� | � |*h�o � c � vF�$|��$�No �N� xFs�z?z4|��M��u�s�orxF} � d

~ u*g � �Mz?xJcNv)q?u��NvYo � zts xF}Nz{qt|-vHz�gi}Nzts�zJg zO� � � xF}Nz�}$z?vHx{�Nz?x+g uNs�f w sku � x;}Nz�vHz?xbu-we|-�r���Nz?x�g{u�s4f�vo � g }Norq?}pzt|-q?}<�Nu � z }$|-v4�Nu � u�s�z�xF}$|�� � �$|�s�zt��xHv@d\�i��wcu�s�x$c$�$|-xYz?�M� � xF}Nz �$s�u�}N�rz � wcu�s � � � oMv~ � � }$|�s � �c� }NoMqf-zts�o �N�gz?x'|-�xd �t������� d � }Nzts�z;wcu�s�z � orx�orv<|��$�$s�u��$s�o |-xHzpxHu�cNvHzW}Nz@c$skoMvYxHorq vHzt|�s�q?}|-�r��u�skoMx;} � v@d

npu�vYx�u-w x;}Nz�q?u � � u��N�r� � orvHq@cNvYvHz � vHzt|�skqQ} � z?xF}Nu � viwcu�s��rzt|�sY�No �N� � |t��z?vHo |��p�Nz?x�g{u�s4f�v � |�f-zv$cNq?q?z?vHvYo � z |�skq<q?}$|��N��z?v�xYuPxF}NzW�Nz?x+g{u�s�f � |�� � z � �N�Mu-�gxF}NzW�$s�u��Bzts�x��Su-w � z?q?u � �Bu�vF|�}Nor�rorx � xHuz � |�� c$|�xHz'xF}Nz � zts�orx u-w�zt|-q?}#qQ}$|��N��z�d � }Nzp�$u�vHvYo }N�rzpq?}$|��N��z?v xF}$|�x qt|���}$z � | � zp|�s�z�zt|-vH�#xHuo � zt��xYo wc��dP��u�s4|����W�$|�o s u-w � |�s�o |�}N�rz?v � o wjx;}Nzts�z orv |��W|�skq q?u��$�Nz?q?xHo �N� xF}Nz � � xF}Nzt�#xF}Norv |�s�q qt|��z?orxF}NztsJ}$z�s�z � zts�vYz � u�s)skz � u � z � d2e_wexF}Nzts�ziorv �Nu |�s�q�q?uN�$�Nz?q?xHo �N��x;}Nz ��� xF}Nzt� |�� |�s�q�qt|��u}Bzj| �$� z �o �#z?orxF}Nzts � o s�z?q?xYoMuN�Ed ~ �r�{qQ}$|��N��z?v |�s�z v$c>}���z?q?x xHuCxF}Nz�q?u��NvHxFsY|-o ��x�xF}$|-x�xF}Nz�s�z?v$cN�rxHo �N�P�Nz?x+g uNs�fq?u���xF|-o �Nv �Nu � o s�z?q?xYz � q?�Nq?�Mz?v�dW�2z�cNvHz � xHu � zt�Nu�xHz�xF}Nz�vHz?x�u-w�z?�ror��o9}N�Mzpq?}$|��N��z?v xYu@|@��sH|��$} �|�� ��� �4' � xHu � zt�Nu�xHz xF}Nz4q?}$|��N��z o �'�ru�� vHq?u�s�z u-w x;}Nz��Nz?x+g{u�s�f s�z?v$cN�rxHo �N� w sku � xF}Nz � u � o���qt|-xYoMuN�'�� � d & o � zt��| � z?q?u � �Bu�vF|�}N�rz � z?xFs�orq � o wb|�� |�s�q xYu � � oMvi| �$� z � uNs � z?�rz?xHz �e� u��N�r��%N�*� � �3/ � � �Nz?z �}$z�z � |-�9c$|-xHz � xHu � z?xHzts � o �Nz � � ' � d2e_wb|�� |�s�q�}$z?x+g{z?zt��� � |�� � � orv s�z � zts�vHz �e� xF}Nzt� u��N�r� %��*� � �3/ � �|�� � %N�*� �3/ � �Nz?z � }$z z � |-�9c$|-xYz � d

� �Nz vHo � �N�rz<}Nz@c$skoMvYxHorq'vHzt|�skqQ} |��M��u�s�orxF} � orv62#yB:�l�22po$l�z : ���_z�d �Md � $�u�}$�NvHuN� ���t������� d��bo s�vHx � g{zq?}Nu�u�vYz | ��sH|��$}Ed � }Nzt� � g{z�z � |�� c$|�xHz � �4' � wcu�s�|-�r� '�� � � |�� �#� |�f-z�xF}Nz q?}$|��N��z%'�wcu�sCg }Norq?}� �4' � oMvi| � |*h�o � c ��� �$s�u � o � z � orx�orv �Bu�vHorxHo � z�d � zixHzts � o �$|-xHz�vYzt|�s�q?}ug }Nzt� x;}Nzts�z�orv��Nu%'Cg�orxF}�|�$u�vHorxHo � z � |�� cNz w0u�s � �4' � d�� vHo �N� � z?q?u � �Bu�vF|�}N�rz � z?xFs�orq?v � g{z�qt|��'| � u�o � s�z?q?u � �>cNxHo �N�'|-�r�bxHzts � v� �4' � |&wcxHzts z � zts���qQ}$|��N��z�d2eK���$|�s�xYoMq@cN� |�s � o w �Nz?orxF}NztsP� � � � � �Nu�s xF}Nz?o s{�$|�s�zt��xHv |�s�z�q?}$|��N��z �e� xF}Nzt�� �4' � s�z � |-o �Nvuc$�NqQ}$|��N��z � wcu�s4|��M� qQ}$|��N��z?v*' o � � u�� � o �N� xF}Nz?vHz'�Nu � z?v |-v��ru��N� |-v�xF}Nz's�z?v�cN�MxYo �N�

���

Page 27: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

�Nz?x+g{u�s�fCorv |-q?�Nq?�Morq�dS� |�� � o � |-xHz?v�wcu�s�x;}Nz�o �NorxHo |-�i��sH|��$} o �Nq?�9c � zpxF}Nz z � �Nx �2��sH|��$} � |psH|�� � u ���sH|��$} � |��NsH|��$} � z?xHzts � o �Nz � }���u��Nz�u-w]xF}Nzj�Bu��r� �Nu � o |-� |-�r��uNs�orxF} � v � z?vYqts�o9}$z � �$s�z � oru�cNvH�r� o � xF}NorvvHz?q?xHoru�� � |�� � xF}Nz4�$skoMuNs��Nz?x+g uNs�fMd

~ �Bu�xHzt��xHo |-�e�$s�u�}N�rz � g�orxF} |������ruNqt|-���KvHzt|�s�q?} � z?xF}Nu � oMv ��z?xHxHo �N�4vYx$cNqrf |-x | �MuNqt|-� � |*hNo � c � dnpz?xF}Nu � v{w0uNs)z?vYqt|��No �N� �ruNqt|-� � |*hNo � |�o �Nq?�9c � z�oMxYztsH|-xHz � }Nor�r���Kq?�Mo � }No �N�p|�� � vHo � cN� |�xHz � |��$�Nzt|��Mo �N�MdeK� qsvxo@z+l�vxo , �Nq=292 ! :B2#q$��1qst�- � g{z |��$�N�M� �MuNqt|-��vHzt|�s�q?}uc$��xHor�Ag{z }Norx{|��ru�qt|�� � |*hNo � c � d � }Nzt� � g zisH|����� u � �r���$zts�x�c$s�}�xF}Nz�q@c$sYs�zt��xi�Nz?x�g{u�s4f�vHxFs�cNq?x�c$s�z � |�� � s�zt�Bzt|-x�xF}Nz4�$sku�q?z?vHv�w0u�s�vHu � z � |��$|-��zt|�}N�rz�Nc � }Bzts�u�worxHztsH|-xHoru��Nv�d

e ��u��Nz � |�sko |���x u-w/pqX� A72#l�vxo , l�tWtMo�l�2#qFt - � z?vHqts�o9}Bz � }���npz?xFs�u��Bu��rorv)z?x |���dC� �t�������?� g{z�o �NorxHo |-�ro#�?zxF}Nz vH��vYxHz � |-x�vYu � z�xHz � �BztsH|-x$c$skz�� � d � }Nzt� � g{z��NoMqf vHu � z�z?�Mor��o9}N�rz qQ}$|��N��z�'�|�x sH|�� � u � � |�� �z � |�� c$|�xHz�xF}Nz�zh$�$s�z?vHvHoru�� � � zh �L� � �4' ��E �

�� d2e0w � � ��� xF}Nzt�:g{z � |�f-zixF}Nz�qQ}$|��N��z�' � u�xF}Nzts g�orvHz �

g{z � |�f-z xF}Nz�q?}$|��N��z\g oMx;}'�$s�u�}$|�}NoM�rorx�� � d � z�s�zt�$zt|-xixF}NorvivHz?�rz?q?xHoru��p|�� � z � |-�9c$|-xHoru��p�$s�uNq?z?vHv��xHo � z?v u�s�c$��xYoM�Og{z � |�f-z��Pq?}$|��N��z?v@d:e_w�g{z � |�f-z �Nu'q?}$|��N��z?v�o ����s�zt�$z?xHorxHoru��Nv � x;}Nzt� g{z�vYxHu��vHzt|�skqQ}No �N�Md � xF}Nzts g�orvHz � g{z �ru*g{zts xF}Nz xYz � �$ztsH|�x$c$s�z�}�� � cN�rxHo �N�r��o �N�#xF}Nz q@c$sHs�zt��x�xYz � �$ztsH|�x$c$s�z��}��W| � z?qt|&�pwK|-q?xHu�s � �� ��� |�� � q?uN��xHo �NcNz�xF}Nz vHzt|�s�q?}P�$s�uNq?z?vHv@dp� z�vHxYu�� vYzt|�s�q?}No �N�po w

g{z4}$| � z��ruQg{zts�z � x;}Nz4xHz � �BztsH|-x$c$skz � u�s�z�xF}$|�� �4xYo � z?v@d � }�cNv � xF}Norvj|-�r��uNs�orxF} � orv q?uN��xFsku��r�Mz � }��� � z4�$|�sY| � z?xHzts�v���

���d��� � � |�� � �Nd � u�o �NorxHo |-�ro#�?z xF}Norv |-�r��u�skoMx;} ��� g ziqt|�� vHx;|�s�xSg oMx;} xF}Nz z � �Nx �

��sH|��$} � |�� � � |�f�z�� � � |�s���z{zt�Nu�cN��}�vYu�xF}$|-x)|-� � u�vYxbz � zts��4z?�ror��o9}N�rz�qQ}$|��N��z{oMv � | � z � xF}�cNvbqtskzt|-xHo �N�|�sH|�� � u � ��sH|��$}Ed ~ �MxYztsH�$|-xHo � z?�r� � g z � |&� vHx;|�s�xJg�orxF}�| �ruQg{zts{xYz � �$ztsH|�x$c$s�z � |�� � cNvHz�u��Nz�u�wxF}Nzo �NorxHo |-�ro��t|�xHoru�� � z?xF}Nu � v � z?vHqtsko }Bz � wcu�s �MuNqt|-��vHzt|�s�q?}Ed

� x;}Nzts � z?x;}Nu � v w0uNs�z?vHqt|��No �N�P�ru�qt|�� � |�h�o � |2o �Nq?� c � z }$z?vHx+�x� skvHx vYzt|�s�q?}�� % u�s w �C�t������� |�� �& o9}>}Nv��vF| � �N�Mo �N�P�_vHz?z � z?q?xHoru�� � d ��� d

� � �� ����� ZBY ��[�������� � ��

�bor��c$s�z � or�r�9cNvHxFsH|-xYz?v |�� |��$�N�rorqt|-xHoru�� u�w x;}Nz?vHz xYz?qQ}$�No#b>cNz?v�xHu4x;}Nzjs�zt|�� �(g{u�sk� � � u � |�o � u-w/eK�B� � zt���xHor� |-xHu�s � |��$|-��z � zt��x � xF|�f-zt� wKs�u � ��z?qf-zts � |�� z?x |-�xd�� �&����� } � d �bor��c$s�z � | orv |4}$|�� � �Kq?u��NvHxFs�cNq?xYz �� |&��z?vHo |��P�Nz?x+g{u�s�f w0uNs4x;}NoMv � u � |-o � � qt|-�r�rz � x;}Nz ~ � |�s � �Nz?x�g{u�s4f � � z?o �N�rorqQ}gz?x |-�xd ���&������� �_xF}Nz�$s�u�}$|�}NoM�rorxHorz?v�|�s�z��Nu�xivF}Nu*g � � dO�bor��c$s�z � q oMv�| � |-xF|�}$|-vYz�u-w �t�$� ����� qt|-vHz?vixF}$|-x�orv�vF| � �N�Mz � wKs�u �xF}Nz ~ � |�s � �Nz?x�g{u�s4fMdO�bor��c$s�z � } oMv�| }��$�$u�x;}Nz?xHorqt|-��$s�oru�si�Nz?x+g uNs�f�wcu�s{x;}Nz � u � |�o �EdJ� z?qrf-zts � |��z?x)|-�xd�� �&����� } � q?u��NvHxFs4cNq?xHz � xF}Norv �Nz?x+g{u�s�f�}�� | �$� o �N� ��� z?�rz?xHo �N� � |�� � s�z � zts�vHo �N��|�skq?vbo � xF}Nz ~ � |�s ��Nz?x+g{u�s�f |�� � }��'| �$� o �N���Nu�orvHz4xHu�xF}Nz4�$sku�}$|�}Nor�roMxYoMz?v u-wbxF}Nz ~ � |�s � �Nz?x+g uNs�fMd

�bor��c$skz �-� vF}Nu*g�v)xF}Nz � u�vYx)�ro9f-z?�r� �Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z{wcu�c$� � }����ruNqt|-�]vHzt|�s�q?} o �NorxHo |-�ro#�?z � g�orxF}xF}Nz��$s�oru�s �Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z\cNvHo �N��xF}Nz � ��z � z?xFs�orq � |���zb>cNo � |-�rzt��x�vF| � �N�rz�vHo#�?z �� � �*��� |�� ��$s�oru�s�viu����Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z?v � z?xYzts � o �Nz � }����2b>c$|-xHoru�� ��� g�orxF} ��� �BE ��� ���@� d{�{u � �$|�s�o �N�xF}Nz xF}$s�z?z)�Nz?x+g{u�s�f{vHx;s�cNq?x$c$s�z?v � g{zbvHz?z)x;}$|-xexF}Nzb�rzt|�sH�Nz � �Nz?x+g{u�s�f{vYxFs�cNq?x$c$s�zborv � cNqQ} q?�Mu�vHztsexYu�xF}$|-x

�\�

Page 28: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

17

25

6 5 4

19

27

20

10 21

37

31

11 32

33

22

15

14

23

13

16

29

8 9

2812

34 35 36

24

30

72618

321

17

25 18 26

1 2 3

6 5 4

19

27

20

10 21

35 3736

31

11 32 34

1224

33

22

15

14

23

13

16

29

30

7 8 9

28

case # x1 x2 x3 x37

1

2

3

4

10,000

3

2

1

3

2

3

2

3

2

2

2

2

3

3

2

4

3

3

1

3

L

L

M O

(a)

(d)

(b)

17

25 18 26

3

6 5 4

19

27

20

10 21

35 3736

31

11 32 34

1224

33

22

15

14

23

13

16

29

30

7 8 9

28

21

AA

A

A

RR

R

R

D

D

DD

R

D

D

(c)

�bor��c$s�z � ���c| �i� }Nz ~ � |�s � �Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z�dG�x} � ~ �$s�oru�s��Nz?x+g{u�s�f zt�Nq?u � o �N�p|5cNvHzts vk}Bz?�roMz;wcv|�}Bu�cNx�xF}Nz ~ � |�s � � u � |-o �Ed5�_q � ~ �t�$� ����� �Kqt|-vYz � |-xF|�}$|-vYz4��zt�NztsH|�xHz � w s�u � xF}Nz ~ � |�s � �Nz?x�g{u�s4fMd� �M� � }Nzj�Nz?x+g{u�s�f �rzt|�sH�Nz � w s�u � xF}Nz��$s�oru�s)�Nz?x+g{u�s�f�|�� � | �t�$� ����� qt|-vHz � |-xF|�}$|-vYz���zt�NztsH|-xYz � wKs�u �xF}Nz ~ � |�s � �Nz?x+g{u�s�fWd ~ s�q?vixF}$|-x |�skz�| �$� z �e��� z?�rz?xHz �e� u�sis�z � zts�vHz � g�orxF}'skz?vF�$z?q?xixHu xF}Nu�vHz4o �CxF}Nz~ � |�s � �Nz?x+g{u�s�fC|�s�z o � � orqt|-xHz � g�orxF} ~�� � � |�� � y � s�z?vF�$z?q?xYo � z?�M��d � � |�f-zt� w s�u � ��z?qf-zts � |��pz?x|-�xd ���&����� }Ed �

� �

Page 29: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

u-w{xF}Nz ~ � |�s � �Nz?x+g{u�s�f xF}$|��CxF}$|�x u-w{xF}Nz �$s�oru�s��Nz?x+g{u�s�fWd��Ec$s�xF}Nzts � u�s�z � xF}Nz � u�o ��x � orvHxFs�o9}>cNxHoru��zt�Nq?u � z � }���x;}Nz4�rzt|�sH�Nz � �Nz?x+g{u�s�f orv � cNqQ} q?�Mu�vHztsixHu xF}$|-x�u-w)x;}Nz ~ � |�s � �Nz?x+g uNs�f xF}$|�� xF}$|-x�u-wxF}Nz4�$s�oru�s �Nz?x�g{u�s4fMd2eK���$|�s�xHorq@cN� |�s � g }Nztskzt|-v�xF}Nz�qts�u�vHv�zt��xFs�u���� u-wx;}Nz.� u�o ��x � orvHxFs�o9}>cNxHoru��Nviu-wbxF}Nz�$s�oru�s��Nz?x+g{u�s�f�g oMx;}Ws�z?v;�$z?q?x xHuCxF}$|-x u-w�xF}Nz ~ � |�s � �Nz?x+g{u�s�f�orv � d �B� x;}Nz qts�u�vHv�zt��xFs�u����pu-w�xF}Nz��u�o ��x � oMvYxFs�o9}>cNxHoru�� u-w]xF}Nz��rzt|�sH�Nz � �Nz?x+g{u�s�fag�orxF} s�z?vF�Bz?q?x{xHu�xF}$|-xbu-wexF}Nz ~ � |�s � �Nz?x+g uNs�f�orv � d ��� d �� }Nz��rzt|�sH�No �N�'|-�r��u�skoMx;} � }$|-viz��ez?q?xHo � z?�r�PcNvHz � xF}Nz � |-x;|�}$|-vHz xHu �Hq?u�sYs�z?q?x�� xF}Nz��$s�oru�sCfN�NuQg �Mz � ��zu-wbxF}Nz\cNvHztsd

� � `�� �E`�V���� �JX �

eK�ps�zt|�� � |-xF|�}$|�vHz?v � u�}NvHzts � |-xHoru��Nviu-w)u��Nz�u�s � uNs�z � |�s�o |�}N�rz?v4o �Cu��Nz4uNs � uNs�z�qt|-vHz?v4|�skz4x�� �Norqt|-�r�r�� orvHvHo �N�Md2e �4x;}NoMvbvYz?q?xHoru�� � g{z)q?u��NvHo � zts zh�xHzt�NvYoMuN�NvbxHu �$s�z � oru�cNv � z?xF}Nu � vbxF}$|-xeqt|��4}$|�� � �rz � orvHvYo �N�� |-xF|�d �2z�qt|�cNxHoru��CxF}Nz s�zt| � ztsixF}$|-xixF}Nz � z?xF}Nu � v�g{z � oMvYq@cNvHv4|-vHv$c � z�x;}$|-x�gi}Nz?xF}Nztsiu�s��Nu�x�|��u�}NvHzts � |-xHoru��2orv � orvHvHo �N� orv o � � zt�Bzt� � zt��x u-w xF}Nz�|-q?x$c$|��)vHxF|�xHz?v4u-wixF}Nz � |�s�o |�}N�rz?v@dR��u�s zh | � �N�Mz �xF}Nz?vHz � z?xF}Nu � vi|�s�z��Nu�x |��$�$s�uN�$s�o |-xHziwcu�s{| � z � oMqt|�� � |-x;|�}$|-vHzCg }Nzts�z � |-x;|�|�}$u�cNx � s4cN� skz?vF�$u��NvYzorv � oMvYvHo �N� o ��x;}Nu�vHz4�$|-xHorzt��xHv�g }Nu:}$z?qt| � z xHuNu�vYoMqf xHu�xF|�f�z�xF}Nz � s�cN�Mdbnpz?xF}Nu � v{wcu�s{| �$� s�z?vHvYo �N�� zt�$zt� � zt�Nq?orz?v�o �pu � orvHvYoMuN�Nv4}$| � zG}$z?zt�Czh$�N�ru�s�z � }����_z�d �Md � y�c>}No ��� �t� � ���?� y{uN}No �Nv5� �t���\���7� |�� �� zt|�s��S� �&������� d

����� � ���� � � ��������� �

�bo s�vHx � �rz?x\cNv�q?u��NvYo � zts xF}Nz�vHo � �N�rz vHorx$c$|-xYoMuN� g }Nzts�zIg{z�u�}NvHzts � z�| vHo �N���rz o �Nq?u � �N�rz?xHz qt|-vHz � o �� u � |�o �$Id��]z?x � � zt�Nu�xHz4x;}Nz � |�s�o |�}N�rz?v��Nu�x�uN}NvHzts � z � o �CxF}Nz4qt|-vYz�d�� � � ztsixF}Nz�|-vHv$c � �NxHoru���u-w�$|�sH| � z?xHzts o � � zt�$zt� � zt�Nqtz � g{z�qt|�� q?u � �>cNxHz�x;}Nz4�$u�vHxYzts�oru�s � orvHx;s�o9}>cNxHoru��Cu-w � � |�v{w0u��M�ru*g�v��

� ��� � � � ��� � � � � � � � � ��� � � ��� � � � � � ��� �� �

�� � � �

�� ���� ��� ������ ��� � � � !� � ��� ���� � ��� � � �P� � ��� �� �

�� � � �� �*� � � / � � �G� � ��� � � �P� � ��� �

� � ��� � ��/ � ��� � � ��� ����� � ��� � � � � � �� �� � � �*� � � � � / � ��� � � ��� ��� � ��� � � � � � � � / � ��� ��� � � � � � �

�)|�qQ}CxHzts � o �Cq@c$s��r�P}$sH|-qf-z?xHv�o �P�Kb c$|-xYoMuN� � � orv�| ��o s�orq?}N�rz?x � orvHxFs�o9}>cNxHoru��Ed � }�cNv � c$�N�rz?vHvG}Bu�xF}� � |�� � |-�r��xF}Nz � |�s�o |�}N�rz?v�o � / � |�s�z u�}NvHzts � z � o �Cqt|-vHz � � xF}Nz �$u�vHxHzts�oru�s � orvHxFs�o9}>cNxHoru��Cu-w � � g�or�M�� ��=���64=#3�� 1�3ONdU64C*7>:*38-�E\5$+,�1WC.3`:*: ,.- 5$C.34U =?3�� 64-g,�NdU5$=P-�,Q5 �Z38C*e��Z+3O:*,�U�C.38D�68D�79<97>5$7V,�: 64C.,�S ,�5*,WC.Nd79-,�S�� C.3`N5$+,�NP64C.a879-�68<>:�3"� 5$+, � <>64C.N -,�5 �Z38C*e � 7>5$+cC.,�:$U\,�1Q5_5*3P5$+6O5R3"� 5$+, � <>68C.N -�,Q5 �Z38C*e?7>:��� Y � Y

���

Page 30: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

}$z�| �ro �Nzt|�siq?u � }No �$|-xHoru�� u-wb��o skoMq?}N�rz?x � orvHxFsko }>cNxYoMuN�Nv@d � cNq?} � orvHxFsko }>cNxYoMuN�Nv4|�s�z4vYu � z?xHo � z?v�qt|��M�rz ���qFz�q=: � 2#o@v��Iq �Qv4ANz�o p � |�� � xF}Nz��$s�u�}$|�}NoM�rorxHorz?vG� � � � ��/ � ��� � � ��� ��� |�� � � �*� � �&� � / � ��� � � ��� � � ���� �������4��� � |�skz�qt|-�r�Mz � �Iq �Qqst�-�:$y�o�� :�qFo�tMvspd

e0w/g{z�u�}NvHzts � z x+g{u�qt|-vHz?v � xF}Nzt� xF}Nz�vYoMx�c$|-xHoru���}$z?q?u � z?v � u�skz q?u � �N�Mzh � }Bz?qt|�cNvHz4x;}Nz�q?u � �>c��xF|-xYoMuN�4u�w�xF}Nz � o#h�o �N�4q?uNz�� q?orzt��xHv)o � � u�� � z?vL� � � o �N�4xF}Nz � zt|��Nvbu-w ��o s�orq?}N�Mz?x � o#h�x�c$s�z?v@d2eK����zt�NztsH|-� �|-vbvF}Nu*g �:�_z�d �Md � o � �{uNu��$ztsb|�� � � zts�v$f�u � orxHv�� �t�������?� x;}Nz q?u � �>cNxF|-xHoru��$|��$q?u � �N�rzh�orx��4u�w xF}Nz{zh$|-q?xq?u � �>cNx;|-xHoru�� u-w � � � � � �� � � � qt|���}Bz4zh$�$u��Nzt��xHo |-��o � xF}Nz��Nc � }$zts{u�w � orvHvYo �N� � |�s�o |�}N�rz4zt��xFs�orz?vio �xF}Nz � |-x;|�}$|-vHz�d

� }�cNv � o �p�$sH|-q?xHorq?z � g{z�s�zb>cNo s�z |��p|��$�$s�u*hNo � |-xHoru��Ed � �Nz |��$�$sku�|-q?}�orv�xHu�|��$�$s�u*h�o � |�xHz4zt|-q?}q?u�sHskz?q?x4�$u�vHxYzts�oru�s � orvHxFs�o9}>cNxHoru�� � � g�orxF} | vHo �N���rz ��o s�orq?}N�Mz?x � orvHxFs�o9}>cNxHoru�� � |�� � q?u���xHo ��cNz xHu�cNvHz�2b>c$|-xHoru�� ��� |-�ru��N�5g oMx;}'x;}Nz�wcu�s � cN� |�wcu�s xF}Nz � zt|��'u�w | ��o s�orqQ}N�rz?x � orvHx;s�o9}>cNxHoru��Ed � z � ztsH|��v$cNq?}|��$�$s�u*hNo � |-xHoru��Nv }$| � z�}$z?zt� � z?vHqts�o9}$z � o �Px;}Nz��MorxHztsY|-x$c$s�z�d���u�s zh | � �N�rz ��� orxHxHzts�o �N��xHuN� � �t� � ���� z?vHqts�o9}Bz?v | � z?xF}Nu � qt|-�r�rz � /z+l�:@vxqsy�tMl 2 A^� , l�vxqFt - � gi}Nzts�z?o �2w0u�s zt|-q?} � � � g{z'�$s�z?xHzt� � x;}$|-x\g{z}$| � ziu�}NvHzts � z � |�w sH|�q?xHoru��$|-�e��c � }Bzts{u-wu�}NvYzts � |-xYoMuN�Nv q?u�sYs�z?vF�$uN� � o �N� xHu xF}$|-x��$|�sY| � z?xHzts vHz?x@d2e ��$|�s�xYoMq@cN� |�s � }Nz4v$cN����z?vHxHv�x;}Nz4|��$�$s�u*h�o � |�xHoru��

� ��� � � � ��� � � � � �� � �

��� �� �� �� ��� � � � � ���� � ��� � � � � � �����

� �Nz � sH|�g�}$|-qf u�w xF}Norv � z?x;}Nu � oMvixF}$|-xiorx�wK|-�rvHz?�r�'o �Nqts�zt|�vHz?v x;}Nz4zb>cNo � |-�rzt��x vF| � �N�rz�vHo#�?z?viu-w)xF}Nz��o s�orqQ}N�rz?x � orvHxFs�o9}>cNxHoru��Nv'|-vYvHu�q?o |-xYz � g�orxF}#zt|-q?} � �� � }Bz?qt|�cNvHz'orx skzt�N� |�q?z?v zt|-q?} � orvHvHo �N� � |�x$c �g�orxF}P|CwKsH|-q?xYoMuN�$|-�{vF| � �N�rz�dS�{u*g{z?�r�{z?x |-�xd�� �t������� v�cN����z?vHx |��W|��$�$sku�|-q?}#xF}$|-x � u�z?v��Nu�x }$| � zxF}Norv �$sku�}N�rz � dS~i| � z?�r� � xF}Nz?��|��$�$skuQhNo � |-xHz� �� }�� |ivHo �N���rz���o s�orq?}N�Mz?xJg }Nu�vHz � zt|��Nv |�� � | � ztsH|-��z� |�s�o |��Nq?z � � �

� � �>� � ��� ��E � � |�s�z)xF}Nz{vF| � z�|-vbxF}Nu�vHz w0uNs�xF}Nz{q?u�sHs�z?q?x���o s�orqQ}N�rz?x � o#h�x�c$s�z�d�� z��Nu�xHzxF}$|-x � orxHxHzts�o �N��xHuN� v|��$�$s�uN|-qQ} � c$�N�ro9f-z��{u*g{z?�r��z?x |���d v � z?xF}Nu � � �$s�u � cNq?z?v)|{vHq?u�sko �N� � z?xFskoMq xF}$|-x|-vHvYoM�N�Nv�zb c$|��evHq?u�s�z?v xHu zb>cNo � |-�rzt��x4�Nz?x+g{u�s�f vHxFs�cNq?x$c$skz?v@d

� }Nz?vHz�|��$�$s�u*h�o � |�xHoru��Nv)�$s�uNq?z?vHvbxF}Nz � |-xF| o �4x;}Nz � |�xF|�}$|-vHz{vHzb>cNzt��xHo |-�r�M� � |�� � � |�f-zicNvHz{u-w]xF}Nz|-vHv�c � �NxHoru���u�w �$|�sY| � z?xHzts{o � � zt�Bzt� � zt�Nqtz�|�� � �$s�u��Bzts�xHorz?v�u-wbxF}Nz4��o s�orq?}N�Mz?x � orvHx;s�o9}>cNxHoru��Ed � xF}Nzts� z?xF}Nu � v��So �Nq?�9c � o �$� & o9}>}Nv vF| � �N�ro �N� � xF}NzI�bn |-�r��u�skoMx;} ��� |�� � ��sH| � orzt��x � z?vHq?zt��x�� �$s�uNq?z?vHv4|-�r�xF}Nz � |-x;| |-x{u��Nq?z � |�� � qt|���}$|�� � �rz�q?u���xHo ��cNu�cNv � u � |-o � � |�s�o |�}N�rz?v�|�� �'� zt�Bzt� � zt��x��$|�sH| � z?xHzts�v@d

����� � ������ � �� �� �� ����& o9}>}Nv vF| � �N�ro �N� �e� z?vYqts�o9}$z � �Pwcu�s zh | � �N�MzO� }�� & z � |��<|�� � & z � |���� �t���*���?� orv4| vF�$z?q?o |-� qt|-vHzu-w)n |�s�f�u � q?}$|-o �'npu���xHz���|�s��ru � z?xF}Nu � v�wcu�si|��$�$s�u*h�o � |�xHz4o ��wczts�zt�Nq?z��x�i|-vHxHo �N��v �/�t� � ��� d & o � zt�� |�s�o |�}N�rz?v � � � � �������8�`� � ��g oMx;}�vHu � z��u�o ��x � orvHxFs�o9}>cNxHoru�� � �$�%� � �?� g{z{qt|��ucNvYz�| & o9}>}Nv)v;| � �N�rztsxHu |��$�$s�u*hNo � |-xHz�x;}Nz�zh �Bz?q?xF|-xHoru�� u-w|�����w(c$�Nq?xHoru�� �2�$� � |-v wcu��r�ruQg v@d2�bo s�vHx � g{z q?}Nu�u�vHz4|�� o �NorxHo |-�vHxF|�xHz4u-w)zt|�qQ} u-w)xF}Nz � |�sko |�}N�Mz?v o � � vHu � zt}Nu*g\d�~ zh�x � g z��Norqrf vHu � z � |�s�o |�}N�rz � � � c$�$|�vHvHor���CorxHv

���

Page 31: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

q@c$sHs�zt��xivHxF|-xHz � |�� � q?u � �>cNxHz�orxHv4�$s�u�}$|�}NoM�rorx�� � orvHxFsko }>cNxYoMuN�p��o � zt�CxF}Nz |-vHvHor��� � zt��xHvixHu xF}Nz4u�xF}Nzts� ����� |�s�o |�}N�rz?v@d � }Nzt� � g{z�vF| � �N�rz�|�vHxF|-xYziw0u�s�� � }$|-vHz � uN� xF}Norvj�$s�uN}$|�}Nor�Morx�� � orvHx;s�o9}>cNxHoru�� � |�� �q?u � �>cNxYz �7� � � dP�bo �$|-�r�r� � g{z orxHztsY|-xHz�xF}Nz'�$s�z � oru�cNv x�g{upvHxHzt�Nv � f-z?zt�No �N�Wx;sH|-qfpu-w�xF}Nz'| � ztsH|-��z� |�� cNziu-w �2�$� � d/e ��xF}Nz��ro � orx�|-v)x;}Nz ��c � }Bztsbu-wevF| � �N�Mz?v{|��$�$s�u�|�qQ}�o ��� �Norx�� � xF}Norv | � ztsY|-��z{orv)zb>c$|-�xHu � ���2�$� � � � � �_xF}Nz zh �Bz?q?xF|-xHoru��pu�w��2�$� � g oMx;} s�z?vF�Bz?q?x4xHu�xF}Nz � oMvYxFs�o9}>cNxHoru�� � �$�%� � ��� �$s�u � o � z �x+g{u q?u�� � orxHoru��Nv'|�s�z � z?x@d��bo s�vHx � xF}Nz & o9}>}Nv�vF| � �N�rzts � cNvYx5}$z�qsz$z+o , A :�q 1 2#o�� � }Nz<�$s�uN}$|�}Nor�Morx��� orvHxFs�o9}>cNxHoru�� � �$� �b� cNvHxS}Bz�v$cNq?}�xF}$|-x2g{z�qt|�� z � zt��x$c$|-�r�r� vF| � �N�rz |���� �Bu�vHvHo9}N�rzivHxF|-xHz{u-wR����o � zt�|���� �$u�vHvYo }N�rz�o �NorxHo |-�{vHxF|-xYz�u�w]��dI��u�s�zh$| � �N�rz � o w � �$� � q?u���x;|-o �Nv��Nu��?ztsku<�$s�u�}$|�}NoM�rorxHorz?v � xF}Nzt�xF}Nz & o9}>}Nv v;| � �N�rztsug oM�r��}$zpo sHs�z � cNq?o9}N�rz�d � z?q?u�� �e� zt|-q?}%� � � cNvHx5}Bz<q?}Nu�vHzt� o ��� �NoMxYz?�M��u-wcxHzt�EdeK�P�$sY|-q?xHorq?z � |��#|-�r��u�s�orxF} � wcu�s � z?xHzts � o �NorvHxHorqt|-�r�r� sku�xF|-xHo �N�CxF}$s�u�cN��}2xF}Nz � |�sko |�}N�Mz?v orv x�� �Norqt|-�r�r�cNvHz � d & uNu � o ��xFs�u � cNq?xHoru��Nv�xHu & o9}>}Nv vF| � �N�Mo �N���So �Nq?�9c � oD�N� � z?xF}Nu � v w0u�s o �NoMxYo |��Mo#�t|-xYoMuN� |�� � |� orvHq@cNvHvHoru��Cu-wbq?u�� � zts���zt�Nq?zO� |�s�z���o � zt��}����bu�s�f � �t������� |�� � ~�zt|-�J� �t������� d

~ u*g � v$c$�$�$u�vYzug{z }$| � z | � |-x;|�}$|-vHz�� � ��� A�������8� � � �ug�orxF} � orvHvHo �N� � |�xF| � |�� � g{zIg�|���xxHup|��$�$s�u*h�o � |�xHz � ��� � � � � �� ��� ��� � d � �Nz � |�s�o |���x�u-w & o }>}Nv�vF| � �N�ro �N�@w0u�s��Bzts w0uNs � o �N�pxF}Norv |�����$s�u*hNo � |-xHoru�� ��uNz?v |-v{wcu��r�ru*g�v@d2�bo s�vHx � g{z�o �NorxHo |-�ro#�?z xF}Nz4�$|�sH| � z?xHztskv � � � vHu � zt}Nu*g\d � z?q?u�� �e� wcu�szt|-q?}pqt|-vHz � � o � � q?u���x;|-o �No �N� � orvHvYo �N� � |-x;| � g{zI���r�)o � x;}Nz � orvHvHo �N� � |-xF|�cNvHo �N�CxF}Nz |-vHvYoM�N�Nz �� |�� cNz?v u-w � � �Md���u�sizh$| � �N�rz � v$c$�$�$u�vYz � |�sko |�}N�Mz?v!� � |�� � � � |�s�zuc$�Nu�}NvHzts � z � o �pqt|-vHz � @d � z���r�{o � � � }�� vF| � �N�ro �N�@w s�u � xF}Nz � orvHxFs�o9}>cNxHoru�� � �*� � � � ����������� �?� |�� � x;}Nzt� ���r��o � � � }�� v;| � ��N�ro �N� w s�u � xF}Nz � orvHxFs�o9}>cNxHoru�� � � � � �9� � � � ������� ��� � d � }NorvivHxHzt��qt|���}$z � uN�NzGcNvHo �N��|���� vHxF|�� � |�s �� |&��z?vHo |�� �Nz?x+g{u�s�f o ��wczts�zt�Nq?z'|-�r��uNs�orxF} � d � }No s �e� g{z skzt|-vHvHor���2xF}Nz �$|�sY| � z?xHzts�v � � �'|-q?q?u�s � o �N�xHu�xF}Nz��$u�vYxHzts�oru�s � orvHxFs�o9}>cNxHoru�� � ��� ��� � � ��� �?� g }Nzts�z�� orv{xF}Nziq?u � �N�rz?xHz �C� |-xF|�}$|-vYz�d/�bo �$|-�r�r� � g{zorxHztsH|-xYz�xF}Nz4�$s�z � oMuNcNv x+g{u4vHxYzt�Nv � |�� � cNvHz�x;}Nz�vF| � �N�rz �'� |-�9cNz?v u�w � ��� |-v |���|��$�$skuQhNo � |-xHoru�� wcu�s� ��� � � � � �� ��� ��� � d � c$��xHo �Nz � �&���*��� � orvHq@cNvHvHz?vixF}Norv�|��$�$s�u�|-q?} o � � uNs�z � z?xF|-or�xd

& o9}>}Nv v;| � �N�ro �N� qt|�� |-�rvHuu}$z\cNvHz � o ���N� |�q?z�u-wevHzt|�s�q?}No �N� u � zts)�Nz?x+g{u�s�f vHxFs4cNq?x$c$s�z?v@d2~i| � z?�r� �g{z�qt|�� � u � o wc� xF}Nz & o9}>}Nv�vF| � �N�Mzts � z?vHqts�o9}$z � o � xF}Nz��$s�z � oru�cNv��$|�sH|-��sY|��$}�vHu xF}$|-xborx{qt|�� x;sH|��NvHo��xHoru�� w sku � u��Nz��Nz?x�g{u�s4f�vHxFs4cNq?x$c$s�z�xHu�|��Nu�xF}Nzts d/��u�sbzh$| � �N�rz � |&wcxHzts�zt|-q?} v;| � �N�ro �N� �$|�vHv)xF}$sku�cN��}xF}Nz��$|�sH| � z?xYzts�vj|�� �'� |-xF|�}$|-vHz � xF}Nz�vF| � �N�rzts�qt|�� z � |-�9c$|-xYz�x;}Nz � � � �� � � � � � w0u�s�z � zts���vHxFs4cNq?x$c$s�zxF}$|-x oMv �Yq?�Mu�vHz � xYu xF}Nz4q@c$sYs�zt��x��Nz?x+g{u�s�f�vHx;s�cNq?x$c$s�z��_z�d �Md � g�orxF}No �'uN�Nz�|�s�q4| �$� oMxYoMuN� �]� z?�Mz?xYoMuN� � u�ss�z � ztskvF|-� � |�� � v;| � �N�rz | �Nzg �Nz?x+g uNs�f vHxFs�cNq?x�c$s�z�|-q?q?uNs � o �N��xHu x;}NoMv � orvHx;s�o9}>cNxHoru����_vHz?z n | � or��|��|�� � y�|9w0zts�x�� ���&���*��� d

����� � � � � � ��� � � � }NzCzh �Bz?q?xF|-xHoru���� � |*h�o � o#�t|-xYoMuN� �x�bn � |��M��u�s�orxF} � oMv'|��S|��$�$s�u*hNo � |-xHoru��g|-�r��u�s�orxF} � xF}$|-x qt|��� � � | �MuNqt|-� � |*hNo � c � u-w�|'�$s�uN}$|�}Nor�Morx�� � � � � � ��� � |�v�| w(c$�Nq?xHoru�� u�w��$|�sH| � z?xHzts�v � �0��z � �NvHxHztsz?x�|-�xd ���t� � � � d & o � zt�'| � |-xF|�}$|-vHz�� � ��� A��������� � � �Ig�orxF} � oMvYvHo �N� � |-xF| � g{z�qt|��C|��$�$s�u*hNo � |-xHz� � � � � �� ��� � |-vbxF}Nz �MuNqt|-� � |*hNo � c � w0u�s � � � � � �� ����������� � wcu�c$� � }���xF}Nz��bn |��M��u�s�orxF} � d2�]o9f-zixF}Nz

���

Page 32: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

& o9}>}Nv{vF| � �N�Mzts � xF}Nz�� n |-�r��u�s�orxF} � qt|�� }$|�� � �rz � u � z?�MvJg�orxF} � orvHvHo �N� � |-xF| � q?u���xHo �NcNu�cNv � u � |-o �� |�s�o |�}N�rz?v � |�� �C� zt�$zt� � zt��x��$|�sY| � z?xHzts�v�d ~ �Mx;}Nu�cN��}CxF}Nzu�bn |��M��u�s�orxF} � xHzt� � v�xHu��$s�u � o � z | �rz?vHv|-q?q@c$sH|�xHz4|��$�$s�u*hNo � |-xHoru�� � orx�x��$�NoMqt|��M�r�Cq?u�� � zts���z?v � u�s�z�b>cNorqrf��r�'xF}$|���| & o9}>}NvivF| � �N�rztsd

� }Nzk� n |��M��u�s�orxF} � qt|���}$z � orzg{z � |-v�| � z?xHzts � o �NorvHxHorq � zts�vYoMuN� u-wxF}Nz & o }>}Nv vF| � �N�rztsdS� o f�zxF}Nz & o9}>}Nv vF| � �N�rzts � g{zu}$z?��o �px;}Nz |��$�$s�u*h�o � |-xYoMuN�'u�w � � � � � �� ��� � }��<|-vYvHor���No �N� � |-�9cNz?v4xYu�� � �vHu � zt}NuQg�d ~�zhNx � sH|-xF}Nzts xF}$|�� vF| � �N�rz<|2q?u � �N�rz?xHz � |-x;|�}$|-vHz � � g z�q?u � �>cNxHzpxF}Nz o �8�>o;:�vxo ,p A�� :�qFo�tMv2pvxl�vxq prvxq9:p w0u�s�xF}Nz � orvHvHo �N� zt��xFskoMz?vio ��xF}Nz � |�xF|�}$|-vHz�d2e �'�$|�s�xYoMq@cN� |�s � g{z�q?u � �>cNxHz

� ��� � � � � � ��� �_��� � � � � � � � � � / � ��� � � � � � � ����� � � �����

� }Nzt��� � |�� � |-�r�exF}Nz � |�s�o |�}N�rz?vio �2/ � |�s�z�uN}NvHzts � z � o � qt|-vHz � � � xF}Nz�xHzts � wcu�s xF}Norv�qt|-vYz4s�zb cNo s�z?v|�x;s�o � o |-�]q?u � �>cNx;|-xHoru�� ��orx orv�z?orxF}NztsO�?zts�u�u�s u��Nz�d � xF}Nzts g�orvHz � g ziqt|��:cNvHz�|���� � |&��z?vHo |�� �Nz?x+g uNs�fo ��w0ztskzt�Nq?z |-�r��uNs�orxF} � xHu�z � |�� c$|�xHz xF}Nz�xHzts � d � }Norv q?u � �>cNxF|-xYoMuN�'orv qt|-�r�Mz � xF}Nz�o��4� o@:@vxl�vxqsy�tRprvxo��u-wbxF}Nz\�bn |-�r��uNs�orxF} � d

~ zhNx � sY|-xF}Nzts xF}$|��CvF| � �N�rz �Nzg � |�� cNz?v w0uNs�� ��� � g zIcNvHz�xF}Nz�zh �Bz?q?xHz � v$c�� q?oMzt��x�vHxF|�xHorvHxHorq?v|-v�o w xF}Nz?�Pg{zts�z�|-q?x$c$|��)v$c�� q?orzt��x vHxF|�xHorvHxHorq?v w s�u � | � |-xF|�}$|�vHz � � |�� � vHz?x�xF}Nz��Nzg � |-�9cNz?v u-w� � �'xHu }$z xF}Nz � u � z?v�u-w�xF}Nz��$u�vYxHzts�oru�s � orvHxFs�o9}>cNxHoru�� � � � � � � � � � �� ��� � d���u�s zh | � �N�rz � o w xF}Nz�$|�sH| � z?xHzts�v � � � }$| � z4| ��o skoMq?}N�rz?x � orvHxFs�o9}>cNxHoru�� � xF}Nzt�:g{z4}$| � z

n<u � z � � � � � ��� � ��� � � � � �� � � � � ��� � ����� � � � ��� � � � ��� ��� � � � �

� }Norv � u � z�zhNoMvYxHv �$s�u � o � z � � � � � ��� � � � � � ��� ��� � � �0� � �������8��� � d��xe_w)�Nu�x � g{z qt|���cNvHz�xF}Nzzh$�$z?q?xF|-xYoMuN� u-w � � o � orxHv��N� |-q?z�d � � }Norv |�vHvHor��� � zt��x{oMv{qt|-�r�rz � xF}Nz �Il$�Qq$�Iq��l�vxqsy�t�pvxo�� u-wexF}Nz��bn|-�r��u�skoMx;} � d

��z � �NvHxHztsI� �t� ��� � vF}Nu*g{z � x;}$|-x � c$� � ztsiq?zts�xF|�o �2s�z?��cN� |�s�orx��'q?u�� � orxHoru��Nv � orxHztsY|-xHoru��Cu-w x;}Nz�zh���$z?q?x;|-xHoru���|�� � � |�h�o � o#�t|-xHoru��gvHxYzt�Nv�g�or�M� q?u�� � zts���zCxHuS| �ruNqt|-� � |*hNo � c � u-w�xF}Nz �$s�uN}$|�}Nor�Morx��� � � � � �� ��� � ����� � d����� � � � � ��� � � ���� �� � �� ��� ��������� �

� u5cNvHz & o9}>}Nv vF| � �N�ro �N� u�s{x;}NzG�bn |-�r��uNs�orxF} � o �'�$sH|�q?xHorq?z � g{z4�Nz?z � xHu�q?u � �>cNxHz xF}Nz � orvHxFs�o9}>c��xHoru��Nv � ��� � � � � $� � �� ��� � z�� q?orzt��xY�M��d � }Nz?vHz q?u � �>cNxF|-xYoMuN�Nv |�s�z{z�� q?orzt��x��$s�u � o � z � xF}Nz �$|�sH| � z?xHzts�v� ��� }$| � z | ��o s�orqQ}N�rz?x � oMvYxFs�o9}>cNxHoru��2u�s�vYu � z�u�xF}Nzts � orvHxFsko }>cNxYoMuN�Cw sku � xF}Nz�zh �Bu��Nzt��xHo |-��w | � or�M��d� }Nzt� xF}Nz � orvHxFs�o9}>cNxHoru��Nv � u �Nu�x }$| � zixF}Norv{wcu�s ��� g z�qt|��5cNvHz���zt�NztsH|-�]u��NxHo � o#�t|-xHoru�� � z?xF}Nu � v�xHu� |*hNo � o#�?z � � � � � �� ��� � � ��� � � & or�r�ez?x |���d �t���>���>� s�z?vHv�z?x |���d �t������� d

n |�����u-w$xF}Nz?vHz{|��$�$s�u�|�qQ}Nz?v��Pwcu�s]zh$| � �N�rz � ��sY| � orzt��x � z?vYq?zt��x � q?uN� � cN��|�xHzb��sH| � orzt��x � |�� � b c$|�vHo��~ zg�xHu�� � z?x;}Nu � v��Szh$�N�ru�orx � zts�o � |-xYo � z?v u-w�xF}Nz�w(c$�Nq?xHoru���xYu }Bz � |�h�o � o#�?z � xYu vF�$z?z � c$� q?u�� � zts&���zt�Nq?z�d�eK� vHu � z�vHorx$c$|�xHoru��Nv � xF}Nz?vHz � ztsko � |-xHo � z?v�qt|���}Bz'q?u � �>cNxHz � z�� q?orzt��xH�r�So �Pq?�ru�vYz � wcu�s � d

�>�

Page 33: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� c$��xYo �Nz�� �t���*�N�4� orvHq@cNvYvHz?v'v$cNq?} � z?xF}Nu � v�o � � z?x;|-or��d ��zts�z � g{z � zt��xHoru��gxF}Nzpqt|-vHz g }Nzts�z |-�r�� |�s�o |�}N�rz?v�o � �|�skz � oMvYqts�z?xHz�dSe ��xF}NorvivHorx$c$|-xHoru�� � yBcNvHvHz?�r�z?xi|-�xd�� �t������� }$| � z�vF}Nu*g � x;}$|-x

� �ru�� � � � � � �� � � ��� ��� �� � � � � ��� � � � � � ��� �

� � g }Nzts�z � ��� � � � � �M��� � orv�xF}Nz zh �Bz?q?xHz � v$c�� q?orzt��x�vHx;|-xHorvHxHorq ��o � zt�P}�� �2b>c$|-xHoru�� ��� d ~ v��Nu�xHz �o �PxF}Nzp�$s�z � oMuNcNv vHz?q?xYoMuN� � xF}Norv xHzts � � |&� }$zCq?u � �>cNxHz � }��P|����PvHxF|�� � |�s ��� |t��z?vHo |��P�Nz?x+g uNs�fo ��w0ztskzt�Nq?z |��M��u�s�orxF} � d

� �� �JYLV\`�V�� � �� � �mY�` ��� �� ��

eK��| � |-x;|�}$|-vHzCg�orxF} � orvHvHo �N� � |�xF| � |��$|�s�xHorq@cN� |�s � |�s�o |�}N�rz � |&�5}Bz�u�}NvHzts � z � o � vHu � z�qt|-vHz?v � u�s orx� |&� �Nz � ztsC}$z u�}NvHzts � z � dSeK� xF}Nz � |-xHxHzts{vYoMx�c$|-xHoru�� � g{z�vF|&� xF}$|�x�xF}Nz � |�s�o |�}N�rz�orv �Nq ,�, o@tMd

~ ��� u-w xF}Nz � z?xF}Nu � v � z?vHqtsko }Bz � o �#x;}Nz'�$s�z � oru�cNv vHz?q?xHoru��#qt|���}Bz�cNvHz � xHup�rzt|�sH� � |&��z?vHo |���Nz?x+g{u�s�f�v q?u���xF|-o �No �N�po � zt��xHo���z � }No �$� zt� � |�s�o |�}N�rz?v@d � }Nz �Nz?x+g uNs�f vHxFs�cNq?x�c$s�z � |&��}$z^�MhNz � |�� �u��N�r�PxF}Nz'�$}���vYoMqt|�� �$s�u�}$|�}Nor�rorxHorz?v�c$�Nq?zts�xF|-o � � u�s^}$u�xF}#x;}Nz'�Nz?x�g{u�s4fpvHxFs�cNq?x�c$s�z'|�� � �$|�sH| � z?xHzts�v� |&��}$zGc$�Nq?ztskxF|-o �Ed � �Nz4zh$| � �N�rz4u�w �rzt|�sH�No �N��xF}Nz��$s�u�}$|�}Nor�rorxHorz?v�u-w)|I�MhNz � vHx;s�cNq?x$c$s�z�g�orxF}C}No � �� zt� � |�sko |�}N�Mz?v orv�xF}Nz ~ cNxHuN�{� |-vHv4|-�r��u�skoMx;} � u-w � }Nz?z?vHz � |��p|�� � � x$cNx���� �&�������?� g }NorqQ}p�$zts w0u�s � vANt>p AA�>o@z@<@q pro , :32�l�p$pq � :$l�vxqFy�t�) � }Nz � u � z?�Ec$� � zts��r��o �N��xF}Nz |��M��u�s�orxF} � orv | � |&��z?vYo |����Nz?x+g{u�s�fag�orxF}| vHo �N���rz�}No �$� zt� � |�s�o |�}N�rz5g }Nu�vHz vHxF|�xHz?v q?uNsHs�z?vF�Bu�� � xHu�xF}Nz:c$�>f��Nu*g �Cq?� |-vHvHz?v�d � }Nz �Nc � }$ztsiu-wvHxF|�xHz?vu�w xF}Nz�}No �$� zt� � |�s�o |�}N�rz�orvSc$�Nq?zts�xF|-o ��|�� � }$|-vb| �$skoMuNs � oMvYxFs�o9}>cNxHoru��Ed ~ �rvHu � xF}Norv)}No �$� zt� � |�s�o��|�}N�rz�s�zt� � zts�v{vHz?xHv{u-weu�}NvHzts � |�}N�rz � |�s�o |�}N�rz?v�q?u�� � orxHoru��$|-�r�r��o � � zt�$zt� � zt��x@d � }Nzj|-�r��uNs�orxF} � vHzt|�s�q?}Nz?vu � zts � |�s�o |-xHoru��Nv�u-w x;}NoMv � u � z?�k�0o �Nq?�9c � o �N� xF}Nz ��c � }$zts u-w{vHxF|-xYz?v4u-w{xF}Nz }No �$� zt� � |�sko |�}N�Mz �7� cNv+�o �N�'| � zts�vYoMuN�'u�w xF}Nzu� n |��M��u�s�orxF} � xHu |��$�$s�u*h�o � |-xYz4xF}Nz��$u�vHxYzts�oru�s �$sku�}$|�}Nor�roMx��Cu-w)zt|-q?} � u � z?�� |�s�o |-xHoru��Ed

e �p| �$� orxHoru�� � g{z4qt|���cNvYz � z?xF}Nu � viwcu�s �rzt|�sH�No �N��g�orxF} � orvHvYo �N� � |-xF| xHu o � zt��xHo wc� �<c$� � zts�c$���q?zts�xF|�o ��x�� � xF}Nzizh�orvHxHzt�Nq?z�u�w �Nzg � |�s�o |�}N�rz?v@dJ~i| � z?�r� � g z�}�� �Bu�xF}Nz?vHo#�?z4| � cNx$c$|-�r�r� zh�q?�9cNvHo � z�|�� �zh$}$|�cNvHxHo � z vHz?x u�w � |&��z?vHo |���� �Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z?v � vHu � z�q?u���xF|-o �No �N�'}No �$� zt� � |�s�o |�}N�rz?v4|�� � vYu � z�Nu�x@d � z |-vHvYoM�N�<�$skoMuNs�v�xHu�zt|-q?}CvHxFs�cNq?x$c$skz |�� � orxHv4�$|�sH| � z?xHztskv � |�� � xF}Nzt�Pc$� � |-xHz�xF}Nz?vHz �$skoMuNs�vg�orxF} � |-xF|IcNvHo �N� uN�Nz�u-w x;}Nz � z?vHqts�o9}$z � |��M��u�s�orxF} � v{wcu�s{}$|�� � �ro �N� � orvHvHo �N� � |-xF|>d

T�� � ZC`�V�X KY � XAZ X �� ��`+X 2Y �JX ]kY

�]o9f-z�|-�r�x$cNxYu�s�o |-�rv � xF}Norvix$cNxHu�sko |��eorv o �Nq?u � �N�rz?xHz�dJ��u�s{xF}Nu�vHz4s�zt| � zts�v o ��xHzts�z?vYxHz � o �C�rzt|�sH�No �N� � u�s�z|�}Bu�cNx4��sY|��$}Norqt|-� � u � z?�rv |�� �W� z?xF}Nu � v w0uNsi�Mzt|�sH�No �N� xF}Nz ��� g z u*�eztsixF}Nz wcu��r�ru*g�o �N�@| �$� oMxYoMuN�$|-�s�z;wczts�zt�Nq?z?v@d ~�� u�s�z � z?xF|-or�rz � �NcNo � z xHu xF}Nz��rorxHztsH|�x$c$s�z4qt|���}$z�wcu�c$� � o � � c$��xHo �Nz�� �t������� d

���

Page 34: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� }$|�sH�No |�f � �t���>�@� �$s�u � o � z?v4|��Czt|-vH���KxHu*� skzt| � o ��xFs�u � cNq?xHoru��pxYu xF}Nz � |&��z?vHo |���� �Nz?x+g{u�s�fCs�zt�$s�z��vHzt��xF|-xHoru��Ed � �Norz?��z?� }$|-�rxHztsiz?x�|-�xd�� �&������� |�� � � z?qf-zts � |�� z?x�|-�xd�� �t����� } � ��o � z�vHo � �N�rz � oMvYq@cNvHvHoru��Nvu-w � z?x;}Nu � viwcu�s �Mzt|�sH�No �N� � |&��z?vHo |��p�Nz?x+g uNs�f�v wcu�s � u � |-o �Nv�q?u���xF|-o �No �N��u��N�r� � orvHqts�z?xHz � |�s�o |�}N�rz?v@d� c$��xYo �Nz\� �&���*��� |�� � � z?qrf-zts � |��4|�� �5& z?or��zts�� �t���*��� �$s�u � o � z � u�s�z � z?x;|-or�Mz ��� orvHq@cNvHvYoMuN�Nv@dS�2h$�$zts��o � zt��xF|-�$q?u � �$|�s�orvHu��Nv�u-w � o��ezts�zt��xb�Mzt|�sH�No �N��|��$�$s�uN|-qQ}Nz?v�qt|��I}$z�w0u�c$� � o � �{uNu��Bztsb|�� � ��zts�v�f-u � orxHv� �t�������?�-~ �ro wczts�orv�|�� � ��u�u��Bzts�� �t���*�N�?� �e|�c$s�orx��?zt� z?x{|-�xd�� �t���*���?� �{u*g{z?�r��z?x�|-�xd�� �&�������?� |�� � � z?qrf��zts � |�� z?x |-�xd�� �t����� } � d

e �p| �$� orxHoru��CxHu � o s�z?q?xYz �W� u � z?�Mv � s�z?vHzt|�s�q?}Nzts�v4}$| � z�|-�rvHu zh$�N�ru�s�z � �NsH|��$}Nviq?u���x;|-o �No �N��c$� � o��s�z?q?xHz � z � ��z?v4|-v4|�fN�NuQg �Mz � ��z s�zt�$s�z?vHzt��xF|-xYoMuN�Ed � }Nz?vYz s�zt�$s�z?vHzt��xF|-xYoMuN�Nv4|�s�z � orvHq@cNvHvHz � �_z�d �Md � o ��e|�c$skoMx4�?zt��� �t�������?�D� zts � | |�� �P� zt|�sk�m� �&�������?� |�� � � s�� � zt��}Bzts�� � �t������� d � |&��z?vYo |�� � z?xF}Nu � viwcu�s�rzt|�sH�No �N� v$cNqQ} � u � z?�rv w s�u � � |�xF|�|�s�z � z?vHqts�o9}Bz � }�� �4|@g o � |�� � �e|�c$s�orx��?zt� � �t������� |�� ��� c$��xHo �Nz� �t���*��� d

�bo �$|-�r�r� � vHz � ztsH|-�]vHu�w0x+g�|�s�z�vY��vHxYz � v w0u�s��Mzt|�sH�No �N� ��sY|��$}Norqt|-� � u � z?�rv�}$| � z\}$z?zt� o � �N�Mz � zt��xHz � d� }Nu � |-v �B� �Norz?��z?� }$|-�rxHzts � |�� ��& or� f�v�� �t������� }$| � zbqtskzt|-xHz � |�vH��vYxHz � xF}$|-x xF|�f-z?ve| �Mzt|�sH�No �N�j�$s�uN}N�Mz �vF�Bz?q?o ��z � |-v | � |&��z?vHo |����Nz?x+g{u�s�f |�� � q?u � �Nor�rz?v�xF}Norv��$s�u�}N�rz � o ��xHu | & o9}>}Nv+�KvF| � �N�rztsiq?u � �>cNxHzts�$s�u��NsH| � d � | � v$}Bzts�� � �t������� |�� � � � ��vH��|�|�s � z?x4|-�xd � �t���*��� }$| � zG}>cNor�rx�vY��vHxYz � v x;}$|-x qt|��'�rzt|�sY�� o s�z?q?xHz �e� c$� � o s�z?q?xHz �e� |�� �<� o#hNz � ��sY|��$}Norqt|-� � u � z?�rvkcNvHo �N��| � |�s�orz?x � u-wbvHq?u�s�o �N� � z?xFs�orq?v@d

� _ �IVaZ�� �� S[ � � mV�X �

e�xF}$|��>f �4| � o � ��}Norqf-zts�o �N� � � s�orqk� u�s � orx�� � ��}$s�orv{n<z?z@f � % uNu�v�y{u � � z?�rvHz � |�� � � | � }$sH|-orq �$� �NxF}wcu�s{xF}Nz?o s{q?u � � zt��xYv�u�� zt|�s��rorzts � zts�vHoru��Nviu-wxF}Norv � |��NcNvHqts�o �Nx@d

� ��3 2Y JV\_ �

� ~ ft|-o9f-z � �t� � � � ~ ft|�o f�z � �\dL� �t� � �N� d ~ �Nzg �ru�uNf |-x{xF}Nz�vYxF|-xHorvHxHorqt|-� � u � z?� o � zt��xHo���qt|-xHoru��Ed��������� z+l�t�prl�:�vxqFy�t>p�y�t� ANvxy\�Il�vxq9:Sy�tWvxz+y�2 �A�&� � � � � � � ��� d

� ~ �ro wczts�orv4|�� � �{uNu��Bzts ���t����� � ~ �ro w0zts�orv � ��de|�� � �{uNu��$zts � & dS� �t������� d ~ �@z � |-�9c$|-xHoru��2u-w�|��p|-�r��u*�s�orxF} � wcu�s o � � cNq?xHo � z��rzt|�sH�No �N�Wu�w � |&��z?vHo |�� }$z?�rorz;w��Nz?x+g{u�s�f�vGcNvHo �N� vHo � cN� |-xHz �P� |-x;|�vHz?xHv�d�e ��Jz�y3:$o�o , qFt -�p\y0/ � o�tMv���Sy�t /ro�z+o@t :�oIy�t� /t :$o�z$vxl�qstMvxn:qst���z�vxq � :@qsl�2��$tMvxo32=2#q -�o�t :�o| � zt|-xHxY�Mz � � ~���$|-��z?v � � �� d�npu�sk��|�� % |�c�w � |��$�Ed

� � | � v$}Bzts�� ���&����� � � | � v$}$ztsk� � $Wd�� �t������� dCn<u � z?�{vHzt|�s�q?}#o �Pq?u���xHo �N��zt�Nq?�#xF|�}N�rz?v5}�� ��u��{uMdPe ���u � ��z � �Gd�|�� � � orxHx;|�f-zts � $Md � z � orxHuNs�v � Sy\��� ANvxl�vxqsy�tMl�2 # vxl�vxq9pvxq9:p � �$|-��z?v ���>� � ���\� d � }��NvHorqt|� zts�� |-� � ��z?o � z?�9}$ztsk�Md

���

Page 35: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� � |&��z?v �E�t����� � � |&��z?v ��� d�� �t������� d ~ �gz?vHvF|&�WxYuQg�|�s � v�vYu�� � o �N�S|#�$s�u�}N�rz � o �PxF}Nz � u�q?xFsko �Nzpu-wq?}$|��Nq?z?v@dJj�qsy\�Io@vxz�q9{*l �W��� � ��� � � ����� dey{zt�$s�o ��xiu-wbu�s�or��o �$|-��g{u�s4f�u-w � � ��� d

� � z?o �N�roMq?}pz?x |���d �A�&����� � � z?o �N�roMq?} � e�d �D� cNzts � uN� � x � �\d � ��}$| � z� � y�d � |�� � �{uNu��$zts �D& dA� �t������� d � }Nz~ � ~ y{n � uN�NoMxYu�s�o �N�4vH�NvHxHz � � ~ qt|-vHz�vYx$c � �Ig�orxF}�x+g{u4�$s�u�}$|�}Nor�rorvHxHorq�o ��w0zts�zt�Nq?zixHz?q?}$�No#b cNz?v{wcu�s}Bz?�Morz;w �Nz?x+g{u�s�f�v@d�e ���Jz+yB:�o$o , qst�-�p�y0/Iv���o # o;:�y�t , � A�z+yO�>o$l�t Sy�t /o@z+o�t :�o\y�t ��z�vxq � :@qsl�2 �$tWvxoB292�q !-No@t :�o\qst���o , q9:@qstMo|��]u�� � uN� � �$|-��z?v ��� � � ��� � d � �$s�o �N��zts � zts�� |-� �W� ztsk�Mo �Ed

� � c$��xHo �Nz �/�t���>� � � c$��xHo �Nz � � d�� �t�����@� d � }Nz?u�sk� s�z�� �Nz � zt��x�u�� � |&��z?vHo |�� �Nz?x+g uNs�f�v�d/eK� �Jz+yB:�o$o , !qst�-�p y / # oB<@o�tMv�� Sy�t /ro�z+o@t :�ouy�t Lt :�o@z�vxl�qstMvxn qFt���z�vxq � :@qsl�2 �$tWvxoB292#q -No@t :�o|S�]u�v ~ �N��z?�rz?v � � ~���$|-��z?v ��� � ��� d�npu�s��N|�� % |�c�w � |��$�Ed

� � c$��xHo �Nz �/�t���*� � � c$��xHo �Nz � � d � �t���*��� d � �BztsH|-xHoru��Nv�wcu�s]�rzt|�sH�No �N��g�orxF} ��sH|��$}Norqt|-� � u � z?�rv@d�� y�ANz�tMl�2y0/ �az$vxq � :�qFl�2 �$tMvxo32=2#q -�o@t :$o��io pro�l�z0:�� � � � �t��� � ����� d

� � c$��xHo �Nz �/�t����� � � c$��xHo �Nz � � d � �&������� d ~ ��cNo � z xHu�x;}Nz �rorxHztsH|�x$c$s�z�u�� �Mzt|�sH�No �N�4��sH|��$}NoMqt|�� � u � z?�rv@d� z?qQ}$�Norqt|-�by{zt�Bu�s�x�eK�O� ��� � ���$� ~ ~ �N~ ~j� z?v�y{z?vHzt|�s�qQ}���zt��xHzts d

� ��}$|�sH�No |�f � �t���>� �4��}$|�sY�No |�f � ��d�� �&���>�@� d � |&��z?vHo |��g�Nz?x+g uNs�f�v^g�orxF}Nu�cNx�xHzt|�skv@d � ����l -�l$�qFtWo ��t� � ��� � � � d

� ��}Nz?z?vYz � |���|�� � � x$cNx�� �E�t����� ����}Nz?z?vHz � |�� �L� de|�� ��� x$cNx�� � $Mdi� �t������� d � |t��z?vHo |��Cq?� |�vHvHo���qt|-xHoru��� ~ cNxHu���� |�vHv � � � }Nz?u�s��p|�� � s�z?v$cN�rxHv�dGe � � |&�N��| �e� �\d ��� o |-xHz?v$f���� � }$|��No sku � & d � �$� ��xF} �L� d � |�� �� xF}Nc$s�cNvF| � � � y�d � z � orxHu�s�v � � , <�l�t :�opuqst��\tWy�w 2#o , -No��kq p :$y�<�o@z�n�l�t , ��l�vxl��qstMqst�- � �$|-��z � �~i~ ~ e � s�z?vYv � n<zt�N�ru � |�s�f � � ~ d

� ��}Norqf-zts�o �N� ���&����� ����}Norqf-zts�o �N� � �udM� �t������� d ~ xFsH|��Nvkw0u�s � |-xHoru��$|-�Nq?}$|�sH|-q?xHztsko��t|�xHoru���u-w]zb cNo � |��Mzt��x� |&��z?vHo |�� �Nz?x+g{u�s�f vHxFs�cNq?x�c$s�z?v@dueK� �iz+y3:$o�o , qFt -�p\y0/ � 2#oB<@o�tMv�� Sy�t /o@z+o�t :�oGy�t /t :$o�z$vxl�qstMvxn�qst��z�vxq � :@qsl�2 �$tWvxoB292�q -�o�t :�o|�npu���xFs�zt|�� �� ��d$npu�s���|�� % |�c�w � |��$�Ed

� ��}Norqf-zts�o �N� z?x |-�xd ���t����� �4��}Norqrf-ztsko �N� � �ud � & z?or��zts � �ud � |�� � � z?qrf�zts � |�� � �udS� �t������� d\�]zt|�sY�No �N�� |&��z?vHo |��#�Nz?x+g uNs�f�v�� � zt|�s�q?} � z?xF}Nu � v |�� � zh �Bzts�o � zt��x;|-� s�z?v$cN�rxHv�dPeK� �iz+y3:$o�o , qFt -�puy0/ � q /v��Sy�t /o@z+o@t :$oIy�t �az$vxq � :�qFl�2��$tWvxoB292�q -�o�t :�o\l�t ,1# vxl�vxq pvxq=: p$|L�bx@dA� |�c � zts � |-�rz � �S� � �$|-��z?v ���&� � �t��� d� uNq?orz?x � wcu�s ~ s�xHo���q?o |-�7e ��xYz?�M�ror��zt�Nq?z o � � xF|-xHorvHxHorq?v@d

� �{uNu��Bzts �E�t����� ����u�u��Bzts ��& dk� �t������� d���u � �>cNxF|-xYoMuN�$|-� q?u � �N�rzh�orx��Su-w �$s�u�}$|�}Nor�rorvHxHorq#o ��wczts�zt�Nq?zcNvHo �N� � |t��z?vHo |���}$z?�rorz;w��Nz?x+g{u�s�f�v\�cy{z?vHzt|�skqQ}C�Nu�xHz � d ��z�vxq � :@qsl�2 �$tMvxo32=2#q -�o�t :�o ���N� � ����� � ����� d

� �{uNu��Bzts�|�� � � zts�v$f-u � oMxYv �E�t����� ����u�u��Bzts � & d]|�� � ��zts�v�f-u � orxHv � ��d2� �t������� d ~ � |&��z?vHo |�� � z?xF}Nu �wcu�s{xF}Nz�o � � cNq?xHoru��Cu-w)�$s�u�}$|�}NoM�rorvHxHorq �Nz?x+g{u�s�f�v)wKs�u � � |-xF|>d���l :���qstMo� �o$l�z$tWqFt - ��� � ����� � �*� �>d

�*�

Page 36: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� �{uNu��Bzts�|�� � � zts�v$f-u � oMxYv �E�t���>� ����u�u��Bzts �D& d$|�� � � zts�v$f-u � orxHv � ��d��9$�|���c$|�sk� �A�&���>�@� d ~ � |&��z?vHo |��� z?x;}Nu � wcu�s]xF}Nz{o � � cNq?xHoru���u-w �$sku�}$|�}Nor�roMvYxHorq �Nz?x+g uNs�f�v w s�u � � |-x;|>d � z?qQ}$�Norqt|-��y�zt�$u�s�x � nPe�� �>� � ���� z?q?xHoru�� u�� npz � orqt|-�7e ��w0uNs � |-xHorq?v � � xF|���wcu�s � � �No � zts�vYoMx���d

� �{u*g{z?�r�]z?x |-�xd ���t����� �4�{u*g z?�r� � y�d � �4|@g o �e� ~ d � |�� � � z@}$|-vHxHo |��No ��� d�� �t������� d ~ q?u � �$|�s�orvHu��#u-wvHzb>cNzt��xHo |-�b�rzt|�sH�No �N� � z?x;}Nu � viwcu�s o �Nq?u � �N�rz?xHz � |�xF|>d � z?q?}$�Norqt|-�)y{zt�Bu�s�x �B���B� ��zt�$|�skx � zt��x u-w� xF|�xHorvHxHorqt|-� � q?orzt�Nq?z � �i�No � zts�vHorx�� �{u��M�rz?��zu�]uN� � u��Ed

� �{u*h �E�t�*��� �4�{u*h � y�d2� �t�*����� d � s�u�}$|�}Nor�rorx�� � w s�zb>cNzt�Nq?�<|�� � s�zt|-vYu��$|�}N�rz�zh �Bz?q?xF|-xHoru��Ed ���Io@z�q=:�l�t�>y�ANz$tWl�2�y0/ � ��n�pq=: p �E�� � � � �B� d

� �4|-�Nc � |�� � ��c>}�� �L�t����� �j�4|���c ���M� d�|�� � ��c>}�� � n�d/� �&���*��� d � � xF}Nz�|��$�$skuQhNo � |-xHoru�� u-w)�$s�u�}��|�}Nor�rorvHxHorq4o ��wczts�zt�Nq?z�d � z?qQ}$�Norqt|-��y{zt�$u�skx n |&� �D� z?q?xHoru�� u�� npz � oMqt|���e ��w0uNs � |-xHorq?v �D� xF|���w0u�s � �i�No��� ztskvHorx � � q?}Nu�u�� u-w npz � orq?o �Nz � � x;|���w0uNs �e� � ~ d

� � ~�� }$s�u�vHoru �E�t���>� ��� ~j� }$s�u�vHoru �Q� dM� �&���>�@� d�� u�qt|-�$zh$�$s�z?vHvYoMuN��� |��N��c$|-��z?v�wcu�s��$s�u�}$|�}Nor�rorvHxHorq � z���Bzt� � zt�Nq?z�d/eK� �iz+y3:$o�o , qFt -�piy / # o3<@o@tWv�� Sy�t /o@z+o@t :$o�y�t /t :$o�z$vxl�qstMvxn�qFt ��z�vxq � :@qsl�2 ��tMvxoB292#q -No@t :$o |�]u�v ~ �N��z?�Mz?v � � ~�� �$|-��z?v ��� � �&��� d�npu�sk��|�� % |�c�w � |��$�Ed

� � z��bo �Nz?xHxHo �L�t� � � � � z��bo �Nz?xHxHo �M� d/� �t� � ��� d � ��o�y�z$nIy0/ �Jz+y 1�l71q92�qsvxn*d�� or�rz?��|�� �6� u��Nv � ~ zg �bu�s4fMd

� ��z & s�u�u�x �M�t� � � ����z & s�uNu�x � n�d�� �t� � ��� d �_�Avxq$�Il�2 # vxl�vxq9pvxq9:$l�2 ��o;:�q9pqsy�t>pdpnpq & sH|�gJ��� or�M� � ~ zg�bu�s4fMd

� ��z � �NvYxHzts z?x |-�xd ���t� ��� ����z � �NvHxHzts ��~ d � � |-o s �e� ~�d � |�� � y�c>}No � � �udJ� �t� ��� � d�n |*h�o � c � �ro9f-z?�ro��}NuNu � wKs�u � o �Nq?u � �N�Mz?xYz � |-xF| � o |ixF}Nzi� n |-�r��u�skoMx;} � d��>y�ANz$tWl�2�y /mv��No �Jy�n*l�2 # vxl�vxq prvxq9:$l 2 # yB:@qso@vxn ������ � � � ��� d

� � ��� u�� � v ���&�\� � �\� ��� uN� � v � $Md/� �t�\� � � d � �NxHo � c � }$sY|��NqQ}No �N�Md � ) �iop )���j # � � ��� � ����� � ����� d� � � |��Nv |�� � n<o �Norz@ft| �2�t���>� �\� � |��Nv � $Md]|�� � npo �NoMz@f&| � �Bd7� �t���>�@� d �_�Avxq$�Iq��l�vxqsy�tPl�2 -�y�z$qsv�����p /ry�ztWo@vxw2y�z4{@p\l�t , -Nz+lO� ��pdbn |�s�q?z?�]��z@fNf-zts�eK�Nq�d � ~�zg �bu�s�fWd

� �]s�� � zt�N}$ztsk� ���t����� �k�]s�� � zt��}Bzts�� � n dN� �t������� d � }Nz)q?}$|-o ����sH|��$}in@|�s�f-u � �$s�u��Bzts�x���d # :�l�t , qFtWl�<@qsl�t�>y�ANz$tWl�2�y0/ # vxl�vxq prvxq9:p �E� � � � ��� � ��� � d

� & |�}$u*g�z?x |-�xd ���&���*� � & |�}Bu*g � ��d � & |-�ror� ��� d � |�� � � �$zt�Nq?zts �N� d>� �t���*�N� dQ�7� q?orzt��xbo � �N�rz � zt��xF|-xYoMuN�u-wb��sH|��$}�|-�r��u�s�orxF} � vCcNvHo �N� q?u���xFsH|�q?xHoru��Ed2eK� �Jz+yB:�o$o , qst�-�pCy0/ � � # d

� & z?oM��zts�|�� � � z?qrf-zts � |�� ���t����� � & z?or��zts � �ud$|�� � � z?qf-zts � |�� � �ud�� y{z � orvHz � ��z@}$s�c$|�s�� ���t������� d ~q?}$|�sH|-q?xYzts�o#�t|-xHoru��2u-w�xF}Nz ��o s�orq?}N�rz?x � orvHxFs�o9}>cNxHoru��P|��$�N�rorqt|�}N�rz'xYu'�rzt|�sH�No �N� � |&��z?vHo |�� �Nz?x+g{u�s�f�v@d� z?qQ}$�Norqt|-�by{zt�Bu�s�xin � yi� � yO� �*� � ���$� n<orqts�u�vHu-wcx � y{z ��� u�� �e� � ~ d

���

Page 37: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� & z � |���|�� �6& z � |�� �E�t���*� � & z � |�� �7� d�|�� �%& z � |�� � �udM� �t������� d � xHuNq?}$|-vHxHorq�s�z?� |*h |�xHoru�� � & o }>}Nv� orvHxFsko }>cNxYoMuN�Nv<|�� � xF}Nz � |&��z?vHo |��gs�z?vHxHu�sY|-xHoru��#u-w4o � |-��z?v@d�������� � z�l�t>pl�:@vxqsy�t>p�y�t �il�vxvxo@z�t��tWl�2#n�prq p�l�t , ��l�: ��qFtWo �$tMvxo32=2#q -�o@t :$o �\� � � ��� � � ��� d

� & oM�r�ez?xi|-�xd ���t����� � & or�M� ��� d � nPc$sHsH|&� � � d � |�� � �WskoM�N}�x � n�d�� �t�����@� d �Jz�l :@vxq9:$l�2 �_�AvxqX�Iq �rl�vxqFy�tWd~ qt| � z � orq � s�z?vHv � ~�zg �buNs�fMd

� & u�u �e�E�t����� � & u�u �e� e4d�� �t������� d �iz+y 14l 1 q=2#qsvxn�l�t , v���o���o�q - ��qFt - y0/� <@q , o@t :$o�dP� |9w �Nzts�v � ~ zg�bu�s4fMd

� & u�u �e�E�t����� � & u�u �e� e�d/� �t������� d % o � � v�u-w)�$s�u�}$|�}Nor�rorx ��d # :�qFo�t :�o �W�t��� � ��� � � ��� �>d� & u�u �e�E�t�\��� � & u�u �e� e4d�� �t�\����� d � ��o�Oprvxq$�Il�vxqFy�t�y0/�Jz�y71�l 1 q=2#qsvxqFo prd2nPe � � s�z?vHv � � | � }$s�o � ��z �n ~ d

� �i|-qf�o �N� ���&� � � �\� |�qrf�o �N� � e4di� �t� � ��� d � ��o �P�Io@z9-�o�t :�ouy0/ �Jz�y71�l 1 q=2#qsvxn*d���| � }$sko � ��z �i�No � zts�vHorx��� s�z?vHv � ~ zg �bu�s4fMd

� �i|-vHxHo �N��v �A�&� � � �G�i|-vHxHo �N��v � � dM� �t� � ��� d$npu���xHz ��|�s��ru4vF| � �N�Mo �N� � z?xF}Nu � v�cNvHo �N��n@|�s�f-u � qQ}$|�o �Nv|�� � x;}Nz?o si|��$�N�rorqt|-xHoru��Nv@dBj�qFy �Go�vxz$q {Ql � � ��� � � � �&��� d

� � z?qrf�zts � |�� �E�t����� �a� z?qf-zts � |�� � �udi� �t������� d ~ xFsY|-q?xF|�}N�rz�|-�r��u�s�orxF} � wcu�s � o |-���Nu�vHo �N� � cN�MxYo �N�rz� orvHzt|-vYz?v@d�e � �iz+y3:$o�o , qFt -�p�y0/Gv���o � q /v�����y�z4{@p ��yO� y�t Lt :�o@z�vxl�qstMvxnuqst ��z�vxq � :@qsl�2 ��tMvxoB292#q -No@t :$o |��o � � vHu�s ��� ~ � �$|-��z?v � � � � �t�>� d ~ vHvHuNq?o |-xHoru��jw0u�sL�i�Nq?zts�xF|-o ��x ��o � ~ s�xYo ��q?o |-�Me ��xYz?�M�ror��zt�Nq?z � npu�c$���xF|�o � � orzg � � ~ d ~ �rvHu�o �P� zt�$s�oru�� � n d � � }$|-q?}�xHzts � y�d � % |��$|-� � �2d � |�� � �]z � � zts � $Md � z � orxHu�skv � Lt :�o@z�vxl�qstMvxnIqFt��z�vxq � :@qsl�2 �$tWvxoB292�q -�o�t :�o���|e�$|-��z?v � � � � � � � d�~ u�s�xF}���� u��r� |�� �e� ~ zg �bu�s4f ���&����� d

� � z?qrf�zts � |���|�� �6& z?or��zts ���t���*� �\��z?qf-zts � |�� � �ud�|�� � & z?or��zts � �ud/�_��z?q?z � }$zts ���t���*�N� dS�]zt|�sY�No �N�� |&��z?vHo |����Nz?x+g{u�s�f�v@d � z?q?}$�Norqt|-�by{zt�$u�skx�n � yO� � yO� ��� � ���$� nporqts�u�vHu�w0x � y{z ��� u�� �e� � ~ d

� � z?qrf�zts � |�� z?x |���d �A�&����� }��G� z?qrf�zts � |�� � �ud � n@| ��� |��No ��~ d � |�� � �2z?�M� � |�� � n�d7� �t����� | � d y�zt|-���g{u�s�� � |��$�N�rorqt|-xHoru��Nv�u�w � |&��z?vHo |����Nz?x+g{u�s�f�v@d Sy\� � A�tWq=:�l�vxqsy�t>p�y0/Iv���o � � �D��� d

� � z?qrf�zts � |�� z?x |���d �A�&����� | �\� z?qrf-zts � |�� � �ud � & z?or��zts � �ud � |�� � ��}Norqrf�zts�o �N� � �ud2� �t����� } � d��]zt|�sY���o �N� � |&��z?vYo |��P�Nz?x�g{u�s4f�v�� � }Nz�q?u � }No �$|-xHoru��Pu�wafN�Nu*g��rz � ��z<|�� � vHxF|-xYoMvYxHorqt|-� � |-xF|�d � l�:��NqFtWo �o�l�z$tWqFt - � xHu |��$�$zt|�s d

� � � ��vH��|�|�s � z?x |���d �A�&���*� �G� � ��vH��|�|�s �e� � d � � f � � x;} � ��d � |�� � � }Norz?vHvYu�� �i� dJ� �t���*�N� d���vHzts v���cNo � zxHu � e � �)y � �$� d � z?qQ}$�Norqt|-��s�zt�Bu�s�x � ��zt�$|�skx � zt��x�u-w�n@|�xF}Nz � |-xHorq?v�|�� � ��u � �>cNxHzts � q?orzt�Nq?z �~ |-�9}$u�sk� � ��zt� � |�s4fMd

� � u*g�|�s �e�M�t� � � �G� uQg�|�s �e� y�d2� �t� � ��� d{��z?q?orvHoru�� |��$|-�r�NvHorv�� � ztskvF�$z?q?xHo � z?v�uN�'o ��wczts�zt�Nq?z �e� z?q?orvHoru�� �|�� � zh$�$ztsko � zt��xF|�xHoru��Ed �Jz+yB:�o$o , qst�-�pCy0/\v���o ������� � ��� � ����� � �*� � d

�\�

Page 38: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� � u*g�|�s �e�M�t����� �G� uQg�|�s �e� y�dA� �&������� dN�]s�u � o � !AcNzt�Nq?z4xHu4skz?�Mz � |��Nq?z�xHu\fN�Nu*g��rz � ��z�d�eK� � �ro � zts � y�d|�� ���$� orxF} � $Wd � z � orxHu�s�v � ��t�� A�o�t :�o �kqsl -�z+l\��p�|�j�oB2#qso4/ ��o@vsp�|�l�t , �ko@:@q pqFy�t ��tMl�2#n�pq9p � q?}$|��NxHzts � d��or�rz?�'|�� � � u��Nv � ~�zg �bu�s�fWd

� � u*g�|�s � |�� � n@|�xF}Nz?vHu�� �E�t����� �G��u*g�|�s �e� y�db|�� � n@|�xF}Nz?vHu�� � $Md�� �t���>�@� d�e � !AcNzt�Nq?z � o |-��sY| � v@de � � u*g�|�s �e� y�db|�� � n |-xF}Nz?vYu�� � $Md � z � orxHuNs�v � �io�l , qst�-�p y�t�v���o �iz�qFt :@q � 2#opul�t , �]�\� 2#q9:$l�vxqFy�t�py0/"��o@:@q prqsy�t��tMl 2�n�pq9p ��� u��9c � z\e+e � �$|-��z?v�� ��� � � ��� d � xFsH|�xHz?��orq���z?q?orvHoru��Nv & s�u�c$� � npzt�N�ru � |�s4f �� ~ d

� $�zt�NvYzt�'|�� ��~ � � zts�vHzt� �L�t����� �+$�zt�NvYzt� � ��d�|�� � ~ � � ztskvHzt� �6� d�� �t������� d ~ �$�$s�u*h�o � |�xHoru��NvPo �� |&��z?vHo |�� }$z?�rorz;w^c$�No � ztskvHz?v wcu�sufN�Nu*g��rz � ��zP}$|-vHz � vH��vYxHz � v@d � z?q?}$�Norqt|-��s�zt�$u�skx � eK�NvHxYoMx�cNxHz'u-w� �Mz?q?x;s�u��Norq � �NvHxHz � v �$~ |�� }Bu�s��5�i�No � zts�vHorx�� ��~ |-�9}Bu�s�� � ��zt� � |�s�fWd

� $�uN}$�NvHu�� ���t����� � $�u�}$�NvHu�� � �t������� d/� u*ggw |-vYx�orv��ru�qt|-��vHzt|�skqQ} � eK� � � #]� �$|-��z?v ��� � ��� d

� % |�}$�Nz � |�� z?x |-�xd ���&����� � % |�}$�Nz � |�� � �ud � � �ru � orq ��� d � |�� �<�{� ztskv$f�� �B~ d � z � orxHu�s�vu� �t������� d �DA , -#!�Io@tWv Lt , o�z /t :$o�z$vxl�qFtWvxn ��� o3A�z�q9pvxq9:p�l�t , j�qFl*popd���| � }$sko � ��zm�i�No � zts�vHorx�� � s�z?vHv � ~ zg �bu�s4fMd

� % |�sY� ���t� � � � % |�sY� � y�dI� �t� � ��� d ~ vHo � �N�rz � zts�o � |-xHoru�� u-w � ��� u�� � v'|-�r��uNs�orxF} � w0uNs u��NxYo � |-�}$sH|��NqQ}No �N��v@d ��o@vxw2y�z4{@p �E� � �\��� � � � � d

� % |-vYv |�� � y�|&wcxHzts�� � �t����� � % |-vHv � y�db|�� � y |&w0xYzts�� �)~ d�� �t��� ��� d � |&��z?v w |-q?xYu�s�v |�� �S� u � z?��c$���q?zts�x;|-o ��x���d � z?qQ}$�Norqt|-�{y{zt�$u�skx � � ��� ��zt�$|�s�x � zt��xiu-w � xF|-xYoMvYxHorq?v � ��|�sH�Nz?��orz npz?�r�MuN�P� �No � ztskvHorx � ���~ d

� % u�s w �E�t��� � � % uNs w � yad � �&������� d�� o �Nzt|�s&�KvF�$|-q?z�}$z?vYx+�x� s�vHxbvHzt|�s�qQ}Ed ��z�vxq � :@qsl�2 ��tMvxoB292#q -No@t :$o �L��� � �M� �D� � d� �e|�c$s�orx��?zt� �/�&����� �\�e|�c$s�orx��?zt� � � d/� �t������� d �o;:�v4A�z+o pky�t Sy�tWvxqFt -�o@t :@n � l 1 2#opd/�i�No � zts�vHorx�� u-w ~ |-���}Bu�s�� � s�z?vHv �N~ |-�9}$u�s�� � ��zt� � |�s�fWd

� �e|�c$s�orx��?zt�'|�� �6� �Norz?��z?� }$|-�rxHzts �2�t����� �G� |�c$s�orx��?zt� � � d�|�� �6� �Norz?��z?� }$|-�rxHzts � �ud�� �t������� d7� u�qt|-� q?u � ��>cNxF|�xHoru��Nv�g oMx;}'�$s�u�}$|�}NoM�rorxHorz?v�u����NsH|��$}Norqt|-�evHx;s�cNq?x$c$s�z?v�|�� � x;}Nz?o s�|��$�N�Morqt|-xYoMuN�'xYu zh$�$zts�xivH�Nv+�xHz � v@d�� ) �iy�n*l�2 # vxl�vxq prvxq9:$l 2 # yB:�qFo�vxnIj � ��� � �t� � � ���*� d

� �e|�c$s�orx��?zt��z?x |���d ���t���*� �a�e|�c$s�orx��?zt� ��� d �-� }Norz?vHvHu�� ��� d � |�� ��� �Norz?��z?� }$|-�rxHzts � �udN� �t���*�N� dt��o |-�N�Nu�vHxHorqvH�NvHxHz � veqts�zt|-xHz � }�� � u � z?��vYz?�Mz?q?xYoMuN� � z?xF}Nu � v�� ~ qt|-vHzbvHx$c � ��dNeK� ��}Nz?z?vHz � |�� �*� d9|�� �4� � � wcu�s �e�y�d � z � orxHu�s�v � � ��l�t ,1# vxl�vxq prvxq9:p ��� �$� u��9c � zI�]z?q?x$c$s�zI~�u�xYz?v�o � � xF|-xYoMvYxHorq?v �����$� �$|-��z?v ��7� � �t��� d� �$s�o �N��zts�� � zts�� |-� � ~�zg �buNs�fMd

� n | � or��|���|�� � y�|&wcxHzts�� ���t���*� ��n@| � oM�N|�� � �ud{|�� � y�|&wcxHzts�� � ~ d�� �t������� d�npu � z?��vYz?�Mz?q?xYoMuN� |�� �|-q?q?uNc$��xHo �N� wcu�s � u � z?��c$�Nq?zts�x;|-o ��x�� o � ��sH|��$}Norqt|-� � u � z?�rv�cNvHo �N� � q?qt| � vig o � � u*g\d � y A�z�tMl�2Ey0/v���o ���Io�z$q9:$l�t # vxl�vxq prvxq9:$l 2 �ap�pry3:@qsl�vxqFy�t �$��� � �&����� � �&�*��� d

� �

Page 39: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� npz?xFs�uN�$u��rorv�z?x |-�xd � �t����� ��npz?xFs�u��Bu��rorv � ~�d � y{u�vYzt��}N�9cNxF} �{~ d � y{u�vHzt�N}N�9cNxF} � n�d �b� z?�r�rzts � ~ d � |�� �� z?�r�Mzts � �Bd�� �t������� d��2b>c$|-xHoru�� u-wvYxF|-xHziqt|-�rq@cN� |-xHoru��Nv�}�� w |�vHx{q?u � �>cNxHo �N� � |�qQ}No �Nz?v@d �>y�ANz$tWl�2�y0/ �No �Iq=:�l�2 � �Nn@pq9:p � ��� � �t��� � � �t����� d

� ~ zt|-� ���t��� � �a~ zt|-� � yadM� �t������� d � s�uN}$|�}Nor�MorvHxYoMqio ��w0ztskzt�Nq?z�cNvHo �N��n |�s�f-u � qQ}$|-o ��npu���xHz{��|�s��ru � z?xF}��u � v@d � z?q?}$�Norqt|-��y{zt�$u�skx � y & � � yO� ��� � ��� ��zt�$|�s�x � zt��x4u�w ��u � �>cNxHzts � q?orzt�Nq?z � �i�No � zts�vHorx�� u-w� u�s�u���xHuMd

� � � � vHxYz �e���t����� � � � � vHxHz �e� � d2� �t������� d ��tPz+o��Az+opo@tMvxqst�-:l�t , pry 2 <�qFt - , o;:�q9pqsy�t��Az+y 1 2�o���prd � }N�xF}Nz?vYoMv � ��zt�$|�s�x � zt��x�u�w7�)�N��o �Nz?zts�o �N�*��� q?u��Nu � orq � �NvHxHz � v � � xF|���wcu�s � �i�No � zts�vHorx���d

� � zt|�sk� �E�t���\� � � zt|�s�� � $Md\� �t��� ��� d �EcNvHoru�� � �$s�u��$|-�N|-xHoru�� � |�� � vYxFs�cNq?x$c$s�o �N�go ��}Bz?�Morz;w �Nz?x+g{u�s�f�v@d��z�vxq � :@qsl�2 �$tWvxoB292�q -�o�t :�o �N��� � �*�W� � ����� d

� � zt|�sk� �E�t����� � � zt|�s�� � $Md2� �t������� d �iz+y 14l 1q92#q9pvxq9: �Jo$l�pry�tWqFt -5qst �$tWvxoB292�q -�o�tMv # n�prvxo���p � �ko�vxw2y�z�{�pGy0/� 2�l A�pq 1 2#o �$t /ro�z�o�t :�o@d n<uNs���|�� % |�c�w � |��$� � � |�� n |-xYz?u � � ~ d

� � zt|�sk� �E�t����� � � zt|�s�� � $Md\� �&������� d ��|�cNvF|-� � o |-��sH| � v w0uNs z � �No s�orqt|-��s�z?vYzt|�s�q?}Ed j�qsy\�Io@vxz�q9{*l � xHu|��$�Bzt|�sd

� � zt|�sk� |�� ��� zts � | ���&���>� � � zt|�s�� � $Wd |�� ��� zts � | �N� dA� �t���>�@� d ~ xF}Nz?u�s���u-weo ��w0ztsYs�z � qt|�cNvF|-xYoMuN�EdAe �~ �r�Mzt� � $Md � �bo9f-z?v � yad � |�� �*� |�� � zg�|��M� � �Bd � z � orxHu�s�v � �\tMy�w 2#o , -�o��io��Az+opo@tWvxl�vxqFy�tGl�t , �Jo$l�pry�tWqFt - ��Jz�y3:$o�o , qFt -�p�y / v��No # o@:$y�t , �$tMvxo�z$tWl�vxqFy�tMl�2 Sy�t /ro�z+o@t :�o � �$|-��z?v ���W� � ����� d�npu�s���|�� % |�c�w � |��$� �~ zg �bu�s�fWd

� � s�z?vHv�z?x |���d �A�&����� � � s�z?vHv � � d ��� z@c>f-u��Mv�f�� � � d � � z?xHxHzts��ro �N� � � d � |�� � �b� |��$�Nzts�� �E� d2� �t������� d � A !�Io@z�q9:$l�2 �io@:@q � op�qst Od � | � }$s�o � ��z\� �No � ztskvHorx � � s�z?vHv � ~ zg �buNs�fMd

� y�| � | � c$s�xF}Noe|�� ��~ ��u���o �Nu � �t����� �4y�| � | � c$s�xF}No � % d]|�� �'~ ��u���o �Nu �B~ d2� �t������� dby{zt|-��xHo � z4zh���Bzts�x�vH�NvHxHz � wcu�s wK|�cN�rx�xHu��MztsY|���x v$c$�$zts � orvHu�s���q?uN��xFsku��xdSeK� � o �$�Norv � � d�|�� ��� |-xYxHu�� � ��d � z � orxHu�skv �Sy �#� A�vxo�z�p�qFt �Jt�-NqFtWo$o�z$qst�- � �$|-��z?v ����� � ����� d ~j� zts�orqt|�� � u�q?orz?x�� u-w�npz?q?}$|��Norqt|-���)�N��o �Nz?zts�v ��{uNs�xHzin@| � ztsH| � � ~ d

� y{orvHv;|��Nzt� �/�&��� � �4y{orvHvF|��Nzt� � $MdS� �t��� � � d � xHuNqQ}$|�vHxHorq�q?u � �N�rzh�orx����sg�orxF} � orvHq@cNvHvHoru�� � d�� y�ANz�tMl�22y0/v���o��Jy�n*l�2 # vxl�vxq prvxq9:$l 2 # yB:�qFo�vxn@| # o@z�qFo p�j �>�N� � ����� � ����� |�� �'����� � �\��� d

� y{uN}No �Nv �/�t���\� �4y{u�}No �Nv � $Md2� �t��� ��� d ~ �Nzg |��$�$s�u�|�qQ} xHu qt|�cNvF|��eo ��w0zts�zt�Nq?z o � � uNs�xF|-�rorx�� vHx�c � oMz?vg�orxF} v$cNvHxF|�o �Nz � zh �Bu�v$c$s�z4skz?v$cN�rxHv@d � l�v���o �Il�vxq9:�l�2 � y , o32#qFt - � ��� �B����� � �t�>�t� d

� y�c>}No � �L�t� � � ��y�c>}No � � �ud�� �t� � ��� d � |&��z?vYo |�� o ��wczts�zt�Nq?z w0u�s�qt|�cNvF|-�]z��ez?q?xHv�� � }Nz4s�u��Mz u-w sH|�� � u � �o#�t|-xHoru��Ed ��tWtMl�2�p�y0/ # vxl�vxq prvxq9:p � � � �*� � ��� d

���

Page 40: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� y�cNvYvHz?�r�z?x |���d ���t���*� � y�cNvYvHz?�r� � � d �E� o � � zts � $Md � |�� � % u��r�Mzts � �ud2� �t���*�N� d ~ � |��NxHo � z �$s�u�}$|�}NoM�rorvHxHorq�Nz?x+g{u�s�f�v@d � z?q?}$�Norqt|-�by{zt�$u�skx � � �C� �*� � ���*��� � �No � ztskvHorx ��u�w ��|-�ro w0uNsH�No | �A� zts�f�z?�Mz?��d

� � | � |���z �E�t���*� � � | � |-��z � �2d/� �&���*��� d � ��o � y�ANt , l�vxqsy�t�p\y0/ # vxl�vxq pvxq=: prd���u � zts � ~ zg �bu�s�fWd

� � q?}�g�|�s � �A�&� � � � � qQ}�g�|�s+� ��& d\� �t� � ��� d � vHxHo � |-xYo �N�Px;}Nz � o � zt�NvHoru�� u-w | � u � z?�xd ��tWtMl�2�p�y0/# vxl�vxq9pvxq9:p �M� � ���>� � ���*� d

� � }$|-q?}�xHzts �E�t����� � � }$|-qQ}�xHzts � y�dS� �&������� d � s�uN}$|�}Nor�MorvHxYoMq o ��w0ztskzt�Nq?z |�� � o � !AcNzt�Nq?z � o |-��sY| � v@d �_� !o�z�l�vxqFy�t�p �io pro�l�z0:�� �D�\� � ����� � ���*� d

� � }$|-q?}�xHzts{z?x |-�xd �E�t����� � � }$|-q?}�xYzts � y�d �B~ � � zts�vYzt� � � d � |�� � � u�} � % d/� �&������� d ��o skz?q?xHz � s�z � cNq?xYoMuN�|-�r��uNs�orxF} � v�|�� �'� z?q?u � �$u�vF|�}N�Mz ��sH|��$}Nv�die ���Jz+yB:�o$o , qst�-�pCy0/Gv���o # q �Qv���Sy�t /ro�z+o@t :�o�y�t Lt :�o@z"!vxl�qstMvxnIqst ��z�vxq � :@qsl�2 �$tMvxo32=2#q -�o@t :$o | � u�vHxHu�� � n ~�� �$|���z?v ��� � � ����� d ~ vHvHuNq?o |�xHoru�� w0uNsS�i�Nq?zts�xF|-o ��x �o � ~ s�xHo���q?o |-�2eK��xHz?�r�roM��zt�Nq?z � n<uNc$��xF|�o � � orzg � � ~ d

� � �Norz?��z?� }$|-�rxHztsiz?x |���d ���t����� � � �Norz?��z?� }$|-�rxHzts � �ud � �4|�g�o �e��~ d � �e|�c$skoMx4�?zt� ��� d � |�� � �{u*g{z?�M� � y�d� �&������� d � |t��z?vHo |���|��$|-�r�NvHorv o ��zh$�$ztskx vH�NvHxHz � v@d # vxl�vxq prvxq9:�l�2 # :@qso@t :$o �$� � �>�t� � ����� d

� � �Norz?��z?� }$|-�rxHzts�|�� � � |�c$s�orx��?zt� �L�t����� � � �Norz?��z?� }$|-�rxHzts � �ud]|�� � � |�c$s�orx��?zt� � � dS� �t������� d � zb>cNzt��xHo |-�c$� � |-xHo �N� u-weq?u�� � orxHoru��$|-���$s�u�}$|�}Nor�rorxHorz?v u�� � o s�z?q?xHz � ��sY|��$}Norqt|-�]vHxFs�cNq?x$c$skz?v@d �ko�vxw2y�z4{@p � ��� � � � � ������ d

� � �No s�xHz?viz?x |-�xd �E�t����� � � �No s�xHz?v �W� d � & �r� � uNc$s � ��d � |�� �6� q?}Nz?o �Nz?v � y�d/� �t������� d Sl�A�pl�vxqFy�t>| �iz+o , q=: !vxqsy�t>|Sl�t , # o�l�z0:���d � �$s�o �N��zts&� � ztsk� |�� � ~�zg �bu�s�fWd

� � cNzts � u�� � x |�� � �{uNu��Bzts ���t����� � � cNzts � u�� � x � ��d|�� � �{uNu��$zts � & di� �t���>�@� d ~ q?u � }No �$|-xYoMuN� u-wzh$|-q?x'|-�r��u�skoMx;} � v w0uNs o ��wczts�zt�Nq?z uN� � |t��z?vHo |���}$z?�rorz;w �Nz?x+g uNs�f�v�d �$tMvxo�z$tWl�vxqsy�tMl�2 � y�ANz�tMl�2�y0/�]�\�Az+y$�*qX�Il�vxo �Jo$l�pry�tWqFt - �N� � ���>� � �*��� d

� � |�s"�H|�� �E�t� ��� � � |�s"�H|�� � y�d2� �t� ��� � d��bo � � o �N� uN�NxHo � |-�/}$sH|��NqQ}No �N��v@d �ko�vxw2y�z�{�p � � � ��� � ��� d� � }Nu � |-v{z?x |-�xd ���&����� � � }Nu � |�v ��~ d � � �Norz?��z?� }$|-�rxHzts � �ud � |�� ��& or� f�v � � dS� �t������� d � cN��v�� ~ �$s�u*���sY| � xYu �Bzts w0uNs � � |t��z?vHo |��Co ��wczts�zt�Nq?z�cNvHo �N� & o }>}Nv�v;| � �N�ro �N�MdueK� � ztsH�$|�s � u � $Md ��� zts���zts � $Wd ��4|�g�o �e�N~ d � |�� �6�$� orxF} ��~ d � z � orxHu�s�v � j�l�n*o prqsl�t # vxl�vxq pvxq=: p � � �$|-��z?v ��� � � �*��� d � h�w0uNs � � �No � zts��vHorx�� � s�z?vHv�d

� � orxHxYzts�o �N��xHu�� �E�t� � � � � orxHxHzts�o �N��xYu�� � �udi� �t� � ��� d:� � � |-xHo �N�W| � o |-�N�Nu�vHxHorq�vH�NvHxHz � cNvHo �N��c$�Nq?uN���� s � z � qt|-vHz?v�d �]�\� 2#qso , # vxl�vxq9pvxq=: p �$��� � ����� � �*� �>d

� �{� zts�v$f�� |�� � % |�}$�Nz � |�� ���t� � � � �{� zts�v$f�� ��~ d�|�� � % |�}$�Nz � |�� � �udJ� �t� � ��� d�$Nc � � � zt��x c$� � ztsc$�Nq?zts�x;|-o ��x�� �S��z@c$skoMvYxHorq?vj|�� � }No |-vHz?v@d # :@qso@t :$o �M�t��� � ���t�*� � ���B�>� d

���

Page 41: 3 5?6$3-8;:@+BA4:C.D5&8FE$GHE IKJ-LM5&ENtomlr.free.fr/Math%E9matiques/Fichiers%20Claude/Auteurs/... · 2009-02-17 · # 0* , 12%# 3 "$ %#% 435 67 8 '( 9 : )=>?2!

� � zts � | |�� ��� zt|�s�� ���&����� � � zts � | ��� d�|�� � � zt|�s�� � $Wd\� �t������� d �2b>cNo � |-�rzt�Nq?zS|�� � vH�$��xF}Nz?vHorv'u-wqt|�cNv;|-� � u � z?�rv@d eK� �iz+y3:$o�o , qFt -�pGy / # q��*v�� Oy�t /o@z+o@t :$o:y�t Lt :�o@z�vxl�qstMvxn�qst ��z�vxq � :@qsl�2 �$tWvxoB292�q !-No@t :�o| � u�vHxHuN� � n ~�� �$|-��z?v ����� � ��� �>d�npu�sk��|�� % |�c�w � |��$�Ed

� � uN�5~ z@c � |��$�C|�� � npu�s���zt�NvHxHztsH� �E�t�*� � � � u���~�z@c � |��$� � $Md-|�� � npu�s���zt�NvHxHztsH� �-� d�� �t��� � � d � ��o !y�z�n:y0/ � l\�Iop\l�t , � :�y�tMy �Gq9:�j�o ��l�<@qsy�z�d � s�o �Nq?z?xHu�� � �No � zts�vYoMx�� � s�z?vHv �>� sko �Nq?z?xYu�� � ~>$Md

� ��o �>f��rzts �L�t�\� � �j��o �>f��Mzts � yadM� �t�\� � � d � }Nz |-vHvYz?vHv � zt��xbu-w �$skoMuNs � orvHxFs�o9}>cNxHoru��Nv{o � � |&��z?vYo |�� |��$|-����NvHorv@d����Io�z$q9:$l�t # vxl�vxq prvxq9:$l 2 �ap�pry3:@qsl�vxqFy�t �>y�A�z�tMl 2 �[��� � ��� � � ����� d

� �bu�s4f �E�t����� � �buNs�f � $Md�� �t������� d j�l�n*opqFl�t&�Io@v���y , p�/y�z v���o l�tMl�2#n�pq9p�y0/ �Iq pC:32�l�p$pq �Jo , y�z qFt�!:�y\��� 2#o@vxo!� A72#vxq=<�l�z$qsl�vxo , q9p :@z+o@vxo , l�vxl�d � }N� x;}Nz?vHorv � ��zt�$|�s�x � zt��x�u-w � xF|�xHorvHxHorq?v � � �No � zts�vYoMx���u-w�W|�vF}No �N��xHu�� � � zt|�xHxH�rz�d

���