Université strasbourg I - Louis Pasteur U.F.R. de mathématique et d

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Université strasbourg I - Louis Pasteur U.F.R. de mathématique et d
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‡Š ŒŽ†‡¨‹ – w ¬ , K‡¬ , Š™†‡~ ( j ¬ ,9’ ¬ , * ŒŽˆ‹Š‡€ƒ¦«€ƒŒŽˆ ~‰† ¨‡Œ — Š¬ b
* ŒŽˆ‹Š‡€ƒ¦«€ƒŒŽˆ‹‚ ~‰† ¨‡Œ — Š¬ ’
* ŒŽ@ˆ D™·Ž† — ~¦«€ƒŒŽˆ‹‚•¬ K
* Œ‹Œ — € – ˆ‰¦©~¦«€ƒŒŽˆy¬ ,0,
* — €ƒ¦«€ š ~ƒ€ƒ¦‡– ¡ ¬ ’,
= – ¡ D ˆ‹€ƒ¦«€ƒŒŽˆy¬ ’
&,f – ³Ÿ‹ – ‚•¬ @ ,
j¥¬ ’ = –£¡ š ŒŽ³ Ÿ‡Œ‰‚«€ƒ¦«€ƒŒŽˆ š£– ƒ“†‹“~€ —˜– ¬ ,
Š™†‡~ – ¬ , = –£¡ š ŒŽ³ Ÿ‡Œ‰‚«€ƒ¦«€ƒŒŽˆ š£– ƒ“†‹“~€ —˜– ·– ¡ ŒŽŠ – ¡ ‚«€ƒ„´† – ¬
K
= – ¡ ‚«Œ — Š —˜– ¬ ’ ‡¬ ’’ K
= – ¡ ¤ – ƒŒŽŸ‡Ÿ – ³ – ˆ¯¦
¨‡~‚«‚ – ¦ – ³Ÿ¢–•¡ — ~¦ † —˜– ¬ ’
µ‡~‰†‹¦ – ¦ – ³Ÿ…–•¡ — ~ª¦ † —˜– ¬ ’ 0,
= – “~‰†‡ˆ‡~ ¬ = € — € š µ‹ – ¦•¬ ’ ¬ KRb
= Œ‰¦«‚ – ˆ 7ªŒ™¬ ’’
= ŒŽ†‡¨‹ – w ¬ , = ŒŽ†‡¨‹ – } – ¡ ¦ — €ƒ„´† – ¬ K
ŠM¬ &…³Ÿ‹€ƒ – ³ – ˆ¯¦«‚ Š – š£–•—˜š  – ‚•¬ KRb
? MŠ ¬ ³ €¶Œ‹ˆy¬ b
™–•ŒŽ—ˆ š ¦ €¶Œ‹ˆ Š ’– ’ Ÿ‡~ — ¦ €¶¦ €¶Œ‹ˆy¬ b e
™ŒŽˆ š ¦ €¶Œ‹ˆ‹‚ µ‹Œ‰ƒŒŽ³°Œ — Ÿ‡µ – ‚ W0wŽ\£¬KK
) ’ b!K
™Œ‹ˆ š ¦«€ƒŒŽˆ‹‚ ³ ŒŽˆ‹ŒŽŠ — € „´† – ‚•¬¥~‰ˆ‡~ ¦ €¶„‡† – ‚
Š‡€ƒ‚ ” ¦ ‚•¬ KRb
™Œ — ³ – ‚•¬ , š•— – –
µ‹Œ‰ƒŒŽ³ Œ — Ÿ‡µ – ‚•¬ K ,
‚ † — u ¬ [ — ~‰Ÿ‡µ –
= €“~‰³~¯ˆ‰¦ u ¬ } – ¡ Š‡€“~ ¬ 0
— €“Ÿ‹ – d°¬ ¬ ’’ K
[ — ~‰Ÿ‡µ – Œ — € – ˆ¯¦´– ¡ ¬
F — Œ A –£š ¦ – † — µ‡~ — ³ ŒŽˆ‹€ƒ„´† – , ¬ ,
F – ¡ ³°G€ vY?ŒŽˆ š ¦«€ƒŒŽˆy¬ K
F ~ — ³°ŒŽˆ‹€ š €ƒ¦‡– ¡ ¬ ’ ¬ ’ – ¡¡  ~ª‚«¦¦«€ š € €ƒ¦´€¶¦‡– ¡ ¬¡ ¬ ’ b
Š– – –£‚Œš ?ŒŽ— ˆ š š ¦«– €ƒŒŽˆ‹’‚› µ‹Œ‰ƒŒŽ³ Œ — Ÿ‡µ – ‚•¬K ³~ —˜š µ – ~ª – ¡ ~¦«Œ‰€ —˜– ¬ ’
F ŒŽŠ‡· – ¬ 0,
›µ¢– ¡ Œ — –” ³ – Š – ¬ ,
›µ¢– ¡ Œ — € – š “~‚«‚«€ƒ„‡† – ¬ ’
F Œ‰ƒŒŽ³°Œ — Ÿ‡µ‹€ – Š – ¬ ’ K
F Œ‰ƒŒŽ³°Œ — Ÿ‡µ‹€ – Š‡€¶‚ š•— – ” ¦ – ¬ KK
t ˆ¯¦ –•— ~ š ¦«€ƒŒŽˆy¬ K
t ˆ¯¤ ~ — €“~‰ˆ š£– Š‘ –£¡ š µ – ƒ – ¬ Œ — Š™~‰ˆy¬ ’ 0 € —˜š µ‹Œ …¬ ’ ¬ ’ KK
~~‰ˆ‹·¯ ~¯ˆ‹Š‡‚•¬ K
~~‰Ÿ‹“~ š € – ˆy¬ ’ ²¬ K
~~‰Ÿ‹“~ š € – ˆ Š‡€ƒ‚ š•— – ¦•¬ ’
~ – ?‚ š µ – ¦ ¬ ’ KRb
~ – ƒŒŽˆ‹·v –•—«— ~‰ˆ‹Š¬ KK
~y€“³°€ƒ¦ –°š ŒŽˆ¯¦«€“ˆŽ† – ¬ ~y€“³°€ƒ¦ – ¦ µ –•— ³ ŒŽŠ ˆ‡~‰³°€ƒ„‡† – ¬
~yŒŽˆ‹· – † — Š –š Œ —«— – ¡  ~ª¦«€ƒŒŽˆy¬ ~yŒŽˆ‹·‹† – † — ¦ µ –•— ³°ŒŽŠ ˆ‡~‰³°€ƒ„‡† – ¬ ’ 9’
™Š †‡~ – ¬ ’ K
³°Œ‹Š‡€GD –£¡ – ¬ ’ ~yŒ‰‚©~‰ˆ‹· – ‚•¬ b
} – ¡ ¦ — €¶„‡† – ¬ ’ ‡¬ ,
} – ¡ ¦ — €¶„‡† – Ÿ‹“~¦ – ~” ‚ € ˆ‹·‹†‹ ~ — €ƒ¦´–¢¡ š ŒŽˆ‹€ƒ„´† – ¬
}~ A˜Œ — ~‰ˆ‡~², ¬ ’’ b
}~ —˜š µ – ~ – ¡ ~¦ Œ‰€ —˜– ¬ ’ ¬b }~¦ — € š£– Š‘ž~ªŠ A ~ š£– ˆ š£– ¬ ’’
}~¦ — € š£– Š – ¤ ~ – ˆ š£– ¬ ’’
}~ f – ƒ¬ ’ ¬ ’ KRb
} ŒŽŠ–”  – Š‘Et‚«€“ˆ‹·™¬ b™¬ } Œ —˜–•— ~²¬ `’
} Œ‰¦«G€ ?Š – š£–•—˜š  – ‚•¬ KRb™¬ 0,
} ŒŽ†‹¤ – ³ – ˆ¯¦«‚ – ¡  –£š ¦ — €ƒ„´† – ‚¥¬ ’ K }†‹ƒ¦«€“Ÿ‹¶€ š ~¦ €¶Œ‹ˆ
?ŒŽˆ š ¦«€ƒŒŽˆ Ÿ‡~ — ?ŒŽˆ š ¦«€ƒŒŽˆy¬ ,
?ŒŽˆ š ¦«€ƒŒŽˆ Ÿ‡~ — ?Œ — ³ – ¬
I – †‡³~‰ˆ‡ˆy¬ ’ ¬ bb
+ ¨‹‚ –•— ¤~‰¨‹ – ¬ ¬ ’’ b
+ µ‡³ ¬ ’ ¬ ’ KRb
F Œ¯ ¬ b
} o €ƒ‚ – – – ˆ , Ÿ‡~ — ~ƒ –”  – ¬ ’ K F…µ‡~ª‚ – ¬
¦ — ~‰ˆ‹‚«€ƒ¦«€ƒŒŽˆy¬
= †‡~ƒ€ƒ¦‡– ¡ Š – F|Œ‰€“ˆ š ~ — – ¡ ¬ , F|Œ‰ ˆ ŒŽo ³ – ³°€“ˆ‹€“³~¬ ,
F — € ˆ š €“Ÿ – Š™† ³~ f‹€“³±†‡³ ¬ ’
¬ ’’ K
¬,K
– ¡ ‚«€ƒŠ™†y¬ b ,
– “~¦«€ƒŒŽˆ Š – ? –•— ³ – ¦ † — – ¬ ’ ¤ ¦ ³ ˆ‰¦ ~‰³°€GD ¡ ¬ Š – – –o µ‡– ~‰³ – ¬ 0, — – ,
} €ƒ‚ – – ˆ ‚‡–•¡ — € – ¬ ’ K ) ]!
šV µ³°— €G~‰v ³€ƒ³ ¦«€ ¬ ~K ƒb™€ƒ¦´¬ ¡ K
– = š•¡ — D ˆ‹€ƒš ¦«€ƒŒŽˆy– ¬ ’
–
&,f – ³Ÿ‹ – ‚•¬
@ ,
V € – · – ¬ V €“ˆ‹·Ž†‹“~ — €ƒ¦‡–
¡ š ŒŽˆ‹€ƒ„´† – ¬ ,
V Ÿ‹€“ˆ D ¬ ’@’ K
V Ÿ‹€“ˆ – † — ¬ ’’ Š – = € — ~ š ¬ ’’ b™¬ ’, V „´† – ƒ – ¦«¦ – ¬ , V ¦«Œ š 7 – ‚¥¬ , ¬
V ¦ — † š ¦ † — – š ŒŽˆ@? Œ — ³ – ¬ K ¬ ‡¬ ’,
V ¦ — † š ¦ † — – ‚ Ÿ‹€“ˆ †‡ˆ‹€ƒ¤ –•— ‚ – ƒ – d o ¬ ’@’ V ³ – ¡ ¦ — € – ‚ Ÿ‹€“ˆy¬ ’,0,
V ‚ ¦ – ” ³ – ‚«¦ ~ª¦«€ƒ‚«¦«€ƒ„´† – ¬ K
~°” ‚ Ÿ‹€“ˆy¬ 0
~°” ¤ –•— ¦ – f ¬ t ›¬ – ³ Ÿ…–•¡ — ~¦©† —˜– ¬ 0
š•— €ƒ¦«€ƒ„‡† – ¬
›µ¢– ¡ Œ — –” ³ – Š – ‚ — – ¡ ‚«€ƒŠ™†‹‚•¬ b ,
— € ~¯ˆ‹·‰ – – ¡ ¦«Œ¯€¶ – ¬ ’ K — Œ ~‰ˆ‹Œ¤ ¬ Rb
Ÿ – ‚ W ’ Z \ – ¦ W Z ’ \£¬KK
…~ — €“~‰¨‹ – ~ – ¡ ~¦ Œ‰€ —˜– ¬
Œ — ŒŽˆ‹Œ¯€ ¬ €¶·‹ˆ –•— ¬ ’ ‹ ¬ ’
V

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