7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680(...

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Transcript of 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680(...

Δ ℜ

α

Δ

Δ

τ

Δ

Δ

α

α

α

Γ Γ Γ Γ Γ

� �

Φ

α

λ λ λ

Γ

Δ

ΓΓ

Γ Γ

Γ

τ

τ

{ }

α

Δ Δ

Δ Δ

ΔΔ

Φ Δ

Δ

Δ Δ

Ω

β

Δ

Δ

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

=

∑=

=

−=

−=≥=

=≥+<≤

=→

∑=

=

=+

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=

−=

⎥⎥⎥⎥

⎢⎢⎢⎢

=

∀ ∑=

=

∑=

Δ−+++++=

+

+=

+Ω=Ω

� � � � � � � �

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Δ Δ

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β

� β

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Δ

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Δ

� Δ

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Δ

β⋅+=Δ+=Δ+

Δ

β⋅+=Δ+=Δ+

++⋅+=Δ+ β

β

� ε

� ε

ε

β⋅=βΔ Δ

Δ

� Δ β

∫ βΔ⋅βΔ⋅βΔ=βΔ ΔΔΔΔ

� Ψ

<=Ψ

β<β=βΨ

βΔ<βΔ=βΔΨ ΔΔΔ

β⋅<β⋅=βΔΨ Δ

βΔ Δ

βΨ=βΔΨ Δ

ββΨ−β+βΨ

βΔβΔΨ−βΔ+βΔΨ

=βΔΔ

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Δ

βΔ

β⋅β=βΔ

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Δ

βΔ Δ Δ

Δ

=βΔ Δ

−Δ β⋅⋅=βΔ

+=

⎥⎥⎦

⎢⎢⎣

+β⋅

=βΔ+

Δ

+=

∏=

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� � �

×

β ∈

β

α

α

Δ

ΦΔ=Δ

Δ

Δ

Δ=Δ

+

Δ+Δ=Δ

Δ Δ−

Δ

Δ=+

Δ+Δ−

+∞→

Δ+Δ=Δ

===

Δ+Δ=Δ

===

Δ+Δ=Δ

===

� � � �

� � � � �

∏=

=

=ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

Δ⋅ℜ⋅+Δ−=

Δ

ℜ Δ

Δ⋅ℜ⋅+=

Δ

Δ

Δ−−=Δ

ΔΔ

Δ

Δ Δ⋅ℜ

Δ

Δ⋅ℜ

Δ−−=

{ }

{ }∑

∑=

=

=

=

=

−−

−=

∑∑=

∑=

−−=

{ }

{ }∑

∑=

=

=

=

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⎥⎦

⎤⎢⎣

⎡ −−=

∑=

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=

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=

=

=

� α

⊗ α

α

α

∏⊗=

Φ

Φ

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Φ

+Φ=

+= φ

⋅=

⎥⎦

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⎡ −−⋅=

++++=

+++⋅+⋅+

=

τ

τ

Δ

≤ ≤ ≤ ≤

Δ

Δ

≤ ≤

Δ

⋅=Δ+ Δ

Δ Δ

Δ

Δ

=

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Δ

Δ

Δ

≤ ≤ ≤ ≤ →

∑ Δ+→

Δ+→=Δ+→

Δ

ΓΓΓΓ

ΓΓ ΓΓ

Δ

Γ+−ΓΓ=Γ

Γ

Γ

Γ−Γ−=Γ

Γ

Γ

Γ

Γ

≤ ≤

≤ ≤

∑=

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∑ τ⋅

≤ ≤ ≤ ≤

Δ

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−=

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ττττ

α

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⎥⎦

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⎡−= α

α

� α

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� α

� ≥−⋅α α

−⋅=

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αα−⋅−⋅−−⋅=

� ≤−⋅ α

ααα −−−−−−−=

α

++−+−+

=

⎩⎨⎧

≥=′−=

=′−=

α

α

α

α

Δ

Δ

α

α

α

α

τ

ττττ

×

==

MMMMMMMM

≤ ≤ ≤ ≤

→ → → → ∑

=

=

→ → → → ∑

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=

→ → → → ∑

=

=

→ → → → ∑

=

=

=

=

→= ∀

ΔΔΔΔ

Δ

Γ

Γ−Γ−=Γ

Γ

Γ

≤ ≤ ≤ ≤

∑=

Δ+ Ρ=

Δ+

==Γ

Γ Γ ΔΓ

ΓΓΓΓ

ΓΓ ΓΓ

Γ + ΔΓΓ + ΔΓΓ + ΔΓΓ + ΔΓ

Γ + ΔΓΓ + ΔΓΓ + ΔΓΓ + ΔΓ

ΓΓΓΓ

ΓΓΓΓ

Γ + ΔΓΓ + ΔΓΓ + ΔΓΓ + ΔΓ

ΓΓΓΓ

Γ + ΔΓΓ + ΔΓΓ + ΔΓΓ + ΔΓ

ΓΓΓΓ

Γ Γ Γ Γ Γ

=∑=

=

Γ ΔΓ

Γ

ΔΓ+Γ

{ } ΔΓ+Γ−ΔΓ+ΓΓ

[ ]{ }ΔΓ+Γ−ΔΓ+ΓΓ

{ }Γ−ΔΓ+Γ

[ ] [ ]{ }ΓΔΓ+Γ−ΔΓ+ΓΓ

{ }Γ−ΔΓ+Γ

ΓΓΓΓ ΓΓΓΓ

Γ Γ Γ Γ Γ Γ Γ Γ

ΓΓΓΓ ΓΓΓΓ

ΓΓΓΓ

Δ

=

∑∑∑∑

∑∑∑∑

∑∑∑∑

∑∑∑∑

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+=

+=

1111 λλλλ λλλλ2222

λλλλ3333

©

−+

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&&

∑=

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∑= ⋅+

−⋅=

&&

&

&

∑ ==

&

&&∑ ∑+=

& &

Δ

Δ ℜ

⎪⎪

⎪⎪

=+

=

=++

=+

=

=+++=++

=+

=

∑ −