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7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

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Page 1: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 2: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 3: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 4: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 5: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 6: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 7: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 8: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 9: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 10: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 11: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 12: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 13: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 14: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 15: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 16: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Δ ℜ

Page 17: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 18: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 19: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 20: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 21: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 22: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

α

Δ

Page 23: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Δ

Page 24: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

τ

Page 25: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Δ

Δ

α

α

α

Γ Γ Γ Γ Γ

Page 26: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 27: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

� �

Page 28: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 29: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Φ

Page 30: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 31: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 32: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 33: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 34: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 35: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

α

λ λ λ

Γ

Δ

ΓΓ

Γ Γ

Γ

τ

τ

{ }

Page 36: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

α

Δ Δ

Δ Δ

ΔΔ

Φ Δ

Δ

Δ Δ

Ω

β

Δ

Δ

Page 37: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 38: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 39: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 40: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 41: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

=

Page 42: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 43: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 44: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 45: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 46: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 47: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 48: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 49: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 50: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

∑=

=

Page 51: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

−=

Page 52: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 53: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 54: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 55: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 56: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 57: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 58: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 59: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

−=≥=

=≥+<≤

=→

Page 60: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

∑=

=

=+

=∑

Page 61: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

=

−=

⎥⎥⎥⎥

⎢⎢⎢⎢

=

∀ ∑=

=

Page 62: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

∑=

Δ−+++++=

+

+=

Page 63: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

+Ω=Ω

Page 64: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Page 65: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

� � � � � � � �

� � � � �

� � � � � �

� � � � �

� �

Page 66: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 67: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw
Page 68: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

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� ⊗

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� ⊗

� ⊗

� ⊗

� ⊗

� ⊗

� ⊗

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Δ Δ

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Σ

β

� β

� β

� β

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Δ

Δ

Δ

Δ

Δ

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� Δ

Δ

Δ

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β⋅+=Δ+=Δ+

Δ

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β⋅+=Δ+=Δ+

++⋅+=Δ+ β

β

� ε

� ε

ε

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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

ΔΔΔ

Δ

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βΔ

β⋅β=βΔ

Δ

Δ

βΔ Δ Δ

Δ

=βΔ Δ

−Δ β⋅⋅=βΔ

+=

⎥⎥⎦

⎢⎢⎣

+β⋅

=βΔ+

Δ

+=

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∏=

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� � � � �

� � �

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×

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β ∈

β

α

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α

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Δ

ΦΔ=Δ

Δ

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Δ

Δ=Δ

+

Δ+Δ=Δ

Δ Δ−

Δ

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Δ=+

Δ+Δ−

+∞→

Δ+Δ=Δ

===

Δ+Δ=Δ

===

Δ+Δ=Δ

===

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� � � �

� � � � �

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∏=

=

=ℜ

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ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

ℜ ℜ

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Δ⋅ℜ⋅+Δ−=

Δ

ℜ Δ

Δ⋅ℜ⋅+=

Δ

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Δ

Δ−−=Δ

ΔΔ

Δ

Δ Δ⋅ℜ

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Δ

Δ⋅ℜ

Δ−−=

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{ }

{ }∑

∑=

=

=

=

=

−−

−=

∑∑=

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∑=

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−−=

{ }

{ }∑

∑=

=

=

=

=

⎥⎦

⎤⎢⎣

⎡ −−=

∑=

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=

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=

=

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=

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=

=

=

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� α

⊗ α

α

α

∏⊗=

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Φ

Φ

Φ

Φ

+Φ=

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+= φ

⋅=

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⎥⎦

⎤⎢⎣

⎡ −−⋅=

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++++=

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+++⋅+⋅+

=

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τ

τ

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Δ

≤ ≤ ≤ ≤

Δ

Δ

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≤ ≤

Δ

⋅=Δ+ Δ

Δ Δ

Δ

Δ

=

Δ+

Δ+

Δ+

Δ+

Δ

Δ

Δ

Δ

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≤ ≤ ≤ ≤ →

∑ Δ+→

Δ+→=Δ+→

Δ

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ΓΓΓΓ

ΓΓ ΓΓ

Δ

Page 206: 7KqVH - u-bordeaux1.frgrenet.drimm.u-bordeaux1.fr/pdf/2005/VASCONCELOS_ELISIO_2005.pdf · 5(680( /hv upvhdx[ g¶dvvdlqlvvhphqw hq )udqfh uhsupvhqwhqw xq frqvlgpudeoh sdwulprlqh grqw

Γ+−ΓΓ=Γ

Γ

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Γ

Γ−Γ−=Γ

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Γ

Γ

Γ

Γ

≤ ≤

≤ ≤

∑=

++−

=

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∑∑=

=

=

=

τ ≠

τ

∑ τ⋅

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≤ ≤ ≤ ≤

Δ

≠=τ ∑

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τ τ

τ

τ

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τ

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−=

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τ

ττττ

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α

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τ

ττττ

τ

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� �

� �

� �

� �

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∑=

=

⋅=

∑=

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� ∑=

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⎥⎦

⎤⎢⎣

⎡−= α

α

� α

� α

� α

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� ≥−⋅α α

−⋅=

� <−⋅α

αα−⋅−⋅−−⋅=

� ≤−⋅ α

ααα −−−−−−−=

α

++−+−+

=

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⎩⎨⎧

≥=′−=

=′−=

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α

α

α

α

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Δ

Δ

α

α

α

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α

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τ

ττττ

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×

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==

MMMMMMMM

≤ ≤ ≤ ≤

→ → → → ∑

=

=

→ → → → ∑

=

=

→ → → → ∑

=

=

→ → → → ∑

=

=

=

=

→= ∀

ΔΔΔΔ

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Δ

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Γ

Γ−Γ−=Γ

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Γ

Γ

≤ ≤ ≤ ≤

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∑=

Δ+ Ρ=

Δ+

==Γ

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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

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ΔΓ+Γ

{ } ΔΓ+Γ−ΔΓ+ΓΓ

[ ]{ }ΔΓ+Γ−ΔΓ+ΓΓ

{ }Γ−ΔΓ+Γ

[ ] [ ]{ }ΓΔΓ+Γ−ΔΓ+ΓΓ

{ }Γ−ΔΓ+Γ

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ΓΓΓΓ ΓΓΓΓ

Γ Γ Γ Γ Γ Γ Γ Γ

ΓΓΓΓ ΓΓΓΓ

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ΓΓΓΓ

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Δ

=

∑∑∑∑

∑∑∑∑

∑∑∑∑

∑∑∑∑

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λλλλ

∑=

� λλλλ, λλλλ2, λλλλ3}

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λλλλ

+=

+=

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1111 λλλλ λλλλ2222

λλλλ3333

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©

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−+

=

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+−

==⋅

&&

∑=

⋅+−

=&&

∑= ⋅+

−⋅=

&&

&

&

∑ ==

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&

&&∑ ∑+=

& &

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