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**1 - 4**of**4**### www.elsevier.com/locate/topol On cellularization for simplicial presheaves and motivic homotopy

"... We construct cellular homotopy theories for categories of simplicial presheaves on small Grothendieck sites and discuss appli-cations to the motivic homotopy category of Morel and Voevodsky. ..."

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We construct cellular homotopy theories for categories of simplicial presheaves on small Grothendieck sites and discuss appli-cations to the motivic homotopy category of Morel and Voevodsky.

### based on joint work with with Andrey Mironov The 10th Pacific Rim Geometry Conference

, 2011

"... An immersion i: N � M of an n-manifold N is Lagrangian if i ∗ (ω) = 0. If i is an embedding, then i(N) is a Lagrangian submanifold of M. A vector field ξ on M is Hamiltonian if the 1-form ω ( · , ξ) is exact. A Lagrangian immersion i: N � M is Hamiltonian minimal (H-minimal) if the variations of t ..."

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of the volume of i(

*N*) along all Hamiltonian vector fields with compact support are zero, i.e. d dt vol(it(*N*)) ∣ = 0, t=0 where it(*N*) is*a*Hamiltonian deformation of i(*N*) = i0(*N*), and vol(it(*N*)) is the volume of the deformed part of it(*N*).*2*Explicit examples of H-minimal Lagrangian submanifolds in*C*m and CP### Intersections of quadrics and H-minimal Lagrangian submanifolds

, 2012

"... An immersion i: N � M of an n-manifold N is Lagrangian if i ∗ (ω) = 0. If i is an embedding, then i(N) is a Lagrangian submanifold of M. A vector field ξ on M is Hamiltonian if the 1-form ω ( · , ξ) is exact. A Lagrangian immersion i: N � M is Hamiltonian minimal (H-minimal) if the variations of t ..."

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An immersion i:

*N*� M of an*n*-manifold*N*is Lagrangian if i ∗ (ω) = 0. If i is an embedding, then i(*N*) is*a*Lagrangian submanifold of M.*A*vector field ξ on M is Hamiltonian if the*1*-form ω ( · , ξ) is exact.*A*Lagrangian immersion i:*N*� M is Hamiltonian minimal (H-minimal) if the variations### Dissertação submetida como requisito parcial para obtenção do grau de Mestre em Finanças

"... An approach based on Extreme Value Theory as a measure to quantify market risk of equity securities and portfolios ..."

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An approach based on Extreme Value Theory as

*a*measure to quantify market risk of equity securities and portfolios**1 - 4**of

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