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On a Class of Fractional Obstacle Type Problems Related to the Distributional Riesz Derivative
In this work, we consider the fractional obstacle problem with a given obstacle ψ in a bounded domain Ω in R, such that Ksψ = {v ∈ H s 0(Ω) : v ≥ ψ a.e. in Ω} 6= ∅, given by u ∈ Ksψ : 〈LAu, v − u〉 ≥
Quantum Invariants of 3-manifolds and NP vs #P
TLDR
This work uses basic tools from quantum computation to give a proof that the SO(3) Witten-Reshetikhin-Turaev (WRT) invariant of 3-manifolds is #P-hard to calculate, and applies this result to a question about the combinatorics of Heegaard splittings.
F_ζ-geometry, Tate motives, and the Habiro ring
In this paper, we propose different notions of F_zeta-geometry, for zeta a root of unity, generalizing notions of over finite fields, the Grothendieck class, and the notion of torification. We relate
3-manifold diagrams and NP vs $\#$P
TLDR
It is shown that, if NP $\neq \#$P, then there exist infinitely many 3-manifold diagrams which cannot be made logarithmically "thin" (relative to their overall size) except perhaps by an exponentially large number of local moves.
F-zeta geometry, Tate motives, and the Habiro ring
In this paper we propose different notions of F_zeta-geometry, for zeta a root of unity, generalizing notions of F_1-geometry (geometry over the "field with one element") based on the behavior of the
On a Class of Nonlocal Obstacle Type Problems Related to the Distributional Riesz Fractional Derivative
In this work, we consider the nonlocal obstacle problem with a given obstacle ψ in a bounded Lipschitz domain Ω in R, such that Kψ = {v ∈ H 0(Ω) : v ≥ ψ a.e. in Ω} 6= ∅, given by u ∈ Kψ : 〈Lau, v −
On an Anisotropic Fractional Stefan-Type Problem with Dirichlet Boundary Conditions
In this work, we consider the fractional Stefan-type problem in a Lipschitz bounded domain Ω ⊂ R with time-dependent Dirichlet boundary condition for the temperature θ = θ(x, t), θ = g on Ω×]0, T [,