We construct a family of integrable volume-preserving maps in R with a bidimensional heteroclinic connection of spherical shape between two fixed points of saddle-focus type. In other contexts, such structures are called Hill’s spherical vortices or spheromaks. We study the splitting of the separatrix under volume-preserving perturbations using a discrete version of the Melnikov method. Firstly...

This paper proposes a nonparametric FPE-like procedure based on the smooth backfitting estimator when the additive structure is a priori known. This procedure can be expected to perform well because of its well-known finite sample performance of the smooth backfitting estimator. Consistency of our procedure is established under very general conditions, including heteroskedasticity.

We study mappings obtained as s-periodic reductions of the lattice Korteweg-De Vries equation. For small s ∈ N we establish upper bounds on the growth of the degree of the numerator of their iterates. These upper bounds appear to be exact. Moreover, we conjecture that for s1, s2 co-prime the growth is ∼ (2s1s2)−1n2, except when s1 + s2 = 4 where the growth is linear ∼ n. Also, we conjecture the...

The first type of specialized encryption scheme that can be used in secure outsourced storage we will look at is property-preserving encryption. This is encryption where some desired property of the plaintexts is intentionally leaked by the ciphertexts. The two main examples we will study are deterministic encryption, which preserves the equality property, and order preserving encryption, which...

We prove that any real-analytic, volume-preserving action of a lattice Γ in a simple Lie group with Q-rank(Γ) ≥ 7 on a closed 4-manifold of nonzero Euler characteristic factors through a finite group action.

We prove that the only finite factor-representations of the HigmanThompson groups {Fn,r}, {Gn,r} are the regular representations and scalar representations arising from group abelianizations. As a corollary, we obtain that any measure-preserving ergodic action of a simple Higman-Thompson group must be essentially free. Finite factor representations of other classes of groups are also discussed.

Let Ω ⊂ R be a bounded Lipschitz domain and consider the Dirichlet energy functional F[u,Ω] := 1 2 Z

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is based on the measure of a supremum, hence combining additive and highly sub-additive components. It is shown that this type of outer measure enables the introd...