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...

1 . Introduction and statement of results Let (3(n) = Y_, In p and B (n) = y_p . j jn ap denote the sum of distinct prime divisors of n and the sum of all prime divisors of n respectively . Both (3(n) and B(n) are additive functions which are in a certain sense large (the average order of B(n) is Tr'n/(6log n), [1]) . For a fixed integer m the number of solutions of B(n) = m, is the number of p...

1. Under suitable smoothness assumptions, quasiperiodicity, and hence the absence of any kind of hyperbolicity, is non-negligible in a measure-theoretical sense [Kol] (under suitable smoothness assumptions). 2. In low regularity (C), failure of non-uniform hyperbolicity (here nonuniform hyperbolicity can be understood as positivity of the metric entropy) is a fairly robust phenomenon in the top...

In the present paper, the Sawada–Kotera equation is considered by Lie symmetry analysis. All of the geometric vector fields to the Sawada–Kotera equation are obtained, and then the symmetry reductions and exact solutions of the Sawada–Kotera equation are investigated. Our results show that symmetry analysis is a very efficient and powerful technique in finding the solution of the proposed equat...