The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682-686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of 2.35 ± 0.18, i...

One can prove the following propositions: (1) For all functions f , g, h such that dom f ∩ dom g ⊆ domh holds f+·g+·h = g+·f+·h. (2) For all functions f , g, h such that f ⊆ g and rng h ∩ dom g ⊆ dom f holds g · h = f · h. (3) For all functions f , g, h such that dom f ⊆ rng g and dom f misses rng h and g domh misses dom f holds f · (g+·h) = f · g. (4) For all functions f1, f2, g1, g2 such that...

For simplicity, we use the following convention: i, n denote natural numbers, a, r, x, y denote real numbers, A denotes a closed-interval subset of R, C denotes a non empty set, and X denotes a set. We now state several propositions: (1) For every element D of divsA such that vol(A) = 0 holds lenD = 1. (2) χA,A is integrable on A and integralχA,A = vol(A). (3) For every partial function f from ...

The present work considers the modeling of turbulent flow in reed type valves of reciprocating compressors and is based on a simplified geometry of the actual valve, that is, a radial diffuser with axial feeding. Despite its simplicity the geometry chosen for the analysis has important flow features present in practical geometries. Due to its claimed capability to predict flow including feature...

Random number generators (RNG) play an important role in many sensor network systems and applications, such as those requiring secure and robust communications. In this paper, we develop a high-security and high-throughput hardware true random number generator, called PUFKEY, which consists of two kinds of physical unclonable function (PUF) elements. Combined with a conditioning algorithm, true...

We report a 12.5 Gb/s physical random number generator (RNG) that uses high-speed threshold detection of the spectrally-sliced incoherent light produced by a fiber amplifier. The system generates a large-amplitude, easily measured, fluctuating signal with bandwidth that is constrained only by the optical filter and electrical detector used. The underlying physical process (spontaneous emission)...

Bloom filters are a probabilistic data structure used to evaluate set membership. A group of hash functions are used to map elements into a Bloom filter and to test elements for membership. In this paper, we propose using multiple groups of hash functions and selecting the group that generates the Bloom filter instance with the smallest number of bits set to 1. We evaluate the performance of th...

In this paper X denotes a set, R, R1, R2 denote binary relations, x, y, z denote sets, and n, m, k denote natural numbers. Let us consider a binary relation R on X. Now we state the propositions: (1) fieldR ⊆ X. (2) If x, y ∈ R, then x, y ∈ X. Now we state the propositions: (3) Let us consider sets X, Y . Then (idX)Y = X ∩ Y . (4) 〈x, y〉 ∈ R |2 X if and only if x, y ∈ X and 〈x, y〉 ∈ R. (5) dom(...

The following three propositions are true: (1) For all binary relations a, b holds a · b = a b. (2) Let X be a set, L be a non empty relational structure, S be a non empty relational substructure of L, f , g be functions from X into the carrier of S, and f , g be functions from X into the carrier of L. If f ′ = f and g = g and f ¬ g, then f ′ ¬ g. (3) Let X be a set, L be a non empty relational...