We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore
logical information. As results we obtain a polynomial simulation
In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half the boundar
y, respectively. For the case of measurements on the whole boundary, the stability estimates are of ln-type and for the case of measurements on slightly more than half of the boundary, we derive estimates that are of ln ln-type.
Without violating causality, we allow performing measurements in time reverse process of a feedback manipulated stochastic system. As a result we come across an entropy production due to the measurement process. This entropy production, in addition t
o the usual system and medium entropy production, constitutes the total entropy roduction of the combined system of the reservoir, the system and the feedback controller. We show that this total entropy production of full system satisfies an integrated fluctuation theorem as well as a detailed fluctuation theorem as expected. We illustrate and verify this idea through explicit calculation and direct simulation in two examples.
We have used an atomistic {it ab initio} approach with no adjustable parameters to compute the lattice thermal conductivity of Si$_{0.5}$Ge$_{0.5}$ with a low concentration of embedded Si or Ge nanoparticles of diameters up to 4.4 nm. Through exact G
reens function calculation of the nanoparticle scattering rates, we find that embedding Ge nanoparticles in $text{Si}_{0.5}text{Ge}_{0.5}$ provides 20% lower thermal conductivities than embedding Si nanoparticles. This contrasts with the Born approximation which predicts an equal amount of reduction for the two cases, irrespective of the sign of the mass difference. Despite these differences, we find that the Born approximation still performs remarkably well, and it permits investigation of larger nanoparticle sizes, up to 60 nm in diameter, not feasible with the exact approach.
Superconductivity is found in 50% K-doped EuFe2As2 sample below 33 K. Our results of electrical resistivity, magnetic susceptibility and 57Fe and 151Eu Mossbauer spectroscopy provide clear evidence that the ordering of the Fe moments observed at 190
K in undoped EuFe2As2 is completely suppressed in our 50% K doped sample, thus there is no coexistence between the Fe magnetic order and the superconducting state. However, short range ordering of the Eu moments is coexisting with the superconducting state below 15 K. A bump in the susceptibility well below Tc as well as a slight broadening of the Fe Mossbauer line below 15 K evidence an interplay between the Eu magnetism and the superconducting state.
