Matrix permanent and quantum entanglement of permutation invariant states

We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing a recently introduced permanent inequality by Carlen, Loss and Lieb, we can prove explicit formulas of the geometric measure for permutation invariant basis states in a simple way.Comment: 10 page

Testing superabsorbent polymer (SAP) sorption properties prior to implementation in concrete: results of a RILEM Round-Robin Test

This article presents the results of a round-robin test performed by 13 international research groups in the framework of the activities of the RILEM Technical Committee 260 RSC "Recommendations for use of superabsorbent polymers in concrete construction''. Two commercially available superabsorbent polymers (SAP) with different chemical compositions and gradings were tested in terms of their kinetics of absorption in different media; demineralized water, cement filtrate solution with a particular cement distributed to every participant and a local cement chosen by the participant. Two absorption test methods were considered; the tea-bag method and the filtration method. The absorption capacity was evaluated as a function of time. The results showed correspondence in behaviour of the SAPs among all participants, but also between the two test methods, even though high scatter was observed at early minutes of testing after immersion. The tea-bag method proved to be more practical in terms of time dependent study, whereby the filtration method showed less variation in the absorption capacity after 24 h. However, absorption followed by intrinsic, ionmediated desorption of a specific SAP sample in the course of time was not detected by the filtration method. This SAP-specific characteristic was only displayed by the tea-bag method. This demonstrates the practical applicability of both test methods, each one having their own strengths and weaknesses at distinct testing times

Even cycle creating paths

We say that two graphs H1, H2 on the same vertex set are G-creating if the union of the two graphs contains G as a subgraph. Let H (n, k) be the maximum number of pairwise Ck-creating Hamiltonian paths of the complete graph Kn. The behavior of H (n, 2k + 1) is much better understood than the behavior of H (n, 2k), the former is an exponential function of n whereas the latter is larger than exponential, for every fixed k. We study H (n, k) for fixed k and n tending to infinity. The only nontrivial upper bound on H (n, 2k) was proved by Cohen, Fachini, and Körner in the case of k = 2: : (Formula presented.) In this paper, we generalize their method to prove that for every k ≥ 2, (Formula presented.) and a similar, slightly better upper bound holds when k is odd. Our proof uses constructions of bipartite, regular, C2k-free graphs with many edges given in papers by Reiman, Benson, Lazebnik, Ustimenko, and Woldar. © 2019 Wiley Periodicals, Inc