Kirchhoff index of a non-complete wheel

In this work, we compute analitycally the Kirchhoff index and effective resistances of a weighted non–complete wheel that has been obtained by adding a vertex to a weighted cycle and some edges conveniently chosen. To this purpose we use the group inverse of the combinatorial LaplacianPostprint (author's final draft

The group inverse of extended symmetric and periodic Jacobi matrices

In this work, we explicitly compute the group inverse of symmetric and periodic Jacobi matrices with constant elements that have been extended by adding a row and a column conveniently de ned. For this purpose, we interpret such matrices as the combinatorial Laplacian of a non-complete wheel that has been obtained by adding a vertex to a cycle and some edges conveniently chosen. The obtained group inverse is an incomplete block matrix with a block Toeplitz structure. In addition, we obtain the e ffective resistances and the Kirchhoff index of non-complete wheels.Preprin

Translation of Time-Reversal Violation in the Neutral K-Meson System into a Table-Top Mechanical System

Weak interactions break time-reversal (T) symmetry in the two-state system of neutral K mesons. We present and discuss a two-state mechanical system, a Foucault-type pendulum on a rotating table, for a full representation of K0 K0bar transitions by the pendulum motions including T violation. The pendulum moves with two different oscillation frequencies and two different magnetic dampings. Its equation of motion is identical with the differential equation for the real part of the CPT-symmetric K-meson wave function. The pendulum is able to represent microscopic CP and T violation with CPT symmetry owing to the macroscopic Coriolis force which breaks the symmetry under reversal-of-motion. Video clips of the pendulum motions are shown as supplementary material.Comment: 11 pages, 5 figures, 1 external url with video clip