‎a $(p‎,‎q)$ graph $g$ is said to have a $k$-odd mean‎ ‎labeling $(k ge 1)$ if there exists an injection $f‎ : ‎v‎ ‎to {0‎, ‎1‎, ‎2‎, ‎ldots‎, ‎2k‎ + ‎2q‎ - ‎3}$ such that the‎ ‎induced map $f^*$ defined on $e$ by $f^*(uv) =‎ ‎leftlceil frac{f(u)+f(v)}{2}rightrceil$ is a‎ ‎bijection from $e$ to ${2k - ‎‎‎1‎, ‎2k‎ + ‎1‎, ‎2k‎ + ‎3‎, ‎ldots‎, ‎2‎ ‎k‎ + ‎2q‎ - ‎3}$‎. ‎a graph that admits $k$...

Long-lived di- and trianions have been formed from fluorofullerenes in the gas phase by electrospray ionization. Fragmentation of multiply charged anions has been induced by multiple low-energy collisions. Two complementary dissociation experiments have been conducted. Firstly, unequivocal connectivity has been established between the precursor ion and the first and second generation of its pro...

A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even-odd rule and the winding number, the former leading to ray-crossing, the latter to angle summation algorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algor...

A class of singlet superconductors with a gap function ∆(k, ωn) which is odd in both momentum and Matsubara frequency was proposed recently [1]. To show an instability in the odd gap channel, a model phonon propagator was used with the p-wave interaction strength larger than the s-wave. We argue that the positive scattering matrix element entering the Eliashberg equations leads to a constraint ...