Angular distribution of positrons in coherent pair production in deformed crystals

We investigate the angular distribution of positrons in the coherent process electronpositron pair creation process by high-energy photons in a periodically deformed single crystal with a complex base. The formula for the corresponding differential cross-section is derived for an arbitrary deformation field. The case is considered in detail when the photon enters into the crystal at small angles with respect to a crystallographic axis. The results of the numerical calculations are presented for${\mathrm{SiO}}_{2}$ and diamond single crystals and Moliere parameterization of the screened atomic potentials in the case of the deformation field generated by the acoustic wave of S-type.Comment: 11 pages, 4 figures, figures and references adde

Measures of edge-uncolorability

The resistance $r(G)$ of a graph $G$ is the minimum number of edges that have to be removed from $G$ to obtain a graph which is $\Delta(G)$-edge-colorable. The paper relates the resistance to other parameters that measure how far is a graph from being $\Delta$-edge-colorable. The first part considers regular graphs and the relation of the resistance to structural properties in terms of 2-factors. The second part studies general (multi-) graphs $G$. Let $r_v(G)$ be the minimum number of vertices that have to be removed from $G$ to obtain a class 1 graph. We show that $\frac{r(G)}{r_v(G)} \leq \lfloor \frac{\Delta(G)}{2} \rfloor$, and that this bound is best possible.Comment: 9 page

On disjoint matchings in cubic graphs

For $i=2,3$ and a cubic graph $G$ let $\nu_{i}(G)$ denote the maximum number of edges that can be covered by $i$ matchings. We show that $\nu_{2}(G)\geq {4/5}| V(G)|$ and $\nu_{3}(G)\geq {7/6}| V(G)|$. Moreover, it turns out that $\nu_{2}(G)\leq \frac{|V(G)|+2\nu_{3}(G)}{4}$.Comment: 41 pages, 8 figures, minor chage

Flux pinning properties of superconductors with an array of blind holes

We performed ac-susceptibility measurements to explore the vortex dynamics and the flux pinning properties of superconducting Pb films with an array of micro-holes (antidots) and non-fully perforated holes (blind holes). A lower ac-shielding together with a smaller extension of the linear regime for the lattice of blind holes indicates that these centers provide a weaker pinning potential than antidots. Moreover, we found that the maximum number of flux quanta trapped by a pinning site, i.e. the saturation number ns, is lower for the blind hole array.Comment: 6 figures, 6 page