A proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices v, w the set of colours appearing on the edges incident with v is not equal to the set of colours appearing on the edges incident with w. Let ndi(G) be the least number of colours required for a proper neighbour-distinguishing edge colouring of G. We prove that for d ≥ 4, a random d-regular grap...

For a fixed rational number g 6∈ {−1, 0, 1} and integers a and d we consider the sets Ng(a, d), respectively Rg(a, d), of primes p for which the order, respectively the index of g(mod p) is congruent to a(mod d). Under the Generalized Riemann Hypothesis (GRH), it is known that these sets have a natural density δg(a, d), respectively ρg(a, d). It is shown that these densities can be expressed as...

This paper analyzes sources of contributions to virtually all candidates for Pennsylvania legislative office in 1982 who reported raising or spending more than $250 any six reporting periods. Contributions totaling nearly $7,750,000 were examined. Almost half came amounts greater $250. About 20% from $50 less individuals: an equal proportion individuals giving between and Political Action Commi...

the influences of anionic sodium dodecylsulfate (sds) and cationic hexadecyltrimethylammonium bromide (htab) surfactants on the incorporation and distribution of barium hexaferrite nanoparticles in the electrodeposited cofe-bafe12o19 composite thin films were studied. sulphate bathes with natural ph containing 0 to 2 g/l surfactants were used for electroplating at room temperature. field emissi...

Using a notion of rank for Hechler forcing we show: 1) assuming ω 1 = ω L 1 , there is no real in V [d] which is eventually different from the reals in L[d], where d is Hechler over V ; 2) adding one Hechler real makes the invariants on the left-hand side of Cichoń’s diagram equal ω1 and those on the right-hand side equal 2 ω and produces a maximal almost disjoint family of subsets of ω of size...

We investigated the influence of Mg feeding frequency on the variation in serum Mg concentration and tissue Mg levels in Mg-deficient rats. Sprague-Dawley rats, which had been fed a Mg-deficient diet for 14 d, were divided into 3 groups that were kept on 3 diets differing in their Mg content. The rats were fed 0.5-fold (Mg250 group), 1-fold (Mg500 group), or 1.5-fold (Mg750 group) the amounts o...

Much is known about the propagation of waves through periodic arrangements of identical scatterers, such as through a photonic crystal. Here, we consider a simple realization: scalar waves through a regular two-dimensional array of identical small circles. We are interested in the effect of random disorder: the circles remain identical, but their centres are given small random displacements. We...