An algorithm for the min concave cost flow problem

A method is presented to solve that class of network flow problems, which may be formulated as one source - multiple destination minimum cost flow problems with concave costs. The global optimum is searched using a branch and bound procedure, in which the enumeration scheme is based on a characterization of the optimal solution set, while linear relaxations of the original problem provide lower bounds.     

Almost self-centered graphs

The center of a graph is the set of vertices with minimum eccentricity. Graphs in which all vertices are central are called self-centered graphs. In this paper almost self-centered (ASC) graphs are introduced as the graphs with exactly two non-central vertices. The block structure of these graphs is described and constructions for generating such graphs are proposed. Embeddings of arbitrary graphs into ASC graphs are studied. In particular it is shown that any graph can be embedded into an ASC graph of prescribed radius. Embeddings into ASC graphs of radius two are studied in more detail. ASC index of a graph G is introduced as the smallest number of vertices needed to add to G such that G is an induced subgraph of an ASC graph.     

Microseparations of cesium and barium in glass

A chemical micro-separation of Cs and Ba in complex glass with a high lanthanide content is presented. High purity silica, with and without Cs and Ba fortification, was subjected to identical dissolution, microseparation, and analysis as a control glass matrix. Dissolution was performed with hot concentrated nitric and hydrofluoric acids followed by fluoride complexation with boric acid, evolution of excess boric acid as methyl borate, and finally conversion to soluble nitrate species in 3 M nitric acid. Separation was performed with a miniature gas pressurized extraction chromatography system using a column packed with Eichrom Sr resin^™. High purity 3 M nitric acid was used to rinse Cs through the column and high purity 1% acetic acid was used to strip Ba from the resin. Quantitative recovery of both Cs (99.5 ± 0.7%) and Ba (99.1 ± 2.0%) was achieved in the lanthanide glass matrix and no statistically significant difference was observed in Cs or Ba recovery in the control high purity silica.     

Convex excess in partial cubes

The convex excess ce(G) of a graph G is introduced as where the summation goes over all convex cycles of G. It is proved that for a partial cube G with n vertices, m edges, and isometric dimension i(G), inequality 2n?m?i(G)?ce(G)≤2 holds. Moreover, the equality holds if and only if the so‐called zone graphs of G are trees. This answers the question from Bre r et al. [Tiled partial cubes, J Graph Theory 40 (2002) 91–103] whether partial cubes admit this kind of inequalities. It is also shown that a suggested inequality from Bre r et al. [Tiled partial cubes, J Graph Theory 40 (2002) 91–103] does not hold. Copyright © 2011 John Wiley & Sons, Ltd.     

Convex Sets in Lexicographic Products of Graphs

Geodesic convex sets, Steiner convex sets, and J-convex (alias induced path convex) sets of lexicographic products of graphs are characterized. The geodesic case in particular rectifies Theorem 3.1 in Canoy and Garces (Graphs Combin 18(4):787–793, 2002).