Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width

The Multicut problem can be defined as: given a graph G and a collection of pairs of distinct vertices {s_i,t_i} of G, find a minimum set of edges of G whose removal disconnects each s_i from the corresponding t_i. Multicut is known to be NP-hard and Max SNP-hard even when the input graph is restricted to being a tree. The main result of the paper is a polynomial-time approximation scheme (PTAS) for Multicut in unweighted graphs with bounded degree and bounded tree-width. That is, for any ε>0, we present a polynomial-time (1+ε)-approximation algorithm. In the particular case when the input is a bounded-degree tree, we have a linear-time implementation of the algorithm. We also provide some hardness results: we prove that Multicut is still NP-hard for binary trees and that it is Max SNP-hard if we drop any of the three conditions (unweighted, bounded-degree, bounded tree-width). Finally we show that some of these results extend to the vertex version of Multicut and to a directed version of Multicut.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

First measurement of the ϱ spectral function in nuclear collisions

The NA60 experiment at the CERN SPS has studied low-mass muon pairs in 158 A GeV In–In collisions. A strong excess of pairs is observed above the yield expected from neutral meson decays. The unprecedented sample size close to 400000 events and the good mass resolution of about 2% made it possible to isolate the excess by subtraction of the decay sources. The shape of the resulting mass spectrum shows some non-trivial centrality dependence, but is largely consistent with a dominant contribution from π⁺π^-→ϱ→μ⁺μ^- annihilation. The associated ϱ spectral function exhibits considerable broadening, but essentially no shift in mass. The p_T-differential mass spectra show the excess to be much stronger at low p_T than at high p_T. The results are compared to theoretical model predictions; they tend to rule out models linking hadron masses directly to the chiral condensate. PACS 25.75.-q; 12.38.Mh; 13.85.Qk     

Mathematical modeling of crystallization analysis fractionation (Crystaf) of polyethylene

Four polyethylene samples (PE) with different molecular weight distributions (MWD) were analyzed by crystallization analysis fractionation (Crystaf) at several cooling rates to investigate the effect of MWD and cooling rate on their Crystaf profiles. Using these results, we developed a mathematical model for Crystaf that considers crystallization kinetic effects, which are ignored in all previous Crystaf models. The Crystaf model we proposed can fit the experimental Crystaf profiles of the 4 polyethylene resins very well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2749–2759, 2006     

Group algebras of Kleinian type and groups of units

The algebras of Kleinian type are finite-dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type and the group algebras of Kleinian type. As an application, we characterize the group rings RG, with R an order in a number field and G a finite group, such that the group of units of RG is virtually a direct product of free-by-free groups.     

On the phase structure of the compact abelian lattice Higgs model

This paper studies the vacuum overlap order parameter proposed by Fredenhagen and Marcu in the case of the compactU(1) gauge model with the Wilson action coupled to a Higgs field with fixed length ||=1. The existence of two distinct phases inD space-time dimensions (D4) is established.     

In-trees and plane embeddings of outerplanar graphs

A notion of anin-tree is introduced. It is then used to characterize and count plane embeddings of outerplanar graphs. In-trees have also been applied in the study of independent vertex covers of faces in outerplanar graphs.This research was partially supported by the grant RP.I.09, from the Institute of Informatics, University of Warsaw. Hospitality of the Institute of Datalogy, University of Copenhagen where this research has been completed is gratefully acknowledged.