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A Most General Edge Elimination Polynomial - Thickening of Edges

Hoffmann C.

Fundamenta Informaticae

2010

Vol. 98, nr 4

373-378

We consider a graph polynomial ξ(G; x, y, z) introduced by Ilia Averbouch,BennyGodlin, and Johann A.Makowsky (2008). This graph polynomial simultaneously generalizes the Tutte polynomial as well as a bivariate chromatic polynomial defined by Klaus Dohmen, Andr'e Pönitz, and Peter Tittmann (2003). We derive an identity which relates the graph polynomial of a thickened graph (i.e. a graph with each edge replaced by k copies of it) to of the original graph. As a consequence, we observe that at every point (x, y, z), except for points lying within some set of dimension 2, evaluating ξ is #P-hard. Thus, supports Johann A. Makowsky's difficult point conjecture for graph polynomials (2008).

Pitting corrosion in the wet section of the automotive exhaust systems

Hoffmann C., Gümpel P.

Journal of Achievements in Materials and Manufacturing Engineering

2009

Vol. 34, nr 2

115-121

Purpose: In the rear section of the automotive exhaust systems condensates bearing appreciable chloride ion concentrations and often low pH-values together with particles of electrochemical active soot can lead to pronounced pitting corrosion on the inner surfaces. For selection of an appropriate material that can enable cost-effective construction, the corrosion resistance of different candidate grades has to be rated. Design/methodology/approach: The different types of occurring corrosion, both general attack and pitting corrosion demands a combination of evaluation methods of the corrosion attack: mass loss measurements and the measure of the average depth of a certain number of pits with an optical 3D-Measuring System MicroCAD were used. Findings: The two methods for the evaluation of the corrosion attack provide the same ranking of the materials. Both methods are complementary to each other and together they provide a noticeable differentiation between some of the investigated materials. Research limitations/implications: The average depth of the pits gives no information about the entire rate of the corrosion attack, about the total number of the pits and their depth. In the future, research with the same optical 3D-Measuring System MicroCAD and new software will be carried out. This will form a structured analysis of the entire pits for the quantification of the corrosion. Practical implications: A higher quantification of the pitting corrosion leads to a better rating of the different stainless steel grades for using them in the wet section of the automotive exhaust systems. Originality/value: The evaluation of the pitting corrosion by means of the new measurement methods with the optical 3D-Measuring System MicroCAD is more accurate, work fast and is an obligatory complement of the previous methods of evaluation of the pitting corrosion: mass loss and the depth of the deepest pit.