An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a graph G is defined to have vertices the arcs of G such that two arcs uv, xy are adjacent if and only if (v, u, x, y) is a 3-arc of G. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-...

An arc modelling is a valuable and useful tool to evaluate the switching performance of lowvoltage switching devices (LVSDs) during breaking operation before testing real products. Moreover, it helps improve interruption capability of LVSDs and optimize them. This paper focuses on the numerical simulation of the arc behavior in AC devices before zero current and prediction of the re-ignition af...

A digraph D = (V, A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V , i.e., hamiltonian path. We prove a conjecture of Quintas [7]: if D is arc-traceable, then the condensation of D is a directed path. We show that the converse of this conjecture is false by providing an example of an upset tournament which is not arc-traceable. We then giv...

S U M M A R Y Continuum models are used to investigate the large-scale deformation associated with the subduction of aseismic ridges. Formulated in the horizontal plane using thin viscous sheet theory, these models measure the horizontal transmission of stress through the arc lithosphere accompanying ridge subduction. Modelling was used to compare the Tonga arc and Louisville ridge collision wi...

A subgroup G of automorphisms of a graph X is said to be 2 -arc-transitive if it is vertexand edgebut not arc-transitive. The graph X is said to be 2 -arc-transitive if Aut X is 1 2 -arc-transitive. The interplay of two different concepts, maps and hypermaps on one side and 2 -arc-transitive group actions on graphs on the other, is investigated. The correspondence between regular maps and 2 -ar...

An adaptive control based on fuzzy logic has been implemented for Gas Tungsten Arc Welding (GTAW). This adaptive controller eliminates the problems frequently experienced with traditional Automatic Voltage Control (AVC) systems, which do not adequately perform for all operational conditions because of the non-linear relationship between the arc voltage, current and arc length. This paper examin...

We revisit a problem solved in 1963 by Zaanen & Luxemburg in this monthly: what is the largest possible length of the graph of a monotonic function on an interval? And is there such a function that attains this length? This is an interesting and intriguing problem with a somewhat surprising answer, that should be of interest to a broad spectrum of mathematicians starting with upper level underg...

Available online 19 November 2008

Received November 15, 2016. Abstract. There are several examples of enumerative equivalences in the study of lattice walks where a trade-off appears between a stronger domain constraint and a stronger endpoint constraint. We present a strategy, based on arc diagrams, that gives a bijective explanation of this phenomenon for two kinds of 2D walks (simple walks and hesitating walks). For both ste...