By a generalized arc we mean a continuum with exactly two non-separating points; an arc is a metrizable generalized arc. It is well known that any two arcs are homeomorphic (to the real closed unit interval); we show that any two generalized arcs are co-elementarily equivalent, and that co-elementary images of generalized arcs are generalized arcs. We also show that if f : X → Y is a function b...

First we discuss the description of inverse polynomial images of [−1, 1], which consists of two Jordan arcs, by the endpoints of the arcs only. The polynomial which generates the two Jordan arcs is given explicitly in terms of Jacobi’s theta functions. Then the main emphasis is put on the case where the two arcs are symmetric with respect to the real line. For instance it is demonstrated that t...

We introduce an algorithm for computing Voronoi diagrams of points, straight-line segments and circular arcs in the two-dimensional Euclidean plane. Based on a randomized incremental insertion, we achieve a Voronoi algorithm that runs in expected time O(n log n) for a total of n points, segments and arcs, if at most a constant number of segments and arcs is incident upon every point. Our theore...

Given a k-arc-strong tournament T , we estimate the minimum number of arcs possible in a k-arc-strong spanning subdigraph of T . We give a construction which shows that for each k ≥ 2 there are tournaments T on n vertices such that every k-arc-strong spanning subdigraph of T contains at least nk+ k(k−1) 2 arcs. In fact, the tournaments in our construction have the property that every spanning s...

Quiet time arcs observed from the Greenland all-sky camera network have been ordered in corrected geomagnetic latitude/time mass plots according to the values of the Y and Z components of the IMF. Two different patterns of discrete quiet arcs occur. In one system the arcs are ordered along the statistical auroral oval; in the other, which we have called the polar cap pattern of discrete arcs, t...

We obtained a full computer classification of all complete arcs in the Desarguesian projective plane of order 31 using essentially the same methods as for earlier results for planes of smaller order, i.e., isomorph-free backtracking using canonical augmentation. We tabulate the resulting numbers of complete arcs according to size and automorphism group. We give explicit descriptions for all com...

Three-dimensional Weyl semimetals have pairs of topologically protected nodes, whose projections onto the surface Brillouin zone are end points zero energy states called Fermi arcs. At endpoints arcs, extend into and hybridized with bulk. Here, we consider a two-dimensional junction two identical surfaces twisted respect to each other tunnel-coupled. Confining ourselves commensurate angles (suc...

A proper circular-arc (PCA) model is a pairM = (C,A) where C is a circle and A is a family of inclusion-free arcs on C in which no two arcs of A cover C. A PCA model U is a (c, `, d, ds)-CA model when C has circumference c, all the arcs in A have length `, all the extremes of the arcs in A are at a distance at least d, and all the beginning points of the arcs in A are at a distance at least d+ ...

A full classification (up to equivalence) of all complete k-arcs in the Desarguesian projective planes of order 27 and 29 was obtained by computer. The resulting numbers of complete arcs are tabulated according to size of the arc and type of the automorphism group, and also according to the type of algebraic curve into which they can be embedded. For the arcs with the larger automorphism groups...

This article examines the ways in which Fflur Dafydd’s 2008 novel Twenty Thousand Saints negotiates notions of the island space in a post-devolution Welsh context. It argues that the novel is a rich site in the analysis of the literary dimension of what Baldacchino describes as the “island-mainland [...] dialectic” (Baldacchino, 2006, p. 10). Set on Bardsey, a real small island off the coast of...