In this paper, we generalize the so-called Korchmáros—Mazzocca arcs, that is, point sets of size q + t intersecting each line in 0, 2 or points a finite projective plane order q. For ≠ 2, means set is incident with exactly one meeting points. PG(2, pn), change definition above to any integer m and describe all examples when not divisible by p. We also study mod p variants these objects, give un...

This article presents the basic place/transition net structure definition for building various types of Petri nets. The basic net structure fields include places, transitions, and arcs (place-transition, transition-place) which may be supplemented with other fields (e.g., capacity, weight, marking, etc.) as needed. The theorems included in this article are divided into the following categories:...

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...

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...