A split complete weight enumerator in six variables is used to study the 3-colored designs held by codewords of xed composition in Type III codes containing the all-one codeword. In particular the ternary Golay code contains 3-colored 3-designs. We conjecture that every weight class in a Type III code with the all-one codeword holds 3-colored 3-designs.

The monochromatic tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum integer k such that whenever the edges of G are colored with r colors, the vertices of G can be covered by at most k vertex-disjoint monochromatic trees. In general, to determine this number is very difficult. For 2-edge-colored complete multipartite graph, Kaneko, Kano, and Suzuki gave the ex...

Earlier studies have demonstrated that among the eight differently colored ground traps tested in the greenhouse, black colored traps were the most effective compared with the performances of brown, yellow, red, grey, blue, white, and green traps. In the present study, efficiency of ground traps with different shades of black (black thick, pure black, mix black and black medium) were evaluated ...

Let G(V,E) be a k-uniform hypergraph. A hyperedge e ∈ E is said to be properly (r, p) colored by an r-coloring of vertices in V if e contains vertices of at least p distinct colors in the rcoloring. An r-coloring of vertices in V is called a strong (r, p) coloring if every hyperedge e∈E is properly (r, p) colored by the r-coloring. We study the maximum number of hyperedges that can be properly ...

The article studies the interrelation of Languages of Colored Petri Nets and Traditional formal languages. The author constructed the graph of Colored Petri Net, which generates L Context-free language. This language may not be modeled using standard Petri Nets [1]. The Venn graph and diagram that the author modified [1], show the interrelation between languages of Colored Petri Nets and some T...

Given an integer 1 ≤ j < n, define the (j)-coloring of a n-dimensional hypercube Hn to be the 2-coloring of the edges of Hn in which all edges in dimension i, 1 ≤ i ≤ j, have color 1 and all other edges have color 2. Cheng et al. [Proper distance in edge-colored hypercubes, Applied Mathematics and Computation 313 (2017) 384-391.] determined the number of distinct shortest properly colored paths...

A graph is k-linked (k-edge-linked), k ≥ 1, if for each k pairs of vertices x1, y1, · · · , xk, yk, there exist k pairwise vertex-disjoint (respectively edge-disjoint) paths, one per pair xi and yi, i = 1, 2, · · · , k. Here we deal with the properly-edge-colored version of the k-linked (kedge-linked) problem in edge-colored graphs. In particular, we give conditions on colored degrees and/or nu...

A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum positive integer p such that whenever the edges of the graph G are colored with r colors, the vertices of G can be covered by at most p vertex-disjoint heterochromatic trees. In this paper we determi...

The colored Jones polynomial of links has two natural normalizations: one in which the n-colored unknot evaluates to [n + 1], the quantum dimension of the (n + 1)-dimensional irreducible representation of quantum sl(2), and the other in which it evaluates to 1. For each normalization we construct a bigraded cohomology theory of links with the colored Jones polynomial as the Euler characteristic.

This paper presents a novel strategy for the vector control of IPMSM, without signal injection. The overall performance of the motion-sensorless control depends strongly on the accuracy of the rotor position and speed estimation. The proposed state observer is based on the concept of the “active flux” (or “torque producing flux”), which “turns all the salient–pole rotor ac machines into nonsali...