The Debye series is developed for electromagnetic scattering by a spheroid in order to decompose the far-zone fields into various physical processes. The geometrical rainbow angle and supernumerary spacing parameter are determined from the Debye intensity by fitting the results to an Airy function and comparing them to their assumed values in ray optics and Airy theory, respectively. Eccentrici...

A k-dominating set is a set D k V such that every vertex i 2 V nD k has at least k i neighbours in D k. The k-domination number k (G) of G is the cardinality of a smallest k-dominating set of G. For k 1 = ::: = k n = 1, k-domination corresponds to the usual concept of domination. Our approach yields an improvement of an upper bound for the domination number found then the conception of k-domina...

The regularity of an edge ideal of a finite simple graph G is at least the induced matching number of G and is at most the minimum matching number of G. If G possesses a dominating induced matching, i.e., an induced matching which forms a maximal matching, then the induced matching number of G is equal to the minimum matching number of G. In the present paper, from viewpoints of both combinator...

Inspired by the Hardy–Littlewood maximal function, we propose a novel pooling strategy which is called maxfun pooling. It presented both as viable alternative to some of most popular functions, such max and average pooling, way interpolating between these two algorithms. We demonstrate features with applications: first in context convolutional sparse coding, then for image classification.

A rainbow colouring of a connected graph G is a colouring of the edges of G such that every pair of vertices in G is connected by at least one path in which no two edges are coloured the same. The minimum number of colours required to rainbow colour G is called its rainbow connection number. Chakraborty, Fischer, Matsliah and Yuster have shown that it is NP-hard to compute the rainbow connectio...

The Rainbow k-Coloring problem asks whether the edges of a given graph can be colored in k colors so that every pair of vertices is connected by a rainbow path, i.e., a path with all edges of different colors. Our main result states that for any k ≥ 2, there is no algorithm for Rainbow k-Coloring running in time 2 3/2), unless ETH fails. Motivated by this negative result we consider two paramet...

A rainbow subgraph of an edge-colored graph is a subgraph whose edges have distinct colors. The color degree of a vertex v is the number of different colors on edges incident to v. Wang and Li conjectured that for k > 4, every edge-colored graph with minimum color degree at least k contains a rainbow matching of size at least ⌈k/2⌉. We prove the slightly weaker statement that a rainbow matching...