Flat objects of a finitely accessible additive category C are described in terms of some objects of the associated functor category of C, called strongly flat functors. We study closure properties of the class of strongly flat functors, and we use them to deduce the known result that every object of a finitely accessible abelian category has a flat cover.

Tropical reefs are dynamic ecosystems that host diverse coral assemblages with different life-history strategies. Here, we quantified how juvenile (<50 mm) coral demographics influenced benthic coral structure in reef flat and reef slope habitats on the southern Great Barrier Reef, Australia. Permanent plots and settlement tiles were monitored every six months for three years in each habitat. T...

We introduce the notion of the strong (r, p) cover number χc(G,k,r, p) for k-uniform hypergraphs G(V,E), where χc(G,k,r, p) denotes the minimum number of r-colorings of vertices in V such that each hyperedge in E contains at least min(p,k) vertices of distinct colors in at least one of the χc(G,k,r, p) r-colorings. We derive the exact values of χc(Kk n ,k,r, p) for small values of n, k, r and p...

A folding of a simple polygon into a convex polyhedron is accomplished by glueing portions of the perimeter of the polygon together to form a polyhedron. A polygon Q is a flat n-folding of a polygon P if P can be folded to exactly cover the surface of Q n times, with no part of the surface of P left over. In this paper we focus on a specific type of flat 2-foldings, flat 2-foldings that wrap Q;...

We show that there exists a Martin-Löf random degree which has a strong minimal cover.

We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes. AMS Classification 20F67; 20F06

The reload cost refers to the cost that occurs along a path on an edge-colored graph when it traverses an internal vertex between two edges of different colors. Galbiati et al. [1] introduced the Minimum Reload Cost Cycle Cover problem, which is to find a set of vertex-disjoint cycles spanning all vertices with minimum reload cost. They proved that this problem is strongly NP-hard and not appro...

let s be a monoid and x a class of s-acts which is closed under coproducts. the object of this article is to find conditions under which all s-acts have x-precovering. we have shown that the existence of torsion-free precovering implies the existence of torsion-free covering. this work is an attempt to further facilitate the study of the conjecture that all s-acts have flat cover.

Given a finite set of straight line segments S in R and some k ∈ N, is there a subset V of points on segments in S with |V | ≤ k such that each segment of S contains at least one point in V ? This is a special case of the set covering problem where the family of subsets given can be taken as a set of intersections of the straight line segments in S. Requiring that the given subsets can be inter...