in this paper $s$ is a monoid with a left zero and $a_s$ (or $a$) is a unitary right $s$-act. it is shown that a monoid $s$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $s$-act is quasi-projective. also it is shown that if every right $s$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...

In this paper $S$ is a monoid with a left zero and $A_S$ (or $A$) is a unitary right $S$-act. It is shown that a monoid $S$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $S$-act is quasi-projective. Also it is shown that if every right $S$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...

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...

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 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

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.

Can folding a piece of paper flat make it larger? We explore whether a shape S must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries S → R2). The underlying problem is motivated by computational origami, and is related to other covering and fixturing problems, such as Lebesgue’s universal cover problem and force ...

In terms of the duality property of injective preenvelopes and flat precovers, we get an equivalent characterization of left Noetherian rings. For a left and right Noetherian ring R, we prove that the flat dimension of the injective envelope of any (Gorenstein) flat left R-module is at most the flat dimension of the injective envelope of RR. Then we get that the injective envelope of RR is (Gor...

This paper addresses a novel steganography method for images. Most statistical steganalysis algorithms are strong to defeat previous steganography algorithms. RS steganalysis and pixel difference histogram analysis are two well-known statistical steganalysis algorithms which detect non-random changes caused by embedding a secret message into cover image. In this paper, we first explain how two ...