We prove a generalization of the Flat Cover Conjecture by showing for any ring R that (1) each (right R-) module has a Ker Ext(−, C)-cover, for any class of pure-injective modules C, and that (2) each module has a Ker Tor(−,B)-cover, for any class of left R-modules B. For Dedekind domains, we describe Ker Ext(−, C) explicitly for any class of cotorsion modules C; in particular, we prove that (1...

Let C be a given circuit of a bridgeless cubic graph G. It was conjectured by Seymour that G has a circuit double cover (CDC) containing the given circuit C. This conjecture (strong CDC [SCDC] conjecture) has been verified by Fleischner and Häggkvist for various families of graphs and circuits. In this article, some of these earlier results have been improved: Contract grant sponsor: NSF-China;...

A reversible data hiding scheme based on double image encryptions and spatial correlation comparisons is proposed, which improves the performance of two previous methods when dealing with flat cover images. A grayscale cover image is first encrypted. The four LSBs of each block pixel in the resulting encrypted image are encrypted once more to embed a message bit, thereby solving the problem of ...

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of weight $D_s$, does not draw from curvature band but has a purely band-geometric origin. mean-field description, non-zero Chern number or fragile topology sets lower bound for which, via Berezinskii-Kosterlitz-Thouless mechanism, might explain relatively high superconducting trans...

Introduction Outcomes attributable to the research funded through the 2005 NCPPT grant can be summarized as follows: 1) Protocols for the detection of archaeological sites through the analysis of commercially available synthetic aperture radar (SAR) and multispectral images. Previously existing protocols for site detection through image analysis had utilized images generated from synthetic aper...

We prove that among finite graph algebras and among finite flat graph algebras, dualizability, full dualizability, strong dualizability and entropicity are all equivalent. Any finite (flat) graph algebra which is not dualizable must be inherently non-κ-dualizable for every infinite cardinal κ. A new, general method for proving strong duality is presented.

Convex polygons, shapes bounded by straight lines in which all of the corners point outward, are simplest shapes, but despite their simplicity, there many unsolved problems concerning polygons. Some polygons have nice property that they fit together espcially well, so you can use lots copies them to cover a large surface form what is called tiling. For some such as triangles, it easy see how ti...

As wildland fire frequency increases around the globe, a better understanding of the patterns of plant community recovery in burned landscapes is needed to improve rehabilitation efforts. We measured establishment of seeded species, colonization of Bromus tectorum and other nonnative annual plants, and recovery of nonseeded native species in topographically distinct areas within five fires that...

Recently two different concepts of covers of acts over monoids have been studied by a number of authors and many interesting results discovered. One of these concepts is based on coessential epimorphisms and the other is based on Enochs’ definition of a flat cover of a module over a ring. Two recent papers have suggested that in the former case, strongly flat covers are not unique. We show that...