Properties of (most general) non-commutative torsors or A-B torsors are analysed. Starting with pre-torsors it is shown that they are equivalent to a certain class of Galois extensions of algebras by corings. It is then concluded that every faithfully flat unital pre-torsor admits a (left and right) flat (bimodule) connection. It is shown that a class of faithfully flat pre-torsors induces equi...

We introduce an NP-complete special case of the Weighted Set Cover problem and show its fixed-parameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given collection C of subsets of a some base set S should be “tree-like.” That is, the subsets in C can...

Changes to the dynamics of the Greenland ice sheet can be forced by various mechanisms including surface-melt-induced ice acceleration and oceanic forcing of marine-terminating glaciers. We use observations of ice motion to examine the surface melt-induced dynamic response of a land-terminating outlet glacier in southwest Greenland to the exceptional melting observed in 2012. During summer, mel...

This study examines experimentally, in situ, the influence of four scales of heterogeneity (0, 1, 10, 100 mm) and the hierarchical combination of those scales of heterogeneity (0 + 1 + 10, 0 + 1 + 100, 0 + 10 + 100, 0 + 1 + 10 + 100 mm) on the early establishment of a sessile marine littoral epibenthic community. The study was carried out in St. Andrews, New Brunswick (Canada) from July to Octo...

We describe a 3/2-approximation algorithm, LSE, for computing a b-Edge Cover of minimum weight in a graph with weights on the edges. The b-Edge Cover problem is a generalization of the better-known Edge Cover problem in graphs, where the objective is to choose a subset C of edges in the graph such that at least a specified number b(v) of edges in C are incident on each vertex v. In the weighted...

We exhibit a surprising connection between the following two concepts: Brown representability which arises in stable homotopy theory, and flat covers which arise in module theory. It is shown that Brown representability holds for a compactly generated triangulated category if and only if for every additive functor from the category of compact objects into the category of abelian groups a flat c...

The notion of a $\mathcal C$-filtered object, where C$ is some (typically small) collection objects in Grothendieck category, has become ubiquitous since the solution Flat Cover Conjecture around year 2000. We introduce

Literature about entropy generation analysis of a wavy enclosure is scare. In this paper. a FORTRAN cod using an explicit finite-volume method was provided for estimating the entropy production due to the natural convection heat transfer in a cosine wavy absorber solar collector. The volumetric entropy generation terms both the heat transfer term and the friction term were straightly calculated...

The flat plate solar collector (FPSC) is a well-known energy harvesting tool that minimizes the strain on traditional production approach while also promoting future use of renewable energy. Thus, Increasing performance this worth effort. As world's consumption continues to grow, there has been an increased focus potential for nanotechnology improvements reduce usage. Recent scientific research...

The cover image is based on the Research Article Catecholaminergic axon innervation and morphology in flat-mounts of atria ventricles mice by Ariege Bizanti et al., https://doi.org/10.1002/cne.25444. Image Credit: Zixi Cheng.