Weak coalgebra-Galois extensions are studied. A notion of an invertible weak entwining structure is introduced. It is proven that, within an invertible weak entwining structure, the surjectivity of the canonical map implies bijectivity provided the structure coalgebra C is either coseparable or projective as a C-comodule.

Abstract. One of the major results of [N. Robertson and P. D. Seymour. Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B, 63(1):65–110, 1995], also known as the weak structure theorem, reveals the local structure of graphs excluding some graph as a minor: each such graph G either has small treewidth or contains the subdivision of a planar graph (a wall) that can be arrang...

Let $(X,d)$ be a compactmetric space and let $K$ be a nonempty compact subset of $X$. Let $alpha in (0, 1]$ and let ${rm Lip}(X,K,d^ alpha)$ denote the Banach algebra of all  continuous complex-valued functions $f$ on$X$ for which$$p_{(K,d^alpha)}(f)=sup{frac{|f(x)-f(y)|}{d^alpha(x,y)} : x,yin K , xneq y}

One of the key elements to understanding the structure of the nucleon is the role of its quark-antiquark sea in its ground state properties such as charge, mass, magnetism and spin. In the last decade, parity-violating electron scattering has emerged as an important tool in this area, because of its ability to isolate the contribution of strange quark-antiquark pairs to the nucleon's charge and...

There is an ongoing debate in the literature as to whether the effects of averaging out inhomogeneities (“backreaction”) in Cosmology can be large enough to account for the acceleration of the scale factor in the FLRW models. In particular, some simple models of structure formation studied in the literature seem to indicate that this is indeed possible, and it has also been suggested that the p...

This paper demonstrates the e ectiveness of the weak information structure for human information sharing. The weak information structure is an information representation which connects various information media without de ning the semantics rigorously. By leaving the interpretation of the semantics to tacit human background knowledge, it becomes compact and robust. To investigate how e ective t...

We model weak gravitational lensing of light by large-scale structure using ray tracing through N-body simulations. The method is described with particular attention paid to numerical convergence. We investigate some of the key approximations in the multi-plane ray tracing algorithm. Our simulated shear and convergence maps are used to explore how well standard assumptions about weak lensing ho...

BACKGROUND The objective of this work was to investigate the hypothesis that eukaryotic Internal Ribosome Entry Sites (IRES) lack secondary structure and to examine the generality of the hypothesis. METHODOLOGY/PRINCIPAL FINDINGS IRESs of the yeast and the fruit fly are located in the 5'UTR immediately upstream of the initiation codon. The minimum folding energy (MFE) of 60 nt RNA segments im...