Duality for Finite Hopf Algebras Explained by Corings

We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra. We also provide a coring analogue for a theorem of H.-J. Schneider, which generalizes and unifies the duality theorem for finite Hopf algebras and its refinements. This paper was written while the first author visited the Mathematics Departments of Syracuse University and California State University Dominguez Hills. He would like to thank both departments for their hospitality.     

Visualisation of interlaboratory comparison results in PomPlots

In this work a novel graphical method is applied to the presentation of intercomparison results. This is demonstrated with the results of a recent intercomparison in measuring the ¹³⁷Cs, ⁴⁰K, and ⁹⁰Sr activity concentration in milk powder. The “PomPlot”, an intuitive graphical method, is used for producing a summary overview of the participants’ results of a common measurand. The “PomPlot” displays (relative) deviations of individual results from the reference value on the horizontal axis and (relative) uncertainties on the vertical axis.     

Complexation of gadolinium(III) ions on top of nanometre-sized magnetoliposomes

The complex of diethylenetriaminepentaacetate (DTPA) with the paramagnetic gadolinium ion [Gd(III)] is a well-known blood pool contrast agent for magnetic resonance imaging (MRI). To obtain MRI pictures from other anatomical structures, for instance from tissues containing cells with phagocytic activity, larger colloidal complexes have to be constructed. Therefore, in view of modifying the physiological behaviour, the DTPA chelate was first hydrophobized by covalently linking it to phosphatidylethanolamine (PE), and the resulting conjugate was then incorporated into nanometre-sized, sonicated phospholipid vesicles. Qualitative information on the affinity of the PE–DTPA derivative for Gd(III) ions was derived from competition experiments using the dye Arsenazo. Furthermore, it was found that only the membranotropic adducts residing in the outer shell of the vesicle bilayer are accessible to the lanthanide ion. The vesicular particulate was also used as a vehicle to transport PE–DTPA into the coating of so-called magnetoliposomes which consist of nanometre-sized iron oxide cores onto which a phospholipid bilayer is strongly chemisorbed. After loading the resulting structures with Gd(III), this new type of magnetoliposome may offer unique potentialities as a novel bi-label MRI contrast medium.     

Anion recognition by alpha-arylazo-N-confused calix[4]pyrroles

The first example of substitution reaction in the free alpha-position of N-confused calix[4]pyrroles is reported: azo-coupling with various arenediazonium salts. The obtained azocompounds were used for studies of their anion-binding properties by UV-Vis spectroscopy.     

An Interference Approach to Perturbed Angular Correlation Spectroscopy

This paper recalls the formalism of H. J. Leisi, which shows an alternative way to understand Perturbed Angular Correlation Spectroscopy: as a quantum interference effect. This revised version was published online in July 2006 with corrections to the Cover Date.     

Monoidal Ring and Coring Structures Obtained from Wreaths and Cowreaths

Let A be an algebra in a monoidal category \({\cal C}\) , and let X be an object in \({\cal C}\) . We study A-(co)ring structures on the left A-module A???X. These correspond to (co)algebra structures in \(EM({\cal C})(A)\) , the Eilenberg-Moore category associated to \({\cal C}\) and A. The ring structures are in bijective correspondence to wreaths in \({\cal C}\) , and their category of representations is the category of representations over the induced wreath product. The coring structures are in bijective correspondence to cowreaths in \({\cal C}\) , and their category of corepresentations is the category of generalized entwined modules. We present several examples coming from (co)actions of Hopf algebras and their generalizations. Various notions of smash products that have appeared in the literature appear as special cases of our construction.     

Galois theory for comatrix corings: Descent theory, Morita theory, Frobenius and separability properties

El Kaoutit and Gómez-Torrecillas introduced comatrix corings, generalizing Sweedler's canonical coring, and proved a new version of the Faithfully Flat Descent Theorem. They also introduced Galois corings as corings isomorphic to a comatrix coring. In this paper, we further investigate this theory. We prove a new version of the Joyal-Tierney Descent Theorem, and generalize the Galois Coring Structure Theorem. We associate a Morita context to a coring with a fixed comodule, and relate it to Galois-type properties of the coring. An affineness criterion is proved in the situation where the coring is coseparable. Further properties of the Morita context are studied in the situation where the coring is (co)Frobenius.

     

Classification of partial difference sets in Abelian groups of order $$4p^2$$

In this article we provide a complete classification of regular partial difference sets in Abelian groups of order \(4p^2\), p an odd prime. It turns out that the known examples are the only examples. These are, up to complements, the trivial examples, the PCP examples, and a sporadic example in \(\mathbb {Z}_2^2\times \mathbb {Z}_3^2\).