Exchange Leavitt path algebras and stable rank

We characterize those Leavitt path algebras which are exchange rings in terms of intrinsic properties of the graph and show that the values of the stable rank for these algebras are 1, 2 or ∞. Concrete criteria in terms of properties of the underlying graph are given for each case

Nonstable K-Theory for graph algebras

We compute the monoid V (LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals of V (LK(E)). When K is the field C of complex numbers, the algebra LC(E) is a dense subalgebra of the graph C -algebra C (E), and we show that the inclusion map induces an isomorphism between the corresponding monoids. As a consequence, the graph C*-algebra of any row-finite graph turns out to satisfy the stable weak cancellation propert

Quantum-well induced giant spin-orbit splitting

We report on the observation of a giant spin-orbit splitting of quantum-well states in the unoccupied electronic structure of a Bi monolayer on Cu(111). Up to now, Rashba-type splittings of this size have been reported exclusively for surface states in a partial band gap. With these quantum-well states we have experimentally identified a second class of states that show a huge spin-orbit splitting. First-principles electronic structure calculations show that the origin of the spin-orbit splitting is due to the perpendicular potential at the surface and interface of the ultrathin Bi film. This finding allows for the direct possibility to tailor spin-orbit splitting by means of thin-film nanofabrication

A fast and direct liquid chromatography-mass spectrometry method to detect and quantify polyunsaturated aldehydes and polar oxylipins in diatoms

Polyunsaturated aldehydes (PUAs) are a group of microalgal metabolites that have attracted a lot of attention due to their biological activity. Determination of PUAs has become an important routine procedure in plankton and biofilm investigations, especially those that deal with chemically mediated interactions. Here we introduce a fast and direct derivatization free method that allows quantifying PUAs in the nanomolar range, sufficient to undertake the analysis from cultures and field samples. The sample preparation requires one simple filtration step and the initiation of PUA formation by cell disruption. After centrifugation the samples are ready for measurement without any further handling. Within one chromatographic run this method additionally allows us to monitor the formation of the polar oxylipins arising from the cleavage of precursor fatty acids. The robust method is based on analyte separation and detection using ultra high performance liquid chromatography-atmospheric pressure chemical ionization mass spectrometry (UHPLC-APCI MS) and enables high throughput investigations by employing an analysis time of only 5 min. Our protocol thus provides an alternative and extension to existing PUA determinations based on gas chromatographymass spectrometry (GC-MS) with shorter run times and without any chemical derivatization. It also enables researchers with widely available LC-MS analytical platforms to monitor PUAs. Additionally, non-volatile oxylipins such as x-oxo-acids and related compounds can be elucidated and monitored