Selenides and diselenides containing oxadiazoles: a new class of functionalised materials

A simple and efficient procedure for the synthesis of a new class of organoselenium liquid crystal compounds was developed. The coupling of aryl bromides with elemental selenium was catalysed using copper oxide nanopowder in the presence of potassium hydroxide employing dimethyl sulfoxide as the solvent. This is the first report of the synthesis and characterisation of liquid crystal-based diselenides. Their mesophases were characterised by polarising optical microscopy and differential scanning calorimetry. Compounds 1, 2 and 4b exhibited the smectic A phase. In addition, these compounds showed weak blue fluorescence in solution (λ_{max. em.} 350–405 nm) and a Stokes shift of around 90 nm.     

Chain Dominated Orders

We study finite partial orders which have a chain such that every element of the order either belongs to this chain or has all its covers in this chain. We show that such orders are exactly the orders being both interval orders and truncated lattices. We prove that their jump number is polynomially tractable and that their dimension is unbounded. We also show that every order admits a visibility model having such an order as host.     

Computing on-line the lattice of maximal antichains of posets

We consider the on-line computation of the lattice of maximal antichains of a finite poset . This on-line computation satisfies what we call the linear extension hypothesis: the new incoming vertex is always maximal in the current subposet of . In addition to its theoretical interest, this abstraction of the lattice of antichains of a poset has structural properties which give it interesting practical behavior. In particular, the lattice of maximal antichains may be useful for testing distributed computations, for which purpose the lattice of antichains is already widely used. Our on-line algorithm has a run time complexity of , where |P| is the number of elements of the poset, , |MA(P)| is the number of maximal antichains of and (P) is the width of . This is more efficient than the best off-line algorithms known so far.     

Towards the reconstruction of posets

The reconstruction conjecture for posets is the following: Every finite posetP of more than three elements is uniquely determined — up to isomorphism — by its collection of (unlabelled) one-element-deleted subposets P–{x}:xV(P).We show that disconnected posets, posets with a least (respectively, greatest) element, series decomposable posets, series-parallel posets and interval orders are reconstructible and that N-free orders are recognizable.We show that the following parameters are reconstructible: the number of minimal (respectively, maximal) elements, the level-structure, the ideal-size sequence of the maximal elements, the ideal-size (respectively, filter-size) sequence of any fixed level of the HASSE-diagram and the number of edges of the HASSE-diagram.This is considered to be a first step towards a proof of the reconstruction conjecture for posets.Research partly supported by DAAD.     

Fe(III)-Catalyzed direct C3 chalcogenylation of indole: The effect of iodide ions

A mild and efficient iron (III)-catalyzed C3 chalcogenylation of indoles has been developed and the role of the iodide ions in this transformation was investigated. EPR experiments revealed the reduction of Fe(III) to Fe(II) under the reaction conditions, supporting the formation of molecular iodine in the system, which in effect catalyze the reaction. The scope of the chalcogenylation was broad and the synthesis of more functionalized 3-selenylindoles was explored.     

Combined Experimental and Simulation Studies Suggest a Revised Mode of Action of the Anti‐Alzheimer Disease Drug NQ‐Trp

Inhibition of the aggregation of the monomeric peptide β‐amyloid (Aβ) into oligomers is a widely studied therapeutic approach in Alzheimer’s disease (AD). Many small molecules have been reported to work in this way, including 1,4‐naphthoquinon‐2‐yl‐L ‐tryptophan (NQ‐Trp). NQ‐Trp has been reported to inhibit aggregation, to rescue cells from Aβ toxicity, and showed complete phenotypic recovery in an in vivo AD model. In this work we investigated its molecular mechanism by using a combined approach of experimental and theoretical studies, and obtained converging results. NQ‐Trp is a relatively weak inhibitor and the fluorescence data obtained by employing the fluorophore widely used to monitor aggregation into fibrils can be misinterpreted due to the inner filter effect. Simulations and NMR experiments showed that NQ‐Trp has no specific “binding site“‐type interaction with mono‐ and dimeric Aβ, which could explain its low inhibitory efficiency. This suggests that the reported anti‐AD activity of NQ‐Trp‐type molecules in in vivo models has to involve another mechanism. This study has revealed the potential pitfalls in the development of aggregation inhibitors for amyloidogenic peptides, which are of general interest for all the molecules studied in the context of inhibiting the formation of toxic aggregates.     

Partial Orders on Weak Orders Convex Subsets

We study a visibility relation on the nonempty connected convex subsets of a finite partially ordered set and we investigate the partial orders representable as a visibility relation of such subsets of a weak order. Moreover, we consider restrictions where the subsets of the weak order are total orders or isomorphic total orders.     

Line directionality of orders

Some orders can be represented by translating convex figures in the plane. It is proved thatN-free and interval orders admit such representations with an unbounded number of directions. Weak orders, tree-like orders and two-dimensional orders of height one are shown to be two- directional. In all cases line segments can be used as convex sets.     

ContributionsTree-visibility orders

We introduce a new class of partially ordered sets, called tree-visibility orders, containing interval orders, duals of generalized interval orders and height one orders. We give a characterization of tree-visibility orders by an infinite family of minimal forbidden suborders. Furthermore, we present an efficient recognition algorithm for tree-visibility orders.     

Inductive Characterizations of Finite Interval Orders and Semiorders

We introduce an inductive definition for two classes of orders. By simple proofs, we show that one corresponds to the interval orders class and that the other is exactly the semiorders class.