Coalgebraic representations of distributive lattices with operators

We present a framework for extending Stone's representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive lattices with operators in the original theory. We characterize the topological counterpart of these algebras in terms of suitable coalgebras on spectral spaces. We work out some of these coalgebraic representations, including a new representation theorem for distributive lattices with monotone operators.     

Formation of Zn(1-x)MnxS nanowires within mesoporous silica of different pore sizes

Arrays of highly ordered Zn(1-x)MnxS quantum wires with x ranging from 0.01 to 0.3 and with lateral dimensions of 3, 6, and 9 nm were synthesized within mesoporous SiO2 host structures of the MCM-41 and SBA-15 type. The hexagonal symmetry of these arrays (space group p6m) and the high degree of order was confirmed by X-ray diffraction and transmission electron microscopy (TEM) studies. Physisorption measurements show the progressive filling of the pores of the SiO2 host structures, while TEM and Raman studies reveal the wire-like character of the incorporated Zn(1-x)MnxS nanostructures. X-ray absorption near-edge structure, extended X-ray absorption fine structure, photoluminescence excitation (PLE), and electron paramagnetic resonance studies confirm the good crystalline quality of the incorporated Zn(1-x)MnxS guest species and, in particular, that the Mn2+ ions are randomly distributed and are situated on tetrahedrally coordinated cation sites of the Zn(1-x)MnxS wires for all x up to 0.3. The amount of Mn2+ ions loosely bound to the surface of the Zn(1-x)MnxS nanowires is less than 4% of the total Mn content even for the 3 nm nanostructures up to the highest Mn content of x = 0.3. The effects of the reduction of the lateral dimensions on electronic properties of the diluted magnetic semiconductor were studied by PLE spectroscopy. Due to the quantum confinement of the excitons in the wires an increase of the direct band gap with decreasing particle size is observed.     

Asymmetric Synthesis of 3-Hydroxyprolines by Photocyclization of N-(2-Benzoylethyl)glycinamides

The chiral N-(2-benzoylethyl)-N-tosylglycinamides 1a-c were prepared from the C₂-symmetric pyrrolidines 5a-c . Irradiation of these ketones 1a-c gave cis-3-hydroxyprolinamides 10-12 in moderate to good yields (Scheme 3). The de of the photocyclizations depended on the size of the substituents in positions C(2) and C(5) of the chiral pyrrolidine auxiliaries. In addition, the de varied with the reaction temperature, allowing the determination of activation-parameter differences. The structure of products 10-12 were established by NMR and X-ray analyses.     

An FTIR study of the surface chemistry of the dynamic Si(100) surface during etching in alkaline solution

In situ FTIR spectroscopy has been used in the attenuated total reflectance (ATR) mode to investigate the surface chemistry of etching Si(100) surfaces in aqueous KOH. The effect of solution concentration and electrode potential on the Si-H vibrations has been explored and the experimental results compared with density functional theory calculations. In addition. the kinetics of surface passivation of n-Si(100) has been investigated using FTIR spectroscopy.