Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle

We investigate heteroclinic orbits between equilibria and rotating waves for scalar semilinear parabolic reaction-advection-diffusion equations with periodic boundary conditions. Using zero number properties of the solutions and the phase shift equivariance of the equation, we establish a necessary and sufficient condition for the existence of a heteroclinic connection between any pair of hyperbolic equilibria or rotating waves.     

Biphotonic recording effect of polarization gratings based on dye-doped liquid crystal films

This study investigates a holographic recording effect of biphotonic polarization gratings (BPGs) written on dye-doped liquid crystal (DDLC) films. One linearly polarized green light (λ_G = 514.5 nm) and a polarization-modulated interference pattern formed by two mutually coherent orthogonal (±45° with respect to the polarization of the green light) polarized red lights simultaneously excite the DDLC films to generate a BPG. The formation of BPGs depends primarily on the dichroism of the dye molecules and a sequence of mechanisms: photoisomerization, anisotropic adsorption and inhibition of dye adsorption. The cis-isomer absorbance-modulated distribution associated with the red polarization-modulation pattern induces the dye adsorption-modulated pattern, in turn, yielding the permanent BPG which generates a modulated twisted nematic (TN) structure pattern in the sample. It is found that each BPG is verified to be electrically switchable and thermally erasable. The switching time is in the order of milliseconds. Additionally, the recording time to form a BPG decreases with increasing intensity of the green pump beam.     

Quasiparticle bandstructures of covalent semiconductors and their surfaces

The exchange-correlation self-energies and quasiparticle shifts are calculated for band states of covalent materials (diamond, silicon) and their (001) 2×1 surface in order to solve the bulk and surface band-gap problem of the LDA. The screening properties are described by a model dielectric function taking into account the spatial nonlocality in the surface case assuming specular electron reflection. The wave functions are expanded in terms of localized orbitals. The quasiparticle bandstructures obtained are in reasonable agreement with experimental results.     

Das asymptotische Verhalten der Peanokerne einiger interpolatorischer Quadraturverfahren

Summary Interpolatory quadrature formulae consist in replacing by wherep _f denotes the interpolating polynomial off with respect to a certain knot setX. The remainder may in many cases be written as wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP _X (t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis.

     

Solid-phase synthesis of imidazo[4,5-b]pyridin-2-ones and related urea derivatives by cyclative cleavage of a carbamate linkage

A solid-phase synthesis of substituted cyclic urea derivatives as potential heterocyclic library scaffolds is described. 2-Amino-3-nitropyridine is attached to Wang resin via a carbamate linkage. Reduction of the nitro group was achieved with SnCl(2).2H(2)O. Reductive alkylation with a range of substituted benzaldehydes followed by cyclative cleavage afforded a small library of 3-substituted imidazo[4,5-b]pyridine-2-ones in 33-45% yield and 59-88% purity. Subsequently, this methodology was applied to the synthesis of 3-substituted imidazo[4,5-f]quinolin-2-ones.     

Synthesis, structure determination, and spectroscopic/computational characterization of a series of Fe(II)-thiolate model complexes: implications for Fe-S bonding in superoxide reductases

A combined synthetic/spectroscopic/computational approach has been employed to prepare and characterize a series of Fe(II)-thiolate complexes that model the square-pyramidal [Fe(II)(N(His))(4)(S(Cys))] structure of the reduced active site of superoxide reductases (SORs), a class of enzymes that detoxify superoxide in air-sensitive organisms. The high-spin (S = 2) Fe(II) complexes [(Me(4)cyclam)Fe(SC(6)H(4)-p-OMe)]OTf (2) and [FeL]PF(6) (3) (where Me(4)cyclam = 1,4,8,11-tetramethylcyclam and L is the pentadentate monoanion of 1-thioethyl-4,8,11-trimethylcyclam) were synthesized and subjected to structural, magnetic, and electrochemical characterization. X-ray crystallographic studies confirm that 2 and 3 possess an N(4)S donor set similar to that found for the SOR active site and reveal molecular geometries intermediate between square pyramidal and trigonal bipyramidal for both complexes. Electronic absorption, magnetic circular dichroism (MCD), and variable-temperature variable-field MCD (VTVH-MCD) spectroscopies were utilized, in conjunction with density functional theory (DFT) and semiemperical INDO/S-CI calculations, to probe the ground and excited states of complexes 2 and 3, as well as the previously reported Fe(II) SOR model [(L(8)py(2))Fe(SC(6)H(4)-p-Me)]BF(4) (1) (where L(8)py(2) is a tetradentate pyridyl-appended diazacyclooctane macrocycle). These studies allow for a detailed interpretation of the S-->Fe(II) charge transfer transitions observed in the absorption and MCD spectra of complexes 1-3 and provide significant insights into the nature of Fe(II)-S bonding in complexes with axial thiolate ligation. Of the three models investigated, complex 3 exhibits an absorption spectrum that is particularly similar to the one reported for the reduced SOR enzyme (SOR(red)), suggesting that this model accurately mimics key elements of the electronic structure of the enzyme active site; namely, highly covalent Fe-S pi- and sigma-interactions. These spectral similarities are shown to arise from the fact that 3 contains an alkyl thiolate tethered to the equatorial cyclam ring, resulting in a thiolate orientation that is very similar to the one adopted by the Cys residue in the SOR(red) active site. Possible implications of our results with respect to the electronic structure and reactivity of SOR(red) are discussed.