Spectral theory for algebraic combinations of Toeplitz and composition operators

We determine the essential spectra of algebraic combinations of Toeplitz operators with continuous symbol and composition operators induced by a class of linear-fractional non-automorphisms of the unit disk. The operators in question act on the Hardy space H² on the unit disk. Our method is to realize the C^*-algebra that they generate as an extension of the compact operators by a concrete C^*-algebra whose invertible elements are easily characterized.     

Crystal and Molecular Structure Analysis of 2-Methylimidazole

Abstract  

The crystal structure of the title compound, C₄H₆N₂, has been determined using X-ray diffraction at 100 K. The crystal of 2-methylimidazole is in orthorhombic crystal system with space group P2₁2₁2₁ (Z = 4), lattice parameters: a = 5.9957(12) ?, b = 8.1574(16) ? and c = 9.7010(19) ?, V = 474.47(16) ?. The molecule of 2-methylimidazole is approximately planar. The maximum deviation from the least-squares imidazole plane, calculated for all non-H atoms is 0.006(2) ?. N–H···N hydrogen bonds link the molecules together, forming infinite chains of hydrogen bond pattern C(4) defined by the graph-set analysis. Two chains, which are almost antiparallel to each other, pass through each unit cell. The dihedral angle between the mean planes of molecules forming these intersecting chains is 76.90(4)°. No evidence was found for disorder of the hydrogen-bonding proton between the atoms N1 and N3. The significance of this study lies in the analysis of the interactions occurring via hydrogen bonds in this structure, as well as, in the comparison drawn between the molecular structure of 2-methylimidazole and those of several of other imidazole derivatives possessing a hydrogen atom in the N1 position.     

Photoinduced Electron Transfer Involving a Naphthalimide Chromophore in Switchable and Flexible [2]Rotaxanes

The interlocking of ring and axle molecular components in rotaxanes provides a way to combine chromophoric, electron-donor and electron-acceptor moieties in the same molecular entity, in order to reproduce the features of photosynthetic reaction centers. To this aim, the photoinduced electron transfer processes involving a 1,8-naphthalimide chromophore, embedded in several rotaxane-based dyads, were investigated by steady-state and time-resolved absorption and luminescence spectroscopic experiments in the 300 fs–10 ns time window. Different rotaxanes built around the dialkylammonium/ dibenzo[24]crown-8 ether supramolecular motif were designed and synthesized to decipher the relevance of key structural factors, such as the chemical deactivation of the ammonium-crown ether recognition, the presence of a secondary site for the ring along the axle, and the covalent functionalization of the macrocycle with a phenothiazine electron donor. Indeed, the conformational freedom of these compounds gives rise to a rich dynamic behavior induced by light and may provide opportunities for investigating and understanding phenomena that take place in complex (bio)molecular architectures.     

Metallic Glass Films with Nanostructured Periodic Density Fluctuations Supported on Si/SiO2 as an Efficient Hydrogen Sorber

Nanostructured metallic glass films (NMGF) can exhibit surface and intrinsic effects that give rise to unique physical and chemical properties. Here, a facile synthesis and electrochemical, structural, and morphologic characterization of Pd-Au-Si based MGs of approximately 50 nm thickness supported on Si/SiO₂ is reported. Impressively, the maximum total hydrogen charge stored in the Pd-Au-Si nanofilm is equal to that in polycrystalline Pd films with 1 μm thickness in 0.1 m H₂SO₄ electrolyte. The same NMGF has a volumetric desorption charge that is more than eight times and 25 % higher than that of polycrystalline PdNF and Pd-Cu-Si NMGF with the same thickness supported on Si/SiO₂, respectively. A significant number of nanovoids originating from PdH_x crystals, and an increase in the average interatomic spacing is detected in Pd-Au-Si NMGF by high-resolution TEM. Such a high amount of hydrogen sorption is linked to the unique density fluctuations without any chemical segregation exclusively observed for this NMGF.     

On the cell-dependent vibrations and wave propagation in uniperiodic cylindrical shells

Continuum Mechanics and Thermodynamics - The objects of consideration are thin linearly elastic Kirchhoff–Love-type circular cylindrical shells having a periodically micro-heterogeneous...     

Pressure-assisted strategy for the synthesis of vinyl pyrrolidone-based macro-star photoiniferters. A route to star block copolymers

Star-shaped 1-vinyl-2-pyrrolidone (VP)-based polymers having four pendant arms were produced via high-pressure RAFT using the trithiocarbonate-functionalized core. The use of compression (p = 250 MPa) significantly reduced or eliminated star-star/star-chain coupling side reactions and termination process characteristics the for “core-first” R-type approach, still allowing for a “pseudo-living” reaction course up to very high monomer conversion (>98%). Consequently, tailored and highly living star-shaped poly(1-vinyl-2-pyrrolidone)s (PVP) in a wide range of molecular weights M _n = 2.0–175.6 kg/mol (Đ = 1.18–1.80) have been obtained. The chain extension of the produced polymer was carried out with methyl methacrylate (MMA) via photo-induced RAFT (λ = 365 nm) in the presence of tertiary amine catalyst, yielding well-defined amphiphilic star-shaped block copolymers. DSC measurements showed that synthesized star-shaped PVP homopolymers revealed much lower glass transition temperature values compared to their commercially supplied linear analogs.     

Effects of the Brookite Phase on the Properties of Different Nanostructured TiO2 Phases Photocatalytically Active Towards the Degradation of N-Phenylurea

Different sol-gel synthesis methods were used to obtain four nanostructured mesoporous TiO₂ samples for an efficient photocatalytic degradation of the emerging contaminant N-phenylurea under either simulated solar light (1 Sun) or UV light. Particularly, two TiO₂ samples were obtained by means of as many template-assisted syntheses, whereas other two TiO₂ samples were obtained by a greener template-free procedure, implying acidic conditions and, then, calcination at either 200 °C or 600 °C. In one case, anatase was obtained, whereas in the other three cases mixed crystalline phases were obtained. The four TiO₂ samples were characterized by X-ray powder diffraction (followed by Rietveld analysis); Transmission Electron Microscopy; N₂ adsorption/desorption at −196 °C; Diffuse Reflectance UV/Vis spectroscopy and ζ-potential measurements. A commercial TiO₂ powder (i. e., Degussa P25) was used for comparison. Differences among the synthesized samples were observed not only in their quantitative phase composition, but also in their nanoparticles morphology (shape and size), specific surface area, pore size distribution and pH_IEP (pH at isoelectric point), whereas the samples band-gap did not vary sizably. The samples showed different photocatalytic behavior in terms of N-phenylurea degradation, which are ascribed to their different physico-chemical properties and, especially, to their phase composition, stemming from the different synthesis conditions.     

Analysis of a bacterial model with nutrient‐dependent degenerate diffusion

We introduce and study a degenerate reaction‐diffusion system that can serve as a model prototype for the pattern formation of a bacterial multicellular community where the bacteria produce biofilm, grow and spread in the presence of a nutrient. Under proper conditions on the reaction terms, we prove the global existence and the uniqueness of solutions and illustrate the possible model behaviour in numerical simulations for a two‐dimensional setting. Copyright © 2014 John Wiley & Sons, Ltd.