The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegő type

We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szeg? weight functions consisting of any one of the four Chebyshev weights divided by the polynomial \(\rho (t)=1-\frac {4\gamma }{(1+\gamma )^{2}}\,t^{2},\quad t\in (-1,1),\ -1<\gamma \le 0\). For analytic functions, the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points ? 1 and sum of semi-axes ρ > 1, for the given quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed by S. Notaris (Numer. Math. 103, 99–127, 2006).     

Configurational Isomerism in Polyoxovanadates

A water‐soluble derivative of the polyoxovanadate {V₁₅E₆O₄₂} (E=semimetal) archetype enables the study of cluster shell rearrangements driven by supramolecular interactions. A reaction unique to E=Sb, induced exclusively by ligand metathesis in peripheral [Ni(ethylenediamine)₃]²⁺ counterions, results in the formation of the metastable α₁* configurational isomer of the {V₁₄Sb₈O₄₂} cluster type. Contrary to all other polyoxovanadate shell architectures, this isomer comprises an inward‐oriented vanadyl group and is ca. 50 and 12 kJ mol^?1 higher in energy than the previously isolated α and β isomers, respectively. We discuss this unexpected reaction in light of supramolecular Sb?O???V and Sb?O???Sb contacts manifested in {V₁₄Sb₈O₄₂}₂ dimers detected in the solid state. ESI MS experiments confirm the stability of these dimers also in solution and in the gas phase. DFT calculations indicate that other, as of yet elusive isomers of {V₁₄Sb₈}, might be accessible as well.     

Structure and charge-state dependence of the gas-phase ionization energy of proteins

Photoionization of protein ions: The ionization energy of polyprotonated protein cations in the gas phase measured using VUV synchrotron radiation appears to be correlated with the charge state z of the protein and its tertiary structure. A simple electrostatic model accounts for the results and also shows predictive capabilities to derive a mean radius R(m) of the protein ion from the ionization energy, and vice versa.     

Microstructural impact of anodic coatings on the electrochemical chlorine evolution reaction

Sol-gel Ru(0.3)Sn(0.7)O(2) electrode coatings with crack-free and mud-crack surface morphology deposited onto a Ti-substrate are prepared for a comparative investigation of the microstructural effect on the electrochemical activity for Cl(2) production and the Cl(2) bubble evolution behaviour. For comparison, a state-of-the-art mud-crack commercial Ru(0.3)Ti(0.7)O(2) coating is used. The compact coating is potentially durable over a long term compared to the mud-crack coating due to the reduced penetration of the electrolyte. Ti L-edge X-ray absorption spectroscopy confirms that a TiO(x) interlayer is formed between the mud-crack Ru(0.3)Sn(0.7)O(2) coating and the underlying Ti-substrate due to the attack of the electrolyte. Meanwhile, the compact coating shows enhanced activity in comparison to the commercial coating, benefiting from the nanoparticle-nanoporosity architecture. The dependence of the overall electrode polarization behaviour on the local activity and the bubble evolution behaviour for the Ru(0.3)Sn(0.7)O(2) coatings with different surface microstructure are evaluated by means of scanning electrochemical microscopy and microscopic bubble imaging.     

Electrochemical production, characterization, and application of MWCNTs

The subject of this study is production of carbon nanotubes (CNTs) using an original procedure of reduction of lithium molten salts onto graphite cathode; their structural characterization and application as support material for electrocatalysts aimed for hydrogen evolution. As-produced CNTs were characterized by means of scanning and transmission electron microscopy (SEM and TEM), Raman spectroscopy, and thermogravimetric and differential thermal analysis (DTA). SEM and TEM images have shown that nanotubes are mostly of curved shape with length of 1–20 μm and diameter of 20–40 nm. Raman peaks indicate that the crystallinity of produced nanotubes is rather low. The obtained results suggest that formed product contains up to 80 % multiwalled carbon nanotubes (MWCNTs), while the rest being non-reacted graphite and fullerenes. DTA curves show that combustion process of the nanotubes takes place in two stages, i.e., at 450 and 720 °C. At the lower temperature, combustion of MWCNTs occurs, while at higher one, fullerenes and non-reacted graphite particles burn. As-produced MWCNTs were used as electrocatalyst’s support materials and their performance was compared with that of traditional carbon support material Vulcan XC-72. MWNTs have shown almost twice higher real surface area, and electrocatalyst deposited on them showed better catalytic activity than corresponding one deposited on Vulcan XC-72.     

Electrochemical behavior and antioxidant activity of tetradentate Schiff bases and their copper(II) complexes

This study describes the effects of the substituents on electrochemical behavior and antioxidant activity of the six tetradentate Schiff bases, containing ethane-1,2-diamine or propane-1,2-diamine as the amine part and pentane-2,4-dione and/or 1-phenylbutane-1,3-dione as ??-diketone, and corresponding copper(II) complexes. Cyclic voltammograms of these compounds were recorded in dimethylsulfoxide and 0.1?M sodium perchlorate as supporting electrolyte with glassy carbon as working electrode at different scan rates. The voltammograms of Schiff bases alone showed only one irreversible peak. Voltammograms recorded for complexes showed the presence of quasi-reversible processes taking place at the metal center and reversible process at the ligand part. Both steric and inductive effects of substituents and structure of imine bridge of Schiff base ligands as well as complexes were discussed. These effects appear relevant for the antioxidant activity. Antioxidant activity of the investigated compounds expressed as Trolox equivalent antioxidant capacity is also discussed. The electrochemical behavior showed a high correlation with the antioxidant activity for investigated compounds.