Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision

Journal of Fourier Analysis and Applications - We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ( $$SG$$ ), which is a fractal set that can be viewed as a limit...     

One-sided invertibility of discrete operators with bounded coefficients

Aequationes mathematicae - For $$p\in (1,\infty )$$ , we establish several criteria of one-sided invertibility on spaces $$l^p=l^p(\mathbb {Z})$$ for discrete band-dominated operators being either...     

Chemical versus Electrochemical Synthesis of Carbon Nano‐onion/Polypyrrole Composites for Supercapacitor Electrodes

The development of high‐surface‐area carbon electrodes with a defined pore size distribution and the incorporation of pseudo‐active materials to optimize the overall capacitance and conductivity without destroying the stability are at present important research areas. Composite electrodes of carbon nano‐onions (CNOs) and polypyrrole (Ppy) were fabricated to improve the specific capacitance of a supercapacitor. The carbon nanostructures were uniformly coated with Ppy by chemical polymerization or by electrochemical potentiostatic deposition to form homogenous composites or bilayers. The materials were characterized by transmission‐ and scanning electron microscopy, differential thermogravimetric analyses, FTIR spectroscopy, piezoelectric microgravimetry, and cyclic voltammetry. The composites show higher mechanical and electrochemical stabilities, with high specific capacitances of up to about 800 F g^?1 for the CNOs/SDS/Ppy composites (chemical synthesis) and about 1300 F g^?1 for the CNOs/Ppy bilayer (electrochemical deposition).     

Synthesis of Highly Substituted γ‐Butyrolactones by a Gold‐Catalyzed Cascade Reaction of Benzyl Esters

Easily accessible benzylic esters of 3‐butynoic acids in a gold‐catalyzed cyclization/rearrangement cascade reaction provided 3‐propargyl γ‐butyrolactones with the alkene and the carbonyl group not being conjugated. Crossover experiments showed that the formation of the new C?C bond is an intermolecular process. Initially propargylic–benzylic esters were used, but alkyl‐substituted benzylic esters worked equally well. In the case of the propargylic–benzylic products, a simple treatment of the products with aluminum oxide initiated a twofold tautomerization to the allenyl‐substituted γ‐butyrolactones with conjugation of the carbonyl group, the olefin, and the allene. The synthetic sequence can be conducted stepwise or as a one‐pot cascade reaction with similar yields. Even in the presence of the gold catalyst the new allene remains intact.     

Biodistribution study of free and microencapsulated 6‐methylcoumarin in Wistar rats by HPLC

A sensitive, specific and reproducible HPLC method has been developed and validated for the quantitative determination of 6‐methylcoumarin (6MC) in plasma and other tissues in Wistar rats. A C₁₈ column was used with UV detection at 321 nm and a gradient system consisting of methanol‐deionized water was used as mobile phase. The retention time for 6MC was 14.921 min and no interfering peaks were observed for any of the matrices. Linear relationships (r² > 0.997) were obtained between the peak height ratios and the corresponding biological sample concentrations over the range 0.4–12.8 µg/mL. Precision and accuracy were evaluated; the coefficient of variation and the relative error for all of the organs were <2 and 7%, respectively. The limit of quantitation was 0.20 µg/mL for the heart and 0.30 µg/mL for the other tissues evaluated. This HPLC method was successfully used in the determination of 6MC in the biodistribution study after administration of 200 mg/kg of both 6MC‐free and 6MC‐loaded polymeric microparticles. In this study, extensive 6MC was found, in both free and microencapsulated forms, in all the organs tested. The 6MC‐free showed a range of between 1.7 and 11.5 µg/g, while the microencapsulated 6MC showed concentrations of between 6.35 and 17.7 µg/g, suggesting that 6MC improved absorption rate. Copyright © 2014 John Wiley & Sons, Ltd.