The Complete Asymptotic Expansion for Bernstein–Durrmeyer Operators with Jacobi Weights

The purpose of this paper is the investigation of the local asymptotic behavior of the Bernstein-Durrmeyer polynomials and their derivatives with respect to Jacobi-weights. The main result is the complete asymptotic expansion for these polynomials and their derivatives. All coefficients are calculated explicitely.     

Pressurised hot water extraction in continuous flow mode for thermolabile compounds: extraction of polyphenols in red onions

Extraction and analysis of labile compounds in complex sample matrices, such as plants, is often a big analytical challenge. In this work, the use of a “green and clean” pressurised hot water extraction (PHWE) approach performed in continuous flow mode is explored. Experimental data for extraction and degradation kinetics of selected compounds were utilised to develop a continuous flow extraction (CFE) method targeting thermolabile polyphenols in red onions, with detection by high-performance liquid chromatography (HPLC)–diode array detection (DAD)–mass spectrometry (MS). Water containing ethanol and formic acid was used as extraction solvent. Method performance was focused on extraction yield with minimal analyte degradation. By adjusting the flow rate of the extraction solvent, degradation effects were minimised, and complete extraction could be achieved within 60 min. The CFE extraction yields of the polyphenols investigated were 80–90 % of the theoretically calculated quantitative yields and were significantly higher than the yields obtained by conventional methanol extraction and static batch extraction (70–79 and 58–67 % of the theoretical yields, respectively). The precision of the developed method was lower than 8 % expressed as relative standard deviation.

The topological behaviour of a diffeomorphism near a fixed point

A topological Linearization Theorem for flows by K. Palmer is extended to the case of maps.     

Single and double asymmetric induction in Diels-Alder cycloadditions with chiral acylnitroso dienophiles

Diels-Alder reaction of the achiral 1-silyloxybutadiene 1a with the chiral acyinitroso dienophile 2a gave cycloadduct 4 in high diastereomeric excess (d.e. > 98 %), a result which is undoubtedly due to the C-2 symmetrical chiral dimethylpyrrolidine inductor. Excellent d.e. was also observed when the (R)-prolinol dienophile 2d was reacted with the chiral diene 1b (d.e. = 96 %), whereas cycloaddition of the (S) enantiomer 2e with 1b gave only poor asymmetric induction (d.e. = 4 %). These two latter examples nicely illustrate the influence of “matched pair” (1b/2d) versus “mismatched pair” (1b/2e) upon double asymmetric induction. All herein reported Diels-Alder cycloadditions were regiospecific.     

The influence of fluoride and sulphate on buffers usef for the determination of the pH and speciation of protolytes in seawater

Various aspects of the measurement of pH in seawater are described. The assumptions underlying the assignment of a pH to a buffer are discussed, as well as the links to the alkalinity tritation and calculations of carbonate speciation. Although the corretion for fluoride is small, the correction for sulphate (0.129) can be significant.