A refinement of Vietoris' inequality for sine polynomials

Let where In 1958, Vietoris proved that σ_n (x) is positive for all n ≥ 1 and x ∈ (0, π). We establish the following refinement. The inequalities hold for all natural numbers n and real numbers n ≥ 1 and x ∈ (0, π) if and only if      

Inequalities of Fejér-Jackson Type

 We complement, extend, and sharpen some known inequalities for sine sums. Our main result is the following refinement of the classical Fejér-Jackson inequality: For all integers n ⩾ 2 and real numbers x ∈ (0,π) we have

Spherically invariant processes: Their nonlinear structure,discrimination, and estimation

The structure of the nonlinear space of a spherically invariant process is studied and the problem of discriminating between two spherically invariant processes as well as the problem of nonlinear estimation for spherically invariant processes are solved.     

Fine-tuning of the diffusion dimension of –OH groups for high resolution DOSY NMR applications in crude enzymatic transformations and mixtures of organic compounds

A convenient DOSY methodology was developed that can be applied directly in crude reaction products or mixtures containing polyphenol organic compounds, for the rapid identification of their various components without any prior separation or isolation. The method is based on the resolution enhancement of the resonances of the –OH protons and the fine-tuning of their diffusion coefficients to the molecular diffusion coefficient; this can be achieved in DMSO-d₆ in combination with the addition of picric acid and the use of temperatures near the freezing point of the solution. This method, which does not modify the apparent molecular diffusion, allowed the recording of high resolution DOSY spectra, both in crude enzymatic reactions and mixtures of organic compounds based on the phenolic OH NMR spectral region which is much less crowded and, thus, much more informative compared to the aromatic region.     

Unexpected enzyme-catalyzed regioselective acylation of flavonoid aglycones and rapid product screening

Unprecedented regioselective acylation of flavonoid aglycones was achieved using Candida antarctica lipase B (CALB). The rapid screening of product formation was performed by the use of the high resolution phenol-type OH (1)H NMR spectral region recorded after the addition of picric acid.     

Absolutely monotonic functions related to Euler’s gamma function and Barnes’ double and triple gamma function

It is shown that the remainders in asymptotic expansions of the logarithm of Barnes double and triple gamma function and Euler’s gamma function are Laplace transformations of positive multiples of absolutely monotonic functions. Applications concerning positivity of sums involving Bernoulli numbers are given.     

Ammonia oxidation to nitrogen mediated by electrogenerated active chlorine on Ti/PtOx-IrO2

The electrochemical oxidation of ammonia (NH₃ and/or NH₄⁺) in the presence of chloride was investigated on a Ti/PtO_x–IrO₂ electrode. It was shown that ammonia is effectively removed from solution via electrogenerated active chlorine. Based on mass balances, nitrogen is postulated to be the main product of ammonia electrolysis. In the bulk, the concentration of chloramines was low. This could be explained by the fact that the oxidation of ammonia takes place close to the electrode surface where an excess of chlorine relative to ammonia is ensured during the process. This results in the oxidation of ammonia to N₂ and in a local pH decrease. As a result, chloramines were decomposed in the proximity of the electrode prior to diffusing into the bulk.