Coated-wire organic ion-selective electrodes in titrations based on ion-pair formation : Determination of arenediazonium salts with sodium tetraphenylborate

Titrimetric determinations of arenediazonium salts can be based on ion-pair formation between the diazonium cation and tetraphenylborate. Titrations are done under cooling with ice and are followed potentiometrically with organic ion-selective electrodes comprising PVC membranes plasticized with polar solvents and coated on aluminium wires. The method was tested in determinations of arenediazonium salts derived from 20 aromatic amines, including aniline, toluidines, naphthylamines and their derivatives. Except for compounds containing hydrophylic groups such as —COOH and —OH, the potentiometric titration curves have well defined end-points. The results are reproducible, with relative standard deviations in the range 0.4–1.4% at the millimolar level. The method can be used for reliable determinations of arenediazonium salts in analytical control of azo dyestuff production.     

A note on general solution of Stokes equations

Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).     

Analytic Atomic Screening Parameters for Slater Type Orbitals

Screening parameters to be used in Slater Type Orbitals were obtained in analytic form. The values compared well with the numerical results given by Clementi and Roetti (after a laborious process of optimization) and with the phenomenological values of Jung and Gould. The analytic formulation is based on the splitting of the two-body operator 1/r_st as the sum of effective one-body operators.     

On the criteria for integrability of the Liénard equation

The Liénard equation is of a high importance from both mathematical and physical points of view. However a question about integrability of this equation has not been completely answered yet. Here we provide a new criterion for integrability of the Liénard equation using an approach based on nonlocal transformations. We also obtain some of the previously known criteria for integrability of the Liénard equation as a straightforward consequence of our approach’s application. We illustrate our results by several new examples of integrable Liénard equations.     

Asymptotic expansions of the moments of extremes from general error distribution

In this paper, we derive the asymptotic expansions of the moments of normalized partial maxima for general error distribution. A byproduct is to deduce the convergence rates of the moments of normalized maxima to the moments of the corresponding extreme value distribution.