On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.

Carbon-, sulfur-, and phosphorus-based charge transfer reactions in inductively coupled plasma–atomic emission spectrometry

In this work, the influence of carbon-, sulfur-, and phosphorus-based charge transfer reactions on the emission signal of 34 elements (Ag, Al, As, Au, B, Ba, Be, Ca, Cd, Co, Cr, Cu, Fe, Ga, Hg, I, In, Ir, K, Li, Mg, Mn, Na, Ni, P, Pb, Pd, Pt, S, Sb, Se, Sr, Te, and Zn) in axially viewed inductively coupled plasma–atomic emission spectrometry has been investigated. To this end, atomic and ionic emission signals for diluted glycerol, sulfuric acid, and phosphoric acid solutions were registered and results were compared to those obtained for a 1% w w− 1 nitric acid solution. Experimental results show that the emission intensities of As, Se, and Te atomic lines are enhanced by charge transfer from carbon, sulfur, and phosphorus ions. Iodine and P atomic emission is enhanced by carbon- and sulfur-based charge transfer whereas the Hg atomic emission signal is enhanced only by carbon. Though signal enhancement due to charge transfer reactions is also expected for ionic emission lines of the above-mentioned elements, no experimental evidence has been found with the exception of Hg ionic lines operating carbon solutions. The effect of carbon, sulfur, and phosphorus charge transfer reactions on atomic emission depends on (i) wavelength characteristics. In general, signal enhancement is more pronounced for electronic transitions involving the highest upper energy levels; (ii) plasma experimental conditions. The use of robust conditions (i.e. high r.f. power and lower nebulizer gas flow rates) improves carbon, sulfur, and phosphorus ionization in the plasma and, hence, signal enhancement; and (iii) the presence of other concomitants (e.g. K or Ca). Easily ionizable elements reduce ionization in the plasma and consequently reduce signal enhancement due to charge transfer reactions.

Non-spectral interferences due to the presence of sulfuric acid in inductively coupled plasma mass spectrometry

Results of a systematic study concerning non-spectral interferences from sulfuric acid containing matrices on a large number of elements in inductively coupled plasma–mass spectrometry (ICP-MS) are presented in this work. The signals obtained with sulfuric acid solutions of different concentrations (up to 5% w w− 1) have been compared with the corresponding signals for a 1% w w− 1− nitric acid solution at different experimental conditions (i.e., sample uptake rates, nebulizer gas flows and r.f. powers). The signals observed for 128Te+, 78Se+ and 75As+ were significantly higher when using sulfuric acid matrices (up to 2.2-fold for 128Te+ and 78Se+ and 1.8-fold for 75As+ in the presence of 5 w w-1 sulfuric acid) for the whole range of experimental conditions tested. This is in agreement with previously reported observations. The signal for 31P+ is also higher (1.1-fold) in the presence of sulfuric acid. The signal enhancements for 128Te+, 78Se+, 75As+ and 31P+ are explained in relation to an increase in the analyte ion population as a result of charge transfer reactions involving S+ species in the plasma. Theoretical data suggest that Os, Sb, Pt, Ir, Zn and Hg could also be involved in sulfur-based charge transfer reactions, but no experimental evidence has been found. The presence of sulfuric acid gives rise to lower ion signals (about 10–20% lower) for the other nuclides tested, thus indicating the negative matrix effect caused by changes in the amount of analyte loading of the plasma. The elemental composition of a certified low-density polyethylene sample (ERM-EC681K) was determined by ICP-MS after two different sample digestion procedures, one of them including sulfuric acid. Element concentrations were in agreement with the certified values, irrespective of the acids used for the digestion. These results demonstrate that the use of matrix-matched standards allows the accurate determination of the tested elements in a sulfuric acid matrix.