Simultaneous liquid chromatographic determination of metals and organic compounds in pharmaceutical and food-supplement formulations using evaporative light scattering detection

A novel method for the non-derivatization liquid chromatographic determination of metals (potassium, aluminium, calcium and magnesium) and organic compounds (ascorbate and aspartate) was developed and validated based on evaporative light scattering detection (ELSD). Separation of calcium, magnesium and aluminium was achieved by the cation exchange column Dionex CS-14 and an aqueous TFA mobile phase according to the following time program: 0-6 min TFA 0.96 mL L⁻¹, 6-7 min linear gradient from TFA 0.96-6.4 mL L⁻¹. Separation of potassium, magnesium and aspartate was achieved by the lipophilic C₁₈ Waters Spherisorb column and isocratic aqueous 0.2 mL L⁻¹ TFA mobile phase. Separation of sodium, magnesium, ascorbate and citrate was also achieved by the C₁₈ analytical column, according to the following elution program: 0-2.5 min aqueous nonafluoropentanoic acid (NFPA) 0.5 mL L⁻¹; 2.5-3.5 min linear gradient from 0.5 mL L⁻¹ NFPA to 1.0 mL L⁻¹ TFA. In all cases, evaporation temperature was 70 °C, pressure of the nebulizing gas (nitrogen) 3.5 bar, gain 11 and the flow rate 1.0 mL min⁻¹. Resolution among calcium and magnesium was 1.8, while for all other separations was ≥3.2. Double logarithmic calibration curves were obtained within various ranges from 3-24 to 34-132 μg mL⁻¹, and with good correlation (r > 0.996). Asymmetry factor ranged from 0.9 to 1.9 and limit of detection from 1.3 (magnesium) to 17 μg mL⁻¹ (ascorbate).The developed method was applied for the assay of potassium, magnesium, calcium, aluminium, aspartate and ascorbate in pharmaceuticals and food-supplements. The accuracy of the method was evaluated using spiked samples (%recovery 95-105%, %R.S.D. < 2) and the absence of constant or proportional errors was confirmed by dilution experiments.     

Natural examples of -complete sets in analysis

The purpose of this paper is to show that given any non-negative real number , the set of entire functions whose order is equal to is -complete, and the set of all sequences of entire functions whose orders converge to is -complete.

     

Sharp Sobolev type inequalities for higher fractional derivativesInégalités optimales de type Sobolev pour les dérivées fractionelles d'ordre supérieur

On $\text{R}{}^{\mathrm{n}}$, n?1 and n≠2, we prove the existence of a sharp constant for Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. For n>2s and $\text{q=}\text{2n}\text{n?2s}$ any function $\text{f∈}\text{H}{}^{\mathrm{s}}\text{(}\text{R}{}^{\mathrm{n}}\text{)}$ satisfies

$\text{6f6}{}^2{}_{\mathrm{q}}\text{?S}{}_{\mathrm{n,s}}\text{(?Δ)}{}^{\mathrm{s/2}}\text{f}{}^2{}_2\text{,}$

where the operator (?Δ)^s in Fourier spaces is defined by $\text{(?Δ)}{}^{\mathrm{s}}\text{f}\text{(k):=(2π|k|)}{}^{\mathrm{2s}}\text{f}\text{(k)}$. To cite this article: A. Cotsiolis, N.C. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 801–804.     

Elliptic problems with discontinuities

In this paper we prove two existence theorems for elliptic problems with discontinuities. The first one is a noncoercive Dirichlet problem and the second one is a Neumann problem. We do not use the method of upper and lower solutions. For Neumann problems we assume that f is nondecreasing. We use the critical point theory for locally Lipschitz functionals.