On a characterization of polynomials by divided differences

Summary We consider the functional equationf[x ₁,x ₂,, x _n ] =h(x ₁ + +x _n ) (x ₁,,x _n K, x _j x _k forj k), (D) wheref[x ₁,x ₂,,x _n ] denotes the (n – 1)-st divided difference off and prove Theorem. Let n be an integer, n 2, let K be a field, char(K) 2, with # K 8(n – 2) + 2. Let, furthermore, f, h: K K be functions. Then we have that f, h fulfil (D) if, and only if, there are constants a_j K, 0 j n (a := a_n, b := a_{n – 1}) such thatf = ax ⁿ +bx ^{n – 1} + +a ₀ and h = ax + b.     

The relative importance of temperature and isotope effects on the dipole oscillator strength distribution of H2

Summary The calculation of the effects of temperature and isotopic composition on the energy weighted moments of the dipole oscillator strength distribution of H₂ in the random phase approximation to the polarization propagator are reported. It is seen that the effect of isotopic composition is small, while that of temperature is of an order accessible to experiment. We find that all the mean excitation energiesI , for =–1, 0, 1, decrease with temperature as does the dipole oscillator strength momentS() for >0, while the opposite is true for <0. These effects are interpreted in terms of the bond length dependence of the excitation energies.     

The structure of magnesium alanate

Mg(AlH(4))(2) was produced as a nanocrystalline powder by metathesis of NaAlH(4) and MgCl(2). Starting with a structure estimation which was developed from an evaluation of FTIR data and comparison of structural properties of two solvent adducts, quantum chemical calculations were performed on the density functional theory (DFT) level. The calculated atomic positions were used to simulate an X-ray powder diffraction pattern, based on a trigonal unit cell. The simulated pattern was congruent to experimental data. Thus, magnesium alanate exhibits a CdI(2) layer structure, the layers being formed by Mg atoms occupying the Cd sites and AlH(4) tedrahedra occupying the sites of the iodine atoms in CdI(2).     

Separation and determination of alditols and sugars by high-pH anion-exchange chromatography with pulsed amperometric detection

Carbohydrates such as alditols (polyols or sugar alcohols), monosaccharides and disaccharides are separated as anions by anion-exchange chromatography with a sodium hydroxide eluent, MA1 CarboPac column and pulsed amperometric detection. We report a high-pH anion-exchange chromatographic-pulsed amperometric detection (HPAEC-PAD) method that determines all the polyols used as food additives in food products and the most commonly found mono- and disaccharides on a routine basis. The linearity, repeatability, internal reproducibility and accuracy are described. The applicability of the method has been demonstrated by the analysis of 46 relevant samples and by participation twice in the Food Analysis Performance Assessment Scheme (FAPAS) testing programme for food additives.     

Analysis of various classes of drugs by capillary supercritical fluid chromatography

Three classes of drugs were screened for analysis feasibility by capillary column supercritical fluid chromatography. These included steroids, therapeutic antibiotic drugs, and drugs of abuse, such as cannabinoids. Supercritical fluid carbon dioxide was used as the mobile phase in conjunction with a methylpolysiloxane stationary phase capillary column and a flame ionization detector. All compounds considered were analyzed either as single component solutions, simple mixtures, or in actual complex mixtures.