Multiple Wilson and Jacobi–Piñeiro polynomials

We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite–Padé polynomials) of type II. These polynomials can be written as a Jacobi–Piñeiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by Koornwinder. Here we need to introduce Jacobi and Jacobi–Piñeiro polynomials with complex parameters. Some explicit formulas are provided for both Jacobi–Piñeiro and multiple Wilson polynomials, one of them in terms of Kampé de Fériet series. Finally, we look at some limiting relations and construct a part of a multiple AT-Askey table.     

Development of a digital freeprogrammable function generator for high precision double motion Mössbauer-drives

Construction and use of a function generator are presented. The flexible outline allows a high precision control for all required velocity profiles.     

Advantages of Odd Random Phase Multisine Electrochemical Impedance Measurements

Electrochemical impedance spectroscopy (EIS) is a powerful technique to study electrochemical processes and to perform screening tasks. Recently an integrated measuring and modeling methodology for EIS based on a multisine excitation signal was developed. A key issue in this methodology is the data analysis, allowing us to rapidly quantify the reliability of the measured data. In this paper, a comparison is made between classical single‐sine and the proposed multisine measurements on the same system. The fitting of the impedance data obtained by single‐or multisine excitation and using different weighting factors is also discussed. In addition to the advantages reported in earlier work, it is concluded that, of all investigated frequencies, the odd random phase multisine excitation yields the highest quality data in the shortest measurement time.     

IRMPD spectroscopy of anionic group II metal nitrate cluster ions

Anionic group II metal nitrate clusters of the formula [M₂(NO₃)₅]⁻, where M₂ = Mg₂, MgCa, Ca₂, and Sr₂, are investigated by infrared multiple photon dissociation (IRMPD) spectroscopy to obtain vibrational spectra in the mid-IR region. The IR spectra are dominated by the symmetric and the antisymmetric nitrate stretches, with the latter split into high and low-frequency components due to the distortion of nitrate anion symmetry by interactions with the cation. Density functional theory (DFT) is used to predict geometries and vibrational spectra for comparison to the experimental spectra. Calculations yield two stable isomers: the first one contains two terminal nitrate anions on each cation and a single bridging nitrate (“mono-bridging”), while the second structure features a single terminal nitrate on each cation with three bridging nitrate ligands (“tri-bridging”). The tri-bridging isomer is calculated to be lower in energy than the mono-bridging one for all species. Theoretical spectra of the tri-bridging structure provide a better qualitative match to the experimental infrared spectra of [Mg₂(NO₃)₅]⁻ and [MgCa(NO₃)₅]⁻. However, the profile of the low-frequency ν ₃ band for the Mg₂ complex suggests a third possible isomer not predicted by theory. The IRMPD spectra of the Ca₂ and Sr₂ complexes are better reconciled by a weighted summation of the spectra of both isomers suggesting that a mixture of structures is present.